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Title: A System Of Logic, Ratiocinative And Inductive

Author: John Stuart Mill

Release Date: January 31, 2009 [Ebook #27942]

Language: English

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***START OF THE PROJECT GUTENBERG EBOOK A SYSTEM OF LOGIC, RATIOCINATIVE AND INDUCTIVE***





                            A SYSTEM OF LOGIC,

                       RATIOCINATIVE AND INDUCTIVE,

                      BEING A CONNECTED VIEW OF THE

                         PRINCIPLES OF EVIDENCE,

                                 AND THE

                   METHODS OF SCIENTIFIC INVESTIGATION.

                                    by

                            JOHN STUART MILL.

                             Eighth Edition.

                                New York:

                      Harper & Brothers, Publishers,

                             Franklin Square.

                                  1882.





CONTENTS


Preface To The First Edition.
Preface To The Third And Fourth Editions.
Introduction.
Book I. Of Names And Propositions.
   Chapter I. Of The Necessity Of Commencing With An Analysis Of Language.
   Chapter II. Of Names.
   Chapter III. Of The Things Denoted By Names.
   Chapter IV. Of Propositions.
   Chapter V. Of The Import Of Propositions.
   Chapter VI. Of Propositions Merely Verbal.
   Chapter VII. Of The Nature Of Classification, And The Five Predicables.
   Chapter VIII. Of Definition.
Book II. On Reasoning.
   Chapter I. Of Inference, Or Reasoning, In General.
   Chapter II. Of Ratiocination, Or Syllogism.
   Chapter III. Of The Functions And Logical Value Of The Syllogism.
   Chapter IV. Of Trains Of Reasoning, And Deductive Sciences.
   Chapter V. Of Demonstration, And Necessary Truths.
   Chapter VI. The Same Subject Continued.
   Chapter VII. Examination Of Some Opinions Opposed To The Preceding
   Doctrines.
Book III. Of Induction.
   Chapter I. Preliminary Observations On Induction In General.
   Chapter II. Of Inductions Improperly So Called.
   Chapter III. Of The Ground Of Induction.
   Chapter IV. Of Laws Of Nature.
   Chapter V. Of The Law Of Universal Causation.
   Chapter VI. On The Composition Of Causes.
   Chapter VII. On Observation And Experiment.
   Chapter VIII. Of The Four Methods Of Experimental Inquiry.
   Chapter IX. Miscellaneous Examples Of The Four Methods.
   Chapter X. Of Plurality Of Causes, And Of The Intermixture Of Effects.
   Chapter XI. Of The Deductive Method.
   Chapter XII. Of The Explanation Of Laws Of Nature.
   Chapter XIII. Miscellaneous Examples Of The Explanation Of Laws Of
   Nature.
   Chapter XIV. Of The Limits To The Explanation Of Laws Of Nature; And Of
   Hypotheses.
   Chapter XV. Of Progressive Effects; And Of The Continued Action Of
   Causes.
   Chapter XVI. Of Empirical Laws.
   Chapter XVII. Of Chance And Its Elimination.
   Chapter XVIII. Of The Calculation Of Chances.
   Chapter XIX. Of The Extension Of Derivative Laws To Adjacent Cases.
   Chapter XX. Of Analogy.
   Chapter XXI. Of The Evidence Of The Law Of Universal Causation.
   Chapter XXII. Of Uniformities Of Co-Existence Not Dependent On
   Causation.
   Chapter XXIV. Of The Remaining Laws Of Nature.
   Chapter XXV. Of The Grounds Of Disbelief.
Book IV. Of Operations Subsidiary To Induction.
   Chapter I. Of Observation And Description.
   Chapter II. Of Abstraction, Or The Formation Of Conceptions.
   Chapter III. Of Naming, As Subsidiary To Induction.
   Chapter IV. Of The Requisites Of A Philosophical Language, And The
   Principles Of Definition.
   Chapter V. On The Natural History Of The Variations In The Meaning Of
   Terms.
   Chapter VI. The Principles Of A Philosophical Language Further
   Considered.
   Chapter VII. Of Classification, As Subsidiary To Induction.
   Chapter VIII. Of Classification By Series.
Book V. On Fallacies.
   Chapter I. Of Fallacies In General.
   Chapter II. Classification Of Fallacies.
   Chapter III. Fallacies Of Simple Inspection; Or A Priori Fallacies.
   Chapter IV. Fallacies Of Observation.
   Chapter V. Fallacies Of Generalization.
   Chapter VI. Fallacies Of Ratiocination.
   Chapter VII. Fallacies Of Confusion.
Book VI. On The Logic Of The Moral Sciences.
   Chapter I. Introductory Remarks.
   Chapter II. Of Liberty And Necessity.
   Chapter III. That There Is, Or May Be, A Science Of Human Nature.
   Chapter IV. Of The Laws Of Mind.
   Chapter V. Of Ethology, Or The Science Of The Formation Of Character.
   Chapter VI. General Considerations On The Social Science.
   Chapter VII. Of The Chemical, Or Experimental, Method In The Social
   Science.
   Chapter VIII. Of The Geometrical, Or Abstract, Method.
   Chapter IX. Of The Physical, Or Concrete Deductive, Method.
   Chapter X. Of The Inverse Deductive, Or Historical, Method.
   Chapter XI. Additional Elucidations Of The Science Of History.
   Chapter XII. Of The Logic Of Practice, Or Art; Including Morality And
   Policy.
Footnotes






PREFACE TO THE FIRST EDITION.


This book makes no pretense of giving to the world a new theory of the
intellectual operations. Its claim to attention, if it possess any, is
grounded on the fact that it is an attempt, not to supersede, but to
embody and systematize, the best ideas which have been either promulgated
on its subject by speculative writers, or conformed to by accurate
thinkers in their scientific inquiries.

To cement together the detached fragments of a subject, never yet treated
as a whole; to harmonize the true portions of discordant theories, by
supplying the links of thought necessary to connect them, and by
disentangling them from the errors with which they are always more or less
interwoven, must necessarily require a considerable amount of original
speculation. To other originality than this, the present work lays no
claim. In the existing state of the cultivation of the sciences, there
would be a very strong presumption against any one who should imagine that
he had effected a revolution in the theory of the investigation of truth,
or added any fundamentally new process to the practice of it. The
improvement which remains to be effected in the methods of philosophizing
(and the author believes that they have much need of improvement) can only
consist in performing more systematically and accurately operations with
which, at least in their elementary form, the human intellect, in some one
or other of its employments, is already familiar.

In the portion of the work which treats of Ratiocination, the author has
not deemed it necessary to enter into technical details which may be
obtained in so perfect a shape from the existing treatises on what is
termed the Logic of the Schools. In the contempt entertained by many
modern philosophers for the syllogistic art, it will be seen that he by no
means participates; though the scientific theory on which its defense is
usually rested appears to him erroneous: and the view which he has
suggested of the nature and functions of the Syllogism may, perhaps,
afford the means of conciliating the principles of the art with as much as
is well grounded in the doctrines and objections of its assailants.

The same abstinence from details could not be observed in the First Book,
on Names and Propositions; because many useful principles and distinctions
which were contained in the old Logic have been gradually omitted from the
writings of its later teachers; and it appeared desirable both to revive
these, and to reform and rationalize the philosophical foundation on which
they stood. The earlier chapters of this preliminary Book will
consequently appear, to some readers, needlessly elementary and
scholastic. But those who know in what darkness the nature of our
knowledge, and of the processes by which it is obtained, is often involved
by a confused apprehension of the import of the different classes of Words
and Assertions, will not regard these discussions as either frivolous, or
irrelevant to the topics considered in the later Books.

On the subject of Induction, the task to be performed was that of
generalizing the modes of investigating truth and estimating evidence, by
which so many important and recondite laws of nature have, in the various
sciences, been aggregated to the stock of human knowledge. That this is
not a task free from difficulty may be presumed from the fact that even at
a very recent period, eminent writers (among whom it is sufficient to name
Archbishop Whately, and the author of a celebrated article on Bacon in the
_Edinburgh Review_) have not scrupled to pronounce it impossible.(1) The
author has endeavored to combat their theory in the manner in which
Diogenes confuted the skeptical reasonings against the possibility of
motion; remembering that Diogenes’s argument would have been equally
conclusive, though his individual perambulations might not have extended
beyond the circuit of his own tub.

Whatever may be the value of what the author has succeeded in effecting on
this branch of his subject, it is a duty to acknowledge that for much of
it he has been indebted to several important treatises, partly historical
and partly philosophical, on the generalities and processes of physical
science, which have been published within the last few years. To these
treatises, and to their authors, he has endeavored to do justice in the
body of the work. But as with one of these writers, Dr. Whewell, he has
occasion frequently to express differences of opinion, it is more
particularly incumbent on him in this place to declare, that without the
aid derived from the facts and ideas contained in that gentleman’s
“History of the Inductive Sciences,” the corresponding portion of this
work would probably not have been written.

The concluding Book is an attempt to contribute toward the solution of a
question which the decay of old opinions, and the agitation that disturbs
European society to its inmost depths, render as important in the present
day to the practical interests of human life, as it must at all times be
to the completeness of our speculative knowledge—viz.: Whether moral and
social phenomena are really exceptions to the general certainty and
uniformity of the course of nature; and how far the methods by which so
many of the laws of the physical world have been numbered among truths
irrevocably acquired and universally assented to, can be made instrumental
to the formation of a similar body of received doctrine in moral and
political science.





PREFACE TO THE THIRD AND FOURTH EDITIONS.


Several criticisms, of a more or less controversial character, on this
work, have appeared since the publication of the second edition; and Dr.
Whewell has lately published a reply to those parts of it in which some of
his opinions were controverted.(2)

I have carefully reconsidered all the points on which my conclusions have
been assailed. But I have not to announce a change of opinion on any
matter of importance. Such minor oversights as have been detected, either
by myself or by my critics, I have, in general silently, corrected: but it
is not to be inferred that I agree with the objections which have been
made to a passage, in every instance in which I have altered or canceled
it. I have often done so, merely that it might not remain a
stumbling-block, when the amount of discussion necessary to place the
matter in its true light would have exceeded what was suitable to the
occasion.

To several of the arguments which have been urged against me, I have
thought it useful to reply with some degree of minuteness; not from any
taste for controversy, but because the opportunity was favorable for
placing my own conclusions, and the grounds of them, more clearly and
completely before the reader. Truth on these subjects is militant, and can
only establish itself by means of conflict. The most opposite opinions can
make a plausible show of evidence while each has the statement of its own
case; and it is only possible to ascertain which of them is in the right,
after hearing and comparing what each can say against the other, and what
the other can urge in its defense.

Even the criticisms from which I most dissent have been of great service
to me, by showing in what places the exposition most needed to be
improved, or the argument strengthened. And I should have been well
pleased if the book had undergone a much greater amount of attack; as in
that case I should probably have been enabled to improve it still more
than I believe I have now done.

                  -------------------------------------

In the subsequent editions, the attempt to improve the work by additions
and corrections, suggested by criticism or by thought, has been continued.
The additions and corrections in the present (eighth) edition, which are
not very considerable, are chiefly such as have been suggested by
Professor Bain’s “Logic,” a book of great merit and value. Mr. Bain’s view
of the science is essentially the same with that taken in the present
treatise, the differences of opinion being few and unimportant compared
with the agreements; and he has not only enriched the exposition by many
applications and illustrative details, but has appended to it a minute and
very valuable discussion of the logical principles specially applicable to
each of the sciences—a task for which the encyclopedical character of his
knowledge peculiarly qualified him. I have in several instances made use
of his exposition to improve my own, by adopting, and occasionally by
controverting, matter contained in his treatise.

The longest of the additions belongs to the chapter on Causation, and is a
discussion of the question how far, if at all, the ordinary mode of
stating the law of Cause and Effect requires modification to adapt it to
the new doctrine of the Conservation of Force—a point still more fully and
elaborately treated in Mr. Bain’s work.





INTRODUCTION.


§ 1. There is as great diversity among authors in the modes which they
have adopted of defining logic, as in their treatment of the details of
it. This is what might naturally be expected on any subject on which
writers have availed themselves of the same language as a means of
delivering different ideas. Ethics and jurisprudence are liable to the
remark in common with logic. Almost every writer having taken a different
view of some of the particulars which these branches of knowledge are
usually understood to include; each has so framed his definition as to
indicate beforehand his own peculiar tenets, and sometimes to beg the
question in their favor.

This diversity is not so much an evil to be complained of, as an
inevitable and in some degree a proper result of the imperfect state of
those sciences. It is not to be expected that there should be agreement
about the definition of any thing, until there is agreement about the
thing itself. To define, is to select from among all the properties of a
thing, those which shall be understood to be designated and declared by
its name; and the properties must be well known to us before we can be
competent to determine which of them are fittest to be chosen for this
purpose. Accordingly, in the case of so complex an aggregation of
particulars as are comprehended in any thing which can be called a
science, the definition we set out with is seldom that which a more
extensive knowledge of the subject shows to be the most appropriate. Until
we know the particulars themselves, we can not fix upon the most correct
and compact mode of circumscribing them by a general description. It was
not until after an extensive and accurate acquaintance with the details of
chemical phenomena, that it was found possible to frame a rational
definition of chemistry; and the definition of the science of life and
organization is still a matter of dispute. So long as the sciences are
imperfect, the definitions must partake of their imperfection; and if the
former are progressive, the latter ought to be so too. As much, therefore,
as is to be expected from a definition placed at the commencement of a
subject, is that it should define the scope of our inquiries: and the
definition which I am about to offer of the science of logic, pretends to
nothing more than to be a statement of the question which I have put to
myself, and which this book is an attempt to resolve. The reader is at
liberty to object to it as a definition of logic; but it is at all events
a correct definition of the subject of this volume.

§ 2. Logic has often been called the Art of Reasoning. A writer(3) who has
done more than any other person to restore this study to the rank from
which it had fallen in the estimation of the cultivated class in our own
country, has adopted the above definition with an amendment; he has
defined Logic to be the Science, as well as the Art, of reasoning; meaning
by the former term, the analysis of the mental process which takes place
whenever we reason, and by the latter, the rules, grounded on that
analysis, for conducting the process correctly. There can be no doubt as
to the propriety of the emendation. A right understanding of the mental
process itself, of the conditions it depends on, and the steps of which it
consists, is the only basis on which a system of rules, fitted for the
direction of the process, can possibly be founded. Art necessarily
presupposes knowledge; art, in any but its infant state, presupposes
scientific knowledge: and if every art does not bear the name of a
science, it is only because several sciences are often necessary to form
the groundwork of a single art. So complicated are the conditions which
govern our practical agency, that to enable one thing to be _done_, it is
often requisite to _know_ the nature and properties of many things.

Logic, then, comprises the science of reasoning, as well as an art,
founded on that science. But the word Reasoning, again, like most other
scientific terms in popular use, abounds in ambiguities. In one of its
acceptations, it means syllogizing; or the mode of inference which may be
called (with sufficient accuracy for the present purpose) concluding from
generals to particulars. In another of its senses, to reason is simply to
infer any assertion, from assertions already admitted: and in this sense
induction is as much entitled to be called reasoning as the demonstrations
of geometry.

Writers on logic have generally preferred the former acceptation of the
term: the latter, and more extensive signification is that in which I mean
to use it. I do this by virtue of the right I claim for every author, to
give whatever provisional definition he pleases of his own subject. But
sufficient reasons will, I believe, unfold themselves as we advance, why
this should be not only the provisional but the final definition. It
involves, at all events, no arbitrary change in the meaning of the word;
for, with the general usage of the English language, the wider
signification, I believe, accords better than the more restricted one.

§ 3. But reasoning, even in the widest sense of which the word is
susceptible, does not seem to comprehend all that is included, either in
the best, or even in the most current, conception of the scope and
province of our science. The employment of the word Logic to denote the
theory of Argumentation, is derived from the Aristotelian, or, as they are
commonly termed, the scholastic, logicians. Yet even with them, in their
systematic treatises, Argumentation was the subject only of the third
part: the two former treated of Terms, and of Propositions; under one or
other of which heads were also included Definition and Division. By some,
indeed, these previous topics were professedly introduced only on account
of their connection with reasoning, and as a preparation for the doctrine
and rules of the syllogism. Yet they were treated with greater minuteness,
and dwelt on at greater length, than was required for that purpose alone.
More recent writers on logic have generally understood the term as it was
employed by the able author of the Port Royal Logic; viz., as equivalent
to the Art of Thinking. Nor is this acceptation confined to books, and
scientific inquiries. Even in ordinary conversation, the ideas connected
with the word Logic include at least precision of language, and accuracy
of classification: and we perhaps oftener hear persons speak of a logical
arrangement, or of expressions logically defined, than of conclusions
logically deduced from premises. Again, a man is often called a great
logician, or a man of powerful logic, not for the accuracy of his
deductions, but for the extent of his command over premises; because the
general propositions required for explaining a difficulty or refuting a
sophism, copiously and promptly occur to him: because, in short, his
knowledge, besides being ample, is well under his command for
argumentative use. Whether, therefore, we conform to the practice of those
who have made the subject their particular study, or to that of popular
writers and common discourse, the province of logic will include several
operations of the intellect not usually considered to fall within the
meaning of the terms Reasoning and Argumentation.

These various operations might be brought within the compass of the
science, and the additional advantage be obtained of a very simple
definition, if, by an extension of the term, sanctioned by high
authorities, we were to define logic as the science which treats of the
operations of the human understanding in the pursuit of truth. For to this
ultimate end, naming, classification, definition, and all other operations
over which logic has ever claimed jurisdiction, are essentially
subsidiary. They may all be regarded as contrivances for enabling a person
to know the truths which are needful to him, and to know them at the
precise moment at which they are needful. Other purposes, indeed, are also
served by these operations; for instance, that of imparting our knowledge
to others. But, viewed with regard to this purpose, they have never been
considered as within the province of the logician. The sole object of
Logic is the guidance of one’s own thoughts: the communication of those
thoughts to others falls under the consideration of Rhetoric, in the large
sense in which that art was conceived by the ancients; or of the still
more extensive art of Education. Logic takes cognizance of our
intellectual operations only as they conduce to our own knowledge, and to
our command over that knowledge for our own uses. If there were but one
rational being in the universe, that being might be a perfect logician;
and the science and art of logic would be the same for that one person as
for the whole human race.

§ 4. But, if the definition which we formerly examined included too
little, that which is now suggested has the opposite fault of including
too much.

Truths are known to us in two ways: some are known directly, and of
themselves; some through the medium of other truths. The former are the
subject of Intuition, or Consciousness;(4) the latter, of Inference. The
truths known by intuition are the original premises from which all others
are inferred. Our assent to the conclusion being grounded on the truth of
the premises, we never could arrive at any knowledge by reasoning, unless
something could be known antecedently to all reasoning.

Examples of truths known to us by immediate consciousness, are our own
bodily sensations and mental feelings. I know directly, and of my own
knowledge, that I was vexed yesterday, or that I am hungry to-day.
Examples of truths which we know only by way of inference, are occurrences
which took place while we were absent, the events recorded in history, or
the theorems of mathematics. The two former we infer from the testimony
adduced, or from the traces of those past occurrences which still exist;
the latter, from the premises laid down in books of geometry, under the
title of definitions and axioms. Whatever we are capable of knowing must
belong to the one class or to the other; must be in the number of the
primitive data, or of the conclusions which can be drawn from these.

With the original data, or ultimate premises of our knowledge; with their
number or nature, the mode in which they are obtained, or the tests by
which they may be distinguished; logic, in a direct way at least, has, in
the sense in which I conceive the science, nothing to do. These questions
are partly not a subject of science at all, partly that of a very
different science.

Whatever is known to us by consciousness is known beyond possibility of
question. What one sees or feels, whether bodily or mentally, one can not
but be sure that one sees or feels. No science is required for the purpose
of establishing such truths; no rules of art can render our knowledge of
them more certain than it is in itself. There is no logic for this portion
of our knowledge.

But we may fancy that we see or feel what we in reality infer. A truth, or
supposed truth, which is really the result of a very rapid inference, may
seem to be apprehended intuitively. It has long been agreed by thinkers of
the most opposite schools, that this mistake is actually made in so
familiar an instance as that of the eyesight. There is nothing of which we
appear to ourselves to be more directly conscious than the distance of an
object from us. Yet it has long been ascertained, that what is perceived
by the eye, is at most nothing more than a variously colored surface; that
when we fancy we see distance, all we really see is certain variations of
apparent size, and degrees of faintness of color; that our estimate of the
object’s distance from us is the result partly of a rapid inference from
the muscular sensations accompanying the adjustment of the focal distance
of the eye to objects unequally remote from us, and partly of a comparison
(made with so much rapidity that we are unconscious of making it) between
the size and color of the object as they appear at the time, and the size
and color of the same or of similar objects as they appeared when close at
hand, or when their degree of remoteness was known by other evidence. The
perception of distance by the eye, which seems so like intuition, is thus,
in reality, an inference grounded on experience; an inference, too, which
we learn to make; and which we make with more and more correctness as our
experience increases; though in familiar cases it takes place so rapidly
as to appear exactly on a par with those perceptions of sight which are
really intuitive, our perceptions of color.(5)

Of the science, therefore, which expounds the operations of the human
understanding in the pursuit of truth, one essential part is the inquiry:
What are the facts which are the objects of intuition or consciousness,
and what are those which we merely infer? But this inquiry has never been
considered a portion of logic. Its place is in another and a perfectly
distinct department of science, to which the name metaphysics more
particularly belongs: that portion of mental philosophy which attempts to
determine what part of the furniture of the mind belongs to it originally,
and what part is constructed out of materials furnished to it from
without. To this science appertain the great and much debated questions of
the existence of matter; the existence of spirit, and of a distinction
between it and matter; the reality of time and space, as things without
the mind, and distinguishable from the objects which are said to exist in
them. For in the present state of the discussion on these topics, it is
almost universally allowed that the existence of matter or of spirit, of
space or of time, is in its nature unsusceptible of being proved; and that
if any thing is known of them, it must be by immediate intuition. To the
same science belong the inquiries into the nature of Conception,
Perception, Memory, and Belief; all of which are operations of the
understanding in the pursuit of truth; but with which, as phenomena of the
mind, or with the possibility which may or may not exist of analyzing any
of them into simpler phenomena, the logician as such has no concern. To
this science must also be referred the following, and all analogous
questions: To what extent our intellectual faculties and our emotions are
innate—to what extent the result of association: Whether God and duty are
realities, the existence of which is manifest to us _a priori_ by the
constitution of our rational faculty; or whether our ideas of them are
acquired notions, the origin of which we are able to trace and explain;
and the reality of the objects themselves a question not of consciousness
or intuition, but of evidence and reasoning.

The province of logic must be restricted to that portion of our knowledge
which consists of inferences from truths previously known; whether those
antecedent data be general propositions, or particular observations and
perceptions. Logic is not the science of Belief, but the science of Proof,
or Evidence. In so far as belief professes to be founded on proof, the
office of logic is to supply a test for ascertaining whether or not the
belief is well grounded. With the claims which any proposition has to
belief on the evidence of consciousness—that is, without evidence in the
proper sense of the word—logic has nothing to do.

§ 5. By far the greatest portion of our knowledge, whether of general
truths or of particular facts, being avowedly matter of inference, nearly
the whole, not only of science, but of human conduct, is amenable to the
authority of logic. To draw inferences has been said to be the great
business of life. Every one has daily, hourly, and momentary need of
ascertaining facts which he has not directly observed; not from any
general purpose of adding to his stock of knowledge, but because the facts
themselves are of importance to his interests or to his occupations. The
business of the magistrate, of the military commander, of the navigator,
of the physician, of the agriculturist, is merely to judge of evidence,
and to act accordingly. They all have to ascertain certain facts, in order
that they may afterward apply certain rules, either devised by themselves
or prescribed for their guidance by others; and as they do this well or
ill, so they discharge well or ill the duties of their several callings.
It is the only occupation in which the mind never ceases to be engaged;
and is the subject, not of logic, but of knowledge in general.

Logic, however, is not the same thing with knowledge, though the field of
logic is co-extensive with the field of knowledge. Logic is the common
judge and arbiter of all particular investigations. It does not undertake
to find evidence, but to determine whether it has been found. Logic
neither observes, nor invents, nor discovers; but judges. It is no part of
the business of logic to inform the surgeon what appearances are found to
accompany a violent death. This he must learn from his own experience and
observation, or from that of others, his predecessors in his peculiar
pursuit. But logic sits in judgment on the sufficiency of that observation
and experience to justify his rules, and on the sufficiency of his rules
to justify his conduct. It does not give him proofs, but teaches him what
makes them proofs, and how he is to judge of them. It does not teach that
any particular fact proves any other, but points out to what conditions
all facts must conform, in order that they may prove other facts. To
decide whether any given fact fulfills these conditions, or whether facts
can be found which fulfill them in a given case, belongs exclusively to
the particular art or science, or to our knowledge of the particular
subject.

It is in this sense that logic is, what it was so expressively called by
the schoolmen and by Bacon, _ars artium_; the science of science itself.
All science consists of data and conclusions from those data, of proofs
and what they prove: now logic points out what relations must subsist
between data and whatever can be concluded from them, between proof and
every thing which it can prove. If there be any such indispensable
relations, and if these can be precisely determined, every particular
branch of science, as well as every individual in the guidance of his
conduct, is bound to conform to those relations, under the penalty of
making false inferences—of drawing conclusions which are not grounded in
the realities of things. Whatever has at any time been concluded justly,
whatever knowledge has been acquired otherwise than by immediate
intuition, depended on the observance of the laws which it is the province
of logic to investigate. If the conclusions are just, and the knowledge
real, those laws, whether known or not, have been observed.

§ 6. We need not, therefore, seek any further for a solution of the
question, so often agitated, respecting the utility of logic. If a science
of logic exists, or is capable of existing, it must be useful. If there be
rules to which every mind consciously or unconsciously conforms in every
instance in which it infers rightly, there seems little necessity for
discussing whether a person is more likely to observe those rules, when he
knows the rules, than when he is unacquainted with them.

A science may undoubtedly be brought to a certain, not inconsiderable,
stage of advancement, without the application of any other logic to it
than what all persons, who are said to have a sound understanding, acquire
empirically in the course of their studies. Mankind judged of evidence,
and often correctly, before logic was a science, or they never could have
made it one. And they executed great mechanical works before they
understood the laws of mechanics. But there are limits both to what
mechanicians can do without principles of mechanics, and to what thinkers
can do without principles of logic. A few individuals, by extraordinary
genius, or by the accidental acquisition of a good set of intellectual
habits, may work without principles in the same way, or nearly the same
way, in which they would have worked if they had been in possession of
principles. But the bulk of mankind require either to understand the
theory of what they are doing, or to have rules laid down for them by
those who have understood the theory. In the progress of science from its
easiest to its more difficult problems, each great step in advance has
usually had either as its precursor, or as its accompaniment and necessary
condition, a corresponding improvement in the notions and principles of
logic received among the most advanced thinkers. And if several of the
more difficult sciences are still in so defective a state; if not only so
little is proved, but disputation has not terminated even about the little
which seemed to be so; the reason perhaps is, that men’s logical notions
have not yet acquired the degree of extension, or of accuracy, requisite
for the estimation of the evidence proper to those particular departments
of knowledge.

§ 7. Logic, then, is the science of the operations of the understanding
which are subservient to the estimation of evidence: both the process
itself of advancing from known truths to unknown, and all other
intellectual operations in so far as auxiliary to this. It includes,
therefore, the operation of Naming; for language is an instrument of
thought, as well as a means of communicating our thoughts. It includes,
also, Definition, and Classification. For, the use of these operations
(putting all other minds than one’s own out of consideration) is to serve
not only for keeping our evidences and the conclusions from them permanent
and readily accessible in the memory, but for so marshaling the facts
which we may at any time be engaged in investigating, as to enable us to
perceive more clearly what evidence there is, and to judge with fewer
chances of error whether it be sufficient. These, therefore, are
operations specially instrumental to the estimation of evidence, and, as
such, are within the province of Logic. There are other more elementary
processes, concerned in all thinking, such as Conception, Memory, and the
like; but of these it is not necessary that Logic should take any peculiar
cognizance, since they have no special connection with the problem of
Evidence, further than that, like all other problems addressed to the
understanding, it presupposes them.

Our object, then, will be, to attempt a correct analysis of the
intellectual process called Reasoning or Inference, and of such other
mental operations as are intended to facilitate this: as well as, on the
foundation of this analysis, and _pari passu_ with it, to bring together
or frame a set of rules or canons for testing the sufficiency of any given
evidence to prove any given proposition.

With respect to the first part of this undertaking, I do not attempt to
decompose the mental operations in question into their ultimate elements.
It is enough if the analysis as far as it goes is correct, and if it goes
far enough for the practical purposes of logic considered as an art. The
separation of a complicated phenomenon into its component parts is not
like a connected and interdependent chain of proof. If one link of an
argument breaks, the whole drops to the ground; but one step toward an
analysis holds good and has an independent value, though we should never
be able to make a second. The results which have been obtained by
analytical chemistry are not the less valuable, though it should be
discovered that all which we now call simple substances are really
compounds. All other things are at any rate compounded of those elements:
whether the elements themselves admit of decomposition, is an important
inquiry, but does not affect the certainty of the science up to that
point.

I shall, accordingly, attempt to analyze the process of inference, and the
processes subordinate to inference, so far only as may be requisite for
ascertaining the difference between a correct and an incorrect performance
of those processes. The reason for thus limiting our design, is evident.
It has been said by objectors to logic, that we do not learn to use our
muscles by studying their anatomy. The fact is not quite fairly stated;
for if the action of any of our muscles were vitiated by local weakness,
or other physical defect, a knowledge of their anatomy might be very
necessary for effecting a cure. But we should be justly liable to the
criticism involved in this objection, were we, in a treatise on logic, to
carry the analysis of the reasoning process beyond the point at which any
inaccuracy which may have crept into it must become visible. In learning
bodily exercises (to carry on the same illustration) we do, and must,
analyze the bodily motions so far as is necessary for distinguishing those
which ought to be performed from those which ought not. To a similar
extent, and no further, it is necessary that the logician should analyze
the mental processes with which Logic is concerned. Logic has no interest
in carrying the analysis beyond the point at which it becomes apparent
whether the operations have in any individual case been rightly or wrongly
performed: in the same manner as the science of music teaches us to
discriminate between musical notes, and to know the combinations of which
they are susceptible, but not what number of vibrations in a second
correspond to each; which, though useful to be known, is useful for
totally different purposes. The extension of Logic as a Science is
determined by its necessities as an Art: whatever it does not need for its
practical ends, it leaves to the larger science which may be said to
correspond, not to any particular art, but to art in general; the science
which deals with the constitution of the human faculties; and to which, in
the part of our mental nature which concerns Logic, as well as in all
other parts, it belongs to decide what are ultimate facts, and what are
resolvable into other facts. And I believe it will be found that most of
the conclusions arrived at in this work have no necessary connection with
any particular views respecting the ulterior analysis. Logic is common
ground on which the partisans of Hartley and of Reid, of Locke and of
Kant, may meet and join hands. Particular and detached opinions of all
these thinkers will no doubt occasionally be controverted, since all of
them were logicians as well as metaphysicians; but the field on which
their principal battles have been fought, lies beyond the boundaries of
our science.

It can not, indeed, be pretended that logical principles can be altogether
irrelevant to those more abstruse discussions; nor is it possible but that
the view we are led to take of the problem which logic proposes, must have
a tendency favorable to the adoption of some one opinion, on these
controverted subjects, rather than another. For metaphysics, in
endeavoring to solve its own peculiar problem, must employ means, the
validity of which falls under the cognizance of logic. It proceeds, no
doubt, as far as possible, merely by a closer and more attentive
interrogation of our consciousness, or more properly speaking, of our
memory; and so far is not amenable to logic. But wherever this method is
insufficient to attain the end of its inquiries, it must proceed, like
other sciences, by means of evidence. Now, the moment this science begins
to draw inferences from evidence, logic becomes the sovereign judge
whether its inferences are well grounded, or what other inferences would
be so.

This, however, constitutes no nearer or other relation between logic and
metaphysics, than that which exists between logic and every other science.
And I can conscientiously affirm that no one proposition laid down in this
work has been adopted for the sake of establishing, or with any reference
to its fitness for being employed in establishing, preconceived opinions
in any department of knowledge or of inquiry on which the speculative
world is still undecided.(6)





                                 Book I.


OF NAMES AND PROPOSITIONS.


“La scolastique, qui produisit dans la logique, comme dans la morale, et
dans une partie de la métaphysique, une subtilité, une précision d’idées,
dont l’habitude inconnue aux anciens, a contribué plus qu’on ne croit au
progrès de la bonne philosophie.”—CONDORCET, _Vie de Turgot_.

“To the schoolmen the vulgar languages are principally indebted for what
precision and analytic subtlety they possess.”—SIR W. HAMILTON,
_Discussions in Philosophy_.




                                Chapter I.


Of The Necessity Of Commencing With An Analysis Of Language.


§ 1. It is so much the established practice of writers on logic to
commence their treatises by a few general observations (in most cases, it
is true, rather meagre) on Terms and their varieties, that it will,
perhaps, scarcely be required from me, in merely following the common
usage, to be as particular in assigning my reasons, as it is usually
expected that those should be who deviate from it.

The practice, indeed, is recommended by considerations far too obvious to
require a formal justification. Logic is a portion of the Art of Thinking:
Language is evidently, and by the admission of all philosophers, one of
the principal instruments or helps of thought; and any imperfection in the
instrument, or in the mode of employing it, is confessedly liable, still
more than in almost any other art, to confuse and impede the process, and
destroy all ground of confidence in the result. For a mind not previously
versed in the meaning and right use of the various kinds of words, to
attempt the study of methods of philosophizing, would be as if some one
should attempt to become an astronomical observer, having never learned to
adjust the focal distance of his optical instruments so as to see
distinctly.

Since Reasoning, or Inference, the principal subject of logic, is an
operation which usually takes place by means of words, and in complicated
cases can take place in no other way; those who have not a thorough
insight into the signification and purposes of words, will be under
chances, amounting almost to certainty, of reasoning or inferring
incorrectly. And logicians have generally felt that unless, in the very
first stage, they removed this source of error; unless they taught their
pupil to put away the glasses which distort the object, and to use those
which are adapted to his purpose in such a manner as to assist, not
perplex, his vision; he would not be in a condition to practice the
remaining part of their discipline with any prospect of advantage.
Therefore it is that an inquiry into language, so far as is needful to
guard against the errors to which it gives rise, has at all times been
deemed a necessary preliminary to the study of logic.

But there is another reason, of a still more fundamental nature, why the
import of words should be the earliest subject of the logician’s
consideration: because without it he can not examine into the import of
Propositions. Now this is a subject which stands on the very threshold of
the science of logic.

The object of logic, as defined in the Introductory Chapter, is to
ascertain how we come by that portion of our knowledge (much the greatest
portion) which is not intuitive: and by what criterion we can, in matters
not self-evident, distinguish between things proved and things not proved,
between what is worthy and what is unworthy of belief. Of the various
questions which present themselves to our inquiring faculties, some
receive an answer from direct consciousness, others, if resolved at all,
can only be resolved by means of evidence. Logic is concerned with these
last. But before inquiring into the mode of resolving questions, it is
necessary to inquire what are those which offer themselves; what questions
are conceivable; what inquiries are there, to which mankind have either
obtained, or been able to imagine it possible that they should obtain, an
answer. This point is best ascertained by a survey and analysis of
Propositions.

§ 2. The answer to every question which it is possible to frame, must be
contained in a Proposition, or Assertion. Whatever can be an object of
belief, or even of disbelief, must, when put into words, assume the form
of a proposition. All truth and all error lie in propositions. What, by a
convenient misapplication of an abstract term, we call a Truth, means
simply a True Proposition; and errors are false propositions. To know the
import of all possible propositions would be to know all questions which
can be raised, all matters which are susceptible of being either believed
or disbelieved. How many kinds of inquiries can be propounded; how many
kinds of judgments can be made; and how many kinds of propositions it is
possible to frame with a meaning, are but different forms of one and the
same question. Since, then, the objects of all Belief and of all Inquiry
express themselves in propositions, a sufficient scrutiny of Propositions
and of their varieties will apprise us what questions mankind have
actually asked of themselves, and what, in the nature of answers to those
questions, they have actually thought they had grounds to believe.

Now the first glance at a proposition shows that it is formed by putting
together two names. A proposition, according to the common simple
definition, which is sufficient for our purpose is, _discourse, in which
something is affirmed or denied of something_. Thus, in the proposition,
Gold is yellow, the quality yellow is affirmed of the substance _gold_. In
the proposition, Franklin was not born in England, the fact expressed by
the words _born in England_ is denied of the man Franklin.

Every proposition consists of three parts: the Subject, the Predicate, and
the Copula. The predicate is the name denoting that which is affirmed or
denied. The subject is the name denoting the person or thing which
something is affirmed or denied of. The copula is the sign denoting that
there is an affirmation or denial, and thereby enabling the hearer or
reader to distinguish a proposition from any other kind of discourse.
Thus, in the proposition, The earth is round, the Predicate is the word
_round_, which denotes the quality affirmed, or (as the phrase is)
predicated: _the earth_, words denoting the object which that quality is
affirmed of, compose the Subject; the word _is_, which serves as the
connecting mark between the subject and predicate, to show that one of
them is affirmed of the other, is called the Copula.

Dismissing, for the present, the copula, of which more will be said
hereafter, every proposition, then, consists of at least two names—brings
together two names, in a particular manner. This is already a first step
toward what we are in quest of. It appears from this, that for an act of
belief, _one_ object is not sufficient; the simplest act of belief
supposes, and has something to do with, _two_ objects—two names, to say
the least; and (since the names must be names of something) two _namable
things_. A large class of thinkers would cut the matter short by saying,
two _ideas_. They would say, that the subject and predicate are both of
them names of ideas; the idea of gold, for instance, and the idea of
yellow; and that what takes place (or part of what takes place) in the act
of belief consists in bringing (as it is often expressed) one of these
ideas under the other. But this we are not yet in a condition to say:
whether such be the correct mode of describing the phenomenon, is an after
consideration. The result with which for the present we must be contented,
is, that in every act of belief _two_ objects are in some manner taken
cognizance of; that there can be no belief claimed, or question
propounded, which does not embrace two distinct (either material or
intellectual) subjects of thought; each of them capable, or not, of being
conceived by itself, but incapable of being believed by itself.

I may say, for instance, “the sun.” The word has a meaning, and suggests
that meaning to the mind of any one who is listening to me. But suppose I
ask him, Whether it is true: whether he believes it? He can give no
answer. There is as yet nothing to believe, or to disbelieve. Now,
however, let me make, of all possible assertions respecting the sun, the
one which involves the least of reference to any object besides itself;
let me say, “the sun exists.” Here, at once, is something which a person
can say he believes. But here, instead of only one, we find two distinct
objects of conception: the sun is one object; existence is another. Let it
not be said that this second conception, existence, is involved in the
first; for the sun may be conceived as no longer existing. “The sun” does
not convey all the meaning that is conveyed by “the sun exists:” “my
father” does not include all the meaning of “my father exists,” for he may
be dead; “a round square” does not include the meaning of “a round square
exists,” for it does not and can not exist. When I say “the sun,” “my
father,” or a “round square,” I do not call upon the hearer for any belief
or disbelief, nor can either the one or the other be afforded me; but if I
say, “the sun exists,” “my father exists,” or “a round square exists,” I
call for belief; and should, in the first of the three instances, meet
with it; in the second, with belief or disbelief, as the case might be; in
the third, with disbelief.

§ 3. This first step in the analysis of the object of belief, which,
though so obvious, will be found to be not unimportant, is the only one
which we shall find it practicable to make without a preliminary survey of
language. If we attempt to proceed further in the same path, that is, to
analyze any further the import of Propositions; we find forced upon us, as
a subject of previous consideration, the import of Names. For every
proposition consists of two names; and every proposition affirms or denies
one of these names, of the other. Now what we do, what passes in our mind,
when we affirm or deny two names of one another, must depend on what they
are names of; since it is with reference to that, and not to the mere
names themselves, that we make the affirmation or denial. Here, therefore,
we find a new reason why the signification of names, and the relation
generally between names and the things signified by them, must occupy the
preliminary stage of the inquiry we are engaged in.

It may be objected that the meaning of names can guide us at most only to
the opinions, possibly the foolish and groundless opinions, which mankind
have formed concerning things, and that as the object of philosophy is
truth, not opinion, the philosopher should dismiss words and look into
things themselves, to ascertain what questions can be asked and answered
in regard to them. This advice (which no one has it in his power to
follow) is in reality an exhortation to discard the whole fruits of the
labors of his predecessors, and conduct himself as if he were the first
person who had ever turned an inquiring eye upon nature. What does any
one’s personal knowledge of Things amount to, after subtracting all which
he has acquired by means of the words of other people? Even after he has
learned as much as people usually do learn from others, will the notions
of things contained in his individual mind afford as sufficient a basis
for a _catalogue raisonné_ as the notions which are in the minds of all
mankind?

In any enumeration and classification of Things, which does not set out
from their names, no varieties of things will of course be comprehended
but those recognized by the particular inquirer; and it will still remain
to be established, by a subsequent examination of names, that the
enumeration has omitted nothing which ought to have been included. But if
we begin with names, and use them as our clue to the things, we bring at
once before us all the distinctions which have been recognized, not by a
single inquirer, but by all inquirers taken together. It doubtless may,
and I believe it will, be found, that mankind have multiplied the
varieties unnecessarily, and have imagined distinctions among things,
where there were only distinctions in the manner of naming them. But we
are not entitled to assume this in the commencement. We must begin by
recognizing the distinctions made by ordinary language. If some of these
appear, on a close examination, not to be fundamental, the enumeration of
the different kinds of realities may be abridged accordingly. But to
impose upon the facts in the first instance the yoke of a theory, while
the grounds of the theory are reserved for discussion in a subsequent
stage, is not a course which a logician can reasonably adopt.




                               Chapter II.


Of Names.


§ 1. “A name,” says Hobbes,(7) “is a word taken at pleasure to serve for a
mark which may raise in our mind a thought like to some thought we had
before, and which being pronounced to others, may be to them a sign of
what thought the speaker had(8) before in his mind.” This simple
definition of a name, as a word (or set of words) serving the double
purpose of a mark to recall to ourselves the likeness of a former thought,
and a sign to make it known to others, appears unexceptionable. Names,
indeed, do much more than this; but whatever else they do, grows out of,
and is the result of this: as will appear in its proper place.

Are names more properly said to be the names of things, or of our ideas of
things? The first is the expression in common use; the last is that of
some metaphysicians, who conceived that in adopting it they were
introducing a highly important distinction. The eminent thinker, just
quoted, seems to countenance the latter opinion. “But seeing,” he
continues, “names ordered in speech (as is defined) are signs of our
conceptions, it is manifest they are not signs of the things themselves;
for that the sound of this word _stone_ should be the sign of a stone, can
not be understood in any sense but this, that he that hears it collects
that he that pronounces it thinks of a stone.”

If it be merely meant that the conception alone, and not the thing itself,
is recalled by the name, or imparted to the hearer, this of course can not
be denied. Nevertheless, there seems good reason for adhering to the
common usage, and calling (as indeed Hobbes himself does in other places)
the word _sun_ the name of the sun, and not the name of our idea of the
sun. For names are not intended only to make the hearer conceive what we
conceive, but also to inform him what we believe. Now, when I use a name
for the purpose of expressing a belief, it is a belief concerning the
thing itself, not concerning my idea of it. When I say, “the sun is the
cause of day,” I do not mean that my idea of the sun causes or excites in
me the idea of day; or in other words, that thinking of the sun makes me
think of day. I mean, that a certain physical fact, which is called the
sun’s presence (and which, in the ultimate analysis, resolves itself into
sensations, not ideas) causes another physical fact, which is called day.
It seems proper to consider a word as the _name_ of that which we intend
to be understood by it when we use it; of that which any fact that we
assert of it is to be understood of; that, in short, concerning which,
when we employ the word, we intend to give information. Names, therefore,
shall always be spoken of in this work as the names of things themselves,
and not merely of our ideas of things.

But the question now arises, of what things? and to answer this it is
necessary to take into consideration the different kinds of names.

§ 2. It is usual, before examining the various classes into which names
are commonly divided, to begin by distinguishing from names of every
description, those words which are not names, but only parts of names.
Among such are reckoned particles, as _of_, _to_, _truly_, _often_; the
inflected cases of nouns substantive, as _me_, _him_, _John’s_; and even
adjectives, as _large_, _heavy_. These words do not express things of
which any thing can be affirmed or denied. We can not say, Heavy fell, or
A heavy fell; Truly, or A truly, was asserted; Of, or An of, was in the
room. Unless, indeed, we are speaking of the mere words themselves, as
when we say, Truly is an English word, or, Heavy is an adjective. In that
case they are complete names—viz., names of those particular sounds, or of
those particular collections of written characters. This employment of a
word to denote the mere letters and syllables of which it is composed, was
termed by the schoolmen the _suppositio materialis_ of the word. In any
other sense we can not introduce one of these words into the subject of a
proposition, unless in combination with other words; as, A heavy _body_
fell, A truly _important fact_ was asserted, A _member_ of _parliament_
was in the room.

An adjective, however, is capable of standing by itself as the predicate
of a proposition; as when we say, Snow is white; and occasionally even as
the subject, for we may say, White is an agreeable color. The adjective is
often said to be so used by a grammatical ellipsis: Snow is white, instead
of Snow is a white object; White is an agreeable color, instead of, A
white color, or, The color white, is agreeable. The Greeks and Romans were
allowed, by the rules of their language, to employ this ellipsis
universally in the subject as well as in the predicate of a proposition.
In English this can not, generally speaking, be done. We may say, The
earth is round; but we can not say, Round is easily moved; we must say, A
round object. This distinction, however, is rather grammatical than
logical. Since there is no difference of meaning between _round_, and _a
round object_, it is only custom which prescribes that on any given
occasion one shall be used, and not the other. We shall, therefore,
without scruple, speak of adjectives as names, whether in their own right,
or as representative of the more circuitous forms of expression above
exemplified. The other classes of subsidiary words have no title whatever
to be considered as names. An adverb, or an accusative case, can not under
any circumstances (except when their mere letters and syllables are spoken
of) figure as one of the terms of a proposition.

Words which are not capable of being used as names, but only as parts of
names, were called by some of the schoolmen Syncategorematic terms: from
σὺν, with, and κατηγορέω, to predicate, because it was only _with_ some
other word that they could be predicated. A word which could be used
either as the subject or predicate of a proposition without being
accompanied by any other word, was termed by the same authorities a
Categorematic term. A combination of one or more Categorematic, and one or
more Syncategorematic words, as A heavy body, or A court of justice, they
sometimes called a _mixed_ term; but this seems a needless multiplication
of technical expressions. A mixed term is, in the only useful sense of the
word, Categorematic. It belongs to the class of what have been called
many-worded names.

For, as one word is frequently not a name, but only part of a name, so a
number of words often compose one single name, and no more. These words,
“The place which the wisdom or policy of antiquity had destined for the
residence of the Abyssinian princes,” form in the estimation of the
logician only one name; one Categorematic term. A mode of determining
whether any set of words makes only one name, or more than one, is by
predicating something of it, and observing whether, by this predication,
we make only one assertion or several. Thus, when we say, John Nokes, who
was the mayor of the town, died yesterday—by this predication we make but
one assertion; whence it appears that “John Nokes, who was the mayor of
the town,” is no more than one name. It is true that in this proposition,
besides the assertion that John Nokes died yesterday, there is included
another assertion, namely, that John Nokes was mayor of the town. But this
last assertion was already made: we did not make it by adding the
predicate, “died yesterday.” Suppose, however, that the words had been,
John Nokes _and_ the mayor of the town, they would have formed two names
instead of one. For when we say, John Nokes and the mayor of the town died
yesterday, we make two assertions: one, that John Nokes died yesterday;
the other, that the mayor of the town died yesterday.

It being needless to illustrate at any greater length the subject of
many-worded names, we proceed to the distinctions which have been
established among names, not according to the words they are composed of,
but according to their signification.

§ 3. All names are names of something, real or imaginary; but all things
have not names appropriated to them individually. For some individual
objects we require, and consequently have, separate distinguishing names;
there is a name for every person, and for every remarkable place. Other
objects, of which we have not occasion to speak so frequently, we do not
designate by a name of their own; but when the necessity arises for naming
them, we do so by putting together several words, each of which, by
itself, might be and is used for an indefinite number of other objects; as
when I say, _this stone_: “this” and “stone” being, each of them, names
that may be used of many other objects besides the particular one meant,
though the only object of which they can both be used at the given moment,
consistently with their signification, may be the one of which I wish to
speak.

Were this the sole purpose for which names, that are common to more things
than one, could be employed; if they only served, by mutually limiting
each other, to afford a designation for such individual objects as have no
names of their own: they could only be ranked among contrivances for
economizing the use of language. But it is evident that this is not their
sole function. It is by their means that we are enabled to assert
_general_ propositions; to affirm or deny any predicate of an indefinite
number of things at once. The distinction, therefore, between _general_
names, and _individual_ or _singular_ names, is fundamental; and may be
considered as the first grand division of names.

A general name is familiarly defined, a name which is capable of being
truly affirmed, in the same sense, of each of an indefinite number of
things. An individual or singular name is a name which is only capable of
being truly affirmed, in the same sense, of one thing.

Thus, _man_ is capable of being truly affirmed of John, George, Mary, and
other persons without assignable limit; and it is affirmed of all of them
in the same sense; for the word man expresses certain qualities, and when
we predicate it of those persons, we assert that they all possess those
qualities. But _John_ is only capable of being truly affirmed of one
single person, at least in the same sense. For, though there are many
persons who bear that name, it is not conferred upon them to indicate any
qualities, or any thing which belongs to them in common; and can not be
said to be affirmed of them in any _sense_ at all, consequently not in the
same sense. “The king who succeeded William the Conqueror,” is also an
individual name. For, that there can not be more than one person of whom
it can be truly affirmed, is implied in the meaning of the words. Even
“_the_ king,” when the occasion or the context defines the individual of
whom it is to be understood, may justly be regarded as an individual name.

It is not unusual, by way of explaining what is meant by a general name,
to say that it is the name of a _class_. But this, though a convenient
mode of expression for some purposes, is objectionable as a definition,
since it explains the clearer of two things by the more obscure. It would
be more logical to reverse the proposition, and turn it into a definition
of the word _class_: “A class is the indefinite multitude of individuals
denoted by a general name.”

It is necessary to distinguish _general_ from _collective_ names. A
general name is one which can be predicated of _each_ individual of a
multitude; a collective name can not be predicated of each separately, but
only of all taken together. “The 76th regiment of foot in the British
army,” which is a collective name, is not a general but an individual
name; for though it can be predicated of a multitude of individual
soldiers taken jointly, it can not be predicated of them severally. We may
say, Jones is a soldier, and Thompson is a soldier, and Smith is a
soldier, but we can not say, Jones is the 76th regiment, and Thompson is
the 76th regiment, and Smith is the 76th regiment. We can only say, Jones,
and Thompson, and Smith, and Brown, and so forth (enumerating all the
soldiers), are the 76th regiment.

“The 76th regiment” is a collective name, but not a general one: “a
regiment” is both a collective and a general name. General with respect to
all individual regiments, of each of which separately it can be affirmed:
collective with respect to the individual soldiers of whom any regiment is
composed.

§ 4. The second general division of names is into _concrete_ and
_abstract_. A concrete name is a name which stands for a thing; an
abstract name is a name which stands for an attribute of a thing. Thus
_John_, _the sea_, _this table_, are names of things. _White_, also, is a
name of a thing, or rather of things. Whiteness, again, is the name of a
quality or attribute of those things. Man is a name of many things;
humanity is a name of an attribute of those things. _Old_ is a name of
things: _old age_ is a name of one of their attributes.

I have used the words concrete and abstract in the sense annexed to them
by the schoolmen, who, notwithstanding the imperfections of their
philosophy, were unrivaled in the construction of technical language, and
whose definitions, in logic at least, though they never went more than a
little way into the subject, have seldom, I think, been altered but to be
spoiled. A practice, however, has grown up in more modern times, which, if
not introduced by Locke, has gained currency chiefly from his example, of
applying the expression “abstract name” to all names which are the result
of abstraction or generalization, and consequently to all general names,
instead of confining it to the names of attributes. The metaphysicians of
the Condillac school—whose admiration of Locke, passing over the
profoundest speculations of that truly original genius, usually fastens
with peculiar eagerness upon his weakest points—have gone on imitating him
in this abuse of language, until there is now some difficulty in restoring
the word to its original signification. A more wanton alteration in the
meaning of a word is rarely to be met with; for the expression _general
name_, the exact equivalent of which exists in all languages I am
acquainted with, was already available for the purpose to which _abstract_
has been misappropriated, while the misappropriation leaves that important
class of words, the names of attributes, without any compact distinctive
appellation. The old acceptation, however, has not gone so completely out
of use as to deprive those who still adhere to it of all chance of being
understood. By _abstract_, then, I shall always, in Logic proper, mean the
opposite of _concrete_; by an abstract name, the name of an attribute; by
a concrete name, the name of an object.

Do abstract names belong to the class of general, or to that of singular
names? Some of them are certainly general. I mean those which are names
not of one single and definite attribute, but of a class of attributes.
Such is the word _color_, which is a name common to whiteness, redness,
etc. Such is even the word whiteness, in respect of the different shades
of whiteness to which it is applied in common: the word magnitude, in
respect of the various degrees of magnitude and the various dimensions of
space; the word weight, in respect of the various degrees of weight. Such
also is the word _attribute_ itself, the common name of all particular
attributes. But when only one attribute, neither variable in degree nor in
kind, is designated by the name; as visibleness; tangibleness; equality;
squareness; milk-whiteness; then the name can hardly be considered
general; for though it denotes an attribute of many different objects, the
attribute itself is always conceived as one, not many.(9) To avoid
needless logomachies, the best course would probably be to consider these
names as neither general nor individual, and to place them in a class
apart.

It may be objected to our definition of an abstract name, that not only
the names which we have called abstract, but adjectives, which we have
placed in the concrete class, are names of attributes; that _white_, for
example, is as much the name of the color as _whiteness_ is. But (as
before remarked) a word ought to be considered as the name of that which
we intend to be understood by it when we put it to its principal use, that
is, when we employ it in predication. When we say snow is white, milk is
white, linen is white, we do not mean it to be understood that snow, or
linen, or milk, is a color. We mean that they are things having the color.
The reverse is the case with the word whiteness; what we affirm to _be_
whiteness is not snow, but the color of snow. Whiteness, therefore, is the
name of the color exclusively: white is a name of all things whatever
having the color; a name, not of the quality whiteness, but of every white
object. It is true, this name was given to all those various objects on
account of the quality; and we may therefore say, without impropriety,
that the quality forms part of its signification; but a name can only be
said to stand for, or to be a name of, the things of which it can be
predicated. We shall presently see that all names which can be said to
have any signification, all names by applying which to an individual we
give any information respecting that individual, may be said to _imply_ an
attribute of some sort; but they are not names of the attribute; it has
its own proper abstract name.

§ 5. This leads to the consideration of a third great division of names,
into _connotative_ and _non-connotative_, the latter sometimes, but
improperly, called _absolute_. This is one of the most important
distinctions which we shall have occasion to point out, and one of those
which go deepest into the nature of language.

A non-connotative term is one which signifies a subject only, or an
attribute only. A connotative term is one which denotes a subject, and
implies an attribute. By a subject is here meant any thing which possesses
attributes. Thus John, or London, or England, are names which signify a
subject only. Whiteness, length, virtue, signify an attribute only. None
of these names, therefore, are connotative. But _white_, _long_,
_virtuous_, are connotative. The word white, denotes all white things, as
snow, paper, the foam of the sea, etc., and implies, or in the language of
the schoolmen, _connotes_,(10) the attribute _whiteness_. The word white
is not predicated of the attribute, but of the subjects, snow, etc.; but
when we predicate it of them, we convey the meaning that the attribute
whiteness belongs to them. The same may be said of the other words above
cited. Virtuous, for example, is the name of a class, which includes
Socrates, Howard, the Man of Ross, and an undefinable number of other
individuals, past, present, and to come. These individuals, collectively
and severally, can alone be said with propriety to be denoted by the word:
of them alone can it properly be said to be a name. But it is a name
applied to all of them in consequence of an attribute which they are
supposed to possess in common, the attribute which has received the name
of virtue. It is applied to all beings that are considered to possess this
attribute; and to none which are not so considered.

All concrete general names are connotative. The word _man_, for example,
denotes Peter, Jane, John, and an indefinite number of other individuals,
of whom, taken as a class, it is the name. But it is applied to them,
because they possess, and to signify that they possess, certain
attributes. These seem to be, corporeity, animal life, rationality, and a
certain external form, which for distinction we call the human. Every
existing thing, which possessed all these attributes, would be called a
man; and any thing which possessed none of them, or only one, or two, or
even three of them without the fourth, would not be so called. For
example, if in the interior of Africa there were to be discovered a race
of animals possessing reason equal to that of human beings, but with the
form of an elephant, they would not be called men. Swift’s Houyhnhnms
would not be so called. Or if such newly-discovered beings possessed the
form of man without any vestige of reason, it is probable that some other
name than that of man would be found for them. How it happens that there
can be any doubt about the matter, will appear hereafter. The word _man_,
therefore, signifies all these attributes, and all subjects which possess
these attributes. But it can be predicated only of the subjects. What we
call men, are the subjects, the individual Stiles and Nokes; not the
qualities by which their humanity is constituted. The name, therefore, is
said to signify the subjects _directly_, the attributes _indirectly_; it
_denotes_ the subjects, and implies, or involves, or indicates, or as we
shall say henceforth _connotes_, the attributes. It is a connotative name.

Connotative names have hence been also called _denominative_, because the
subject which they denote is denominated by, or receives a name from the
attribute which they connote. Snow, and other objects, receive the name
white, because they possess the attribute which is called whiteness;
Peter, James, and others receive the name man because they possess the
attributes which are considered to constitute humanity. The attribute, or
attributes, may therefore be said to denominate those objects, or to give
them a common name.(11)

It has been seen that all concrete general names are connotative. Even
abstract names, though the names only of attributes, may in some instances
be justly considered as connotative; for attributes themselves may have
attributes ascribed to them; and a word which denotes attributes may
connote an attribute of those attributes. Of this description, for
example, is such a word as _fault_; equivalent to _bad_ or _hurtful
quality_. This word is a name common to many attributes, and connotes
hurtfulness, an attribute of those various attributes. When, for example,
we say that slowness, in a horse, is a fault, we do not mean that the slow
movement, the actual change of pace of the slow horse, is a bad thing, but
that the property or peculiarity of the horse, from which it derives that
name, the quality of being a slow mover, is an undesirable peculiarity.

In regard to those concrete names which are not general but individual, a
distinction must be made.

Proper names are not connotative: they denote the individuals who are
called by them; but they do not indicate or imply any attributes as
belonging to those individuals. When we name a child by the name Paul, or
a dog by the name Cæsar, these names are simply marks used to enable those
individuals to be made subjects of discourse. It may be said, indeed, that
we must have had some reason for giving them those names rather than any
others; and this is true; but the name, once given, is independent of the
reason. A man may have been named John, because that was the name of his
father; a town may have been named Dartmouth, because it is situated at
the mouth of the Dart. But it is no part of the signification of the word
John, that the father of the person so called bore the same name; nor even
of the word Dartmouth, to be situated at the mouth of the Dart. If sand
should choke up the mouth of the river, or an earthquake change its
course, and remove it to a distance from the town, the name of the town
would not necessarily be changed. That fact, therefore, can form no part
of the signification of the word; for otherwise, when the fact confessedly
ceased to be true, no one would any longer think of applying the name.
Proper names are attached to the objects themselves, and are not dependent
on the continuance of any attribute of the object.

But there is another kind of names, which, although they are individual
names—that is, predicable only of one object—are really connotative. For,
though we may give to an individual a name utterly unmeaning, which we
call a proper name—a word which answers the purpose of showing what thing
it is we are talking about, but not of telling any thing about it; yet a
name peculiar to an individual is not necessarily of this description. It
may be significant of some attribute, or some union of attributes, which,
being possessed by no object but one, determines the name exclusively to
that individual. “The sun” is a name of this description; “God,” when used
by a monotheist, is another. These, however, are scarcely examples of what
we are now attempting to illustrate, being, in strictness of language,
general, not individual names: for, however they may be _in fact_
predicable only of one object, there is nothing in the meaning of the
words themselves which implies this: and, accordingly, when we are
imagining and not affirming, we may speak of many suns; and the majority
of mankind have believed, and still believe, that there are many gods. But
it is easy to produce words which are real instances of connotative
individual names. It may be part of the meaning of the connotative name
itself, that there can exist but one individual possessing the attribute
which it connotes: as, for instance, “the _only_ son of John Stiles;” “the
_first_ emperor of Rome.” Or the attribute connoted may be a connection
with some determinate event, and the connection may be of such a kind as
only one individual could have; or may at least be such as only one
individual actually had; and this may be implied in the form of the
expression. “The father of Socrates” is an example of the one kind (since
Socrates could not have had two fathers); “the author of the Iliad,” “the
murderer of Henri Quatre,” of the second. For, though it is conceivable
that more persons than one might have participated in the authorship of
the Iliad, or in the murder of Henri Quatre, the employment of the article
_the_ implies that, in fact, this was not the case. What is here done by
the word _the_, is done in other cases by the context: thus, “Cæsar’s
army” is an individual name, if it appears from the context that the army
meant is that which Cæsar commanded in a particular battle. The still more
general expressions, “the Roman army,” or “the Christian army,” may be
individualized in a similar manner. Another case of frequent occurrence
has already been noticed; it is the following: The name, being a
many-worded one, may consist, in the first place, of a _general_ name,
capable therefore in itself of being affirmed of more things than one, but
which is, in the second place, so limited by other words joined with it,
that the entire expression can only be predicated of one object,
consistently with the meaning of the general term. This is exemplified in
such an instance as the following: “the present prime minister of
England.” Prime Minister of England is a general name; the attributes
which it connotes may be possessed by an indefinite number of persons: in
succession however, not simultaneously; since the meaning of the name
itself imports (among other things) that there can be only one such person
at a time. This being the case, and the application of the name being
afterward limited by the article and the word _present_, to such
individuals as possess the attributes at one indivisible point of time, it
becomes applicable only to one individual. And as this appears from the
meaning of the name, without any extrinsic proof, it is strictly an
individual name.

From the preceding observations it will easily be collected, that whenever
the names given to objects convey any information—that is, whenever they
have properly any meaning—the meaning resides not in what they _denote_,
but in what they _connote_. The only names of objects which connote
nothing are _proper_ names; and these have, strictly speaking, no
signification.(12)

If, like the robber in the Arabian Nights, we make a mark with chalk on a
house to enable us to know it again, the mark has a purpose, but it has
not properly any meaning. The chalk does not declare any thing about the
house; it does not mean, This is such a person’s house, or This is a house
which contains booty. The object of making the mark is merely distinction.
I say to myself, All these houses are so nearly alike that if I lose sight
of them I shall not again be able to distinguish that which I am now
looking at, from any of the others; I must therefore contrive to make the
appearance of this one house unlike that of the others, that I may
hereafter know when I see the mark—not indeed any attribute of the
house—but simply that it is the same house which I am now looking at.
Morgiana chalked all the other houses in a similar manner, and defeated
the scheme: how? simply by obliterating the difference of appearance
between that house and the others. The chalk was still there, but it no
longer served the purpose of a distinctive mark.

When we impose a proper name, we perform an operation in some degree
analogous to what the robber intended in chalking the house. We put a
mark, not indeed upon the object itself, but, so to speak, upon the idea
of the object. A proper name is but an unmeaning mark which we connect in
our minds with the idea of the object, in order that whenever the mark
meets our eyes or occurs to our thoughts, we may think of that individual
object. Not being attached to the thing itself, it does not, like the
chalk, enable us to distinguish the object when we see it; but it enables
us to distinguish it when it is spoken of, either in the records of our
own experience, or in the discourse of others; to know that what we find
asserted in any proposition of which it is the subject, is asserted of the
individual thing with which we were previously acquainted.

When we predicate of any thing its proper name; when we say, pointing to a
man, this is Brown or Smith, or pointing to a city, that it is York, we do
not, merely by so doing, convey to the reader any information about them,
except that those are their names. By enabling him to identify the
individuals, we may connect them with information previously possessed by
him; by saying, This is York, we may tell him that it contains the
Minster. But this is in virtue of what he has previously heard concerning
York; not by any thing implied in the name. It is otherwise when objects
are spoken of by connotative names. When we say, The town is built of
marble, we give the hearer what may be entirely new information, and this
merely by the signification of the many-worded connotative name, “built of
marble.” Such names are not signs of the mere objects, invented because we
have occasion to think and speak of those objects individually; but signs
which accompany an attribute; a kind of livery in which the attribute
clothes all objects which are recognized as possessing it. They are not
mere marks, but more, that is to say, significant marks; and the
connotation is what constitutes their significance.

As a proper name is said to be the name of the one individual which it is
predicated of, so (as well from the importance of adhering to analogy, as
for the other reasons formerly assigned) a connotative name ought to be
considered a name of all the various individuals which it is predicable
of, or in other words _denotes_, and not of what it connotes. But by
learning what things it is a name of, we do not learn the meaning of the
name: for to the same thing we may, with equal propriety, apply many
names, not equivalent in meaning. Thus, I call a certain man by the name
Sophroniscus: I call him by another name, The father of Socrates. Both
these are names of the same individual, but their meaning is altogether
different; they are applied to that individual for two different purposes:
the one, merely to distinguish him from other persons who are spoken of;
the other to indicate a fact relating to him, the fact that Socrates was
his son. I further apply to him these other expressions: a man, a Greek,
an Athenian, a sculptor, an old man, an honest man, a brave man. All these
are, or may be, names of Sophroniscus, not indeed of him alone, but of him
and each of an indefinite number of other human beings. Each of these
names is applied to Sophroniscus for a different reason, and by each
whoever understands its meaning is apprised of a distinct fact or number
of facts concerning him; but those who knew nothing about the names except
that they were applicable to Sophroniscus, would be altogether ignorant of
their meaning. It is even possible that I might know every single
individual of whom a given name could be with truth affirmed, and yet
could not be said to know the meaning of the name. A child knows who are
its brothers and sisters, long before it has any definite conception of
the nature of the facts which are involved in the signification of those
words.

In some cases it is not easy to decide precisely how much a particular
word does or does not connote; that is, we do not exactly know (the case
not having arisen) what degree of difference in the object would occasion
a difference in the name. Thus, it is clear that the word man, besides
animal life and rationality, connotes also a certain external form; but it
would be impossible to say precisely what form; that is, to decide how
great a deviation from the form ordinarily found in the beings whom we are
accustomed to call men, would suffice in a newly-discovered race to make
us refuse them the name of man. Rationality, also, being a quality which
admits of degrees, it has never been settled what is the lowest degree of
that quality which would entitle any creature to be considered a human
being. In all such cases, the meaning of the general name is so far
unsettled and vague; mankind have not come to any positive agreement about
the matter. When we come to treat of Classification, we shall have
occasion to show under what conditions this vagueness may exist without
practical inconvenience; and cases will appear in which the ends of
language are better promoted by it than by complete precision; in order
that, in natural history for instance, individuals or species of no very
marked character may be ranged with those more strongly characterized
individuals or species to which, in all their properties taken together,
they bear the nearest resemblance.

But this partial uncertainty in the connotation of names can only be free
from mischief when guarded by strict precautions. One of the chief
sources, indeed, of lax habits of thought, is the custom of using
connotative terms without a distinctly ascertained connotation, and with
no more precise notion of their meaning than can be loosely collected from
observing what objects they are used to denote. It is in this manner that
we all acquire, and inevitably so, our first knowledge of our vernacular
language. A child learns the meaning of the words _man_, or _white_, by
hearing them applied to a variety of individual objects, and finding out,
by a process of generalization and analysis which he could not himself
describe, what those different objects have in common. In the case of
these two words the process is so easy as to require no assistance from
culture; the objects called human beings, and the objects called white,
differing from all others by qualities of a peculiarly definite and
obvious character. But in many other cases, objects bear a general
resemblance to one another, which leads to their being familiarly classed
together under a common name, while, without more analytic habits than the
generality of mankind possess, it is not immediately apparent what are the
particular attributes, upon the possession of which in common by them all,
their general resemblance depends. When this is the case, people use the
name without any recognized connotation, that is, without any precise
meaning; they talk, and consequently think, vaguely, and remain contented
to attach only the same degree of significance to their own words, which a
child three years old attaches to the words brother and sister. The child
at least is seldom puzzled by the starting up of new individuals, on whom
he is ignorant whether or not to confer the title; because there is
usually an authority close at hand competent to solve all doubts. But a
similar resource does not exist in the generality of cases; and new
objects are continually presenting themselves to men, women, and children,
which they are called upon to class _proprio motu_. They, accordingly, do
this on no other principle than that of superficial similarity, giving to
each new object the name of that familiar object, the idea of which it
most readily recalls, or which, on a cursory inspection, it seems to them
most to resemble: as an unknown substance found in the ground will be
called, according to its texture, earth, sand, or a stone. In this manner,
names creep on from subject to subject, until all traces of a common
meaning sometimes disappear, and the word comes to denote a number of
things not only independently of any common attribute, but which have
actually no attribute in common; or none but what is shared by other
things to which the name is capriciously refused.(13) Even scientific
writers have aided in this perversion of general language from its
purpose; sometimes because, like the vulgar, they knew no better; and
sometimes in deference to that aversion to admit new words, which induces
mankind, on all subjects not considered technical, to attempt to make the
original stock of names serve with but little augmentation to express a
constantly increasing number of objects and distinctions, and,
consequently, to express them in a manner progressively more and more
imperfect.

To what a degree this loose mode of classing and denominating objects has
rendered the vocabulary of mental and moral philosophy unfit for the
purposes of accurate thinking, is best known to whoever has most meditated
on the present condition of those branches of knowledge. Since, however,
the introduction of a new technical language as the vehicle of
speculations on subjects belonging to the domain of daily discussion, is
extremely difficult to effect, and would not be free from inconvenience
even if effected, the problem for the philosopher, and one of the most
difficult which he has to resolve, is, in retaining the existing
phraseology, how best to alleviate its imperfections. This can only be
accomplished by giving to every general concrete name which there is
frequent occasion to predicate, a definite and fixed connotation; in order
that it may be known what attributes, when we call an object by that name,
we really mean to predicate of the object. And the question of most nicety
is, how to give this fixed connotation to a name, with the least possible
change in the objects which the name is habitually employed to denote;
with the least possible disarrangement, either by adding or subtraction,
of the group of objects which, in however imperfect a manner, it serves to
circumscribe and hold together; and with the least vitiation of the truth
of any propositions which are commonly received as true.

This desirable purpose, of giving a fixed connotation where it is wanting,
is the end aimed at whenever any one attempts to give a definition of a
general name already in use; every definition of a connotative name being
an attempt either merely to declare, or to declare and analyze, the
connotation of the name. And the fact, that no questions which have arisen
in the moral sciences have been subjects of keener controversy than the
definitions of almost all the leading expressions, is a proof how great an
extent the evil to which we have adverted has attained.

Names with indeterminate connotation are not to be confounded with names
which have more than one connotation, that is to say, ambiguous words. A
word may have several meanings, but all of them fixed and recognized ones;
as the word _post_, for example, or the word _box_, the various senses of
which it would be endless to enumerate. And the paucity of existing names,
in comparison with the demand for them, may often render it advisable and
even necessary to retain a name in this multiplicity of acceptations,
distinguishing these so clearly as to prevent their being confounded with
one another. Such a word may be considered as two or more names,
accidentally written and spoken alike.(14)

§ 6. The fourth principal division of names, is into _positive_ and
_negative_. Positive, as _man_, _tree_, _good_; negative, as _not-man_,
_not-tree_, _not-good_. To every positive concrete name, a corresponding
negative one might be framed. After giving a name to any one thing, or to
any plurality of things, we might create a second name which should be a
name of all things whatever, except that particular thing or things. These
negative names are employed whenever we have occasion to speak
collectively of all things other than some thing or class of things. When
the positive name is connotative, the corresponding negative name is
connotative likewise; but in a peculiar way, connoting not the presence
but the absence of an attribute. Thus, _not-white_ denotes all things
whatever except white things; and connotes the attribute of not possessing
whiteness. For the non-possession of any given attribute is also an
attribute, and may receive a name as such; and thus negative concrete
names may obtain negative abstract names to correspond to them.(15)

Names which are positive in form are often negative in reality, and others
are really positive though their form is negative. The word
_inconvenient_, for example, does not express the mere absence of
convenience; it expresses a positive attribute—that of being the cause of
discomfort or annoyance. So the word _unpleasant_, notwithstanding its
negative form, does not connote the mere absence of pleasantness, but a
less degree of what is signified by the word _painful_, which, it is
hardly necessary to say, is positive. _Idle_, on the other hand, is a word
which, though positive in form, expresses nothing but what would be
signified either by the phrase _not working_, or by the phrase _not
disposed to work_; and _sober_, either by _not drunk_ or by _not drunken_.

There is a class of names called _privative_. A privative name is
equivalent in its signification to a positive and a negative name taken
together; being the name of something which has once had a particular
attribute, or for some other reason might have been expected to have it,
but which has it not. Such is the word _blind_, which is not equivalent to
_not seeing_, or to _not capable of seeing_, for it would not, except by a
poetical or rhetorical figure, be applied to stocks and stones. A thing is
not usually said to be blind, unless the class to which it is most
familiarly referred, or to which it is referred on the particular
occasion, be chiefly composed of things which can see, as in the case of a
blind man, or a blind horse; or unless it is supposed for any reason that
it ought to see; as in saying of a man, that he rushed blindly into an
abyss, or of philosophers or the clergy that the greater part of them are
blind guides. The names called privative, therefore, connote two things;
the absence of certain attributes, and the presence of others, from which
the presence also of the former might naturally have been expected.

§ 7. The fifth leading division of names is into _relative_ and
_absolute_, or let us rather say, _relative_ and _non-relative_; for the
word absolute is put upon much too hard duty in metaphysics, not to be
willingly spared when its services can be dispensed with. It resembles the
word _civil_ in the language of jurisprudence, which stands for the
opposite of criminal, the opposite of ecclesiastical, the opposite of
military, the opposite of political—in short, the opposite of any positive
word which wants a negative.

Relative names are such as father, son; ruler, subject; like; equal;
unlike; unequal; longer, shorter; cause, effect. Their characteristic
property is, that they are always given in pairs. Every relative name
which is predicated of an object, supposes another object (or objects), of
which we may predicate either that same name or another relative name
which is said to be the _correlative_ of the former. Thus, when we call
any person a son, we suppose other persons who must be called parents.
When we call any event a cause, we suppose another event which is an
effect. When we say of any distance that it is longer, we suppose another
distance which is shorter. When we say of any object that it is like, we
mean that it is like some other object, which is also said to be like the
first. In this last case both objects receive the same name; the relative
term is its own correlative.

It is evident that these words, when concrete, are, like other concrete
general names, connotative; they denote a subject, and connote an
attribute; and each of them has, or might have, a corresponding abstract
name, to denote the attribute connoted by the concrete. Thus the concrete
_like_ has its abstract _likeness_; the concretes, father and son, have,
or might have, the abstracts, paternity, and filiety, or sonship. The
concrete name connotes an attribute, and the abstract name which answers
to it denotes that attribute. But of what nature is the attribute? Wherein
consists the peculiarity in the connotation of a relative name?

The attribute signified by a relative name, say some, is a relation; and
this they give, if not as a sufficient explanation, at least as the only
one attainable. If they are asked, What then is a relation? they do not
profess to be able to tell. It is generally regarded as something
peculiarly recondite and mysterious. I can not, however, perceive in what
respect it is more so than any other attribute; indeed, it appears to me
to be so in a somewhat less degree. I conceive rather, that it is by
examining into the signification of relative names, or, in other words,
into the nature of the attribute which they connote, that a clear insight
may best be obtained into the nature of all attributes: of all that is
meant by an attribute.

It is obvious, in fact, that if we take any two correlative names,
_father_ and _son_ for instance, though the objects _de_noted by the names
are different, they both, in a certain sense, connote the same thing. They
can not, indeed, be said to connote the same _attribute_: to be a father,
is not the same thing as to be a son. But when we call one man a father,
another a son, what we mean to affirm is a set of facts, which are exactly
the same in both cases. To predicate of A that he is the father of B, and
of B that he is the son of A, is to assert one and the same fact in
different words. The two propositions are exactly equivalent: neither of
them asserts more or asserts less than the other. The paternity of A and
the filiety of B are not two facts, but two modes of expressing the same
fact. That fact, when analysed, consists of a series of physical events or
phenomena, in which both A and B are parties concerned, and from which
they both derive names. What those names really connote, is this series of
events: that is the meaning, and the whole meaning, which either of them
is intended to convey. The series of events may be said to _constitute_
the relation; the schoolmen called it the foundation of the relation,
_fundamentum relationis_.

In this manner any fact, or series of facts, in which two different
objects are implicated, and which is therefore predicable of both of them,
may be either considered as constituting an attribute of the one, or an
attribute of the other. According as we consider it in the former, or in
the latter aspect, it is connoted by the one or the other of the two
correlative names. _Father_ connotes the fact, regarded as constituting an
attribute of A; _son_ connotes the same fact, as constituting an attribute
of B. It may evidently be regarded with equal propriety in either light.
And all that appears necessary to account for the existence of relative
names, is, that whenever there is a fact in which two individuals are
concerned, an attribute grounded on that fact may be ascribed to either of
these individuals.

A name, therefore, is said to be relative, when, over and above the object
which it denotes, it implies in its signification the existence of another
object, also deriving a denomination from the same fact which is the
ground of the first name. Or (to express the same meaning in other words)
a name is relative, when, being the name of one thing, its signification
can not be explained but by mentioning another. Or we may state it
thus—when the name can not be employed in discourse so as to have a
meaning, unless the name of some other thing than what it is itself the
name of, be either expressed or understood. These definitions are all, at
bottom, equivalent, being modes of variously expressing this one
distinctive circumstance—that every other attribute of an object might,
without any contradiction, be conceived still to exist if no object
besides that one had ever existed;(16) but those of its attributes which
are expressed by relative names, would on that supposition be swept away.

§ 8. Names have been further distinguished into _univocal_ and
_æquivocal_: these, however, are not two kinds of names, but two different
modes of employing names. A name is univocal, or applied univocally, with
respect to all things of which it can be predicated _in the same sense_;
it is æquivocal, or applied æquivocally, as respects those things of which
it is predicated in different senses. It is scarcely necessary to give
instances of a fact so familiar as the double meaning of a word. In
reality, as has been already observed, an æquivocal or ambiguous word is
not one name, but two names, accidentally coinciding in sound. _File_
meaning a steel instrument, and _file_ meaning a line of soldiers, have no
more title to be considered one word, because written alike, than _grease_
and _Greece_ have, because they are pronounced alike. They are one sound,
appropriated to form two different words.

An intermediate case is that of a name used _analogically_ or
metaphorically; that is, a name which is predicated of two things, not
univocally, or exactly in the same signification, but in significations
somewhat similar, and which being derived one from the other, one of them
may be considered the primary, and the other a secondary signification. As
when we speak of a brilliant light and a brilliant achievement. The word
is not applied in the same sense to the light and to the achievement; but
having been applied to the light in its original sense, that of brightness
to the eye, it is transferred to the achievement in a derivative
signification, supposed to be somewhat like the primitive one. The word,
however, is just as properly two names instead of one, in this case, as in
that of the most perfect ambiguity. And one of the commonest forms of
fallacious reasoning arising from ambiguity, is that of arguing from a
metaphorical expression as if it were literal; that is, as if a word, when
applied metaphorically, were the same name as when taken in its original
sense: which will be seen more particularly in its place.




                               Chapter III.


Of The Things Denoted By Names.


§ 1. Looking back now to the commencement of our inquiry, let us attempt
to measure how far it has advanced. Logic, we found, is the Theory of
Proof. But proof supposes something provable, which must be a Proposition
or Assertion; since nothing but a Proposition can be an object of belief,
or therefore of proof. A Proposition is, discourse which affirms or denies
something of some other thing. This is one step: there must, it seems, be
two things concerned in every act of belief. But what are these Things?
They can be no other than those signified by the two names, which being
joined together by a copula constitute the Proposition. If, therefore, we
knew what all names signify, we should know every thing which, in the
existing state of human knowledge, is capable either of being made a
subject of affirmation or denial, or of being itself affirmed or denied of
a subject. We have accordingly, in the preceding chapter, reviewed the
various kinds of Names, in order to ascertain what is signified by each of
them. And we have now carried this survey far enough to be able to take an
account of its results, and to exhibit an enumeration of all kinds of
Things which are capable of being made predicates, or of having any thing
predicated of them: after which to determine the import of Predication,
that is, of Propositions, can be no arduous task.

The necessity of an enumeration of Existences, as the basis of Logic, did
not escape the attention of the schoolmen, and of their master Aristotle,
the most comprehensive, if not also the most sagacious, of the ancient
philosophers. The Categories, or Predicaments—the former a Greek word, the
latter its literal translation in the Latin language—were believed to be
an enumeration of all things capable of being named; an enumeration by the
_summa genera_, _i.e._, the most extensive classes into which things could
be distributed; which, therefore, were so many highest Predicates, one or
other of which was supposed capable of being affirmed with truth of every
namable thing whatsoever. The following are the classes into which,
according to this school of philosophy, Things in general might be
reduced:

Οὐσία, Substantia.
Ποσὸν, Quantitas.
Ποιόν, Qualitas.
Πρός τι, Relatio.
Ποιεῖν, Actio.
Πάσχειν, Passio.
Ποῦ, Ubi.
Πότε, Quando.
Κεῖσθακ, Situs.
Ἔχειν, Habitus.

The imperfections of this classification are too obvious to require, and
its merits are not sufficient to reward, a minute examination. It is a
mere catalogue of the distinctions rudely marked out by the language of
familiar life, with little or no attempt to penetrate, by philosophic
analysis, to the _rationale_ even of those common distinctions. Such an
analysis, however superficially conducted, would have shown the
enumeration to be both redundant and defective. Some objects are omitted,
and others repeated several times under different heads. It is like a
division of animals into men, quadrupeds, horses, asses, and ponies. That,
for instance, could not be a very comprehensive view of the nature of
Relation which could exclude action, passivity, and local situation from
that category. The same observation applies to the categories Quando (or
position in time), and Ubi (or position in space); while the distinction
between the latter and Situs is merely verbal. The incongruity of erecting
into a _summum genus_ the class which forms the tenth category is
manifest. On the other hand, the enumeration takes no notice of any thing
besides substances and attributes. In what category are we to place
sensations, or any other feelings and states of mind; as hope, joy, fear;
sound, smell, taste; pain, pleasure; thought, judgment, conception, and
the like? Probably all these would have been placed by the Aristotelian
school in the categories of _actio_ and _passio_; and the relation of such
of them as are active, to their objects, and of such of them as are
passive, to their causes, would rightly be so placed; but the things
themselves, the feelings or states of mind, wrongly. Feelings, or states
of consciousness, are assuredly to be accounted among realities, but they
can not be reckoned either among substances or attributes.(17)

§ 2. Before recommencing, under better auspices, the attempt made with
such imperfect success by the early logicians, we must take notice of an
unfortunate ambiguity in all the concrete names which correspond to the
most general of all abstract terms, the word Existence. When we have
occasion for a name which shall be capable of denoting whatever exists, as
contradistinguished from non-entity or Nothing, there is hardly a word
applicable to the purpose which is not also, and even more familiarly,
taken in a sense in which it denotes only substances. But substances are
not all that exists; attributes, if such things are to be spoken of, must
be said to exist; feelings certainly exist. Yet when we speak of an
_object_, or of a _thing_, we are almost always supposed to mean a
substance. There seems a kind of contradiction in using such an expression
as that one _thing_ is merely an attribute of another thing. And the
announcement of a Classification of Things would, I believe, prepare most
readers for an enumeration like those in natural history, beginning with
the great divisions of animal, vegetable, and mineral, and subdividing
them into classes and orders. If, rejecting the word Thing, we endeavor to
find another of a more general import, or at least more exclusively
confined to that general import, a word denoting all that exists, and
connoting only simple existence; no word might be presumed fitter for such
a purpose than _being_: originally the present participle of a verb which
in one of its meanings is exactly equivalent to the verb _exists_; and
therefore suitable, even by its grammatical formation, to be the concrete
of the abstract _existence_. But this word, strange as the fact may
appear, is still more completely spoiled for the purpose which it seemed
expressly made for, than the word Thing. _Being_ is, by custom, exactly
synonymous with substance; except that it is free from a slight taint of a
second ambiguity; being implied impartially to matter and to mind, while
substance, though originally and in strictness applicable to both, is apt
to suggest in preference the idea of matter. Attributes are never called
Beings; nor are feelings. A Being is that which excites feelings, and
which possesses attributes. The soul is called a Being; God and angels are
called Beings; but if we were to say, extension, color, wisdom, virtue,
are beings, we should perhaps be suspected of thinking with some of the
ancients, that the cardinal virtues are animals; or, at the least, of
holding with the Platonic school the doctrine of self-existent Ideas, or
with the followers of Epicurus that of Sensible Forms, which detach
themselves in every direction from bodies, and by coming in contact with
our organs, cause our perceptions. We should be supposed, in short, to
believe that Attributes are Substances.

In consequence of this perversion of the word Being, philosophers looking
about for something to supply its place, laid their hands upon the word
Entity, a piece of barbarous Latin, invented by the schoolmen to be used
as an abstract name, in which class its grammatical form would seem to
place it: but being seized by logicians in distress to stop a leak in
their terminology, it has ever since been used as a concrete name. The
kindred word _essence_, born at the same time and of the same parents,
scarcely underwent a more complete transformation when, from being the
abstract of the verb _to be_, it came to denote something sufficiently
concrete to be inclosed in a glass bottle. The word Entity, since it
settled down into a concrete name, has retained its universality of
signification somewhat less impaired than any of the names before
mentioned. Yet the same gradual decay to which, after a certain age, all
the language of psychology seems liable, has been at work even here. If
you call virtue an _entity_, you are indeed somewhat less strongly
suspected of believing it to be a substance than if you called it a
_being_; but you are by no means free from the suspicion. Every word which
was originally intended to connote mere existence, seems, after a time, to
enlarge its connotation to _separate_ existence, or existence freed from
the condition of belonging to a substance; which condition being precisely
what constitutes an attribute, attributes are gradually shut out; and
along with them feelings, which in ninety-nine cases out of a hundred have
no other name than that of the attribute which is grounded on them.
Strange that when the greatest embarrassment felt by all who have any
considerable number of thoughts to express, is to find a sufficient
variety of precise words fitted to express them, there should be no
practice to which even scientific thinkers are more addicted than that of
taking valuable words to express ideas which are sufficiently expressed by
other words already appropriated to them.

When it is impossible to obtain good tools, the next best thing is to
understand thoroughly the defects of those we have. I have therefore
warned the reader of the ambiguity of the names which, for want of better,
I am necessitated to employ. It must now be the writer’s endeavor so to
employ them as in no case to leave the meaning doubtful or obscure. No one
of the above terms being altogether unambiguous, I shall not confine
myself to any one, but shall employ on each occasion the word which seems
least likely in the particular case to lead to misunderstanding; nor do I
pretend to use either these or any other words with a rigorous adherence
to one single sense. To do so would often leave us without a word to
express what is signified by a known word in some one or other of its
senses: unless authors had an unlimited license to coin new words,
together with (what it would be more difficult to assume) unlimited power
of making readers understand them. Nor would it be wise in a writer, on a
subject involving so much of abstraction, to deny himself the advantage
derived from even an improper use of a term, when, by means of it, some
familiar association is called up which brings the meaning home to the
mind, as it were by a flash.

The difficulty both to the writer and reader, of the attempt which must be
made to use vague words so as to convey a precise meaning, is not wholly a
matter of regret. It is not unfitting that logical treatises should afford
an example of that, to facilitate which is among the most important uses
of logic. Philosophical language will for a long time, and popular
language still longer, retain so much of vagueness and ambiguity, that
logic would be of little value if it did not, among its other advantages,
exercise the understanding in doing its work neatly and correctly with
these imperfect tools.

After this preamble it is time to proceed to our enumeration. We shall
commence with Feelings, the simplest class of namable things; the term
Feeling being of course understood in its most enlarged sense.



I. Feelings, Or States of Consciousness.


§ 3. A Feeling and a State of consciousness are, in the language of
philosophy, equivalent expressions: every thing is a feeling of which the
mind is conscious; every thing which it _feels_, or, in other words, which
forms a part of its own sentient existence. In popular language Feeling is
not always synonymous with State of Consciousness; being often taken more
peculiarly for those states which are conceived as belonging to the
sensitive, or to the emotional, phasis of our nature, and sometimes, with
a still narrower restriction, to the emotional alone, as distinguished
from what are conceived as belonging to the percipient or to the
intellectual phasis. But this is an admitted departure from correctness of
language; just as, by a popular perversion the exact converse of this, the
word Mind is withdrawn from its rightful generality of signification, and
restricted to the intellect. The still greater perversion by which Feeling
is sometimes confined not only to bodily sensations, but to the sensations
of a single sense, that of touch, needs not be more particularly adverted
to.

Feeling, in the proper sense of the term, is a genus, of which Sensation,
Emotion, and Thought, are subordinate species. Under the word Thought is
here to be included whatever we are internally conscious of when we are
said to think; from the consciousness we have when we think of a red color
without having it before our eyes, to the most recondite thoughts of a
philosopher or poet. Be it remembered, however, that by a thought is to be
understood what passes in the mind itself, and not any object external to
the mind, which the person is commonly said to be thinking of. He may be
thinking of the sun, or of God, but the sun and God are not thoughts; his
mental image, however, of the sun, and his idea of God, are thoughts;
states of his mind, not of the objects themselves; and so also is his
belief of the existence of the sun, or of God; or his disbelief, if the
case be so. Even imaginary objects (which are said to exist only in our
ideas) are to be distinguished from our ideas of them. I may think of a
hobgoblin, as I may think of the loaf which was eaten yesterday, or of the
flower which will bloom to-morrow. But the hobgoblin which never existed
is not the same thing with my idea of a hobgoblin, any more than the loaf
which once existed is the same thing with my idea of a loaf, or the flower
which does not yet exist, but which will exist, is the same with my idea
of a flower. They are all, not thoughts, but objects of thought; though at
the present time all the objects are alike non-existent.

In like manner, a Sensation is to be carefully distinguished from the
object which causes the sensation; our sensation of white from a white
object: nor is it less to be distinguished from the attribute whiteness,
which we ascribe to the object in consequence of its exciting the
sensation. Unfortunately for clearness and due discrimination in
considering these subjects, our sensations seldom receive separate names.
We have a name for the objects which produce in us a certain sensation:
the word _white_. We have a name for the quality in those objects, to
which we ascribe the sensation: the name _whiteness_. But when we speak of
the sensation itself (as we have not occasion to do this often except in
our scientific speculations), language, which adapts itself for the most
part only to the common uses of life, has provided us with no
single-worded or immediate designation; we must employ a circumlocution,
and say, The sensation of white, or The sensation of whiteness; we must
denominate the sensation either from the object, or from the attribute, by
which it is excited. Yet the sensation, though it never _does_, might very
well be _conceived_ to exist, without any thing whatever to excite it. We
can conceive it as arising spontaneously in the mind. But if it so arose,
we should have no name to denote it which would not be a misnomer. In the
case of our sensations of hearing we are better provided; we have the word
Sound, and a whole vocabulary of words to denote the various kinds of
sounds. For as we are often conscious of these sensations in the absence
of any perceptible object, we can more easily conceive having them in the
absence of any object whatever. We need only shut our eyes and listen to
music, to have a conception of a universe with nothing in it except
sounds, and ourselves hearing them: and what is easily conceived
separately, easily obtains a separate name. But in general our names of
sensations denote indiscriminately the sensation and the attribute. Thus,
_color_ stands for the sensations of white, red, etc., but also for the
quality in the colored object. We talk of the colors of things as among
their _properties_.

§ 4. In the case of sensations, another distinction has also to be kept in
view, which is often confounded, and never without mischievous
consequences. This is, the distinction between the sensation itself, and
the state of the bodily organs which precedes the sensation, and which
constitutes the physical agency by which it is produced. One of the
sources of confusion on this subject is the division commonly made of
feelings into Bodily and Mental. Philosophically speaking, there is no
foundation at all for this distinction: even sensations are states of the
sentient mind, not states of the body, as distinguished from it. What I am
conscious of when I see the color blue, is a feeling of blue color, which
is one thing; the picture on my retina, or the phenomenon of hitherto
mysterious nature which takes place in my optic nerve or in my brain, is
another thing, of which I am not at all conscious, and which scientific
investigation alone could have apprised me of. These are states of my
body; but the sensation of blue, which is the consequence of these states
of body, is not a state of body: that which perceives and is conscious is
called Mind. When sensations are called bodily feelings, it is only as
being the class of feelings which are immediately occasioned by bodily
states; whereas the other kinds of feelings, thoughts, for instance, or
emotions, are immediately excited not by any thing acting upon the bodily
organs, but by sensations, or by previous thoughts. This, however, is a
distinction not in our feelings, but in the agency which produces our
feelings: all of them when actually produced are states of mind.

Besides the affection of our bodily organs from without, and the sensation
thereby produced in our minds, many writers admit a third link in the
chain of phenomena, which they call a Perception, and which consists in
the recognition of an external object as the exciting cause of the
sensation. This perception, they say, is an _act_ of the mind, proceeding
from its own spontaneous activity; while in a sensation the mind is
passive, being merely acted upon by the outward object. And according to
some metaphysicians, it is by an act of the mind, similar to perception,
except in not being preceded by any sensation, that the existence of God,
the soul, and other hyperphysical objects, is recognized.

These acts of what is termed perception, whatever be the conclusion
ultimately come to respecting their nature, must, I conceive, take their
place among the varieties of feelings or states of mind. In so classing
them, I have not the smallest intention of declaring or insinuating any
theory as to the law of mind in which these mental processes may be
supposed to originate, or the conditions under which they may be
legitimate or the reverse. Far less do I mean (as Dr. Whewell seems to
suppose must be meant in an analogous case(18)) to indicate that as they
are “_merely_ states of mind,” it is superfluous to inquire into their
distinguishing peculiarities. I abstain from the inquiry as irrelevant to
the science of logic. In these so-called perceptions, or direct
recognitions by the mind, of objects, whether physical or spiritual, which
are external to itself, I can see only cases of belief; but of belief
which claims to be intuitive, or independent of external evidence. When a
stone lies before me, I am conscious of certain sensations which I receive
from it; but if I say that these sensations come to me from an external
object which I _perceive_, the meaning of these words is, that receiving
the sensations, I intuitively _believe_ that an external cause of those
sensations exists. The laws of intuitive belief, and the conditions under
which it is legitimate, are a subject which, as we have already so often
remarked, belongs not to logic, but to the science of the ultimate laws of
the human mind.

To the same region of speculation belongs all that can be said respecting
the distinction which the German metaphysicians and their French and
English followers so elaborately draw between the _acts_ of the mind and
its merely passive _states_; between what it receives from, and what it
gives to, the crude materials of its experience. I am aware that with
reference to the view which those writers take of the primary elements of
thought and knowledge, this distinction is fundamental. But for the
present purpose, which is to examine, not the original groundwork of our
knowledge, but how we come by that portion of it which is not original;
the difference between active and passive states of mind is of secondary
importance. For us, they all are states of mind, they all are feelings; by
which, let it be said once more, I mean to imply nothing of passivity, but
simply that they are psychological facts, facts which take place in the
mind, and are to be carefully distinguished from the external or physical
facts with which they may be connected either as effects or as causes.

§ 5. Among active states of mind, there is, however, one species which
merits particular attention, because it forms a principal part of the
connotation of some important classes of names. I mean _volitions_, or
acts of the will. When we speak of sentient beings by relative names, a
large portion of the connotation of the name usually consists of the
actions of those beings; actions past, present, and possible or probable
future. Take, for instance, the words Sovereign and Subject. What meaning
do these words convey, but that of innumerable actions, done or to be done
by the sovereign and the subjects, to or in regard to one another
reciprocally? So with the words physician and patient, leader and
follower, tutor and pupil. In many cases the words also connote actions
which would be done under certain contingencies by persons other than
those denoted: as the words mortgagor and mortgagee, obligor and obligee,
and many other words expressive of legal relation, which connote what a
court of justice would do to enforce the legal obligation if not
fulfilled. There are also words which connote actions previously done by
persons other than those denoted either by the name itself or by its
correlative; as the word brother. From these instances, it may be seen how
large a portion of the connotation of names consists of actions. Now what
is an action? Not one thing, but a series of two things: the state of mind
called a volition, followed by an effect. The volition or intention to
produce the effect, is one thing; the effect produced in consequence of
the intention, is another thing; the two together constitute the action. I
form the purpose of instantly moving my arm; that is a state of my mind:
my arm (not being tied or paralytic) moves in obedience to my purpose;
that is a physical fact, consequent on a state of mind. The intention,
followed by the fact, or (if we prefer the expression) the fact when
preceded and caused by the intention, is called the action of moving my
arm.

§ 6. Of the first leading division of namable things, viz., Feelings or
States of Consciousness, we began by recognizing three subdivisions;
Sensations, Thoughts, and Emotions. The first two of these we have
illustrated at considerable length; the third, Emotions, not being
perplexed by similar ambiguities, does not require similar
exemplification. And, finally, we have found it necessary to add to these
three a fourth species, commonly known by the name Volitions. We shall now
proceed to the two remaining classes of namable things; all things which
are regarded as external to the mind being considered as belonging either
to the class of Substances or to that of Attributes.



II. Substances.


Logicians have endeavored to define Substance and Attribute; but their
definitions are not so much attempts to draw a distinction between the
things themselves, as instructions what difference it is customary to make
in the grammatical structure of the sentence, according as we are speaking
of substances or of attributes. Such definitions are rather lessons of
English, or of Greek, Latin, or German, than of mental philosophy. An
attribute, say the school logicians, must be the attribute _of_ something;
color, for example, must be the color _of_ something; goodness must be the
goodness _of_ something; and if this something should cease to exist, or
should cease to be connected with the attribute, the existence of the
attribute would be at an end. A substance, on the contrary, is
self-existent; in speaking about it, we need not put _of_ after its name.
A stone is not the stone of any thing; the moon is not the moon _of_ any
thing, but simply the moon. Unless, indeed, the name which we choose to
give to the substance be a relative name; if so, it must be followed
either by _of_, or by some other particle, implying, as that preposition
does, a reference to something else: but then the other characteristic
peculiarity of an attribute would fail; the _something_ might be
destroyed, and the substance might still subsist. Thus, a father must be
the father _of_ something, and so far resembles an attribute, in being
referred to something besides himself: if there were no child, there would
be no father: but this, when we look into the matter, only means that we
should not call him father. The man called father might still exist though
there were no child, as he existed before there was a child; and there
would be no contradiction in supposing him to exist, though the whole
universe except himself were destroyed. But destroy all white substances,
and where would be the attribute whiteness? Whiteness, without any white
thing, is a contradiction in terms.

This is the nearest approach to a solution of the difficulty, that will be
found in the common treatises on logic. It will scarcely be thought to be
a satisfactory one. If an attribute is distinguished from a substance by
being the attribute _of_ something, it seems highly necessary to
understand what is meant by _of_; a particle which needs explanation too
much itself, to be placed in front of the explanation of any thing else.
And as for the self-existence of substance, it is very true that a
substance may be conceived to exist without any other substance, but so
also may an attribute without any other attribute: and we can no more
imagine a substance without attributes than we can imagine attributes
without a substance.

Metaphysicians, however, have probed the question deeper, and given an
account of Substance considerably more satisfactory than this. Substances
are usually distinguished as Bodies or Minds. Of each of these,
philosophers have at length provided us with a definition which seems
unexceptionable.

§ 7. A body, according to the received doctrine of modern metaphysicians,
may be defined, the external cause to which we ascribe our sensations.
When I see and touch a piece of gold, I am conscious of a sensation of
yellow color, and sensations of hardness and weight; and by varying the
mode of handling, I may add to these sensations many others completely
distinct from them. The sensations are all of which I am directly
conscious; but I consider them as produced by something not only existing
independently of my will, but external to my bodily organs and to my mind.
This external something I call a body.

It may be asked, how come we to ascribe our sensations to any external
cause? And is there sufficient ground for so ascribing them? It is known,
that there are metaphysicians who have raised a controversy on the point;
maintaining that we are not warranted in referring our sensations to a
cause such as we understand by the word Body, or to any external cause
whatever. Though we have no concern here with this controversy, nor with
the metaphysical niceties on which it turns, one of the best ways of
showing what is meant by Substance is, to consider what position it is
necessary to take up, in order to maintain its existence against
opponents.

It is certain, then, that a part of our notion of a body consists of the
notion of a number of sensations of our own, or of other sentient beings,
habitually occurring simultaneously. My conception of the table at which I
am writing is compounded of its visible form and size, which are complex
sensations of sight; its tangible form and size, which are complex
sensations of our organs of touch and of our muscles; its weight, which is
also a sensation of touch and of the muscles; its color, which is a
sensation of sight; its hardness, which is a sensation of the muscles; its
composition, which is another word for all the varieties of sensation
which we receive under various circumstances from the wood of which it is
made, and so forth. All or most of these various sensations frequently
are, and, as we learn by experience, always might be, experienced
simultaneously, or in many different orders of succession at our own
choice: and hence the thought of any one of them makes us think of the
others, and the whole becomes mentally amalgamated into one mixed state of
consciousness, which, in the language of the school of Locke and Hartley,
is termed a Complex Idea.

Now, there are philosophers who have argued as follows: If we conceive an
orange to be divested of its natural color without acquiring any new one;
to lose its softness without becoming hard, its roundness without becoming
square or pentagonal, or of any other regular or irregular figure
whatever; to be deprived of size, of weight, of taste, of smell; to lose
all its mechanical and all its chemical properties, and acquire no new
ones; to become, in short, invisible, intangible, imperceptible not only
by all our senses, but by the senses of all other sentient beings, real or
possible; nothing, say these thinkers, would remain. For of what nature,
they ask, could be the residuum? and by what token could it manifest its
presence? To the unreflecting its existence seems to rest on the evidence
of the senses. But to the senses nothing is apparent except the
sensations. We know, indeed, that these sensations are bound together by
some law; they do not come together at random, but according to a
systematic order, which is part of the order established in the universe.
When we experience one of these sensations, we usually experience the
others also, or know that we have it in our power to experience them. But
a fixed law of connection, making the sensations occur together, does not,
say these philosophers, necessarily require what is called a substratum to
support them. The conception of a substratum is but one of many possible
forms in which that connection presents itself to our imagination; a mode
of, as it were, realizing the idea. If there be such a substratum, suppose
it at this instant miraculously annihilated, and let the sensations
continue to occur in the same order, and how would the substratum be
missed? By what signs should we be able to discover that its existence had
terminated? Should we not have as much reason to believe that it still
existed as we now have? And if we should not then be warranted in
believing it, how can we be so now? A body, therefore, according to these
metaphysicians, is not any thing intrinsically different from the
sensations which the body is said to produce in us; it is, in short, a set
of sensations, or rather, of possibilities of sensation, joined together
according to a fixed law.

The controversies to which these speculations have given rise, and the
doctrines which have been developed in the attempt to find a conclusive
answer to them, have been fruitful of important consequences to the
Science of Mind. The sensations (it was answered) which we are conscious
of, and which we receive, not at random, but joined together in a certain
uniform manner, imply not only a law or laws of connection, but a cause
external to our mind, which cause, by its own laws, determines the laws
according to which the sensations are connected and experienced. The
schoolmen used to call this external cause by the name we have already
employed, a _substratum_; and its attributes (as they expressed
themselves) _inhered_, literally _stuck_, in it. To this substratum the
name Matter is usually given in philosophical discussions. It was soon,
however, acknowledged by all who reflected on the subject, that the
existence of matter can not be proved by extrinsic evidence. The answer,
therefore, now usually made to Berkeley and his followers, is, that the
belief is intuitive; that mankind, in all ages, have felt themselves
compelled, by a necessity of their nature, to refer their sensations to an
external cause: that even those who deny it in theory, yield to the
necessity in practice, and both in speech, thought, and feeling, do,
equally with the vulgar, acknowledge their sensations to be the effects of
something external to them: this knowledge, therefore, it is affirmed, is
as evidently intuitive as our knowledge of our sensations themselves is
intuitive. And here the question merges in the fundamental problem of
metaphysics properly so called: to which science we leave it.

But although the extreme doctrine of the Idealist metaphysicians, that
objects are nothing but our sensations and the laws which connect them,
has not been generally adopted by subsequent thinkers; the point of most
real importance is one on which those metaphysicians are now very
generally considered to have made out their case: viz., that _all we know_
of objects is the sensations which they give us, and the order of the
occurrence of those sensations. Kant himself, on this point, is as
explicit as Berkeley or Locke. However firmly convinced that there exists
a universe of “Things in themselves,” totally distinct from the universe
of phenomena, or of things as they appear to our senses; and even when
bringing into use a technical expression (_Noumenon_) to denote what the
thing is in itself, as contrasted with the _representation_ of it in our
minds; he allows that this representation (the matter of which, he says,
consists of our sensations, though the form is given by the laws of the
mind itself) is all we know of the object: and that the real nature of the
Thing is, and by the constitution of our faculties ever must remain, at
least in the present state of existence, an impenetrable mystery to us.
“Of things absolutely or in themselves,” says Sir William Hamilton,(19)
“be they external, be they internal, we know nothing, or know them only as
incognizable; and become aware of their incomprehensible existence, only
as this is indirectly and accidentally revealed to us, through certain
qualities related to our faculties of knowledge, and which qualities,
again, we can not think as unconditional, irrelative, existent in and of
ourselves. All that we know is therefore phenomenal—phenomenal of the
unknown.”(20) The same doctrine is laid down in the clearest and strongest
terms by M. Cousin, whose observations on the subject are the more worthy
of attention, as, in consequence of the ultra-German and ontological
character of his philosophy in other respects, they may be regarded as the
admissions of an opponent.(21)

There is not the slightest reason for believing that what we call the
sensible qualities of the object are a type of any thing inherent in
itself, or bear any affinity to its own nature. A cause does not, as such,
resemble its effects; an east wind is not like the feeling of cold, nor
heat like the steam of boiling water. Why then should matter resemble our
sensations? Why should the inmost nature of fire or water resemble the
impressions made by those objects upon our senses?(22) Or on what
principle are we authorized to deduce from the effects, any thing
concerning the cause, except that it is a cause adequate to produce those
effects? It may, therefore, safely be laid down as a truth both obvious in
itself, and admitted by all whom it is at present necessary to take into
consideration, that, of the outward world, we know and can know absolutely
nothing, except the sensations which we experience from it.(23)

§ 8. Body having now been defined the external cause, and (according to
the more reasonable opinion) the unknown external cause, to which we refer
our sensations; it remains to frame a definition of Mind. Nor, after the
preceding observations, will this be difficult. For, as our conception of
a body is that of an unknown exciting cause of sensations, so our
conception of a mind is that of an unknown recipient or percipient, of
them; and not of them alone, but of all our other feelings. As body is
understood to be the mysterious something which excites the mind to feel,
so mind is the mysterious something which feels and thinks. It is
unnecessary to give in the case of mind, as we gave in the case of matter,
a particular statement of the skeptical system by which its existence as a
Thing in itself, distinct from the series of what are denominated its
states, is called in question. But it is necessary to remark, that on the
inmost nature (whatever be meant by inmost nature) of the thinking
principle, as well as on the inmost nature of matter, we are, and with our
faculties must always remain, entirely in the dark. All which we are aware
of, even in our own minds, is (in the words of James Mill) a certain
“thread of consciousness;” a series of feelings, that is, of sensations,
thoughts, emotions, and volitions, more or less numerous and complicated.
There is a something I call Myself, or, by another form of expression, my
mind, which I consider as distinct from these sensations, thoughts, etc.;
a something which I conceive to be not the thoughts, but the being that
has the thoughts, and which I can conceive as existing forever in a state
of quiescence, without any thoughts at all. But what this being is, though
it is myself, I have no knowledge, other than the series of its states of
consciousness. As bodies manifest themselves to me only through the
sensations of which I regard them as the causes, so the thinking
principle, or mind, in my own nature, makes itself known to me only by the
feelings of which it is conscious. I know nothing about myself, save my
capacities of feeling or being conscious (including, of course, thinking
and willing): and were I to learn any thing new concerning my own nature,
I can not with my present faculties conceive this new information to be
any thing else, than that I have some additional capacities, as yet
unknown to me, of feeling, thinking, or willing.

Thus, then, as body is the unsentient cause to which we are naturally
prompted to refer a certain portion of our feelings, so mind may be
described as the sentient _subject_ (in the scholastic sense of the term)
of all feelings; that which has or feels them. But of the nature of either
body or mind, further than the feelings which the former excites, and
which the latter experiences, we do not, according to the best existing
doctrine, know any thing; and if any thing, logic has nothing to do with
it, or with the manner in which the knowledge is acquired. With this
result we may conclude this portion of our subject, and pass to the third
and only remaining class or division of Namable Things.



III. Attributes: and, first, Qualities.


§ 9. From what has already been said of Substance, what is to be said of
Attribute is easily deducible. For if we know not, and can not know, any
thing of bodies but the sensations which they excite in us or in others,
those sensations must be all that we can, at bottom, mean by their
attributes; and the distinction which we verbally make between the
properties of things and the sensations we receive from them, must
originate in the convenience of discourse rather than in the nature of
what is signified by the terms.

Attributes are usually distributed under the three heads of Quality,
Quantity, and Relation. We shall come to the two latter presently: in the
first place we shall confine ourselves to the former.

Let us take, then, as our example, one of what are termed the sensible
qualities of objects, and let that example be whiteness. When we ascribe
whiteness to any substance, as, for instance, snow; when we say that snow
has the quality whiteness, what do we really assert? Simply, that when
snow is present to our organs, we have a particular sensation, which we
are accustomed to call the sensation of white. But how do I know that snow
is present? Obviously by the sensations which I derive from it, and not
otherwise. I infer that the object is present, because it gives me a
certain assemblage or series of sensations. And when I ascribe to it the
attribute whiteness, my meaning is only, that, of the sensations composing
this group or series, that which I call the sensation of white color is
one.

This is one view which may be taken of the subject. But there is also
another and a different view. It may be said, that it is true we _know_
nothing of sensible objects, except the sensations they excite in us; that
the fact of our receiving from snow the particular sensation which is
called a sensation of white, is the _ground_ on which we ascribe to that
substance the quality whiteness; the sole proof of its possessing that
quality. But because one thing may be the sole evidence of the existence
of another thing, it does not follow that the two are one and the same.
The attribute whiteness (it may be said) is not the fact of receiving the
sensation, but something in the object itself; a _power_ inherent in it;
something _in virtue_ of which the object produces the sensation. And when
we affirm that snow possesses the attribute whiteness, we do not merely
assert that the presence of snow produces in us that sensation, but that
it does so through, and by reason of, that power or quality.

For the purposes of logic it is not of material importance which of these
opinions we adopt. The full discussion of the subject belongs to the other
department of scientific inquiry, so often alluded to under the name of
metaphysics; but it may be said here, that for the doctrine of the
existence of a peculiar species of entities called qualities, I can see no
foundation except in a tendency of the human mind which is the cause of
many delusions. I mean, the disposition, wherever we meet with two names
which are not precisely synonymous, to suppose that they must be the names
of two different things; whereas in reality they may be names of the same
thing viewed in two different lights, or under different suppositions as
to surrounding circumstances. Because _quality_ and _sensation_ can not be
put indiscriminately one for the other, it is supposed that they can not
both signify the same thing, namely, the impression or feeling with which
we are affected through our senses by the presence of an object; though
there is at least no absurdity in supposing that this identical impression
or feeling may be called a sensation when considered merely in itself, and
a quality when looked at in relation to any one of the numerous objects,
the presence of which to our organs excites in our minds that among
various other sensations or feelings. And if this be admissible as a
supposition, it rests with those who contend for an entity _per se_ called
a quality, to show that their opinion is preferable, or is any thing in
fact but a lingering remnant of the old doctrine of occult causes; the
very absurdity which Molière so happily ridiculed when he made one of his
pedantic physicians account for the fact that opium produces sleep by the
maxim, Because it has a soporific virtue.

It is evident that when the physician stated that opium has a soporific
virtue, he did not account for, but merely asserted over again, the fact
that it produces sleep. In like manner, when we say that snow is white
because it has the quality of whiteness, we are only re-asserting in more
technical language the fact that it excites in us the sensation of white.
If it be said that the sensation must have some cause, I answer, its cause
is the presence of the assemblage of phenomena which is termed the object.
When we have asserted that as often as the object is present, and our
organs in their normal state, the sensation takes place, we have stated
all that we know about the matter. There is no need, after assigning a
certain and intelligible cause, to suppose an occult cause besides, for
the purpose of enabling the real cause to produce its effect. If I am
asked, why does the presence of the object cause this sensation in me, I
can not tell: I can only say that such is my nature, and the nature of the
object; that the fact forms a part of the constitution of things. And to
this we must at last come, even after interpolating the imaginary entity.
Whatever number of links the chain of causes and effects may consist of,
how any one link produces the one which is next to it, remains equally
inexplicable to us. It is as easy to comprehend that the object should
produce the sensation directly and at once, as that it should produce the
same sensation by the aid of something else called the _power_ of
producing it.

But, as the difficulties which may be felt in adopting this view of the
subject can not be removed without discussions transcending the bounds of
our science, I content myself with a passing indication, and shall, for
the purposes of logic, adopt a language compatible with either view of the
nature of qualities. I shall say—what at least admits of no dispute—that
the quality of whiteness ascribed to the object snow, is _grounded_ on its
exciting in us the sensation of white; and adopting the language already
used by the school logicians in the case of the kind of attributes called
Relations, I shall term the sensation of white the _foundation_ of the
quality whiteness. For logical purposes the sensation is the only
essential part of what is meant by the word; the only part which we ever
can be concerned in proving. When that is proved, the quality is proved;
if an object excites a sensation, it has, of course, the power of exciting
it.



IV. Relations.


§ 10. The _qualities_ of a body, we have said, are the attributes grounded
on the sensations which the presence of that particular body to our organs
excites in our minds. But when we ascribe to any object the kind of
attribute called a Relation, the foundation of the attribute must be
something in which other objects are concerned besides itself and the
percipient.

As there may with propriety be said to be a relation between any two
things to which two correlative names are or may be given, we may expect
to discover what constitutes a relation in general, if we enumerate the
principal cases in which mankind have imposed correlative names, and
observe what these cases have in common.

What, then, is the character which is possessed in common by states of
circumstances so heterogeneous and discordant as these: one thing _like_
another; one thing _unlike_ another; one thing _near_ another; one thing
_far from_ another; one thing _before_, _after_, _along with_ another; one
thing _greater_, _equal_, _less_, than another; one thing the _cause_ of
another, the _effect_ of another; one person the _master_, _servant_,
_child_, _parent_, _debtor_, _creditor_, _sovereign_, _subject_,
_attorney_, _client_, of another, and so on?

Omitting, for the present, the case of Resemblance, (a relation which
requires to be considered separately,) there seems to be one thing common
to all these cases, and only one; that in each of them there exists or
occurs, or has existed or occurred, or may be expected to exist or occur,
some fact or phenomenon, into which the two things which are said to be
related to each other, both enter as parties concerned. This fact, or
phenomenon, is what the Aristotelian logicians called the _fundamentum
relationis_. Thus in the relation of greater and less between two
magnitudes, the _fundamentum relationis_ is the fact that one of the two
magnitudes could, under certain conditions, be included in, without
entirely filling, the space occupied by the other magnitude. In the
relation of master and servant, the _fundamentum relationis_ is the fact
that the one has undertaken, or is compelled, to perform certain services
for the benefit and at the bidding of the other. Examples might be
indefinitely multiplied; but it is already obvious that whenever two
things are said to be related, there is some fact, or series of facts,
into which they both enter; and that whenever any two things are involved
in some one fact, or series of facts, we may ascribe to those two things a
mutual relation grounded on the fact. Even if they have nothing in common
but what is common to all things, that they are members of the universe,
we call that a relation, and denominate them fellow-creatures,
fellow-beings, or fellow-denizens of the universe. But in proportion as
the fact into which the two objects enter as parts is of a more special
and peculiar, or of a more complicated nature, so also is the relation
grounded upon it. And there are as many conceivable relations as there are
conceivable kinds of fact in which two things can be jointly concerned.

In the same manner, therefore, as a quality is an attribute grounded on
the fact that a certain sensation or sensations are produced in us by the
object, so an attribute grounded on some fact into which the object enters
jointly with another object, is a relation between it and that other
object. But the fact in the latter case consists of the very same kind of
elements as the fact in the former; namely, states of consciousness. In
the case, for example, of any legal relation, as debtor and creditor,
principal and agent, guardian and ward, the _fundamentum relationis_
consists entirely of thoughts, feelings, and volitions (actual or
contingent), either of the persons themselves or of other persons
concerned in the same series of transactions; as, for instance, the
intentions which would be formed by a judge, in case a complaint were made
to his tribunal of the infringement of any of the legal obligations
imposed by the relation; and the acts which the judge would perform in
consequence; acts being (as we have already seen) another word for
intentions followed by an effect, and that effect being but another word
for sensations, or some other feelings, occasioned either to the agent
himself or to somebody else. There is no part of what the names expressive
of the relation imply, that is not resolvable into states of
consciousness; outward objects being, no doubt, supposed throughout as the
causes by which some of those states of consciousness are excited, and
minds as the subjects by which all of them are experienced, but neither
the external objects nor the minds making their existence known otherwise
than by the states of consciousness.

Cases of relation are not always so complicated as those to which we last
alluded. The simplest of all cases of relation are those expressed by the
words antecedent and consequent, and by the word simultaneous. If we say,
for instance, that dawn preceded sunrise, the fact in which the two
things, dawn and sunrise, were jointly concerned, consisted only of the
two things themselves; no third thing entered into the fact or phenomenon
at all. Unless, indeed, we choose to call the succession of the two
objects a third thing; but their succession is not something added to the
things themselves; it is something involved in them. Dawn and sunrise
announce themselves to our consciousness by two successive sensations. Our
consciousness of the succession of these sensations is not a third
sensation or feeling added to them; we have not first the two feelings,
and then a feeling of their succession. To have two feelings at all,
implies having them either successively, or else simultaneously.
Sensations, or other feelings, being given, succession and
simultaneousness are the two conditions, to the alternative of which they
are subjected by the nature of our faculties; and no one has been able, or
needs expect, to analyze the matter any further.

§ 11. In a somewhat similar position are two other sorts of relations,
Likeness and Unlikeness. I have two sensations; we will suppose them to be
simple ones; two sensations of white, or one sensation of white and
another of black. I call the first two sensations _like_; the last two
_unlike_. What is the fact or phenomenon constituting the _fundamentum_ of
this relation? The two sensations first, and then what we call a feeling
of resemblance, or of want of resemblance. Let us confine ourselves to the
former case. Resemblance is evidently a feeling; a state of the
consciousness of the observer. Whether the feeling of the resemblance of
the two colors be a third state of consciousness, which I have _after_
having the two sensations of color, or whether (like the feeling of their
succession) it is involved in the sensations themselves, may be a matter
of discussion. But in either case, these feelings of resemblance, and of
its opposite dissimilarity, are parts of our nature; and parts so far from
being capable of analysis, that they are presupposed in every attempt to
analyze any of our other feelings. Likeness and unlikeness, therefore, as
well as antecedence, sequence, and simultaneousness, must stand apart
among relations, as things _sui generis_. They are attributes grounded on
facts, that is, on states of consciousness, but on states which are
peculiar, unresolvable, and inexplicable.

But, though likeness or unlikeness can not be resolved into any thing
else, complex cases of likeness or unlikeness can be resolved into simpler
ones. When we say of two things which consist of parts, that they are like
one another, the likeness of the wholes does admit of analysis; it is
compounded of likenesses between the various parts respectively, and of
likeness in their arrangement. Of how vast a variety of resemblances of
parts must that resemblance be composed, which induces us to say that a
portrait, or a landscape, is like its original. If one person mimics
another with any success, of how many simple likenesses must the general
or complex likeness be compounded: likeness in a succession of bodily
postures; likeness in voice, or in the accents and intonations of the
voice; likeness in the choice of words, and in the thoughts or sentiments
expressed, whether by word, countenance, or gesture.

All likeness and unlikeness of which we have any cognizance, resolve
themselves into likeness and unlikeness between states of our own, or some
other, mind. When we say that one body is like another, (since we know
nothing of bodies but the sensations which they excite,) we mean really
that there is a resemblance between the sensations excited by the two
bodies, or between some portions at least of those sensations. If we say
that two attributes are like one another (since we know nothing of
attributes except the sensations or states of feeling on which they are
grounded), we mean really that those sensations, or states of feeling,
resemble each other. We may also say that two relations are alike. The
fact of resemblance between relations is sometimes called _analogy_,
forming one of the numerous meanings of that word. The relation in which
Priam stood to Hector, namely, that of father and son, resembles the
relation in which Philip stood to Alexander; resembles it so closely that
they are called the same relation. The relation in which Cromwell stood to
England resembles the relation in which Napoleon stood to France, though
not so closely as to be called the same relation. The meaning in both
these instances must be, that a resemblance existed between the facts
which constituted the _fundamentum relationis_.

This resemblance may exist in all conceivable gradations, from perfect
undistinguishableness to something extremely slight. When we say, that a
thought suggested to the mind of a person of genius is like a seed cast
into the ground, because the former produces a multitude of other
thoughts, and the latter a multitude of other seeds, this is saying that
between the relation of an inventive mind to a thought contained in it,
and the relation of a fertile soil to a seed contained in it, there exists
a resemblance: the real resemblance being in the two _fundamenta
relationis_, in each of which there occurs a germ, producing by its
development a multitude of other things similar to itself. And as,
whenever two objects are jointly concerned in a phenomenon, this
constitutes a relation between those objects, so, if we suppose a second
pair of objects concerned in a second phenomenon, the slightest
resemblance between the two phenomena is sufficient to admit of its being
said that the two relations resemble; provided, of course, the points of
resemblance are found in those portions of the two phenomena respectively
which are connoted by the relative names.

While speaking of resemblance, it is necessary to take notice of an
ambiguity of language, against which scarcely any one is sufficiently on
his guard. Resemblance, when it exists in the highest degree of all,
amounting to undistinguishableness, is often called identity, and the two
similar things are said to be the same. I say often, not always; for we do
not say that two visible objects, two persons, for instance, are the same,
because they are so much alike that one might be mistaken for the other:
but we constantly use this mode of expression when speaking of feelings;
as when I say that the sight of any object gives me the _same_ sensation
or emotion to-day that it did yesterday, or the _same_ which it gives to
some other person. This is evidently an incorrect application of the word
_same_; for the feeling which I had yesterday is gone, never to return;
what I have to-day is another feeling, exactly like the former, perhaps,
but distinct from it; and it is evident that two different persons can not
be experiencing the same feeling, in the sense in which we say that they
are both sitting at the same table. By a similar ambiguity we say, that
two persons are ill of the _same_ disease; that two persons hold the
_same_ office; not in the sense in which we say that they are engaged in
the same adventure, or sailing in the same ship, but in the sense that
they fill offices exactly similar, though, perhaps, in distant places.
Great confusion of ideas is often produced, and many fallacies engendered,
in otherwise enlightened understandings, by not being sufficiently alive
to the fact (in itself not always to be avoided), that they use the same
name to express ideas so different as those of identity and
undistinguishable resemblance. Among modern writers, Archbishop Whately
stands almost alone in having drawn attention to this distinction, and to
the ambiguity connected with it.

Several relations, generally called by other names, are really cases of
resemblance. As, for example, equality; which is but another word for the
exact resemblance commonly called identity, considered as subsisting
between things in respect of their _quantity_. And this example forms a
suitable transition to the third and last of the three heads under which,
as already remarked, Attributes are commonly arranged.



V. Quantity.


§ 12. Let us imagine two things, between which there is no difference
(that is, no dissimilarity), except in quantity alone; for instance, a
gallon of water, and more than a gallon of water. A gallon of water, like
any other external object, makes its presence known to us by a set of
sensations which it excites. Ten gallons of water are also an external
object, making its presence known to us in a similar manner; and as we do
not mistake ten gallons of water for a gallon of water, it is plain that
the set of sensations is more or less different in the two cases. In like
manner, a gallon of water, and a gallon of wine, are two external objects,
making their presence known by two sets of sensations, which sensations
are different from each other. In the first case, however, we say that the
difference is in quantity; in the last there is a difference in quality,
while the quantity of the water and of the wine is the same. What is the
real distinction between the two cases? It is not within the province of
Logic to analyze it; nor to decide whether it is susceptible of analysis
or not. For us the following considerations are sufficient: It is evident
that the sensations I receive from the gallon of water, and those I
receive from the gallon of wine, are not the same, that is, not precisely
alike; neither are they altogether unlike: they are partly similar, partly
dissimilar; and that in which they resemble is precisely that in which
alone the gallon of water and the ten gallons do not resemble. That in
which the gallon of water and the gallon of wine are like each other, and
in which the gallon and the ten gallons of water are unlike each other, is
called their quantity. This likeness and unlikeness I do not pretend to
explain, no more than any other kind of likeness or unlikeness. But my
object is to show, that when we say of two things that they differ in
quantity, just as when we say that they differ in quality, the assertion
is always grounded on a difference in the sensations which they excite.
Nobody, I presume, will say, that to see, or to lift, or to drink, ten
gallons of water, does not include in itself a different set of sensations
from those of seeing, lifting, or drinking one gallon; or that to see or
handle a foot-rule, and to see or handle a yard-measure made exactly like
it, are the same sensations. I do not undertake to say what the difference
in the sensations is. Every body knows, and nobody can tell; no more than
any one could tell what white is to a person who had never had the
sensation. But the difference, so far as cognizable by our faculties, lies
in the sensations. Whatever difference we say there is in the things
themselves, is, in this as in all other cases, grounded, and grounded
exclusively, on a difference in the sensations excited by them.



VI. Attributes Concluded.


§ 13. Thus, then, all the attributes of bodies which are classed under
Quality or Quantity, are grounded on the sensations which we receive from
those bodies, and may be defined, the powers which the bodies have of
exciting those sensations. And the same general explanation has been found
to apply to most of the attributes usually classed under the head of
Relation. They, too, are grounded on some fact or phenomenon into which
the related objects enter as parts; that fact or phenomenon having no
meaning and no existence to us, except the series of sensations or other
states of consciousness by which it makes itself known; and the relation
being simply the power or capacity which the object possesses of taking
part along with the correlated object in the production of that series of
sensations or states of consciousness. We have been obliged, indeed, to
recognize a somewhat different character in certain peculiar relations,
those of succession and simultaneity, of likeness and unlikeness. These,
not being grounded on any fact or phenomenon distinct from the related
objects themselves, do not admit of the same kind of analysis. But these
relations, though not, like other relations, grounded on states of
consciousness, are themselves states of consciousness: resemblance is
nothing but our feeling of resemblance; succession is nothing but our
feeling of succession. Or, if this be disputed (and we can not, without
transgressing the bounds of our science, discuss it here), at least our
knowledge of these relations, and even our possibility of knowledge, is
confined to those which subsist between sensations, or other states of
consciousness; for, though we ascribe resemblance, or succession, or
simultaneity, to objects and to attributes, it is always in virtue of
resemblance or succession or simultaneity in the sensations or states of
consciousness which those objects excite, and on which those attributes
are grounded.

§ 14. In the preceding investigation we have, for the sake of simplicity,
considered bodies only, and omitted minds. But what we have said, is
applicable, _mutatis mutandis_, to the latter. The attributes of minds, as
well as those of bodies, are grounded on states of feeling or
consciousness. But in the case of a mind, we have to consider its own
states, as well as those which it produces in other minds. Every attribute
of a mind consists either in being itself affected in a certain way, or
affecting other minds in a certain way. Considered in itself, we can
predicate nothing of it but the series of its own feelings. When we say of
any mind, that it is devout, or superstitious, or meditative, or cheerful,
we mean that the ideas, emotions, or volitions implied in those words,
form a frequently recurring part of the series of feelings, or states of
consciousness, which fill up the sentient existence of that mind.

In addition, however, to those attributes of a mind which are grounded on
its own states of feeling, attributes may also be ascribed to it, in the
same manner as to a body, grounded on the feelings which it excites in
other minds. A mind does not, indeed, like a body, excite sensations, but
it may excite thoughts or emotions. The most important example of
attributes ascribed on this ground, is the employment of terms expressive
of approbation or blame. When, for example, we say of any character, or
(in other words) of any mind, that it is admirable, we mean that the
contemplation of it excites the sentiment of admiration; and indeed
somewhat more, for the word implies that we not only feel admiration, but
approve that sentiment in ourselves. In some cases, under the semblance of
a single attribute, two are really predicated: one of them, a state of the
mind itself; the other, a state with which other minds are affected by
thinking of it. As when we say of any one that he is generous. The word
generosity expresses a certain state of mind, but being a term of praise,
it also expresses that this state of mind excites in us another mental
state, called approbation. The assertion made, therefore, is twofold, and
of the following purport: Certain feelings form habitually a part of this
person’s sentient existence; and the idea of those feelings of his,
excites the sentiment of approbation in ourselves or others.

As we thus ascribe attributes to minds on the ground of ideas and
emotions, so may we to bodies on similar grounds, and not solely on the
ground of sensations: as in speaking of the beauty of a statue; since this
attribute is grounded on the peculiar feeling of pleasure which the statue
produces in our minds; which is not a sensation, but an emotion.



VII. General Results.


§ 15. Our survey of the varieties of Things which have been, or which are
capable of being, named—which have been, or are capable of being, either
predicated of other Things, or themselves made the subject of
predications—is now concluded.

Our enumeration commenced with Feelings. These we scrupulously
distinguished from the objects which excite them, and from the organs by
which they are, or may be supposed to be, conveyed. Feelings are of four
sorts: Sensations, Thoughts, Emotions, and Volitions. What are called
Perceptions are merely a particular case of Belief, and Belief is a kind
of thought. Actions are merely volitions followed by an effect.

After Feelings we proceeded to Substances. These are either Bodies or
Minds. Without entering into the grounds of the metaphysical doubts which
have been raised concerning the existence of Matter and Mind as objective
realities, we stated as sufficient for us the conclusion in which the best
thinkers are now for the most part agreed, that all we can know of Matter
is the sensations which it gives us, and the order of occurrence of those
sensations; and that while the substance Body is the unknown cause of our
sensations, the substance Mind is the unknown recipient.

The only remaining class of Namable Things is Attributes; and these are of
three kinds, Quality, Relation, and Quantity. Qualities, like substances,
are known to us no otherwise than by the sensations or other states of
consciousness which they excite: and while, in compliance with common
usage, we have continued to speak of them as a distinct class of Things,
we showed that in predicating them no one means to predicate any thing but
those sensations or states of consciousness, on which they may be said to
be grounded, and by which alone they can be defined or described.
Relations, except the simple cases of likeness and unlikeness, succession
and simultaneity, are similarly grounded on some fact or phenomenon, that
is, on some series of sensations or states of consciousness, more or less
complicated. The third species of Attribute, Quantity, is also manifestly
grounded on something in our sensations or states of feeling, since there
is an indubitable difference in the sensations excited by a larger and a
smaller bulk, or by a greater or a less degree of intensity, in any object
of sense or of consciousness. All attributes, therefore, are to us nothing
but either our sensations and other states of feeling, or something
inextricably involved therein; and to this even the peculiar and simple
relations just adverted to are not exceptions. Those peculiar relations,
however, are so important, and, even if they might in strictness be
classed among states of consciousness, are so fundamentally distinct from
any other of those states, that it would be a vain subtlety to bring them
under that common description, and it is necessary that they should be
classed apart.(24)

As the result, therefore, of our analysis, we obtain the following as an
enumeration and classification of all Namable Things:

1st. Feelings, or States of Consciousness.

2d. The Minds which experience those feelings.

3d. The Bodies, or external objects which excite certain of those
feelings, together with the powers or properties whereby they excite them;
these latter (at least) being included rather in compliance with common
opinion, and because their existence is taken for granted in the common
language from which I can not prudently deviate, than because the
recognition of such powers or properties as real existences appears to be
warranted by a sound philosophy.

4th, and last. The Successions and Co-existences, the Likenesses and
Unlikenesses, between feelings or states of consciousness. Those
relations, when considered as subsisting between other things, exist in
reality only between the states of consciousness which those things, if
bodies, excite, if minds, either excite or experience.

This, until a better can be suggested, may serve as a substitute for the
Categories of Aristotle considered as a classification of Existences. The
practical application of it will appear when we commence the inquiry into
the Import of Propositions; in other words, when we inquire what it is
which the mind actually believes, when it gives what is called its assent
to a proposition.

These four classes comprising, if the classification be correct, all
Namable Things, these or some of them must of course compose the
signification of all names: and of these, or some of them, is made up
whatever we call a fact.

For distinction’s sake, every fact which is solely composed of feelings or
states of consciousness considered as such, is often called a
Psychological or Subjective fact; while every fact which is composed,
either wholly or in part, of something different from these, that is, of
substances and attributes, is called an Objective fact. We may say, then,
that every objective fact is grounded on a corresponding subjective one;
and has no meaning to us (apart from the subjective fact which corresponds
to it), except as a name for the unknown and inscrutable process by which
that subjective or psychological fact is brought to pass.




                               Chapter IV.


Of Propositions.


§ 1. In treating of Propositions, as already in treating of Names, some
considerations of a comparatively elementary nature respecting their form
and varieties must be premised, before entering upon that analysis of the
import conveyed by them, which is the real subject and purpose of this
preliminary book.

A proposition, we have before said, is a portion of discourse in which a
predicate is affirmed or denied of a subject. A predicate and a subject
are all that is necessarily required to make up a proposition: but as we
can not conclude from merely seeing two names put together, that they are
a predicate and a subject, that is, that one of them is intended to be
affirmed or denied of the other, it is necessary that there should be some
mode or form of indicating that such is the intention; some sign to
distinguish a predication from any other kind of discourse. This is
sometimes done by a slight alteration of one of the words, called an
_inflection_; as when we say, Fire burns; the change of the second word
from _burn_ to _burns_ showing that we mean to affirm the predicate burn
of the subject fire. But this function is more commonly fulfilled by the
word _is_, when an affirmation is intended, _is not_, when a negation; or
by some other part of the verb _to be_. The word which thus serves the
purpose of a sign of predication is called, as we formerly observed, the
_copula_. It is important that there should be no indistinctness in our
conception of the nature and office of the copula; for confused notions
respecting it are among the causes which have spread mysticism over the
field of logic, and perverted its speculations into logomachies.

It is apt to be supposed that the copula is something more than a mere
sign of predication; that it also signifies existence. In the proposition,
Socrates is just, it may seem to be implied not only that the quality
_just_ can be affirmed of Socrates, but moreover that Socrates _is_, that
is to say, exists. This, however, only shows that there is an ambiguity in
the word _is_; a word which not only performs the function of the copula
in affirmations, but has also a meaning of its own, in virtue of which it
may itself be made the predicate of a proposition. That the employment of
it as a copula does not necessarily include the affirmation of existence,
appears from such a proposition as this, A centaur is a fiction of the
poets; where it can not possibly be implied that a centaur exists, since
the proposition itself expressly asserts that the thing has no real
existence.

Many volumes might be filled with the frivolous speculations concerning
the nature of Being (το ὄν, οὐσία, Ens, Entitas, Essentia, and the like),
which have arisen from overlooking this double meaning of the word _to
be_; from supposing that when it signifies _to exist_, and when it
signifies to _be_ some specified thing, as to _be_ a man, to _be_
Socrates, to _be_ seen or spoken of, to _be_ a phantom, even to _be_ a
nonentity, it must still, at bottom, answer to the same idea; and that a
meaning must be found for it which shall suit all these cases. The fog
which rose from this narrow spot diffused itself at an early period over
the whole surface of metaphysics. Yet it becomes us not to triumph over
the great intellects of Plato and Aristotle because we are now able to
preserve ourselves from many errors into which they, perhaps inevitably,
fell. The fire-teazer of a modern steam-engine produces by his exertions
far greater effects than Milo of Crotona could, but he is not therefore a
stronger man. The Greeks seldom knew any language but their own. This
rendered it far more difficult for them than it is for us, to acquire a
readiness in detecting ambiguities. One of the advantages of having
accurately studied a plurality of languages, especially of those languages
which eminent thinkers have used as the vehicle of their thoughts, is the
practical lesson we learn respecting the ambiguities of words, by finding
that the same word in one language corresponds, on different occasions, to
different words in another. When not thus exercised, even the strongest
understandings find it difficult to believe that things which have a
common name, have not in some respect or other a common nature; and often
expend much labor very unprofitably (as was frequently done by the two
philosophers just mentioned) in vain attempts to discover in what this
common nature consists. But, the habit once formed, intellects much
inferior are capable of detecting even ambiguities which are common to
many languages: and it is surprising that the one now under consideration,
though it exists in the modern languages as well as in the ancient, should
have been overlooked by almost all authors. The quantity of futile
speculation which had been caused by a misapprehension of the nature of
the copula, was hinted at by Hobbes; but Mr. James Mill(25) was, I
believe, the first who distinctly characterized the ambiguity, and pointed
out how many errors in the received systems of philosophy it has had to
answer for. It has, indeed, misled the moderns scarcely less than the
ancients, though their mistakes, because our understandings are not yet so
completely emancipated from their influence, do not appear equally
irrational.

We shall now briefly review the principal distinctions which exist among
propositions, and the technical terms most commonly in use to express
those distinctions.

§ 2. A proposition being a portion of discourse in which something is
affirmed or denied of something, the first division of propositions is
into affirmative and negative. An affirmative proposition is that in which
the predicate is _affirmed_ of the subject; as, Cæsar is dead. A negative
proposition is that in which the predicate is _denied_ of the subject; as,
Cæsar is not dead. The copula, in this last species of proposition,
consists of the words _is not_, which are the sign of negation; _is_ being
the sign of affirmation.

Some logicians, among whom may be mentioned Hobbes, state this distinction
differently; they recognize only one form of copula, _is_, and attach the
negative sign to the predicate. “Cæsar is dead,” and “Cæsar is not dead,”
according to these writers, are propositions agreeing not in the subject
and predicate, but in the subject only. They do not consider “dead,” but
“not dead,” to be the predicate of the second proposition, and they
accordingly define a negative proposition to be one in which the predicate
is a negative name. The point, though not of much practical moment,
deserves notice as an example (not unfrequent in logic) where by means of
an apparent simplification, but which is merely verbal, matters are made
more complex than before. The notion of these writers was, that they could
get rid of the distinction between affirming and denying, by treating
every case of denying as the affirming of a negative name. But what is
meant by a negative name? A name expressive of the _absence_ of an
attribute. So that when we affirm a negative name, what we are really
predicating is absence and not presence; we are asserting not that any
thing is, but that something is not; to express which operation no word
seems so proper as the word denying. The fundamental distinction is
between a fact and the non-existence of that fact; between seeing
something and not seeing it, between Cæsar’s being dead and his not being
dead; and if this were a merely verbal distinction, the generalization
which brings both within the same form of assertion would be a real
simplification: the distinction, however, being real, and in the facts, it
is the generalization confounding the distinction that is merely verbal;
and tends to obscure the subject, by treating the difference between two
kinds of truths as if it were only a difference between two kinds of
words. To put things together, and to put them or keep them asunder, will
remain different operations, whatever tricks we may play with language.

A remark of a similar nature may be applied to most of those distinctions
among propositions which are said to have reference to their _modality_;
as, difference of tense or time; the sun _did_ rise, the sun _is_ rising,
the sun _will_ rise. These differences, like that between affirmation and
negation, might be glossed over by considering the incident of time as a
mere modification of the predicate: thus, The sun is _an object having
risen_, The sun is _an object now rising_, The sun is _an object to rise
hereafter_. But the simplification would be merely verbal. Past, present,
and future, do not constitute so many different kinds of rising; they are
designations belonging to the event asserted, to the _sun’s_ rising
to-day. They affect, not the predicate, but the applicability of the
predicate to the particular subject. That which we affirm to be past,
present, or future, is not what the subject signifies, nor what the
predicate signifies, but specifically and expressly what the predication
signifies; what is expressed only by the proposition as such, and not by
either or both of the terms. Therefore the circumstance of time is
properly considered as attaching to the copula, which is the sign of
predication, and not to the predicate. If the same can not be said of such
modifications as these, Cæsar _may_ be dead; Cæsar is _perhaps_ dead; it
is _possible_ that Cæsar is dead; it is only because these fall altogether
under another head, being properly assertions not of any thing relating to
the fact itself, but of the state of our own mind in regard to it; namely,
our absence of disbelief of it. Thus “Cæsar may be dead” means “I am not
sure that Cæsar is alive.”

§ 3. The next division of propositions is into Simple and Complex; more
aptly (by Professor Bain(26)) termed Compound. A simple proposition is
that in which one predicate is affirmed or denied of one subject. A
compound proposition is that in which there is more than one predicate, or
more than one subject, or both.

At first sight this division has the air of an absurdity; a solemn
distinction of things into one and more than one; as if we were to divide
horses into single horses and teams of horses. And it is true that what is
called a complex (or compound) proposition is often not a proposition at
all, but several propositions, held together by a conjunction. Such, for
example, is this: Cæsar is dead, and Brutus is alive: or even this, Cæsar
is dead, _but_ Brutus is alive. There are here two distinct assertions;
and we might as well call a street a complex house, as these two
propositions a complex proposition. It is true that the syncategorematic
words _and_ and _but_ have a meaning; but that meaning is so far from
making the two propositions one, that it adds a third proposition to them.
All particles are abbreviations, and generally abbreviations of
propositions; a kind of short-hand, whereby something which, to be
expressed fully, would have required a proposition or a series of
propositions, is suggested to the mind at once. Thus the words, Cæsar is
dead and Brutus is alive, are equivalent to these: Cæsar is dead; Brutus
is alive; it is desired that the two preceding propositions should be
thought of together. If the words were, Cæsar is dead, _but_ Brutus is
alive, the sense would be equivalent to the same three propositions
together with a fourth; “between the two preceding propositions there
exists a contrast:” viz., either between the two facts themselves, or
between the feelings with which it is desired that they should be
regarded.

In the instances cited the two propositions are kept visibly distinct,
each subject having its separate predicate, and each predicate its
separate subject. For brevity, however, and to avoid repetition, the
propositions are often blended together: as in this, “Peter and James
preached at Jerusalem and in Galilee,” which contains four propositions:
Peter preached at Jerusalem, Peter preached in Galilee, James preached at
Jerusalem, James preached in Galilee.

We have seen that when the two or more propositions comprised in what is
called a complex proposition are stated absolutely, and not under any
condition or proviso, it is not a proposition at all, but a plurality of
propositions; since what it expresses is not a single assertion, but
several assertions, which, if true when joined, are true also when
separated. But there is a kind of proposition which, though it contains a
plurality of subjects and of predicates, and may be said in one sense of
the word to consist of several propositions, contains but one assertion;
and its truth does not at all imply that of the simple propositions which
compose it. An example of this is, when the simple propositions are
connected by the particle _or_; as, either A is B or C is D; or by the
particle _if_; as, A is B if C is D. In the former case, the proposition
is called _disjunctive_, in the latter, _conditional_: the name
_hypothetical_ was originally common to both.

As has been well remarked by Archbishop Whately and others, the
disjunctive form is resolvable into the conditional; every disjunctive
proposition being equivalent to two or more conditional ones. “Either A is
B or C is D,” means, “if A is not B, C is D; and if C is not D, A is B.”
All hypothetical propositions, therefore, though disjunctive in form, are
conditional in meaning; and the words hypothetical and conditional may be,
as indeed they generally are, used synonymously. Propositions in which the
assertion is not dependent on a condition, are said, in the language of
logicians, to be _categorical_.

A hypothetical proposition is not, like the pretended complex propositions
which we previously considered, a mere aggregation of simple propositions.
The simple propositions which form part of the words in which it is
couched, form no part of the assertion which it conveys. When we say, If
the Koran comes from God, Mohammed is the prophet of God, we do not intend
to affirm either that the Koran does come from God, or that Mohammed is
really his prophet. Neither of these simple propositions may be true, and
yet the truth of the hypothetical proposition may be indisputable. What is
asserted is not the truth of either of the propositions, but the
inferribility of the one from the other. What, then, is the subject, and
what the predicate of the hypothetical proposition? “The Koran” is not the
subject of it, nor is “Mohammed:” for nothing is affirmed or denied either
of the Koran or of Mohammed. The real subject of the predication is the
entire proposition, “Mohammed is the prophet of God;” and the affirmation
is, that this is a legitimate inference from the proposition, “The Koran
comes from God.” The subject and predicate, therefore, of a hypothetical
proposition are names of propositions. The subject is some one
proposition. The predicate is a general relative name applicable to
propositions; of this form—“an inference from so and so.” A fresh instance
is here afforded of the remark, that particles are abbreviations; since
“_If_ A is B, C is D,” is found to be an abbreviation of the following:
“The proposition C is D, is a legitimate inference from the proposition A
is B.”

The distinction, therefore, between hypothetical and categorical
propositions is not so great as it at first appears. In the conditional,
as well as in the categorical form, one predicate is affirmed of one
subject, and no more: but a conditional proposition is a proposition
concerning a proposition; the subject of the assertion is itself an
assertion. Nor is this a property peculiar to hypothetical propositions.
There are other classes of assertions concerning propositions. Like other
things, a proposition has attributes which may be predicated of it. The
attribute predicated of it in a hypothetical proposition, is that of being
an inference from a certain other proposition. But this is only one of
many attributes that might be predicated. We may say, That the whole is
greater than its part, is an axiom in mathematics: That the Holy Ghost
proceeds from the Father alone, is a tenet of the Greek Church: The
doctrine of the divine right of kings was renounced by Parliament at the
Revolution: The infallibility of the Pope has no countenance from
Scripture. In all these cases the subject of the predication is an entire
proposition. That which these different predicates are affirmed of, is
_the proposition_, “the whole is greater than its part;” _the
proposition_, “the Holy Ghost proceeds from the Father alone;” _the
proposition_, “kings have a divine right;” _the proposition_, “the Pope is
infallible.”

Seeing, then, that there is much less difference between hypothetical
propositions and any others, than one might be led to imagine from their
form, we should be at a loss to account for the conspicuous position which
they have been selected to fill in treatises on logic, if we did not
remember that what they predicate of a proposition, namely, its being an
inference from something else, is precisely that one of its attributes
with which most of all a logician is concerned.

§ 4. The next of the common divisions of Propositions is into Universal,
Particular, Indefinite, and Singular: a distinction founded on the degree
of generality in which the name, which is the subject of the proposition,
is to be understood. The following are examples:

_All men_ are mortal—Universal.
_Some men_ are mortal—Particular.
_Man_ is mortal—Indefinite.
_Julius Cæsar_ is mortal—Singular.

The proposition is Singular, when the subject is an individual name. The
individual name needs not be a proper name. “The Founder of Christianity
was crucified,” is as much a singular proposition as “Christ was
crucified.”

When the name which is the subject of the proposition is a general name,
we may intend to affirm or deny the predicate, either of all the things
that the subject denotes, or only of some. When the predicate is affirmed
or denied of all and each of the things denoted by the subject, the
proposition is universal; when of some undefined portion of them only, it
is particular. Thus, All men are mortal; Every man is mortal; are
universal propositions. No man is immortal, is also a universal
proposition, since the predicate, immortal, is denied of each and every
individual denoted by the term man; the negative proposition being exactly
equivalent to the following, Every man is not-immortal. But “some men are
wise,” “some men are not wise,” are particular propositions; the predicate
_wise_ being in the one case affirmed and in the other denied not of each
and every individual denoted by the term man, but only of each and every
one of some portion of those individuals, without specifying what portion;
for if this were specified, the proposition would be changed either into a
singular proposition, or into a universal proposition with a different
subject; as, for instance, “all _properly instructed_ men are wise.” There
are other forms of particular propositions; as, “_Most_ men are
imperfectly educated:” it being immaterial how large a portion of the
subject the predicate is asserted of, as long as it is left uncertain how
that portion is to be distinguished from the rest.(27)

When the form of the expression does not clearly show whether the general
name which is the subject of the proposition is meant to stand for all the
individuals denoted by it, or only for some of them, the proposition is,
by some logicians, called Indefinite; but this, as Archbishop Whately
observes, is a solecism, of the same nature as that committed by some
grammarians when in their list of genders they enumerate the _doubtful_
gender. The speaker must mean to assert the proposition either as a
universal or as a particular proposition, though he has failed to declare
which: and it often happens that though the words do not show which of the
two he intends, the context, or the custom of speech, supplies the
deficiency. Thus, when it is affirmed that “Man is mortal,” nobody doubts
that the assertion is intended of all human beings; and the word
indicative of universality is commonly omitted, only because the meaning
is evident without it. In the proposition, “Wine is good,” it is
understood with equal readiness, though for somewhat different reasons,
that the assertion is not intended to be universal, but particular.(28) As
is observed by Professor Bain,(29) the chief examples of Indefinite
propositions occur “with names of material, which are the subjects
sometimes of universal, and at other times of particular predication.
‘Food is chemically constituted by carbon, oxygen, etc.,’ is a proposition
of universal quantity; the meaning is all food—all kinds of food. ‘Food is
necessary to animal life’ is a case of particular quantity; the meaning is
some sort of food, not necessarily all sorts. ‘Metal is requisite in order
to strength’ does not mean all kinds of metal. ‘Gold will make a way,’
means a portion of gold.”

When a general name stands for each and every individual which it is a
name of, or in other words, which it denotes, it is said by logicians to
be _distributed_, or taken distributively. Thus, in the proposition, All
men are mortal, the subject, Man, is distributed, because mortality is
affirmed of each and every man. The predicate, Mortal, is not distributed,
because the only mortals who are spoken of in the proposition are those
who happen to be men; while the word may, for aught that appears, and in
fact does, comprehend within it an indefinite number of objects besides
men. In the proposition, Some men are mortal, both the predicate and the
subject are undistributed. In the following, No men have wings, both the
predicate and the subject are distributed. Not only is the attribute of
having wings denied of the entire class Man, but that class is severed and
cast out from the whole of the class Winged, and not merely from some part
of that class.

This phraseology, which is of great service in stating and demonstrating
the rules of the syllogism, enables us to express very concisely the
definitions of a universal and a particular proposition. A universal
proposition is that of which the subject is distributed; a particular
proposition is that of which the subject is undistributed.

There are many more distinctions among propositions than those we have
here stated, some of them of considerable importance. But, for explaining
and illustrating these, more suitable opportunities will occur in the
sequel.




                                Chapter V.


Of The Import Of Propositions.


§ 1. An inquiry into the nature of propositions must have one of two
objects: to analyze the state of mind called Belief, or to analyze what is
believed. All language recognizes a difference between a doctrine or
opinion, and the fact of entertaining the opinion; between assent, and
what is assented to.

Logic, according to the conception here formed of it, has no concern with
the nature of the act of judging or believing; the consideration of that
act, as a phenomenon of the mind, belongs to another science.
Philosophers, however, from Descartes downward, and especially from the
era of Leibnitz and Locke, have by no means observed this distinction; and
would have treated with great disrespect any attempt to analyze the import
of Propositions, unless founded on an analysis of the act of Judgment. A
proposition, they would have said, is but the expression in words of a
Judgment. The thing expressed, not the mere verbal expression, is the
important matter. When the mind assents to a proposition, it judges. Let
us find out what the mind does when it judges, and we shall know what
propositions mean, and not otherwise.

Conformably to these views, almost all the writers on Logic in the last
two centuries, whether English, German, or French, have made their theory
of Propositions, from one end to the other, a theory of Judgments. They
considered a Proposition, or a Judgment, for they used the two words
indiscriminately, to consist in affirming or denying one _idea_ of
another. To judge, was to put two ideas together, or to bring one idea
under another, or to compare two ideas, or to perceive the agreement or
disagreement between two ideas: and the whole doctrine of Propositions,
together with the theory of Reasoning (always necessarily founded on the
theory of Propositions), was stated as if Ideas, or Conceptions, or
whatever other term the writer preferred as a name for mental
representations generally, constituted essentially the subject-matter and
substance of those operations.

It is, of course, true, that in any case of judgment, as for instance when
we judge that gold is yellow, a process takes place in our minds, of which
some one or other of these theories is a partially correct account. We
must have the idea of gold and the idea of yellow, and these two ideas
must be brought together in our mind. But in the first place, it is
evident that this is only a part of what takes place; for we may put two
ideas together without any act of belief; as when we merely imagine
something, such as a golden mountain; or when we actually disbelieve: for
in order even to disbelieve that Mohammed was an apostle of God, we must
put the idea of Mohammed and that of an apostle of God together. To
determine what it is that happens in the case of assent or dissent besides
putting two ideas together, is one of the most intricate of metaphysical
problems. But whatever the solution may be, we may venture to assert that
it can have nothing whatever to do with the import of propositions; for
this reason, that propositions (except sometimes when the mind itself is
the subject treated of) are not assertions respecting our ideas of things,
but assertions respecting the things themselves. In order to believe that
gold is yellow, I must, indeed, have the idea of gold, and the idea of
yellow, and something having reference to those ideas must take place in
my mind; but my belief has not reference to the ideas, it has reference to
the things. What I believe, is a fact relating to the outward thing, gold,
and to the impression made by that outward thing upon the human organs;
not a fact relating to my conception of gold, which would be a fact in my
mental history, not a fact of external nature. It is true, that in order
to believe this fact in external nature, another fact must take place in
my mind, a process must be performed upon my ideas; but so it must in
every thing else that I do. I can not dig the ground unless I have the
idea of the ground, and of a spade, and of all the other things I am
operating upon, and unless I put those ideas together.(30) But it would be
a very ridiculous description of digging the ground to say that it is
putting one idea into another. Digging is an operation which is performed
upon the things themselves, though it can not be performed unless I have
in my mind the ideas of them. And in like manner, believing is an act
which has for its subject the facts themselves, though a previous mental
conception of the facts is an indispensable condition. When I say that
fire causes heat, do I mean that my idea of fire causes my idea of heat?
No: I mean that the natural phenomenon, fire, causes the natural
phenomenon, heat. When I mean to assert any thing respecting the ideas, I
give them their proper name, I call them ideas: as when I say, that a
child’s idea of a battle is unlike the reality, or that the ideas
entertained of the Deity have a great effect on the characters of mankind.

The notion that what is of primary importance to the logician in a
proposition, is the relation between the two _ideas_ corresponding to the
subject and predicate (instead of the relation between the two _phenomena_
which they respectively express), seems to me one of the most fatal errors
ever introduced into the philosophy of Logic; and the principal cause why
the theory of the science has made such inconsiderable progress during the
last two centuries. The treatises on Logic, and on the branches of Mental
Philosophy connected with Logic, which have been produced since the
intrusion of this cardinal error, though sometimes written by men of
extraordinary abilities and attainments, almost always tacitly imply a
theory that the investigation of truth consists in contemplating and
handling our ideas, or conceptions of things, instead of the things
themselves: a doctrine tantamount to the assertion, that the only mode of
acquiring knowledge of nature is to study it at second hand, as
represented in our own minds. Meanwhile, inquiries into every kind of
natural phenomena were incessantly establishing great and fruitful truths
on most important subjects, by processes upon which these views of the
nature of Judgment and Reasoning threw no light, and in which they
afforded no assistance whatever. No wonder that those who knew by
practical experience how truths are arrived at, should deem a science
futile, which consisted chiefly of such speculations. What has been done
for the advancement of Logic since these doctrines came into vogue, has
been done not by professed logicians, but by discoverers in the other
sciences; in whose methods of investigation many principles of logic, not
previously thought of, have successively come forth into light, but who
have generally committed the error of supposing that nothing whatever was
known of the art of philosophizing by the old logicians, because their
modern interpreters have written to so little purpose respecting it.

We have to inquire, then, on the present occasion, not into Judgment, but
judgments; not into the act of believing, but into the thing believed.
What is the immediate object of belief in a Proposition? What is the
matter of fact signified by it? What is it to which, when I assert the
proposition, I give my assent, and call upon others to give theirs? What
is that which is expressed by the form of discourse called a Proposition,
and the conformity of which to fact constitutes the truth of the
proposition?

§ 2. One of the clearest and most consecutive thinkers whom this country
or the world has produced, I mean Hobbes, has given the following answer
to this question. In every proposition (says he) what is signified is, the
belief of the speaker that the predicate is a name of the same thing of
which the subject is a name; and if it really is so, the proposition is
true. Thus the proposition, All men are living beings (he would say) is
true, because _living being_ is a name of every thing of which _man_ is a
name. All men are six feet high, is not true, because _six feet high_ is
not a name of every thing (though it is of some things) of which _man_ is
a name.

What is stated in this theory as the definition of a true proposition,
must be allowed to be a property which all true propositions possess. The
subject and predicate being both of them names of things, if they were
names of quite different things the one name could not, consistently with
its signification, be predicated of the other. If it be true that some men
are copper-colored, it must be true—and the proposition does really
assert—that among the individuals denoted by the name man, there are some
who are also among those denoted by the name copper-colored. If it be true
that all oxen ruminate, it must be true that all the individuals denoted
by the name ox are also among those denoted by the name ruminating; and
whoever asserts that all oxen ruminate, undoubtedly does assert that this
relation subsists between the two names.

The assertion, therefore, which, according to Hobbes, is the only one made
in any proposition, really is made in every proposition: and his analysis
has consequently one of the requisites for being the true one. We may go a
step further; it is the only analysis that is rigorously true of all
propositions without exception. What he gives as the meaning of
propositions, is part of the meaning of all propositions, and the whole
meaning of some. This, however, only shows what an extremely minute
fragment of meaning it is quite possible to include within the logical
formula of a proposition. It does not show that no proposition means more.
To warrant us in putting together two words with a copula between them, it
is really enough that the thing or things denoted by one of the names
should be capable, without violation of usage, of being called by the
other name also. If, then, this be all the meaning necessarily implied in
the form of discourse called a Proposition, why do I object to it as the
scientific definition of what a proposition means? Because, though the
mere collocation which makes the proposition a proposition, conveys no
more than this scanty amount of meaning, that same collocation combined
with other circumstances, that _form_ combined with other _matter_, does
convey more, and the proposition in those other circumstances does assert
more, than merely that relation between the two names.

The only propositions of which Hobbes’s principle is a sufficient account,
are that limited and unimportant class in which both the predicate and the
subject are proper names. For, as has already been remarked, proper names
have strictly no meaning; they are mere marks for individual objects: and
when a proper name is predicated of another proper name, all the
signification conveyed is, that both the names are marks for the same
object. But this is precisely what Hobbes produces as a theory of
predication in general. His doctrine is a full explanation of such
predications as these: Hyde was Clarendon, or, Tully is Cicero. It
exhausts the meaning of those propositions. But it is a sadly inadequate
theory of any others. That it should ever have been thought of as such,
can be accounted for only by the fact, that Hobbes, in common with the
other Nominalists, bestowed little or no attention upon the _connotation_
of words; and sought for their meaning exclusively in what they _denote_:
as if all names had been (what none but proper names really are) marks put
upon individuals; and as if there were no difference between a proper and
a general name, except that the first denotes only one individual, and the
last a greater number.

It has been seen, however, that the meaning of all names, except proper
names and that portion of the class of abstract names which are not
connotative, resides in the connotation. When, therefore, we are analyzing
the meaning of any proposition in which the predicate and the subject, or
either of them, are connotative names, it is to the connotation of those
terms that we must exclusively look, and not to what they _denote_, or in
the language of Hobbes (language so far correct) are names of.

In asserting that the truth of a proposition depends on the conformity of
import between its terms, as, for instance, that the proposition, Socrates
is wise, is a true proposition, because Socrates and wise are names
applicable to, or, as he expresses it, names of, the same person; it is
very remarkable that so powerful a thinker should not have asked himself
the question, But how came they to be names of the same person? Surely not
because such was the intention of those who invented the words. When
mankind fixed the meaning of the word wise, they were not thinking of
Socrates, nor, when his parents gave him the name of Socrates, were they
thinking of wisdom. The names _happen_ to fit the same person because of a
certain _fact_, which fact was not known, nor in being, when the names
were invented. If we want to know what the fact is, we shall find the clue
to it in the _connotation_ of the names.

A bird or a stone, a man, or a wise man, means simply, an object having
such and such attributes. The real meaning of the word man, is those
attributes, and not Smith, Brown, and the remainder of the individuals.
The word _mortal_, in like manner connotes a certain attribute or
attributes; and when we say, All men are mortal, the meaning of the
proposition is, that all beings which possess the one set of attributes,
possess also the other. If, in our experience, the attributes connoted by
_man_ are always accompanied by the attribute connoted by _mortal_, it
will follow as a consequence, that the class _man_ will be wholly included
in the class _mortal_, and that _mortal_ will be a name of all things of
which _man_ is a name: but why? Those objects are brought under the name,
by possessing the attributes connoted by it: but their possession of the
attributes is the real condition on which the truth of the proposition
depends; not their being called by the name. Connotative names do not
precede, but follow, the attributes which they connote. If one attribute
happens to be always found in conjunction with another attribute, the
concrete names which answer to those attributes will of course be
predicable of the same subjects, and may be said, in Hobbes’s language (in
the propriety of which on this occasion I fully concur), to be two names
for the same things. But the possibility of a concurrent application of
the two names, is a mere consequence of the conjunction between the two
attributes, and was, in most cases, never thought of when the names were
introduced and their signification fixed. That the diamond is combustible,
was a proposition certainly not dreamed of when the words Diamond and
Combustible first received their meaning; and could not have been
discovered by the most ingenious and refined analysis of the signification
of those words. It was found out by a very different process, namely, by
exerting the senses, and learning from them, that the attribute of
combustibility existed in the diamonds upon which the experiment was
tried; the number or character of the experiments being such, that what
was true of those individuals might be concluded to be true of all
substances “called by the name,” that is, of all substances possessing the
attributes which the name connotes. The assertion, therefore, when
analyzed, is, that wherever we find certain attributes, there will be
found a certain other attribute: which is not a question of the
signification of names, but of laws of nature; the order existing among
phenomena.

§ 3. Although Hobbes’s theory of Predication has not, in the terms in
which he stated it, met with a very favorable reception from subsequent
thinkers, a theory virtually identical with it, and not by any means so
perspicuously expressed, may almost be said to have taken the rank of an
established opinion. The most generally received notion of Predication
decidedly is that it consists in referring something to a class, _i.e._,
either placing an individual under a class, or placing one class under
another class. Thus, the proposition, Man is mortal, asserts, according to
this view of it, that the class man is included in the class mortal.
“Plato is a philosopher,” asserts that the individual Plato is one of
those who compose the class philosopher. If the proposition is negative,
then instead of placing something in a class, it is said to exclude
something from a class. Thus, if the following be the proposition, The
elephant is not carnivorous; what is asserted (according to this theory)
is, that the elephant is excluded from the class carnivorous, or is not
numbered among the things comprising that class. There is no real
difference, except in language, between this theory of Predication and the
theory of Hobbes. For a class _is_ absolutely nothing but an indefinite
number of individuals denoted by a general name. The name given to them in
common, is what makes them a class. To refer any thing to a class,
therefore, is to look upon it as one of the things which are to be called
by that common name. To exclude it from a class, is to say that the common
name is not applicable to it.

How widely these views of predication have prevailed, is evident from
this, that they are the basis of the celebrated _dictum de omni et nullo_.
When the syllogism is resolved, by all who treat of it, into an inference
that what is true of a class is true of all things whatever that belong to
the class; and when this is laid down by almost all professed logicians as
the ultimate principle to which all reasoning owes its validity; it is
clear that in the general estimation of logicians, the propositions of
which reasonings are composed can be the expression of nothing but the
process of dividing things into classes, and referring every thing to its
proper class.

This theory appears to me a signal example of a logical error very often
committed in logic, that of ὕστερον προτέρον, or explaining a thing by
something which presupposes it. When I say that snow is white, I may and
ought to be thinking of snow as a class, because I am asserting a
proposition as true of all snow: but I am certainly not thinking of white
objects as a class; I am thinking of no white object whatever except snow,
but only of that, and of the sensation of white which it gives me. When,
indeed, I have judged, or assented to the propositions, that snow is
white, and that several other things are also white, I gradually begin to
think of white objects as a class, including snow and those other things.
But this is a conception which followed, not preceded, those judgments,
and therefore can not be given as an explanation of them. Instead of
explaining the effect by the cause, this doctrine explains the cause by
the effect, and is, I conceive, founded on a latent misconception of the
nature of classification.

There is a sort of language very generally prevalent in these discussions,
which seems to suppose that classification is an arrangement and grouping
of definite and known individuals: that when names were imposed, mankind
took into consideration all the individual objects in the universe,
distributed them into parcels or lists, and gave to the objects of each
list a common name, repeating this operation _toties quoties_ until they
had invented all the general names of which language consists; which
having been once done, if a question subsequently arises whether a certain
general name can be truly predicated of a certain particular object, we
have only (as it were) to read the roll of the objects upon which that
name was conferred, and see whether the object about which the question
arises is to be found among them. The framers of language (it would seem
to be supposed) have predetermined all the objects that are to compose
each class, and we have only to refer to the record of an antecedent
decision.

So absurd a doctrine will be owned by nobody when thus nakedly stated; but
if the commonly received explanations of classification and naming do not
imply this theory, it requires to be shown how they admit of being
reconciled with any other.

General names are not marks put upon definite objects; classes are not
made by drawing a line round a given number of assignable individuals. The
objects which compose any given class are perpetually fluctuating. We may
frame a class without knowing the individuals, or even any of the
individuals, of which it may be composed; we may do so while believing
that no such individuals exist. If by the _meaning_ of a general name are
to be understood the things which it is the name of, no general name,
except by accident, has a fixed meaning at all, or ever long retains the
same meaning. The only mode in which any general name has a definite
meaning, is by being a name of an indefinite variety of things; namely, of
all things, known or unknown, past, present, or future, which possess
certain definite attributes. When, by studying not the meaning of words,
but the phenomena of nature, we discover that these attributes are
possessed by some object not previously known to possess them (as when
chemists found that the diamond was combustible), we include this new
object in the class; but it did not already belong to the class. We place
the individual in the class because the proposition is true; the
proposition is not true because the object is placed in the class.(31)

It will appear hereafter, in treating of reasoning, how much the theory of
that intellectual process has been vitiated by the influence of these
erroneous notions, and by the habit which they exemplify of assimilating
all the operations of the human understanding which have truth for their
object, to processes of mere classification and naming. Unfortunately, the
minds which have been entangled in this net are precisely those which have
escaped the other cardinal error commented upon in the beginning of the
present chapter. Since the revolution which dislodged Aristotle from the
schools, logicians may almost be divided into those who have looked upon
reasoning as essentially an affair of Ideas, and those who have looked
upon it as essentially an affair of Names.

Although, however, Hobbes’s theory of Predication, according to the
well-known remark of Leibnitz, and the avowal of Hobbes himself,(32)
renders truth and falsity completely arbitrary, with no standard but the
will of men, it must not be concluded that either Hobbes, or any of the
other thinkers who have in the main agreed with him, did in fact consider
the distinction between truth and error as less real, or attached less
importance to it, than other people. To suppose that they did so would
argue total unacquaintance with their other speculations. But this shows
how little hold their doctrine possessed over their own minds. No person,
at bottom, ever imagined that there was nothing more in truth than
propriety of expression; than using language in conformity to a previous
convention. When the inquiry was brought down from generals to a
particular case, it has always been acknowledged that there is a
distinction between verbal and real questions; that some false
propositions are uttered from ignorance of the meaning of words, but that
in others the source of the error is a misapprehension of things; that a
person who has not the use of language at all may form propositions
mentally, and that they may be untrue—that is, he may believe as matters
of fact what are not really so. This last admission can not be made in
stronger terms than it is by Hobbes himself,(33) though he will not allow
such erroneous belief to be called falsity, but only error. And he has
himself laid down, in other places, doctrines in which the true theory of
predication is by implication contained. He distinctly says that general
names are given to things on account of their attributes, and that
abstract names are the names of those attributes. “Abstract is that which
in any subject denotes the cause of the concrete name.... And these causes
of names are the same with the causes of our conceptions, namely, some
power of action, or affection, of the thing conceived, which some call the
manner by which any thing works upon our senses, but by most men they are
called _accidents_.”(34) It is strange that having gone so far, he should
not have gone one step further, and seen that what he calls the cause of
the concrete name, is in reality the meaning of it; and that when we
predicate of any subject a name which is given _because_ of an attribute
(or, as he calls it, an accident), our object is not to affirm the name,
but, by means of the name, to affirm the attribute.

§ 4. Let the predicate be, as we have said, a connotative term; and to
take the simplest case first, let the subject be a proper name: “The
summit of Chimborazo is white.” The word white connotes an attribute which
is possessed by the individual object designated by the words “summit of
Chimborazo;” which attribute consists in the physical fact, of its
exciting in human beings the sensation which we call a sensation of white.
It will be admitted that, by asserting the proposition, we wish to
communicate information of that physical fact, and are not thinking of the
names, except as the necessary means of making that communication. The
meaning of the proposition, therefore, is, that the individual thing
denoted by the subject, has the attributes connoted by the predicate.

If we now suppose the subject also to be a connotative name, the meaning
expressed by the proposition has advanced a step further in complication.
Let us first suppose the proposition to be universal, as well as
affirmative: “All men are mortal.” In this case, as in the last, what the
proposition asserts (or expresses a belief of) is, of course, that the
objects denoted by the subject (man) possess the attributes connoted by
the predicate (mortal). But the characteristic of this case is, that the
objects are no longer _individually_ designated. They are pointed out only
by some of their attributes: they are the objects called men, that is,
possessing the attributes connoted by the name man; and the only thing
known of them may be those attributes: indeed, as the proposition is
general, and the objects denoted by the subject are therefore indefinite
in number, most of them are not known individually at all. The assertion,
therefore, is not, as before, that the attributes which the predicate
connotes are possessed by any given individual, or by any number of
individuals previously known as John, Thomas, etc., but that those
attributes are possessed by each and every individual possessing certain
other attributes; that whatever has the attributes connoted by the
subject, has also those connoted by the predicate; that the latter set of
attributes _constantly accompany_ the former set. Whatever has the
attributes of man has the attribute of mortality; mortality constantly
accompanies the attributes of man.(35)

If it be remembered that every attribute is _grounded_ on some fact or
phenomenon, either of outward sense or of inward consciousness, and that
to _possess_ an attribute is another phrase for being the cause of, or
forming part of, the fact or phenomenon upon which the attribute is
grounded; we may add one more step to complete the analysis. The
proposition which asserts that one attribute always accompanies another
attribute, really asserts thereby no other thing than this, that one
phenomenon always accompanies another phenomenon; insomuch that where we
find the latter, we have assurance of the existence of the former. Thus,
in the proposition, All men are mortal, the word man connotes the
attributes which we ascribe to a certain kind of living creatures, on the
ground of certain phenomena which they exhibit, and which are partly
physical phenomena, namely the impressions made on our senses by their
bodily form and structure, and partly mental phenomena, namely the
sentient and intellectual life which they have of their own. All this is
understood when we utter the word man, by any one to whom the meaning of
the word is known. Now, when we say, Man is mortal, we mean that wherever
these various physical and mental phenomena are all found, there we have
assurance that the other physical and mental phenomenon, called death,
will not fail to take place. The proposition does not affirm _when_; for
the connotation of the word _mortal_ goes no further than to the
occurrence of the phenomenon at some time or other, leaving the particular
time undecided.

§ 5. We have already proceeded far enough, not only to demonstrate the
error of Hobbes, but to ascertain the real import of by far the most
numerous class of propositions. The object of belief in a proposition,
when it asserts any thing more than the meaning of words, is generally, as
in the cases which we have examined, either the co-existence or the
sequence of two phenomena. At the very commencement of our inquiry, we
found that every act of belief implied two Things: we have now ascertained
what, in the most frequent case, these two things are, namely, two
Phenomena; in other words, two states of consciousness; and what it is
which the proposition affirms (or denies) to subsist between them, namely,
either succession or co-existence. And this case includes innumerable
instances which no one, previous to reflection, would think of referring
to it. Take the following example: A generous person is worthy of honor.
Who would expect to recognize here a case of co-existence between
phenomena? But so it is. The attribute which causes a person to be termed
generous, is ascribed to him on the ground of states of his mind, and
particulars of his conduct: both are phenomena: the former are facts of
internal consciousness; the latter, so far as distinct from the former,
are physical facts, or perceptions of the senses. Worthy of honor admits
of a similar analysis. Honor, as here used, means a state of approving and
admiring emotion, followed on occasion by corresponding outward acts.
“Worthy of honor” connotes all this, together with our approval of the act
of showing honor. All these are phenomena; states of internal
consciousness, accompanied or followed by physical facts. When we say, A
generous person is worthy of honor, we affirm co-existence between the two
complicated phenomena connoted by the two terms respectively. We affirm,
that wherever and whenever the inward feelings and outward facts implied
in the word generosity have place, then and there the existence and
manifestation of an inward feeling, honor, would be followed in our minds
by another inward feeling, approval.

After the analysis, in a former chapter, of the import of names, many
examples are not needed to illustrate the import of propositions. When
there is any obscurity, or difficulty, it does not lie in the meaning of
the proposition, but in the meaning of the names which compose it; in the
extremely complicated connotation of many words; the immense multitude and
prolonged series of facts which often constitute the phenomenon connoted
by a name. But where it is seen what the phenomenon is, there is seldom
any difficulty in seeing that the assertion conveyed by the proposition
is, the co-existence of one such phenomenon with another; or the
succession of one such phenomenon to another: so that where the one is
found, we may calculate on finding the other, though perhaps not
conversely.

This, however, though the most common, is not the only meaning which
propositions are ever intended to convey. In the first place, sequences
and co-existences are not only asserted respecting Phenomena; we make
propositions also respecting those hidden causes of phenomena, which are
named substances and attributes. A substance, however, being to us nothing
but either that which causes, or that which is conscious of, phenomena;
and the same being true, _mutatis mutandis_, of attributes; no assertion
can be made, at least with a meaning, concerning these unknown and
unknowable entities, except in virtue of the Phenomena by which alone they
manifest themselves to our faculties. When we say Socrates was
contemporary with the Peloponnesian war, the foundation of this assertion,
as of all assertions concerning substances, is an assertion concerning the
phenomena which they exhibit—namely, that the series of facts by which
Socrates manifested himself to mankind, and the series of mental states
which constituted his sentient existence, went on simultaneously with the
series of facts known by the name of the Peloponnesian war. Still, the
proposition as commonly understood does not assert that alone; it asserts
that the Thing in itself, the _noumenon_ Socrates, was existing, and doing
or experiencing those various facts during the same time. Co-existence and
sequence, therefore, may be affirmed or denied not only between phenomena,
but between noumena, or between a noumenon and phenomena. And both of
noumena and of phenomena we may affirm simple existence. But what is a
noumenon? An unknown cause. In affirming, therefore, the existence of a
noumenon, we affirm causation. Here, therefore, are two additional kinds
of fact, capable of being asserted in a proposition. Besides the
propositions which assert Sequence or Co-existence, there are some which
assert simple Existence;(36) and others assert Causation, which, subject
to the explanations which will follow in the Third Book, must be
considered provisionally as a distinct and peculiar kind of assertion.

§ 6. To these four kinds of matter-of-fact or assertion, must be added a
fifth, Resemblance. This was a species of attribute which we found it
impossible to analyze; for which no _fundamentum_, distinct from the
objects themselves, could be assigned. Besides propositions which assert a
sequence or co-existence between two phenomena, there are therefore also
propositions which assert resemblance between them; as, This color is like
that color; The heat of to-day is _equal_ to the heat of yesterday. It is
true that such an assertion might with some plausibility be brought within
the description of an affirmation of sequence, by considering it as an
assertion that the simultaneous contemplation of the two colors is
_followed_ by a specific feeling termed the feeling of resemblance. But
there would be nothing gained by incumbering ourselves, especially in this
place, with a generalization which may be looked upon as strained. Logic
does not undertake to analyze mental facts into their ultimate elements.
Resemblance between two phenomena is more intelligible in itself than any
explanation could make it, and under any classification must remain
specifically distinct from the ordinary cases of sequence and
co-existence.

It is sometimes said, that all propositions whatever, of which the
predicate is a general name, do, in point of fact, affirm or deny
resemblance. All such propositions affirm that a thing belongs to a class;
but things being classed together according to their resemblance, every
thing is of course classed with the things which it is supposed to
resemble most; and thence, it may be said, when we affirm that Gold is a
metal, or that Socrates is a man, the affirmation intended is, that gold
resembles other metals, and Socrates other men, more nearly than they
resemble the objects contained in any other of the classes co-ordinate
with these.

There is some slight degree of foundation for this remark, but no more
than a slight degree. The arrangement of things into classes, such as the
class _metal_, or the class _man_, is grounded indeed on a resemblance
among the things which are placed in the same class, but not on a mere
general resemblance: the resemblance it is grounded on consists in the
possession by all those things, of certain common peculiarities; and those
peculiarities it is which the terms connote, and which the propositions
consequently assert; not the resemblance. For though when I say, Gold is a
metal, I say by implication that if there be any other metals it must
resemble them, yet if there were no other metals I might still assert the
proposition with the same meaning as at present, namely, that gold has the
various properties implied in the word metal; just as it might be said,
Christians are men, even if there were no men who were not Christians.
Propositions, therefore, in which objects are referred to a class because
they possess the attributes constituting the class, are so far from
asserting nothing but resemblance, that they do not, properly speaking,
assert resemblance at all.

But we remarked some time ago (and the reasons of the remark will be more
fully entered into in a subsequent Book(37)) that there is sometimes a
convenience in extending the boundaries of a class so as to include things
which possess in a very inferior degree, if in any, some of the
characteristic properties of the class—provided they resemble that class
more than any other, insomuch that the general propositions which are true
of the class, will be nearer to being true of those things than any other
equally general propositions. For instance, there are substances called
metals which have very few of the properties by which metals are commonly
recognized; and almost every great family of plants or animals has a few
anomalous genera or species on its borders, which are admitted into it by
a sort of courtesy, and concerning which it has been matter of discussion
to what family they properly belonged. Now when the class-name is
predicated of any object of this description, we do, by so predicating it,
affirm resemblance and nothing more. And in order to be scrupulously
correct it ought to be said, that in every case in which we predicate a
general name, we affirm, not absolutely that the object possesses the
properties designated by the name, but that it _either_ possesses those
properties, or if it does not, at any rate resembles the things which do
so, more than it resembles any other things. In most cases, however, it is
unnecessary to suppose any such alternative, the latter of the two grounds
being very seldom that on which the assertion is made: and when it is,
there is generally some slight difference in the form of the expression,
as, This species (or genus) is _considered_, or _may be ranked_, as
belonging to such and such a family: we should hardly say positively that
it does belong to it, unless it possessed unequivocally the properties of
which the class-name is scientifically significant.

There is still another exceptional case, in which, though the predicate is
the name of a class, yet in predicating it we affirm nothing but
resemblance, the class being founded not on resemblance in any given
particular, but on general unanalyzable resemblance. The classes in
question are those into which our simple sensations, or other simple
feelings, are divided. Sensations of white, for instance, are classed
together, not because we can take them to pieces, and say they are alike
in this, and not alike in that, but because we feel them to be alike
altogether, though in different degrees. When, therefore, I say, The color
I saw yesterday was a white color, or, The sensation I feel is one of
tightness, in both cases the attribute I affirm of the color or of the
other sensation is mere resemblance—simple _likeness_ to sensations which
I have had before, and which have had those names bestowed upon them. The
names of feelings, like other concrete general names, are connotative; but
they connote a mere resemblance. When predicated of any individual
feeling, the information they convey is that of its likeness to the other
feelings which we have been accustomed to call by the same name. Thus much
may suffice in illustration of the kind of propositions in which the
matter-of-fact asserted (or denied) is simple Resemblance.

Existence, Co-existence, Sequence, Causation, Resemblance: one or other of
these is asserted (or denied) in every proposition which is not merely
verbal. This five-fold division is an exhaustive classification of
matters-of-fact; of all things that can be believed, or tendered for
belief; of all questions that can be propounded, and all answers that can
be returned to them.

Professor Bain(38) distinguishes two kinds of Propositions of
Co-existence. “In the one kind, account is taken of Place; they may be
described as propositions of Order in Place.” In the other kind, the
co-existence which is predicated is termed by Mr. Bain Co-inherence of
Attributes. “This is a distinct variety of Propositions of Co-existence.
Instead of an arrangement in place with numerical intervals, we have the
concurrence of two or more attributes or powers in the same part or
locality. A mass of gold contains, in every atom, the concurring
attributes that mark the substance—weight, hardness, color, lustre,
incorrosibility, etc. An animal, besides having parts situated in place,
has co-inhering functions in the same parts, exerted by the very same
masses and molecules of its substance.... The Mind, which affords no
Propositions of Order in Place, has co-inhering functions. We affirm mind
to contain Feeling, Will, and Thought, not in local separation, but in
commingling exercise. The concurring properties of minerals, of plants,
and of the bodily and the mental structure of animals, are united in
affirmations of co-inherence.”

The distinction is real and important. But, as has been seen, an
Attribute, when it is any thing but a simple unanalyzable Resemblance
between the subject and some other things, consists in causing impressions
of some sort on consciousness. Consequently, the co-inherence of two
attributes is but the co-existence of the two states of consciousness
implied in their meaning: with the difference, however, that this
co-existence is sometimes potential only, the attribute being considered
as in existence, though the fact on which it is grounded may not be
actually, but only potentially present. Snow, for instance, is, with great
convenience, said to be white even in a state of total darkness, because,
though we are not now conscious of the color, we shall be conscious of it
as soon as morning breaks. Co-inherence of attributes is therefore still a
case, though a complex one, of co-existence of states of consciousness; a
totally different thing, however, from Order in Place. Being a part of
simultaneity, it belongs not to Place but to Time.

We may therefore (and we shall sometimes find it a convenience) instead of
Co-existence and Sequence, say, for greater particularity, Order in Place
and Order in Time: Order in Place being a specific mode of co-existence,
not necessary to be more particularly analyzed here; while the mere fact
of co-existence, whether between actual sensations, or between the
potentialities of causing them, known by the name of attributes, may be
classed, together with Sequence, under the head of Order in Time.

§ 7. In the foregoing inquiry into the import of propositions, we have
thought it necessary to analyze directly those alone, in which the terms
of the proposition (or the predicate at least) are concrete terms. But, in
doing so, we have indirectly analyzed those in which the terms are
abstract. The distinction between an abstract term and its corresponding
concrete, does not turn upon any difference in what they are appointed to
signify; for the real signification of a concrete general name is, as we
have so often said, its connotation; and what the concrete term connotes,
forms the entire meaning of the abstract name. Since there is nothing in
the import of an abstract name which is not in the import of the
corresponding concrete, it is natural to suppose that neither can there be
any thing in the import of a proposition of which the terms are abstract,
but what there is in some proposition which can be framed of concrete
terms.

And this presumption a closer examination will confirm. An abstract name
is the name of an attribute, or combination of attributes. The
corresponding concrete is a name given to things, because of, and in order
to express, their possessing that attribute, or that combination of
attributes. When, therefore, we predicate of any thing a concrete name,
the attribute is what we in reality predicate of it. But it has now been
shown that in all propositions of which the predicate is a concrete name,
what is really predicated is one of five things: Existence, Co-existence,
Causation, Sequence, or Resemblance. An attribute, therefore, is
necessarily either an existence, a co-existence, a causation, a sequence,
or a resemblance. When a proposition consists of a subject and predicate
which are abstract terms, it consists of terms which must necessarily
signify one or other of these things. When we predicate of any thing an
abstract name, we affirm of the thing that it is one or other of these
five things; that it is a case of Existence, or of Co-existence, or of
Causation, or of Sequence, or of Resemblance.

It is impossible to imagine any proposition expressed in abstract terms,
which can not be transformed into a precisely equivalent proposition in
which the terms are concrete; namely, either the concrete names which
connote the attributes themselves, or the names of the _fundamenta_ of
those attributes; the facts or phenomena on which they are grounded. To
illustrate the latter case, let us take this proposition, of which the
subject only is an abstract name, “Thoughtlessness is dangerous.”
Thoughtlessness is an attribute, grounded on the facts which we call
thoughtless actions; and the proposition is equivalent to this,
Thoughtless actions are dangerous. In the next example the predicate as
well as the subject are abstract names: “Whiteness is a color;” or “The
color of snow is a whiteness.” These attributes being grounded on
sensations, the equivalent propositions in the concrete would be, The
sensation of white is one of the sensations called those of color—The
sensation of sight, caused by looking at snow, is one of the sensations
called sensations of white. In these propositions, as we have before seen,
the matter-of-fact asserted is a Resemblance. In the following examples,
the concrete terms are those which directly correspond to the abstract
names; connoting the attribute which these denote. “Prudence is a virtue:”
this may be rendered, “All prudent persons, _in so far as_ prudent, are
virtuous:” “Courage is deserving of honor;” thus, “All courageous persons
are deserving of honor _in so far_ as they are courageous:” which is
equivalent to this—“All courageous persons deserve an addition to the
honor, or a diminution of the disgrace, which would attach to them on
other grounds.”

In order to throw still further light upon the import of propositions of
which the terms are abstract, we will subject one of the examples given
above to a minuter analysis. The proposition we shall select is the
following: “Prudence is a virtue.” Let us substitute for the word virtue
an equivalent but more definite expression, such as “a mental quality
beneficial to society,” or “a mental quality pleasing to God,” or whatever
else we adopt as the definition of virtue. What the proposition asserts is
a sequence, accompanied with causation; namely, that benefit to society,
or that the approval of God, is consequent on, and caused by, prudence.
Here is a sequence; but between what? We understand the consequent of the
sequence, but we have yet to analyze the antecedent. Prudence is an
attribute; and, in connection with it, two things besides itself are to be
considered; prudent persons, who are the _subjects_ of the attribute, and
prudential conduct, which may be called the _foundation_ of it. Now is
either of these the antecedent? and, first, is it meant, that the approval
of God, or benefit to society, is attendant upon all prudent _persons_?
No; except _in so far_ as they are prudent; for prudent persons who are
scoundrels can seldom, on the whole, be beneficial to society, nor can
they be acceptable to a good being. Is it upon prudential _conduct_, then,
that divine approbation and benefit to mankind are supposed to be
invariably consequent? Neither is this the assertion meant, when it is
said that prudence is a virtue; except with the same reservation as
before, and for the same reason, namely, that prudential conduct, although
in _so far as_ it is prudential it is beneficial to society, may yet, by
reason of some other of its qualities, be productive of an injury
outweighing the benefit, and deserve a displeasure exceeding the
approbation which would be due to the prudence. Neither the substance,
therefore (viz., the person), nor the phenomenon (the conduct), is an
antecedent on which the other term of the sequence is universally
consequent. But the proposition, “Prudence is a virtue,” is a universal
proposition. What is it, then, upon which the proposition affirms the
effects in question to be universally consequent? Upon that in the person,
and in the conduct, which causes them to be called prudent, and which is
equally in them when the action, though prudent, is wicked; namely, a
correct foresight of consequences, a just estimation of their importance
to the object in view, and repression of any unreflecting impulse at
variance with the deliberate purpose. These, which are states of the
person’s mind, are the real antecedent in the sequence, the real cause in
the causation, asserted by the proposition. But these are also the real
ground, or foundation, of the attribute Prudence; since wherever these
states of mind exist we may predicate prudence, even before we know
whether any conduct has followed. And in this manner every assertion
respecting an attribute, may be transformed into an assertion exactly
equivalent respecting the fact or phenomenon which is the ground of the
attribute. And no case can be assigned, where that which is predicated of
the fact or phenomenon, does not belong to one or other of the five
species formerly enumerated: it is either simple Existence, or it is some
Sequence, Co-existence, Causation, or Resemblance.

And as these five are the only things which can be affirmed, so are they
the only things which can be denied. “No horses are web-footed” denies
that the attributes of a horse ever co-exist with web-feet. It is scarcely
necessary to apply the same analysis to Particular affirmations and
negations. “Some birds are web-footed,” affirms that, with the attributes
connoted by _bird_, the phenomenon web-feet is sometimes co-existent:
“Some birds are not web-footed,” asserts that there are other instances in
which this co-existence does not have place. Any further explanation of a
thing which, if the previous exposition has been assented to, is so
obvious, may here be spared.




                               Chapter VI.


Of Propositions Merely Verbal.


§ 1. As a preparation for the inquiry which is the proper object of Logic,
namely, in what manner propositions are to be proved, we have found it
necessary to inquire what they contain which requires, or is susceptible
of, proof; or (which is the same thing) what they assert. In the course of
this preliminary investigation into the import of Propositions, we
examined the opinion of the Conceptualists, that a proposition is the
expression of a relation between two ideas; and the doctrine of the
extreme Nominalists, that it is the expression of an agreement or
disagreement between the meanings of two names. We decided that, as
general theories, both of these are erroneous; and that, though
propositions may be made both respecting names and respecting ideas,
neither the one nor the other are the subject-matter of Propositions
considered generally. We then examined the different kinds of
Propositions, and found that, with the exception of those which are merely
verbal, they assert five different kinds of matters of fact, namely,
Existence, Order in Place, Order in Time, Causation, and Resemblance; that
in every proposition one of these five is either affirmed, or denied, of
some fact or phenomenon, or of some object the unknown source of a fact or
phenomenon.

In distinguishing, however, the different kinds of matters of fact
asserted in propositions, we reserved one class of propositions, which do
not relate to any matter of fact, in the proper sense of the term at all,
but to the meaning of names. Since names and their signification are
entirely arbitrary, such propositions are not, strictly speaking,
susceptible of truth or falsity, but only of conformity or disconformity
to usage or convention; and all the proof they are capable of, is proof of
usage; proof that the words have been employed by others in the
acceptation in which the speaker or writer desires to use them. These
propositions occupy, however, a conspicuous place in philosophy; and their
nature and characteristics are of as much importance in logic, as those of
any of the other classes of propositions previously adverted to.

If all propositions respecting the signification of words were as simple
and unimportant as those which served us for examples when examining
Hobbes’s theory of predication, viz., those of which the subject and
predicate are proper names, and which assert only that those names have,
or that they have not, been conventionally assigned to the same
individual, there would be little to attract to such propositions the
attention of philosophers. But the class of merely verbal propositions
embraces not only much more than these, but much more than any
propositions which at first sight present themselves as verbal;
comprehending a kind of assertions which have been regarded not only as
relating to things, but as having actually a more intimate relation with
them than any other propositions whatever. The student in philosophy will
perceive that I allude to the distinction on which so much stress was laid
by the schoolmen, and which has been retained either under the same or
under other names by most metaphysicians to the present day, viz., between
what were called _essential_, and what were called _accidental_,
propositions, and between essential and accidental properties or
attributes.

§ 2. Almost all metaphysicians prior to Locke, as well as many since his
time, have made a great mystery of Essential Predication, and of
predicates which are said to be of the _essence_ of the subject. The
essence of a thing, they said, was that without which the thing could
neither be, nor be conceived to be. Thus, rationality was of the essence
of man, because without rationality, man could not be conceived to exist.
The different attributes which made up the essence of the thing were
called its essential properties; and a proposition in which any of these
were predicated of it was called an Essential Proposition, and was
considered to go deeper into the nature of the thing, and to convey more
important information respecting it, than any other proposition could do.
All properties, not of the essence of the thing, were called its
accidents; were supposed to have nothing at all, or nothing comparatively,
to do with its inmost nature; and the propositions in which any of these
were predicated of it were called Accidental Propositions. A connection
may be traced between this distinction, which originated with the
schoolmen, and the well-known dogmas of _substantiæ secundæ_ or general
substances, and _substantial forms_, doctrines which under varieties of
language pervaded alike the Aristotelian and the Platonic schools, and of
which more of the spirit has come down to modern times than might be
conjectured from the disuse of the phraseology. The false views of the
nature of classification and generalization which prevailed among the
schoolmen, and of which these dogmas were the technical expression, afford
the only explanation which can be given of their having misunderstood the
real nature of those Essences which held so conspicuous a place in their
philosophy. They said, truly, that _man_ can not be conceived without
rationality. But though _man_ can not, a being may be conceived exactly
like a man in all points except that one quality, and those others which
are the conditions or consequences of it. All, therefore, which is really
true in the assertion that man can not be conceived without rationality,
is only, that if he had not rationality, he would not be reputed a man.
There is no impossibility in conceiving the _thing_, nor, for aught we
know, in its existing: the impossibility is in the conventions of
language, which will not allow the thing, even if it exist, to be called
by the name which is reserved for rational beings. Rationality, in short,
is involved in the meaning of the word man: is one of the attributes
connoted by the name. The essence of man, simply means the whole of the
attributes connoted by the word; and any one of those attributes taken
singly, is an essential property of man.

But these reflections, so easy to us, would have been difficult to persons
who thought, as most of the later Aristotelians did, that objects were
made what they were called, that gold (for instance) was made gold, not by
the possession of certain properties to which mankind have chosen to
attach that name, but by participation in the nature of a general
substance, called gold in general, which substance, together with all the
properties that belonged to it, _inhered_ in every individual piece of
gold.(39) As they did not consider these universal substances to be
attached to all general names, but only to some, they thought that an
object borrowed only a part of its properties from a universal substance,
and that the rest belonged to it individually: the former they called its
essence, and the latter its accidents. The scholastic doctrine of essences
long survived the theory on which it rested, that of the existence of real
entities corresponding to general terms; and it was reserved for Locke, at
the end of the seventeenth century, to convince philosophers that the
supposed essences of classes were merely the signification of their names;
nor, among the signal services which his writings rendered to philosophy,
was there one more needful or more valuable.

Now, as the most familiar of the general names by which an object is
designated usually connotes not one only, but several attributes of the
object, each of which attributes separately forms also the bond of union
of some class, and the meaning of some general name; we may predicate of a
name which connotes a variety of attributes, another name which connotes
only one of these attributes, or some smaller number of them than all. In
such cases, the universal affirmative proposition will be true; since
whatever possesses the whole of any set of attributes, must possess any
part of that same set. A proposition of this sort, however, conveys no
information to any one who previously understood the whole meaning of the
terms. The propositions, Every man is a corporeal being, Every man is a
living creature, Every man is rational, convey no knowledge to any one who
was already aware of the entire meaning of the word _man_, for the meaning
of the word includes all this: and that every _man_ has the attributes
connoted by all these predicates, is already asserted when he is called a
man. Now, of this nature are all the propositions which have been called
essential. They are, in fact, identical propositions.

It is true that a proposition which predicates any attribute, even though
it be one implied in the name, is in most cases understood to involve a
tacit assertion that there _exists_ a thing corresponding to the name, and
possessing the attributes connoted by it; and this implied assertion may
convey information, even to those who understood the meaning of the name.
But all information of this sort, conveyed by all the essential
propositions of which man can be made the subject, is included in the
assertion, Men exist. And this assumption of real existence is, after all,
the result of an imperfection of language. It arises from the ambiguity of
the copula, which, in addition to its proper office of a mark to show that
an assertion is made, is also, as formerly remarked, a concrete word
connoting existence. The actual existence of the subject of the
proposition is therefore only apparently, not really, implied in the
predication, if an essential one: we may say, A ghost is a disembodied
spirit, without believing in ghosts. But an accidental, or non-essential,
affirmation, does imply the real existence of the subject, because in the
case of a non-existent subject there is nothing for the proposition to
assert. Such a proposition as, The ghost of a murdered person haunts the
couch of the murderer, can only have a meaning if understood as implying a
belief in ghosts; for since the signification of the word ghost implies
nothing of the kind, the speaker either means nothing, or means to assert
a thing which he wishes to be believed to have really taken place.

It will be hereafter seen that when any important consequences seem to
follow, as in mathematics, from an essential proposition, or, in other
words, from a proposition involved in the meaning of a name, what they
really flow from is the tacit assumption of the real existence of the
objects so named. Apart from this assumption of real existence, the class
of propositions in which the predicate is of the essence of the subject
(that is, in which the predicate connotes the whole or part of what the
subject connotes, but nothing besides) answer no purpose but that of
unfolding the whole or some part of the meaning of the name, to those who
did not previously know it. Accordingly, the most useful, and in
strictness the only useful kind of essential propositions, are
Definitions: which, to be complete, should unfold the whole of what is
involved in the meaning of the word defined; that is (when it is a
connotative word), the whole of what it connotes. In defining a name,
however, it is not usual to specify its entire connotation, but so much
only as is sufficient to mark out the objects usually denoted by it from
all other known objects. And sometimes a merely accidental property, not
involved in the meaning of the name, answers this purpose equally well.
The various kinds of definition which these distinctions give rise to, and
the purposes to which they are respectively subservient, will be minutely
considered in the proper place.

§ 3. According to the above view of essential propositions, no proposition
can be reckoned such which relates to an individual by name, that is, in
which the subject is a proper name. Individuals have no essences. When the
schoolmen talked of the essence of an individual, they did not mean the
properties implied in its name, for the names of individuals imply no
properties. They regarded as of the essence of an individual, whatever was
of the essence of the species in which they were accustomed to place that
individual; _i.e._, of the class to which it was most familiarly referred,
and to which, therefore, they conceived that it by nature belonged. Thus,
because the proposition Man is a rational being, was an essential
proposition, they affirmed the same thing of the proposition, Julius Cæsar
is a rational being. This followed very naturally if genera and species
were to be considered as entities, distinct from, but _inhering_ in, the
individuals composing them. If _man_ was a substance inhering in each
individual man, the _essence_ of man (whatever that might mean) was
naturally supposed to accompany it; to inhere in John Thompson, and to
form the _common essence_ of Thompson and Julius Cæsar. It might then be
fairly said, that rationality, being of the essence of Man, was of the
essence also of Thompson. But if Man altogether be only the individual men
and a name bestowed upon them in consequence of certain common properties,
what becomes of John Thompson’s essence?

A fundamental error is seldom expelled from philosophy by a single
victory. It retreats slowly, defends every inch of ground, and often,
after it has been driven from the open country, retains a footing in some
remote fastness. The essences of individuals were an unmeaning figment
arising from a misapprehension of the essences of classes, yet even Locke,
when he extirpated the parent error, could not shake himself free from
that which was its fruit. He distinguished two sorts of essences, Real and
Nominal. His nominal essences were the essences of classes, explained
nearly as we have now explained them. Nor is any thing wanting to render
the third book of Locke’s Essay a nearly unexceptional treatise on the
connotation of names, except to free its language from the assumption of
what are called Abstract Ideas, which unfortunately is involved in the
phraseology, though not necessarily connected with the thoughts contained
in that immortal Third Book.(40) But besides nominal essences, he admitted
real essences, or essences of individual objects, which he supposed to be
the causes of the sensible properties of those objects. We know not (said
he) what these are (and this acknowledgment rendered the fiction
comparatively innocuous); but if we did, we could, from them alone,
demonstrate the sensible properties of the object, as the properties of
the triangle are demonstrated from the definition of the triangle. I shall
have occasion to revert to this theory in treating of Demonstration, and
of the conditions under which one property of a thing admits of being
demonstrated from another property. It is enough here to remark that,
according to this definition, the real essence of an object has, in the
progress of physics, come to be conceived as nearly equivalent, in the
case of bodies, to their corpuscular structure: what it is now supposed to
mean in the case of any other entities, I would not take upon myself to
define.

§ 4. An essential proposition, then, is one which is purely verbal; which
asserts of a thing under a particular name, only what is asserted of it in
the fact of calling it by that name; and which, therefore, either gives no
information, or gives it respecting the name, not the thing.
Non-essential, or accidental propositions, on the contrary, may be called
Real Propositions, in opposition to Verbal. They predicate of a thing some
fact not involved in the signification of the name by which the
proposition speaks of it; some attribute not connoted by that name. Such
are all propositions concerning things individually designated, and all
general or particular propositions in which the predicate connotes any
attribute not connoted by the subject. All these, if true, add to our
knowledge: they convey information, not already involved in the names
employed. When I am told that all, or even that some objects, which have
certain qualities, or which stand in certain relations, have also certain
other qualities, or stand in certain other relations, I learn from this
proposition a new fact; a fact not included in my knowledge of the meaning
of the words, nor even of the existence of Things answering to the
signification of those words. It is this class of propositions only which
are in themselves instructive, or from which any instructive propositions
can be inferred.(41)

Nothing has probably contributed more to the opinion so long prevalent of
the futility of the school logic, than the circumstance that almost all
the examples used in the common school books to illustrate the doctrine of
predication and that of the syllogism, consist of essential propositions.
They were usually taken either from the branches or from the main trunk of
the Predicamental Tree, which included nothing but what was of the
_essence_ of the species: _Omne corpus est substantia_, _Omne animal est
corpus_, _Omnis homo est corpus_, _Omnis homo est animal_, _Omnis homo est
rationalis_, and so forth. It is far from wonderful that the syllogistic
art should have been thought to be of no use in assisting correct
reasoning, when almost the only propositions which, in the hands of its
professed teachers, it was employed to prove, were such as every one
assented to without proof the moment he comprehended the meaning of the
words; and stood exactly on a level, in point of evidence, with the
premises from which they were drawn. I have, therefore, throughout this
work, avoided the employment of essential propositions as examples, except
where the nature of the principle to be illustrated specifically required
them.

§ 5. With respect to propositions which do convey information—which assert
something of a Thing, under a name that does not already presuppose what
is about to be asserted; there are two different aspects in which these,
or rather such of them as are general propositions, may be considered: we
may either look at them as portions of speculative truth, or as memoranda
for practical use. According as we consider propositions in one or the
other of these lights, their import may be conveniently expressed in one
or in the other of two formulas.

According to the formula which we have hitherto employed, and which is
best adapted to express the import of the proposition as a portion of our
theoretical knowledge, All men are mortal, means that the attributes of
man are always accompanied by the attribute mortality: No men are gods,
means that the attributes of man are never accompanied by the attributes,
or at least never by all the attributes, signified by the word god. But
when the proposition is considered as a memorandum for practical use, we
shall find a different mode of expressing the same meaning better adapted
to indicate the office which the proposition performs. The practical use
of a proposition is, to apprise or remind us what we have to expect, in
any individual case which comes within the assertion contained in the
proposition. In reference to this purpose, the proposition, All men are
mortal, means that the attributes of man are _evidence of_, are a _mark_
of, mortality; an indication by which the presence of that attribute is
made manifest. No men are gods, means that the attributes of man are a
mark or evidence that some or all of the attributes understood to belong
to a god are not there; that where the former are, we need not expect to
find the latter.

These two forms of expression are at bottom equivalent; but the one points
the attention more directly to what a proposition means, the latter to the
manner in which it is to be used.

Now it is to be observed that Reasoning (the subject to which we are next
to proceed) is a process into which propositions enter not as ultimate
results, but as means to the establishment of other propositions. We may
expect, therefore, that the mode of exhibiting the import of a general
proposition which shows it in its application to practical use, will best
express the function which propositions perform in Reasoning. And
accordingly, in the theory of Reasoning, the mode of viewing the subject
which considers a Proposition as asserting that one fact or phenomenon is
a _mark_ or _evidence_ of another fact or phenomenon, will be found almost
indispensable. For the purposes of that Theory, the best mode of defining
the import of a proposition is not the mode which shows most clearly what
it is in itself, but that which most distinctly suggests the manner in
which it may be made available for advancing from it to other
propositions.




                               Chapter VII.


Of The Nature Of Classification, And The Five Predicables.


§ 1. In examining into the nature of general propositions, we have
adverted much less than is usual with logicians to the ideas of a Class,
and Classification; ideas which, since the Realist doctrine of General
Substances went out of vogue, have formed the basis of almost every
attempt at a philosophical theory of general terms and general
propositions. We have considered general names as having a meaning, quite
independently of their being the names of classes. That circumstance is in
truth accidental, it being wholly immaterial to the signification of the
name whether there are many objects, or only one, to which it happens to
be applicable, or whether there be any at all. God is as much a general
term to the Christian or Jew as to the Polytheist; and dragon, hippogriff,
chimera, mermaid, ghost, are as much so as if real objects existed,
corresponding to those names. Every name the signification of which is
constituted by attributes, is potentially a name of an indefinite number
of objects; but it needs not be actually the name of any; and if of any,
it may be the name of only one. As soon as we employ a name to connote
attributes, the things, be they more or fewer, which happen to possess
those attributes, are constituted _ipso facto_ a class. But in predicating
the name we predicate only the attributes; and the fact of belonging to a
class does not, in many cases, come into view at all.

Although, however, Predication does not presuppose Classification, and
though the theory of Names and of Propositions is not cleared up, but only
encumbered, by intruding the idea of classification into it, there is
nevertheless a close connection between Classification and the employment
of General Names. By every general name which we introduce, we create a
class, if there be any things, real or imaginary, to compose it; that is,
any Things corresponding to the signification of the name. Classes,
therefore, mostly owe their existence to general language. But general
language, also, though that is not the most common case, sometimes owes
its existence to classes. A general, which is as much as to say a
significant, name, is indeed mostly introduced because we have a
signification to express by it; because we need a word by means of which
to predicate the attributes which it connotes. But it is also true that a
name is sometimes introduced because we have found it convenient to create
a class; because we have thought it useful for the regulation of our
mental operations, that a certain group of objects should be thought of
together. A naturalist, for purposes connected with his particular
science, sees reason to distribute the animal or vegetable creation into
certain groups rather than into any others, and he requires a name to
bind, as it were, each of his groups together. It must not, however, be
supposed that such names, when introduced, differ in any respect, as to
their mode of signification, from other connotative names. The classes
which they denote are, as much as any other classes, constituted by
certain common attributes, and their names are significant of those
attributes, and of nothing else. The names of Cuvier’s classes and orders,
_Plantigrades_, _Digitigrades_, etc., are as much the expression of
attributes as if those names had preceded, instead of grown out of, his
classification of animals. The only peculiarity of the case is, that the
convenience of classification was here the primary motive for introducing
the names; while in other cases the name is introduced as a means of
predication, and the formation of a class denoted by it is only an
indirect consequence.

The principles which ought to regulate Classification, as a logical
process subservient to the investigation of truth, can not be discussed to
any purpose until a much later stage of our inquiry. But, of
Classification as resulting from, and implied in, the fact of employing
general language, we can not forbear to treat here, without leaving the
theory of general names, and of their employment in predication, mutilated
and formless.

§ 2. This portion of the theory of general language is the subject of what
is termed the doctrine of the Predicables; a set of distinctions handed
down from Aristotle, and his follower Porphyry, many of which have taken a
firm root in scientific, and some of them even in popular, phraseology.
The predicables are a fivefold division of General Names, not grounded as
usual on a difference in their meaning, that is, in the attribute which
they connote, but on a difference in the kind of class which they denote.
We may predicate of a thing five different varieties of class-name:

A _genus_ of the thing: (γὲνος).
A _species_: (εἶσος).
A _differentia_: (διαφορὰ).
A _proprium_: (ἰδιών).
An _accidens_: (συμβεβηκός).

It is to be remarked of these distinctions, that they express, not what
the predicate is in its own meaning, but what relation it bears to the
subject of which it happens on the particular occasion to be predicated.
There are not some names which are exclusively genera, and others which
are exclusively species, or differentiæ; but the same name is referred to
one or another predicable, according to the subject of which it is
predicated on the particular occasion. _Animal_, for instance, is a genus
with respect to man, or John; a species with respect to Substance, or
Being. _Rectangular_ is one of the Differentiæ of a geometrical square; it
is merely one of the Accidentia of the table at which I am writing. The
words genus, species, etc., are therefore relative terms; they are names
applied to certain predicates, to express the relation between them and
some given subject: a relation grounded, as we shall see, not on what the
predicate connotes, but on the class which it denotes, and on the place
which, in some given classification, that class occupies relatively to the
particular subject.

§ 3. Of these five names, two, Genus and Species, are not only used by
naturalists in a technical acceptation not precisely agreeing with their
philosophical meaning, but have also acquired a popular acceptation, much
more general than either. In this popular sense any two classes, one of
which includes the whole of the other and more, may be called a Genus and
a Species. Such, for instance, are Animal and Man; Man and Mathematician.
Animal is a Genus; Man and Brute are its two species; or we may divide it
into a greater number of species, as man, horse, dog, etc. _Biped_, or
_two-footed animal_, may also be considered a genus, of which man and bird
are two species. _Taste_ is a genus, of which sweet taste, sour taste,
salt taste, etc., are species. _Virtue_ is a genus; justice, prudence,
courage, fortitude, generosity, etc., are its species.

The same class which is a genus with reference to the sub-classes or
species included in it, may be itself a species with reference to a more
comprehensive, or, as it is often called, a superior genus. Man is a
species with reference to animal, but a genus with reference to the
species Mathematician. Animal is a genus, divided into two species, man
and brute; but animal is also a species, which, with another species,
vegetable, makes up the genus, organized being. Biped is a genus with
reference to man and bird, but a species with respect to the superior
genus, animal. Taste is a genus divided into species, but also a species
of the genus sensation. Virtue, a genus with reference to justice,
temperance, etc., is one of the species of the genus, mental quality.

In this popular sense the words Genus and Species have passed into common
discourse. And it should be observed that in ordinary parlance, not the
name of the class, but the class itself, is said to be the genus or
species; not, of course, the class in the sense of each individual of the
class, but the individuals collectively, considered as an aggregate whole;
the name by which the class is designated being then called not the genus
or species, but the generic or specific name. And this is an admissible
form of expression; nor is it of any importance which of the two modes of
speaking we adopt, provided the rest of our language is consistent with
it; but, if we call the class itself the genus, we must not talk of
predicating the genus. We predicate of man the _name_ mortal; and by
predicating the name, we may be said, in an intelligible sense, to
predicate what the name expresses, the _attribute_ mortality; but in no
allowable sense of the word predication do we predicate of man the _class_
mortal. We predicate of him the fact of belonging to the class.

By the Aristotelian logicians, the terms genus and species were used in a
more restricted sense. They did not admit every class which could be
divided into other classes to be a genus, or every class which could be
included in a larger class to be a species. Animal was by them considered
a genus; man and brute co-ordinate species under that genus: _biped_,
however, would not have been admitted to be a genus with reference to man,
but a _proprium_ or _accidens_ only. It was requisite, according to their
theory, that genus and species should be of the _essence_ of the subject.
Animal was of the essence of man; biped was not. And in every
classification they considered some one class as the lowest or _infima_
species. Man, for instance, was a lowest species. Any further divisions
into which the class might be capable of being broken down, as man into
white, black, and red man, or into priest and layman, they did not admit
to be species.

It has been seen, however, in the preceding chapter, that the distinction
between the essence of a class, and the attributes or properties which are
not of its essence—a distinction which has given occasion to so much
abstruse speculation, and to which so mysterious a character was formerly,
and by many writers is still, attached—amounts to nothing more than the
difference between those attributes of the class which are, and those
which are not, involved in the signification of the class-name. As applied
to individuals, the word Essence, we found, has no meaning, except in
connection with the exploded tenets of the Realists; and what the
schoolmen chose to call the essence of an individual, was simply the
essence of the class to which that individual was most familiarly
referred.

Is there no difference, then, save this merely verbal one, between the
classes which the schoolmen admitted to be genera or species, and those to
which they refused the title? Is it an error to regard some of the
differences which exist among objects as differences _in kind_ (_genere_
or _specie_), and others only as differences in the accidents? Were the
schoolmen right or wrong in giving to some of the classes into which
things may be divided, the name of _kinds_, and considering others as
secondary divisions, grounded on differences of a comparatively
superficial nature? Examination will show that the Aristotelians did mean
something by this distinction, and something important; but which, being
but indistinctly conceived, was inadequately expressed by the phraseology
of essences, and the various other modes of speech to which they had
recourse.

§ 4. It is a fundamental principle in logic, that the power of framing
classes is unlimited, as long as there is any (even the smallest)
difference to found a distinction upon. Take any attribute whatever, and
if some things have it, and others have not, we may ground on the
attribute a division of all things into two classes; and we actually do
so, the moment we create a name which connotes the attribute. The number
of possible classes, therefore, is boundless; and there are as many actual
classes (either of real or of imaginary things) as there are general
names, positive and negative together.

But if we contemplate any one of the classes so formed, such as the class
animal or plant, or the class sulphur or phosphorus, or the class white or
red, and consider in what particulars the individuals included in the
class differ from those which do not come within it, we find a very
remarkable diversity in this respect between some classes and others.
There are some classes, the things contained in which differ from other
things only in certain particulars which may be numbered, while others
differ in more than can be numbered, more even than we need ever expect to
know. Some classes have little or nothing in common to characterize them
by, except precisely what is connoted by the name: white things, for
example, are not distinguished by any common properties except whiteness;
or if they are, it is only by such as are in some way dependent on, or
connected with, whiteness. But a hundred generations have not exhausted
the common properties of animals or of plants, of sulphur or of
phosphorus; nor do we suppose them to be exhaustible, but proceed to new
observations and experiments, in the full confidence of discovering new
properties which were by no means implied in those we previously knew.
While, if any one were to propose for investigation the common properties
of all things which are of the same color, the same shape, or the same
specific gravity, the absurdity would be palpable. We have no ground to
believe that any such common properties exist, except such as may be shown
to be involved in the supposition itself, or to be derivable from it by
some law of causation. It appears, therefore, that the properties, on
which we ground our classes, sometimes exhaust all that the class has in
common, or contain it all by some mode of implication; but in other
instances we make a selection of a few properties from among not only a
greater number, but a number inexhaustible by us, and to which as we know
no bounds, they may, so far as we are concerned, be regarded as infinite.

There is no impropriety in saying that, of these two classifications, the
one answers to a much more radical distinction in the things themselves,
than the other does. And if any one even chooses to say that the one
classification is made by nature, the other by us for our convenience, he
will be right; provided he means no more than this: Where a certain
apparent difference between things (though perhaps in itself of little
moment) answers to we know not what number of other differences, pervading
not only their known properties, but properties yet undiscovered, it is
not optional but imperative to recognize this difference as the foundation
of a specific distinction; while, on the contrary, differences that are
merely finite and determinate, like those designated by the words white,
black, or red, may be disregarded if the purpose for which the
classification is made does not require attention to those particular
properties. The differences, however, are made by nature, in both cases;
while the recognition of those differences as grounds of classification
and of naming, is, equally in both cases, the act of man: only in the one
case, the ends of language and of classification would be subverted if no
notice were taken of the difference, while in the other case, the
necessity of taking notice of it depends on the importance or unimportance
of the particular qualities in which the difference happens to consist.

Now, these classes, distinguished by unknown multitudes of properties, and
not solely by a few determinate ones—which are parted off from one another
by an unfathomable chasm, instead of a mere ordinary ditch with a visible
bottom—are the only classes which, by the Aristotelian logicians, were
considered as genera or species. Differences which extended only to a
certain property or properties, and there terminated, they considered as
differences only in the _accidents_ of things; but where any class
differed from other things by an infinite series of differences, known and
unknown, they considered the distinction as one of _kind_, and spoke of it
as being an _essential_ difference, which is also one of the current
meanings of that vague expression at the present day.

Conceiving the schoolmen to have been justified in drawing a broad line of
separation between these two kinds of classes and of class-distinctions, I
shall not only retain the division itself, but continue to express it in
their language. According to that language, the proximate (or lowest) Kind
to which any individual is referrible, is called its species. Conformably
to this, Isaac Newton would be said to be of the species man. There are
indeed numerous sub-classes included in the class man, to which Newton
also belongs; for example, Christian, and Englishman, and Mathematician.
But these, though distinct classes, are not, in our sense of the term,
distinct Kinds of men. A Christian, for example, differs from other human
beings; but he differs only in the attribute which the word expresses,
namely, belief in Christianity, and whatever else that implies, either as
involved in the fact itself, or connected with it through some law of
cause and effect. We should never think of inquiring what properties,
unconnected with Christianity, either as cause or effect, are common to
all Christians and peculiar to them; while in regard to all Men,
physiologists are perpetually carrying on such an inquiry; nor is the
answer ever likely to be completed. Man, therefore, we may call a species;
Christian, or Mathematician, we can not.

Note here, that it is by no means intended to imply that there may not be
different Kinds, or logical species, of man. The various races and
temperaments, the two sexes, and even the various ages, may be differences
of kind, within our meaning of the term. I do not say that they are so.
For in the progress of physiology it may almost be said to be made out,
that the differences which really exist between different races, sexes,
etc., follow as consequences, under laws of nature, from a small number of
primary differences which can be precisely determined, and which, as the
phrase is, _account for_ all the rest. If this be so, these are not
distinctions in kind; no more than Christian, Jew, Mussulman, and Pagan, a
difference which also carries many consequences along with it. And in this
way classes are often mistaken for real Kinds, which are afterward proved
not to be so. But if it turned out that the differences were not capable
of being thus accounted for, then Caucasian, Mongolian, Negro, etc., would
be really different Kinds of human beings, and entitled to be ranked as
species by the logician; though not by the naturalist. For (as already
noticed) the word species is used in a different signification in logic
and in natural history. By the naturalist, organized beings are not
usually said to be of different species, if it is supposed that they have
descended from the same stock. That, however, is a sense artificially
given to the word, for the technical purposes of a particular science. To
the logician, if a negro and a white man differ in the same manner
(however less in degree) as a horse and a camel do, that is, if their
differences are inexhaustible, and not referrible to any common cause,
they are different species, whether they are descended from common
ancestors or not. But if their differences can all be traced to climate
and habits, or to some one or a few special differences in structure, they
are not, in the logician’s view, specifically distinct.

When the _infima species_, or proximate Kind, to which an individual
belongs, has been ascertained, the properties common to that Kind include
necessarily the whole of the common properties of every other real Kind to
which the individual can be referrible. Let the individual, for example,
be Socrates, and the proximate Kind, man. Animal, or living creature, is
also a real kind, and includes Socrates; but, since it likewise includes
man, or in other words, since all men are animals, the properties common
to animals form a portion of the common properties of the sub-class, man.
And if there be any class which includes Socrates without including man,
that class is not a real Kind. Let the class, for example, be
_flat-nosed_; that being a class which includes Socrates, without
including all men. To determine whether it is a real Kind, we must ask
ourselves this question: Have all flat-nosed animals, in addition to
whatever is implied in their flat noses, any common properties, other than
those which are common to all animals whatever? If they had; if a flat
nose were a mark or index to an indefinite number of other peculiarities,
not deducible from the former by an ascertainable law, then out of the
class man we might cut another class, flat-nosed man, which, according to
our definition, would be a Kind. But if we could do this, man would not
be, as it was assumed to be, the proximate Kind. Therefore, the properties
of the proximate Kind do comprehend those (whether known or unknown) of
all other Kinds to which the individual belongs; which was the point we
undertook to prove. And hence, every other Kind which is predicable of the
individual, will be to the proximate Kind in the relation of a genus,
according to even the popular acceptation of the terms genus and species;
that is, it will be a larger class, including it and more.

We are now able to fix the logical meaning of these terms. Every class
which is a real Kind, that is, which is distinguished from all other
classes by an indeterminate multitude of properties not derivable from one
another, is either a genus or a species. A Kind which is not divisible
into other Kinds, can not be a genus, because it has no species under it;
but it is itself a species, both with reference to the individuals below
and to the genera above (Species Prædicabilis and Species Subjicibilis).
But every Kind which admits of division into real Kinds (as animal into
mammal, bird, fish, etc., or bird into various species of birds) is a
genus to all below it, a species to all genera in which it is itself
included. And here we may close this part of the discussion, and pass to
the three remaining predicables, Differentia, Proprium, and Accidens.

§ 5. To begin with Differentia. This word is correlative with the words
genus and species, and as all admit, it signifies the attribute which
distinguishes a given species from every other species of the same genus.
This is so far clear: but we may still ask, which of the distinguishing
attributes it signifies. For we have seen that every Kind (and a species
must be a Kind) is distinguished from other Kinds, not by any one
attribute, but by an indefinite number. Man, for instance, is a species of
the genus animal: Rational (or rationality, for it is of no consequence
here whether we use the concrete or the abstract form) is generally
assigned by logicians as the Differentia; and doubtless this attribute
serves the purpose of distinction: but it has also been remarked of man,
that he is a cooking animal; the only animal that dresses its food. This,
therefore, is another of the attributes by which the species man is
distinguished from other species of the same genus: would this attribute
serve equally well for a differentia? The Aristotelians say No; having
laid it down that the differentia must, like the genus and species, be of
the _essence_ of the subject.

And here we lose even that vestige of a meaning grounded in the nature of
the things themselves, which may be supposed to be attached to the word
essence when it is said that genus and species must be of the essence of
the thing. There can be no doubt that when the schoolmen talked of the
essences of things as opposed to their accidents, they had confusedly in
view the distinction between differences of kind, and the differences
which are not of kind; they meant to intimate that genera and species must
be Kinds. Their notion of the essence of a thing was a vague notion of a
something which makes it what it is, _i.e._, which makes it the Kind of
thing that it is—which causes it to have all that variety of properties
which distinguish its Kind. But when the matter came to be looked at more
closely, nobody could discover what caused the thing to have all those
properties, nor even that there was any thing which caused it to have
them. Logicians, however, not liking to admit this, and being unable to
detect what made the thing to be what it was, satisfied themselves with
what made it to be what it was called. Of the innumerable properties,
known and unknown, that are common to the class man, a portion only, and
of course a very small portion, are connoted by its name; these few,
however, will naturally have been thus distinguished from the rest either
for their greater obviousness, or for greater supposed importance. These
properties, then, which were connoted by the name, logicians seized upon,
and called them the essence of the species; and not stopping there, they
affirmed them, in the case of the _infima species_, to be the essence of
the individual too; for it was their maxim, that the species contained the
“whole essence” of the thing. Metaphysics, that fertile field of delusion
propagated by language, does not afford a more signal instance of such
delusion. On this account it was that rationality, being connoted by the
name man, was allowed to be a differentia of the class; but the
peculiarity of cooking their food, not being connoted, was relegated to
the class of accidental properties.

The distinction, therefore, between Differentia, Proprium, and Accidens,
is not grounded in the nature of things, but in the connotation of names;
and we must seek it there, if we wish to find what it is.

From the fact that the genus includes the species, in other words
_de_notes more than the species, or is predicable of a greater number of
individuals, it follows that the species must connote more than the genus.
It must connote all the attributes which the genus connotes, or there
would be nothing to prevent it from denoting individuals not included in
the genus. And it must connote something besides, otherwise it would
include the whole genus. Animal denotes all the individuals denoted by
man, and many more. Man, therefore, must connote all that animal connotes,
otherwise there might be men who are not animals; and it must connote
something more than animal connotes, otherwise all animals would be men.
This surplus of connotation—this which the species connotes over and above
the connotation of the genus—is the Differentia, or specific difference;
or, to state the same proposition in other words, the Differentia is that
which must be added to the connotation of the genus, to complete the
connotation of the species.

The word man, for instance, exclusively of what it connotes in common with
animal, also connotes rationality, and at least some approximation to that
external form which we all know, but which as we have no name for it
considered in itself, we are content to call the human. The Differentia,
or specific difference, therefore, of man, as referred to the genus
animal, is that outward form and the possession of reason. The
Aristotelians said, the possession of reason, without the outward form.
But if they adhered to this, they would have been obliged to call the
Houyhnhnms men. The question never arose, and they were never called upon
to decide how such a case would have affected their notion of
essentiality. However this may be, they were satisfied with taking such a
portion of the differentia as sufficed to distinguish the species from all
other _existing_ things, though by so doing they might not exhaust the
connotation of the name.

§ 6. And here, to prevent the notion of differentia from being restricted
within too narrow limits, it is necessary to remark, that a species, even
as referred to the same genus, will not always have the same differentia,
but a different one, according to the principle and purpose which preside
over the particular classification. For example, a naturalist surveys the
various kinds of animals, and looks out for the classification of them
most in accordance with the order in which, for zoological purposes, he
considers it desirable that we should think of them. With this view he
finds it advisable that one of his fundamental divisions should be into
warm-blooded and cold-blooded animals; or into animals which breathe with
lungs and those which breathe with gills; or into carnivorous, and
frugivorous or graminivorous; or into those which walk on the flat part
and those which walk on the extremity of the foot, a distinction on which
two of Cuvier’s families are founded. In doing this, the naturalist
creates as many new classes; which are by no means those to which the
individual animal is familiarly and spontaneously referred; nor should we
ever think of assigning to them so prominent a position in our arrangement
of the animal kingdom, unless for a preconceived purpose of scientific
convenience. And to the liberty of doing this there is no limit. In the
examples we have given, most of the classes are real Kinds, since each of
the peculiarities is an index to a multitude of properties belonging to
the class which it characterizes: but even if the case were otherwise—if
the other properties of those classes could all be derived, by any process
known to us, from the one peculiarity on which the class is founded—even
then, if these derivative properties were of primary importance for the
purposes of the naturalist, he would be warranted in founding his primary
divisions on them.

If, however, practical convenience is a sufficient warrant for making the
main demarcations in our arrangement of objects run in lines not
coinciding with any distinction of Kind, and so creating genera and
species in the popular sense which are not genera or species in the
rigorous sense at all; _à fortiori_ must we be warranted, when our genera
and species _are_ real genera and species, in marking the distinction
between them by those of their properties which considerations of
practical convenience most strongly recommend. If we cut a species out of
a given genus—the species man, for instance, out of the genus animal—with
an intention on our part that the peculiarity by which we are to be guided
in the application of the name man should be rationality, then rationality
is the differentia of the species man. Suppose, however, that being
naturalists, we, for the purposes of our particular study, cut out of the
genus animal the same species man, but with an intention that the
distinction between man and all other species of animal should be, not
rationality, but the possession of “four incisors in each jaw, tusks
solitary, and erect posture.” It is evident that the word man, when used
by us as naturalists, no longer connotes rationality, but connotes the
three other properties specified; for that which we have expressly in view
when we impose a name, assuredly forms part of the meaning of that name.
We may, therefore, lay it down as a maxim, that wherever there is a Genus,
and a Species marked out from that genus by an assignable differentia, the
name of the species must be connotative, and must connote the differentia;
but the connotation may be special—not involved in the signification of
the term as ordinarily used, but given to it when employed as a term of
art or science. The word Man in common use, connotes rationality and a
certain form, but does not connote the number or character of the teeth;
in the Linnæan system it connotes the number of incisor and canine teeth,
but does not connote rationality nor any particular form. The word _man_
has, therefore, two different meanings; though not commonly considered as
ambiguous, because it happens in both cases to _de_note the same
individual objects. But a case is conceivable in which the ambiguity would
become evident: we have only to imagine that some new kind of animal were
discovered, having Linnæus’s three characteristics of humanity, but not
rational, or not of the human form. In ordinary parlance, these animals
would not be called men; but in natural history they must still be called
so by those, if any there should be, who adhere to the Linnæan
classification; and the question would arise, whether the word should
continue to be used in two senses, or the classification be given up, and
the technical sense of the term be abandoned along with it.

Words not otherwise connotative may, in the mode just adverted to, acquire
a special or technical connotation. Thus the word whiteness, as we have so
often remarked, connotes nothing; it merely denotes the attribute
corresponding to a certain sensation: but if we are making a
classification of colors, and desire to justify, or even merely to point
out, the particular place assigned to whiteness in our arrangement, we may
define it “the color produced by the mixture of all the simple rays;” and
this fact, though by no means implied in the meaning of the word whiteness
as ordinarily used, but only known by subsequent scientific investigation,
is part of its meaning in the particular essay or treatise, and becomes
the differentia of the species.(42)

The differentia, therefore, of a species may be defined to be, that part
of the connotation of the specific name, whether ordinary or special and
technical, which distinguishes the species in question from all other
species of the genus to which on the particular occasion we are referring
it.

§ 7. Having disposed of Genus, Species, and Differentia, we shall not find
much difficulty in attaining a clear conception of the distinction between
the other two predicables, as well as between them and the first three.

In the Aristotelian phraseology, Genus and Differentia are of the
_essence_ of the subject; by which, as we have seen, is really meant that
the properties signified by the genus and those signified by the
differentia, form part of the connotation of the name denoting the
species. Proprium and Accidens, on the other hand, form no part of the
essence, but are predicated of the species only _accidentally_. Both are
Accidents, in the wider sense in which the accidents of a thing are
opposed to its essence; though, in the doctrine of the Predicables,
Accidens is used for one sort of accident only, Proprium being another
sort. Proprium, continue the schoolmen, is predicated _accidentally_,
indeed, but _necessarily_; or, as they further explain it, signifies an
attribute which is not indeed part of the essence, but which flows from,
or is a consequence of, the essence, and is, therefore, inseparably
attached to the species; _e.g._, the various properties of a triangle,
which, though no part of its definition, must necessarily be possessed by
whatever comes under that definition. Accidens, on the contrary, has no
connection whatever with the essence, but may come and go, and the species
still remain what it was before. If a species could exist without its
Propria, it must be capable of existing without that on which its Propria
are necessarily consequent, and therefore without its essence, without
that which constitutes it a species. But an Accidens, whether separable or
inseparable from the species in actual experience, may be supposed
separated, without the necessity of supposing any other alteration; or at
least, without supposing any of the essential properties of the species to
be altered, since with them an Accidens has no connection.

A Proprium, therefore, of the species, may be defined, any attribute which
belongs to all the individuals included in the species, and which, though
not connoted by the specific name (either ordinarily if the classification
we are considering be for ordinary purposes, or specially if it be for a
special purpose), yet follows from some attribute which the name either
ordinarily or specially connotes.

One attribute may follow from another in two ways; and there are
consequently two kinds of Proprium. It may follow as a conclusion follows
premises, or it may follow as an effect follows a cause. Thus, the
attribute of having the opposite sides equal, which is not one of those
connoted by the word Parallelogram, nevertheless follows from those
connoted by it, namely, from having the opposite sides straight lines and
parallel, and the number of sides four. The attribute, therefore, of
having the opposite sides equal, is a Proprium of the class parallelogram;
and a Proprium of the first kind, which follows from the connoted
attributes by way of _demonstration_. The attribute of being capable of
understanding language, is a Proprium of the species man, since without
being connoted by the word, it follows from an attribute which the word
does connote, viz., from the attribute of rationality. But this is a
Proprium of the second kind, which follows by way of _causation_. How it
is that one property of a thing follows, or can be inferred, from another;
under what conditions this is possible, and what is the exact meaning of
the phrase; are among the questions which will occupy us in the two
succeeding Books. At present it needs only be said, that whether a
Proprium follows by demonstration or by causation, it follows
_necessarily_; that is to say, its not following would be inconsistent
with some law which we regard as a part of the constitution either of our
thinking faculty or of the universe.

§ 8. Under the remaining predicable, Accidens, are included all attributes
of a thing which are neither involved in the signification of the name
(whether ordinarily or as a term of art), nor have, so far as we know, any
necessary connection with attributes which are so involved. They are
commonly divided into Separable and Inseparable Accidents. Inseparable
accidents are those which—although we know of no connection between them
and the attributes constitutive of the species, and although, therefore,
so far as we are aware, they might be absent without making the name
inapplicable and the species a different species—are yet never in fact
known to be absent. A concise mode of expressing the same meaning is, that
inseparable accidents are properties which are universal to the species,
but not necessary to it. Thus, blackness is an attribute of a crow, and,
as far as we know, a universal one. But if we were to discover a race of
white birds, in other respects resembling crows, we should not say, These
are not crows; we should say, These are white crows. Crow, therefore, does
not connote blackness; nor, from any of the attributes which it does
connote, whether as a word in popular use or as a term of art, could
blackness be inferred. Not only, therefore, can we conceive a white crow,
but we know of no reason why such an animal should not exist. Since,
however, none but black crows are known to exist, blackness, in the
present state of our knowledge, ranks as an accident, but an inseparable
accident, of the species crow.

Separable Accidents are those which are found, in point of fact, to be
sometimes absent from the species; which are not only not necessary, but
not even universal. They are such as do not belong to every individual of
the species, but only to some individuals; or if to all, not at all times.
Thus the color of a European is one of the separable accidents of the
species man, because it is not an attribute of all human creatures. Being
born, is also (speaking in the logical sense) a separable accident of the
species man, because, though an attribute of all human beings, it is so
only at one particular time. _A fortiori_ those attributes which are not
constant even in the same individual, as, to be in one or in another
place, to be hot or cold, sitting or walking, must be ranked as separable
accidents.




                              Chapter VIII.


Of Definition.


§ 1. One necessary part of the theory of Names and of Propositions remains
to be treated of in this place: the theory of Definitions. As being the
most important of the class of propositions which we have characterized as
purely verbal, they have already received some notice in the chapter
preceding the last. But their fuller treatment was at that time postponed,
because definition is so closely connected with classification, that,
until the nature of the latter process is in some measure understood, the
former can not be discussed to much purpose.

The simplest and most correct notion of a Definition is, a proposition
declaratory of the meaning of a word; namely, either the meaning which it
bears in common acceptation, or that which the speaker or writer, for the
particular purposes of his discourse, intends to annex to it.

The definition of a word being the proposition which enunciates its
meaning, words which have no meaning are unsusceptible of definition.
Proper names, therefore, can not be defined. A proper name being a mere
mark put upon an individual, and of which it is the characteristic
property to be destitute of meaning, its meaning can not of course be
declared; though we may indicate by language, as we might indicate still
more conveniently by pointing with the finger, upon what individual that
particular mark has been, or is intended to be, put. It is no definition
of “John Thomson” to say he is “the son of General Thomson;” for the name
John Thomson does not express this. Neither is it any definition of “John
Thomson” to say he is “the man now crossing the street.” These
propositions may serve to make known who is the particular man to whom the
name belongs, but that may be done still more unambiguously by pointing to
him, which, however, has not been esteemed one of the modes of definition.

In the case of connotative names, the meaning, as has been so often
observed, is the connotation; and the definition of a connotative name, is
the proposition which declares its connotation. This might be done either
directly or indirectly. The direct mode would be by a proposition in this
form: “Man” (or whatsoever the word may be) “is a name connoting such and
such attributes,” or “is a name which, when predicated of any thing,
signifies the possession of such and such attributes by that thing.” Or
thus: Man is every thing which possesses such and such attributes: Man is
every thing which possesses corporeity, organization, life, rationality,
and certain peculiarities of external form.

This form of definition is the most precise and least equivocal of any;
but it is not brief enough, and is besides too technical for common
discourse. The more usual mode of declaring the connotation of a name, is
to predicate of it another name or names of known signification, which
connote the same aggregation of attributes. This may be done either by
predicating of the name intended to be defined, another connotative name
exactly synonymous, as, “Man is a human being,” which is not commonly
accounted a definition at all; or by predicating two or more connotative
names, which make up among them the whole connotation of the name to be
defined. In this last case, again, we may either compose our definition of
as many connotative names as there are attributes, each attribute being
connoted by one, as, Man is a corporeal, organized, animated, rational
being, shaped so and so; or we employ names which connote several of the
attributes at once, as, Man is a rational _animal_, shaped so and so.

The definition of a name, according to this view of it, is the sum total
of all the _essential_ propositions which can be framed with that name for
their subject. All propositions the truth of which is implied in the name,
all those which we are made aware of by merely hearing the name, are
included in the definition, if complete, and may be evolved from it
without the aid of any other premises; whether the definition expresses
them in two or three words, or in a larger number. It is, therefore, not
without reason that Condillac and other writers have affirmed a definition
to be an _analysis_. To resolve any complex whole into the elements of
which it is compounded, is the meaning of analysis: and this we do when we
replace one word which connotes a set of attributes collectively, by two
or more which connote the same attributes singly, or in smaller groups.

§ 2. From this, however, the question naturally arises, in what manner are
we to define a name which connotes only a single attribute: for instance,
“white,” which connotes nothing but whiteness; “rational,” which connotes
nothing but the possession of reason. It might seem that the meaning of
such names could only be declared in two ways; by a synonymous term, if
any such can be found; or in the direct way already alluded to: “White is
a name connoting the attribute whiteness.” Let us see, however, whether
the analysis of the meaning of the name, that is, the breaking down of
that meaning into several parts, admits of being carried farther. Without
at present deciding this question as to the word _white_, it is obvious
that in the case of _rational_ some further explanation may be given of
its meaning than is contained in the proposition, “Rational is that which
possesses the attribute of reason;” since the attribute reason itself
admits of being defined. And here we must turn our attention to the
definitions of attributes, or rather of the names of attributes, that is,
of abstract names.

In regard to such names of attributes as are connotative, and express
attributes of those attributes, there is no difficulty: like other
connotative names, they are defined by declaring their connotation. Thus
the word _fault_ may be defined, “a quality productive of evil or
inconvenience.” Sometimes, again, the attribute to be defined is not one
attribute, but a union of several: we have only, therefore, to put
together the names of all the attributes taken separately, and we obtain
the definition of the name which belongs to them all taken together; a
definition which will correspond exactly to that of the corresponding
concrete name. For, as we define a concrete name by enumerating the
attributes which it connotes, and as the attributes connoted by a concrete
name form the entire signification of the corresponding abstract name, the
same enumeration will serve for the definition of both. Thus, if the
definition of a _human being_ be this, “a being, corporeal, animated,
rational, shaped so and so,” the definition of _humanity_ will be
corporeity and animal life, combined with rationality, and with such and
such a shape.

When, on the other hand, the abstract name does not express a complication
of attributes, but a single attribute, we must remember that every
attribute is grounded on some fact or phenomenon, from which, and which
alone, it derives its meaning. To that fact or phenomenon, called in a
former chapter the foundation of the attribute, we must, therefore, have
recourse for its definition. Now, the foundation of the attribute may be a
phenomenon of any degree of complexity, consisting of many different
parts, either co-existent or in succession. To obtain a definition of the
attribute, we must analyze the phenomenon into these parts. Eloquence, for
example, is the name of one attribute only; but this attribute is grounded
on external effects of a complicated nature, flowing from acts of the
person to whom we ascribe the attribute; and by resolving this phenomenon
of causation into its two parts, the cause and the effect, we obtain a
definition of eloquence, viz. the power of influencing the feelings by
speech or writing.

A name, therefore, whether concrete or abstract, admits of definition,
provided we are able to analyze, that is, to distinguish into parts, the
attribute or set of attributes which constitute the meaning both of the
concrete name and of the corresponding abstract: if a set of attributes,
by enumerating them; if a single attribute, by dissecting the fact or
phenomenon (whether of perception or of internal consciousness) which is
the foundation of the attribute. But, further, even when the fact is one
of our simple feelings or states of consciousness, and therefore
unsusceptible of analysis, the names both of the object and of the
attribute still admit of definition; or rather, would do so if all our
simple feelings had names. Whiteness may be defined, the property or power
of exciting the sensation of white. A white object may be defined, an
object which excites the sensation of white. The only names which are
unsusceptible of definition, because their meaning is unsusceptible of
analysis, are the names of the simple feelings themselves. These are in
the same condition as proper names. They are not indeed, like proper
names, unmeaning; for the words _sensation of white_ signify, that the
sensation which I so denominate resembles other sensations which I
remember to have had before, and to have called by that name. But as we
have no words by which to recall those former sensations, except the very
word which we seek to define, or some other which, being exactly
synonymous with it, requires definition as much, words can not unfold the
signification of this class of names; and we are obliged to make a direct
appeal to the personal experience of the individual whom we address.

§ 3. Having stated what seems to be the true idea of a Definition, I
proceed to examine some opinions of philosophers, and some popular
conceptions on the subject, which conflict more or less with that idea.

The only adequate definition of a name is, as already remarked, one which
declares the facts, and the whole of the facts, which the name involves in
its signification. But with most persons the object of a definition does
not embrace so much; they look for nothing more, in a definition, than a
guide to the correct use of the term—a protection against applying it in a
manner inconsistent with custom and convention. Any thing, therefore, is
to them a sufficient definition of a term, which will serve as a correct
index to what the term _de_notes; though not embracing the whole, and
sometimes, perhaps, not even any part, of what it connotes. This gives
rise to two sorts of imperfect, or unscientific definition; Essential but
incomplete Definitions, and Accidental Definitions, or Descriptions. In
the former, a connotative name is defined by a part only of its
connotation; in the latter, by something which forms no part of the
connotation at all.

An example of the first kind of imperfect definitions is the following:
Man is a rational animal. It is impossible to consider this as a complete
definition of the word Man, since (as before remarked) if we adhered to it
we should be obliged to call the Houyhnhnms men; but as there happen to be
no Houyhnhnms, this imperfect definition is sufficient to mark out and
distinguish from all other things, the objects at present denoted by
“man;” all the beings actually known to exist, of whom the name is
predicable. Though the word is defined by some only among the attributes
which it connotes, not by all, it happens that all known objects which
possess the enumerated attributes, possess also those which are omitted;
so that the field of predication which the word covers, and the employment
of it which is conformable to usage, are as well indicated by the
inadequate definition as by an adequate one. Such definitions, however,
are always liable to be overthrown by the discovery of new objects in
nature.

Definitions of this kind are what logicians have had in view, when they
laid down the rule, that the definition of a species should be _per genus
et differentiam_. Differentia being seldom taken to mean the whole of the
peculiarities constitutive of the species, but some one of those
peculiarities only, a complete definition would be _per genus et
differentias_, rather than _differentiam_. It would include, with the name
of the superior genus, not merely _some_ attribute which distinguishes the
species intended to be defined from all other species of the same genus,
but _all_ the attributes implied in the name of the species, which the
name of the superior genus has not already implied. The assertion,
however, that a definition must of necessity consist of a genus and
differentiæ, is not tenable. It was early remarked by logicians, that the
_summum genus_ in any classification, having no genus superior to itself,
could not be defined in this manner. Yet we have seen that all names,
except those of our elementary feelings, are susceptible of definition in
the strictest sense; by setting forth in words the constituent parts of
the fact or phenomenon, of which the connotation of every word is
ultimately composed.

§ 4. Although the first kind of imperfect definition (which defines a
connotative term by a part only of what it connotes, but a part sufficient
to mark out correctly the boundaries of its denotation), has been
considered by the ancients, and by logicians in general, as a complete
definition; it has always been deemed necessary that the attributes
employed should really form part of the connotation; for the rule was that
the definition must be drawn from the _essence_ of the class; and this
would not have been the case if it had been in any degree made up of
attributes not connoted by the name. The second kind of imperfect
definition, therefore, in which the name of a class is defined by any of
its accidents—that is, by attributes which are not included in its
connotation—has been rejected from the rank of genuine Definition by all
logicians, and has been termed Description.

This kind of imperfect definition, however, takes its rise from the same
cause as the other, namely, the willingness to accept as a definition any
thing which, whether it expounds the meaning of the name or not, enables
us to discriminate the things denoted by the name from all other things,
and consequently to employ the term in predication without deviating from
established usage. This purpose is duly answered by stating any (no matter
what) of the attributes which are common to the whole of the class, and
peculiar to it; or any combination of attributes which happens to be
peculiar to it, though separately each of those attributes may be common
to it with some other things. It is only necessary that the definition (or
description) thus formed, should be _convertible_ with the name which it
professes to define; that is, should be exactly co-extensive with it,
being predicable of every thing of which it is predicable, and of nothing
of which it is not predicable; though the attributes specified may have no
connection with those which mankind had in view when they formed or
recognized the class, and gave it a name. The following are correct
definitions of Man, according to this test: Man is a mammiferous animal,
having (by nature) two hands (for the human species answers to this
description, and no other animal does): Man is an animal who cooks his
food: Man is a featherless biped.

What would otherwise be a mere description, may be raised to the rank of a
real definition by the peculiar purpose which the speaker or writer has in
view. As was seen in the preceding chapter, it may, for the ends of a
particular art or science, or for the more convenient statement of an
author’s particular doctrines, be advisable to give to some general name,
without altering its denotation, a special connotation, different from its
ordinary one. When this is done, a definition of the name by means of the
attributes which make up the special connotation, though in general a mere
accidental definition or description, becomes on the particular occasion
and for the particular purpose a complete and genuine definition. This
actually occurs with respect to one of the preceding examples, “Man is a
mammiferous animal having two hands,” which is the scientific definition
of man, considered as one of the species in Cuvier’s distribution of the
animal kingdom.

In cases of this sort, though the definition is still a declaration of the
meaning which in the particular instance the name is appointed to convey,
it can not be said that to state the meaning of the word is the purpose of
the definition. The purpose is not to expound a name, but a
classification. The special meaning which Cuvier assigned to the word Man
(quite foreign to its ordinary meaning, though involving no change in the
denotation of the word), was incidental to a plan of arranging animals
into classes on a certain principle, that is, according to a certain set
of distinctions. And since the definition of Man according to the ordinary
connotation of the word, though it would have answered every other purpose
of a definition, would not have pointed out the place which the species
ought to occupy in that particular classification; he gave the word a
special connotation, that he might be able to define it by the kind of
attributes on which, for reasons of scientific convenience, he had
resolved to found his division of animated nature.

Scientific definitions, whether they are definitions of scientific terms,
or of common terms used in a scientific sense, are almost always of the
kind last spoken of: their main purpose is to serve as the landmarks of
scientific classification. And since the classifications in any science
are continually modified as scientific knowledge advances, the definitions
in the sciences are also constantly varying. A striking instance is
afforded by the words Acid and Alkali, especially the former. As
experimental discovery advanced, the substances classed with acids have
been constantly multiplying, and by a natural consequence the attributes
connoted by the word have receded and become fewer. At first it connoted
the attributes, of combining with an alkali to form a neutral substance
(called a salt); being compounded of a base and oxygen; causticity to the
taste and touch; fluidity, etc. The true analysis of muriatic acid, into
chlorine and hydrogen, caused the second property, composition from a base
and oxygen, to be excluded from the connotation. The same discovery fixed
the attention of chemists upon hydrogen as an important element in acids;
and more recent discoveries having led to the recognition of its presence
in sulphuric, nitric, and many other acids, where its existence was not
previously suspected, there is now a tendency to include the presence of
this element in the connotation of the word. But carbonic acid, silica,
sulphurous acid, have no hydrogen in their composition; that property can
not, therefore, be connoted by the term, unless those substances are no
longer to be considered acids. Causticity and fluidity have long since
been excluded from the characteristics of the class, by the inclusion of
silica and many other substances in it; and the formation of neutral
bodies by combination with alkalis, together with such electro-chemical
peculiarities as this is supposed to imply, are now the only _differentiæ_
which form the fixed connotation of the word Acid, as a term of chemical
science.

What is true of the definition of any term of science, is of course true
of the definition of a science itself; and accordingly (as observed in the
Introductory Chapter of this work), the definition of a science must
necessarily be progressive and provisional. Any extension of knowledge or
alteration in the current opinions respecting the subject-matter, may lead
to a change more or less extensive in the particulars included in the
science; and its composition being thus altered, it may easily happen that
a different set of characteristics will be found better adapted as
differentiæ for defining its name.

In the same manner in which a special or technical definition has for its
object to expound the artificial classification out of which it grows; the
Aristotelian logicians seem to have imagined that it was also the business
of ordinary definition to expound the ordinary, and what they deemed the
natural, classification of things, namely, the division of them into
Kinds; and to show the place which each Kind occupies, as superior,
collateral, or subordinate, among other Kinds. This notion would account
for the rule that all definition must necessarily be _per genus et
differentiam_, and would also explain why a single differentia was deemed
sufficient. But to expound, or express in words, a distinction of Kind,
has already been shown to be an impossibility: the very meaning of a Kind
is, that the properties which distinguish it do not grow out of one
another, and can not therefore be set forth in words, even by implication,
otherwise than by enumerating them all: and all are not known, nor are
ever likely to be so. It is idle, therefore, to look to this as one of the
purposes of a definition: while, if it be only required that the
definition of a Kind should indicate what kinds include it or are included
by it, any definitions which expound the connotation of the names will do
this: for the name of each class must necessarily connote enough of its
properties to fix the boundaries of the class. If the definition,
therefore, be a full statement of the connotation, it is all that a
definition can be required to be.(43)

§ 5. Of the two incomplete and popular modes of definition, and in what
they differ from the complete or philosophical mode, enough has now been
said. We shall next examine an ancient doctrine, once generally prevalent
and still by no means exploded, which I regard as the source of a great
part of the obscurity hanging over some of the most important processes of
the understanding in the pursuit of truth. According to this, the
definitions of which we have now treated are only one of two sorts into
which definitions may be divided, viz., definitions of names, and
definitions of things. The former are intended to explain the meaning of a
term; the latter, the nature of a thing; the last being incomparably the
most important.

This opinion was held by the ancient philosophers, and by their followers,
with the exception of the Nominalists; but as the spirit of modern
metaphysics, until a recent period, has been on the whole a Nominalist
spirit, the notion of definitions of things has been to a certain extent
in abeyance, still continuing, however, to breed confusion in logic, by
its consequences indeed rather than by itself. Yet the doctrine in its own
proper form now and then breaks out, and has appeared (among other places)
where it was scarcely to be expected, in a justly admired word, Archbishop
Whately’s _Logic_.(44) In a review of that work published by me in the
_Westminster __ Review_ for January, 1828, and containing some opinions
which I no longer entertain, I find the following observations on the
question now before us; observations with which my present view of that
question is still sufficiently in accordance.

“The distinction between nominal and real definitions, between definitions
of words and what are called definitions of things, though conformable to
the ideas of most of the Aristotelian logicians, can not, as it appears to
us, be maintained. We apprehend that no definition is ever intended to
‘explain and unfold the nature of a thing.’ It is some confirmation of our
opinion, that none of those writers who have thought that there were
definitions of things, have ever succeeded in discovering any criterion by
which the definition of a thing can be distinguished from any other
proposition relating to the thing. The definition, they say, unfolds the
nature of the thing: but no definition can unfold its whole nature; and
every proposition in which any quality whatever is predicated of the
thing, unfolds some part of its nature. The true state of the case we take
to be this. All definitions are of names, and of names only; but, in some
definitions, it is clearly apparent, that nothing is intended except to
explain the meaning of the word; while in others, besides explaining the
meaning of the word, it is intended to be implied that there exists a
thing, corresponding to the word. Whether this be or be not implied in any
given case, can not be collected from the mere form of the expression. ‘A
centaur is an animal with the upper parts of a man and the lower parts of
a horse,’ and ‘A triangle is a rectilineal figure with three sides,’ are,
in form, expressions precisely similar; although in the former it is not
implied that any _thing_, conformable to the term, really exists, while in
the latter it is; as may be seen by substituting in both definitions, the
word _means_ for _is_. In the first expression, ‘A centaur means an
animal,’ etc., the sense would remain unchanged: in the second, ‘A
triangle means,’ etc., the meaning would be altered, since it would be
obviously impossible to deduce any of the truths of geometry from a
proposition expressive only of the manner in which we intend to employ a
particular sign.

“There are, therefore, expressions, commonly passing for definitions,
which include in themselves more than the mere explanation of the meaning
of a term. But it is not correct to call an expression of this sort a
peculiar kind of definition. Its difference from the other kind consists
in this, that it is not a definition, but a definition and something more.
The definition above given of a triangle, obviously comprises not one, but
two propositions, perfectly distinguishable. The one is, ‘There may exist
a figure, bounded by three straight lines;’ the other, ‘And this figure
may be termed a triangle.’ The former of these propositions is not a
definition at all: the latter is a mere nominal definition, or explanation
of the use and application of a term. The first is susceptible of truth or
falsehood, and may therefore be made the foundation of a train of
reasoning. The latter can neither be true nor false; the only character it
is susceptible of is that of conformity or disconformity to the ordinary
usage of language.”

There is a real distinction, then, between definitions of names, and what
are erroneously called definitions of things; but it is, that the latter,
along with the meaning of a name, covertly asserts a matter of fact. This
covert assertion is not a definition, but a postulate. The definition is a
mere identical proposition, which gives information only about the use of
language, and from which no conclusions affecting matters of fact can
possibly be drawn. The accompanying postulate, on the other hand, affirms
a fact, which may lead to consequences of every degree of importance. It
affirms the actual or possible existence of Things possessing the
combination of attributes set forth in the definition; and this, if true,
may be foundation sufficient on which to build a whole fabric of
scientific truth.

We have already made, and shall often have to repeat, the remark, that the
philosophers who overthrew Realism by no means got rid of the consequences
of Realism, but retained long afterward, in their own philosophy, numerous
propositions which could only have a rational meaning as part of a
Realistic system. It had been handed down from Aristotle, and probably
from earlier times, as an obvious truth, that the science of Geometry is
deduced from definitions. This, so long as a definition was considered to
be a proposition “unfolding the nature of the thing,” did well enough. But
Hobbes followed, and rejected utterly the notion that a definition
declares the nature of the thing, or does any thing but state the meaning
of a name; yet he continued to affirm as broadly as any of his
predecessors, that the ἀρχαὶ, _principia_, or original premises of
mathematics, and even of all science, are definitions; producing the
singular paradox, that systems of scientific truth, nay, all truths
whatever at which we arrive by reasoning, are deduced from the arbitrary
conventions of mankind concerning the signification of words.

To save the credit of the doctrine that definitions are the premises of
scientific knowledge, the proviso is sometimes added, that they are so
only under a certain condition, namely, that they be framed conformably to
the phenomena of nature; that is, that they ascribe such meanings to terms
as shall suit objects actually existing. But this is only an instance of
the attempt so often made, to escape from the necessity of abandoning old
language after the ideas which it expresses have been exchanged for
contrary ones. From the meaning of a name (we are told) it is possible to
infer physical facts, provided the name has corresponding to it an
existing thing. But if this proviso be necessary, from which of the two is
the inference really drawn? From the existence of a thing having the
properties, or from the existence of a name meaning them?

Take, for instance, any of the definitions laid down as premises in
Euclid’s Elements; the definition, let us say, of a circle. This, being
analyzed, consists of two propositions; the one an assumption with respect
to a matter of fact, the other a genuine definition. “A figure may exist,
having all the points in the line which bounds it equally distant from a
single point within it:” “Any figure possessing this property is called a
circle.” Let us look at one of the demonstrations which are said to depend
on this definition, and observe to which of the two propositions contained
in it the demonstration really appeals. “About the centre A, describe the
circle B C D.”

Here is an assumption that a figure, such as the definition expresses,
_may_ be described; which is no other than the postulate, or covert
assumption, involved in the so-called definition. But whether that figure
be called a circle or not is quite immaterial. The purpose would be as
well answered, in all respects except brevity, were we to say, “Through
the point B, draw a line returning into itself, of which every point shall
be at an equal distance from the point A.” By this the definition of a
circle would be got rid of, and rendered needless; but not the postulate
implied in it; without that the demonstration could not stand. The circle
being now described, let us proceed to the consequence. “Since B C D is a
circle, the radius B A is equal to the radius C A.” B A is equal to C A,
not because B C D is a circle, but because B C D is a figure with the
radii equal. Our warrant for assuming that such a figure about the centre
A, with the radius B A, may be made to exist, is the postulate. Whether
the admissibility of these postulates rests on intuition, or on proof, may
be a matter of dispute; but in either case they are the premises on which
the theorems depend; and while these are retained it would make no
difference in the certainty of geometrical truths, though every definition
in Euclid, and every technical term therein defined, were laid aside.

It is, perhaps, superfluous to dwell at so much length on what is so
nearly self-evident; but when a distinction, obvious as it may appear, has
been confounded, and by powerful intellects, it is better to say too much
than too little for the purpose of rendering such mistakes impossible in
future. I will, therefore detain the reader while I point out one of the
absurd consequences flowing from the supposition that definitions, as
such, are the premises in any of our reasonings, except such as relate to
words only. If this supposition were true, we might argue correctly from
true premises, and arrive at a false conclusion. We should only have to
assume as a premise the definition of a nonentity; or rather of a name
which has no entity corresponding to it. Let this, for instance, be our
definition:


    A dragon is a serpent breathing flame.


This proposition, considered only as a definition, is indisputably
correct. A dragon _is_ a serpent breathing flame: the word _means_ that.
The tacit assumption, indeed (if there were any such understood
assertion), of the existence of an object with properties corresponding to
the definition, would, in the present instance, be false. Out of this
definition we may carve the premises of the following syllogism:


    A dragon is a thing which breathes flame:
    A dragon is a serpent:


From which the conclusion is,


    Therefore some serpent or serpents breathe flame:


an unexceptionable syllogism in the first mode of the third figure, in
which both premises are true and yet the conclusion false; which every
logician knows to be an absurdity. The conclusion being false and the
syllogism correct, the premises can not be true. But the premises,
considered as parts of a definition, are true. Therefore, the premises
considered as parts of a definition can not be the real ones. The real
premises must be—


    A dragon is a _really existing_ thing which breathes flame:
    A dragon is a _really existing_ serpent:


which implied premises being false, the falsity of the conclusion presents
no absurdity.

If we would determine what conclusion follows from the same ostensible
premises when the tacit assumption of real existence is left out, let us,
according to the recommendation in a previous page, substitute _means_ for
_is_. We then have—


    Dragon is _a word meaning_ a thing which breathes flame:
    Dragon is _a word meaning_ a serpent:


From which the conclusion is,


    Some _word or words which mean_ a serpent, also mean a thing which
    breathes flame:


where the conclusion (as well as the premises) is true, and is the only
kind of conclusion which can ever follow from a definition, namely, a
proposition relating to the meaning of words.

There is still another shape into which we may transform this syllogism.
We may suppose the middle term to be the designation neither of a thing
nor of a name, but of an idea. We then have—


    The _idea of_ a dragon is _an idea of_ a thing which breathes
                flame:
    The _idea of_ a dragon is _an idea of_ a serpent:
    Therefore, there is _an idea of_ a serpent, which is _an idea of_
                a thing breathing flame.


Here the conclusion is true, and also the premises; but the premises are
not definitions. They are propositions affirming that an idea existing in
the mind, includes certain ideal elements. The truth of the conclusion
follows from the existence of the psychological phenomenon called the idea
of a dragon; and therefore still from the tacit assumption of a matter of
fact.(45)

When, as in this last syllogism, the conclusion is a proposition
respecting an idea, the assumption on which it depends may be merely that
of the existence of an idea. But when the conclusion is a proposition
concerning a Thing, the postulate involved in the definition which stands
as the apparent premise, is the existence of a thing conformable to the
definition, and not merely of an idea conformable to it. This assumption
of real existence we always convey the impression that we intend to make,
when we profess to define any name which is already known to be a name of
really existing objects. On this account it is, that the assumption was
not necessarily implied in the definition of a dragon, while there was no
doubt of its being included in the definition of a circle.

§ 6. One of the circumstances which have contributed to keep up the
notion, that demonstrative truths follow from definitions rather than from
the postulates implied in those definitions, is, that the postulates, even
in those sciences which are considered to surpass all others in
demonstrative certainty, are not always exactly true. It is not true that
a circle exists, or can be described, which has all its radii _exactly_
equal. Such accuracy is ideal only; it is not found in nature, still less
can it be realized by art. People had a difficulty, therefore, in
conceiving that the most certain of all conclusions could rest on premises
which, instead of being certainly true, are certainly not true to the full
extent asserted. This apparent paradox will be examined when we come to
treat of Demonstration; where we shall be able to show that as much of the
postulate is true, as is required to support as much as is true of the
conclusion. Philosophers, however, to whom this view had not occurred, or
whom it did not satisfy, have thought it indispensable that there should
be found in definitions something _more_ certain, or at least more
accurately true, than the implied postulate of the real existence of a
corresponding object. And this something they flattered themselves they
had found, when they laid it down that a definition is a statement and
analysis not of the mere meaning of a word, nor yet of the nature of a
thing, but of an idea. Thus, the proposition, “A circle is a plane figure
bounded by a line all the points of which are at an equal distance from a
given point within it,” was considered by them, not as an assertion that
any real circle has that property (which would not be exactly true), but
that we _conceive_ a circle as having it; that our abstract idea of a
circle is an idea of a figure with its radii exactly equal.

Conformably to this it is said, that the subject-matter of mathematics,
and of every other demonstrative science, is not things as they really
exist, but abstractions of the mind. A geometrical line is a line without
breadth; but no such line exists in nature; it is a notion merely
suggested to the mind by its experience of nature. The definition (it is
said) is a definition of this mental line, not of any actual line: and it
is only of the mental line, not of any line existing in nature, that the
theorems of geometry are accurately true.

Allowing this doctrine respecting the nature of demonstrative truth to be
correct (which, in a subsequent place, I shall endeavor to prove that it
is not); even on that supposition, the conclusions which seem to follow
from a definition, do not follow from the definition as such, but from an
implied postulate. Even if it be true that there is no object in nature
answering to the definition of a line, and that the geometrical properties
of lines are not true of any lines in nature, but only of the idea of a
line; the definition, at all events, postulates the real existence of such
an idea: it assumes that the mind can frame, or rather has framed, the
notion of length without breadth, and without any other sensible property
whatever. To me, indeed, it appears that the mind can not form any such
notion; it can not conceive length without breadth; it can only, in
contemplating objects, attend to their length, exclusively of their other
sensible qualities, and so determine what properties may be predicated of
them in virtue of their length alone. If this be true, the postulate
involved in the geometrical definition of a line, is the real existence,
not of length without breadth, but merely of length, that is, of long
objects. This is quite enough to support all the truths of geometry, since
every property of a geometrical line is really a property of all physical
objects in so far as possessing length. But even what I hold to be the
false doctrine on the subject, leaves the conclusion that our reasonings
are grounded on the matters of fact postulated in definitions, and not on
the definitions themselves, entirely unaffected; and accordingly this
conclusion is one which I have in common with Dr. Whewell, in his
_Philosophy of the Inductive Sciences_: though, on the nature of
demonstrative truth, Dr. Whewell’s opinions are greatly at variance with
mine. And here, as in many other instances, I gladly acknowledge that his
writings are eminently serviceable in clearing from confusion the initial
steps in the analysis of the mental processes, even where his views
respecting the ultimate analysis are such as (though with unfeigned
respect) I can not but regard as fundamentally erroneous.

§ 7. Although, according to the opinion here presented, Definitions are
properly of names only, and not of things, it does not follow from this
that definitions are arbitrary. How to define a name, may not only be an
inquiry of considerable difficulty and intricacy, but may involve
considerations going deep into the nature of the things which are denoted
by the name. Such, for instance, are the inquiries which form the subjects
of the most important of Plato’s Dialogues; as, “What is rhetoric?” the
topic of the Gorgias, or, “What is justice?” that of the Republic. Such,
also, is the question scornfully asked by Pilate, “What is truth?” and the
fundamental question with speculative moralists in all ages, “What is
virtue?”

It would be a mistake to represent these difficult and noble inquiries as
having nothing in view beyond ascertaining the conventional meaning of a
name. They are inquiries not so much to determine what is, as what should
be, the meaning of a name; which, like other practical questions of
terminology, requires for its solution that we should enter, and sometimes
enter very deeply, into the properties not merely of names but of the
things named.

Although the meaning of every concrete general name resides in the
attributes which it connotes, the objects were named before the
attributes; as appears from the fact that in all languages, abstract names
are mostly compounds or other derivatives of the concrete names which
correspond to them. Connotative names, therefore, were, after proper
names, the first which were used: and in the simpler cases, no doubt, a
distinct connotation was present to the minds of those who first used the
name, and was distinctly intended by them to be conveyed by it. The first
person who used the word white, as applied to snow or to any other object,
knew, no doubt, very well what quality he intended to predicate, and had a
perfectly distinct conception in his mind of the attribute signified by
the name.

But where the resemblances and differences on which our classifications
are founded are not of this palpable and easily determinable kind;
especially where they consist not in any one quality but in a number of
qualities, the effects of which, being blended together, are not very
easily discriminated, and referred each to its true source; it often
happens that names are applied to namable objects, with no distinct
connotation present to the minds of those who apply them. They are only
influenced by a general resemblance between the new object and all or some
of the old familiar objects which they have been accustomed to call by
that name. This, as we have seen, is the law which even the mind of the
philosopher must follow, in giving names to the simple elementary feelings
of our nature: but, where the things to be named are complex wholes, a
philosopher is not content with noticing a general resemblance; he
examines what the resemblance consists in: and he only gives the same name
to things which resemble one another in the same definite particulars. The
philosopher, therefore, habitually employs his general names with a
definite connotation. But language was not made, and can only in some
small degree be mended, by philosophers. In the minds of the real arbiters
of language, general names, especially where the classes they denote can
not be brought before the tribunal of the outward senses to be identified
and discriminated, connote little more than a vague gross resemblance to
the things which they were earliest, or have been most, accustomed to call
by those names. When, for instance, ordinary persons predicate the words
_just_ or _unjust_ of any action, _noble_ or _mean_ of any sentiment,
expression, or demeanor, _statesman_ or _charlatan_ of any personage
figuring in politics, do they mean to affirm of those various subjects any
determinate attributes, of whatever kind? No: they merely recognize, as
they think, some likeness, more or less vague and loose, between these and
some other things which they have been accustomed to denominate or to hear
denominated by those appellations.

Language, as Sir James Mackintosh used to say of governments, “is not
made, but grows.” A name is not imposed at once and by previous purpose
upon a _class_ of objects, but is first applied to one thing, and then
extended by a series of transitions to another and another. By this
process (as has been remarked by several writers, and illustrated with
great force and clearness by Dugald Stewart in his Philosophical Essays) a
name not unfrequently passes by successive links of resemblance from one
object to another, until it becomes applied to things having nothing in
common with the first things to which the name was given; which, however,
do not, for that reason, drop the name; so that it at last denotes a
confused huddle of objects, having nothing whatever in common; and
connotes nothing, not even a vague and general resemblance. When a name
has fallen into this state, in which by predicating it of any object we
assert literally nothing about the object, it has become unfit for the
purposes either of thought or of the communication of thought; and can
only be made serviceable by stripping it of some part of its multifarious
denotation, and confining it to objects possessed of some attributes in
common, which it may be made to connote. Such are the inconveniences of a
language which “is not made, but grows.” Like the governments which are in
a similar case, it may be compared to a road which is not made but has
made itself: it requires continual mending in order to be passable.

From this it is already evident, why the question respecting the
definition of an abstract name is often one of so much difficulty. The
question, What is justice? is, in other words, What is the attribute which
mankind mean to predicate when they call an action just? To which the
first answer is, that having come to no precise agreement on the point,
they do not mean to predicate distinctly any attribute at all.
Nevertheless, all believe that there is some common attribute belonging to
all the actions which they are in the habit of calling just. The question
then must be, whether there is any such common attribute? and, in the
first place, whether mankind agree sufficiently with one another as to the
particular actions which they do or do not call just, to render the
inquiry, what quality those actions have in common, a possible one: if so,
whether the actions really have any quality in common; and if they have,
what it is. Of these three, the first alone is an inquiry into usage and
convention; the other two are inquiries into matters of fact. And if the
second question (whether the actions form a class at all) has been
answered negatively, there remains a fourth, often more arduous than all
the rest, namely, how best to form a class artificially, which the name
may denote.

And here it is fitting to remark, that the study of the spontaneous growth
of languages is of the utmost importance to those who would logically
remodel them. The classifications rudely made by established language,
when retouched, as they almost all require to be, by the hands of the
logician, are often themselves excellently suited to his purposes. As
compared with the classifications of a philosopher, they are like the
customary law of a country, which has grown up as it were spontaneously,
compared with laws methodized and digested into a code: the former are a
far less perfect instrument than the latter; but being the result of a
long, though unscientific, course of experience, they contain a mass of
materials which may be made very usefully available in the formation of
the systematic body of written law. In like manner, the established
grouping of objects under a common name, even when founded only on a gross
and general resemblance, is evidence, in the first place, that the
resemblance is obvious, and therefore considerable; and, in the next
place, that it is a resemblance which has struck great numbers of persons
during a series of years and ages. Even when a name, by successive
extensions, has come to be applied to things among which there does not
exist this gross resemblance common to them all, still at every step in
its progress we shall find such a resemblance. And these transitions of
the meaning of words are often an index to real connections between the
things denoted by them, which might otherwise escape the notice of
thinkers; of those at least who, from using a different language, or from
any difference in their habitual associations, have fixed their attention
in preference on some other aspect of the things. The history of
philosophy abounds in examples of such oversights, committed for want of
perceiving the hidden link that connected together the seemingly disparate
meanings of some ambiguous word.(46)

Whenever the inquiry into the definition of the name of any real object
consists of any thing else than a mere comparison of authorities, we
tacitly assume that a meaning must be found for the name, compatible with
its continuing to denote, if possible all, but at any rate the greater or
the more important part, of the things of which it is commonly predicated.
The inquiry, therefore, into the definition, is an inquiry into the
resemblances and differences among those things: whether there be any
resemblance running through them all; if not, through what portion of them
such a general resemblance can be traced: and finally, what are the common
attributes, the possession of which gives to them all, or to that portion
of them, the character of resemblance which has led to their being classed
together. When these common attributes have been ascertained and
specified, the name which belongs in common to the resembling objects
acquires a distinct instead of a vague connotation; and by possessing this
distinct connotation, becomes susceptible of definition.

In giving a distinct connotation to the general name, the philosopher will
endeavor to fix upon such attributes as, while they are common to all the
things usually denoted by the name, are also of greatest importance in
themselves; either directly, or from the number, the conspicuousness, or
the interesting character, of the consequences to which they lead. He will
select, as far as possible, such _differentiæ_ as lead to the greatest
number of interesting _propria_. For these, rather than the more obscure
and recondite qualities on which they often depend, give that general
character and aspect to a set of objects, which determine the groups into
which they naturally fall. But to penetrate to the more hidden agreement
on which these obvious and superficial agreements depend, is often one of
the most difficult of scientific problems. As it is among the most
difficult, so it seldom fails to be among the most important. And since
upon the result of this inquiry respecting the causes of the properties of
a class of things, there incidentally depends the question what shall be
the meaning of a word; some of the most profound and most valuable
investigations which philosophy presents to us, have been introduced by,
and have offered themselves under the guise of, inquiries into the
definition of a name.





                                 Book II.


OF REASONING.


    Διωρισμένων δε τούτων λέγωμεν ἤδη, διά τίνων, καὶ πότε, καὶ πῶς
    γίνεται πᾶς συλλογισμός ὕστερον δὲ λεκτέον περὶ ἀποδείξεως.
    Πρότερον γὰρ περὶ συλλογισμοῦ λεκτέον, ἥ περὶ ἀποδείξεως, διὰ τὸ
    καθόλου μᾶλλον εἰναὶ τὸν συλλογισμόν. Ἡ μέν γὰρ ἀπόδειξις,
    συλλογισμός τις; ὁ συλλογισμός δὲ ού πᾶς, ἀπόδειξις.—ARIST.,
    _Analyt. Prior._, l. i., cap. 4.




                                Chapter I.


Of Inference, Or Reasoning, In General.


§ 1. In the preceding Book, we have been occupied not with the nature of
Proof, but with the nature of Assertion: the import conveyed by a
Proposition, whether that Proposition be true or false; not the means by
which to discriminate true from false Propositions. The proper subject,
however, of Logic is Proof. Before we could understand what Proof is, it
was necessary to understand what that is to which proof is applicable;
what that is which can be a subject of belief or disbelief, of affirmation
or denial; what, in short, the different kinds of Propositions assert.

This preliminary inquiry we have prosecuted to a definite result.
Assertion, in the first place, relates either to the meaning of words, or
to some property of the things which words signify. Assertions respecting
the meaning of words, among which definitions are the most important, hold
a place, and an indispensable one, in philosophy; but as the meaning of
words is essentially arbitrary, this class of assertions are not
susceptible of truth or falsity, nor therefore of proof or disproof.
Assertions respecting Things, or what may be called Real Propositions, in
contradistinction to verbal ones, are of various sorts. We have analyzed
the import of each sort, and have ascertained the nature of the things
they relate to, and the nature of what they severally assert respecting
those things. We found that whatever be the form of the proposition, and
whatever its nominal subject or predicate, the real subject of every
proposition is some one or more facts or phenomena of consciousness, or
some one or more of the hidden causes or powers to which we ascribe those
facts; and that what is predicated or asserted, either in the affirmative
or negative, of those phenomena or those powers, is always either
Existence, Order in Place, Order in Time, Causation, or Resemblance. This,
then, is the theory of the Import of Propositions, reduced to its ultimate
elements: but there is another and a less abstruse expression for it,
which, though stopping short in an earlier stage of the analysis, is
sufficiently scientific for many of the purposes for which such a general
expression is required. This expression recognizes the commonly received
distinction between Subject and Attribute, and gives the following as the
analysis of the meaning of propositions:—Every Proposition asserts, that
some given subject does or does not possess some attribute; or that some
attribute is or is not (either in all or in some portion of the subjects
in which it is met with) conjoined with some other attribute.

We shall now for the present take our leave of this portion of our
inquiry, and proceed to the peculiar problem of the Science of Logic,
namely, how the assertions, of which we have analyzed the import, are
proved or disproved; such of them, at least, as, not being amenable to
direct consciousness or intuition, are appropriate subjects of proof.

We say of a fact or statement, that it is proved, when we believe its
truth by reason of some other fact or statement from which it is said to
_follow_. Most of the propositions, whether affirmative or negative,
universal, particular, or singular, which we believe, are not believed on
their own evidence, but on the ground of something previously assented to,
from which they are said to be _inferred_. To infer a proposition from a
previous proposition or propositions; to give credence to it, or claim
credence for it, as a conclusion from something else; is to _reason_, in
the most extensive sense of the term. There is a narrower sense, in which
the name reasoning is confined to the form of inference which is termed
ratiocination, and of which the syllogism is the general type. The reasons
for not conforming to this restricted use of the term were stated in an
earlier stage of our inquiry, and additional motives will be suggested by
the considerations on which we are now about to enter.

§ 2. In proceeding to take into consideration the cases in which
inferences can legitimately be drawn, we shall first mention some cases in
which the inference is apparent, not real; and which require notice
chiefly that they may not be confounded with cases of inference properly
so called. This occurs when the proposition ostensibly inferred from
another, appears on analysis to be merely a repetition of the same, or
part of the same, assertion, which was contained in the first. All the
cases mentioned in books of Logic as examples of equipollency or
equivalence of propositions, are of this nature. Thus, if we were to
argue, No man is incapable of reason, for every man is rational; or, All
men are mortal, for no man is exempt from death; it would be plain that we
were not proving the proposition, but only appealing to another mode of
wording it, which may or may not be more readily comprehensible by the
hearer, or better adapted to suggest the real proof, but which contains in
itself no shadow of proof.

Another case is where, from a universal proposition, we affect to infer
another which differs from it only in being particular: as All A is B,
therefore Some A is B: No A is B, therefore Some A is not B. This, too, is
not to conclude one proposition from another, but to repeat a second time
something which had been asserted at first; with the difference, that we
do not here repeat the whole of the previous assertion, but only an
indefinite part of it.

A third case is where, the antecedent having affirmed a predicate of a
given subject, the consequent affirms of the same subject something
already connoted by the former predicate: as, Socrates is a man, therefore
Socrates is a living creature; where all that is connoted by living
creature was affirmed of Socrates when he was asserted to be a man. If the
propositions are negative, we must invert their order, thus: Socrates is
not a living creature, therefore he is not a man; for if we deny the less,
the greater, which includes it, is already denied by implication. These,
therefore, are not really cases of inference; and yet the trivial examples
by which, in manuals of Logic, the rules of the syllogism are illustrated,
are often of this ill-chosen kind; formal demonstrations of conclusions to
which whoever understands the terms used in the statement of the data, has
already, and consciously, assented.(47)

The most complex case of this sort of apparent inference is what is called
the Conversion of propositions; which consists in turning the predicate
into a subject, and the subject into a predicate, and framing out of the
same terms thus reversed, another proposition, which must be true if the
former is true. Thus, from the particular affirmative proposition, Some A
is B, we may infer that Some B is A. From the universal negative, No A is
B, we may conclude that No B is A. From the universal affirmative
proposition, All A is B, it can not be inferred that all B is A; though
all water is liquid, it is not implied that all liquid is water; but it is
implied that some liquid is so; and hence the proposition, All A is B, is
legitimately convertible into Some B is A. This process, which converts a
universal proposition into a particular, is termed conversion _per
accidens_. From the proposition, Some A is not B, we can not even infer
that some B is not A; though some men are not Englishmen, it does not
follow that some Englishmen are not men. The only mode usually recognized
of converting a particular negative proposition, is in the form, Some A is
not B, therefore something which is not B is A; and this is termed
conversion by contraposition. In this case, however, the predicate and
subject are not merely reversed, but one of them is changed. Instead of
[A] and [B], the terms of the new proposition are [a thing which is not
B], and [A]. The original proposition, Some A _is not_ B, is first changed
into a proposition equipollent with it, Some A _is_ “a thing which is not
B;” and the proposition, being now no longer a particular negative, but a
particular affirmative, admits of conversion in the first mode, or as it
is called, _simple_ conversion.(48)

In all these cases there is not really any inference; there is in the
conclusion no new truth, nothing but what was already asserted in the
premises, and obvious to whoever apprehends them. The fact asserted in the
conclusion is either the very same fact, or part of the fact, asserted in
the original proposition. This follows from our previous analysis of the
Import of Propositions. When we say, for example, that some lawful
sovereigns are tyrants, what is the meaning of the assertion? That the
attributes connoted by the term “lawful sovereign,” and the attributes
connoted by the term “tyrant,” sometimes co-exist in the same individual.
Now this is also precisely what we mean, when we say that some tyrants are
lawful sovereigns; which, therefore, is not a second proposition inferred
from the first, any more than the English translation of Euclid’s Elements
is a collection of theorems different from and consequences of, those
contained in the Greek original. Again, if we assert that no great general
is a rash man, we mean that the attributes connoted by “great general,”
and those connoted by “rash,” never co-exist in the same subject; which is
also the exact meaning which would be expressed by saying, that no rash
man is a great general. When we say that all quadrupeds are warm-blooded,
we assert, not only that the attributes connoted by “quadruped” and those
connoted by “warm-blooded” sometimes co-exist, but that the former never
exist without the latter: now the proposition, Some warm-blooded creatures
are quadrupeds, expresses the first half of this meaning, dropping the
latter half; and therefore has been already affirmed in the antecedent
proposition, All quadrupeds are warm-blooded. But that _all_ warm-blooded
creatures are quadrupeds, or, in other words, that the attributes connoted
by “warm-blooded” never exist without those connoted by “quadruped,” has
not been asserted, and can not be inferred. In order to re-assert, in an
inverted form, the whole of what was affirmed in the proposition, All
quadrupeds are warm-blooded, we must convert it by contraposition, thus,
Nothing which is not warm-blooded is a quadruped. This proposition, and
the one from which it is derived, are exactly equivalent, and either of
them may be substituted for the other; for, to say that when the
attributes of a quadruped are present, those of a warm-blooded creature
are present, is to say that when the latter are absent the former are
absent.

In a manual for young students, it would be proper to dwell at greater
length on the conversion and equipollency of propositions. For though that
can not be called reasoning or inference which is a mere re-assertion in
different words of what had been asserted before, there is no more
important intellectual habit, nor any the cultivation of which falls more
strictly within the province of the art of logic, than that of discerning
rapidly and surely the identity of an assertion when disguised under
diversity of language. That important chapter in logical treatises which
relates to the Opposition of Propositions, and the excellent technical
language which logic provides for distinguishing the different kinds or
modes of opposition, are of use chiefly for this purpose. Such
considerations as these, that contrary propositions may both be false, but
can not both be true; that subcontrary propositions may both be true, but
can not both be false; that of two contradictory propositions one must be
true and the other false; that of two subalternate propositions the truth
of the universal proves the truth of the particular, and the falsity of
the particular proves the falsity of the universal, but not _vicè
versa_;(49) are apt to appear, at first sight, very technical and
mysterious, but when explained, seem almost too obvious to require so
formal a statement, since the same amount of explanation which is
necessary to make the principles intelligible, would enable the truths
which they convey to be apprehended in any particular case which can
occur. In this respect, however, these axioms of logic are on a level with
those of mathematics. That things which are equal to the same thing are
equal to one another, is as obvious in any particular case as it is in the
general statement: and if no such general maxim had ever been laid down,
the demonstrations in Euclid would never have halted for any difficulty in
stepping across the gap which this axiom at present serves to bridge over.
Yet no one has ever censured writers on geometry, for placing a list of
these elementary generalizations at the head of their treatises, as a
first exercise to the learner of the faculty which will be required in him
at every step, that of apprehending a _general_ truth. And the student of
logic, in the discussion even of such truths as we have cited above,
acquires habits of circumspect interpretation of words, and of exactly
measuring the length and breadth of his assertions, which are among the
most indispensable conditions of any considerable mental attainment, and
which it is one of the primary objects of logical discipline to cultivate.

§ 3. Having noticed, in order to exclude from the province of Reasoning or
Inference properly so called, the cases in which the progression from one
truth to another is only apparent, the logical consequent being a mere
repetition of the logical antecedent; we now pass to those which are cases
of inference in the proper acceptation of the term, those in which we set
out from known truths, to arrive at others really distinct from them.

Reasoning, in the extended sense in which I use the term, and in which it
is synonymous with Inference, is popularly said to be of two kinds:
reasoning from particulars to generals, and reasoning from generals to
particulars; the former being called Induction, the latter Ratiocination
or Syllogism. It will presently be shown that there is a third species of
reasoning, which falls under neither of these descriptions, and which,
nevertheless, is not only valid, but is the foundation of both the others.

It is necessary to observe, that the expressions, reasoning from
particulars to generals, and reasoning from generals to particulars, are
recommended by brevity rather than by precision, and do not adequately
mark, without the aid of a commentary, the distinction between Induction
(in the sense now adverted to) and Ratiocination. The meaning intended by
these expressions is, that Induction is inferring a proposition from
propositions _less general_ than itself, and Ratiocination is inferring a
proposition from propositions _equally_ or _more_ general. When, from the
observation of a number of individual instances, we ascend to a general
proposition, or when, by combining a number of general propositions, we
conclude from them another proposition still more general, the process,
which is substantially the same in both instances, is called Induction.
When from a general proposition, not alone (for from a single proposition
nothing can be concluded which is not involved in the terms), but by
combining it with other propositions, we infer a proposition of the same
degree of generality with itself, or a less general proposition, or a
proposition merely individual, the process is Ratiocination. When, in
short, the conclusion is more general than the largest of the premises,
the argument is commonly called Induction; when less general, or equally
general, it is Ratiocination.

As all experience begins with individual cases, and proceeds from them to
generals, it might seem most conformable to the natural order of thought
that Induction should be treated of before we touch upon Ratiocination. It
will, however, be advantageous, in a science which aims at tracing our
acquired knowledge to its sources, that the inquirer should commence with
the latter rather than with the earlier stages of the process of
constructing our knowledge; and should trace derivative truths backward to
the truths from which they are deduced, and on which they depend for their
evidence, before attempting to point out the original spring from which
both ultimately take their rise. The advantages of this order of
proceeding in the present instance will manifest themselves as we advance,
in a manner superseding the necessity of any further justification or
explanation.

Of Induction, therefore, we shall say no more at present, than that it at
least is, without doubt, a process of real inference. The conclusion in an
induction embraces more than is contained in the premises. The principle
or law collected from particular instances, the general proposition in
which we embody the result of our experience, covers a much larger extent
of ground than the individual experiments which form its basis. A
principle ascertained by experience, is more than a mere summing up of
what has been specifically observed in the individual cases which have
been examined; it is a generalization grounded on those cases, and
expressive of our belief, that what we there found true is true in an
indefinite number of cases which we have not examined, and are never
likely to examine. The nature and grounds of this inference, and the
conditions necessary to make it legitimate, will be the subject of
discussion in the Third Book: but that such inference really takes place
is not susceptible of question. In every induction we proceed from truths
which we knew, to truths which we did not know; from facts certified by
observation, to facts which we have not observed, and even to facts not
capable of being now observed; future facts, for example; but which we do
not hesitate to believe on the sole evidence of the induction itself.

Induction, then, is a real process of Reasoning or Inference. Whether, and
in what sense, as much can be said of the Syllogism, remains to be
determined by the examination into which we are about to enter.




                               Chapter II.


Of Ratiocination, Or Syllogism.


§ 1. The analysis of the Syllogism has been so accurately and fully
performed in the common manuals of Logic, that in the present work, which
is not designed as a manual, it is sufficient to recapitulate, _memoriæ
causâ_, the leading results of that analysis, as a foundation for the
remarks to be afterward made on the functions of the Syllogism, and the
place which it holds in science.

To a legitimate syllogism it is essential that there should be three, and
no more than three, propositions, namely, the conclusion, or proposition
to be proved, and two other propositions which together prove it, and
which are called the premises. It is essential that there should be three,
and no more than three, terms, namely, the subject and predicate of the
conclusion, and another called the middle term, which must be found in
both premises, since it is by means of it that the other two terms are to
be connected together. The predicate of the conclusion is called the major
term of the syllogism; the subject of the conclusion is called the minor
term. As there can be but three terms, the major and minor terms must each
be found in one, and only one, of the premises, together with the middle
term which is in them both. The premise which contains the middle term and
the major term is called the major premise; that which contains the middle
term and the minor term is called the minor premise.

Syllogisms are divided by some logicians into three _figures_, by others
into four, according to the position of the middle term, which may either
be the subject in both premises, the predicate in both, or the subject in
one and the predicate in the other. The most common case is that in which
the middle term is the subject of the major premise and the predicate of
the minor. This is reckoned as the first figure. When the middle term is
the predicate in both premises, the syllogism belongs to the second
figure; when it is the subject in both, to the third. In the fourth figure
the middle term is the subject of the minor premise and the predicate of
the major. Those writers who reckon no more than three figures, include
this case in the first.

Each figure is divided into _moods_, according to what are called the
_quantity_ and _quality_ of the propositions, that is, according as they
are universal or particular, affirmative or negative. The following are
examples of all the legitimate moods, that is, all those in which the
conclusion correctly follows from the premises. A is the minor term, C the
major, B the middle term.

FIRST FIGURE.

All B is C   No B is C    All B is C    No B is C
All A is B   All A is B   Some A is B   Some A is B
therefore    therefore    therefore     therefore
All A is C   No A is C    Some A is C   Some A is not C

SECOND FIGURE.

No C is B    All C is B   No C is B         All C is B
All A is B   No A is B    Some A is B       Some A is not B
therefore    therefore    therefore         therefore
No A is C    No A is C    Some A is not C   Some A is not C

THIRD FIGURE.

All B is    No B is C   Some B is   All B is    Some B is   No B is C
C                       C           C           not C
All B is    All B is    All B is    Some B is   All B is    Some B is
A           A           A           A           A           A
therefore   therefore   therefore   therefore   therefore   therefore
Some A is   Some A is   Some A is   Some A is   Some A is   Some A is
C           not C       C           C           not C       not C

FOURTH FIGURE.

All C is B    All C is B   Some C is B   No C is B    No C is B
All B is A    No B is A    All B is A    All B is A   Some B is A
therefore     therefore    therefore     therefore    therefore
Some A is C   Some A is    Some A is C   Some A is    Some A is
              not C                      not C        not C

In these exemplars, or blank forms for making syllogisms, no place is
assigned to _singular_ propositions; not, of course, because such
propositions are not used in ratiocination, but because, their predicate
being affirmed or denied of the whole of the subject, they are ranked, for
the purposes of the syllogism, with universal propositions. Thus, these
two syllogisms—

All men are mortal,     All men are mortal,
All kings are men,      Socrates is a man,
therefore               therefore
All kings are mortal,   Socrates is mortal,

are arguments precisely similar, and are both ranked in the first mood of
the first figure.(50)

The reasons why syllogisms in any of the above forms are legitimate, that
is, why, if the premises are true, the conclusion must inevitably be so,
and why this is not the case in any other possible mood (that is, in any
other combination of universal and particular, affirmative and negative
propositions), any person taking interest in these inquiries may be
presumed to have either learned from the common-school books of the
syllogistic logic, or to be capable of discovering for himself. The reader
may, however, be referred, for every needful explanation, to Archbishop
Whately’s _Elements of Logic_, where he will find stated with
philosophical precision, and explained with remarkable perspicuity, the
whole of the common doctrine of the syllogism.

All valid ratiocination; all reasoning by which, from general propositions
previously admitted, other propositions equally or less general are
inferred; may be exhibited in some of the above forms. The whole of
Euclid, for example, might be thrown without difficulty into a series of
syllogisms, regular in mood and figure.

Though a syllogism framed according to any of these formulæ is a valid
argument, all correct ratiocination admits of being stated in syllogisms
of the first figure alone. The rules for throwing an argument in any of
the other figures into the first figure, are called rules for the
_reduction_ of syllogisms. It is done by the _conversion_ of one or other,
or both, of the premises. Thus an argument in the first mood of the second
figure, as—

No C is B
All A is B
therefore
No A is C,

may be reduced as follows. The proposition, No C is B, being a universal
negative, admits of simple conversion, and may be changed into No B is C,
which, as we showed, is the very same assertion in other words—the same
fact differently expressed. This transformation having been effected, the
argument assumes the following form:

No B is C
All A is B
therefore
No A is C,

which is a good syllogism in the second mood of the first figure. Again,
an argument in the first mood of the third figure must resemble the
following:

All B is C
All B is A
therefore
Some A is C,

where the minor premise, All B is A, conformably to what was laid down in
the last chapter respecting universal affirmatives, does not admit of
simple conversion, but may be converted _per accidens_, thus, Some A is B;
which, though it does not express the whole of what is asserted in the
proposition All B is A, expresses, as was formerly shown, part of it, and
must therefore be true if the whole is true. We have, then, as the result
of the reduction, the following syllogism in the third mood of the first
figure:

All B is C
Some A is B,

from which it obviously follows, that

Some A is C.

In the same manner, or in a manner on which after these examples it is not
necessary to enlarge, every mood of the second, third, and fourth figures
may be reduced to some one of the four moods of the first. In other words,
every conclusion which can be proved in any of the last three figures, may
be proved in the first figure from the same premises, with a slight
alteration in the mere manner of expressing them. Every valid
ratiocination, therefore, may be stated in the first figure, that is, in
one of the following forms:

Every B is C   No B is C
All A is B,    All A is B,
Some A is B,   Some A is B,
therefore      therefore
All A is C.    No A is C.
Some A is C.   Some A is not C.

Or, if more significant symbols are preferred:

To prove an affirmative, the argument must admit of being stated in this
form:

All animals are mortal;
All men/Some men/Socrates are animals;
therefore
All men/Some men/Socrates are mortal.

To prove a negative, the argument must be capable of being expressed in
this form:

No one who is capable of self-control is necessarily vicious;

No one who is capable of self-control is necessarily vicious;
All negroes/Some negroes/Mr. A’s negro are capable of self-control;
therefore
No negroes are/Some negroes are not/Mr. A’s negro is not necessarily
vicious.

Though all ratiocination admits of being thrown into one or the other of
these forms, and sometimes gains considerably by the transformation, both
in clearness and in the obviousness of its consequence; there are, no
doubt, cases in which the argument falls more naturally into one of the
other three figures, and in which its conclusiveness is more apparent at
the first glance in those figures, than when reduced to the first. Thus,
if the proposition were that pagans may be virtuous, and the evidence to
prove it were the example of Aristides; a syllogism in the third figure,

Aristides was virtuous,
Aristides was a pagan,
therefore
Some pagan was virtuous,

would be a more natural mode of stating the argument, and would carry
conviction more instantly home, than the same ratiocination strained into
the first figure, thus—

Aristides was virtuous,
Some pagan was Aristides,
therefore
Some pagan was virtuous.

A German philosopher, Lambert, whose _Neues Organon_ (published in the
year 1764) contains among other things one of the most elaborate and
complete expositions which had ever been made of the syllogistic doctrine,
has expressly examined what sort of arguments fall most naturally and
suitably into each of the four figures; and his investigation is
characterized by great ingenuity and clearness of thought.(51) The
argument, however, is one and the same, in whichever figure it is
expressed; since, as we have already seen, the premises of a syllogism in
the second, third, or fourth figure, and those of the syllogism in the
first figure to which it may be reduced, are the same premises in every
thing except language, or, at least, as much of them as contributes to the
proof of the conclusion is the same. We are therefore at liberty, in
conformity with the general opinion of logicians, to consider the two
elementary forms of the first figure as the universal types of all correct
ratiocination; the one, when the conclusion to be proved is affirmative,
the other, when it is negative; even though certain arguments may have a
tendency to clothe themselves in the forms of the second, third, and
fourth figures; which, however, can not possibly happen with the only
class of arguments which are of first-rate scientific importance, those in
which the conclusion is a universal affirmative, such conclusions being
susceptible of proof in the first figure alone.(52)

§ 2. On examining, then, these two general formulæ, we find that in both
of them, one premise, the major, is a universal proposition; and according
as this is affirmative or negative, the conclusion is so too. All
ratiocination, therefore, starts from a _general_ proposition, principle,
or assumption: a proposition in which a predicate is affirmed or denied of
an entire class; that is, in which some attribute, or the negation of some
attribute, is asserted of an indefinite number of objects distinguished by
a common characteristic, and designated, in consequence, by a common name.

The other premise is always affirmative, and asserts that something (which
may be either an individual, a class, or part of a class) belongs to, or
is included in, the class respecting which something was affirmed or
denied in the major premise. It follows that the attribute affirmed or
denied of the entire class may (if that affirmation or denial was correct)
be affirmed or denied of the object or objects alleged to be included in
the class: and this is precisely the assertion made in the conclusion.

Whether or not the foregoing is an adequate account of the constituent
parts of the syllogism, will be presently considered; but as far as it
goes it is a true account. It has accordingly been generalized, and
erected into a logical maxim, on which all ratiocination is said to be
founded, insomuch that to reason, and to apply the maxim, are supposed to
be one and the same thing. The maxim is, That whatever can be affirmed (or
denied) of a class, may be affirmed (or denied) of every thing included in
the class. This axiom, supposed to be the basis of the syllogistic theory,
is termed by logicians the _dictum de omni et nullo_.

This maxim, however, when considered as a principle of reasoning, appears
suited to a system of metaphysics once indeed generally received, but
which for the last two centuries has been considered as finally abandoned,
though there have not been wanting in our own day attempts at its revival.
So long as what are termed Universals were regarded as a peculiar kind of
substances, having an objective existence distinct from the individual
objects classed under them, the _dictum de omni_ conveyed an important
meaning; because it expressed the intercommunity of nature, which it was
necessary on that theory that we should suppose to exist between those
general substances and the particular substances which were subordinated
to them. That every thing predicable of the universal was predicable of
the various individuals contained under it, was then no identical
proposition, but a statement of what was conceived as a fundamental law of
the universe. The assertion that the entire nature and properties of the
_substantia secunda_ formed part of the nature and properties of each of
the individual substances called by the same name; that the properties of
Man, for example, were properties of all men; was a proposition of real
significance when man did not _mean_ all men, but something inherent in
men, and vastly superior to them in dignity. Now, however, when it is
known that a class, a universal, a genus or species, is not an entity _per
se_, but neither more nor less than the individual substances themselves
which are placed in the class, and that there is nothing real in the
matter except those objects, a common name given to them, and common
attributes indicated by the name; what, I should be glad to know, do we
learn by being told, that whatever can be affirmed of a class, may be
affirmed of every object contained in the class? The class _is_ nothing
but the objects contained in it: and the _dictum de omni_ merely amounts
to the identical proposition, that whatever is true of certain objects, is
true of each of those objects. If all ratiocination were no more than the
application of this maxim to particular cases, the syllogism would indeed
be, what it has so often been declared to be, solemn trifling. The _dictum
de omni_ is on a par with another truth, which in its time was also
reckoned of great importance, “Whatever is, is.” To give any real meaning
to the _dictum de omni_, we must consider it not as an axiom, but as a
definition; we must look upon it as intended to explain, in a circuitous
and paraphrastic manner, the meaning of the word _class_.

An error which seemed finally refuted and dislodged from thought, often
needs only put on a new suit of phrases, to be welcomed back to its old
quarters, and allowed to repose unquestioned for another cycle of ages.
Modern philosophers have not been sparing in their contempt for the
scholastic dogma that genera and species are a peculiar kind of
substances, which general substances being the only permanent things,
while the individual substances comprehended under them are in a perpetual
flux, knowledge, which necessarily imports stability, can only have
relation to those general substances or universals, and not to the facts
or particulars included under them. Yet, though nominally rejected, this
very doctrine, whether disguised under the Abstract Ideas of Locke (whose
speculations, however, it has less vitiated than those of perhaps any
other writer who has been infected with it), under the ultra-nominalism of
Hobbes and Condillac, or the ontology of the later German schools, has
never ceased to poison philosophy. Once accustomed to consider scientific
investigation as essentially consisting in the study of universals, men
did not drop this habit of thought when they ceased to regard universals
as possessing an independent existence: and even those who went the length
of considering them as mere names, could not free themselves from the
notion that the investigation of truth consisted entirely or partly in
some kind of conjuration or juggle with those names. When a philosopher
adopted fully the Nominalist view of the signification of general
language, retaining along with it the _dictum de omni_ as the foundation
of all reasoning, two such premises fairly put together were likely, if he
was a consistent thinker, to land him in rather startling conclusions.
Accordingly it has been seriously held, by writers of deserved celebrity,
that the process of arriving at new truths by reasoning consists in the
mere substitution of one set of arbitrary signs for another; a doctrine
which they suppose to derive irresistible confirmation from the example of
algebra. If there were any process in sorcery or necromancy more
preternatural than this, I should be much surprised. The culminating point
of this philosophy is the noted aphorism of Condillac, that a science is
nothing, or scarcely any thing, but _une langue bien faite_; in other
words, that the one sufficient rule for discovering the nature and
properties of objects is to name them properly: as if the reverse were not
the truth, that it is impossible to name them properly except in
proportion as we are already acquainted with their nature and properties.
Can it be necessary to say, that none, not even the most trivial knowledge
with respect to Things, ever was or could be originally got at by any
conceivable manipulation of mere names, as such; and that what can be
learned from names, is only what somebody who used the names knew before?
Philosophical analysis confirms the indication of common sense, that the
function of names is but that of enabling us to _remember_ and to
_communicate_ our thoughts. That they also strengthen, even to an
incalculable extent, the power of thought itself, is most true: but they
do this by no intrinsic and peculiar virtue; they do it by the power
inherent in an artificial memory, an instrument of which few have
adequately considered the immense potency. As an artificial memory,
language truly is, what it has so often been called, an instrument of
thought; but it is one thing to be the instrument, and another to be the
exclusive subject upon which the instrument is exercised. We think,
indeed, to a considerable extent, by means of names, but what we think of,
are the things called by those names; and there can not be a greater error
than to imagine that thought can be carried on with nothing in our mind
but names, or that we can make the names think for us.

§ 3. Those who considered the _dictum de omni_ as the foundation of the
syllogism, looked upon arguments in a manner corresponding to the
erroneous view which Hobbes took of propositions. Because there are some
propositions which are merely verbal, Hobbes, in order apparently that his
definition might be rigorously universal, defined a proposition as if no
propositions declared any thing except the meaning of words. If Hobbes was
right; if no further account than this could be given of the import of
propositions; no theory could be given but the commonly received one, of
the combination of propositions in a syllogism. If the minor premise
asserted nothing more than that something belongs to a class, and if the
major premise asserted nothing of that class except that it is included in
another class, the conclusion would only be that what was included in the
lower class is included in the higher, and the result, therefore, nothing
except that the classification is consistent with itself. But we have seen
that it is no sufficient account of the meaning of a proposition, to say
that it refers something to, or excludes something from, a class. Every
proposition which conveys real information asserts a matter of fact,
dependent on the laws of nature, and not on classification. It asserts
that a given object does or does not possess a given attribute; or it
asserts that two attributes, or sets of attributes, do or do not
(constantly or occasionally) co-exist. Since such is the purport of all
propositions which convey any real knowledge, and since ratiocination is a
mode of acquiring real knowledge, any theory of ratiocination which does
not recognize this import of propositions, can not, we may be sure, be the
true one.

Applying this view of propositions to the two premises of a syllogism, we
obtain the following results. The major premise, which, as already
remarked, is always universal, asserts, that all things which have a
certain attribute (or attributes) have or have not along with it, a
certain other attribute (or attributes). The minor premise asserts that
the thing or set of things which are the subject of that premise, have the
first-mentioned attribute; and the conclusion is, that they have (or that
they have not), the second. Thus in our former example,

All men are mortal,
Socrates is a man,
therefore
Socrates is mortal,

the subject and predicate of the major premise are connotative terms,
denoting objects and connoting attributes. The assertion in the major
premise is, that along with one of the two sets of attributes, we always
find the other: that the attributes connoted by “man” never exist unless
conjoined with the attribute called mortality. The assertion in the minor
premise is that the individual named Socrates possesses the former
attributes; and it is concluded that he possesses also the attribute
mortality. Or, if both the premises are general propositions, as

All men are mortal,
All kings are men,
therefore
All kings are mortal,

the minor premise asserts that the attributes denoted by kingship only
exist in conjunction with those signified by the word man. The major
asserts as before, that the last-mentioned attributes are never found
without the attribute of mortality. The conclusion is, that wherever the
attributes of kingship are found, that of mortality is found also.

If the major premise were negative, as, No men are omnipotent, it would
assert, not that the attributes connoted by “man” never exist without, but
that they never exist with, those connoted by “omnipotent:” from which,
together with the minor premise, it is concluded, that the same
incompatibility exists between the attribute omnipotence and those
constituting a king. In a similar manner we might analyze any other
example of the syllogism.

If we generalize this process, and look out for the principle or law
involved in every such inference, and presupposed in every syllogism, the
propositions of which are any thing more than merely verbal; we find, not
the unmeaning _dictum de omni et nullo_, but a fundamental principle, or
rather two principles, strikingly resembling the axioms of mathematics.
The first, which is the principle of affirmative syllogisms, is, that
things which co-exist with the same thing, co-exist with one another: or
(still more precisely) a thing which co-exists with another thing, which
other co-exists with a third thing, also co-exists with that third thing.
The second is the principle of negative syllogisms, and is to this effect:
that a thing which co-exists with another thing, with which other a third
thing does not co-exist, is not co-existent with that third thing. These
axioms manifestly relate to facts, and not to conventions; and one or
other of them is the ground of the legitimacy of every argument in which
facts and not conventions are the matter treated of.(53)

§ 4. It remains to translate this exposition of the syllogism from the one
into the other of the two languages in which we formerly remarked(54) that
all propositions, and of course therefore all combinations of
propositions, might be expressed. We observed that a proposition might be
considered in two different lights; as a portion of our knowledge of
nature, or as a memorandum for our guidance. Under the former, or
speculative aspect, an affirmative general proposition is an assertion of
a speculative truth, viz., that whatever has a certain attribute has a
certain other attribute. Under the other aspect, it is to be regarded not
as a part of our knowledge, but as an aid for our practical exigencies, by
enabling us, when we see or learn that an object possesses one of the two
attributes, to infer that it possesses the other; thus employing the first
attribute as a mark or evidence of the second. Thus regarded, every
syllogism comes within the following general formula:

Attribute A is a mark of attribute B,
The given object has the mark A,
therefore
The given object has the attribute B.

Referred to this type, the arguments which we have lately cited as
specimens of the syllogism, will express themselves in the following
manner:

The attributes of man are a mark of the attribute mortality,
Socrates has the attributes of man,
therefore
Socrates has the attribute mortality.

And again,

The attributes of man are a mark of the attribute mortality,
The attributes of a king are a mark of the attributes of man,
therefore
The attributes of a king are a mark of the attribute mortality.

And, lastly,

The attributes of man are a mark of the absence of the attribute
omnipotence,
The attributes of a king are a mark of the attributes of man,
therefore
The attributes of a king are a mark of the absence of the attribute
signified by the word omnipotent (or, are evidence of the absence of that
attribute).

To correspond with this alteration in the form of the syllogisms, the
axioms on which the syllogistic process is founded must undergo a
corresponding transformation. In this altered phraseology, both those
axioms may be brought under one general expression; namely, that whatever
has any mark, has that which it is a mark of. Or, when the minor premise
as well as the major is universal, we may state it thus: Whatever is a
mark of any mark, is a mark of that which this last is a mark of. To trace
the identity of these axioms with those previously laid down, may be left
to the intelligent reader. We shall find, as we proceed, the great
convenience of the phraseology into which we have last thrown them, and
which is better adapted than any I am acquainted with, to express with
precision and force what is aimed at, and actually accomplished, in every
case of the ascertainment of a truth by ratiocination.(55)




                               Chapter III.


Of The Functions And Logical Value Of The Syllogism.


§ 1. We have shown what is the real nature of the truths with which the
Syllogism is conversant, in contradistinction to the more superficial
manner in which their import is conceived in the common theory; and what
are the fundamental axioms on which its probative force or conclusiveness
depends. We have now to inquire, whether the syllogistic process, that of
reasoning from generals to particulars, is, or is not, a process of
inference; a progress from the known to the unknown: a means of coming to
a knowledge of something which we did not know before.

Logicians have been remarkably unanimous in their mode of answering this
question. It is universally allowed that a syllogism is vicious if there
be any thing more in the conclusion than was assumed in the premises. But
this is, in fact, to say, that nothing ever was, or can be, proved by
syllogism, which was not known, or assumed to be known, before. Is
ratiocination, then, not a process of inference? And is the syllogism, to
which the word reasoning has so often been represented to be exclusively
appropriate, not really entitled to be called reasoning at all? This seems
an inevitable consequence of the doctrine, admitted by all writers on the
subject, that a syllogism can prove no more than is involved in the
premises. Yet the acknowledgment so explicitly made, has not prevented one
set of writers from continuing to represent the syllogism as the correct
analysis of what the mind actually performs in discovering and proving the
larger half of the truths, whether of science or of daily life, which we
believe; while those who have avoided this inconsistency, and followed out
the general theorem respecting the logical value of the syllogism to its
legitimate corollary, have been led to impute uselessness and frivolity to
the syllogistic theory itself, on the ground of the _petitio principii_
which they allege to be inherent in every syllogism. As I believe both
these opinions to be fundamentally erroneous, I must request the attention
of the reader to certain considerations, without which any just
appreciation of the true character of the syllogism, and the functions it
performs in philosophy, appears to me impossible; but which seem to have
been either overlooked, or insufficiently adverted to, both by the
defenders of the syllogistic theory and by its assailants.

§ 2. It must be granted that in every syllogism, considered as an argument
to prove the conclusion, there is a _petitio principii_. When we say,

All men are mortal,
Socrates is a man,
therefore
Socrates is mortal;

it is unanswerably urged by the adversaries of the syllogistic theory,
that the proposition, Socrates is mortal, is presupposed in the more
general assumption, All men are mortal: that we can not be assured of the
mortality of all men, unless we are already certain of the mortality of
every individual man: that if it be still doubtful whether Socrates, or
any other individual we choose to name, be mortal or not, the same degree
of uncertainty must hang over the assertion, All men are mortal: that the
general principle, instead of being given as evidence of the particular
case, can not itself be taken for true without exception, until every
shadow of doubt which could affect any case comprised with it, is
dispelled by evidence _aliundè_; and then what remains for the syllogism
to prove? That, in short, no reasoning from generals to particulars can,
as such, prove any thing: since from a general principle we can not infer
any particulars, but those which the principle itself assumes as known.

This doctrine appears to me irrefragable; and if logicians, though unable
to dispute it, have usually exhibited a strong disposition to explain it
away, this was not because they could discover any flaw in the argument
itself, but because the contrary opinion seemed to rest on arguments
equally indisputable. In the syllogism last referred to, for example, or
in any of those which we previously constructed, is it not evident that
the conclusion may, to the person to whom the syllogism is presented, be
actually and _bona fide_ a new truth? Is it not matter of daily experience
that truths previously unthought of, facts which have not been, and can
not be, directly observed, are arrived at by way of general reasoning? We
believe that the Duke of Wellington is mortal. We do not know this by
direct observation, so long as he is not yet dead. If we were asked how,
this being the case, we know the duke to be mortal, we should probably
answer, Because all men are so. Here, therefore, we arrive at the
knowledge of a truth not (as yet) susceptible of observation, by a
reasoning which admits of being exhibited in the following syllogism:

All men are mortal,
The Duke of Wellington is a man,
therefore
The Duke of Wellington is mortal.

And since a large portion of our knowledge is thus acquired, logicians
have persisted in representing the syllogism as a process of inference or
proof; though none of them has cleared up the difficulty which arises from
the inconsistency between that assertion, and the principle, that if there
be any thing in the conclusion which was not already asserted in the
premises, the argument is vicious. For it is impossible to attach any
serious scientific value to such a mere salvo, as the distinction drawn
between being involved _by implication_ in the premises, and being
directly asserted in them. When Archbishop Whately says(56) that the
object of reasoning is “merely to expand and unfold the assertions wrapped
up, as it were, and implied in those with which we set out, and to bring a
person to perceive and acknowledge the full force of that which he has
admitted,” he does not, I think, meet the real difficulty requiring to be
explained, namely, how it happens that a science, like geometry, _can_ be
all “wrapped up” in a few definitions and axioms. Nor does this defense of
the syllogism differ much from what its assailants urge against it as an
accusation, when they charge it with being of no use except to those who
seek to press the consequences of an admission into which a person has
been entrapped without having considered and understood its full force.
When you admitted the major premise, you asserted the conclusion; but,
says Archbishop Whately, you asserted it by implication merely: this,
however, can here only mean that you asserted it unconsciously; that you
did not know you were asserting it; but, if so, the difficulty revives in
this shape—Ought you not to have known? Were you warranted in asserting
the general proposition without having satisfied yourself of the truth of
every thing which it fairly includes? And if not, is not the syllogistic
art _prima facie_ what its assailants affirm it to be, a contrivance for
catching you in a trap, and holding you fast in it?(57)

§ 3. From this difficulty there appears to be but one issue. The
proposition that the Duke of Wellington is mortal, is evidently an
inference; it is got at as a conclusion from something else; but do we, in
reality, conclude it from the proposition, All men are mortal? I answer,
no.

The error committed is, I conceive, that of overlooking the distinction
between two parts of the process of philosophizing, the inferring part,
and the registering part; and ascribing to the latter the functions of the
former. The mistake is that of referring a person to his own notes for the
origin of his knowledge. If a person is asked a question, and is at the
moment unable to answer it, he may refresh his memory by turning to a
memorandum which he carries about with him. But if he were asked, how the
fact came to his knowledge, he would scarcely answer, because it was set
down in his note-book: unless the book was written, like the Koran, with a
quill from the wing of the angel Gabriel.

Assuming that the proposition, The Duke of Wellington is mortal, is
immediately an inference from the proposition, All men are mortal; whence
do we derive our knowledge of that general truth? Of course from
observation. Now, all which man can observe are individual cases. From
these all general truths must be drawn, and into these they may be again
resolved; for a general truth is but an aggregate of particular truths; a
comprehensive expression, by which an indefinite number of individual
facts are affirmed or denied at once. But a general proposition is not
merely a compendious form for recording and preserving in the memory a
number of particular facts, all of which have been observed.
Generalization is not a process of mere naming, it is also a process of
inference. From instances which we have observed, we feel warranted in
concluding, that what we found true in those instances, holds in all
similar ones, past, present, and future, however numerous they may be. We
then, by that valuable contrivance of language which enables us to speak
of many as if they were one, record all that we have observed, together
with all that we infer from our observations, in one concise expression;
and have thus only one proposition, instead of an endless number, to
remember or to communicate. The results of many observations and
inferences, and instructions for making innumerable inferences in
unforeseen cases, are compressed into one short sentence.

When, therefore, we conclude from the death of John and Thomas, and every
other person we ever heard of in whose case the experiment had been fairly
tried, that the Duke of Wellington is mortal like the rest; we may,
indeed, pass through the generalization, All men are mortal, as an
intermediate stage; but it is not in the latter half of the process, the
descent from all men to the Duke of Wellington, that the _inference_
resides. The inference is finished when we have asserted that all men are
mortal. What remains to be performed afterward is merely deciphering our
own notes.

Archbishop Whately has contended that syllogizing, or reasoning from
generals to particulars, is not, agreeably to the vulgar idea, a peculiar
_mode_ of reasoning, but the philosophical analysis of _the_ mode in which
all men reason, and must do so if they reason at all. With the deference
due to so high an authority, I can not help thinking that the vulgar
notion is, in this case, the more correct. If, from our experience of
John, Thomas, etc., who once were living, but are now dead, we are
entitled to conclude that all human beings are mortal, we might surely
without any logical inconsequence have concluded at once from those
instances, that the Duke of Wellington is mortal. The mortality of John,
Thomas, and others is, after all, the whole evidence we have for the
mortality of the Duke of Wellington. Not one iota is added to the proof by
interpolating a general proposition. Since the individual cases are all
the evidence we can possess, evidence which no logical form into which we
choose to throw it can make greater than it is; and since that evidence is
either sufficient in itself, or, if insufficient for the one purpose, can
not be sufficient for the other; I am unable to see why we should be
forbidden to take the shortest cut from these sufficient premises to the
conclusion, and constrained to travel the “high priori road,” by the
arbitrary fiat of logicians. I can not perceive why it should be
impossible to journey from one place to another unless we “march up a
hill, and then march down again.” It may be the safest road, and there may
be a resting-place at the top of the hill, affording a commanding view of
the surrounding country; but for the mere purpose of arriving at our
journey’s end, our taking that road is perfectly optional; it is a
question of time, trouble, and danger.

Not only _may_ we reason from particulars to particulars without passing
through generals, but we perpetually do so reason. All our earliest
inferences are of this nature. From the first dawn of intelligence we draw
inferences, but years elapse before we learn the use of general language.
The child, who, having burned his fingers, avoids to thrust them again
into the fire, has reasoned or inferred, though he has never thought of
the general maxim, Fire burns. He knows from memory that he has been
burned, and on this evidence believes, when he sees a candle, that if he
puts his finger into the flame of it, he will be burned again. He believes
this in every case which happens to arise; but without looking, in each
instance, beyond the present case. He is not generalizing; he is inferring
a particular from particulars. In the same way, also, brutes reason. There
is no ground for attributing to any of the lower animals the use of signs,
of such a nature as to render general propositions possible. But those
animals profit by experience, and avoid what they have found to cause them
pain, in the same manner, though not always with the same skill, as a
human creature. Not only the burned child, but the burned dog, dreads the
fire.

I believe that, in point of fact, when drawing inferences from our
personal experience, and not from maxims handed down to us by books or
tradition, we much oftener conclude from particulars to particulars
directly, than through the intermediate agency of any general proposition.
We are constantly reasoning from ourselves to other people, or from one
person to another, without giving ourselves the trouble to erect our
observations into general maxims of human or external nature. When we
conclude that some person will, on some given occasion, feel or act so and
so, we sometimes judge from an enlarged consideration of the manner in
which human beings in general, or persons of some particular character,
are accustomed to feel and act; but much oftener from merely recollecting
the feelings and conduct of the same person in some previous instance, or
from considering how we should feel or act ourselves. It is not only the
village matron, who, when called to a consultation upon the case of a
neighbor’s child, pronounces on the evil and its remedy simply on the
recollection and authority of what she accounts the similar case of her
Lucy. We all, where we have no definite maxims to steer by, guide
ourselves in the same way: and if we have an extensive experience, and
retain its impressions strongly, we may acquire in this manner a very
considerable power of accurate judgment, which we may be utterly incapable
of justifying or of communicating to others. Among the higher order of
practical intellects there have been many of whom it was remarked how
admirably they suited their means to their ends, without being able to
give any sufficient reasons for what they did; and applied, or seemed to
apply, recondite principles which they were wholly unable to state. This
is a natural consequence of having a mind stored with appropriate
particulars, and having been long accustomed to reason at once from these
to fresh particulars, without practicing the habit of stating to one’s
self or to others the corresponding general propositions. An old warrior,
on a rapid glance at the outlines of the ground, is able at once to give
the necessary orders for a skillful arrangement of his troops; though if
he has received little theoretical instruction, and has seldom been called
upon to answer to other people for his conduct, he may never have had in
his mind a single general theorem respecting the relation between ground
and array. But his experience of encampments, in circumstances more or
less similar, has left a number of vivid, unexpressed, ungeneralized
analogies in his mind, the most appropriate of which, instantly suggesting
itself, determines him to a judicious arrangement.

The skill of an uneducated person in the use of weapons, or of tools, is
of a precisely similar nature. The savage who executes unerringly the
exact throw which brings down his game, or his enemy, in the manner most
suited to his purpose, under the operation of all the conditions
necessarily involved, the weight and form of the weapon, the direction and
distance of the object, the action of the wind, etc., owes this power to a
long series of previous experiments, the results of which he certainly
never framed into any verbal theorems or rules. The same thing may
generally be said of any other extraordinary manual dexterity. Not long
ago a Scotch manufacturer procured from England, at a high rate of wages,
a working dyer, famous for producing very fine colors, with the view of
teaching to his other workmen the same skill. The workman came; but his
mode of proportioning the ingredients, in which lay the secret of the
effects he produced, was by taking them up in handfuls, while the common
method was to weigh them. The manufacturer sought to make him turn his
handling system into an equivalent weighing system, that the general
principle of his peculiar mode of proceeding might be ascertained. This,
however, the man found himself quite unable to do, and therefore could
impart his skill to nobody. He had, from the individual cases of his own
experience, established a connection in his mind between fine effects of
color, and tactual perceptions in handling his dyeing materials; and from
these perceptions he could, in any particular case, infer the means to be
employed, and the effects which would be produced, but could not put
others in possession of the grounds on which he proceeded, from having
never generalized them in his own mind, or expressed them in language.

Almost every one knows Lord Mansfield’s advice to a man of practical good
sense, who, being appointed governor of a colony, had to preside in its
courts of justice, without previous judicial practice or legal education.
The advice was to give his decision boldly, for it would probably be
right; but never to venture on assigning reasons, for they would almost
infallibly be wrong. In cases like this, which are of no uncommon
occurrence, it would be absurd to suppose that the bad reason was the
source of the good decision. Lord Mansfield knew that if any reason were
assigned it would be necessarily an afterthought, the judge being _in
fact_ guided by impressions from past experience, without the circuitous
process of framing general principles from them, and that if he attempted
to frame any such he would assuredly fail. Lord Mansfield, however, would
not have doubted that a man of equal experience who had also a mind stored
with general propositions derived by legitimate induction from that
experience, would have been greatly preferable as a judge, to one, however
sagacious, who could not be trusted with the explanation and justification
of his own judgments. The cases of men of talent performing wonderful
things they know not how, are examples of the rudest and most spontaneous
form of the operations of superior minds. It is a defect in them, and
often a source of errors, not to have generalized as they went on; but
generalization, though a help, the most important indeed of all helps, is
not an essential.

Even the scientifically instructed, who possess, in the form of general
propositions, a systematic record of the results of the experience of
mankind, need not always revert to those general propositions in order to
apply that experience to a new case. It is justly remarked by Dugald
Stewart, that though the reasonings in mathematics depend entirely on the
axioms, it is by no means necessary to our seeing the conclusiveness of
the proof, that the axioms should be expressly adverted to. When it is
inferred that AB is equal to CD because each of them is equal to EF, the
most uncultivated understanding, as soon as the propositions were
understood, would assent to the inference, without having ever heard of
the general truth that “things which are equal to the same thing are equal
to one another.” This remark of Stewart, consistently followed out, goes
to the root, as I conceive, of the philosophy of ratiocination; and it is
to be regretted that he himself stopped short at a much more limited
application of it. He saw that the general propositions on which a
reasoning is said to depend, may, in certain cases, be altogether omitted,
without impairing its probative force. But he imagined this to be a
peculiarity belonging to axioms; and argued from it, that axioms are not
the foundations or first principles of geometry, from which all the other
truths of the science are synthetically deduced (as the laws of motion and
of the composition of forces in dynamics, the equal mobility of fluids in
hydrostatics, the laws of reflection and refraction in optics, are the
first principles of those sciences); but are merely necessary assumptions,
self-evident indeed, and the denial of which would annihilate all
demonstration, but from which, as premises, nothing can be demonstrated.
In the present, as in many other instances, this thoughtful and elegant
writer has perceived an important truth, but only by halves. Finding, in
the case of geometrical axioms, that general names have not any talismanic
virtue for conjuring new truths out of the well where they lie hid, and
not seeing that this is equally true in every other case of
generalization, he contended that axioms are in their nature barren of
consequences, and that the really fruitful truths, the real first
principles of geometry, are the definitions; that the definition, for
example, of the circle is to the properties of the circle, what the laws
of equilibrium and of the pressure of the atmosphere are to the rise of
the mercury in the Torricellian tube. Yet all that he had asserted
respecting the function to which the axioms are confined in the
demonstrations of geometry, holds equally true of the definitions. Every
demonstration in Euclid might be carried on without them. This is apparent
from the ordinary process of proving a proposition of geometry by means of
a diagram. What assumption, in fact, do we set out from, to demonstrate by
a diagram any of the properties of the circle? Not that in all circles the
radii are equal, but only that they are so in the circle ABC. As our
warrant for assuming this, we appeal, it is true, to the definition of a
circle in general; but it is only necessary that the assumption be granted
in the case of the particular circle supposed. From this, which is not a
general but a singular proposition, combined with other propositions of a
similar kind, some of which _when generalized_ are called definitions, and
other axioms, we prove that a certain conclusion is true, not of all
circles, but of the particular circle ABC; or at least would be so, if the
facts precisely accorded with our assumptions. The enunciation, as it is
called, that is, the general theorem which stands at the head of the
demonstration, is not the proposition actually demonstrated. One instance
only is demonstrated: but the process by which this is done, is a process
which, when we consider its nature, we perceive might be exactly copied in
an indefinite number of other instances; in every instance which conforms
to certain conditions. The contrivance of general language furnishing us
with terms which connote these conditions, we are able to assert this
indefinite multitude of truths in a single expression, and this expression
is the general theorem. By dropping the use of diagrams, and substituting,
in the demonstrations, general phrases for the letters of the alphabet, we
might prove the general theorem directly, that is, we might demonstrate
all the cases at once; and to do this we must, of course, employ as our
premises, the axioms and definitions in their general form. But this only
means, that if we can prove an individual conclusion by assuming an
individual fact, then in whatever case we are warranted in making an
exactly similar assumption, we may draw an exactly similar conclusion. The
definition is a sort of notice to ourselves and others, what assumptions
we think ourselves entitled to make. And so in all cases, the general
propositions, whether called definitions, axioms, or laws of nature, which
we lay down at the beginning of our reasonings, are merely abridged
statements, in a kind of short-hand, of the particular facts, which, as
occasion arises, we either think we may proceed on as proved, or intend to
assume. In any one demonstration it is enough if we assume for a
particular case suitably selected, what by the statement of the definition
or principle we announce that we intend to assume in all cases which may
arise. The definition of the circle, therefore, is to one of Euclid’s
demonstrations, exactly what, according to Stewart, the axioms are; that
is, the demonstration does not depend on it, but yet if we deny it the
demonstration fails. The proof does not rest on the general assumption,
but on a similar assumption confined to the particular case: that case,
however, being chosen as a specimen or paradigm of the whole class of
cases included in the theorem, there can be no ground for making the
assumption in that case which does not exist in every other; and to deny
the assumption as a general truth, is to deny the right of making it in
the particular instance.

There are, undoubtedly, the most ample reasons for stating both the
principles and the theorems in their general form, and these will be
explained presently, so far as explanation is requisite. But, that
unpracticed learners, even in making use of one theorem to demonstrate
another, reason rather from particular to particular than from the general
proposition, is manifest from the difficulty they find in applying a
theorem to a case in which the configuration of the diagram is extremely
unlike that of the diagram by which the original theorem was demonstrated.
A difficulty which, except in cases of unusual mental power, long practice
can alone remove, and removes chiefly by rendering us familiar with all
the configurations consistent with the general conditions of the theorem.

§ 4. From the considerations now adduced, the following conclusions seem
to be established. All inference is from particulars to particulars:
General propositions are merely registers of such inferences already made,
and short formulæ for making more: The major premise of a syllogism,
consequently, is a formula of this description: and the conclusion is not
an inference drawn _from_ the formula, but an inference drawn _according_
to the formula: the real logical antecedent, or premise, being the
particular facts from which the general proposition was collected by
induction. Those facts, and the individual instances which supplied them,
may have been forgotten: but a record remains, not indeed descriptive of
the facts themselves, but showing how those cases may be distinguished,
respecting which, the facts, when known, were considered to warrant a
given inference. According to the indications of this record we draw our
conclusion: which is, to all intents and purposes, a conclusion from the
forgotten facts. For this it is essential that we should read the record
correctly: and the rules of the syllogism are a set of precautions to
insure our doing so.

This view of the functions of the syllogism is confirmed by the
consideration of precisely those cases which might be expected to be least
favorable to it, namely, those in which ratiocination is independent of
any previous induction. We have already observed that the syllogism, in
the ordinary course of our reasoning, is only the latter half of the
process of traveling from premises to a conclusion. There are, however,
some peculiar cases in which it is the whole process. Particulars alone
are capable of being subjected to observation; and all knowledge which is
derived from observation, begins, therefore, of necessity, in particulars;
but our knowledge may, in cases of certain descriptions, be conceived as
coming to us from other sources than observation. It may present itself as
coming from testimony, which, on the occasion and for the purpose in hand,
is accepted as of an authoritative character: and the information thus
communicated, may be conceived to comprise not only particular facts but
general propositions, as when a scientific doctrine is accepted without
examination on the authority of writers, or a theological doctrine on that
of Scripture. Or the generalization may not be, in the ordinary sense, an
assertion at all, but a command; a law, not in the philosophical, but in
the moral and political sense of the term: an expression of the desire of
a superior, that we, or any number of other persons, shall conform our
conduct to certain general instructions. So far as this asserts a fact,
namely, a volition of the legislator, that fact is an individual fact, and
the proposition, therefore, is not a general proposition. But the
description therein contained of the conduct which it is the will of the
legislator that his subjects should observe, is general. The proposition
asserts, not that all men _are_ any thing, but that all men _shall_ do
something.

In both these cases the generalities are the original data, and the
particulars are elicited from them by a process which correctly resolves
itself into a series of syllogisms. The real nature, however, of the
supposed deductive process, is evident enough. The only point to be
determined is, whether the authority which declared the general
proposition, intended to include this case in it; and whether the
legislator intended his command to apply to the present case among others,
or not. This is ascertained by examining whether the case possesses the
marks by which, as those authorities have signified, the cases which they
meant to certify or to influence may be known. The object of the inquiry
is to make out the witness’s or the legislator’s intention, through the
indication given by their words. This is a question, as the Germans
express it, of hermeneutics. The operation is not a process of inference,
but a process of interpretation.

In this last phrase we have obtained an expression which appears to me to
characterize, more aptly than any other, the functions of the syllogism in
all cases. When the premises are given by authority, the function of
Reasoning is to ascertain the testimony of a witness, or the will of a
legislator, by interpreting the signs in which the one has intimated his
assertion and the other his command. In like manner, when the premises are
derived from observation, the function of Reasoning is to ascertain what
we (or our predecessors) formerly thought might be inferred from the
observed facts, and to do this by interpreting a memorandum of ours, or of
theirs. The memorandum reminds us, that from evidence, more or less
carefully weighed, it formerly appeared that a certain attribute might be
inferred wherever we perceive a certain mark. The proposition, All men are
mortal (for instance) shows that we have had experience from which we
thought it followed that the attributes connoted by the term man, are a
mark of mortality. But when we conclude that the Duke of Wellington is
mortal, we do not infer this from the memorandum, but from the former
experience. All that we infer from the memorandum is our own previous
belief, (or that of those who transmitted to us the proposition),
concerning the inferences which that former experience would warrant.

This view of the nature of the syllogism renders consistent and
intelligible what otherwise remains obscure and confused in the theory of
Archbishop Whately and other enlightened defenders of the syllogistic
doctrine, respecting the limits to which its functions are confined. They
affirm in as explicit terms as can be used, that the sole office of
general reasoning is to prevent inconsistency in our opinions; to prevent
us from assenting to any thing, the truth of which would contradict
something to which we had previously on good grounds given our assent. And
they tell us, that the sole ground which a syllogism affords for assenting
to the conclusion, is that the supposition of its being false, combined
with the supposition that the premises are true, would lead to a
contradiction in terms. Now this would be but a lame account of the real
grounds which we have for believing the facts which we learn from
reasoning, in contradistinction to observation. The true reason why we
believe that the Duke of Wellington will die, is that his fathers, and our
fathers, and all other persons who were contemporary with them, have died.
Those facts are the real premises of the reasoning. But we are not led to
infer the conclusion from those premises, by the necessity of avoiding any
verbal inconsistency. There is no contradiction in supposing that all
those persons have died, and that the Duke of Wellington may,
notwithstanding, live forever. But there would be a contradiction if we
first, on the ground of those same premises, made a general assertion
including and covering the case of the Duke of Wellington, and then
refused to stand to it in the individual case. There is an inconsistency
to be avoided between the memorandum we make of the inferences which may
be justly drawn in future cases, and the inferences we actually draw in
those cases when they arise. With this view we interpret our own formula,
precisely as a judge interprets a law: in order that we may avoid drawing
any inferences not conformable to our former intention, as a judge avoids
giving any decision not conformable to the legislator’s intention. The
rules for this interpretation are the rules of the syllogism: and its sole
purpose is to maintain consistency between the conclusions we draw in
every particular case, and the previous general directions for drawing
them; whether those general directions were framed by ourselves as the
result of induction, or were received by us from an authority competent to
give them.

§ 5. In the above observations it has, I think, been shown, that, though
there is always a process of reasoning or inference where a syllogism is
used, the syllogism is not a correct analysis of that process of reasoning
or inference; which is, on the contrary (when not a mere inference from
testimony), an inference from particulars to particulars; authorized by a
previous inference from particulars to generals, and substantially the
same with it; of the nature, therefore, of Induction. But while these
conclusions appear to me undeniable, I must yet enter a protest, as strong
as that of Archbishop Whately himself, against the doctrine that the
syllogistic art is useless for the purposes of reasoning. The reasoning
lies in the act of generalization, not in interpreting the record of that
act; but the syllogistic form is an indispensable collateral security for
the correctness of the generalization itself.

It has already been seen, that if we have a collection of particulars
sufficient for grounding an induction, we need not frame a general
proposition; we may reason at once from those particulars to other
particulars. But it is to be remarked withal, that whenever, from a set of
particular cases, we can legitimately draw any inference, we may
legitimately make our inference a general one. If, from observation and
experiment, we can conclude to one new case, so may we to an indefinite
number. If that which has held true in our past experience will therefore
hold in time to come, it will hold not merely in some individual case, but
in all cases of some given description. Every induction, therefore, which
suffices to prove one fact, proves an indefinite multitude of facts: the
experience which justifies a single prediction must be such as will
suffice to bear out a general theorem. This theorem it is extremely
important to ascertain and declare, in its broadest form of generality;
and thus to place before our minds, in its full extent, the whole of what
our evidence must prove if it proves any thing.

This throwing of the whole body of possible inferences from a given set of
particulars, into one general expression, operates as a security for their
being just inferences, in more ways than one. First, the general principle
presents a larger object to the imagination than any of the singular
propositions which it contains. A process of thought which leads to a
comprehensive generality, is felt as of greater importance than one which
terminates in an insulated fact; and the mind is, even unconsciously, led
to bestow greater attention upon the process, and to weigh more carefully
the sufficiency of the experience appealed to, for supporting the
inference grounded upon it. There is another, and a more important,
advantage. In reasoning from a course of individual observations to some
new and unobserved case, which we are but imperfectly acquainted with (or
we should not be inquiring into it), and in which, since we are inquiring
into it, we probably feel a peculiar interest; there is very little to
prevent us from giving way to negligence, or to any bias which may affect
our wishes or our imagination, and, under that influence, accepting
insufficient evidence as sufficient. But if, instead of concluding
straight to the particular case, we place before ourselves an entire class
of facts—the whole contents of a general proposition, every tittle of
which is legitimately inferable from our premises, if that one particular
conclusion is so; there is then a considerable likelihood that if the
premises are insufficient, and the general inference therefore,
groundless, it will comprise within it some fact or facts the reverse of
which we already know to be true; and we shall thus discover the error in
our generalization by a _reductio ad impossibile_.

Thus if, during the reign of Marcus Aurelius, a subject of the Roman
empire, under the bias naturally given to the imagination and expectations
by the lives and characters of the Antonines, had been disposed to expect
that Commodus would be a just ruler; supposing him to stop there, he might
only have been undeceived by sad experience. But if he reflected that this
expectation could not be justifiable unless from the same evidence he was
warranted in concluding some general proposition, as, for instance, that
all Roman emperors are just rulers; he would immediately have thought of
Nero, Domitian, and other instances, which, showing the falsity of the
general conclusion, and therefore the insufficiency of the premises, would
have warned him that those premises could not prove in the instance of
Commodus, what they were inadequate to prove in any collection of cases in
which his was included.

The advantage, in judging whether any controverted inference is
legitimate, of referring to a parallel case, is universally acknowledged.
But by ascending to the general proposition, we bring under our view not
one parallel case only, but all possible parallel cases at once; all cases
to which the same set of evidentiary considerations are applicable.

When, therefore, we argue from a number of known cases to another case
supposed to be analogous, it is always possible, and generally
advantageous, to divert our argument into the circuitous channel of an
induction from those known cases to a general proposition, and a
subsequent application of that general proposition to the unknown case.
This second part of the operation, which, as before observed, is
essentially a process of interpretation, will be resolvable into a
syllogism or a series of syllogisms, the majors of which will be general
propositions embracing whole classes of cases; every one of which
propositions must be true in all its extent, if the argument is
maintainable. If, therefore, any fact fairly coming within the range of
one of these general propositions, and consequently asserted by it, is
known or suspected to be other than the proposition asserts it to be, this
mode of stating the argument causes us to know or to suspect that the
original observations, which are the real grounds of our conclusion, are
not sufficient to support it. And in proportion to the greater chance of
our detecting the inconclusiveness of our evidence, will be the increased
reliance we are entitled to place in it if no such evidence of defect
shall appear.

The value, therefore, of the syllogistic form, and of the rules for using
it correctly, does not consist in their being the form and the rules
according to which our reasonings are necessarily, or even usually, made;
but in their furnishing us with a mode in which those reasonings may
always be represented, and which is admirably calculated, if they are
inconclusive, to bring their inconclusiveness to light. An induction from
particulars to generals, followed by a syllogistic process from those
generals to other particulars, is a form in which we may always state our
reasonings if we please. It is not a form in which we _must_ reason, but
it is a form in which we _may_ reason, and into which it is indispensable
to throw our reasoning, when there is any doubt of its validity: though
when the case is familiar and little complicated, and there is no
suspicion of error, we may, and do, reason at once from the known
particular cases to unknown ones.(58)

These are the uses of syllogism, as a mode of verifying any given
argument. Its ulterior uses, as respects the general course of our
intellectual operations, hardly require illustration, being in fact the
acknowledged uses of general language. They amount substantially to this,
that the inductions may be made once for all: a single careful
interrogation of experience may suffice, and the result may be registered
in the form of a general proposition, which is committed to memory or to
writing, and from which afterward we have only to syllogize. The
particulars of our experiments may then be dismissed from the memory, in
which it would be impossible to retain so great a multitude of details;
while the knowledge which those details afforded for future use, and which
would otherwise be lost as soon as the observations were forgotten, or as
their record became too bulky for reference, is retained in a commodious
and immediately available shape by means of general language.

Against this advantage is to be set the countervailing inconvenience, that
inferences originally made on insufficient evidence become consecrated,
and, as it were, hardened into general maxims; and the mind cleaves to
them from habit, after it has outgrown any liability to be misled by
similar fallacious appearances if they were now for the first time
presented; but having forgotten the particulars, it does not think of
revising its own former decision. An inevitable drawback, which, however
considerable in itself, forms evidently but a small set-off against the
immense benefits of general language.

The use of the syllogism is in truth no other than the use of general
propositions in reasoning. We _can_ reason without them; in simple and
obvious cases we habitually do so; minds of great sagacity can do it in
cases not simple and obvious, provided their experience supplies them with
instances essentially similar to every combination of circumstances likely
to arise. But other minds, and the same minds where they have not the same
pre-eminent advantages of personal experience, are quite helpless without
the aid of general propositions, wherever the case presents the smallest
complication; and if we made no general propositions, few persons would
get much beyond those simple inferences which are drawn by the more
intelligent of the brutes. Though not necessary to reasoning, general
propositions are necessary to any considerable progress in reasoning. It
is, therefore, natural and indispensable to separate the process of
investigation into two parts; and obtain general formulæ for determining
what inferences may be drawn, before the occasion arises for drawing the
inferences. The work of drawing them is then that of applying the formulæ;
and the rules of syllogism are a system of securities for the correctness
of the application.

§ 6. To complete the series of considerations connected with the
philosophical character of the syllogism, it is requisite to consider,
since the syllogism is not the universal type of the reasoning process,
what is the real type. This resolves itself into the question, what is the
nature of the minor premise, and in what manner it contributes to
establish the conclusion: for as to the major, we now fully understand,
that the place which it nominally occupies in our reasonings, properly
belongs to the individual facts or observations of which it expresses the
general result; the major itself being no real part of the argument, but
an intermediate halting-place for the mind, interposed by an artifice of
language between the real premises and the conclusion, by way of a
security, which it is in a most material degree, for the correctness of
the process. The minor, however, being an indispensable part of the
syllogistic expression of an argument, without doubt either is, or
corresponds to, an equally indispensable part of the argument itself, and
we have only to inquire what part.

It is perhaps worth while to notice here a speculation of a philosopher to
whom mental science is much indebted, but who, though a very penetrating,
was a very hasty thinker, and whose want of due circumspection rendered
him fully as remarkable for what he did not see, as for what he saw. I
allude to Dr. Thomas Brown, whose theory of ratiocination is peculiar. He
saw the _petitio principii_ which is inherent in every syllogism, if we
consider the major to be itself the evidence by which the conclusion is
proved, instead of being, what in fact it is, an assertion of the
existence of evidence sufficient to prove any conclusion of a given
description. Seeing this, Dr. Brown not only failed to see the immense
advantage, in point of security for correctness, which is gained by
interposing this step between the real evidence and the conclusion; but he
thought it incumbent on him to strike out the major altogether from the
reasoning process, without substituting any thing else, and maintained
that our reasonings consist only of the minor premise and the conclusion,
Socrates is a man, therefore Socrates is mortal: thus actually
suppressing, as an unnecessary step in the argument, the appeal to former
experience. The absurdity of this was disguised from him by the opinion he
adopted, that reasoning is merely analyzing our own general notions, or
abstract ideas; and that the proposition, Socrates is mortal, is evolved
from the proposition, Socrates is a man, simply by recognizing the notion
of mortality as already contained in the notion we form of a man.

After the explanations so fully entered into on the subject of
propositions, much further discussion can not be necessary to make the
radical error of this view of ratiocination apparent. If the word man
connoted mortality; if the meaning of “mortal” were involved in the
meaning of “man;” we might, undoubtedly, evolve the conclusion from the
minor alone, because the minor would have already asserted it. But if, as
is in fact the case, the word man does not connote mortality, how does it
appear that in the mind of every person who admits Socrates to be a man,
the idea of man must include the idea of mortality? Dr. Brown could not
help seeing this difficulty, and in order to avoid it, was led, contrary
to his intention, to re-establish, under another name, that step in the
argument which corresponds to the major, by affirming the necessity of
_previously perceiving_ the relation between the idea of man and the idea
of mortal. If the reasoner has not previously perceived this relation, he
will not, says Dr. Brown, infer because Socrates is a man, that Socrates
is mortal. But even this admission, though amounting to a surrender of the
doctrine that an argument consists of the minor and the conclusion alone,
will not save the remainder of Dr. Brown’s theory. The failure of assent
to the argument does not take place merely because the reasoner, for want
of due analysis, does not perceive that his idea of man includes the idea
of mortality; it takes place, much more commonly, because in his mind that
relation between the two ideas has never existed. And in truth it never
does exist, except as the result of experience. Consenting, for the sake
of the argument, to discuss the question on a supposition of which we have
recognized the radical incorrectness, namely, that the meaning of a
proposition relates to the ideas of the things spoken of, and not to the
things themselves; I must yet observe, that the idea of man, as a
universal idea, the common property of all rational creatures, can not
involve any thing but what is strictly implied in the name. If any one
includes in his own private idea of man, as no doubt is always the case,
some other attributes, such for instance as mortality, he does so only as
the consequence of experience, after having satisfied himself that all men
possess that attribute: so that whatever the idea contains, in any
person’s mind, beyond what is included in the conventional signification
of the word, has been added to it as the result of assent to a
proposition; while Dr. Brown’s theory requires us to suppose, on the
contrary, that assent to the proposition is produced by evolving, through
an analytic process, this very element out of the idea. This theory,
therefore, may be considered as sufficiently refuted; and the minor
premise must be regarded as totally insufficient to prove the conclusion,
except with the assistance of the major, or of that which the major
represents, namely, the various singular propositions expressive of the
series of observations, of which the generalization called the major
premise is the result.

In the argument, then, which proves that Socrates is mortal, one
indispensable part of the premises will be as follows: “My father, and my
father’s father, A, B, C, and an indefinite number of other persons, were
mortal;” which is only an expression in different words of the observed
fact that they have died. This is the major premise divested of the
_petitio principii_, and cut down to as much as is really known by direct
evidence.

In order to connect this proposition with the conclusion Socrates is
mortal, the additional link necessary is such a proposition as the
following: “Socrates resembles my father, and my father’s father, and the
other individuals specified.” This proposition we assert when we say that
Socrates is a man. By saying so we likewise assert in what respect he
resembles them, namely, in the attributes connoted by the word man. And we
conclude that he further resembles them in the attribute mortality.

§ 7. We have thus obtained what we were seeking, a universal type of the
reasoning process. We find it resolvable in all cases into the following
elements: Certain individuals have a given attribute; an individual or
individuals resemble the former in certain other attributes; therefore
they resemble them also in the given attribute. This type of ratiocination
does not claim, like the syllogism, to be conclusive from the mere form of
the expression; nor can it possibly be so. That one proposition does or
does not assert the very fact which was already asserted in another, may
appear from the form of the expression, that is, from a comparison of the
language; but when the two propositions assert facts which are _bona fide_
different, whether the one fact proves the other or not can never appear
from the language, but must depend on other considerations. Whether, from
the attributes in which Socrates resembles those men who have heretofore
died, it is allowable to infer that he resembles them also in being
mortal, is a question of Induction; and is to be decided by the principles
or canons which we shall hereafter recognize as tests of the correct
performance of that great mental operation.

Meanwhile, however, it is certain, as before remarked, that if this
inference can be drawn as to Socrates, it can be drawn as to all others
who resemble the observed individuals in the same attributes in which he
resembles them; that is (to express the thing concisely) of all mankind.
If, therefore, the argument be admissible in the case of Socrates, we are
at liberty, once for all, to treat the possession of the attributes of man
as a mark, or satisfactory evidence, of the attribute of mortality. This
we do by laying down the universal proposition, All men are mortal, and
interpreting this, as occasion arises, in its application to Socrates and
others. By this means we establish a very convenient division of the
entire logical operation into two steps; first, that of ascertaining what
attributes are marks of mortality; and, secondly, whether any given
individuals possess those marks. And it will generally be advisable, in
our speculations on the reasoning process, to consider this double
operation as in fact taking place, and all reasoning as carried on in the
form into which it must necessarily be thrown to enable us to apply to it
any test of its correct performance.

Although, therefore, all processes of thought in which the ultimate
premises are particulars, whether we conclude from particulars to a
general formula, or from particulars to other particulars according to
that formula, are equally Induction; we shall yet, conformably to usage,
consider the name Induction as more peculiarly belonging to the process of
establishing the general proposition, and the remaining operation, which
is substantially that of interpreting the general proposition, we shall
call by its usual name, Deduction. And we shall consider every process by
which any thing is inferred respecting an unobserved case, as consisting
of an Induction followed by a Deduction; because, although the process
needs not necessarily be carried on in this form, it is always susceptible
of the form, and must be thrown into it when assurance of scientific
accuracy is needed and desired.

§ 8. The theory of the syllogism laid down in the preceding pages, has
obtained, among other important adhesions, three of peculiar value: those
of Sir John Herschel,(59) Dr. Whewell,(60) and Mr. Bailey;(61) Sir John
Herschel considering the doctrine, though not strictly “a discovery,”
having been anticipated by Berkeley,(62) to be “one of the greatest steps
which have yet been made in the philosophy of Logic.” “When we consider”
(to quote the further words of the same authority) “the inveteracy of the
habits and prejudices which it has cast to the winds,” there is no cause
for misgiving in the fact that other thinkers, no less entitled to
consideration, have formed a very different estimate of it. Their
principal objection can not be better or more succinctly stated than by
borrowing a sentence from Archbishop Whately.(63) “In every case where an
inference is drawn from Induction (unless that name is to be given to a
mere random guess without any grounds at all) we must form a judgment that
the instance or instances adduced are _sufficient_ to authorize the
conclusion; that it is _allowable_ to take these instances as a sample
warranting an inference respecting the whole class;” and the expression of
this judgment in words (it has been said by several of my critics) _is_
the major premise.

I quite admit that the major is an affirmation of the sufficiency of the
evidence on which the conclusion rests. That it is so, is the very essence
of my own theory. And whoever admits that the major premise is _only_
this, adopts the theory in its essentials.

But I can not concede that this recognition of the sufficiency of the
evidence—that is, of the correctness of the induction—is a part of the
induction itself; unless we ought to say that it is a part of every thing
we do, to satisfy ourselves that it has been done rightly. We conclude
from known instances to unknown by the impulse of the generalizing
propensity; and (until after a considerable amount of practice and mental
discipline) the question of the sufficiency of the evidence is only raised
by a retrospective act, turning back upon our own footsteps, and examining
whether we were warranted in doing what we have provisionally done. To
speak of this reflex operation as part of the original one, requiring to
be expressed in words in order that the verbal formula may correctly
represent the psychological process, appears to me false psychology.(64)
We review our syllogistic as well as our inductive processes, and
recognize that they have been correctly performed; but logicians do not
add a third premise to the syllogism, to express this act of recognition.
A careful copyist verifies his transcript by collating it with the
original; and if no error appears, he recognizes that the transcript has
been correctly made. But we do not call the examination of the copy a part
of the act of copying.

The conclusion in an induction is inferred from the evidence itself, and
not from a recognition of the sufficiency of the evidence; as I infer that
my friend is walking toward me because I see him, and not because I
recognize that my eyes are open, and that eyesight is a means of
knowledge. In all operations which require care, it is good to assure
ourselves that the process has been performed accurately; but the testing
of the process is not the process itself; and, besides, may have been
omitted altogether, and yet the process be correct. It is precisely
because that operation is omitted in ordinary unscientific reasoning, that
there is any thing gained in certainty by throwing reasoning into the
syllogistic form. To make sure, as far as possible, that it shall not be
omitted, we make the testing operation a part of the reasoning process
itself. We insist that the inference from particulars to particulars shall
pass through a general proposition. But this is a security for good
reasoning, not a condition of all reasoning; and in some cases not even a
security. Our most familiar inferences are all made before we learn the
use of general propositions; and a person of untutored sagacity will
skillfully apply his acquired experience to adjacent cases, though he
would bungle grievously in fixing the limits of the appropriate general
theorem. But though he may conclude rightly, he never, properly speaking,
knows whether he has done so or not; he has not tested his reasoning. Now,
this is precisely what forms of reasoning do for us. We do not need them
to enable us to reason, but to enable us to know whether we reason
correctly.

In still further answer to the objection, it may be added that—even when
the test has been applied, and the sufficiency of the evidence
recognized—if it is sufficient to support the general proposition, it is
sufficient also to support an inference from particulars to particulars
without passing through the general proposition. The inquirer who has
logically satisfied himself that the conditions of legitimate induction
were realized in the cases A, B, C, would be as much justified in
concluding directly to the Duke of Wellington as in concluding to all men.
The general conclusion is never legitimate, unless the particular one
would be so too; and in no sense, intelligible to me, can the particular
conclusion be said to be drawn from the general one. Whenever there is
ground for drawing any conclusion at all from particular instances, there
is ground for a general conclusion; but that this general conclusion
should be actually drawn, however useful, can not be an indispensable
condition of the validity of the inference in the particular case. A man
gives away sixpence by the same power by which he disposes of his whole
fortune; but it is not necessary to the legality of the smaller act, that
he should make a formal assertion of his right to the greater one.

Some additional remarks, in reply to minor objections, are appended.(65)

§ 9. The preceding considerations enable us to understand the true nature
of what is termed, by recent writers, Formal Logic, and the relation
between it and Logic in the widest sense. Logic, as I conceive it, is the
entire theory of the ascertainment of reasoned or inferred truth. Formal
Logic, therefore, which Sir William Hamilton from his own point of view,
and Archbishop Whately from his, have represented as the whole of Logic
properly so called, is really a very subordinate part of it, not being
directly concerned with the process of Reasoning or Inference in the sense
in which that process is a part of the Investigation of Truth. What, then,
is Formal Logic? The name seems to be properly applied to all that portion
of doctrine which relates to the equivalence of different modes of
expression; the rules for determining when assertions in a given form
imply or suppose the truth or falsity of other assertions. This includes
the theory of the Import of Propositions, and of their Conversion,
Æquipollence, and Opposition; of those falsely called Inductions (to be
hereafter spoken of)(66), in which the apparent generalization is a mere
abridged statement of cases known individually; and finally, of the
syllogism: while the theory of Naming, and of (what is inseparably
connected with it) Definition, though belonging still more to the other
and larger kind of logic than to this, is a necessary preliminary to this.
The end aimed at by Formal Logic, and attained by the observance of its
precepts, is not truth, but consistency. It has been seen that this is the
only direct purpose of the rules of the syllogism; the intention and
effect of which is simply to keep our inferences or conclusions in
complete consistency with our general formulæ or directions for drawing
them. The Logic of Consistency is a necessary auxiliary to the logic of
truth, not only because what is inconsistent with itself or with other
truths can not be true, but also because truth can only be successfully
pursued by drawing inferences from experience, which, if warrantable at
all, admit of being generalized, and, to test their warrantableness,
require to be exhibited in a generalized form; after which the correctness
of their application to particular cases is a question which specially
concerns the Logic of Consistency. This Logic, not requiring any
preliminary knowledge of the processes or conclusions of the various
sciences, may be studied with benefit in a much earlier stage of education
than the Logic of Truth: and the practice which has empirically obtained
of teaching it apart, through elementary treatises which do not attempt to
include any thing else, though the reasons assigned for the practice are
in general very far from philosophical, admits of philosophical
justification.




                               Chapter IV.


Of Trains Of Reasoning, And Deductive Sciences.


§ 1. In our analysis of the syllogism, it appeared that the minor premise
always affirms a resemblance between a new case and some cases previously
known; while the major premise asserts something which, having been found
true of those known cases, we consider ourselves warranted in holding true
of any other case resembling the former in certain given particulars.

If all ratiocinations resembled, as to the minor premise, the examples
which were exclusively employed in the preceding chapter; if the
resemblance, which that premise asserts, were obvious to the senses, as in
the proposition “Socrates is a man,” or were at once ascertainable by
direct observation; there would be no necessity for trains of reasoning,
and Deductive or Ratiocinative Sciences would not exist. Trains of
reasoning exist only for the sake of extending an induction founded, as
all inductions must be, on observed cases, to other cases in which we not
only can not directly observe the fact which is to be proved, but can not
directly observe even the mark which is to prove it.

§ 2. Suppose the syllogism to be, All cows ruminate, the animal which is
before me is a cow, therefore it ruminates. The minor, if true at all, is
obviously so: the only premise the establishment of which requires any
anterior process of inquiry, is the major; and provided the induction of
which that premise is the expression was correctly performed, the
conclusion respecting the animal now present will be instantly drawn;
because, as soon as she is compared with the formula, she will be
identified as being included in it. But suppose the syllogism to be the
following: All arsenic is poisonous, the substance which is before me is
arsenic, therefore it is poisonous. The truth of the minor may not here be
obvious at first sight; it may not be intuitively evident, but may itself
be known only by inference. It may be the conclusion of another argument,
which, thrown into the syllogistic form, would stand thus: Whatever when
lighted produces a dark spot on a piece of white porcelain held in the
flame, which spot is soluble in hypochloride of calcium, is arsenic; the
substance before me conforms to this condition; therefore it is arsenic.
To establish, therefore, the ultimate conclusion, The substance before me
is poisonous, requires a process, which, in order to be syllogistically
expressed, stands in need of two syllogisms; and we have a Train of
Reasoning.

When, however, we thus add syllogism to syllogism, we are really adding
induction to induction. Two separate inductions must have taken place to
render this chain of inference possible; inductions founded, probably, on
different sets of individual instances, but which converge in their
results, so that the instance which is the subject of inquiry comes within
the range of them both. The record of these inductions is contained in the
majors of the two syllogisms. First, we, or others for us, have examined
various objects which yielded under the given circumstances a dark spot
with the given property, and found that they possessed the properties
connoted by the word arsenic; they were metallic, volatile, their vapor
had a smell of garlic, and so forth. Next, we, or others for us, have
examined various specimens which possessed this metallic and volatile
character, whose vapor had this smell, etc., and have invariably found
that they were poisonous. The first observation we judge that we may
extend to all substances whatever which yield that particular kind of dark
spot; the second, to all metallic and volatile substances resembling those
we examined; and consequently, not to those only which are seen to be
such, but to those which are concluded to be such by the prior induction.
The substance before us is only seen to come within one of these
inductions; but by means of this one, it is brought within the other. We
are still, as before, concluding from particulars to particulars; but we
are now concluding from particulars observed, to other particulars which
are not, as in the simple case, _seen_ to resemble them in material
points, but _inferred_ to do so, because resembling them in something
else, which we have been led by quite a different set of instances to
consider as a mark of the former resemblance.

This first example of a train of reasoning is still extremely simple, the
series consisting of only two syllogisms. The following is somewhat more
complicated: No government, which earnestly seeks the good of its
subjects, is likely to be overthrown; some particular government earnestly
seeks the good of its subjects, therefore it is not likely to be
overthrown. The major premise in this argument we shall suppose not to be
derived from considerations _a priori_, but to be a generalization from
history, which, whether correct or erroneous, must have been founded on
observation of governments concerning whose desire of the good of their
subjects there was no doubt. It has been found, or thought to be found,
that these were not easily overthrown, and it has been deemed that those
instances warranted an extension of the same predicate to any and every
government which resembles them in the attribute of desiring earnestly the
good of its subjects. But _does_ the government in question thus resemble
them? This may be debated _pro_ and _con_ by many arguments, and must, in
any case, be proved by another induction; for we can not directly observe
the sentiments and desires of the persons who carry on the government. To
prove the minor, therefore, we require an argument in this form: Every
government which acts in a certain manner, desires the good of its
subjects; the supposed government acts in that particular manner,
therefore it desires the good of its subjects. But is it true that the
government acts in the manner supposed? This minor also may require proof;
still another induction, as thus: What is asserted by intelligent and
disinterested witnesses, may be believed to be true; that the government
acts in this manner, is asserted by such witnesses, therefore it may be
believed to be true. The argument hence consists of three steps. Having
the evidence of our senses that the case of the government under
consideration resembles a number of former cases, in the circumstance of
having something asserted respecting it by intelligent and disinterested
witnesses, we infer, first, that, as in those former instances, so in this
instance, the assertion is true. Secondly, what was asserted of the
government being that it acts in a particular manner, and other
governments or persons having been observed to act in the same manner, the
government in question is brought into known resemblance with those other
governments or persons; and since they were known to desire the good of
the people, it is thereupon, by a second induction, inferred that the
particular government spoken of, desires the good of the people. This
brings that government into known resemblance with the other governments
which were thought likely to escape revolution, and thence, by a third
induction, it is concluded that this particular government is also likely
to escape. This is still reasoning from particulars to particulars, but we
now reason to the new instance from three distinct sets of former
instances: to one only of those sets of instances do we directly perceive
the new one to be similar; but from that similarity we inductively infer
that it has the attribute by which it is assimilated to the next set, and
brought within the corresponding induction; after which by a repetition of
the same operation we infer it to be similar to the third set, and hence a
third induction conducts us to the ultimate conclusion.

§ 3. Notwithstanding the superior complication of these examples, compared
with those by which in the preceding chapter we illustrated the general
theory of reasoning, every doctrine which we then laid down holds equally
true in these more intricate cases. The successive general propositions
are not steps in the reasoning, are not intermediate links in the chain of
inference, between the particulars observed and those to which we apply
the observation. If we had sufficiently capacious memories, and a
sufficient power of maintaining order among a huge mass of details, the
reasoning could go on without any general propositions; they are mere
formulæ for inferring particulars from particulars. The principle of
general reasoning is (as before explained), that if, from observation of
certain known particulars, what was seen to be true of them can be
inferred to be true of any others, it may be inferred of all others which
are of a certain description. And in order that we may never fail to draw
this conclusion in a new case when it can be drawn correctly, and may
avoid drawing it when it can not, we determine once for all what are the
distinguishing marks by which such cases may be recognized. The subsequent
process is merely that of identifying an object, and ascertaining it to
have those marks; whether we identify it by the very marks themselves, or
by others which we have ascertained (through another and a similar
process) to be marks of those marks. The real inference is always from
particulars to particulars, from the observed instances to an unobserved
one: but in drawing this inference, we conform to a formula which we have
adopted for our guidance in such operations, and which is a record of the
criteria by which we thought we had ascertained that we might distinguish
when the inference could, and when it could not, be drawn. The real
premises are the individual observations, even though they may have been
forgotten, or, being the observations of others and not of ourselves, may,
to us, never have been known: but we have before us proof that we or
others once thought them sufficient for an induction, and we have marks to
show whether any new case is one of those to which, if then known, the
induction would have been deemed to extend. These marks we either
recognize at once, or by the aid of other marks, which by another previous
induction we collected to be marks of the first. Even these marks of marks
may only be recognized through a third set of marks; and we may have a
train of reasoning, of any length, to bring a new case within the scope of
an induction grounded on particulars its similarity to which is only
ascertained in this indirect manner.

Thus, in the preceding example, the ultimate inductive inference was, that
a certain government was not likely to be overthrown; this inference was
drawn according to a formula in which desire of the public good was set
down as a mark of not being likely to be overthrown; a mark of this mark
was, acting in a particular manner; and a mark of acting in that manner
was, being asserted to do so by intelligent and disinterested witnesses:
this mark, the government under discussion was recognized by the senses as
possessing. Hence that government fell within the last induction, and by
it was brought within all the others. The perceived resemblance of the
case to one set of observed particular cases, brought it into known
resemblance with another set, and that with a third.

In the more complex branches of knowledge, the deductions seldom consist,
as in the examples hitherto exhibited, of a single chain, _a_ a mark of
_b, b_ of _c, c_ of _d_, therefore _a_ a mark of _d_. They consist (to
carry on the same metaphor) of several chains united at the extremity, as
thus: _a_ a mark of _d, b_ of _e, c_ of _f, d e f_ of _n_, therefore _a b
c_ a mark of _n_. Suppose, for example, the following combination of
circumstances: 1st, rays of light impinging on a reflecting surface; 2d,
that surface parabolic; 3d, those rays parallel to each other and to the
axis of the surface. It is to be proved that the concourse of these three
circumstances is a mark that the reflected rays will pass through the
focus of the parabolic surface. Now, each of the three circumstances is
singly a mark of something material to the case. Rays of light impinging
on a reflecting surface are a mark that those rays will be reflected at an
angle equal to the angle of incidence. The parabolic form of the surface,
is a mark that, from any point of it, a line drawn to the focus and a line
parallel to the axis will make equal angles with the surface. And finally,
the parallelism of the rays to the axis is a mark that their angle of
incidence coincides with one of these equal angles. The three marks taken
together are therefore a mark of all these three things united. But the
three united are evidently a mark that the angle of reflection must
coincide with the other of the two equal angles, that formed by a line
drawn to the focus; and this again, by the fundamental axiom concerning
straight lines, is a mark that the reflected rays pass through the focus.
Most chains of physical deduction are of this more complicated type; and
even in mathematics such are abundant, as in all propositions where the
hypothesis includes numerous conditions: “_If_ a circle be taken, and _if_
within that circle a point be taken, not the centre, and _if_ straight
lines be drawn from that point to the circumference, then,” etc.

§ 4. The considerations now stated remove a serious difficulty from the
view we have taken of reasoning; which view might otherwise have seemed
not easily reconcilable with the fact that there are Deductive or
Ratiocinative Sciences. It might seem to follow, if all reasoning be
induction, that the difficulties of philosophical investigation must lie
in the inductions exclusively, and that when these were easy, and
susceptible of no doubt or hesitation, there could be no science, or, at
least, no difficulties in science. The existence, for example, of an
extensive Science of Mathematics, requiring the highest scientific genius
in those who contributed to its creation, and calling for a most continued
and vigorous exertion of intellect in order to appropriate it when
created, may seem hard to be accounted for on the foregoing theory. But
the considerations more recently adduced remove the mystery, by showing,
that even when the inductions themselves are obvious, there may be much
difficulty in finding whether the particular case which is the subject of
inquiry comes within them; and ample room for scientific ingenuity in so
combining various inductions, as, by means of one within which the case
evidently falls, to bring it within others in which it can not be directly
seen to be included.

When the more obvious of the inductions which can be made in any science
from direct observations, have been made, and general formulas have been
framed, determining the limits within which these inductions are
applicable; as often as a new case can be at once seen to come within one
of the formulas, the induction is applied to the new case, and the
business is ended. But new cases are continually arising, which do not
obviously come within any formula whereby the question we want solved in
respect of them could be answered. Let us take an instance from geometry:
and as it is taken only for illustration, let the reader concede to us for
the present, what we shall endeavor to prove in the next chapter, that the
first principles of geometry are results of induction. Our example shall
be the fifth proposition of the first book of Euclid. The inquiry is, Are
the angles at the base of an isosceles triangle equal or unequal? The
first thing to be considered is, what inductions we have, from which we
can infer equality or inequality. For inferring equality we have the
following formulæ: Things which being applied to each other coincide, are
equals. Things which are equal to the same thing are equals. A whole and
the sum of its parts are equals. The sums of equal things are equals. The
differences of equal things are equals. There are no other original
formulæ to prove equality. For inferring inequality we have the following:
A whole and its parts are unequals. The sums of equal things and unequal
things are unequals. The differences of equal things and unequal things
are unequals. In all, eight formulæ. The angles at the base of an
isosceles triangle do not obviously come within any of these. The formulæ
specify certain marks of equality and of inequality, but the angles can
not be perceived intuitively to have any of those marks. On examination it
appears that they have; and we ultimately succeed in bringing them within
the formula, “The differences of equal things are equal.” Whence comes the
difficulty of recognizing these angles as the differences of equal things?
Because each of them is the difference not of one pair only, but of
innumerable pairs of angles; and out of these we had to imagine and select
two, which could either be intuitively perceived to be equals, or
possessed some of the marks of equality set down in the various formulæ.
By an exercise of ingenuity, which, on the part of the first inventor,
deserves to be regarded as considerable, two pairs of angles were hit
upon, which united these requisites. First, it could be perceived
intuitively that their differences were the angles at the base; and,
secondly, they possessed one of the marks of equality, namely, coincidence
when applied to one another. This coincidence, however, was not perceived
intuitively, but inferred, in conformity to another formula.

For greater clearness, I subjoin an analysis of the demonstration. Euclid,
it will be remembered, demonstrates his fifth proposition by means of the
fourth. This it is not allowable for us to do, because we are undertaking
to trace deductive truths not to prior deductions, but to their original
inductive foundation. We must, therefore, use the premises of the fourth
proposition instead of its conclusion, and prove the fifth directly from
first principles. To do so requires six formulas. (We presuppose an
equilateral triangle, whose vertices are A, D, E, with point B on the side
AD, and point C on the side AE, such that BC is parallel to DE. We must
begin, as in Euclid, by prolonging the equal sides AB, AC, to equal
distances, and joining the extremities BE, DC.)

FIRST FORMULA.—_The sums of equals are equal._

AD and AE are sums of equals by the supposition. Having that mark of
equality, they are concluded by this formula to be equal.

SECOND FORMULA.—_Equal straight lines or angles, being applied to one
another, coincide._

AC, AB, are within this formula by supposition; AD, AE, have been brought
within it by the preceding step. The angle at A considered as an angle of
the triangle ABE, and the same angle considered as an angle of the
triangle ACD, are of course within the formula. All these pairs,
therefore, possess the property which, according to the second formula, is
a mark that when applied to one another they will coincide. Conceive them,
then, applied to one another, by turning over the triangle ABE, and laying
it on the triangle ACD in such a manner that AB of the one shall lie upon
AC of the other. Then, by the equality of the angles, AE will lie on AD.
But AB and AC, AE and AD are equals; therefore they will coincide
altogether, and of course at their extremities, D, E, and B, C.

THIRD FORMULA.—_Straight lines, having their extremities coincident,
coincide._

BE and CD have been brought within this formula by the preceding
induction; they will, therefore, coincide.

FOURTH FORMULA.—_Angles, having their sides coincident, coincide._

The third induction having shown that BE and CD coincide, and the second
that AB, AC, coincide, the angles ABE and ACD are thereby brought within
the fourth formula, and accordingly coincide.

FIFTH FORMULA.—_Things which coincide are equal._

The angles ABE and ACD are brought within this formula by the induction
immediately preceding. This train of reasoning being also applicable,
_mutatis mutandis_, to the angles EBC, DCB, these also are brought within
the fifth formula. And, finally,

SIXTH FORMULA.—_The differences of equals are equal._

The angle ABC being the difference of ABE, CBE, and the angle ACB being
the difference of ACD, DCB; which have been proved to be equals; ABC and
ACB are brought within the last formula by the whole of the previous
process.

The difficulty here encountered is chiefly that of figuring to ourselves
the two angles at the base of the triangle ABC as remainders made by
cutting one pair of angles out of another, while each pair shall be
corresponding angles of triangles which have two sides and the intervening
angle equal. It is by this happy contrivance that so many different
inductions are brought to bear upon the same particular case. And this not
being at all an obvious thought, it may be seen from an example so near
the threshold of mathematics, how much scope there may well be for
scientific dexterity in the higher branches of that and other sciences, in
order so to combine a few simple inductions, as to bring within each of
them innumerable cases which are not obviously included in it; and how
long, and numerous, and complicated may be the processes necessary for
bringing the inductions together, even when each induction may itself be
very easy and simple. All the inductions involved in all geometry are
comprised in those simple ones, the formulæ of which are the Axioms, and a
few of the so-called Definitions. The remainder of the science is made up
of the processes employed for bringing unforeseen cases within these
inductions; or (in syllogistic language) for proving the minors necessary
to complete the syllogisms; the majors being the definitions and axioms.
In those definitions and axioms are laid down the whole of the marks, by
an artful combination of which it has been found possible to discover and
prove all that is proved in geometry. The marks being so few, and the
inductions which furnish them being so obvious and familiar; the
connecting of several of them together, which constitutes Deductions, or
Trains of Reasoning, forms the whole difficulty of the science, and, with
a trifling exception, its whole bulk; and hence Geometry is a Deductive
Science.

§ 5. It will be seen hereafter(67) that there are weighty scientific
reasons for giving to every science as much of the character of a
Deductive Science as possible; for endeavoring to construct the science
from the fewest and the simplest possible inductions, and to make these,
by any combinations however complicated, suffice for proving even such
truths, relating to complex cases, as could be proved, if we chose, by
inductions from specific experience. Every branch of natural philosophy
was originally experimental; each generalization rested on a special
induction, and was derived from its own distinct set of observations and
experiments. From being sciences of pure experiment, as the phrase is, or,
to speak more correctly, sciences in which the reasonings mostly consist
of no more than one step, and are expressed by single syllogisms, all
these sciences have become to some extent, and some of them in nearly the
whole of their extent, sciences of pure reasoning; whereby multitudes of
truths, already known by induction from as many different sets of
experiments, have come to be exhibited as deductions or corollaries from
inductive propositions of a simpler and more universal character. Thus
mechanics, hydrostatics, optics, acoustics, thermology, have successively
been rendered mathematical; and astronomy was brought by Newton within the
laws of general mechanics. Why it is that the substitution of this
circuitous mode of proceeding for a process apparently much easier and
more natural, is held, and justly, to be the greatest triumph of the
investigation of nature, we are not, in this stage of our inquiry,
prepared to examine. But it is necessary to remark, that although, by this
progressive transformation, all sciences tend to become more and more
Deductive, they are not, therefore, the less Inductive; every step in the
Deduction is still an Induction. The opposition is not between the terms
Deductive and Inductive, but between Deductive and Experimental. A science
is experimental, in proportion as every new case, which presents any
peculiar features, stands in need of a new set of observations and
experiments—a fresh induction. It is deductive, in proportion as it can
draw conclusions, respecting cases of a new kind, by processes which bring
those cases under old inductions; by ascertaining that cases which can not
be observed to have the requisite marks, have, however, marks of those
marks.

We can now, therefore, perceive what is the generic distinction between
sciences which can be made Deductive, and those which must as yet remain
Experimental. The difference consists in our having been able, or not yet
able, to discover marks of marks. If by our various inductions we have
been able to proceed no further than to such propositions as these, _a_ a
mark of _b_, or _a_ and _b_ marks of one another, _c_ a mark of _d_, or c
and _d_ marks of one another, without any thing to connect _a_ or _b_ with
_c_ or _d_; we have a science of detached and mutually independent
generalizations, such as these, that acids redden vegetable blues, and
that alkalies color them green; from neither of which propositions could
we, directly or indirectly, infer the other: and a science, so far as it
is composed of such propositions, is purely experimental. Chemistry, in
the present state of our knowledge, has not yet thrown off this character.
There are other sciences, however, of which the propositions are of this
kind: _a_ a mark of _b, b_ a mark of _c, c_ of _d, d_ of _e_, etc. In
these sciences we can mount the ladder from _a_ to _e_ by a process of
ratiocination; we can conclude that _a_ is a mark of _e_, and that every
object which has the mark _a_ has the property _e_, although, perhaps, we
never were able to observe _a_ and _e_ together, and although even _d_,
our only direct mark of _e_, may not be perceptible in those objects, but
only inferable. Or, varying the first metaphor, we may be said to get from
_a_ to _e_ underground: the marks _b_, _c_, _d_, which indicate the route,
must all be possessed somewhere by the objects concerning which we are
inquiring; but they are below the surface: _a_ is the only mark that is
visible, and by it we are able to trace in succession all the rest.

§ 6. We can now understand how an experimental may transform itself into a
deductive science by the mere progress of experiment. In an experimental
science, the inductions, as we have said, lie detached, as, _a_ a mark of
_b, c_ a mark of _d_, _e_ a mark of _f_, and so on: now, a new set of
instances, and a consequent new induction, may at any time bridge over the
interval between two of these unconnected arches; _b_, for example, may be
ascertained to be a mark of _c_, which enables us thenceforth to prove
deductively that _a_ is a mark of _c_. Or, as sometimes happens, some
comprehensive induction may raise an arch high in the air, which bridges
over hosts of them at once; _b_, _d_, _f_, and all the rest, turning out
to be marks of some one thing, or of things between which a connection has
already been traced. As when Newton discovered that the motions, whether
regular or apparently anomalous, of all the bodies of the solar system
(each of which motions had been inferred by a separate logical operation,
from separate marks), were all marks of moving round a common centre, with
a centripetal force varying directly as the mass, and inversely as the
square of the distance from that centre. This is the greatest example
which has yet occurred of the transformation, at one stroke, of a science
which was still to a great degree merely experimental, into a deductive
science.

Transformations of the same nature, but on a smaller scale, continually
take place in the less advanced branches of physical knowledge, without
enabling them to throw off the character of experimental sciences. Thus
with regard to the two unconnected propositions before cited, namely,
Acids redden vegetable blues, Alkalies make them green; it is remarked by
Liebig, that all blue coloring matters which are reddened by acids (as
well as, reciprocally, all red coloring matters which are rendered blue by
alkalies) contain nitrogen: and it is quite possible that this
circumstance may one day furnish a bond of connection between the two
propositions in question, by showing that the antagonistic action of acids
and alkalies in producing or destroying the color blue, is the result of
some one, more general, law. Although this connecting of detached
generalizations is so much gain, it tends but little to give a deductive
character to any science as a whole; because the new courses of
observation and experiment, which thus enable us to connect together a few
general truths, usually make known to us a still greater number of
unconnected new ones. Hence chemistry, though similar extensions and
simplifications of its generalizations are continually taking place, is
still in the main an experimental science; and is likely so to continue
unless some comprehensive induction should be hereafter arrived at, which,
like Newton’s, shall connect a vast number of the smaller known inductions
together, and change the whole method of the science at once. Chemistry
has already one great generalization, which, though relating to one of the
subordinate aspects of chemical phenomena, possesses within its limited
sphere this comprehensive character; the principle of Dalton, called the
atomic theory, or the doctrine of chemical equivalents: which by enabling
us to a certain extent to foresee the proportions in which two substances
will combine, before the experiment has been tried, constitutes
undoubtedly a source of new chemical truths obtainable by deduction, as
well as a connecting principle for all truths of the same description
previously obtained by experiment.

§ 7. The discoveries which change the method of a science from
experimental to deductive, mostly consist in establishing, either by
deduction or by direct experiment, that the varieties of a particular
phenomenon uniformly accompany the varieties of some other phenomenon
better known. Thus the science of sound, which previously stood in the
lowest rank of merely experimental science, became deductive when it was
proved by experiment that every variety of sound was consequent on, and
therefore a mark of, a distinct and definable variety of oscillatory
motion among the particles of the transmitting medium. When this was
ascertained, it followed that every relation of succession or co-existence
which obtained between phenomena of the more known class, obtained also
between the phenomena which correspond to them in the other class. Every
sound, being a mark of a particular oscillatory motion, became a mark of
every thing which, by the laws of dynamics, was known to be inferable from
that motion; and every thing which by those same laws was a mark of any
oscillatory motion among the particles of an elastic medium, became a mark
of the corresponding sound. And thus many truths, not before suspected,
concerning sound, become deducible from the known laws of the propagation
of motion through an elastic medium; while facts already empirically known
respecting sound, become an indication of corresponding properties of
vibrating bodies, previously undiscovered.

But the grand agent for transforming experimental into deductive sciences,
is the science of number. The properties of number, alone among all known
phenomena, are, in the most rigorous sense, properties of all things
whatever. All things are not colored, or ponderable, or even extended; but
all things are numerable. And if we consider this science in its whole
extent, from common arithmetic up to the calculus of variations, the
truths already ascertained seem all but infinite, and admit of indefinite
extension.

These truths, though affirmable of all things whatever, of course apply to
them only in respect of their quantity. But if it comes to be discovered
that variations of quality in any class of phenomena, correspond regularly
to variations of quantity either in those same or in some other phenomena;
every formula of mathematics applicable to quantities which vary in that
particular manner, becomes a mark of a corresponding general truth,
respecting the variations in quality which accompany them: and the science
of quantity being (as far as any science can be) altogether deductive, the
theory of that particular kind of qualities becomes, to this extent,
deductive likewise.

The most striking instance in point which history affords (though not an
example of an experimental science rendered deductive, but of an
unparalleled extension given to the deductive process in a science which
was deductive already), is the revolution in geometry which originated
with Descartes, and was completed by Clairaut. These great mathematicians
pointed out the importance of the fact, that to every variety of position
in points, direction in lines, or form in curves or surfaces (all of which
are Qualities), there corresponds a peculiar relation of quantity between
either two or three rectilineal co-ordinates; insomuch that if the law
were known according to which those co-ordinates vary relatively to one
another, every other geometrical property of the line or surface in
question, whether relating to quantity or quality, would be capable of
being inferred. Hence it followed that every geometrical question could be
solved, if the corresponding algebraical one could; and geometry received
an accession (actual or potential) of new truths, corresponding to every
property of numbers which the progress of the calculus had brought, or
might in future bring, to light. In the same general manner, mechanics,
astronomy, and in a less degree, every branch of natural philosophy
commonly so called, have been made algebraical. The varieties of physical
phenomena with which those sciences are conversant, have been found to
answer to determinable varieties in the quantity of some circumstance or
other; or at least to varieties of form or position, for which
corresponding equations of quantity had already been, or were susceptible
of being, discovered by geometers.

In these various transformations, the propositions of the science of
number do but fulfill the function proper to all propositions forming a
train of reasoning, viz., that of enabling us to arrive in an indirect
method, by marks of marks, at such of the properties of objects as we can
not directly ascertain (or not so conveniently) by experiment. We travel
from a given visible or tangible fact, through the truths of numbers, to
the facts sought. The given fact is a mark that a certain relation
subsists between the quantities of some of the elements concerned; while
the fact sought presupposes a certain relation between the quantities of
some other elements: now, if these last quantities are dependent in some
known manner upon the former, or _vicè versa_, we can argue from the
numerical relation between the one set of quantities, to determine that
which subsists between the other set; the theorems of the calculus
affording the intermediate links. And thus one of the two physical facts
becomes a mark of the other, by being a mark of a mark of a mark of it.




                                Chapter V.


Of Demonstration, And Necessary Truths.


§ 1. If, as laid down in the two preceding chapters, the foundation of all
sciences, even deductive or demonstrative sciences, is Induction; if every
step in the ratiocinations even of geometry is an act of induction; and if
a train of reasoning is but bringing many inductions to bear upon the same
subject of inquiry, and drawing a case within one induction by means of
another; wherein lies the peculiar certainty always ascribed to the
sciences which are entirely, or almost entirely, deductive? Why are they
called the Exact Sciences? Why are mathematical certainty, and the
evidence of demonstration, common phrases to express the very highest
degree of assurance attainable by reason? Why are mathematics by almost
all philosophers, and (by some) even those branches of natural philosophy
which, through the medium of mathematics, have been converted into
deductive sciences, considered to be independent of the evidence of
experience and observation, and characterized as systems of Necessary
Truth?

The answer I conceive to be, that this character of necessity, ascribed to
the truths of mathematics, and (even with some reservations to be
hereafter made) the peculiar certainty attributed to them, is an illusion;
in order to sustain which, it is necessary to suppose that those truths
relate to, and express the properties of, purely imaginary objects. It is
acknowledged that the conclusions of geometry are deduced, partly at
least, from the so-called Definitions, and that those definitions are
assumed to be correct representations, as far as they go, of the objects
with which geometry is conversant. Now we have pointed out that, from a
definition as such, no proposition, unless it be one concerning the
meaning of a word, can ever follow; and that what apparently follows from
a definition, follows in reality from an implied assumption that there
exists a real thing conformable thereto. This assumption, in the case of
the definitions of geometry, is not strictly true: there exist no real
things exactly conformable to the definitions. There exist no points
without magnitude; no lines without breadth, nor perfectly straight; no
circles with all their radii exactly equal, nor squares with all their
angles perfectly right. It will perhaps be said that the assumption does
not extend to the actual, but only to the possible, existence of such
things. I answer that, according to any test we have of possibility, they
are not even possible. Their existence, so far as we can form any
judgment, would seem to be inconsistent with the physical constitution of
our planet at least, if not of the universe. To get rid of this
difficulty, and at the same time to save the credit of the supposed system
of necessary truth, it is customary to say that the points, lines,
circles, and squares which are the subject of geometry, exist in our
conceptions merely, and are part of our minds; which minds, by working on
their own materials, construct an _a priori_ science, the evidence of
which is purely mental, and has nothing whatever to do with outward
experience. By howsoever high authorities this doctrine may have been
sanctioned, it appears to me psychologically incorrect. The points, lines,
circles, and squares which any one has in his mind, are (I apprehend)
simply copies of the points, lines, circles, and squares which he has
known in his experience. Our idea of a point, I apprehend to be simply our
idea of the _minimum visibile_, the smallest portion of surface which we
can see. A line, as defined by geometers, is wholly inconceivable. We can
reason about a line as if it had no breadth; because we have a power,
which is the foundation of all the control we can exercise over the
operations of our minds; the power, when a perception is present to our
senses, or a conception to our intellects, of _attending_ to a part only
of that perception or conception, instead of the whole. But we can not
_conceive_ a line without breadth; we can form no mental picture of such a
line: all the lines which we have in our minds are lines possessing
breadth. If any one doubts this, we may refer him to his own experience. I
much question if any one who fancies that he can conceive what is called a
mathematical line, thinks so from the evidence of his consciousness: I
suspect it is rather because he supposes that unless such a conception
were possible, mathematics could not exist as a science: a supposition
which there will be no difficulty in showing to be entirely groundless.

Since, then, neither in nature, nor in the human mind, do there exist any
objects exactly corresponding to the definitions of geometry, while yet
that science can not be supposed to be conversant about nonentities;
nothing remains but to consider geometry as conversant with such lines,
angles, and figures, as really exist; and the definitions, as they are
called, must be regarded as some of our first and most obvious
generalizations concerning those natural objects. The correctness of those
generalizations, as generalizations, is without a flaw: the equality of
all the radii of a circle is true of all circles, so far as it is true of
any one: but it is not exactly true of any circle; it is only nearly true;
so nearly that no error of any importance in practice will be incurred by
feigning it to be exactly true. When we have occasion to extend these
inductions, or their consequences, to cases in which the error would be
appreciable—to lines of perceptible breadth or thickness, parallels which
deviate sensibly from equidistance, and the like—we correct our
conclusions, by combining with them a fresh set of propositions relating
to the aberration; just as we also take in propositions relating to the
physical or chemical properties of the material, if those properties
happen to introduce any modification into the result; which they easily
may, even with respect to figure and magnitude, as in the case, for
instance, of expansion by heat. So long, however, as there exists no
practical necessity for attending to any of the properties of the object
except its geometrical properties, or to any of the natural irregularities
in those, it is convenient to neglect the consideration of the other
properties and of the irregularities, and to reason as if these did not
exist: accordingly, we formally announce in the definitions, that we
intend to proceed on this plan. But it is an error to suppose, because we
resolve to confine our attention to a certain number of the properties of
an object, that we therefore conceive, or have an idea of, the object,
denuded of its other properties. We are thinking, all the time, of
precisely such objects as we have seen and touched, and with all the
properties which naturally belong to them; but, for scientific
convenience, we feign them to be divested of all properties, except those
which are material to our purpose, and in regard to which we design to
consider them.

The peculiar accuracy, supposed to be characteristic of the first
principles of geometry, thus appears to be fictitious. The assertions on
which the reasonings of the science are founded, do not, any more than in
other sciences, exactly correspond with the fact; but we suppose that they
do so, for the sake of tracing the consequences which follow from the
supposition. The opinion of Dugald Stewart respecting the foundations of
geometry, is, I conceive, substantially correct; that it is built on
hypotheses; that it owes to this alone the peculiar certainty supposed to
distinguish it; and that in any science whatever, by reasoning from a set
of hypotheses, we may obtain a body of conclusions as certain as those of
geometry, that is, as strictly in accordance with the hypotheses, and as
irresistibly compelling assent, _on condition_ that those hypotheses are
true.(68)

When, therefore, it is affirmed that the conclusions of geometry are
necessary truths, the necessity consists in reality only in this, that
they correctly follow from the suppositions from which they are deduced.
Those suppositions are so far from being necessary, that they are not even
true; they purposely depart, more or less widely, from the truth. The only
sense in which necessity can be ascribed to the conclusions of any
scientific investigation, is that of legitimately following from some
assumption, which, by the conditions of the inquiry, is not to be
questioned. In this relation, of course, the derivative truths of every
deductive science must stand to the inductions, or assumptions, on which
the science is founded, and which, whether true or untrue, certain or
doubtful in themselves, are always supposed certain for the purposes of
the particular science. And therefore the conclusions of all deductive
sciences were said by the ancients to be necessary propositions. We have
observed already that to be predicated necessarily was characteristic of
the predicable Proprium, and that a proprium was any property of a thing
which could be deduced from its essence, that is, from the properties
included in its definition.

§ 2. The important doctrine of Dugald Stewart, which I have endeavored to
enforce, has been contested by Dr. Whewell, both in the dissertation
appended to his excellent _Mechanical Euclid_, and in his elaborate work
on the _Philosophy of the Inductive Sciences_; in which last he also
replies to an article in the Edinburgh Review (ascribed to a writer of
great scientific eminence), in which Stewart’s opinion was defended
against his former strictures. The supposed refutation of Stewart consists
in proving against him (as has also been done in this work) that the
premises of geometry are not definitions, but assumptions of the real
existence of things corresponding to those definitions. This, however, is
doing little for Dr. Whewell’s purpose; for it is these very assumptions
which are asserted to be hypotheses, and which he, if he denies that
geometry is founded on hypotheses, must show to be absolute truths. All he
does, however, is to observe, that they, at any rate, are not _arbitrary_
hypotheses; that we should not be at liberty to substitute other
hypotheses for them; that not only “a definition, to be admissible, must
necessarily refer to and agree with some conception which we can
distinctly frame in our thoughts,” but that the straight lines, for
instance, which we define, must be “those by which angles are contained,
those by which triangles are bounded, those of which parallelism may be
predicated, and the like.”(69) And this is true; but this has never been
contradicted. Those who say that the premises of geometry are hypotheses,
are not bound to maintain them to be hypotheses which have no relation
whatever to fact. Since an hypothesis framed for the purpose of scientific
inquiry must relate to something which has real existence (for there can
be no science respecting nonentities), it follows that any hypothesis we
make respecting an object, to facilitate our study of it, must not involve
any thing which is distinctly false, and repugnant to its real nature: we
must not ascribe to the thing any property which it has not; our liberty
extends only to slightly exaggerating some of those which it has (by
assuming it to be completely what it really is very nearly), and
suppressing others, under the indispensable obligation of restoring them
whenever, and in as far as, their presence or absence would make any
material difference in the truth of our conclusions. Of this nature,
accordingly, are the first principles involved in the definitions of
geometry. That the hypotheses should be of this particular character, is,
however, no further necessary, than inasmuch as no others could enable us
to deduce conclusions which, with due corrections, would be true of real
objects: and in fact, when our aim is only to illustrate truths, and not
to investigate them, we are not under any such restriction. We might
suppose an imaginary animal, and work out by deduction, from the known
laws of physiology, its natural history; or an imaginary commonwealth, and
from the elements composing it, might argue what would be its fate. And
the conclusions which we might thus draw from purely arbitrary hypotheses,
might form a highly useful intellectual exercise: but as they could only
teach us what _would_ be the properties of objects which do not really
exist, they would not constitute any addition to our knowledge of nature:
while, on the contrary, if the hypothesis merely divests a real object of
some portion of its properties, without clothing it in false ones, the
conclusions will always express, under known liability to correction,
actual truth.

§ 3. But though Dr. Whewell has not shaken Stewart’s doctrine as to the
hypothetical character of that portion of the first principles of geometry
which are involved in the so-called definitions, he has, I conceive,
greatly the advantage of Stewart on another important point in the theory
of geometrical reasoning; the necessity of admitting, among those first
principles, axioms as well as definitions. Some of the axioms of Euclid
might, no doubt, be exhibited in the form of definitions, or might be
deduced, by reasoning, from propositions similar to what are so called.
Thus, if instead of the axiom, Magnitudes which can be made to coincide
are equal, we introduce a definition, “Equal magnitudes are those which
may be so applied to one another as to coincide;” the three axioms which
follow (Magnitudes which are equal to the same are equal to one another—If
equals are added to equals, the sums are equal—If equals are taken from
equals, the remainders are equal), may be proved by an imaginary
superposition, resembling that by which the fourth proposition of the
first book of Euclid is demonstrated. But though these and several others
may be struck out of the list of first principles, because, though not
requiring demonstration, they are susceptible of it; there will be found
in the list of axioms two or three fundamental truths, not capable of
being demonstrated: among which must be reckoned the proposition that two
straight lines can not inclose a space (or its equivalent, Straight lines
which coincide in two points coincide altogether), and some property of
parallel lines, other than that which constitutes their definition: one of
the most suitable for the purpose being that selected by Professor
Playfair: “Two straight lines which intersect each other can not both of
them be parallel to a third straight line.”(70)

The axioms, as well those which are indemonstrable as those which admit of
being demonstrated, differ from that other class of fundamental principles
which are involved in the definitions, in this, that they are true without
any mixture of hypothesis. That things which are equal to the same thing
are equal to one another, is as true of the lines and figures in nature,
as it would be of the imaginary ones assumed in the definitions. In this
respect, however, mathematics are only on a par with most other sciences.
In almost all sciences there are some general propositions which are
exactly true, while the greater part are only more or less distant
approximations to the truth. Thus in mechanics, the first law of motion
(the continuance of a movement once impressed, until stopped or slackened
by some resisting force) is true without qualification or error. The
rotation of the earth in twenty-four hours, of the same length as in our
time, has gone on since the first accurate observations, without the
increase or diminution of one second in all that period. These are
inductions which require no fiction to make them be received as accurately
true: but along with them there are others, as for instance the
propositions respecting the figure of the earth, which are but
approximations to the truth; and in order to use them for the further
advancement of our knowledge, we must feign that they are exactly true,
though they really want something of being so.

§ 4. It remains to inquire, what is the ground of our belief in
axioms—what is the evidence on which they rest? I answer, they are
experimental truths; generalizations from observation. The proposition,
Two straight lines can not inclose a space—or, in other words, Two
straight lines which have once met, do not meet again, but continue to
diverge—is an induction from the evidence of our senses.

This opinion runs counter to a scientific prejudice of long standing and
great strength, and there is probably no proposition enunciated in this
work for which a more unfavorable reception is to be expected. It is,
however, no new opinion; and even if it were so, would be entitled to be
judged, not by its novelty, but by the strength of the arguments by which
it can be supported. I consider it very fortunate that so eminent a
champion of the contrary opinion as Dr. Whewell has found occasion for a
most elaborate treatment of the whole theory of axioms, in attempting to
construct the philosophy of the mathematical and physical sciences on the
basis of the doctrine against which I now contend. Whoever is anxious that
a discussion should go to the bottom of the subject, must rejoice to see
the opposite side of the question worthily represented. If what is said by
Dr. Whewell, in support of an opinion which he has made the foundation of
a systematic work, can be shown not to be conclusive, enough will have
been done, without going elsewhere in quest of stronger arguments and a
more powerful adversary.

It is not necessary to show that the truths which we call axioms are
originally _suggested_ by observation, and that we should never have known
that two straight lines can not inclose a space if we had never seen a
straight line: thus much being admitted by Dr. Whewell, and by all, in
recent times, who have taken his view of the subject. But they contend,
that it is not experience which _proves_ the axiom; but that its truth is
perceived _a priori_, by the constitution of the mind itself, from the
first moment when the meaning of the proposition is apprehended; and
without any necessity for verifying it by repeated trials, as is requisite
in the case of truths really ascertained by observation.

They can not, however, but allow that the truth of the axiom, Two straight
lines can not inclose a space, even if evident independently of
experience, is also evident from experience. Whether the axiom needs
confirmation or not, it receives confirmation in almost every instant of
our lives; since we can not look at any two straight lines which intersect
one another, without seeing that from that point they continue to diverge
more and more. Experimental proof crowds in upon us in such endless
profusion, and without one instance in which there can be even a suspicion
of an exception to the rule, that we should soon have stronger ground for
believing the axiom, even as an experimental truth, than we have for
almost any of the general truths which we confessedly learn from the
evidence of our senses. Independently of _a priori_ evidence, we should
certainly believe it with an intensity of conviction far greater than we
accord to any ordinary physical truth: and this too at a time of life much
earlier than that from which we date almost any part of our acquired
knowledge, and much too early to admit of our retaining any recollection
of the history of our intellectual operations at that period. Where then
is the necessity for assuming that our recognition of these truths has a
different origin from the rest of our knowledge, when its existence is
perfectly accounted for by supposing its origin to be the same? when the
causes which produce belief in all other instances, exist in this
instance, and in a degree of strength as much superior to what exists in
other cases, as the intensity of the belief itself is superior? The burden
of proof lies on the advocates of the contrary opinion: it is for them to
point out some fact, inconsistent with the supposition that this part of
our knowledge of nature is derived from the same sources as every other
part.(71)

This, for instance, they would be able to do, if they could prove
chronologically that we had the conviction (at least practically) so early
in infancy as to be anterior to those impressions on the senses, upon
which, on the other theory, the conviction is founded. This, however, can
not be proved: the point being too far back to be within the reach of
memory, and too obscure for external observation. The advocates of the _a
priori_ theory are obliged to have recourse to other arguments. These are
reducible to two, which I shall endeavor to state as clearly and as
forcibly as possible.

§ 5. In the first place it is said, that if our assent to the proposition
that two straight lines can not inclose a space, were derived from the
senses, we could only be convinced of its truth by actual trial, that is,
by seeing or feeling the straight lines; whereas, in fact, it is seen to
be true by merely thinking of them. That a stone thrown into water goes to
the bottom, may be perceived by our senses, but mere thinking of a stone
thrown into the water would never have led us to that conclusion: not so,
however, with the axioms relating to straight lines: if I could be made to
conceive what a straight line is, without having seen one, I should at
once recognize that two such lines can not inclose a space. Intuition is
“imaginary looking;”(72) but experience must be real looking: if we see a
property of straight lines to be true by merely fancying ourselves to be
looking at them, the ground of our belief can not be the senses, or
experience; it must be something mental.

To this argument it might be added in the case of this particular axiom
(for the assertion would not be true of all axioms), that the evidence of
it from actual ocular inspection is not only unnecessary, but
unattainable. What says the axiom? That two straight lines _can not_
inclose a space; that after having once intersected, if they are prolonged
to infinity they do not meet, but continue to diverge from one another.
How can this, in any single case, be proved by actual observation? We may
follow the lines to any distance we please; but we can not follow them to
infinity: for aught our senses can testify, they may, immediately beyond
the farthest point to which we have traced them, begin to approach, and at
last meet. Unless, therefore, we had some other proof of the impossibility
than observation affords us, we should have no ground for believing the
axiom at all.

To these arguments, which I trust I can not be accused of understating, a
satisfactory answer will, I conceive, be found, if we advert to one of the
characteristic properties of geometrical forms—their capacity of being
painted in the imagination with a distinctness equal to reality: in other
words, the exact resemblance of our ideas of form to the sensations which
suggest them. This, in the first place, enables us to make (at least with
a little practice) mental pictures of all possible combinations of lines
and angles, which resemble the realities quite as well as any which we
could make on paper; and in the next place, make those pictures just as
fit subjects of geometrical experimentation as the realities themselves;
inasmuch as pictures, if sufficiently accurate, exhibit of course all the
properties which would be manifested by the realities at one given
instant, and on simple inspection: and in geometry we are concerned only
with such properties, and not with that which pictures could not exhibit,
the mutual action of bodies one upon another. The foundations of geometry
would therefore be laid in direct experience, even if the experiments
(which in this case consist merely in attentive contemplation) were
practiced solely upon what we call our ideas, that is, upon the diagrams
in our minds, and not upon outward objects. For in all systems of
experimentation we take some objects to serve as representatives of all
which resemble them; and in the present case the conditions which qualify
a real object to be the representative of its class, are completely
fulfilled by an object existing only in our fancy. Without denying,
therefore, the possibility of satisfying ourselves that two straight lines
can not inclose a space, by merely thinking of straight lines without
actually looking at them; I contend, that we do not believe this truth on
the ground of the imaginary intuition simply, but because we know that the
imaginary lines exactly resemble real ones, and that we may conclude from
them to real ones with quite as much certainty as we could conclude from
one real line to another. The conclusion, therefore, is still an induction
from observation. And we should not be authorized to substitute
observation of the image in our mind, for observation of the reality, if
we had not learned by long-continued experience that the properties of the
reality are faithfully represented in the image; just as we should be
scientifically warranted in describing an animal which we have never seen,
from a picture made of it with a daguerreotype; but not until we had
learned by ample experience, that observation of such a picture is
precisely equivalent to observation of the original.

These considerations also remove the objection arising from the
impossibility of ocularly following the lines in their prolongation to
infinity. For though, in order actually to see that two given lines never
meet, it would be necessary to follow them to infinity; yet without doing
so we may know that if they ever do meet, or if, after diverging from one
another, they begin again to approach, this must take place not at an
infinite, but at a finite distance. Supposing, therefore, such to be the
case, we can transport ourselves thither in imagination, and can frame a
mental image of the appearance which one or both of the lines must present
at that point, which we may rely on as being precisely similar to the
reality. Now, whether we fix our contemplation upon this imaginary
picture, or call to mind the generalizations we have had occasion to make
from former ocular observation, we learn by the evidence of experience,
that a line which, after diverging from another straight line, begins to
approach to it, produces the impression on our senses which we describe by
the expression, “a bent line,” not by the expression, “a straight
line.”(73)

The preceding argument, which is, to my mind unanswerable, merges,
however, in a still more comprehensive one, which is stated most clearly
and conclusively by Professor Bain. The psychological reason why axioms,
and indeed many propositions not ordinarily classed as such, may be
learned from the idea only without referring to the fact, is that in the
process of acquiring the idea we have learned the fact. The proposition is
assented to as soon as the terms are understood, because in learning to
understand the terms we have acquired the experience which proves the
proposition to be true. “We required,” says Mr. Bain,(74) “concrete
experience in the first instance, to attain to the notion of whole and
part; but the notion, once arrived at, implies that the whole is greater.
In fact, we could not have the notion without an experience tantamount to
this conclusion.... When we have mastered the notion of straightness, we
have also mastered that aspect of it expressed by the affirmation that two
straight lines can not inclose a space. No intuitive or innate powers or
perceptions are needed in such case.... We can not have the full meaning
of Straightness, without going through a comparison of straight objects
among themselves, and with their opposites, bent or crooked objects. The
result of this comparison is, _inter alia_, that straightness in two lines
is seen to be incompatible with inclosing a space; the inclosure of space
involves crookedness in at least one of the lines.” And similarly, in the
case of every first principle,(75) “the same knowledge that makes it
understood, suffices to verify it.” The more this observation is
considered the more (I am convinced) it will be felt to go to the very
root of the controversy.

§ 6. The first of the two arguments in support of the theory that axioms
are _a priori_ truths, having, I think, been sufficiently answered; I
proceed to the second, which is usually the most relied on. Axioms (it is
asserted) are conceived by us not only as true, but as universally and
necessarily true. Now, experience can not possibly give to any proposition
this character. I may have seen snow a hundred times, and may have seen
that it was white, but this can not give me entire assurance even that all
snow is white; much less that snow _must_ be white. “However many
instances we may have observed of the truth of a proposition, there is
nothing to assure us that the next case shall not be an exception to the
rule. If it be strictly true that every ruminant animal yet known has
cloven hoofs, we still can not be sure that some creature will not
hereafter be discovered which has the first of these attributes, without
having the other.... Experience must always consist of a limited number of
observations; and, however numerous these may be, they can show nothing
with regard to the infinite number of cases in which the experiment has
not been made.” Besides, Axioms are not only universal, they are also
necessary. Now “experience can not offer the smallest ground for the
necessity of a proposition. She can observe and record what has happened;
but she can not find, in any case, or in any accumulation of cases, any
reason for what _must_ happen. She may see objects side by side; but she
can not see a reason why they must ever be side by side. She finds certain
events to occur in succession; but the succession supplies, in its
occurrence, no reason for its recurrence. She contemplates external
objects; but she can not detect any internal bond, which indissolubly
connects the future with the past, the possible with the real. To learn a
proposition by experience, and to see it to be necessarily true, are two
altogether different processes of thought.”(76) And Dr. Whewell adds, “If
any one does not clearly comprehend this distinction of necessary and
contingent truths, he will not be able to go along with us in our
researches into the foundations of human knowledge; nor, indeed, to pursue
with success any speculation on the subject.”(77)

In the following passage, we are told what the distinction is, the
non-recognition of which incurs this denunciation. “Necessary truths are
those in which we not only learn that the proposition _is_ true, but see
that it _must be_ true; in which the negation of the truth is not only
false, but impossible; in which we can not, even by an effort of
imagination, or in a supposition, conceive the reverse of that which is
asserted. That there are such truths can not be doubted. We may take, for
example, all relations of number. Three and Two added together make Five.
We can not conceive it to be otherwise. We can not, by any freak of
thought, imagine Three and Two to make Seven.”(78)

Although Dr. Whewell has naturally and properly employed a variety of
phrases to bring his meaning more forcibly home, he would, I presume,
allow that they are all equivalent; and that what he means by a necessary
truth, would be sufficiently defined, a proposition the negation of which
is not only false but inconceivable. I am unable to find in any of his
expressions, turn them what way you will, a meaning beyond this, and I do
not believe he would contend that they mean any thing more.

This, therefore, is the principle asserted: that propositions, the
negation of which is inconceivable, or in other words, which we can not
figure to ourselves as being false, must rest on evidence of a higher and
more cogent description than any which experience can afford.

Now I can not but wonder that so much stress should be laid on the
circumstance of inconceivableness, when there is such ample experience to
show, that our capacity or incapacity of conceiving a thing has very
little to do with the possibility of the thing in itself; but is in truth
very much an affair of accident, and depends on the past history and
habits of our own minds. There is no more generally acknowledged fact in
human nature, than the extreme difficulty at first felt in conceiving any
thing as possible, which is in contradiction to long established and
familiar experience; or even to old familiar habits of thought. And this
difficulty is a necessary result of the fundamental laws of the human
mind. When we have often seen and thought of two things together, and have
never in any one instance either seen or thought of them separately, there
is by the primary law of association an increasing difficulty, which may
in the end become insuperable, of conceiving the two things apart. This is
most of all conspicuous in uneducated persons, who are in general utterly
unable to separate any two ideas which have once become firmly associated
in their minds; and if persons of cultivated intellect have any advantage
on the point, it is only because, having seen and heard and read more, and
being more accustomed to exercise their imagination, they have experienced
their sensations and thoughts in more varied combinations, and have been
prevented from forming many of these inseparable associations. But this
advantage has necessarily its limits. The most practiced intellect is not
exempt from the universal laws of our conceptive faculty. If daily habit
presents to any one for a long period two facts in combination, and if he
is not led during that period either by accident or by his voluntary
mental operations to think of them apart, he will probably in time become
incapable of doing so even by the strongest effort; and the supposition
that the two facts can be separated in nature, will at last present itself
to his mind with all the characters of an inconceivable phenomenon.(79)
There are remarkable instances of this in the history of science:
instances in which the most instructed men rejected as impossible, because
inconceivable, things which their posterity, by earlier practice and
longer perseverance in the attempt, found it quite easy to conceive, and
which every body now knows to be true. There was a time when men of the
most cultivated intellects, and the most emancipated from the dominion of
early prejudice, could not credit the existence of antipodes; were unable
to conceive, in opposition to old association, the force of gravity acting
upward instead of downward. The Cartesians long rejected the Newtonian
doctrine of the gravitation of all bodies toward one another, on the faith
of a general proposition, the reverse of which seemed to them to be
inconceivable—the proposition that a body can not act where it is not. All
the cumbrous machinery of imaginary vortices, assumed without the smallest
particle of evidence, appeared to these philosophers a more rational mode
of explaining the heavenly motions, than one which involved what seemed to
them so great an absurdity.(80)

And they no doubt found it as impossible to conceive that a body should
act upon the earth from the distance of the sun or moon, as we find it to
conceive an end to space or time, or two straight lines inclosing a space.
Newton himself had not been able to realize the conception, or we should
not have had his hypothesis of a subtle ether, the occult cause of
gravitation; and his writings prove, that though he deemed the particular
nature of the intermediate agency a matter of conjecture, the necessity of
_some_ such agency appeared to him indubitable.

If, then, it be so natural to the human mind, even in a high state of
culture, to be incapable of conceiving, and on that ground to believe
impossible, what is afterward not only found to be conceivable but proved
to be true; what wonder if in cases where the association is still older,
more confirmed, and more familiar, and in which nothing ever occurs to
shake our conviction, or even suggest to us any conception at variance
with the association, the acquired incapacity should continue, and be
mistaken for a natural incapacity? It is true, our experience of the
varieties in nature enables us, within certain limits, to conceive other
varieties analogous to them. We can conceive the sun or moon falling; for
though we never saw them fall, nor ever, perhaps, imagined them falling,
we have seen so many other things fall, that we have innumerable familiar
analogies to assist the conception; which, after all, we should probably
have some difficulty in framing, were we not well accustomed to see the
sun and moon move (or appear to move), so that we are only called upon to
conceive a slight change in the direction of motion, a circumstance
familiar to our experience. But when experience affords no model on which
to shape the new conception, how is it possible for us to form it? How,
for example, can we imagine an end to space or time? We never saw any
object without something beyond it, nor experienced any feeling without
something following it. When, therefore, we attempt to conceive the last
point of space, we have the idea irresistibly raised of other points
beyond it. When we try to imagine the last instant of time, we can not
help conceiving another instant after it. Nor is there any necessity to
assume, as is done by a modern school of metaphysicians, a peculiar
fundamental law of the mind to account for the feeling of infinity
inherent in our conceptions of space and time; that apparent infinity is
sufficiently accounted for by simpler and universally acknowledged laws.

Now, in the case of a geometrical axiom, such, for example, as that two
straight lines can not inclose a space—a truth which is testified to us by
our very earliest impressions of the external world—how is it possible
(whether those external impressions be or be not the ground of our belief)
that the reverse of the proposition _could_ be otherwise than
inconceivable to us? What analogy have we, what similar order of facts in
any other branch of our experience, to facilitate to us the conception of
two straight lines inclosing a space? Nor is even this all. I have already
called attention to the peculiar property of our impressions of form, that
the ideas or mental images exactly resemble their prototypes, and
adequately represent them for the purposes of scientific observation. From
this, and from the intuitive character of the observation, which in this
case reduces itself to simple inspection, we can not so much as call up in
our imagination two straight lines, in order to attempt to conceive them
inclosing a space, without by that very act repeating the scientific
experiment which establishes the contrary. Will it really be contended
that the inconceivableness of the thing, in such circumstances, proves any
thing against the experimental origin of the conviction? Is it not clear
that in whichever mode our belief in the proposition may have originated,
the impossibility of our conceiving the negative of it must, on either
hypothesis, be the same? As, then, Dr. Whewell exhorts those who have any
difficulty in recognizing the distinction held by him between necessary
and contingent truths, to study geometry—a condition which I can assure
him I have conscientiously fulfilled—I, in return, with equal confidence,
exhort those who agree with him, to study the general laws of association;
being convinced that nothing more is requisite than a moderate familiarity
with those laws, to dispel the illusion which ascribes a peculiar
necessity to our earliest inductions from experience, and measures the
possibility of things in themselves, by the human capacity of conceiving
them.

I hope to be pardoned for adding, that Dr. Whewell himself has both
confirmed by his testimony the effect of habitual association in giving to
an experimental truth the appearance of a necessary one, and afforded a
striking instance of that remarkable law in his own person. In his
_Philosophy of the Inductive Sciences_ he continually asserts, that
propositions which not only are not self-evident, but which we know to
have been discovered gradually, and by great efforts of genius and
patience, have, when once established, appeared so self-evident that, but
for historical proof, it would have been impossible to conceive that they
had not been recognized from the first by all persons in a sound state of
their faculties. “We now despise those who, in the Copernican controversy,
could not conceive the apparent motion of the sun on the heliocentric
hypothesis; or those who, in opposition to Galileo, thought that a uniform
force might be that which generated a velocity proportional to the space;
or those who held there was something absurd in Newton’s doctrine of the
different refrangibility of differently colored rays; or those who
imagined that when elements combine, their sensible qualities must be
manifest in the compound; or those who were reluctant to give up the
distinction of vegetables into herbs, shrubs, and trees. We can not help
thinking that men must have been singularly dull of comprehension, to find
a difficulty in admitting what is to us so plain and simple. We have a
latent persuasion that we in their place should have been wiser and more
clear-sighted; that we should have taken the right side, and given our
assent at once to the truth. Yet in reality such a persuasion is a mere
delusion. The persons who, in such instances as the above, were on the
losing side, were very far, in most cases, from being persons more
prejudiced, or stupid, or narrow-minded, than the greater part of mankind
now are; and the cause for which they fought was far from being a
manifestly bad one, till it had been so decided by the result of the
war.... So complete has been the victory of truth in most of these
instances, that at present we can hardly imagine the struggle to have been
necessary. _The very essence of these triumphs is, that they lead us to
regard the views we reject as not only false but inconceivable._”(81)

This last proposition is precisely what I contend for; and I ask no more,
in order to overthrow the whole theory of its author on the nature of the
evidence of axioms. For what is that theory? That the truth of axioms can
not have been learned from experience, because their falsity is
inconceivable. But Dr. Whewell himself says, that we are continually led,
by the natural progress of thought, to regard as inconceivable what our
forefathers not only conceived but believed, nay even (he might have
added) were unable to conceive the reverse of. He can not intend to
justify this mode of thought: he can not mean to say, that we can be right
in regarding as inconceivable what others have conceived, and as
self-evident what to others did not appear evident at all. After so
complete an admission that inconceivableness is an accidental thing, not
inherent in the phenomenon itself, but dependent on the mental history of
the person who tries to conceive it, how can he ever call upon us to
reject a proposition as impossible on no other ground than its
inconceivableness? Yet he not only does so, but has unintentionally
afforded some of the most remarkable examples which can be cited of the
very illusion which he has himself so clearly pointed out. I select as
specimens, his remarks on the evidence of the three laws of motion, and of
the atomic theory.

With respect to the laws of motion, Dr. Whewell says: “No one can doubt
that, in historical fact, these laws were collected from experience. That
such is the case, is no matter of conjecture. We know the time, the
persons, the circumstances, belonging to each step of each discovery.”(82)
After this testimony, to adduce evidence of the fact would be superfluous.
And not only were these laws by no means intuitively evident, but some of
them were originally paradoxes. The first law was especially so. That a
body, once in motion, would continue forever to move in the same direction
with undiminished velocity unless acted upon by some new force, was a
proposition which mankind found for a long time the greatest difficulty in
crediting. It stood opposed to apparent experience of the most familiar
kind, which taught that it was the nature of motion to abate gradually,
and at last terminate of itself. Yet when once the contrary doctrine was
firmly established, mathematicians, as Dr. Whewell observes, speedily
began to believe that laws, thus contradictory to first appearances, and
which, even after full proof had been obtained, it had required
generations to render familiar to the minds of the scientific world, were
under “a demonstrable necessity, compelling them to be such as they are
and no other;” and he himself, though not venturing “absolutely to
pronounce” that _all_ these laws “can be rigorously traced to an absolute
necessity in the nature of things,”(83) does actually so think of the law
just mentioned; of which he says: “Though the discovery of the first law
of motion was made, historically speaking, by means of experiment, we have
now attained a point of view in which we see that it might have been
certainly known to be true, independently of experience.”(84) Can there be
a more striking exemplification than is here afforded, of the effect of
association which we have described? Philosophers, for generations, have
the most extraordinary difficulty in putting certain ideas together; they
at last succeed in doing so; and after a sufficient repetition of the
process, they first fancy a natural bond between the ideas, then
experience a growing difficulty, which at last, by the continuation of the
same progress, becomes an impossibility, of severing them from one
another. If such be the progress of an experimental conviction of which
the date is of yesterday, and which is in opposition to first appearances,
how must it fare with those which are conformable to appearances familiar
from the first dawn of intelligence, and of the conclusiveness of which,
from the earliest records of human thought, no skeptic has suggested even
a momentary doubt?

The other instance which I shall quote is a truly astonishing one, and may
be called the _reductio ad absurdum_ of the theory of inconceivableness.
Speaking of the laws of chemical composition, Dr. Whewell says:(85) “That
they could never have been clearly understood, and therefore never firmly
established, without laborious and exact experiments, is certain; but yet
we may venture to say, that being once known, they possess an evidence
beyond that of mere experiment. _For how in fact can we conceive
combinations, otherwise than as definite in kind and quality?_ If we were
to suppose each element ready to combine with any other indifferently, and
indifferently in any quantity, we should have a world in which all would
be confusion and indefiniteness. There would be no fixed kinds of bodies.
Salts, and stones, and ores, would approach to and graduate into each
other by insensible degrees. Instead of this, we know that the world
consists of bodies distinguishable from each other by definite
differences, capable of being classified and named, and of having general
propositions asserted concerning them. And as _we can not conceive a world
in which this should not be the case_, it would appear that we can not
conceive a state of things in which the laws of the combination of
elements should not be of that definite and measured kind which we have
above asserted.”

That a philosopher of Dr. Whewell’s eminence should gravely assert that we
can not conceive a world in which the simple elements should combine in
other than definite proportions; that by dint of meditating on a
scientific truth, the original discoverer of which was still living, he
should have rendered the association in his own mind between the idea of
combination and that of constant proportions so familiar and intimate as
to be unable to conceive the one fact without the other; is so signal an
instance of the mental law for which I am contending, that one word more
in illustration must be superfluous.

In the latest and most complete elaboration of his metaphysical system
(the _Philosophy of Discovery_), as well as in the earlier discourse on
the _Fundamental Antithesis of Philosophy_, reprinted as an appendix to
that work, Dr. Whewell, while very candidly admitting that his language
was open to misconception, disclaims having intended to say that mankind
in general can _now_ perceive the law of definite proportions in chemical
combination to be a necessary truth. All he meant was that philosophical
chemists in a future generation may possibly see this. “Some truths may be
seen by intuition, but yet the intuition of them may be a rare and a
difficult attainment.”(86) And he explains that the inconceivableness
which, according to his theory, is the test of axioms, “depends entirely
upon the clearness of the Ideas which the axioms involve. So long as those
ideas are vague and indistinct, the contrary of an axiom may be assented
to, though it can not be distinctly conceived. It may be assented to, not
because it is possible, but because we do not see clearly what is
possible. To a person who is only beginning to think geometrically, there
may appear nothing absurd in the assertion that two straight lines may
inclose a space. And in the same manner, to a person who is only beginning
to think of mechanical truths, it may not appear to be absurd, that in
mechanical processes, Reaction should be greater or less than Action; and
so, again, to a person who has not thought steadily about Substance, it
may not appear inconceivable, that by chemical operations, we should
generate new matter, or destroy matter which already exists.”(87)
Necessary truths, therefore, are not those of which we can not conceive,
but “those of which we can not _distinctly_ conceive, the contrary.”(88)
So long as our ideas are indistinct altogether, we do not know what is or
is not capable of being distinctly conceived; but, by the ever increasing
distinctness with which scientific men apprehend the general conceptions
of science, they in time come to perceive that there are certain laws of
nature, which, though historically and as a matter of fact they were
learned from experience, we can not, now that we know them, distinctly
conceive to be other than they are.

The account which I should give of this progress of the scientific mind is
somewhat different. After a general law of nature has been ascertained,
men’s minds do not at first acquire a complete facility of familiarly
representing to themselves the phenomena of nature in the character which
that law assigns to them. The habit which constitutes the scientific cast
of mind, that of conceiving facts of all descriptions conformably to the
laws which regulate them—phenomena of all descriptions according to the
relations which have been ascertained really to exist between them; this
habit, in the case of newly-discovered relations, comes only by degrees.
So long as it is not thoroughly formed, no necessary character is ascribed
to the new truth. But in time, the philosopher attains a state of mind in
which his mental picture of nature spontaneously represents to him all the
phenomena with which the new theory is concerned, in the exact light in
which the theory regards them: all images or conceptions derived from any
other theory, or from the confused view of the facts which is anterior to
any theory, having entirely disappeared from his mind. The mode of
representing facts which results from the theory, has now become, to his
faculties, the only natural mode of conceiving them. It is a known truth,
that a prolonged habit of arranging phenomena in certain groups, and
explaining them by means of certain principles, makes any other
arrangement or explanation of these facts be felt as unnatural: and it may
at last become as difficult to him to represent the facts to himself in
any other mode, as it often was, originally, to represent them in that
mode.

But, further (if the theory is true, as we are supposing it to be), any
other mode in which he tries, or in which he was formerly accustomed, to
represent the phenomena, will be seen by him to be inconsistent with the
facts that suggested the new theory—facts which now form a part of his
mental picture of nature. And since a contradiction is always
inconceivable, his imagination rejects these false theories, and declares
itself incapable of conceiving them. Their inconceivableness to him does
not, however, result from any thing in the theories themselves,
intrinsically and _a priori_ repugnant to the human faculties; it results
from the repugnance between them and a portion of the facts; which facts
as long as he did not know, or did not distinctly realize in his mental
representations, the false theory did not appear other than conceivable;
it becomes inconceivable, merely from the fact that contradictory elements
can not be combined in the same conception. Although, then, his real
reason for rejecting theories at variance with the true one, is no other
than that they clash with his experience, he easily falls into the belief,
that he rejects them because they are inconceivable, and that he adopts
the true theory because it is self-evident, and does not need the evidence
of experience at all.

This I take to be the real and sufficient explanation of the paradoxical
truth, on which so much stress is laid by Dr. Whewell, that a
scientifically cultivated mind is actually, in virtue of that cultivation,
unable to conceive suppositions which a common man conceives without the
smallest difficulty. For there is nothing inconceivable in the
suppositions themselves; the impossibility is in combining them with facts
inconsistent with them, as part of the same mental picture; an obstacle of
course only felt by those who know the facts, and are able to perceive the
inconsistency. As far as the suppositions themselves are concerned, in the
case of many of Dr. Whewell’s necessary truths the negative of the axiom
is, and probably will be as long as the human race lasts, as easily
conceivable as the affirmative. There is no axiom (for example) to which
Dr. Whewell ascribes a more thorough character of necessity and
self-evidence, than that of the indestructibility of matter. That this is
a true law of nature I fully admit; but I imagine there is no human being
to whom the opposite supposition is inconceivable—who has any difficulty
in imagining a portion of matter annihilated: inasmuch as its apparent
annihilation, in no respect distinguishable from real by our unassisted
senses, takes place every time that water dries up, or fuel is consumed.
Again, the law that bodies combine chemically in definite proportions is
undeniably true; but few besides Dr. Whewell have reached the point which
he seems personally to have arrived at (though he only dares prophesy
similar success to the multitude after the lapse of generations), that of
being unable to conceive a world in which the elements are ready to
combine with one another “indifferently in any quantity;” nor is it likely
that we shall ever rise to this sublime height of inability, so long as
all the mechanical mixtures in our planet, whether solid, liquid, or
aëriform, exhibit to our daily observation the very phenomenon declared to
be inconceivable.

According to Dr. Whewell, these and similar laws of nature can not be
drawn from experience, inasmuch as they are, on the contrary, assumed in
the interpretation of experience. Our inability to “add to or diminish the
quantity of matter in the world,” is a truth which “neither is nor can be
derived from experience; for the experiments which we make to verify it
presuppose its truth.... When men began to use the balance in chemical
analysis, they did not prove by trial, but took for granted, as
self-evident, that the weight of the whole must be found in the aggregate
weight of the elements.”(89) True, it is assumed; but, I apprehend, no
otherwise than as all experimental inquiry assumes provisionally some
theory or hypothesis, which is to be finally held true or not, according
as the experiments decide. The hypothesis chosen for this purpose will
naturally be one which groups together some considerable number of facts
already known. The proposition that the material of the world, as
estimated by weight, is neither increased nor diminished by any of the
processes of nature or art, had many appearances in its favor to begin
with. It expressed truly a great number of familiar facts. There were
other facts which it had the appearance of conflicting with, and which
made its truth, as a universal law of nature, at first doubtful. Because
it was doubtful, experiments were devised to verify it. Men assumed its
truth hypothetically, and proceeded to try whether, on more careful
examination, the phenomena which apparently pointed to a different
conclusion, would not be found to be consistent with it. This turned out
to be the case; and from that time the doctrine took its place as a
universal truth, but as one proved to be such by experience. That the
theory itself preceded the proof of its truth—that it had to be conceived
before it could be proved, and in order that it might be proved—does not
imply that it was self-evident, and did not need proof. Otherwise all the
true theories in the sciences are necessary and self-evident; for no one
knows better than Dr. Whewell that they all began by being assumed, for
the purpose of connecting them by deductions with those facts of
experience on which, as evidence, they now confessedly rest.(90)




                               Chapter VI.


The Same Subject Continued.


§ 1. In the examination which formed the subject of the last chapter, into
the nature of the evidence of those deductive sciences which are commonly
represented to be systems of necessary truth, we have been led to the
following conclusions. The results of those sciences are indeed necessary,
in the sense of necessarily following from certain first principles,
commonly called axioms and definitions; that is, of being certainly true
if those axioms and definitions are so; for the word necessity, even in
this acceptation of it, means no more than certainty. But their claim to
the character of necessity in any sense beyond this, as implying an
evidence independent of and superior to observation and experience, must
depend on the previous establishment of such a claim in favor of the
definitions and axioms themselves. With regard to axioms, we found that,
considered as experimental truths, they rest on superabundant and obvious
evidence. We inquired, whether, since this is the case, it be imperative
to suppose any other evidence of those truths than experimental evidence,
any other origin for our belief of them than an experimental origin. We
decided, that the burden of proof lies with those who maintain the
affirmative, and we examined, at considerable length, such arguments as
they have produced. The examination having led to the rejection of those
arguments, we have thought ourselves warranted in concluding that axioms
are but a class, the most universal class, of inductions from experience;
the simplest and easiest cases of generalization from the facts furnished
to us by our senses or by our internal consciousness.

While the axioms of demonstrative sciences thus appeared to be
experimental truths, the definitions, as they are incorrectly called, in
those sciences, were found by us to be generalizations from experience
which are not even, accurately speaking, truths; being propositions in
which, while we assert of some kind of object, some property or properties
which observation shows to belong to it, we at the same time deny that it
possesses any other properties, though in truth other properties do in
every individual instance accompany, and in almost all instances modify,
the property thus exclusively predicated. The denial, therefore, is a mere
fiction, or supposition, made for the purpose of excluding the
consideration of those modifying circumstances, when their influence is of
too trifling amount to be worth considering, or adjourning it, when
important to a more convenient moment.

From these considerations it would appear that Deductive or Demonstrative
Sciences are all, without exception, Inductive Sciences; that their
evidence is that of experience; but that they are also, in virtue of the
peculiar character of one indispensable portion of the general formulæ
according to which their inductions are made, Hypothetical Sciences. Their
conclusions are only true on certain suppositions, which are, or ought to
be, approximations to the truth, but are seldom, if ever, exactly true;
and to this hypothetical character is to be ascribed the peculiar
certainty, which is supposed to be inherent in demonstration.

What we have now asserted, however, cannot be received as universally true
of Deductive or Demonstrative Sciences, until verified by being applied to
the most remarkable of all those sciences, that of Numbers; the theory of
the Calculus; Arithmetic and Algebra. It is harder to believe of the
doctrines of this science than of any other, either that they are not
truths _a priori_, but experimental truths, or that their peculiar
certainty is owing to their being not absolute but only conditional
truths. This, therefore, is a case which merits examination apart; and the
more so, because on this subject we have a double set of doctrines to
contend with; that of the _a priori_ philosophers on one side; and on the
other, a theory the most opposite to theirs, which was at one time very
generally received, and is still far from being altogether exploded, among
metaphysicians.

§ 2. This theory attempts to solve the difficulty apparently inherent in
the case, by representing the propositions of the science of numbers as
merely verbal, and its processes as simple transformations of language,
substitutions of one expression for another. The proposition, Two and one
is equal to three, according to these writers, is not a truth, is not the
assertion of a really existing fact, but a definition of the word three; a
statement that mankind have agreed to use the name three as a sign exactly
equivalent to two and one; to call by the former name whatever is called
by the other more clumsy phrase. According to this doctrine, the longest
process in algebra is but a succession of changes in terminology, by which
equivalent expressions are substituted one for another; a series of
translations of the same fact, from one into another language; though how,
after such a series of translations, the fact itself comes out changed (as
when we demonstrate a new geometrical theorem by algebra), they have not
explained; and it is a difficulty which is fatal to their theory.

It must be acknowledged that there are peculiarities in the processes of
arithmetic and algebra which render the theory in question very plausible,
and have not unnaturally made those sciences the stronghold of Nominalism.
The doctrine that we can discover facts, detect the hidden processes of
nature, by an artful manipulation of language, is so contrary to common
sense, that a person must have made some advances in philosophy to believe
it: men fly to so paradoxical a belief to avoid, as they think, some even
greater difficulty, which the vulgar do not see. What has led many to
believe that reasoning is a mere verbal process, is, that no other theory
seemed reconcilable with the nature of the Science of Numbers. For we do
not carry any ideas along with us when we use the symbols of arithmetic or
of algebra. In a geometrical demonstration we have a mental diagram, if
not one on paper; AB, AC, are present to our imagination as lines,
intersecting other lines, forming an angle with one another, and the like;
but not so _a_ and _b_. These may represent lines or any other magnitudes,
but those magnitudes are never thought of; nothing is realized in our
imagination but _a_ and _b_. The ideas which, on the particular occasion,
they happen to represent, are banished from the mind during every
intermediate part of the process, between the beginning, when the premises
are translated from things into signs, and the end, when the conclusion is
translated back from signs into things. Nothing, then, being in the
reasoner’s mind but the symbols, what can seem more inadmissible than to
contend that the reasoning process has to do with any thing more? We seem
to have come to one of Bacon’s Prerogative Instances; an _experimentum
crucis_ on the nature of reasoning itself.

Nevertheless, it will appear on consideration, that this apparently so
decisive instance is no instance at all; that there is in every step of an
arithmetical or algebraical calculation a real induction, a real inference
of facts from facts; and that what disguises the induction is simply its
comprehensive nature, and the consequent extreme generality of the
language. All numbers must be numbers of something: there are no such
things as numbers in the abstract. _Ten_ must mean ten bodies, or ten
sounds, or ten beatings of the pulse. But though numbers must be numbers
of something, they may be numbers of any thing. Propositions, therefore,
concerning numbers, have the remarkable peculiarity that they are
propositions concerning all things whatever; all objects, all existences
of every kind, known to our experience. All things possess quantity;
consist of parts which can be numbered; and in that character possess all
the properties which are called properties of numbers. That half of four
is two, must be true whatever the word four represents, whether four
hours, four miles, or four pounds weight. We need only conceive a thing
divided into four equal parts (and all things may be conceived as so
divided), to be able to predicate of it every property of the number four,
that is, every arithmetical proposition in which the number four stands on
one side of the equation. Algebra extends the generalization still
farther: every number represents that particular number of all things
without distinction, but every algebraical symbol does more, it represents
all numbers without distinction. As soon as we conceive a thing divided
into equal parts, without knowing into what number of parts, we may call
it _a_ or _x_, and apply to it, without danger of error, every algebraical
formula in the books. The proposition, 2 (_a_ + _b_)= 2 _a_ + 2 _b_, is a
truth co-extensive with all nature. Since then algebraical truths are true
of all things whatever, and not, like those of geometry, true of lines
only or of angles only, it is no wonder that the symbols should not excite
in our minds ideas of any things in particular. When we demonstrate the
forty-seventh proposition of Euclid, it is not necessary that the words
should raise in us an image of all right-angled triangles, but only of
some one right-angled triangle: so in algebra we need not, under the
symbol _a_, picture to ourselves all things whatever, but only some one
thing; why not, then, the letter itself? The mere written characters, _a_,
_b_, _x_, _y_, _z_, serve as well for representatives of Things in
general, as any more complex and apparently more concrete conception. That
we are conscious of them, however, in their character of things, and not
of mere signs, is evident from the fact that our whole process of
reasoning is carried on by predicating of them the properties of things.
In resolving an algebraic equation, by what rules do we proceed? By
applying at each step to _a_, _b_, and _x_, the proposition that equals
added to equals make equals; that equals taken from equals leave equals;
and other propositions founded on these two. These are not properties of
language, or of signs as such, but of magnitudes, which is as much as to
say, of all things. The inferences, therefore, which are successively
drawn, are inferences concerning things, not symbols; though as any Things
whatever will serve the turn, there is no necessity for keeping the idea
of the Thing at all distinct, and consequently the process of thought may,
in this case, be allowed without danger to do what all processes of
thought, when they have been performed often, will do if permitted,
namely, to become entirely mechanical. Hence the general language of
algebra comes to be used familiarly without exciting ideas, as all other
general language is prone to do from mere habit, though in no other case
than this can it be done with complete safety. But when we look back to
see from whence the probative force of the process is derived, we find
that at every single step, unless we suppose ourselves to be thinking and
talking of the things, and not the mere symbols, the evidence fails.

There is another circumstance, which, still more than that which we have
now mentioned, gives plausibility to the notion that the propositions of
arithmetic and algebra are merely verbal. That is, that when considered as
propositions respecting Things, they all have the appearance of being
identical propositions. The assertion, Two and one is equal to three,
considered as an assertion respecting objects, as for instance, “Two
pebbles and one pebble are equal to three pebbles,” does not affirm
equality between two collections of pebbles, but absolute identity. It
affirms that if we put one pebble to two pebbles, those very pebbles are
three. The objects, therefore, being the very same, and the mere assertion
that “objects are themselves” being insignificant, it seems but natural to
consider the proposition, Two and one is equal to three, as asserting mere
identity of signification between the two names.

This, however, though it looks so plausible, will not bear examination.
The expression “two pebbles and one pebble,” and the expression “three
pebbles,” stand indeed for the same aggregation of objects, but they by no
means stand for the same physical fact. They are names of the same
objects, but of those objects in two different states: though they
_de_note the same things, their _con_notation is different. Three pebbles
in two separate parcels, and three pebbles in one parcel, do not make the
same impression on our senses; and the assertion that the very same
pebbles may by an alteration of place and arrangement be made to produce
either the one set of sensations or the other, though a very familiar
proposition, is not an identical one. It is a truth known to us by early
and constant experience: an inductive truth; and such truths are the
foundation of the science of Number. The fundamental truths of that
science all rest on the evidence of sense; they are proved by showing to
our eyes and our fingers that any given number of objects—ten balls, for
example—may by separation and re-arrangement exhibit to our senses all the
different sets of numbers the sums of which is equal to ten. All the
improved methods of teaching arithmetic to children proceed on a knowledge
of this fact. All who wish to carry the child’s _mind_ along with them in
learning arithmetic; all who wish to teach numbers, and not mere
ciphers—now teach it through the evidence of the senses, in the manner we
have described.

We may, if we please, call the proposition, “Three is two and one,” a
definition of the number three, and assert that arithmetic, as it has been
asserted that geometry, is a science founded on definitions. But they are
definitions in the geometrical sense, not the logical; asserting not the
meaning of a term only, but along with it an observed matter of fact. The
proposition, “A circle is a figure bounded by a line which has all its
points equally distant from a point within it,” is called the definition
of a circle; but the proposition from which so many consequences follow,
and which is really a first principle in geometry, is, that figures
answering to this description exist. And thus we may call “Three is two
and one” a definition of three; but the calculations which depend on that
proposition do not follow from the definition itself, but from an
arithmetical theorem presupposed in it, namely, that collections of
objects exist, which while they impress the senses thus, [Symbol: three
circles, two above one], may be separated into two parts, thus, [Symbol:
two circles, a space, and a third circle]. This proposition being granted,
we term all such parcels Threes, after which the enunciation of the
above-mentioned physical fact will serve also for a definition of the word
Three.

The Science of Number is thus no exception to the conclusion we previously
arrived at, that the processes even of deductive sciences are altogether
inductive, and that their first principles are generalizations from
experience. It remains to be examined whether this science resembles
geometry in the further circumstance, that some of its inductions are not
exactly true; and that the peculiar certainty ascribed to it, on account
of which its propositions are called Necessary Truths, is fictitious and
hypothetical, being true in no other sense than that those propositions
legitimately follow from the hypothesis of the truth of premises which are
avowedly mere approximations to truth.

§ 3. The inductions of arithmetic are of two sorts: first, those which we
have just expounded, such as One and one are two, Two and one are three,
etc., which may be called the definitions of the various numbers, in the
improper or geometrical sense of the word Definition; and secondly, the
two following axioms: The sums of equals are equal, The differences of
equals are equal. These two are sufficient; for the corresponding
propositions respecting unequals may be proved from these by a _reductio
ad absurdum_.

These axioms, and likewise the so-called definitions, are, as has already
been said, results of induction; true of all objects whatever, and, as it
may seem, exactly true, without the hypothetical assumption of unqualified
truth where an approximation to it is all that exists. The conclusions,
therefore, it will naturally be inferred, are exactly true, and the
science of number is an exception to other demonstrative sciences in this,
that the categorical certainty which is predicable of its demonstrations
is independent of all hypothesis.

On more accurate investigation, however, it will be found that, even in
this case, there is one hypothetical element in the ratiocination. In all
propositions concerning numbers, a condition is implied, without which
none of them would be true; and that condition is an assumption which may
be false. The condition is, that 1=1; that all the numbers are numbers of
the same or of equal units. Let this be doubtful, and not one of the
propositions of arithmetic will hold true. How can we know that one pound
and one pound make two pounds, if one of the pounds may be troy, and the
other avoirdupois? They may not make two pounds of either, or of any
weight. How can we know that a forty-horse power is always equal to
itself, unless we assume that all horses are of equal strength? It is
certain that 1 is always equal in _number_ to 1; and where the mere number
of objects, or of the parts of an object, without supposing them to be
equivalent in any other respect, is all that is material, the conclusions
of arithmetic, so far as they go to that alone, are true without mixture
of hypothesis. There are such cases in statistics; as, for instance, an
inquiry into the amount of the population of any country. It is
indifferent to that inquiry whether they are grown people or children,
strong or weak, tall or short; the only thing we want to ascertain is
their number. But whenever, from equality or inequality of number,
equality or inequality in any other respect is to be inferred, arithmetic
carried into such inquiries becomes as hypothetical a science as geometry.
All units must be assumed to be equal in that other respect; and this is
never accurately true, for one actual pound weight is not exactly equal to
another, nor one measured mile’s length to another; a nicer balance, or
more accurate measuring instruments, would always detect some difference.


    What is commonly called mathematical certainty, therefore, which
    comprises the twofold conception of unconditional truth and
    perfect accuracy, is not an attribute of all mathematical truths,
    but of those only which relate to pure Number, as distinguished
    from Quantity in the more enlarged sense; and only so long as we
    abstain from supposing that the numbers are a precise index to
    actual quantities. The certainty usually ascribed to the
    conclusions of geometry, and even to those of mechanics, is
    nothing whatever but certainty of inference. We can have full
    assurance of particular results under particular suppositions, but
    we can not have the same assurance that these suppositions are
    accurately true, nor that they include all the data which may
    exercise an influence over the result in any given instance.


§ 4. It appears, therefore, that the method of all Deductive Sciences is
hypothetical. They proceed by tracing the consequences of certain
assumptions; leaving for separate consideration whether the assumptions
are true or not, and if not exactly true, whether they are a sufficiently
near approximation to the truth. The reason is obvious. Since it is only
in questions of pure number that the assumptions are exactly true, and
even there only so long as no conclusions except purely numerical ones are
to be founded on them; it must, in all other cases of deductive
investigation, form a part of the inquiry, to determine how much the
assumptions want of being exactly true in the case in hand. This is
generally a matter of observation, to be repeated in every fresh case; or
if it has to be settled by argument instead of observation, may require in
every different case different evidence, and present every degree of
difficulty, from the lowest to the highest. But the other part of the
process—namely, to determine what else may be concluded if we find, and in
proportion as we find, the assumptions to be true—may be performed once
for all, and the results held ready to be employed as the occasions turn
up for use. We thus do all beforehand that can be so done, and leave the
least possible work to be performed when cases arise and press for a
decision. This inquiry into the inferences which can be drawn from
assumptions, is what properly constitutes Demonstrative Science.

It is of course quite as practicable to arrive at new conclusions from
facts assumed, as from facts observed; from fictitious, as from real,
inductions. Deduction, as we have seen, consists of a series of inferences
in this form—_a_ is a mark of _b_, _b_ of _c_, _c_ of _d_, therefore _a_
is a mark of _d_, which last may be a truth inaccessible to direct
observation. In like manner it is allowable to say, _suppose_ that a were
a mark of _b_, _b_ of _c_, and _c_ of _d_, _a_ would be a mark of _d_,
which last conclusion was not thought of by those who laid down the
premises. A system of propositions as complicated as geometry might be
deduced from assumptions which are false; as was done by Ptolemy,
Descartes, and others, in their attempts to explain synthetically the
phenomena of the solar system on the supposition that the apparent motions
of the heavenly bodies were the real motions, or were produced in some way
more or less different from the true one. Sometimes the same thing is
knowingly done, for the purpose of showing the falsity of the assumption;
which is called a _reductio ad absurdum_. In such cases, the reasoning is
as follows: _a_ is a mark of _b_, and _b_ of _c_; now if c were also a
mark of _d, a_ would be a mark of _d_; but _d_ is known to be a mark of
the absence of _a_; consequently _a_ would be a mark of its own absence,
which is a contradiction; therefore _c_ is not a mark of _d_.

§ 5. It has even been held by some writers, that all ratiocination rests
in the last resort on a _reductio ad absurdum_; since the way to enforce
assent to it, in case of obscurity, would be to show that if the
conclusion be denied we must deny some one at least of the premises,
which, as they are all supposed true, would be a contradiction. And in
accordance with this, many have thought that the peculiar nature of the
evidence of ratiocination consisted in the impossibility of admitting the
premises and rejecting the conclusion without a contradiction in terms.
This theory, however, is inadmissible as an explanation of the grounds on
which ratiocination itself rests. If any one denies the conclusion
notwithstanding his admission of the premises, he is not involved in any
direct and express contradiction until he is compelled to deny some
premise; and he can only be forced to do this by a _reductio ad absurdum_,
that is, by another ratiocination: now, if he denies the validity of the
reasoning process itself, he can no more be forced to assent to the second
syllogism than to the first. In truth, therefore, no one is ever forced to
a contradiction in terms: he can only be forced to a contradiction (or
rather an infringement) of the fundamental maxim of ratiocination, namely,
that whatever has a mark, has what it is a mark of; or (in the case of
universal propositions), that whatever is a mark of any thing, is a mark
of whatever else that thing is a mark of. For in the case of every correct
argument, as soon as thrown into the syllogistic form, it is evident
without the aid of any other syllogism, that he who, admitting the
premises, fails to draw the conclusion, does not conform to the above
axiom.

We have now proceeded as far in the theory of Deduction as we can advance
in the present stage of our inquiry. Any further insight into the subject
requires that the foundation shall have been laid of the philosophic
theory of Induction itself; in which theory that of Deduction, as a mode
of Induction, which we have now shown it to be, will assume spontaneously
the place which belongs to it, and will receive its share of whatever
light may be thrown upon the great intellectual operation of which it
forms so important a part.




                               Chapter VII.


Examination Of Some Opinions Opposed To The Preceding Doctrines.


§ 1. Polemical discussion is foreign to the plan of this work. But an
opinion which stands in need of much illustration, can often receive it
most effectually, and least tediously, in the form of a defense against
objections. And on subjects concerning which speculative minds are still
divided, a writer does but half his duty by stating his own doctrine, if
he does not also examine, and to the best of his ability judge, those of
other thinkers.

In the dissertation which Mr. Herbert Spencer has prefixed to his, in many
respects, highly philosophical treatise on the Mind,(91) he criticises
some of the doctrines of the two preceding chapters, and propounds a
theory of his own on the subject of first principles. Mr. Spencer agrees
with me in considering axioms to be “simply our earliest inductions from
experience.” But he differs from me “widely as to the worth of the test of
inconceivableness.” He thinks that it is the ultimate test of all beliefs.
He arrives at this conclusion by two steps. First, we never can have any
stronger ground for believing any thing, than that the belief of it
“invariably exists.” Whenever any fact or proposition is invariably
believed; that is, if I understand Mr. Spencer rightly, believed by all
persons, and by one’s self at all times; it is entitled to be received as
one of the primitive truths, or original premises of our knowledge.
Secondly, the criterion by which we decide whether any thing is invariably
believed to be true, is our inability to conceive it as false. “The
inconceivability of its negation is the test by which we ascertain whether
a given belief invariably exists or not.” “For our primary beliefs, the
fact of invariable existence, tested by an abortive effort to cause their
non-existence, is the only reason assignable.” He thinks this the sole
ground of our belief in our own sensations. If I believe that I feel cold,
I only receive this as true because I can not conceive that I am not
feeling cold. “While the proposition remains true, the negation of it
remains inconceivable.” There are numerous other beliefs which Mr. Spencer
considers to rest on the same basis; being chiefly those, or a part of
those, which the metaphysicians of the Reid and Stewart school consider as
truths of immediate intuition. That there exists a material world; that
this is the very world which we directly and immediately perceive, and not
merely the hidden cause of our perceptions; that Space, Time, Force,
Extension, Figure, are not modes of our consciousness, but objective
realities; are regarded by Mr. Spencer as truths known by the
inconceivableness of their negatives. We can not, he says, by any effort,
conceive these objects of thought as mere states of our mind; as not
having an existence external to us. Their real existence is, therefore, as
certain as our sensations themselves. The truths which are the subject of
direct knowledge, being, according to this doctrine, known to be truths
only by the inconceivability of their negation; and the truths which are
not the object of direct knowledge, being known as inferences from those
which are; and those inferences being believed to follow from the
premises, only because we can not conceive them not to follow;
inconceivability is thus the ultimate ground of all assured beliefs.

Thus far, there is no very wide difference between Mr. Spencer’s doctrine
and the ordinary one of philosophers of the intuitive school, from
Descartes to Dr. Whewell; but at this point Mr. Spencer diverges from
them. For he does not, like them, set up the test of inconceivability as
infallible. On the contrary, he holds that it may be fallacious, not from
any fault in the test itself, but because “men have mistaken for
inconceivable things, some things which were not inconceivable.” And he
himself, in this very book, denies not a few propositions usually regarded
as among the most marked examples of truths whose negations are
inconceivable. But occasional failure, he says, is incident to all tests.
If such failure vitiates “the test of inconceivableness,” it “must
similarly vitiate all tests whatever. We consider an inference logically
drawn from established premises to be true. Yet in millions of cases men
have been wrong in the inferences they have thought thus drawn. Do we
therefore argue that it is absurd to consider an inference true on no
other ground than that it is logically drawn from established premises?
No: we say that though men may have taken for logical inferences,
inferences that were not logical, there nevertheless _are_ logical
inferences, and that we are justified in assuming the truth of what seem
to us such, until better instructed. Similarly, though men may have
thought some things inconceivable which were not so, there may still be
inconceivable things; and the inability to conceive the negation of a
thing, may still be our best warrant for believing it.... Though
occasionally it may prove an imperfect test, yet, as our most certain
beliefs are capable of no better, to doubt any one belief because we have
no higher guarantee for it, is really to doubt all beliefs.” Mr. Spencer’s
doctrine, therefore, does not erect the curable, but only the incurable
limitations of the human conceptive faculty, into laws of the outward
universe.

§ 2. The doctrine, that “a belief which is proved by the inconceivableness
of its negation to invariably exist, is true,” Mr. Spencer enforces by two
arguments, one of which may be distinguished as positive, and the other as
negative.

The positive argument is, that every such belief represents the aggregate
of all past experience. “Conceding the entire truth of” the “position,
that during any phase of human progress, the ability or inability to form
a specific conception wholly depends on the experiences men have had; and
that, by a widening of their experiences, they may, by and by, be enabled
to conceive things before inconceivable to them, it may still be argued
that as, at any time, the best warrant men can have for a belief is the
perfect agreement of all pre-existing experience in support of it, it
follows that, at any time, the inconceivableness of its negation is the
deepest test any belief admits of.... Objective facts are ever impressing
themselves upon us; our experience is a register of these objective facts;
and the inconceivableness of a thing implies that it is wholly at variance
with the register. Even were this all, it is not clear how, if every truth
is primarily inductive, any better test of truth could exist. But it must
be remembered that while many of these facts, impressing themselves upon
us, are occasional; while others again are very general; some are
universal and unchanging. These universal and unchanging facts are, by the
hypothesis, certain to establish beliefs of which the negations are
inconceivable; while the others are not certain to do this; and if they
do, subsequent facts will reverse their action. Hence if, after an immense
accumulation of experiences, there remain beliefs of which the negations
are still inconceivable, most, if not all of them, must correspond to
universal objective facts. If there be ... certain absolute uniformities
in nature; if these uniformities produce, as they must, absolute
uniformities in our experience; and if ... these absolute uniformities in
our experience disable us from conceiving the negations of them; then
answering to each absolute uniformity in nature which we can cognize,
there must exist in us a belief of which the negation is inconceivable,
and which is absolutely true. In this wide range of cases subjective
inconceivableness must correspond to objective impossibility. Further
experience will produce correspondence where it may not yet exist; and we
may expect the correspondence to become ultimately complete. In nearly all
cases this test of inconceivableness must be valid now” (I wish I could
think we were so nearly arrived at omniscience); “and where it is not, it
still expresses the net result of our experience up to the present time;
which is the most that any test can do.”

To this I answer, first, that it is by no means true that the
inconceivability, by us, of the negative of a proposition proves all, or
even any, “pre-existing experience” to be in favor of the affirmative.
There may have been no such pre-existing experiences, but only a mistaken
supposition of experience. How did the inconceivability of antipodes prove
that experience had given any testimony against their possibility? How did
the incapacity men felt of conceiving sunset otherwise than as a motion of
the sun, represent any “net result” of experience in support of its being
the sun and not the earth that moves? It is not experience that is
represented, it is only a superficial semblance of experience. The only
thing proved with regard to real experience, is the negative fact, that
men have _not had_ it of the kind which would have made the inconceivable
proposition conceivable.

Next: Even if it were true that inconceivableness represents the net
result of all past experience, why should we stop at the representative
when we can get at the thing represented? If our incapacity to conceive
the negation of a given supposition is proof of its truth, because proving
that our experience has hitherto been uniform in its favor, the real
evidence for the supposition is not the inconceivableness, but the
uniformity of experience. Now this, which is the substantial and only
proof, is directly accessible. We are not obliged to presume it from an
incidental consequence. If all past experience is in favor of a belief,
let this be stated, and the belief openly rested on that ground: after
which the question arises, what that fact may be worth as evidence of its
truth? For uniformity of experience is evidence in very different degrees:
in some cases it is strong evidence, in others weak, in others it scarcely
amounts to evidence at all. That all metals sink in water, was a uniform
experience, from the origin of the human race to the discovery of
potassium in the present century by Sir Humphry Davy. That all swans are
white, was a uniform experience down to the discovery of Australia. In the
few cases in which uniformity of experience does amount to the strongest
possible proof, as with such propositions as these, Two straight lines can
not inclose a space, Every event has a cause, it is not because their
negations are inconceivable, which is not always the fact; but because the
experience, which has been thus uniform, pervades all nature. It will be
shown in the following Book that none of the conclusions either of
induction or of deduction can be considered certain, except as far as
their truth is shown to be inseparably bound up with truths of this class.

I maintain then, first, that uniformity of past experience is very far
from being universally a criterion of truth. But secondly,
inconceivableness is still further from being a test even of that test.
Uniformity of contrary experience is only one of many causes of
inconceivability. Tradition handed down from a period of more limited
knowledge, is one of the commonest. The mere familiarity of one mode of
production of a phenomenon often suffices to make every other mode appear
inconceivable. Whatever connects two ideas by a strong association may,
and continually does, render their separation in thought impossible; as
Mr. Spencer, in other parts of his speculations, frequently recognizes. It
was not for want of experience that the Cartesians were unable to conceive
that one body could produce motion in another without contact. They had as
much experience of other modes of producing motion as they had of that
mode. The planets had revolved, and heavy bodies had fallen, every hour of
their lives. But they fancied these phenomena to be produced by a hidden
machinery which they did not see, because without it they were unable to
conceive what they did see. The inconceivableness, instead of representing
their experience, dominated and overrode their experience. Without
dwelling further on what I have termed the positive argument of Mr.
Spencer in support of his criterion of truth, I pass to his negative
argument, on which he lays more stress.

§ 3. The negative argument is, that, whether inconceivability be good
evidence or bad, no stronger evidence is to be obtained. That what is
inconceivable can not be true, is postulated in every act of thought. It
is the foundation of all our original premises. Still more it is assumed
in all conclusions from those premises. The invariability of belief,
tested by the inconceivableness of its negation, “is our sole warrant for
every demonstration. Logic is simply a systematization of the process by
which we indirectly obtain this warrant for beliefs that do not directly
possess it. To gain the strongest conviction possible respecting any
complex fact, we either analytically descend from it by successive steps,
each of which we unconsciously test by the inconceivableness of its
negation, until we reach some axiom or truth which we have similarly
tested; or we synthetically ascend from such axiom or truth by such steps.
In either case we connect some isolated belief, with a belief which
invariably exists, by a series of intermediate beliefs which invariably
exist.” The following passage sums up the theory: “When we perceive that
the negation of the belief is inconceivable, we have all possible warrant
for asserting the invariability of its existence: and in asserting this,
we express alike our logical justification of it, and the inexorable
necessity we are under of holding it.... We have seen that this is the
assumption on which every conclusion whatever ultimately rests. We have no
other guarantee for the reality of consciousness, of sensations, of
personal existence; we have no other guarantee for any axiom; we have no
other guarantee for any step in a demonstration. Hence, as being taken for
granted in every act of the understanding, it must be regarded as the
Universal Postulate.” But as this postulate, which we are under an
“inexorable necessity” of holding true, is sometimes false; as “beliefs
that once were shown by the inconceivableness of their negations to
invariably exist, have since been found untrue,” and as “beliefs that now
possess this character may some day share the same fate;” the canon of
belief laid down by Mr. Spencer is, that “the most certain conclusion” is
that “which involves the postulate the fewest times.” Reasoning,
therefore, never ought to prevail against one of the immediate beliefs
(the belief in Matter, in the outward reality of Extension, Space, and the
like), because each of these involves the postulate only once; while an
argument, besides involving it in the premises, involves it again in every
step of the ratiocination, no one of the successive acts of inference
being recognized as valid except because we can not conceive the
conclusion not to follow from the premises.

It will be convenient to take the last part of this argument first. In
every reasoning, according to Mr. Spencer, the assumption of the postulate
is renewed at every step. At each inference we judge that the conclusion
follows from the premises, our sole warrant for that judgment being that
we can not conceive it not to follow. Consequently if the postulate is
fallible, the conclusions of reasoning are more vitiated by that
uncertainty than direct intuitions; and the disproportion is greater, the
more numerous the steps of the argument.

To test this doctrine, let us first suppose an argument consisting only of
a single step, which would be represented by one syllogism. This argument
does rest on an assumption, and we have seen in the preceding chapters
what the assumption is. It is, that whatever has a mark, has what it is a
mark of. The evidence of this axiom I shall not consider at present;(92)
let us suppose it (with Mr. Spencer) to be the inconceivableness of its
reverse.

Let us now add a second step to the argument: we require, what? Another
assumption? No: the same assumption a second time; and so on to a third,
and a fourth. I confess I do not see how, on Mr. Spencer’s own principles,
the repetition of the assumption at all weakens the force of the argument.
If it were necessary the second time to assume some other axiom, the
argument would no doubt be weakened, since it would be necessary to its
validity that both axioms should be true, and it might happen that one was
true and not the other: making two chances of error instead of one. But
since it is the _same_ axiom, if it is true once it is true every time;
and if the argument, being of a hundred links, assumed the axiom a hundred
times, these hundred assumptions would make but one chance of error among
them all. It is satisfactory that we are not obliged to suppose the
deductions of pure mathematics to be among the most uncertain of
argumentative processes, which on Mr. Spencer’s theory they could hardly
fail to be, since they are the longest. But the number of steps in an
argument does not subtract from its reliableness, if no new _premises_, of
an uncertain character, are taken up by the way.(93)

To speak next of the premises. Our assurance of their truth, whether they
be generalities or individual facts, is grounded, in Mr. Spencer’s
opinion, on the inconceivableness of their being false. It is necessary to
advert to a double meaning of the word inconceivable, which Mr. Spencer is
aware of, and would sincerely disclaim founding an argument upon, but from
which his case derives no little advantage notwithstanding. By
inconceivableness is sometimes meant, inability to form or get rid of an
_idea_; sometimes, inability to form or get rid of a _belief_. The former
meaning is the most conformable to the analogy of language; for a
conception always means an idea, and never a belief. The wrong meaning of
“inconceivable” is, however, fully as frequent in philosophical discussion
as the right meaning, and the intuitive school of metaphysicians could not
well do without either. To illustrate the difference, we will take two
contrasted examples. The early physical speculators considered antipodes
incredible, because inconceivable. But antipodes were not inconceivable in
the primitive sense of the word. An idea of them could be formed without
difficulty: they could be completely pictured to the mental eye. What was
difficult, and, as it then seemed, impossible, was to apprehend them as
believable. The idea could be put together, of men sticking on by their
feet to the under side of the earth; but the belief _would_ follow, that
they must fall off. Antipodes were not unimaginable, but they were
unbelievable.

On the other hand, when I endeavor to conceive an end to extension, the
two ideas refuse to come together. When I attempt to form a conception of
the last point of space, I can not help figuring to myself a vast space
beyond that last point. The combination is, under the conditions of our
experience, unimaginable. This double meaning of inconceivable it is very
important to bear in mind, for the argument from inconceivableness almost
always turns on the alternate substitution of each of those meanings for
the other.

In which of these two senses does Mr. Spencer employ the term, when he
makes it a test of the truth of a proposition that its negation is
inconceivable? Until Mr. Spencer expressly stated the contrary, I inferred
from the course of his argument, that he meant unbelievable. He has,
however, in a paper published in the fifth number of the _Fortnightly
Review_, disclaimed this meaning, and declared that by an inconceivable
proposition he means, now and always, “one of which the terms can not, by
any effort, be brought before consciousness in that relation which the
proposition asserts between them—a proposition of which the subject and
predicate offer an insurmountable resistance to union in thought.” We now,
therefore, know positively that Mr. Spencer always endeavors to use the
word inconceivable in this, its proper, sense: but it may yet be
questioned whether his endeavor is always successful; whether the other,
and popular use of the word, does not sometimes creep in with its
associations, and prevent him from maintaining a clear separation between
the two. When, for example, he says, that when I feel cold, I can not
conceive that I am not feeling cold, this expression can not be translated
into “I can not conceive myself not feeling cold,” for it is evident that
I can: the word conceive, therefore, is here used to express the
recognition of a matter of fact—the perception of truth or falsehood;
which I apprehend to be exactly the meaning of an act of belief, as
distinguished from simple conception. Again, Mr. Spencer calls the attempt
to conceive something which is inconceivable “an abortive effort to cause
the non-existence,” not of a conception or mental representation, but of a
belief. There is need, therefore, to revise a considerable part of Mr.
Spencer’s language, if it is to be kept always consistent with his
definition of inconceivability. But in truth the point is of little
importance; since inconceivability, in Mr. Spencer’s theory, is only a
test of truth, inasmuch as it is a test of believability. The
inconceivableness of a supposition is the extreme case of its
unbelievability. This is the very foundation of Mr. Spencer’s doctrine.
The invariability of the belief is with him the real guarantee. The
attempt to conceive the negative is made in order to test the
inevitableness of the belief. It should be called, an attempt to _believe_
the negative. When Mr. Spencer says that while looking at the sun a man
can not conceive that he is looking into darkness, he should have said
that a man can not _believe_ that he is doing so. For it is surely
possible, in broad daylight, to _imagine_ one’s self looking into
darkness.(94) As Mr. Spencer himself says, speaking of the belief of our
own existence, “That he _might_ not exist, he can conceive well enough;
but that he _does_ not exist, he finds it impossible to conceive,” _i.e._,
to believe. So that the statement resolves itself into this: That I exist,
and that I have sensations, I believe, because I can not believe
otherwise. And in this case every one will admit that the impossibility is
real. Any one’s present sensations, or other states of subjective
consciousness, that one person inevitably believes. They are facts known
_per se_: it is impossible to ascend beyond them. Their negative is really
unbelievable, and therefore there is never any question about believing
it. Mr. Spencer’s theory is not needed for these truths.

But according to Mr. Spencer there are other beliefs, relating to other
things than our own subjective feelings, for which we have the same
guarantee—which are, in a similar manner, invariable and necessary. With
regard to these other beliefs, they can not be necessary, since they do
not always exist. There have been, and are, many persons who do not
believe the reality of an external world, still less the reality of
extension and figure as the forms of that external world; who do not
believe that space and time have an existence independent of the mind—nor
any other of Mr. Spencer’s objective intuitions. The negations of these
alleged invariable beliefs are not unbelievable, for they are believed. It
may be maintained, without obvious error, that we can not _imagine_
tangible objects as mere states of our own and other people’s
consciousness; that the perception of them irresistibly suggests to us the
_idea_ of something external to ourselves: and I am not in a condition to
say that this is not the fact (though I do not think any one is entitled
to affirm it of any person besides himself). But many thinkers have
believed, whether they could conceive it or not, that what we represent to
ourselves as material objects, are mere modifications of consciousness;
complex feelings of touch and of muscular action. Mr. Spencer may think
the inference correct from the unimaginable to the unbelievable, because
he holds that belief itself is but the persistence of an idea, and that
what we can succeed in imagining we can not at the moment help
apprehending as believable. But of what consequence is it what we
apprehend at the moment, if the moment is in contradiction to the
permanent state of our mind? A person who has been frightened when an
infant by stories of ghosts, though he disbelieves them in after years
(and perhaps never believed them), may be unable all his life to be in a
dark place, in circumstances stimulating to the imagination, without
mental discomposure. The idea of ghosts, with all its attendant terrors,
is irresistibly called up in his mind by the outward circumstances. Mr.
Spencer may say, that while he is under the influence of this terror he
does not disbelieve in ghosts, but has a temporary and uncontrollable
belief in them. Be it so; but allowing it to be so, which would it be
truest to say of this man on the whole—that he believes in ghosts, or that
he does not believe in them? Assuredly that he does not believe in them.
The case is similar with those who disbelieve a material world. Though
they can not get rid of the idea; though while looking at a solid object
they can not help having the conception, and therefore, according to Mr.
Spencer’s metaphysics, the momentary belief, of its externality; even at
that moment they would sincerely deny holding that belief: and it would be
incorrect to call them other than disbelievers of the doctrine. The belief
therefore is not invariable; and the test of inconceivableness fails in
the only cases to which there could ever be any occasion to apply it.

That a thing may be perfectly believable, and yet may not have become
conceivable, and that we may habitually believe one side of an
alternative, and conceive only in the other, is familiarly exemplified in
the state of mind of educated persons respecting sunrise and sunset. All
educated persons either know by investigation, or believe on the authority
of science, that it is the earth and not the sun which moves: but there
are probably few who habitually _conceive_ the phenomenon otherwise than
as the ascent or descent of the sun. Assuredly no one can do so without a
prolonged trial; and it is probably not easier now than in the first
generation after Copernicus. Mr. Spencer does not say, “In looking at
sunrise it is impossible not to conceive that it is the sun which moves,
therefore this is what every body believes, and we have all the evidence
for it that we can have for any truth.” Yet this would be an exact
parallel to his doctrine about the belief in matter.

The existence of matter, and other Noumena, as distinguished from the
phenomenal world, remains a question of argument, as it was before; and
the very general, but neither necessary nor universal, belief in them,
stands as a psychological phenomenon to be explained, either on the
hypothesis of its truth, or on some other. The belief is not a conclusive
proof of its own truth, unless there are no such things as _idola tribûs_;
but being a fact, it calls on antagonists to show, from what except the
real existence of the thing believed, so general and apparently
spontaneous a belief can have originated. And its opponents have never
hesitated to accept this challenge.(95) The amount of their success in
meeting it will probably determine the ultimate verdict of philosophers on
the question.

§ 4. In the revision, or rather reconstruction, of his “Principles of
Psychology,” as one of the stages or platforms in the imposing structure
of his System of Philosophy, Mr. Spencer has resumed what he justly
terms(96) the “amicable controversy that has been long pending between
us;” expressing at the same time a regret, which I cordially share, that
“this lengthened exposition of a single point of difference, unaccompanied
by an exposition of the numerous points of concurrence, unavoidably
produces an appearance of dissent very far greater than that which
exists.” I believe, with Mr. Spencer, that the difference between us, if
measured by our conclusions, is “superficial rather than substantial;” and
the value I attach to so great an amount of agreement, in the field of
analytic psychology, with a thinker of his force and depth, is such as I
can hardly overstate. But I also agree with him that the difference which
exists in our premises is one of “profound importance, philosophically
considered;” and not to be dismissed while any part of the case of either
of us has not been fully examined and discussed.

In his present statement of the Universal Postulate, Mr. Spencer has
exchanged his former expression, “beliefs which invariably exist,” for the
following: “cognitions of which the predicates invariably exist along with
their subjects.” And he says that “an abortive effort to conceive the
negation of a proposition, shows that the cognition expressed is one of
which the predicate invariably exists along with its subject; and the
discovery that the predicate invariably exists along with its subject, is
the discovery that this cognition is one we are compelled to accept.” Both
these premises of Mr. Spencer’s syllogism I am able to assent to, but in
different senses of the middle term. If the invariable existence of the
predicate along with its subject, is to be understood in the most obvious
meaning, as an existence in actual Nature, or in other words, in our
objective, or sensational, experience, I of course admit that this, once
ascertained, compels us to accept the proposition: but then I do not admit
that the failure of an attempt to conceive the negative, proves the
predicate to be always co-existent with the subject in actual Nature. If,
on the other hand (which I believe to be Mr. Spencer’s meaning) the
invariable existence of the predicate along with the subject is to be
understood only of our conceptive faculty, _i.e._, that the one is
inseparable from the other in our thoughts; then, indeed, the inability to
separate the two ideas proves their inseparable conjunction, here and now,
in the mind which has failed in the attempt; but this inseparability in
thought does not prove a corresponding inseparability in fact; nor even in
the thoughts of other people, or of the same person in a possible future.

“That some propositions have been wrongly accepted as true, because their
negations were supposed inconceivable when they were not,” does not, in
Mr. Spencer’s opinion, “disprove the validity of the test;” not only
because any test whatever “is liable to yield untrue results, either from
incapacity or from carelessness in those who use it,” but because the
propositions in question “were complex propositions, not to be established
by a test applicable to propositions no further decomposable.” “A test
legitimately applicable to a simple proposition, the subject and predicate
of which are in direct relation, can not be legitimately applied to a
complex proposition, the subject and predicate of which are indirectly
related through the many simple propositions implied.” “That things which
are equal to the same thing are equal to one another, is a fact which can
be known by direct comparison of actual or ideal relations.... But that
the square of the hypothenuse of a right-angled triangle equals the sum of
the squares of the other two sides, can not be known immediately by
comparison of two states of consciousness: here the truth can be reached
only mediately, through a series of simple judgments respecting the
likenesses or unlikenesses of certain relations.” Moreover, even when the
proposition admits of being tested by immediate consciousness, people
often neglect to do it. A school-boy, in adding up a column of figures,
will say “35 and 9 are 46,” though this is contrary to the verdict which
consciousness gives when 35 and 9 are really called up before it; but this
is not done. And not only school-boys, but men and thinkers, do not always
“distinctly translate into their equivalent states of consciousness the
words they use.”

It is but just to give Mr. Spencer’s doctrine the benefit of the
limitation he claims—viz., that it is only applicable to propositions
which are assented to on simple inspection, without any intervening media
of proof. But this limitation does not exclude some of the most marked
instances of propositions now known to be false or groundless, but whose
negative was once found inconceivable: such as, that in sunrise and sunset
it is the sun which moves; that gravitation may exist without an
intervening medium; and even the case of antipodes. The distinction drawn
by Mr. Spencer is real; but, in the case of the propositions classed by
him as complex, consciousness, until the media of proof are supplied,
gives no verdict at all: it neither declares the equality of the square of
the hypothenuse with the sum of the squares of the sides to be
inconceivable, nor their inequality to be inconceivable. But in all the
three cases which I have just cited, the inconceivability seems to be
apprehended directly; no train of argument was needed, as in the case of
the square of the hypothenuse, to obtain the verdict of consciousness on
the point. Neither is any of the three a case like that of the
school-boy’s mistake, in which the mind was never really brought into
contact with the proposition. They are cases in which one of two opposite
predicates, _mero adspectu_, seemed to be incompatible with the subject,
and the other, therefore, to be proved always to exist with it.(97)

As now limited by Mr. Spencer, the ultimate cognitions fit to be submitted
to his test are only those of so universal and elementary a character as
to be represented in the earliest and most unvarying experience, or
apparent experience, of all mankind. In such cases the inconceivability of
the negative, if real, is accounted for by the experience: and why (I have
asked) should the truth be tested by the inconceivability, when we can go
further back for proof—namely, to the experience itself? To this Mr.
Spencer answers, that the experiences can not be all recalled to mind, and
if recalled, would be of unmanageable multitude. To test a proposition by
experience seems to him to mean that “before accepting as certain the
proposition that any rectilineal figure must have as many angles as it has
sides,” I have “to think of every triangle, square, pentagon, hexagon,
etc., which I have ever seen, and to verify the asserted relation in each
case.” I can only say, with surprise, that I do not understand this to be
the meaning of an appeal to experience. It is enough to know that one has
been seeing the fact all one’s life, and has never remarked any instance
to the contrary, and that other people, with every opportunity of
observation, unanimously declare the same thing. It is true, even this
experience may be insufficient, and so it might be even if I could recall
to mind every instance of it; but its insufficiency, instead of being
brought to light, is disguised, if instead of sifting the experience
itself, I appeal to a test which bears no relation to the sufficiency of
the experience, but, at the most, only to its familiarity. These remarks
do not lose their force even if we believe, with Mr. Spencer, that mental
tendencies originally derived from experience impress themselves
permanently on the cerebral structure and are transmitted by inheritance,
so that modes of thinking which are acquired by the race become innate and
_a priori_ in the individual, thus representing, in Mr. Spencer’s opinion,
the experience of his progenitors, in addition to his own. All that would
follow from this is, that a conviction might be really innate, _i.e._,
prior to individual experience, and yet not be true, since the inherited
tendency to accept it may have been originally the result of other causes
than its truth.

Mr. Spencer would have a much stronger case, if he could really show that
the evidence of Reasoning rests on the Postulate, or, in other words, that
we believe that a conclusion follows from premises only because we can not
conceive it not to follow. But this statement seems to me to be of the
same kind as one I have previously commented on, viz., that I believe I
see light, because I can not, while the sensation remains, conceive that I
am looking into darkness. Both these statements seem to me incompatible
with the meaning (as very rightly limited by Mr. Spencer) of the verb to
conceive. To say that when I apprehend that A is B and that B is C, I can
not conceive that A is not C, is to my mind merely to say that I am
compelled to _believe_ that A is C. If to conceive be taken in its proper
meaning, viz., to form a mental representation, I _may_ be able to
conceive A as not being C. After assenting, with full understanding, to
the Copernican proof that it is the earth and not the sun that moves, I
not only can conceive, or represent to myself, sunset as a motion of the
sun, but almost every one finds this conception of sunset easier to form,
than that which they nevertheless know to be the true one.

§ 5. Sir William Hamilton holds as I do, that inconceivability is no
criterion of impossibility. “There is no ground for inferring a certain
fact to be impossible, merely from our inability to conceive its
possibility.” “Things there are which _may_, nay _must_, be true, of which
the understanding is wholly unable to construe to itself the
possibility.”(98) Sir William Hamilton is, however, a firm believer in the
_a priori_ character of many axioms, and of the sciences deduced from
them; and is so far from considering those axioms to rest on the evidence
of experience, that he declares certain of them to be true even of
Noumena—of the Unconditioned—of which it is one of the principal aims of
his philosophy to prove that the nature of our faculties debars us from
having any knowledge. The axioms to which he attributes this exceptional
emancipation from the limits which confine all our other possibilities of
knowledge; the chinks through which, as he represents, one ray of light
finds its way to us from behind the curtain which veils from us the
mysterious world of Things in themselves—are the two principles, which he
terms, after the school-men, the Principle of Contradiction, and the
Principle of Excluded Middle: the first, that two contradictory
propositions can not both be true; the second, that they can not both be
false. Armed with these logical weapons, we may boldly face Things in
themselves, and tender to them the double alternative, sure that they must
absolutely elect one or the other side, though we may be forever precluded
from discovering which. To take his favorite example, we can not conceive
the infinite divisibility of matter, and we can not conceive a minimum, or
end to divisibility: yet one or the other must be true.

As I have hitherto said nothing of the two axioms in question, those of
Contradiction and of Excluded Middle, it is not unseasonable to consider
them here. The former asserts that an affirmative proposition and the
corresponding negative proposition can not both be true; which has
generally been held to be intuitively evident. Sir William Hamilton and
the Germans consider it to be the statement in words of a form or law of
our thinking faculty. Other philosophers, not less deserving of
consideration, deem it to be an identical proposition; an assertion
involved in the meaning of terms; a mode of defining Negation, and the
word Not.

I am able to go one step with these last. An affirmative assertion and its
negative are not two independent assertions, connected with each other
only as mutually incompatible. That if the negative be true, the
affirmative must be false, really is a mere identical proposition; for the
negative proposition asserts nothing but the falsity of the affirmative,
and has no other sense or meaning whatever. The Principium Contradictionis
should therefore put off the ambitious phraseology which gives it the air
of a fundamental antithesis pervading nature, and should be enunciated in
the simpler form, that the same proposition can not at the same time be
false and true. But I can go no further with the Nominalists; for I can
not look upon this last as a merely verbal proposition. I consider it to
be, like other axioms, one of our first and most familiar generalizations
from experience. The original foundation of it I take to be, that Belief
and Disbelief are two different mental states, excluding one another. This
we know by the simplest observation of our own minds. And if we carry our
observation outward, we also find that light and darkness, sound and
silence, motion and quiescence, equality and inequality, preceding and
following, succession and simultaneousness, any positive phenomenon
whatever and its negative, are distinct phenomena, pointedly contrasted,
and the one always absent where the other is present. I consider the maxim
in question to be a generalization from all these facts.

In like manner as the Principle of Contradiction (that one of two
contradictories must be false) means that an assertion can not be _both_
true and false, so the Principle of Excluded Middle, or that one of two
contradictories must be true, means that an assertion must be _either_
true or false: either the affirmative is true, or otherwise the negative
is true, which means that the affirmative is false. I can not help
thinking this principle a surprising specimen of a so-called necessity of
Thought, since it is not even true, unless with a large qualification. A
proposition must be either true or false, _provided_ that the predicate be
one which can in any intelligible sense be attributed to the subject; (and
as this is always assumed to be the case in treatises on logic, the axiom
is always laid down there as of absolute truth). “Abracadabra is a second
intention” is neither true nor false. Between the true and the false there
is a third possibility, the Unmeaning: and this alternative is fatal to
Sir William Hamilton’s extension of the maxim to Noumena. That Matter must
either have a minimum of divisibility or be infinitely divisible, is more
than we can ever know. For in the first place, Matter, in any other than
the phenomenal sense of the term, may not exist: and it will scarcely be
said that a nonentity must be either infinitely or finitely divisible. In
the second place, though matter, considered as the occult cause of our
sensations, do really exist, yet what we call divisibility may be an
attribute only of our sensations of sight and touch, and not of their
uncognizable cause. Divisibility may not be predicable at all, in any
intelligible sense, of Things in themselves, nor therefore of Matter in
itself; and the assumed necessity of being either infinitely or finitely
divisible, may be an inapplicable alternative.

On this question I am happy to have the full concurrence of Mr. Herbert
Spencer, from whose paper in the _Fortnightly Review_ I extract the
following passage. The germ of an idea identical with that of Mr. Spencer
may be found in the present chapter, on a preceding page; but in Mr.
Spencer it is not an undeveloped thought, but a philosophical theory.

“When remembering a certain thing as in a certain place, the place and the
thing are mentally represented together; while to think of the
non-existence of the thing in that place implies a consciousness in which
the place is represented, but not the thing. Similarly, if instead of
thinking of an object as colorless, we think of its having color, the
change consists in the addition to the concept of an element that was
before absent from it—the object can not be thought of first as red and
then as not red, without one component of the thought being totally
expelled from the mind by another. The law of the Excluded Middle, then,
is simply a generalization of the universal experience that some mental
states are directly destructive of other states. It formulates a certain
absolutely constant law, that the appearance of any positive mode of
consciousness can not occur without excluding a correlative negative mode;
and that the negative mode can not occur without excluding the correlative
positive mode: the antithesis of positive and negative being, indeed,
merely an expression of this experience. Hence it follows that if
consciousness is not in one of the two modes it must be in the other.”(99)

I must here close this supplementary chapter, and with it the Second Book.
The theory of Induction, in the most comprehensive sense of the term, will
form the subject of the Third.





                                Book III.


OF INDUCTION.


    “According to the doctrine now stated, the highest, or rather the
    only proper object of physics, is to ascertain those established
    conjunctions of successive events, which constitute the order of
    the universe; to record the phenomena which it exhibits to our
    observations, or which it discloses to our experiments; and to
    refer these phenomena to their general laws.”—D. STEWART,
    _Elements of the Philosophy of the Human Mind_, vol. ii., chap.
    iv., sect. 1.

    “In such cases the inductive and deductive methods of inquiry may
    be said to go hand in hand, the one verifying the conclusions
    deduced by the other; and the combination of experiment and
    theory, which may thus be brought to bear in such cases, forms an
    engine of discovery infinitely more powerful than either taken
    separately. This state of any department of science is perhaps of
    all others the most interesting, and that which promises the most
    to research.”—SIR J. HERSCHEL, _Discourse on the Study of Natural
    Philosophy_.




                                Chapter I.


Preliminary Observations On Induction In General.


§ 1. The portion of the present inquiry upon which we are now about to
enter, may be considered as the principal, both from its surpassing in
intricacy all the other branches, and because it relates to a process
which has been shown in the preceding Book to be that in which the
investigation of nature essentially consists. We have found that all
Inference, consequently all Proof, and all discovery of truths not
self-evident, consists of inductions, and the interpretation of
inductions: that all our knowledge, not intuitive, comes to us exclusively
from that source. What Induction is, therefore, and what conditions render
it legitimate, can not but be deemed the main question of the science of
logic—the question which includes all others. It is, however, one which
professed writers on logic have almost entirely passed over. The
generalities of the subject have not been altogether neglected by
metaphysicians; but, for want of sufficient acquaintance with the
processes by which science has actually succeeded in establishing general
truths, their analysis of the inductive operation, even when
unexceptionable as to correctness, has not been specific enough to be made
the foundation of practical rules, which might be for induction itself
what the rules of the syllogism are for the interpretation of induction:
while those by whom physical science has been carried to its present state
of improvement—and who, to arrive at a complete theory of the process,
needed only to generalize, and adapt to all varieties of problems, the
methods which they themselves employed in their habitual pursuits—never
until very lately made any serious attempt to philosophize on the subject,
nor regarded the mode in which they arrived at their conclusions as
deserving of study, independently of the conclusions themselves.

§ 2. For the purposes of the present inquiry, Induction may be defined,
the operation of discovering and proving general propositions. It is true
that (as already shown) the process of indirectly ascertaining individual
facts, is as truly inductive as that by which we establish general truths.
But it is not a different kind of induction; it is a form of the very same
process: since, on the one hand, generals are but collections of
particulars, definite in kind but indefinite in number; and on the other
hand, whenever the evidence which we derive from observation of known
cases justifies us in drawing an inference respecting even one unknown
case, we should on the same evidence be justified in drawing a similar
inference with respect to a whole class of cases. The inference either
does not hold at all, or it holds in all cases of a certain description;
in all cases which, in certain definable respects, resemble those we have
observed.

If these remarks are just; if the principles and rules of inference are
the same whether we infer general propositions or individual facts; it
follows that a complete logic of the sciences would be also a complete
logic of practical business and common life. Since there is no case of
legitimate inference from experience, in which the conclusion may not
legitimately be a general proposition; an analysis of the process by which
general truths are arrived at, is virtually an analysis of all induction
whatever. Whether we are inquiring into a scientific principle or into an
individual fact, and whether we proceed by experiment or by ratiocination,
every step in the train of inferences is essentially inductive, and the
legitimacy of the induction depends in both cases on the same conditions.

True it is that in the case of the practical inquirer, who is endeavoring
to ascertain facts not for the purposes of science but for those of
business, such, for instance, as the advocate or the judge, the chief
difficulty is one in which the principles of induction will afford him no
assistance. It lies not in making his inductions, but in the selection of
them; in choosing from among all general propositions ascertained to be
true, those which furnish marks by which he may trace whether the given
subject possesses or not the predicate in question. In arguing a doubtful
question of fact before a jury, the general propositions or principles to
which the advocate appeals are mostly, in themselves, sufficiently trite,
and assented to as soon as stated: his skill lies in bringing his case
under those propositions or principles; in calling to mind such of the
known or received maxims of probability as admit of application to the
case in hand, and selecting from among them those best adapted to his
object. Success is here dependent on natural or acquired sagacity, aided
by knowledge of the particular subject, and of subjects allied with it.
Invention, though it can be cultivated, can not be reduced to rule; there
is no science which will enable a man to bethink himself of that which
will suit his purpose.

But when he _has_ thought of something, science can tell him whether that
which he has thought of will suit his purpose or not. The inquirer or
arguer must be guided by his own knowledge and sagacity in the choice of
the inductions out of which he will construct his argument. But the
validity of the argument when constructed, depends on principles, and must
be tried by tests which are the same for all descriptions of inquiries,
whether the result be to give A an estate, or to enrich science with a new
general truth. In the one case and in the other, the senses, or testimony,
must decide on the individual facts; the rules of the syllogism will
determine whether, those facts being supposed correct, the case really
falls within the formulæ of the different inductions under which it has
been successively brought; and finally, the legitimacy of the inductions
themselves must be decided by other rules, and these it is now our purpose
to investigate. If this third part of the operation be, in many of the
questions of practical life, not the most, but the least arduous portion
of it, we have seen that this is also the case in some great departments
of the field of science; in all those which are principally deductive, and
most of all in mathematics; where the inductions themselves are few in
number, and so obvious and elementary that they seem to stand in no need
of the evidence of experience, while to combine them so as to prove a
given theorem or solve a problem, may call for the utmost powers of
invention and contrivance with which our species is gifted.

If the identity of the logical processes which prove particular facts and
those which establish general scientific truths, required any additional
confirmation, it would be sufficient to consider that in many branches of
science, single facts have to be proved, as well as principles; facts as
completely individual as any that are debated in a court of justice; but
which are proved in the same manner as the other truths of the science,
and without disturbing in any degree the homogeneity of its method. A
remarkable example of this is afforded by astronomy. The individual facts
on which that science grounds its most important deductions, such facts as
the magnitudes of the bodies of the solar system, their distances from one
another, the figure of the earth, and its rotation, are scarcely any of
them accessible to our means of direct observation: they are proved
indirectly, by the aid of inductions founded on other facts which we can
more easily reach. For example, the distance of the moon from the earth
was determined by a very circuitous process. The share which direct
observation had in the work consisted in ascertaining, at one and the same
instant, the zenith distances of the moon, as seen from two points very
remote from one another on the earth’s surface. The ascertainment of these
angular distances ascertained their supplements; and since the angle at
the earth’s centre subtended by the distance between the two places of
observation was deducible by spherical trigonometry from the latitude and
longitude of those places, the angle at the moon subtended by the same
line became the fourth angle of a quadrilateral of which the other three
angles were known. The four angles being thus ascertained, and two sides
of the quadrilateral being radii of the earth; the two remaining sides and
the diagonal, or, in other words, the moon’s distance from the two places
of observation and from the centre of the earth, could be ascertained, at
least in terms of the earth’s radius, from elementary theorems of
geometry. At each step in this demonstration a new induction is taken in,
represented in the aggregate of its results by a general proposition.

Not only is the process by which an individual astronomical fact was thus
ascertained, exactly similar to those by which the same science
establishes its general truths, but also (as we have shown to be the case
in all legitimate reasoning) a general proposition might have been
concluded instead of a single fact. In strictness, indeed, the result of
the reasoning _is_ a general proposition; a theorem respecting the
distance, not of the moon in particular, but of any inaccessible object;
showing in what relation that distance stands to certain other quantities.
And although the moon is almost the only heavenly body the distance of
which from the earth can really be thus ascertained, this is merely owing
to the accidental circumstances of the other heavenly bodies, which render
them incapable of affording such data as the application of the theorem
requires; for the theorem itself is as true of them as it is of the
moon.(100)

We shall fall into no error, then, if in treating of Induction, we limit
our attention to the establishment of general propositions. The principles
and rules of Induction as directed to this end, are the principles and
rules of all Induction; and the logic of Science is the universal Logic,
applicable to all inquiries in which man can engage.




                               Chapter II.


Of Inductions Improperly So Called.


§ 1. Induction, then, is that operation of the mind, by which we infer
that what we know to be true in a particular case or cases, will be true
in all cases which resemble the former in certain assignable respects. In
other words, Induction is the process by which we conclude that what is
true of certain individuals of a class is true of the whole class, or that
what is true at certain times will be true in similar circumstances at all
times.

This definition excludes from the meaning of the term Induction, various
logical operations, to which it is not unusual to apply that name.

Induction, as above defined, is a process of inference; it proceeds from
the known to the unknown; and any operation involving no inference, any
process in which what seems the conclusion is no wider than the premises
from which it is drawn, does not fall within the meaning of the term. Yet
in the common books of Logic we find this laid down as the most perfect,
indeed the only quite perfect, form of induction. In those books, every
process which sets out from a less general and terminates in a more
general expression—which admits of being stated in the form, “This and
that A are B, therefore every A is B”—is called an induction, whether any
thing be really concluded or not: and the induction is asserted not to be
perfect, unless every single individual of the class A is included in the
antecedent, or premise: that is, unless what we affirm of the class has
already been ascertained to be true of every individual in it, so that the
nominal conclusion is not really a conclusion, but a mere re-assertion of
the premises. If we were to say, All the planets shine by the sun’s light,
from observation of each separate planet, or All the Apostles were Jews,
because this is true of Peter, Paul, John, and every other apostle—these,
and such as these, would, in the phraseology in question, be called
perfect, and the only perfect, Inductions. This, however, is a totally
different kind of induction from ours; it is not an inference from facts
known to facts unknown, but a mere short-hand registration of facts known.
The two simulated arguments which we have quoted, are not generalizations;
the propositions purporting to be conclusions from them, are not really
general propositions. A general proposition is one in which the predicate
is affirmed or denied of an unlimited number of individuals; namely, all,
whether few or many, existing or capable of existing, which possess the
properties connoted by the subject of the proposition. “All men are
mortal” does not mean all now living, but all men past, present, and to
come. When the signification of the term is limited so as to render it a
name not for any and every individual falling under a certain general
description, but only for each of a number of individuals, designated as
such, and as it were counted off individually, the proposition, though it
may be general in its language, is no general proposition, but merely that
number of singular propositions, written in an abridged character. The
operation may be very useful, as most forms of abridged notation are; but
it is no part of the investigation of truth, though often bearing an
important part in the preparation of the materials for that investigation.

As we may sum up a definite number of singular propositions in one
proposition, which will be apparently, but not really, general, so we may
sum up a definite number of general propositions in one proposition, which
will be apparently, but not really, more general. If by a separate
induction applied to every distinct species of animals, it has been
established that each possesses a nervous system, and we affirm thereupon
that all animals have a nervous system; this looks like a generalization,
though as the conclusion merely affirms of all what has already been
affirmed of each, it seems to tell us nothing but what we knew before. A
distinction, however, must be made. If in concluding that all animals have
a nervous system, we mean the same thing and no more as if we had said
“all known animals,” the proposition is not general, and the process by
which it is arrived at is not induction. But if our meaning is that the
observations made of the various species of animals have discovered to us
a law of animal nature, and that we are in a condition to say that a
nervous system will be found even in animals yet undiscovered, this indeed
is an induction; but in this case the general proposition contains more
than the sum of the special propositions from which it is inferred. The
distinction is still more forcibly brought out when we consider, that if
this real generalization be legitimate at all, its legitimacy probably
does not require that we should have examined without exception every
known species. It is the number and nature of the instances, and not their
being the whole of those which happen to be known, that makes them
sufficient evidence to prove a general law: while the more limited
assertion, which stops at all known animals, can not be made unless we
have rigorously verified it in every species. In like manner (to return to
a former example) we might have inferred, not that all _the_ planets, but
that all _planets_, shine by reflected light: the former is no induction;
the latter is an induction, and a bad one, being disproved by the case of
double stars—self-luminous bodies which are properly planets, since they
revolve round a centre.

§ 2. There are several processes used in mathematics which require to be
distinguished from Induction, being not unfrequently called by that name,
and being so far similar to Induction properly so called, that the
propositions they lead to are really general propositions. For example,
when we have proved with respect to the circle, that a straight line can
not meet it in more than two points, and when the same thing has been
successively proved of the ellipse, the parabola, and the hyperbola, it
may be laid down as a universal property of the sections of the cone. The
distinction drawn in the two previous examples can have no place here,
there being no difference between all _known_ sections of the cone and
_all_ sections, since a cone demonstrably can not be intersected by a
plane except in one of these four lines. It would be difficult, therefore,
to refuse to the proposition arrived at, the name of a generalization,
since there is no room for any generalization beyond it. But there is no
induction, because there is no inference: the conclusion is a mere summing
up of what was asserted in the various propositions from which it is
drawn. A case somewhat, though not altogether, similar, is the proof of a
geometrical theorem by means of a diagram. Whether the diagram be on paper
or only in the imagination, the demonstration (as formerly observed(101))
does not prove directly the general theorem; it proves only that the
conclusion, which the theorem asserts generally, is true of the particular
triangle or circle exhibited in the diagram; but since we perceive that in
the same way in which we have proved it of that circle, it might also be
proved of any other circle, we gather up into one general expression all
the singular propositions susceptible of being thus proved, and embody
them in a universal proposition. Having shown that the three angles of the
triangle ABC are together equal to two right angles, we conclude that this
is true of every other triangle, not because it is true of ABC, but for
the same reason which proved it to be true of ABC. If this were to be
called Induction, an appropriate name for it would be, induction by parity
of reasoning. But the term can not properly belong to it; the
characteristic quality of Induction is wanting, since the truth obtained,
though really general, is not believed on the evidence of particular
instances. We do not conclude that all triangles have the property because
some triangles have, but from the ulterior demonstrative evidence which
was the ground of our conviction in the particular instances.

There are nevertheless, in mathematics, some examples of so-called
Induction, in which the conclusion does bear the appearance of a
generalization grounded on some of the particular cases included in it. A
mathematician, when he has calculated a sufficient number of the terms of
an algebraical or arithmetical series to have ascertained what is called
the _law_ of the series, does not hesitate to fill up any number of the
succeeding terms without repeating the calculations. But I apprehend he
only does so when it is apparent from _a priori_ considerations (which
might be exhibited in the form of demonstration) that the mode of
formation of the subsequent terms, each from that which preceded it, must
be similar to the formation of the terms which have been already
calculated. And when the attempt has been hazarded without the sanction of
such general considerations, there are instances on record in which it has
led to false results.

It is said that Newton discovered the binomial theorem by induction; by
raising a binomial successively to a certain number of powers, and
comparing those powers with one another until he detected the relation in
which the algebraic formula of each power stands to the exponent of that
power, and to the two terms of the binomial. The fact is not improbable:
but a mathematician like Newton, who seemed to arrive _per saltum_ at
principles and conclusions that ordinary mathematicians only reached by a
succession of steps, certainly could not have performed the comparison in
question without being led by it to the _a priori_ ground of the law;
since any one who understands sufficiently the nature of multiplication to
venture upon multiplying several lines of symbols at one operation, can
not but perceive that in raising a binomial to a power, the co-efficients
must depend on the laws of permutation and combination: and as soon as
this is recognized, the theorem is demonstrated. Indeed, when once it was
seen that the law prevailed in a few of the lower powers, its identity
with the law of permutation would at once suggest the considerations which
prove it to obtain universally. Even, therefore, such cases as these, are
but examples of what I have called Induction by parity of reasoning, that
is, not really Induction, because not involving inference of a general
proposition from particular instances.

§ 3. There remains a third improper use of the term Induction, which it is
of real importance to clear up, because the theory of Induction has been,
in no ordinary degree, confused by it, and because the confusion is
exemplified in the most recent and elaborate treatise on the inductive
philosophy which exists in our language. The error in question is that of
confounding a mere description, by general terms, of a set of observed
phenomena, with an induction from them.

Suppose that a phenomenon consists of parts, and that these parts are only
capable of being observed separately, and as it were piecemeal. When the
observations have been made, there is a convenience (amounting for many
purposes to a necessity) in obtaining a representation of the phenomenon
as a whole, by combining, or as we may say, piecing these detached
fragments together. A navigator sailing in the midst of the ocean
discovers land: he can not at first, or by any one observation, determine
whether it is a continent or an island; but he coasts along it, and after
a few days finds himself to have sailed completely round it: he then
pronounces it an island. Now there was no particular time or place of
observation at which he could perceive that this land was entirely
surrounded by water: he ascertained the fact by a succession of partial
observations, and then selected a general expression which summed up in
two or three words the whole of what he so observed. But is there any
thing of the nature of an induction in this process? Did he infer any
thing that had not been observed, from something else which had? Certainly
not. He had observed the whole of what the proposition asserts. That the
land in question is an island, is not an inference from the partial facts
which the navigator saw in the course of his circumnavigation; it is the
facts themselves; it is a summary of those facts; the description of a
complex fact, to which those simpler ones are as the parts of a whole.

Now there is, I conceive, no difference in kind between this simple
operation, and that by which Kepler ascertained the nature of the
planetary orbits: and Kepler’s operation, all at least that was
characteristic in it, was not more an inductive act than that of our
supposed navigator.

The object of Kepler was to determine the real path described by each of
the planets, or let us say by the planet Mars (since it was of that body
that he first established the two of his three laws which did not require
a comparison of planets). To do this there was no other mode than that of
direct observation: and all which observation could do was to ascertain a
great number of the successive places of the planet; or rather, of its
apparent places. That the planet occupied successively all these
positions, or at all events, positions which produced the same impressions
on the eye, and that it passed from one of these to another insensibly,
and without any apparent breach of continuity; thus much the senses, with
the aid of the proper instruments, could ascertain. What Kepler did more
than this, was to find what sort of a curve these different points would
make, supposing them to be all joined together. He expressed the whole
series of the observed places of Mars by what Dr. Whewell calls the
general conception of an ellipse. This operation was far from being as
easy as that of the navigator who expressed the series of his observations
on successive points of the coast by the general conception of an island.
But it is the very same sort of operation; and if the one is not an
induction but a description, this must also be true of the other.

The only real induction concerned in the case, consisted in inferring that
because the observed places of Mars were correctly represented by points
in an imaginary ellipse, therefore Mars would continue to revolve in that
same ellipse; and in concluding (before the gap had been filled up by
further observations) that the positions of the planet during the time
which intervened between two observations, must have coincided with the
intermediate points of the curve. For these were facts which had not been
directly observed. They were inferences from the observations; facts
inferred, as distinguished from facts seen. But these inferences were so
far from being a part of Kepler’s philosophical operation, that they had
been drawn long before he was born. Astronomers had long known that the
planets periodically returned to the same places. When this had been
ascertained, there was no induction left for Kepler to make, nor did he
make any further induction. He merely applied his new conception to the
facts inferred, as he did to the facts observed. Knowing already that the
planets continued to move in the same paths; when he found that an ellipse
correctly represented the past path, he knew that it would represent the
future path. In finding a compendious expression for the one set of facts,
he found one for the other: but he found the expression only, not the
inference; nor did he (which is the true test of a general truth) add any
thing to the power of prediction already possessed.

§ 4. The descriptive operation which enables a number of details to be
summed up in a single proposition, Dr. Whewell, by an aptly chosen
expression, has termed the Colligation of Facts. In most of his
observations concerning that mental process I fully agree, and would
gladly transfer all that portion of his book into my own pages. I only
think him mistaken in setting up this kind of operation, which according
to the old and received meaning of the term, is not induction at all, as
the type of induction generally; and laying down, throughout his work, as
principles of induction, the principles of mere colligation.

Dr. Whewell maintains that the general proposition which binds together
the particular facts, and makes them, as it were, one fact, is not the
mere sum of those facts, but something more, since there is introduced a
conception of the mind, which did not exist in the facts themselves. “The
particular facts,” says he,(102) “are not merely brought together, but
there is a new element added to the combination by the very act of thought
by which they are combined.... When the Greeks, after long observing the
motions of the planets, saw that these motions might be rightly considered
as produced by the motion of one wheel revolving in the inside of another
wheel, these wheels were creations of their minds, added to the facts
which they perceived by sense. And even if the wheels were no longer
supposed to be material, but were reduced to mere geometrical spheres or
circles, they were not the less products of the mind alone—something
additional to the facts observed. The same is the case in all other
discoveries. The facts are known, but they are insulated and unconnected,
till the discoverer supplies from his own store a principle of connection.
The pearls are there, but they will not hang together till some one
provides the string.”

Let me first remark that Dr. Whewell, in this passage, blends together,
indiscriminately, examples of both the processes which I am endeavoring to
distinguish from one another. When the Greeks abandoned the supposition
that the planetary motions were produced by the revolution of material
wheels, and fell back upon the idea of “mere geometrical spheres or
circles,” there was more in this change of opinion than the mere
substitution of an ideal curve for a physical one. There was the
abandonment of a theory, and the replacement of it by a mere description.
No one would think of calling the doctrine of material wheels a mere
description. That doctrine was an attempt to point out the force by which
the planets were acted upon, and compelled to move in their orbits. But
when, by a great step in philosophy, the materiality of the wheels was
discarded, and the geometrical forms alone retained, the attempt to
account for the motions was given up, and what was left of the theory was
a mere description of the orbits. The assertion that the planets were
carried round by wheels revolving in the inside of other wheels, gave
place to the proposition, that they moved in the same lines which would be
traced by bodies so carried: which was a mere mode of representing the sum
of the observed facts; as Kepler’s was another and a better mode of
representing the same observations.

It is true that for these simply descriptive operations, as well as for
the erroneous inductive one, a conception of the mind was required. The
conception of an ellipse must have presented itself to Kepler’s mind,
before he could identify the planetary orbits with it. According to Dr.
Whewell, the conception was something added to the facts. He expresses
himself as if Kepler had put something into the facts by his mode of
conceiving them. But Kepler did no such thing. The ellipse was in the
facts before Kepler recognized it; just as the island was an island before
it had been sailed round. Kepler did not _put_ what he had conceived into
the facts, but _saw_ it in them. A conception implies, and corresponds to,
something conceived: and though the conception itself is not in the facts,
but in our mind, yet if it is to convey any knowledge relating to them, it
must be a conception _of_ something which really is in the facts, some
property which they actually possess, and which they would manifest to our
senses, if our senses were able to take cognizance of it. If, for
instance, the planet left behind it in space a visible track, and if the
observer were in a fixed position at such a distance from the plane of the
orbit as would enable him to see the whole of it at once, he would see it
to be an ellipse; and if gifted with appropriate instruments and powers of
locomotion, he could prove it to be such by measuring its different
dimensions. Nay, further: if the track were visible, and he were so placed
that he could see all parts of it in succession, but not all of them at
once, he might be able, by piecing together his successive observations,
to discover both that it was an ellipse and that the planet moved in it.
The case would then exactly resemble that of the navigator who discovers
the land to be an island by sailing round it. If the path was visible, no
one I think would dispute that to identify it with an ellipse is to
describe it: and I can not see why any difference should be made by its
not being directly an object of sense, when every point in it is as
exactly ascertained as if it were so.

Subject to the indispensable condition which has just been stated, I do
not conceive that the part which conceptions have in the operation of
studying facts, has ever been overlooked or undervalued. No one ever
disputed that in order to reason about any thing we must have a conception
of it; or that when we include a multitude of things under a general
expression, there is implied in the expression a conception of something
common to those things. But it by no means follows that the conception is
necessarily pre-existent, or constructed by the mind out of its own
materials. If the facts are rightly classed under the conception, it is
because there is in the facts themselves something of which the conception
is itself a copy; and which if we can not directly perceive, it is because
of the limited power of our organs, and not because the thing itself is
not there. The conception itself is often obtained by abstraction from the
very facts which, in Dr. Whewell’s language, it is afterward called in to
connect. This he himself admits, when he observes (which he does on
several occasions), how great a service would be rendered to the science
of physiology by the philosopher “who should establish a precise, tenable,
and consistent conception of life.”(103) Such a conception can only be
abstracted from the phenomena of life itself; from the very facts which it
is put in requisition to connect. In other cases, no doubt, instead of
collecting the conception from the very phenomena which we are attempting
to colligate, we select it from among those which have been previously
collected by abstraction from other facts. In the instance of Kepler’s
laws, the latter was the case. The facts being out of the reach of being
observed, in any such manner as would have enabled the senses to identify
directly the path of the planet, the conception requisite for framing a
general description of that path could not be collected by abstraction
from the observations themselves; the mind had to supply hypothetically,
from among the conceptions it had obtained from other portions of its
experience, some one which would correctly represent the series of the
observed facts. It had to frame a supposition respecting the general
course of the phenomenon, and ask itself, If this be the general
description, what will the details be? and then compare these with the
details actually observed. If they agreed, the hypothesis would serve for
a description of the phenomenon: if not, it was necessarily abandoned, and
another tried. It is such a case as this which gives rise to the doctrine
that the mind, in framing the descriptions, adds something of its own
which it does not find in the facts.

Yet it is a fact surely, that the planet does describe an ellipse; and a
fact which we could see, if we had adequate visual organs and a suitable
position. Not having these advantages, but possessing the conception of an
ellipse, or (to express the meaning in less technical language) knowing
what an ellipse was, Kepler tried whether the observed places of the
planet were consistent with such a path. He found they were so; and he,
consequently, asserted as a fact that the planet moved in an ellipse. But
this fact, which Kepler did not add to, but found in, the motions of the
planet, namely, that it occupied in succession the various points in the
circumference of a given ellipse, was the very fact, the separate parts of
which had been separately observed; it was the sum of the different
observations.

Having stated this fundamental difference between my opinion and that of
Dr. Whewell, I must add, that his account of the manner in which a
conception is selected, suitable to express the facts, appears to me
perfectly just. The experience of all thinkers will, I believe, testify
that the process is tentative; that it consists of a succession of
guesses; many being rejected, until one at last occurs fit to be chosen.
We know from Kepler himself that before hitting upon the “conception” of
an ellipse, he tried nineteen other imaginary paths, which, finding them
inconsistent with the observations, he was obliged to reject. But as Dr.
Whewell truly says, the successful hypothesis, though a guess, ought
generally to be called, not a lucky, but a skillful guess. The guesses
which serve to give mental unity and wholeness to a chaos of scattered
particulars, are accidents which rarely occur to any minds but those
abounding in knowledge and disciplined in intellectual combinations.

How far this tentative method, so indispensable as a means to the
colligation of facts for purposes of description, admits of application to
Induction itself, and what functions belong to it in that department, will
be considered in the chapter of the present Book which relates to
Hypotheses. On the present occasion we have chiefly to distinguish this
process of Colligation from Induction properly so called; and that the
distinction may be made clearer, it is well to advert to a curious and
interesting remark, which is as strikingly true of the former operation,
as it appears to me unequivocally false of the latter.

In different stages of the progress of knowledge, philosophers have
employed, for the colligation of the same order of facts, different
conceptions. The early rude observations of the heavenly bodies, in which
minute precision was neither attained nor sought, presented nothing
inconsistent with the representation of the path of a planet as an exact
circle, having the earth for its centre. As observations increased in
accuracy, facts were disclosed which were not reconcilable with this
simple supposition: for the colligation of those additional facts, the
supposition was varied; and varied again and again as facts became more
numerous and precise. The earth was removed from the centre to some other
point within the circle; the planet was supposed to revolve in a smaller
circle called an epicycle, round an imaginary point which revolved in a
circle round the earth: in proportion as observation elicited fresh facts
contradictory to these representations, other epicycles and other
eccentrics were added, producing additional complication; until at last
Kepler swept all these circles away, and substituted the conception of an
exact ellipse. Even this is found not to represent with complete
correctness the accurate observations of the present day, which disclose
many slight deviations from an orbit exactly elliptical. Now Dr. Whewell
has remarked that these successive general expressions, though apparently
so conflicting, were all correct: they all answered the purpose of
colligation; they all enabled the mind to represent to itself with
facility, and by a simultaneous glance, the whole body of facts at the
time ascertained: each in its turn served as a correct description of the
phenomena, so far as the senses had up to that time taken cognizance of
them. If a necessity afterward arose for discarding one of these general
descriptions of the planet’s orbit, and framing a different imaginary
line, by which to express the series of observed positions, it was because
a number of new facts had now been added, which it was necessary to
combine with the old facts into one general description. But this did not
affect the correctness of the former expression, considered as a general
statement of the only facts which it was intended to represent. And so
true is this, that, as is well remarked by M. Comte, these ancient
generalizations, even the rudest and most imperfect of them, that of
uniform movement in a circle, are so far from being entirely false, that
they are even now habitually employed by astronomers when only a rough
approximation to correctness is required. “L’astronomie moderne, en
détruisant sans retour les hypothèses primitives, envisagées comme lois
réelles du monde, a soigneusement maintenu leur valeur positive et
permanente, la propriété de représenter commodément les phénomènes quand
il s’agit d’une première ébauche. Nos ressources à cet égard sont même
bien plus étendues, précisément à cause que nous ne nous faisons aucune
illusion sur la réalité des hypothèses; ce qui nous permet d’employer sans
scrupule, en chaque cas, celle que nous jugeons la plus avantageuse.”(104)

Dr. Whewell’s remark, therefore, is philosophically correct. Successive
expressions for the colligation of observed facts, or, in other words,
successive descriptions of a phenomenon as a whole, which has been
observed only in parts, may, though conflicting, be all correct as far as
they go. But it would surely be absurd to assert this of conflicting
inductions.

The scientific study of facts may be undertaken for three different
purposes: the simple description of the facts; their explanation; or their
prediction: meaning by prediction, the determination of the conditions
under which similar facts may be expected again to occur. To the first of
these three operations the name of Induction does not properly belong: to
the other two it does. Now, Dr. Whewell’s observation is true of the first
alone. Considered as a mere description, the circular theory of the
heavenly motions represents perfectly well their general features: and by
adding epicycles without limit, those motions, even as now known to us,
might be expressed with any degree of accuracy that might be required. The
elliptical theory, as a mere description, would have a great advantage in
point of simplicity, and in the consequent facility of conceiving it and
reasoning about it; but it would not really be more true than the other.
Different descriptions, therefore, may be all true: but not, surely,
different explanations. The doctrine that the heavenly bodies moved by a
virtue inherent in their celestial nature; the doctrine that they were
moved by impact (which led to the hypothesis of vortices as the only
impelling force capable of whirling bodies in circles), and the Newtonian
doctrine, that they are moved by the composition of a centripetal with an
original projectile force; all these are explanations, collected by real
induction from supposed parallel cases; and they were all successively
received by philosophers, as scientific truths on the subject of the
heavenly bodies. Can it be said of these, as was said of the different
descriptions, that they are all true as far as they go? Is it not clear
that only one can be true in any degree, and the other two must be
altogether false? So much for explanations: let us now compare different
predictions: the first, that eclipses will occur when one planet or
satellite is so situated as to cast its shadow upon another; the second,
that they will occur when some great calamity is impending over mankind.
Do these two doctrines only differ in the degree of their truth, as
expressing real facts with unequal degrees of accuracy? Assuredly the one
is true, and the other absolutely false.(105)

In every way, therefore, it is evident that to explain induction as the
colligation of facts by means of appropriate conceptions, that is,
conceptions which will really express them, is to confound mere
description of the observed facts with inference from those facts, and
ascribe to the latter what is a characteristic property of the former.

There is, however, between Colligation and Induction, a real correlation,
which it is important to conceive correctly. Colligation is not always
induction; but induction is always colligation. The assertion that the
planets move in ellipses, was but a mode of representing observed facts;
it was but a colligation; while the assertion that they are drawn, or
tend, toward the sun, was the statement of a new fact, inferred by
induction. But the induction, once made, accomplishes the purposes of
colligation likewise. It brings the same facts, which Kepler had connected
by his conception of an ellipse, under the additional conception of bodies
acted upon by a central force, and serves, therefore, as a new bond of
connection for those facts; a new principle for their classification.

Further, the descriptions which are improperly confounded with induction,
are nevertheless a necessary preparation for induction; no less necessary
than correct observation of the facts themselves. Without the previous
colligation of detached observations by means of one general conception,
we could never have obtained any basis for an induction, except in the
case of phenomena of very limited compass. We should not be able to affirm
any predicates at all, of a subject incapable of being observed otherwise
than piecemeal: much less could we extend those predicates by induction to
other similar subjects. Induction, therefore, always presupposes, not only
that the necessary observations are made with the necessary accuracy, but
also that the results of these observations are, so far as practicable,
connected together by general descriptions, enabling the mind to represent
to itself as wholes whatever phenomena are capable of being so
represented.

§ 5. Dr. Whewell has replied at some length to the preceding observations,
restating his opinions, but without (as far as I can perceive) adding any
thing material to his former arguments. Since, however, mine have not had
the good fortune to make any impression upon him, I will subjoin a few
remarks, tending to show more clearly in what our difference of opinion
consists, as well as, in some measure, to account for it.

Nearly all the definitions of induction, by writers of authority, make it
consist in drawing inferences from known cases to unknown; affirming of a
class, a predicate which has been found true of some cases belonging to
the class; concluding because some things have a certain property, that
other things which resemble them have the same property—or because a thing
has manifested a property at a certain time, that it has and will have
that property at other times.

It will scarcely be contended that Kepler’s operation was an Induction in
this sense of the term. The statement, that Mars moves in an elliptical
orbit, was no generalization from individual cases to a class of cases.
Neither was it an extension to all time, of what had been found true at
some particular time. The whole amount of generalization which the case
admitted of, was already completed, or might have been so. Long before the
elliptic theory was thought of, it had been ascertained that the planets
returned periodically to the same apparent places; the series of these
places was, or might have been, completely determined, and the apparent
course of each planet marked out on the celestial globe in an
uninterrupted line. Kepler did not extend an observed truth to other cases
than those in which it had been observed: he did not widen the _subject_
of the proposition which expressed the observed facts. The alteration he
made was in the predicate. Instead of saying, the successive places of
Mars are so and so, he summed them up in the statement, that the
successive places of Mars are points in an ellipse. It is true, this
statement, as Dr. Whewell says, was not the sum of the observations
_merely_; it was the sum of the observations _seen under a new point of
view_.(106) But it was not the sum of _more_ than the observations, as a
real induction is. It took in no cases but those which had been actually
observed, or which could have been inferred from the observations before
the new point of view presented itself. There was not that transition from
known cases to unknown, which constitutes Induction in the original and
acknowledged meaning of the term.

Old definitions, it is true, can not prevail against new knowledge: and if
the Keplerian operation, as a logical process, be really identical with
what takes place in acknowledged induction, the definition of induction
ought to be so widened as to take it in; since scientific language ought
to adapt itself to the true relations which subsist between the things it
is employed to designate. Here then it is that I am at issue with Dr.
Whewell. He does think the operations identical. He allows of no logical
process in any case of induction, other than what there was in Kepler’s
case, namely, guessing until a guess is found which tallies with the
facts; and accordingly, as we shall see hereafter, he rejects all canons
of induction, because it is not by means of them that we guess. Dr.
Whewell’s theory of the logic of science would be very perfect if it did
not pass over altogether the question of Proof. But in my apprehension
there is such a thing as proof, and inductions differ altogether from
descriptions in their relation to that element. Induction is proof; it is
inferring something unobserved from something observed: it requires,
therefore, an appropriate test of proof; and to provide that test, is the
special purpose of inductive logic. When, on the contrary, we merely
collate known observations, and, in Dr. Whewell’s phraseology, connect
them by means of a new conception; if the conception does serve to connect
the observations, we have all we want. As the proposition in which it is
embodied pretends to no other truth than what it may share with many other
modes of representing the same facts, to be consistent with the facts is
all it requires: it neither needs nor admits of proof; though it may serve
to prove other things, inasmuch as, by placing the facts in mental
connection with other facts, not previously seen to resemble them, it
assimilates the case to another class of phenomena, concerning which real
Inductions have already been made. Thus Kepler’s so-called law brought the
orbit of Mars into the class ellipse, and by doing so, proved all the
properties of an ellipse to be true of the orbit: but in this proof
Kepler’s law supplied the minor premise, and not (as is the case with real
Inductions) the major.

Dr. Whewell calls nothing Induction where there is not a new mental
conception introduced, and every thing induction where there is. But this
is to confound two very different things, Invention and Proof. The
introduction of a new conception belongs to Invention: and invention may
be required in any operation, but is the essence of none. A new conception
may be introduced for descriptive purposes, and so it may for inductive
purposes. But it is so far from constituting induction, that induction
does not necessarily stand in need of it. Most inductions require no
conception but what was present in every one of the particular instances
on which the induction is grounded. That all men are mortal is surely an
inductive conclusion; yet no new conception is introduced by it. Whoever
knows that any man has died, has all the conceptions involved in the
inductive generalization. But Dr. Whewell considers the process of
invention which consists in framing a new conception consistent with the
facts, to be not merely a necessary part of all induction, but the whole
of it.

The mental operation which extracts from a number of detached observations
certain general characters in which the observed phenomena resemble one
another, or resemble other known facts, is what Bacon, Locke, and most
subsequent metaphysicians, have understood by the word Abstraction. A
general expression obtained by abstraction, connecting known facts by
means of common characters, but without concluding from them to unknown,
may, I think, with strict logical correctness, be termed a Description;
nor do I know in what other way things can ever be described. My position,
however, does not depend on the employment of that particular word; I am
quite content to use Dr. Whewell’s term Colligation, or the more general
phrases, “mode of representing, or of expressing, phenomena:” provided it
be clearly seen that the process is not Induction, but something radically
different.

What more may usefully be said on the subject of Colligation, or of the
correlative expression invented by Dr. Whewell, the Explication of
Conceptions, and generally on the subject of ideas and mental
representations as connected with the study of facts, will find a more
appropriate place in the Fourth Book, on the Operations Subsidiary to
Induction: to which I must refer the reader for the removal of any
difficulty which the present discussion may have left.




                               Chapter III.


Of The Ground Of Induction.


§ 1. Induction properly so called, as distinguished from those mental
operations, sometimes, though improperly, designated by the name, which I
have attempted in the preceding chapter to characterize, may, then, be
summarily defined as Generalization from Experience. It consists in
inferring from some individual instances in which a phenomenon is observed
to occur, that it occurs in all instances of a certain class; namely, in
all which _resemble_ the former, in what are regarded as the material
circumstances.

In what way the material circumstances are to be distinguished from those
which are immaterial, or why some of the circumstances are material and
others not so, we are not yet ready to point out. We must first observe,
that there is a principle implied in the very statement of what Induction
is; an assumption with regard to the course of nature and the order of the
universe; namely, that there are such things in nature as parallel cases;
that what happens once, will, under a sufficient degree of similarity of
circumstances, happen again, and not only again, but as often as the same
circumstances recur. This, I say, is an assumption, involved in every case
of induction. And, if we consult the actual course of nature, we find that
the assumption is warranted. The universe, so far as known to us, is so
constituted, that whatever is true in any one case, is true in all cases
of a certain description; the only difficulty is, to find what
description.

This universal fact, which is our warrant for all inferences from
experience, has been described by different philosophers in different
forms of language: that the course of nature is uniform; that the universe
is governed by general laws; and the like. One of the most usual of these
modes of expression, but also one of the most inadequate, is that which
has been brought into familiar use by the metaphysicians of the school of
Reid and Stewart. The disposition of the human mind to generalize from
experience—a propensity considered by these philosophers as an instinct of
our nature—they usually describe under some such name as “our intuitive
conviction that the future will resemble the past.” Now it has been well
pointed out by Mr. Bailey,(107) that (whether the tendency be or not an
original and ultimate element of our nature), Time, in its modifications
of past, present, and future, has no concern either with the belief
itself, or with the grounds of it. We believe that fire will burn
to-morrow, because it burned to-day and yesterday; but we believe, on
precisely the same grounds, that it burned before we were born, and that
it burns this very day in Cochin-China. It is not from the past to the
future, as past and future, that we infer, but from the known to the
unknown; from facts observed to facts unobserved; from what we have
perceived, or been directly conscious of, to what has not come within our
experience. In this last predicament is the whole region of the future;
but also the vastly greater portion of the present and of the past.

Whatever be the most proper mode of expressing it, the proposition that
the course of nature is uniform, is the fundamental principle, or general
axiom of Induction. It would yet be a great error to offer this large
generalization as any explanation of the inductive process. On the
contrary, I hold it to be itself an instance of induction, and induction
by no means of the most obvious kind. Far from being the first induction
we make, it is one of the last, or at all events one of those which are
latest in attaining strict philosophical accuracy. As a general maxim,
indeed, it has scarcely entered into the minds of any but philosophers;
nor even by them, as we shall have many opportunities of remarking, have
its extent and limits been always very justly conceived. The truth is,
that this great generalization is itself founded on prior generalizations.
The obscurer laws of nature were discovered by means of it, but the more
obvious ones must have been understood and assented to as general truths
before it was ever heard of. We should never have thought of affirming
that all phenomena take place according to general laws, if we had not
first arrived, in the case of a great multitude of phenomena, at some
knowledge of the laws themselves; which could be done no otherwise than by
induction. In what sense, then, can a principle, which is so far from
being our earliest induction, be regarded as our warrant for all the
others? In the only sense, in which (as we have already seen) the general
propositions which we place at the head of our reasonings when we throw
them into syllogisms, ever really contribute to their validity. As
Archbishop Whately remarks, every induction is a syllogism with the major
premise suppressed; or (as I prefer expressing it) every induction may be
thrown into the form of a syllogism, by supplying a major premise. If this
be actually done, the principle which we are now considering, that of the
uniformity of the course of nature, will appear as the ultimate major
premise of all inductions, and will, therefore, stand to all inductions in
the relation in which, as has been shown at so much length, the major
proposition of a syllogism always stands to the conclusion; not
contributing at all to prove it, but being a necessary condition of its
being proved; since no conclusion is proved, for which there can not be
found a true major premise.(108)

The statement, that the uniformity of the course of nature is the ultimate
major premise in all cases of induction, may be thought to require some
explanation. The immediate major premise in every inductive argument, it
certainly is not. Of that, Archbishop Whately’s must be held to be the
correct account. The induction, “John, Peter, etc., are mortal, therefore
all mankind are mortal,” may, as he justly says, be thrown into a
syllogism by prefixing as a major premise (what is at any rate a necessary
condition of the validity of the argument), namely, that what is true of
John, Peter, etc., is true of all mankind. But how came we by this major
premise? It is not self-evident; nay, in all cases of unwarranted
generalization, it is not true. How, then, is it arrived at? Necessarily
either by induction or ratiocination; and if by induction, the process,
like all other inductive arguments, may be thrown into the form of a
syllogism. This previous syllogism it is, therefore, necessary to
construct. There is, in the long run, only one possible construction. The
real proof that what is true of John, Peter, etc., is true of all mankind,
can only be, that a different supposition would be inconsistent with the
uniformity which we know to exist in the course of nature. Whether there
would be this inconsistency or not, may be a matter of long and delicate
inquiry; but unless there would, we have no sufficient ground for the
major of the inductive syllogism. It hence appears, that if we throw the
whole course of any inductive argument into a series of syllogisms, we
shall arrive by more or fewer steps at an ultimate syllogism, which will
have for its major premise the principle, or axiom, of the uniformity of
the course of nature.(109)

It was not to be expected that in the case of this axiom, any more than of
other axioms, there should be unanimity among thinkers with respect to the
grounds on which it is to be received as true. I have already stated that
I regard it as itself a generalization from experience. Others hold it to
be a principle which, antecedently to any verification by experience, we
are compelled by the constitution of our thinking faculty to assume as
true. Having so recently, and at so much length, combated a similar
doctrine as applied to the axioms of mathematics, by arguments which are
in a great measure applicable to the present case, I shall defer the more
particular discussion of this controverted point in regard to the
fundamental axiom of induction, until a more advanced period of our
inquiry.(110) At present it is of more importance to understand thoroughly
the import of the axiom itself. For the proposition, that the course of
nature is uniform, possesses rather the brevity suitable to popular, than
the precision requisite in philosophical language: its terms require to be
explained, and a stricter than their ordinary signification given to them,
before the truth of the assertion can be admitted.

§ 2. Every person’s consciousness assures him that he does not always
expect uniformity in the course of events; he does not always believe that
the unknown will be similar to the known, that the future will resemble
the past. Nobody believes that the succession of rain and fine weather
will be the same in every future year as in the present. Nobody expects to
have the same dreams repeated every night. On the contrary, every body
mentions it as something extraordinary, if the course of nature is
constant, and resembles itself, in these particulars. To look for
constancy where constancy is not to be expected, as for instance that a
day which has once brought good fortune will always be a fortunate day, is
justly accounted superstition.

The course of nature, in truth, is not only uniform, it is also infinitely
various. Some phenomena are always seen to recur in the very same
combinations in which we met with them at first; others seem altogether
capricious; while some, which we had been accustomed to regard as bound
down exclusively to a particular set of combinations, we unexpectedly find
detached from some of the elements with which we had hitherto found them
conjoined, and united to others of quite a contrary description. To an
inhabitant of Central Africa, fifty years ago, no fact probably appeared
to rest on more uniform experience than this, that all human beings are
black. To Europeans, not many years ago, the proposition, All swans are
white, appeared an equally unequivocal instance of uniformity in the
course of nature. Further experience has proved to both that they were
mistaken; but they had to wait fifty centuries for this experience. During
that long time, mankind believed in a uniformity of the course of nature
where no such uniformity really existed.

According to the notion which the ancients entertained of induction, the
foregoing were cases of as legitimate inference as any inductions
whatever. In these two instances, in which, the conclusion being false,
the ground of inference must have been insufficient, there was,
nevertheless, as much ground for it as this conception of induction
admitted of. The induction of the ancients has been well described by
Bacon, under the name of “Inductio per enumerationem simplicem, ubi non
reperitur instantia contradictoria.” It consists in ascribing the
character of general truths to all propositions which are true in every
instance that we happen to know of. This is the kind of induction which is
natural to the mind when unaccustomed to scientific methods. The tendency,
which some call an instinct, and which others account for by association,
to infer the future from the past, the known from the unknown, is simply a
habit of expecting that what has been found true once or several times,
and never yet found false, will be found true again. Whether the instances
are few or many, conclusive or inconclusive, does not much affect the
matter: these are considerations which occur only on reflection; the
unprompted tendency of the mind is to generalize its experience, provided
this points all in one direction; provided no other experience of a
conflicting character comes unsought. The notion of seeking it, of
experimenting for it, of _interrogating_ nature (to use Bacon’s
expression) is of much later growth. The observation of nature, by
uncultivated intellects, is purely passive: they accept the facts which
present themselves, without taking the trouble of searching for more: it
is a superior mind only which asks itself what facts are needed to enable
it to come to a safe conclusion, and then looks out for these.

But though we have always a propensity to generalize from unvarying
experience, we are not always warranted in doing so. Before we can be at
liberty to conclude that something is universally true because we have
never known an instance to the contrary, we must have reason to believe
that if there were in nature any instances to the contrary, we should have
known of them. This assurance, in the great majority of cases, we can not
have, or can have only in a very moderate degree. The possibility of
having it, is the foundation on which we shall see hereafter that
induction by simple enumeration may in some remarkable cases amount
practically to proof.(111) No such assurance, however, can be had, on any
of the ordinary subjects of scientific inquiry. Popular notions are
usually founded on induction by simple enumeration; in science it carries
us but a little way. We are forced to begin with it; we must often rely on
it provisionally, in the absence of means of more searching investigation.
But, for the accurate study of nature, we require a surer and a more
potent instrument.

It was, above all, by pointing out the insufficiency of this rude and
loose conception of Induction, that Bacon merited the title so generally
awarded to him, of Founder of the Inductive Philosophy. The value of his
own contributions to a more philosophical theory of the subject has
certainly been exaggerated. Although (along with some fundamental errors)
his writings contain, more or less fully developed, several of the most
important principles of the Inductive Method, physical investigation has
now far outgrown the Baconian conception of Induction. Moral and political
inquiry, indeed, are as yet far behind that conception. The current and
approved modes of reasoning on these subjects are still of the same
vicious description against which Bacon protested; the method almost
exclusively employed by those professing to treat such matters
inductively, is the very _inductio per enumerationem simplicem_ which he
condemns; and the experience which we hear so confidently appealed to by
all sects, parties, and interests, is still, in his own emphatic words,
_mera palpatio_.

§ 3. In order to a better understanding of the problem which the logician
must solve if he would establish a scientific theory of Induction, let us
compare a few cases of incorrect inductions with others which are
acknowledged to be legitimate. Some, we know, which were believed for
centuries to be correct, were nevertheless incorrect. That all swans are
white, can not have been a good induction, since the conclusion has turned
out erroneous. The experience, however, on which the conclusion rested,
was genuine. From the earliest records, the testimony of the inhabitants
of the known world was unanimous on the point. The uniform experience,
therefore, of the inhabitants of the known world, agreeing in a common
result, without one known instance of deviation from that result, is not
always sufficient to establish a general conclusion.

But let us now turn to an instance apparently not very dissimilar to this.
Mankind were wrong, it seems, in concluding that all swans were white: are
we also wrong, when we conclude that all men’s heads grow above their
shoulders, and never below, in spite of the conflicting testimony of the
naturalist Pliny? As there were black swans, though civilized people had
existed for three thousand years on the earth without meeting with them,
may there not also be “men whose heads do grow beneath their shoulders,”
notwithstanding a rather less perfect unanimity of negative testimony from
observers? Most persons would answer No; it was more credible that a bird
should vary in its color, than that men should vary in the relative
position of their principal organs. And there is no doubt that in so
saying they would be right: but to say why they are right, would be
impossible, without entering more deeply than is usually done, into the
true theory of Induction.

Again, there are cases in which we reckon with the most unfailing
confidence upon uniformity, and other cases in which we do not count upon
it at all. In some we feel complete assurance that the future will
resemble the past, the unknown be precisely similar to the known. In
others, however invariable may be the result obtained from the instances
which have been observed, we draw from them no more than a very feeble
presumption that the like result will hold in all other cases. That a
straight line is the shortest distance between two points, we do not doubt
to be true even in the region of the fixed stars.(112) When a chemist
announces the existence and properties of a newly-discovered substance, if
we confide in his accuracy, we feel assured that the conclusions he has
arrived at will hold universally, though the induction be founded but on a
single instance. We do not withhold our assent, waiting for a repetition
of the experiment; or if we do, it is from a doubt whether the one
experiment was properly made, not whether if properly made it would be
conclusive. Here, then, is a general law of nature, inferred without
hesitation from a single instance; a universal proposition from a singular
one. Now mark another case, and contrast it with this. Not all the
instances which have been observed since the beginning of the world, in
support of the general proposition that all crows are black, would be
deemed a sufficient presumption of the truth of the proposition, to
outweigh the testimony of one unexceptionable witness who should affirm
that in some region of the earth not fully explored, he had caught and
examined a crow, and had found it to be gray.

Why is a single instance, in some cases, sufficient for a complete
induction, while in others, myriads of concurring instances, without a
single exception known or presumed, go such a very little way toward
establishing a universal proposition? Whoever can answer this question
knows more of the philosophy of logic than the wisest of the ancients, and
has solved the problem of induction.




                               Chapter IV.


Of Laws Of Nature.


§ 1. In the contemplation of that uniformity in the course of nature,
which is assumed in every inference from experience, one of the first
observations that present themselves is, that the uniformity in question
is not properly uniformity, but uniformities. The general regularity
results from the co-existence of partial regularities. The course of
nature in general is constant, because the course of each of the various
phenomena that compose it is so. A certain fact invariably occurs whenever
certain circumstances are present, and does not occur when they are
absent; the like is true of another fact; and so on. From these separate
threads of connection between parts of the great whole which we term
nature, a general tissue of connection unavoidably weaves itself, by which
the whole is held together. If A is always accompanied by D, B by E, and C
by F, it follows that A B is accompanied by D E, A C by D F, B C by E F,
and finally A B C by D E F; and thus the general character of regularity
is produced, which, along with and in the midst of infinite diversity,
pervades all nature.

The first point, therefore, to be noted in regard to what is called the
uniformity of the course of nature, is, that it is itself a complex fact,
compounded of all the separate uniformities which exist in respect to
single phenomena. These various uniformities, when ascertained by what is
regarded as a sufficient induction, we call, in common parlance, Laws of
Nature. Scientifically speaking, that title is employed in a more
restricted sense, to designate the uniformities when reduced to their most
simple expression. Thus in the illustration already employed, there were
seven uniformities; all of which, if considered sufficiently certain,
would, in the more lax application of the term, be called laws of nature.
But of the seven, three alone are properly distinct and independent: these
being presupposed, the others follow of course. The first three,
therefore, according to the stricter acceptation, are called laws of
nature; the remainder not; because they are in truth mere _cases_ of the
first three; virtually included in them; said, therefore, to _result_ from
them: whoever affirms those three has already affirmed all the rest.

To substitute real examples for symbolical ones, the following are three
uniformities, or call them laws of nature: the law that air has weight,
the law that pressure on a fluid is propagated equally in all directions,
and the law that pressure in one direction, not opposed by equal pressure
in the contrary direction, produces motion, which does not cease until
equilibrium is restored. From these three uniformities we should be able
to predict another uniformity, namely, the rise of the mercury in the
Torricellian tube. This, in the stricter use of the phrase, is not a law
of nature. It is the result of laws of nature. It is a _case_ of each and
every one of the three laws: and is the only occurrence by which they
could all be fulfilled. If the mercury were not sustained in the
barometer, and sustained at such a height that the column of mercury were
equal in weight to a column of the atmosphere of the same diameter; here
would be a case, either of the air not pressing upon the surface of the
mercury with the force which is called its weight, or of the downward
pressure on the mercury not being propagated equally in an upward
direction, or of a body pressed in one direction and not in the direction
opposite, either not moving in the direction in which it is pressed, or
stopping before it had attained equilibrium. If we knew, therefore, the
three simple laws, but had never tried the Torricellian experiment, we
might _deduce_ its result from those laws. The known weight of the air,
combined with the position of the apparatus, would bring the mercury
within the first of the three inductions; the first induction would bring
it within the second, and the second within the third, in the manner which
we characterized in treating of Ratiocination. We should thus come to know
the more complex uniformity, independently of specific experience, through
our knowledge of the simpler ones from which it results; though, for
reasons which will appear hereafter, _verification_ by specific experience
would still be desirable, and might possibly be indispensable.

Complex uniformities which, like this, are mere cases of simpler ones, and
have, therefore, been virtually affirmed in affirming those, may with
propriety be called _laws_, but can scarcely, in the strictness of
scientific speech, be termed Laws of Nature. It is the custom in science,
wherever regularity of any kind can be traced, to call the general
proposition which expresses the nature of that regularity, a law; as when,
in mathematics, we speak of the law of decrease of the successive terms of
a converging series. But the expression _law of nature_ has generally been
employed with a sort of tacit reference to the original sense of the word
law, namely, the expression of the will of a superior. When, therefore, it
appeared that any of the uniformities which were observed in nature, would
result spontaneously from certain other uniformities, no separate act of
creative will being supposed necessary for the production of the
derivative uniformities, these have not usually been spoken of as laws of
nature. According to one mode of expression, the question, What are the
laws of nature? may be stated thus: What are the fewest and simplest
assumptions, which being granted, the whole existing order of nature would
result? Another mode of stating it would be thus: What are the fewest
general propositions from which all the uniformities which exist in the
universe might be deductively inferred?

Every great advance which marks an epoch in the progress of science, has
consisted in a step made toward the solution of this problem. Even a
simple colligation of inductions already made, without any fresh extension
of the inductive inference, is already an advance in that direction. When
Kepler expressed the regularity which exists in the observed motions of
the heavenly bodies, by the three general propositions called his laws,
he, in so doing, pointed out three simple suppositions which, instead of a
much greater number, would suffice to construct the whole scheme of the
heavenly motions, so far as it was known up to that time. A similar and
still greater step was made when these laws, which at first did not seem
to be included in any more general truths, were discovered to be cases of
the three laws of motion, as obtaining among bodies which mutually tend
toward one another with a certain force, and have had a certain
instantaneous impulse originally impressed upon them. After this great
discovery, Kepler’s three propositions, though still called laws, would
hardly, by any person accustomed to use language with precision, be termed
laws of nature: that phrase would be reserved for the simpler and more
general laws into which Newton is said to have resolved them.

According to this language, every well-grounded inductive generalization
is either a law of nature, or a result of laws of nature, capable, if
those laws are known, of being predicted from them. And the problem of
Inductive Logic may be summed up in two questions: how to ascertain the
laws of nature; and how, after having ascertained them, to follow them
into their results. On the other hand, we must not suffer ourselves to
imagine that this mode of statement amounts to a real analysis, or to any
thing but a mere verbal transformation of the problem; for the expression,
Laws of Nature, _means_ nothing but the uniformities which exist among
natural phenomena (or, in other words, the results of induction), when
reduced to their simplest expression. It is, however, something to have
advanced so far, as to see that the study of nature is the study of laws,
not _a_ law; of uniformities, in the plural number: that the different
natural phenomena have their separate rules or modes of taking place,
which, though much intermixed and entangled with one another, may, to a
certain extent, be studied apart: that (to resume our former metaphor) the
regularity which exists in nature is a web composed of distinct threads,
and only to be understood by tracing each of the threads separately; for
which purpose it is often necessary to unravel some portion of the web,
and exhibit the fibres apart. The rules of experimental inquiry are the
contrivances for unraveling the web.

§ 2. In thus attempting to ascertain the general order of nature by
ascertaining the particular order of the occurrence of each one of the
phenomena of nature, the most scientific proceeding can be no more than an
improved form of that which was primitively pursued by the human
understanding, while undirected by science. When mankind first formed the
idea of studying phenomena according to a stricter and surer method than
that which they had in the first instance spontaneously adopted, they did
not, conformably to the well-meant but impracticable precept of Descartes,
set out from the supposition that nothing had been already ascertained.
Many of the uniformities existing among phenomena are so constant, and so
open to observation, as to force themselves upon involuntary recognition.
Some facts are so perpetually and familiarly accompanied by certain
others, that mankind learned, as children learn, to expect the one where
they found the other, long before they knew how to put their expectation
into words by asserting, in a proposition, the existence of a connection
between those phenomena. No science was needed to teach that food
nourishes, that water drowns, or quenches thirst, that the sun gives light
and heat, that bodies fall to the ground. The first scientific inquirers
assumed these and the like as known truths, and set out from them to
discover others which were unknown: nor were they wrong in so doing,
subject, however, as they afterward began to see, to an ulterior revision
of these spontaneous generalizations themselves, when the progress of
knowledge pointed out limits to them, or showed their truth to be
contingent on some circumstance not originally attended to. It will
appear, I think, from the subsequent part of our inquiry, that there is no
logical fallacy in this mode of proceeding; but we may see already that
any other mode is rigorously impracticable: since it is impossible to
frame any scientific method of induction, or test of the correctness of
inductions, unless on the hypothesis that some inductions deserving of
reliance have been already made.

Let us revert, for instance, to one of our former illustrations, and
consider why it is that, with exactly the same amount of evidence, both
negative and positive, we did not reject the assertion that there are
black swans, while we should refuse credence to any testimony which
asserted that there were men wearing their heads underneath their
shoulders. The first assertion was more credible than the latter. But why
more credible? So long as neither phenomenon had been actually witnessed,
what reason was there for finding the one harder to be believed than the
other? Apparently because there is less constancy in the colors of
animals, than in the general structure of their anatomy. But how do we
know this? Doubtless, from experience. It appears, then, that we need
experience to inform us, in what degree, and in what cases, or sorts of
cases, experience is to be relied on. Experience must be consulted in
order to learn from it under what circumstances arguments from it will be
valid. We have no ulterior test to which we subject experience in general;
but we make experience its own test. Experience testifies, that among the
uniformities which it exhibits or seems to exhibit, some are more to be
relied on than others; and uniformity, therefore, may be presumed, from
any given number of instances, with a greater degree of assurance, in
proportion as the case belongs to a class in which the uniformities have
hitherto been found more uniform.

This mode of correcting one generalization by means of another, a narrower
generalization by a wider, which common sense suggests and adopts in
practice, is the real type of scientific Induction. All that art can do is
but to give accuracy and precision to this process, and adapt it to all
varieties of cases, without any essential alteration in its principle.

There are of course no means of applying such a test as that above
described, unless we already possess a general knowledge of the prevalent
character of the uniformities existing throughout nature. The
indispensable foundation, therefore, of a scientific formula of induction,
must be a survey of the inductions to which mankind have been conducted in
unscientific practice; with the special purpose of ascertaining what kinds
of uniformities have been found perfectly invariable, pervading all
nature, and what are those which have been found to vary with difference
of time, place, or other changeable circumstances.

§ 3. The necessity of such a survey is confirmed by the consideration,
that the stronger inductions are the touch-stone to which we always
endeavor to bring the weaker. If we find any means of deducing one of the
less strong inductions from stronger ones, it acquires, at once, all the
strength of those from which it is deduced; and even adds to that
strength; since the independent experience on which the weaker induction
previously rested, becomes additional evidence of the truth of the better
established law in which it is now found to be included. We may have
inferred, from historical evidence, that the uncontrolled power of a
monarch, of an aristocracy, or of the majority, will often be abused: but
we are entitled to rely on this generalization with much greater assurance
when it is shown to be a corollary from still better established facts;
the very low degree of elevation of character ever yet attained by the
average of mankind, and the little efficacy, for the most part, of the
modes of education hitherto practiced, in maintaining the predominance of
reason and conscience over the selfish propensities. It is at the same
time obvious that even these more general facts derive an accession of
evidence from the testimony which history bears to the effects of
despotism. The strong induction becomes still stronger when a weaker one
has been bound up with it.

On the other hand, if an induction conflicts with stronger inductions, or
with conclusions capable of being correctly deduced from them, then,
unless on reconsideration it should appear that some of the stronger
inductions have been expressed with greater universality than their
evidence warrants, the weaker one must give way. The opinion so long
prevalent that a comet, or any other unusual appearance in the heavenly
regions, was the precursor of calamities to mankind, or to those at least
who witnessed it; the belief in the veracity of the oracles of Delphi or
Dodona; the reliance on astrology, or on the weather-prophecies in
almanacs, were doubtless inductions supposed to be grounded on
experience:(113) and faith in such delusions seems quite capable of
holding out against a great multitude of failures, provided it be
nourished by a reasonable number of casual coincidences between the
prediction and the event. What has really put an end to these insufficient
inductions, is their inconsistency with the stronger inductions
subsequently obtained by scientific inquiry, respecting the causes on
which terrestrial events really depend; and where those scientific truths
have not yet penetrated, the same or similar delusions still prevail.

It may be affirmed as a general principle, that all inductions, whether
strong or weak, which can be connected by ratiocination, are confirmatory
of one another; while any which lead deductively to consequences that are
incompatible, become mutually each other’s test, showing that one or other
must be given up, or at least more guardedly expressed. In the case of
inductions which confirm each other, the one which becomes a conclusion
from ratiocination rises to at least the level of certainty of the weakest
of those from which it is deduced; while in general all are more or less
increased in certainty. Thus the Torricellian experiment, though a mere
case of three more general laws, not only strengthened greatly the
evidence on which those laws rested, but converted one of them (the weight
of the atmosphere) from a still doubtful generalization into a completely
established doctrine.

If, then, a survey of the uniformities which have been ascertained to
exist in nature, should point out some which, as far as any human purpose
requires certainty, may be considered quite certain and quite universal;
then by means of these uniformities we may be able to raise multitudes of
other inductions to the same point in the scale. For if we can show, with
respect to any inductive inference, that either it must be true, or one of
these certain and universal inductions must admit of an exception; the
former generalization will attain the same certainty, and indefeasibleness
within the bounds assigned to it, which are the attributes of the latter.
It will be proved to be a law; and if not a result of other and simpler
laws, it will be a law of nature.

There are such certain and universal inductions; and it is because there
are such, that a Logic of Induction is possible.




                                Chapter V.


Of The Law Of Universal Causation.


§ 1. The phenomena of nature exist in two distinct relations to one
another; that of simultaneity, and that of succession. Every phenomenon is
related, in a uniform manner, to some phenomena that co-exist with it, and
to some that have preceded and will follow it.

Of the uniformities which exist among synchronous phenomena, the most
important, on every account, are the laws of number; and next to them
those of space, or, in other words, of extension and figure. The laws of
number are common to synchronous and successive phenomena. That two and
two make four, is equally true whether the second two follow the first two
or accompany them. It is as true of days and years as of feet and inches.
The laws of extension and figure (in other words, the theorems of
geometry, from its lowest to its highest branches) are, on the contrary,
laws of simultaneous phenomena only. The various parts of space, and of
the objects which are said to fill space, co-exist; and the unvarying laws
which are the subject of the science of geometry, are an expression of the
mode of their co-existence.

This is a class of laws, or in other words, of uniformities, for the
comprehension and proof of which it is not necessary to suppose any lapse
of time, any variety of facts or events succeeding one another. The
propositions of geometry are independent of the succession of events. All
things which possess extension, or, in other words, which fill space, are
subject to geometrical laws. Possessing extension, they possess figure;
possessing figure, they must possess some figure in particular, and have
all the properties which geometry assigns to that figure. If one body be a
sphere and another a cylinder, of equal height and diameter, the one will
be exactly two-thirds of the other, let the nature and quality of the
material be what it will. Again, each body, and each point of a body, must
occupy some place or position among other bodies; and the position of two
bodies relatively to each other, of whatever nature the bodies be, may be
unerringly inferred from the position of each of them relatively to any
third body.

In the laws of number, then, and in those of space, we recognize in the
most unqualified manner, the rigorous universality of which we are in
quest. Those laws have been in all ages the type of certainty, the
standard of comparison for all inferior degrees of evidence. Their
invariability is so perfect, that it renders us unable even to conceive
any exception to them; and philosophers have been led, though (as I have
endeavored to show) erroneously, to consider their evidence as lying not
in experience, but in the original constitution of the intellect. If,
therefore, from the laws of space and number, we were able to deduce
uniformities of any other description, this would be conclusive evidence
to us that those other uniformities possessed the same rigorous certainty.
But this we can not do. From laws of space and number alone, nothing can
be deduced but laws of space and number.

Of all truths relating to phenomena, the most valuable to us are those
which relate to the order of their succession. On a knowledge of these is
founded every reasonable anticipation of future facts, and whatever power
we possess of influencing those facts to our advantage. Even the laws of
geometry are chiefly of practical importance to us as being a portion of
the premises from which the order of the succession of phenomena may be
inferred. Inasmuch as the motion of bodies, the action of forces, and the
propagation of influences of all sorts, take place in certain lines and
over definite spaces, the properties of those lines and spaces are an
important part of the laws to which those phenomena are themselves
subject. Again, motions, forces, or other influences, and times, are
numerable quantities; and the properties of number are applicable to them
as to all other things. But though the laws of number and space are
important elements in the ascertainment of uniformities of succession,
they can do nothing toward it when taken by themselves. They can only be
made instrumental to that purpose when we combine with them additional
premises, expressive of uniformities of succession already known. By
taking, for instance, as premises these propositions, that bodies acted
upon by an instantaneous force move with uniform velocity in straight
lines; that bodies acted upon by a continuous force move with accelerated
velocity in straight lines; and that bodies acted upon by two forces in
different directions move in the diagonal of a parallelogram, whose sides
represent the direction and quantity of those forces; we may by combining
these truths with propositions relating to the properties of straight
lines and of parallelograms (as that a triangle is half a parallelogram of
the same base and altitude), deduce another important uniformity of
succession, viz., that a body moving round a centre of force describes
areas proportional to the times. But unless there had been laws of
succession in our premises, there could have been no truths of succession
in our conclusions. A similar remark might be extended to every other
class of phenomena really peculiar; and, had it been attended to, would
have prevented many chimerical attempts at demonstrations of the
indemonstrable, and explanations which do not explain.

It is not, therefore, enough for us that the laws of space, which are only
laws of simultaneous phenomenon, and the laws of number, which though true
of successive phenomena do not relate to their succession, possess the
rigorous certainty and universality of which we are in search. We must
endeavor to find some law of succession which has those same attributes,
and is therefore fit to be made the foundation of processes for
discovering, and of a test for verifying, all other uniformities of
succession. This fundamental law must resemble the truths of geometry in
their most remarkable peculiarity, that of never being, in any instance
whatever, defeated or suspended by any change of circumstances.

Now among all those uniformities in the succession of phenomena, which
common observation is sufficient to bring to light, there are very few
which have any, even apparent, pretension to this rigorous
indefeasibility: and of those few, one only has been found capable of
completely sustaining it. In that one, however, we recognize a law which
is universal also in another sense; it is co-extensive with the entire
field of successive phenomena, all instances whatever of succession being
examples of it. This law is the Law of Causation. The truth that every
fact which has a beginning has a cause, is co-extensive with human
experience.

This generalization may appear to some minds not to amount to much, since
after all it asserts only this: “it is a law, that every event depends on
some law:” “it is a law, that there is a law for every thing.” We must
not, however, conclude that the generality of the principle is merely
verbal; it will be found on inspection to be no vague or unmeaning
assertion, but a most important and really fundamental truth.

§ 2. The notion of Cause being the root of the whole theory of Induction,
it is indispensable that this idea should, at the very outset of our
inquiry, be, with the utmost practicable degree of precision, fixed and
determined. If, indeed, it were necessary for the purpose of inductive
logic that the strife should be quelled, which has so long raged among the
different schools of metaphysicians, respecting the origin and analysis of
our idea of causation; the promulgation, or at least the general
reception, of a true theory of induction, might be considered desperate
for a long time to come. But the science of the Investigation of Truth by
means of Evidence, is happily independent of many of the controversies
which perplex the science of the ultimate constitution of the human mind,
and is under no necessity of pushing the analysis of mental phenomenon to
that extreme limit which alone ought to satisfy a metaphysician.

I premise, then, that when in the course of this inquiry I speak of the
cause of any phenomenon, I do not mean a cause which is not itself a
phenomenon; I make no research into the ultimate or ontological cause of
any thing. To adopt a distinction familiar in the writings of the Scotch
metaphysicians, and especially of Reid, the causes with which I concern
myself are not _efficient_, but _physical_ causes. They are causes in that
sense alone, in which one physical fact is said to be the cause of
another. Of the efficient causes of phenomena, or whether any such causes
exist at all, I am not called upon to give an opinion. The notion of
causation is deemed, by the schools of metaphysics most in vogue at the
present moment, to imply a mysterious and most powerful tie, such as can
not, or at least does not, exist between any physical fact and that other
physical fact on which it is invariably consequent, and which is popularly
termed its cause: and thence is deduced the supposed necessity of
ascending higher, into the essences and inherent constitution of things,
to find the true cause, the cause which is not only followed by, but
actually produces, the effect. No such necessity exists for the purposes
of the present inquiry, nor will any such doctrine be found in the
following pages. The only notion of a cause, which the theory of induction
requires, is such a notion as can be gained from experience. The Law of
Causation, the recognition of which is the main pillar of inductive
science, is but the familiar truth, that invariability of succession is
found by observation to obtain between every fact in nature and some other
fact which has preceded it; independently of all considerations respecting
the ultimate mode of production of phenomena, and of every other question
regarding the nature of “Things in themselves.”

Between the phenomena, then, which exist at any instant, and the phenomena
which exist at the succeeding instant, there is an invariable order of
succession; and, as we said in speaking of the general uniformity of the
course of nature, this web is composed of separate fibres; this collective
order is made up of particular sequences, obtaining invariably among the
separate parts. To certain facts, certain facts always do, and, as we
believe, will continue to, succeed. The invariable antecedent is termed
the cause; the invariable consequent, the effect. And the universality of
the law of causation consists in this, that every consequent is connected
in this manner with some particular antecedent, or set of antecedents. Let
the fact be what it may, if it has begun to exist, it was preceded by some
fact or facts, with which it is invariably connected. For every event
there exists some combination of objects or events, some given concurrence
of circumstances, positive and negative, the occurrence of which is always
followed by that phenomenon. We may not have found out what this
concurrence of circumstances may be; but we never doubt that there is such
a one, and that it never occurs without having the phenomenon in question
as its effect or consequence. On the universality of this truth depends
the possibility of reducing the inductive process to rules. The undoubted
assurance we have that there is a law to be found if we only knew how to
find it, will be seen presently to be the source from which the canons of
the Inductive Logic derive their validity.

§ 3. It is seldom, if ever, between a consequent and a single antecedent,
that this invariable sequence subsists. It is usually between a consequent
and the sum of several antecedents; the concurrence of all of them being
requisite to produce, that is, to be certain of being followed by, the
consequent. In such cases it is very common to single out one only of the
antecedents under the denomination of Cause, calling the others merely
Conditions. Thus, if a person eats of a particular dish, and dies in
consequence, that is, would not have died if he had not eaten of it,
people would be apt to say that eating of that dish was the cause of his
death. There needs not, however, be any invariable connection between
eating of the dish and death; but there certainly is, among the
circumstances which took place, some combination or other on which death
is invariably consequent: as, for instance, the act of eating of the dish,
combined with a particular bodily constitution, a particular state of
present health, and perhaps even a certain state of the atmosphere; the
whole of which circumstances perhaps constituted in this particular case
the _conditions_ of the phenomenon, or, in other words, the set of
antecedents which determined it, and but for which it would not have
happened. The real Cause, is the whole of these antecedents; and we have,
philosophically speaking, no right to give the name of cause to one of
them, exclusively of the others. What, in the case we have supposed,
disguises the incorrectness of the expression, is this: that the various
conditions, except the single one of eating the food, were not _events_
(that is, instantaneous changes, or successions of instantaneous changes)
but _states_, possessing more or less of permanency; and might therefore
have preceded the effect by an indefinite length of duration, for want of
the event which was requisite to complete the required concurrence of
conditions: while as soon as that event, eating the food, occurs, no other
cause is waited for, but the effect begins immediately to take place: and
hence the appearance is presented of a more immediate and close connection
between the effect and that one antecedent, than between the effect and
the remaining conditions. But though we may think proper to give the name
of cause to that one condition, the fulfillment of which completes the
tale, and brings about the effect without further delay; this condition
has really no closer relation to the effect than any of the other
conditions has. All the conditions were equally indispensable to the
production of the consequent; and the statement of the cause is
incomplete, unless in some shape or other we introduce them all. A man
takes mercury, goes out-of-doors, and catches cold. We say, perhaps, that
the cause of his taking cold was exposure to the air. It is clear,
however, that his having taken mercury may have been a necessary condition
of his catching cold; and though it might consist with usage to say that
the cause of his attack was exposure to the air, to be accurate we ought
to say that the cause was exposure to the air while under the effect of
mercury.

If we do not, when aiming at accuracy, enumerate all the conditions, it is
only because some of them will in most cases be understood without being
expressed, or because for the purpose in view they may without detriment
be overlooked. For example, when we say, the cause of a man’s death was
that his foot slipped in climbing a ladder, we omit as a thing unnecessary
to be stated the circumstance of his weight, though quite as indispensable
a condition of the effect which took place. When we say that the assent of
the crown to a bill makes it law, we mean that the assent, being never
given until all the other conditions are fulfilled, makes up the sum of
the conditions, though no one now regards it as the principal one. When
the decision of a legislative assembly has been determined by the casting
vote of the chairman, we sometimes say that this one person was the cause
of all the effects which resulted from the enactment. Yet we do not really
suppose that his single vote contributed more to the result than that of
any other person who voted in the affirmative; but, for the purpose we
have in view, which is to insist on his individual responsibility, the
part which any other person had in the transaction is not material.

In all these instances the fact which was dignified with the name of
cause, was the one condition which came last into existence. But it must
not be supposed that in the employment of the term this or any other rule
is always adhered to. Nothing can better show the absence of any
scientific ground for the distinction between the cause of a phenomenon
and its conditions, than the capricious manner in which we select from
among the conditions that which we choose to denominate the cause. However
numerous the conditions may be, there is hardly any of them which may not,
according to the purpose of our immediate discourse, obtain that nominal
pre-eminence. This will be seen by analyzing the conditions of some one
familiar phenomenon. For example, a stone thrown into water falls to the
bottom. What are the conditions of this event? In the first place there
must be a stone, and water, and the stone must be thrown into the water;
but these suppositions forming part of the enunciation of the phenomenon
itself, to include them also among the conditions would be a vicious
tautology; and this class of conditions, therefore, have never received
the name of cause from any but the Aristotelians, by whom they were called
the _material_ cause, _causa materialis_. The next condition is, there
must be an earth: and accordingly it is often said, that the fall of a
stone is caused by the earth; or by a power or property of the earth, or a
force exerted by the earth, all of which are merely roundabout ways of
saying that it is caused by the earth; or, lastly, the earth’s attraction;
which also is only a technical mode of saying that the earth causes the
motion, with the additional particularity that the motion is toward the
earth, which is not a character of the cause, but of the effect. Let us
now pass to another condition. It is not enough that the earth should
exist; the body must be within that distance from it, in which the earth’s
attraction preponderates over that of any other body. Accordingly we may
say, and the expression would be confessedly correct, that the cause of
the stone’s falling is its being _within the sphere_ of the earth’s
attraction. We proceed to a further condition. The stone is immersed in
water: it is therefore a condition of its reaching the ground, that its
specific gravity exceed that of the surrounding fluid, or in other words
that it surpass in weight an equal volume of water. Accordingly any one
would be acknowledged to speak correctly who said, that the cause of the
stone’s going to the bottom is its exceeding in specific gravity the fluid
in which it is immersed.

Thus we see that each and every condition of the phenomenon may be taken
in its turn, and, with equal propriety in common parlance, but with equal
impropriety in scientific discourse, may be spoken of as if it were the
entire cause. And in practice, that particular condition is usually styled
the cause, whose share in the matter is superficially the most
conspicuous, or whose requisiteness to the production of the effect we
happen to be insisting on at the moment. So great is the force of this
last consideration, that it sometimes induces us to give the name of cause
even to one of the negative conditions. We say, for example, The army was
surprised because the sentinel was off his post. But since the sentinel’s
absence was not what created the enemy, or put the soldiers asleep, how
did it cause them to be surprised? All that is really meant is, that the
event would not have happened if he had been at his duty. His being off
his post was no producing cause, but the mere absence of a preventing
cause: it was simply equivalent to his non-existence. From nothing, from a
mere negation, no consequences can proceed. All effects are connected, by
the law of causation, with some set of _positive_ conditions; negative
ones, it is true, being almost always required in addition. In other
words, every fact or phenomenon which has a beginning, invariably arises
when some certain combination of positive facts exists, provided certain
other positive facts do not exist.

There is, no doubt, a tendency (which our first example, that of death
from taking a particular food, sufficiently illustrates) to associate the
idea of causation with the proximate antecedent _event_, rather than with
any of the antecedent _states_, or permanent facts, which may happen also
to be conditions of the phenomenon; the reason being that the event not
only exists, but begins to exist immediately previous; while the other
conditions may have pre-existed for an indefinite time. And this tendency
shows itself very visibly in the different logical fictions which are
resorted to, even by men of science, to avoid the necessity of giving the
name of cause to any thing which had existed for an indeterminate length
of time before the effect. Thus, rather than say that the earth causes the
fall of bodies, they ascribe it to a _force_ exerted by the earth, or an
_attraction_ by the earth, abstractions which they can represent to
themselves as exhausted by each effort, and therefore constituting at each
successive instant a fresh fact, simultaneous with, or only immediately
preceding, the effect. Inasmuch as the coming of the circumstance which
completes the assemblage of conditions, is a change or event, it thence
happens that an event is always the antecedent in closest apparent
proximity to the consequent: and this may account for the illusion which
disposes us to look upon the proximate event as standing more peculiarly
in the position of a cause than any of the antecedent states. But even
this peculiarity, of being in closer proximity to the effect than any
other of its conditions, is, as we have already seen, far from being
necessary to the common notion of a cause; with which notion, on the
contrary, any one of the conditions, either positive or negative, is
found, on occasion, completely to accord.(114)

The cause, then, philosophically speaking, is the sum total of the
conditions, positive and negative taken together; the whole of the
contingencies of every description, which being realized, the consequent
invariably follows. The negative conditions, however, of any phenomenon, a
special enumeration of which would generally be very prolix, may be all
summed up under one head, namely, the absence of preventing or
counteracting causes. The convenience of this mode of expression is mainly
grounded on the fact, that the effects of any cause in counteracting
another cause may in most cases be, with strict scientific exactness,
regarded as a mere extension of its own proper and separate effects. If
gravity retards the upward motion of a projectile, and deflects it into a
parabolic trajectory, it produces, in so doing, the very same kind of
effect, and even (as mathematicians know) the same quantity of effect, as
it does in its ordinary operation of causing the fall of bodies when
simply deprived of their support. If an alkaline solution mixed with an
acid destroys its sourness, and prevents it from reddening vegetable
blues, it is because the specific effect of the alkali is to combine with
the acid, and form a compound with totally different qualities. This
property, which causes of all descriptions possess, of preventing the
effects of other causes by virtue (for the most part) of the same laws
according to which they produce their own,(115) enables us, by
establishing the general axiom that all causes are liable to be
counteracted in their effects by one another, to dispense with the
consideration of negative conditions entirely, and limit the notion of
cause to the assemblage of the positive conditions of the phenomenon: one
negative condition invariably understood, and the same in all instances
(namely, the absence of counteracting causes) being sufficient, along with
the sum of the positive conditions, to make up the whole set of
circumstances on which the phenomenon is dependent.

§ 4. Among the positive conditions, as we have seen that there are some to
which, in common parlance, the term cause is more readily and frequently
awarded, so there are others to which it is, in ordinary circumstances,
refused. In most cases of causation a distinction is commonly drawn
between something which acts, and some other thing which is acted upon;
between an _agent_ and a _patient_. Both of these, it would be universally
allowed, are conditions of the phenomenon; but it would be thought absurd
to call the latter the cause, that title being reserved for the former.
The distinction, however, vanishes on examination, or rather is found to
be only verbal; arising from an incident of mere expression, namely, that
the object said to be acted upon, and which is considered as the scene in
which the effect takes place, is commonly included in the phrase by which
the effect is spoken of, so that if it were also reckoned as part of the
cause, the seeming incongruity would arise of its being supposed to cause
itself. In the instance which we have already had, of falling bodies, the
question was thus put: What is the cause which makes a stone fall? and if
the answer had been “the stone itself,” the expression would have been in
apparent contradiction to the meaning of the word cause. The stone,
therefore, is conceived as the patient, and the earth (or, according to
the common and most unphilosophical practice, an occult quality of the
earth) is represented as the agent or cause. But that there is nothing
fundamental in the distinction may be seen from this, that it is quite
possible to conceive the stone as causing its own fall, provided the
language employed be such as to save the mere verbal incongruity. We might
say that the stone moves toward the earth by the properties of the matter
composing it; and according to this mode of presenting the phenomenon, the
stone itself might without impropriety be called the agent; though, to
save the established doctrine of the inactivity of matter, men usually
prefer here also to ascribe the effect to an occult quality, and say that
the cause is not the stone itself, but the _weight_ or _gravitation_ of
the stone.

Those who have contended for a radical distinction between agent and
patient, have generally conceived the agent as that which causes some
state of, or some change in the state of, another object which is called
the patient. But a little reflection will show that the license we assume
of speaking of phenomena as _states_ of the various objects which take
part in them (an artifice of which so much use has been made by some
philosophers, Brown in particular, for the apparent explanation of
phenomena), is simply a sort of logical fiction, useful sometimes as one
among several modes of expression, but which should never be supposed to
be the enunciation of a scientific truth. Even those attributes of an
object which might seem with greatest propriety to be called states of the
object itself, its sensible qualities, its color, hardness, shape, and the
like, are in reality (as no one has pointed out more clearly than Brown
himself) phenomena of causation, in which the substance is distinctly the
agent, or producing cause, the patient being our own organs, and those of
other sentient beings. What we call states of objects, are always
sequences into which the objects enter, generally as antecedents or
causes; and things are never more active than in the production of those
phenomena in which they are said to be acted upon. Thus, in the example of
a stone falling to the earth, according to the theory of gravitation the
stone is as much an agent as the earth, which not only attracts, but is
itself attracted by, the stone. In the case of a sensation produced in our
organs, the laws of our organization, and even those of our minds, are as
directly operative in determining the effect produced, as the laws of the
outward object. Though we call prussic acid the agent of a person’s death,
the whole of the vital and organic properties of the patient are as
actively instrumental as the poison, in the chain of effects which so
rapidly terminates his sentient existence. In the process of education, we
may call the teacher the agent, and the scholar only the material acted
upon; yet in truth all the facts which pre-existed in the scholar’s mind
exert either co-operating or counteracting agencies in relation to the
teacher’s efforts. It is not light alone which is the agent in vision, but
light coupled with the active properties of the eye and brain, and with
those of the visible object. The distinction between agent and patient is
merely verbal: patients are always agents; in a great proportion, indeed,
of all natural phenomena, they are so to such a degree as to react
forcibly on the causes which acted upon them: and even when this is not
the case, they contribute, in the same manner as any of the other
conditions, to the production of the effect of which they are vulgarly
treated as the mere theatre. All the positive conditions of a phenomenon
are alike agents, alike active; and in any expression of the cause which
professes to be complete, none of them can with reason be excluded, except
such as have already been implied in the words used for describing the
effect; nor by including even these would there be incurred any but a
merely verbal impropriety.

§ 5. There is a case of causation which calls for separate notice, as it
possesses a peculiar feature, and presents a greater degree of complexity
than the common case. It often happens that the effect, or one of the
effects, of a cause, is, not to produce of itself a certain phenomenon,
but to fit something else for producing it. In other words, there is a
case of causation in which the effect is to invest an object with a
certain property. When sulphur, charcoal, and nitre are put together in
certain proportions and in a certain manner, the effect is, not an
explosion, but that the mixture acquires a property by which, in given
circumstances, it will explode. The various causes, natural and
artificial, which educate the human body or the human mind, have for their
principal effect, not to make the body or mind immediately do any thing,
but to endow it with certain properties—in other words, to give assurance
that in given circumstances certain results will take place in it, or as
consequences of it. Physiological agencies often have for the chief part
of their operation to _predispose_ the constitution to some mode of
action. To take a simpler instance than all these: putting a coat of white
paint upon a wall does not merely produce in those who see it done, the
sensation of white; it confers on the wall the permanent property of
giving that kind of sensation. Regarded in reference to the sensation, the
putting on of the paint is a condition of a condition; it is a condition
of the wall’s causing that particular fact. The wall may have been painted
years ago, but it has acquired a property which has lasted till now, and
will last longer; the antecedent condition necessary to enable the wall to
become in its turn a condition, has been fulfilled once for all. In a case
like this, where the immediate consequent in the sequence is a property
produced in an object, no one now supposes the property to be a
substantive entity “inherent” in the object. What has been produced is
what, in other language, may be called a state of preparation in an object
for producing an effect. The ingredients of the gunpowder have been
brought into a state of preparation for exploding as soon as the other
conditions of an explosion shall have occurred. In the case of the
gunpowder, this state of preparation consists in a certain collocation of
its particles relatively to one another. In the example of the wall, it
consists in a new collocation of two things relatively to each other—the
wall and the paint. In the example of the molding influences on the human
mind, its being a collocation at all is only conjectural; for, even on the
materialistic hypothesis, it would remain to be proved that the increased
facility with which the brain sums up a column of figures when it has been
long trained to calculation, is the result of a permanent new arrangement
of some of its material particles. We must, therefore, content ourselves
with what we know, and must include among the effects of causes, the
capacities given to objects of being causes of other effects. This
capacity is not a real thing existing in the objects; it is but a name for
our conviction that they will act in a particular manner when certain new
circumstances arise. We may invest this assurance of future events with a
fictitious objective existence, by calling it a state of the object. But
unless the state consists, as in the case of the gunpowder it does, in a
collocation of particles, it expresses no present fact; it is but the
contingent future fact brought back under another name.

It may be thought that this form of causation requires us to admit an
exception to the doctrine that the conditions of a phenomenon—the
antecedents required for calling it into existence—must all be found among
the facts immediately, not remotely, preceding its commencement. But what
we have arrived at is not a correction, it is only an explanation, of that
doctrine. In the enumeration of the conditions required for the occurrence
of any phenomenon, it always has to be included that objects must be
present, possessed of given properties. It is a condition of the
phenomenon explosion that an object should be present, of one or other of
certain kinds, which for that reason are called explosive. The presence of
one of these objects is a condition immediately precedent to the
explosion. The condition which is not immediately precedent is the cause
which produced, not the explosion, but the explosive property. The
conditions of the explosion itself were all present immediately before it
took place, and the general law, therefore, remains intact.

§ 6. It now remains to advert to a distinction which is of first-rate
importance both for clearing up the notion of cause, and for obviating a
very specious objection often made against the view which we have taken of
the subject.

When we define the cause of any thing (in the only sense in which the
present inquiry has any concern with causes) to be “the antecedent which
it invariably follows,” we do not use this phrase as exactly synonymous
with “the antecedent which it invariably _has_ followed in our past
experience.” Such a mode of conceiving causation would be liable to the
objection very plausibly urged by Dr. Reid, namely, that according to this
doctrine night must be the cause of day, and day the cause of night; since
these phenomena have invariably succeeded one another from the beginning
of the world. But it is necessary to our using the word cause, that we
should believe not only that the antecedent always _has_ been followed by
the consequent, but that, as long as the present constitution of
things(116) endures, it always _will_ be so. And this would not be true of
day and night. We do not believe that night will be followed by day under
all imaginable circumstances, but only that it will be so _provided_ the
sun rises above the horizon. If the sun ceased to rise, which, for aught
we know, may be perfectly compatible with the general laws of matter,
night would be, or might be, eternal. On the other hand, if the sun is
above the horizon, his light not extinct, and no opaque body between us
and him, we believe firmly that unless a change takes place in the
properties of matter, this combination of antecedents will be followed by
the consequent, day; that if the combination of antecedents could be
indefinitely prolonged, it would be always day; and that if the same
combination had always existed, it would always have been day, quite
independently of night as a previous condition. Therefore is it that we do
not call night the cause, nor even a condition, of day. The existence of
the sun (or some such luminous body), and there being no opaque medium in
a straight line(117) between that body and the part of the earth where we
are situated, are the sole conditions; and the union of these, without the
addition of any superfluous circumstance, constitutes the cause. This is
what writers mean when they say that the notion of cause involves the idea
of necessity. If there be any meaning which confessedly belongs to the
term necessity, it is _unconditionalness_. That which is necessary, that
which _must_ be, means that which will be, whatever supposition we may
make in regard to all other things. The succession of day and night
evidently is not necessary in this sense. It is conditional on the
occurrence of other antecedents. That which will be followed by a given
consequent when, and only when, some third circumstance also exists, is
not the cause, even though no case should ever have occurred in which the
phenomenon took place without it.

Invariable sequence, therefore, is not synonymous with causation, unless
the sequence, besides being invariable, is unconditional. There are
sequences, as uniform in past experience as any others whatever, which yet
we do not regard as cases of causation, but as conjunctions in some sort
accidental. Such, to an accurate thinker, is that of day and night. The
one might have existed for any length of time, and the other not have
followed the sooner for its existence; it follows only if certain other
antecedents exist; and where those antecedents existed, it would follow in
any case. No one, probably, ever called night the cause of day; mankind
must so soon have arrived at the very obvious generalization, that the
state of general illumination which we call day would follow from the
presence of a sufficiently luminous body, whether darkness had preceded or
not.

We may define, therefore, the cause of a phenomenon, to be the antecedent,
or the concurrence of antecedents, on which it is invariably and
_unconditionally_ consequent. Or if we adopt the convenient modification
of the meaning of the word cause, which confines it to the assemblage of
positive conditions without the negative, then instead of
“unconditionally,” we must say, “subject to no other than negative
conditions.”

To some it may appear, that the sequence between night and day being
invariable in our experience, we have as much ground in this case as
experience can give in any case, for recognizing the two phenomena as
cause and effect; and that to say that more is necessary—to require a
belief that the succession is unconditional, or, in other words, that it
would be invariable under all changes of circumstances, is to acknowledge
in causation an element of belief not derived from experience. The answer
to this is, that it is experience itself which teaches us that one
uniformity of sequence is conditional and another unconditional. When we
judge that the succession of night and day is a derivative sequence,
depending on something else, we proceed on grounds of experience. It is
the evidence of experience which convinces us that day could equally exist
without being followed by night, and that night could equally exist
without being followed by day. To say that these beliefs are “not
generated by our mere observation of sequence,”(118) is to forget that
twice in every twenty-four hours, when the sky is clear, we have an
_experimentum crucis_ that the cause of day is the sun. We have an
experimental knowledge of the sun which justifies us on experimental
grounds in concluding, that if the sun were always above the horizon there
would be day, though there had been no night, and that if the sun were
always below the horizon there would be night, though there had been no
day. We thus know from experience that the succession of night and day is
not unconditional. Let me add, that the antecedent which is only
conditionally invariable, is not the invariable antecedent. Though a fact
may, in experience, have always been followed by another fact, yet if the
remainder of our experience teaches us that it might not always be so
followed, or if the experience itself is such as leaves room for a
possibility that the known cases may not correctly represent all possible
cases, the hitherto invariable antecedent is not accounted the cause; but
why? Because we are not sure that it _is_ the invariable antecedent.

Such cases of sequence as that of day and night not only do not contradict
the doctrine which resolves causation into invariable sequence, but are
necessarily implied in that doctrine. It is evident, that from a limited
number of unconditional sequences, there will result a much greater number
of conditional ones. Certain causes being given, that is, certain
antecedents which are unconditionally followed by certain consequents; the
mere co-existence of these causes will give rise to an unlimited number of
additional uniformities. If two causes exist together, the effects of both
will exist together; and if many causes co-exist, these causes (by what we
shall term hereafter the intermixture of their laws) will give rise to new
effects, accompanying or succeeding one another in some particular order,
which order will be invariable while the causes continue to co-exist, but
no longer. The motion of the earth in a given orbit round the sun, is a
series of changes which follow one another as antecedents and consequents,
and will continue to do so while the sun’s attraction, and the force with
which the earth tends to advance in a direct line through space, continue
to co-exist in the same quantities as at present. But vary either of these
causes, and this particular succession of motions would cease to take
place. The series of the earth’s motions, therefore, though a case of
sequence invariable within the limits of human experience, is not a case
of causation. It is not unconditional.

This distinction between the relations of succession which, so far as we
know, are unconditional, and those relations, whether of succession or of
co-existence, which, like the earth’s motions, or the succession of day
and night, depend on the existence or on the co-existence of other
antecedent facts—corresponds to the great division which Dr. Whewell and
other writers have made of the field of science, into the investigation of
what they term the Laws of Phenomena, and the investigation of causes; a
phraseology, as I conceive, not philosophically sustainable, inasmuch as
the ascertainment of causes, such causes as the human faculties can
ascertain, namely, causes which are themselves phenomena, is, therefore,
merely the ascertainment of other and more universal Laws of Phenomena.
And let me here observe, that Dr. Whewell, and in some degree even Sir
John Herschel, seem to have misunderstood the meaning of those writers
who, like M. Comté, limit the sphere of scientific investigation to Laws
of Phenomena, and speak of the inquiry into causes as vain and futile. The
causes which M. Comté designates as inaccessible, are efficient causes.
The investigation of physical, as opposed to efficient, causes (including
the study of all the active forces in Nature, considered as facts of
observation) is as important a part of M. Comté’s conception of science as
of Dr. Whewell’s. His objection to the _word_ cause is a mere matter of
nomenclature, in which, as a matter of nomenclature, I consider him to be
entirely wrong. “Those,” it is justly remarked by Mr. Bailey,(119) “who,
like M. Comté, object to designate _events_ as causes, are objecting
without any real ground to a mere but extremely convenient generalization,
to a very useful common name, the employment of which involves, or needs
involve, no particular theory.” To which it may be added, that by
rejecting this form of expression, M. Comté leaves himself without any
term for marking a distinction which, however incorrectly expressed, is
not only real, but is one of the fundamental distinctions in science;
indeed it is on this alone, as we shall hereafter find, that the
possibility rests of framing a rigorous Canon of Induction. And as things
left without a name are apt to be forgotten, a Canon of that description
is not one of the many benefits which the philosophy of Induction has
received from M. Comté’s great powers.

§ 7. Does a cause always stand with its effect in the relation of
antecedent and consequent? Do we not often say of two simultaneous facts
that they are cause and effect—as when we say that fire is the cause of
warmth, the sun and moisture the cause of vegetation, and the like? Since
a cause does not necessarily perish because its effect has been produced,
the two things do very generally co-exist; and there are some appearances,
and some common expressions, seeming to imply not only that causes may,
but that they must, be contemporaneous with their effects. _Cessante causâ
cessat et effectus_, has been a dogma of the schools: the necessity for
the continued existence of the cause in order to the continuance of the
effect, seems to have been once a generally received doctrine. Kepler’s
numerous attempts to account for the motions of the heavenly bodies on
mechanical principles, were rendered abortive by his always supposing that
the agency which set those bodies in motion must continue to operate in
order to keep up the motion which it at first produced. Yet there were at
all times many familiar instances of the continuance of effects, long
after their causes had ceased. A _coup de soleil_ gives a person
brain-fever: will the fever go off as soon as he is moved out of the
sunshine? A sword is run through his body: must the sword remain in his
body in order that he may continue dead? A plowshare once made, remains a
plowshare, without any continuance of heating and hammering, and even
after the man who heated and hammered it has been gathered to his fathers.
On the other hand, the pressure which forces up the mercury in an
exhausted tube must be continued in order to sustain it in the tube. This
(it may be replied) is because another force is acting without
intermission, the force of gravity, which would restore it to its level,
unless counterpoised by a force equally constant. But again: a tight
bandage causes pain, which pain will sometimes go off as soon as the
bandage is removed. The illumination which the sun diffuses over the earth
ceases when the sun goes down.

There is, therefore, a distinction to be drawn. The conditions which are
necessary for the first production of a phenomenon, are occasionally also
necessary for its continuance; though more commonly its continuance
requires no condition except negative ones. Most things, once produced,
continue as they are, until something changes or destroys them; but some
require the permanent presence of the agencies which produced them at
first. These may, if we please, be considered as instantaneous phenomena,
requiring to be renewed at each instant by the cause by which they were at
first generated. Accordingly, the illumination of any given point of space
has always been looked upon as an instantaneous fact, which perishes and
is perpetually renewed as long as the necessary conditions subsist. If we
adopt this language we avoid the necessity of admitting that the
continuance of the cause is ever required to maintain the effect. We may
say, it is not required to maintain, but to reproduce, the effect, or else
to counteract some force tending to destroy it. And this may be a
convenient phraseology. But it is only a phraseology. The fact remains,
that in some cases (though those are a minority) the continuance of the
conditions which produced an effect is necessary to the continuance of the
effect.

As to the ulterior question, whether it is strictly necessary that the
cause, or assemblage of conditions, should precede, by ever so short an
instant, the production of the effect (a question raised and argued with
much ingenuity by Sir John Herschel in an Essay already quoted),(120) the
inquiry is of no consequence for our present purpose. There certainly are
cases in which the effect follows without any interval perceptible by our
faculties; and when there is an interval, we can not tell by how many
intermediate links imperceptible to us that interval may really be filled
up. But even granting that an effect may commence simultaneously with its
cause, the view I have taken of causation is in no way practically
affected. Whether the cause and its effect be necessarily successive or
not, the beginning of a phenomenon is what implies a cause, and causation
is the law of the succession of phenomena. If these axioms be granted, we
can afford, though I see no necessity for doing so, to drop the words
antecedent and consequent as applied to cause and effect. I have no
objection to define a cause, the assemblage of phenomena, which occurring,
some other phenomenon invariably commences, or has its origin. Whether the
effect coincides in point of time with, or immediately follows, the
hindmost of its conditions, is immaterial. At all events, it does not
precede it; and when we are in doubt, between two co-existent phenomena,
which is cause and which effect, we rightly deem the question solved if we
can ascertain which of them preceded the other.

§ 8. It continually happens that several different phenomena, which are
not in the slightest degree dependent or conditional on one another, are
found all to depend, as the phrase is, on one and the same agent; in other
words, one and the same phenomenon is seen to be followed by several sorts
of effects quite heterogeneous, but which go on simultaneously one with
another; provided, of course, that all other conditions requisite for each
of them also exist. Thus, the sun produces the celestial motions; it
produces daylight, and it produces heat. The earth causes the fall of
heavy bodies, and it also, in its capacity of a great magnet, causes the
phenomena of the magnetic needle. A crystal of galena causes the
sensations of hardness, of weight, of cubical form, of gray color, and
many others between which we can trace no interdependence. The purpose to
which the phraseology of Properties and Powers is specially adapted, is
the expression of this sort of cases. When the same phenomenon is followed
(either subject or not to the presence of other conditions) by effects of
different and dissimilar orders, it is usual to say that each different
sort of effect is produced by a different property of the cause. Thus we
distinguish the attractive or gravitative property of the earth, and its
magnetic property: the gravitative, luminiferous, and calorific properties
of the sun: the color, shape, weight, and hardness of a crystal. These are
mere phrases, which explain nothing, and add nothing to our knowledge of
the subject; but, considered as abstract names denoting the connection
between the different effects produced and the object which produces them,
they are a very powerful instrument of abridgment, and of that
acceleration of the process of thought which abridgment accomplishes.

This class of considerations leads to a conception which we shall find to
be of great importance, that of a Permanent Cause, or original natural
agent. There exist in nature a number of permanent causes, which have
subsisted ever since the human race has been in existence, and for an
indefinite and probably an enormous length of time previous. The sun, the
earth, and planets, with their various constituents, air, water, and other
distinguishable substances, whether simple or compound, of which nature is
made up, are such Permanent Causes. These have existed, and the effects or
consequences which they were fitted to produce have taken place (as often
as the other conditions of the production met), from the very beginning of
our experience. But we can give no account of the origin of the Permanent
Causes themselves. Why these particular natural agents existed originally
and no others, or why they are commingled in such and such proportions,
and distributed in such and such a manner throughout space, is a question
we can not answer. More than this: we can discover nothing regular in the
distribution itself; we can reduce it to no uniformity, to no law. There
are no means by which, from the distribution of these causes or agents in
one part of space, we could conjecture whether a similar distribution
prevails in another. The co-existence, therefore, of Primeval Causes
ranks, to us, among merely casual concurrences: and all those sequences or
co-existences among the effects of several such causes, which, though
invariable while those causes co-exist, would, if the co-existence
terminated, terminate along with it, we do not class as cases of
causation, or laws of nature: we can only calculate on finding these
sequences or co-existences where we know by direct evidence, that the
natural agents on the properties of which they ultimately depend, are
distributed in the requisite manner. These Permanent Causes are not always
objects; they are sometimes events, that is to say, periodical cycles of
events, that being the only mode in which events can possess the property
of permanence. Not only, for instance, is the earth itself a permanent
cause, or primitive natural agent, but the earth’s rotation is so too: it
is a cause which has produced, from the earliest period (by the aid of
other necessary conditions), the succession of day and night, the ebb and
flow of the sea, and many other effects, while, as we can assign no cause
(except conjecturally) for the rotation itself, it is entitled to be
ranked as a primeval cause. It is, however, only the _origin_ of the
rotation which is mysterious to us: once begun, its continuance is
accounted for by the first law of motion (that of the permanence of
rectilinear motion once impressed) combined with the gravitation of the
parts of the earth toward one another.

All phenomena without exception which begin to exist, that is, all except
the primeval causes, are effects either immediate or remote of those
primitive facts, or of some combination of them. There is no Thing
produced, no event happening, in the known universe, which is not
connected by a uniformity, or invariable sequence, with some one or more
of the phenomena which preceded it; insomuch that it will happen again as
often as those phenomena occur again, and as no other phenomenon having
the character of a counteracting cause shall co-exist. These antecedent
phenomena, again, were connected in a similar manner with some that
preceded them; and so on, until we reach, as the ultimate step attainable
by us, either the properties of some one primeval cause, or the
conjunction of several. The whole of the phenomena of nature were
therefore the necessary, or, in other words, the unconditional,
consequences of some former collocation of the Permanent Causes.

The state of the whole universe at any instant, we believe to be the
consequence of its state at the previous instant; insomuch that one who
knew all the agents which exist at the present moment, their collocation
in space, and all their properties, in other words, the laws of their
agency, could predict the whole subsequent history of the universe, at
least unless some new volition of a power capable of controlling the
universe should supervene.(121) And if any particular state of the entire
universe could ever recur a second time, all subsequent states would
return too, and history would, like a circulating decimal of many figures,
periodically repeat itself:


    Jam redit et virgo, redeunt Saturnia regna....
    Alter erit tum Tiphys, et altera quæ vehat Argo
    Delectos heroas; erunt quoque altera bella,
    Atque iterum ad Trojam magnus mittetur Achilles.


And though things do not really revolve in this eternal round, the whole
series of events in the history of the universe, past and future, is not
the less capable, in its own nature, of being constructed _a priori_ by
any one whom we can suppose acquainted with the original distribution of
all natural agents, and with the whole of their properties, that is, the
laws of succession existing between them and their effects: saving the far
more than human powers of combination and calculation which would be
required, even in one possessing the data, for the actual performance of
the task.

§ 9. Since every thing which occurs is determined by laws of causation and
collocations of the original causes, it follows that the co-existences
which are observable among effects can not be themselves the subject of
any similar set of laws, distinct from laws of causation. Uniformities
there are, as well of co-existence as of succession, among effects; but
these must in all cases be a mere result either of the identity or of the
co-existence of their causes: if the causes did not co-exist, neither
could the effects. And these causes being also effects of prior causes,
and these of others, until we reach the primeval causes, it follows that
(except in the case of effects which can be traced immediately or remotely
to one and the same cause) the co-existences of phenomena can in no case
be universal, unless the co-existences of the primeval causes to which the
effects are ultimately traceable can be reduced to a universal law: but we
have seen that they can not. There are, accordingly, no original and
independent, in other words no unconditional, uniformities of
co-existence, between effects of different causes; if they co-exist, it is
only because the causes have casually co-existed. The only independent and
unconditional co-existences which are sufficiently invariable to have any
claim to the character of laws, are between different and mutually
independent effects of the same cause; in other words, between different
properties of the same natural agent. This portion of the Laws of Nature
will be treated of in the latter part of the present Book, under the name
of the Specific Properties of Kinds.

§ 10. Since the first publication of the present treatise, the sciences of
physical nature have made a great advance in generalization, through the
doctrine known as the Conservation or Persistence of Force. This imposing
edifice of theory, the building and laying out of which has for some time
been the principal occupation of the most systematic minds among physical
inquirers, consists of two stages: one, of ascertained fact, the other
containing a large element of hypothesis.

To begin with the first. It is proved by numerous facts, both natural and
of artificial production, that agencies which had been regarded as
distinct and independent sources of force—heat, electricity, chemical
action, nervous and muscular action, momentum of moving bodies—are
interchangeable, in definite and fixed quantities, with one another. It
had long been known that these dissimilar phenomena had the power, under
certain conditions, of producing one another: what is new in the theory is
a more accurate estimation of what this production consists in. What
happens is, that the whole or part of the one kind of phenomena
disappears, and is replaced by phenomena of one of the other descriptions,
and that there is an equivalence in quantity between the phenomena that
have disappeared and those which have been produced, insomuch that if the
process be reversed, the very same quantity which had disappeared will
re-appear, without increase or diminution. Thus the amount of heat which
will raise the temperature of a pound of water one degree of the
thermometer, will, if expended, say in the expansion of steam, lift a
weight of 772 pounds one foot, or a weight of one pound 772 feet: and the
same exact quantity of heat can, by certain means, be recovered, through
the expenditure of exactly that amount of mechanical motion.

The establishment of this comprehensive law has led to a change in the
language in which the scientific world had been accustomed to speak of
what are called the Forces of nature. Before this correlation between
phenomena most unlike one another had been ascertained, their unlikeness
had caused them to be referred to so many distinct forces. Now that they
are known to be convertible into one another without loss, they are spoken
of as all of them results of one and the same force, manifesting itself in
different modes. This force (it is said) can only produce a limited and
definite quantity of effect, but always does produce that definite
quantity; and produces it, according to circumstances, in one or another
of the forms, or divides it among several, but so as (according to a scale
of numerical equivalents established by experiment) always to make up the
same sum; and no one of the manifestations can be produced, save by the
disappearance of the equivalent quantity of another, which in its turn, in
appropriate circumstances, will re-appear undiminished. This mutual
interchangeability of the forces of nature, according to fixed numerical
equivalents, is the part of the new doctrine which rests on irrefragable
fact.

To make the statement true, however, it is necessary to add, that an
indefinite and perhaps immense interval of time may elapse between the
disappearance of the force in one form and its re-appearance in another. A
stone thrown up into the air with a given force, and falling back
immediately, will, by the time it reaches the earth, recover the exact
amount of mechanical momentum which was expended in throwing it up,
deduction being made of a small portion of motion which has been
communicated to the air. But if the stone has lodged on a height, it may
not fall back for years, or perhaps ages, and until it does, the force
expended in raising it is temporarily lost, being represented only by
what, in the language of the new theory, is called potential energy. The
coal imbedded in the earth is considered by the theory as a vast reservoir
of force, which has remained dormant for many geological periods, and will
so remain until, by being burned, it gives out the stored-up force in the
form of heat. Yet it is not supposed that this force is a material thing
which can be confined by bounds, as used to be thought of latent heat when
that important phenomenon was first discovered. What is meant is that when
the coal does at last, by combustion, generate a quantity of heat
(transformable like all other heat into mechanical momentum, and the other
forms of force), this extrication of heat is the re-appearance of a force
derived from the sun’s rays, expended myriads of ages ago in the
vegetation of the organic substances which were the material of the coal.

Let us now pass to the higher stage of the theory of Conservation of
Force; the part which is no longer a generalization of proved fact, but a
combination of fact and hypothesis. Stated in few words, it is as follows:
That the Conservation of Force is really the Conservation of Motion; that
in the various interchanges between the forms of force, it is always
motion that is transformed into motion. To establish this, it is necessary
to assume motions which are hypothetical. The supposition is, that there
are motions which manifest themselves to our senses only as heat,
electricity, etc., being molecular motions; oscillations, invisible to us,
among the minute particles of bodies; and that these molecular motions are
transmutable into molar motions (motions of masses), and molar motions
into molecular. Now there is a real basis of fact for this supposition: we
have positive evidence of the existence of molecular motion in these
manifestations of force. In the case of chemical action, for instance, the
particles separate and form new combinations, often with a great visible
disturbance of the mass. In the case of heat, the evidence is equally
conclusive, since heat expands bodies (that is, causes their particles to
move _from_ one another); and if of sufficient amount, changes their mode
of aggregation from solid to liquid, or from liquid to gaseous. Again, the
mechanical actions which produce heat—friction, and the collision of
bodies—must from the nature of the case produce a shock, that is, an
internal motion of particles, which indeed, we find, is often so violent
as to break them permanently asunder. Such facts are thought to warrant
the inference, that it is not, as was supposed, heat that causes the
motion of particles, but the motion of particles that causes heat; the
original cause of both being the previous motion (whether molar or
molecular—collision of bodies or combustion of fuel) which formed the
heating agency. This inference already contains hypothesis; but at least
the supposed cause, the intestine motion of molecules, is a _vera causa_.
But in order to reduce the Conservation of Force to Conservation of
Motion, it was necessary to attribute to motion the heat propagated,
through apparently empty space, from the sun. This required the
supposition (already made for the explanation of the laws of light) of a
subtle ether pervading space, which, though impalpable to us, must have
the property which constitutes matter, that of resistance, since waves are
propagated through it by an impulse from a given point. The ether must be
supposed (a supposition not required by the theory of light) to penetrate
into the minute interstices of all bodies. The vibratory motion supposed
to be taking place in the heated mass of the sun, is considered as
imparted from that mass to the particles of the surrounding ether, and
through them to the particles of the same ether in the interstices of
terrestrial bodies; and this, too, with a sufficient mechanical force to
throw the particles of those bodies into a state of similar vibration,
producing the expansion of their mass, and the sensation of heat in
sentient creatures. All this is hypothesis, though, of its legitimacy as
hypothesis, I do not mean to express any doubt. It would seem to follow as
a consequence from this theory, that Force may and should be defined,
matter in motion. This definition, however, will not stand, for, as has
already been seen, the matter needs not be in _actual_ motion. It is not
necessary to suppose that the motion afterward manifested, is actually
taking place among the molecules of the coal during its sojourn in the
earth;(122) certainly not in the stone which is at rest on the eminence to
which it has been raised. The true definition of Force must be, not
motion, but Potentiality of Motion; and what the doctrine, if established,
amounts to, is, not that there is at all times the same quantity of actual
motion in the universe; but that the possibilities of motion are limited
to a definite quantity, which can not be added to, but which can not be
exhausted; and that all actual motion which takes place in Nature is a
draft upon this limited stock. It needs not all of it have ever existed as
actual motion. There is a vast amount of potential motion in the universe
in the form of gravitation, which it would be a great abuse of hypothesis
to suppose to have been stored up by the expenditure of an equal amount of
actual motion in some former state of the universe. Nor does the motion
produced by gravity take place, so far as we know, at the expense of any
other motion, either molar or molecular.

It is proper to consider whether the adoption of this theory as a
scientific truth, involving as it does a change in the conception hitherto
entertained of the most general physical agencies, requires any
modification in the view I have taken of Causation as a law of nature. As
it appears to me, none whatever. The manifestations which the theory
regards as modes of motion, are as much distinct and separate phenomena
when referred to a single force, as when attributed to several. Whether
the phenomenon is called a transformation of force or the generation of
one, it has its own set or sets of antecedents, with which it is connected
by invariable and unconditional sequence; and that set, or those sets, of
antecedents are its cause. The relation of the Conservation theory to the
principle of Causation is discussed in much detail, and very
instructively, by Professor Bain, in the second volume of his Logic. The
chief practical conclusion drawn by him, bearing on Causation, is, that we
must distinguish in the assemblage of conditions which constitutes the
Cause of a phenomenon, two elements: one, the presence of a force; the
other, the collocation or position of objects which is required in order
that the force may undergo the particular transmutation which constitutes
the phenomenon. Now, it might always have been said with acknowledged
correctness, that a force and a collocation were both of them necessary to
produce any phenomenon. The law of causation is, that change can only be
produced by change. Along with any number of stationary antecedents, which
are collocations, there must be at least one changing antecedent, which is
a force. To produce a bonfire, there must not only be fuel, and air, and a
spark, which are collocations, but chemical action between the air and the
materials, which is a force. To grind corn, there must be a certain
collocation of the parts composing a mill, relatively to one another and
to the corn; but there must also be the gravitation of water, or the
motion of wind, to supply a force. But as the force in these cases was
regarded as a property of the objects in which it is embodied, it seemed
tautology to say that there must be the collocation _and_ the force. As
the collocation must be a collocation of objects possessing the
force-giving property, the collocation, so understood, included the force.

How, then, shall we have to express these facts, if the theory be finally
substantiated that all Force is reducible to a previous Motion? We shall
have to say, that one of the conditions of every phenomenon is an
antecedent Motion. But it will have to be explained that this needs not be
_actual_ motion. The coal which supplies the force exerted in combustion
is not shown to have been exerting that force in the form of molecular
motion in the pit; it was not even exerting pressure. The stone on the
eminence _is_ exerting a pressure, but only equivalent to its weight, not
to the additional momentum it would acquire by falling. The antecedent,
therefore, is not a force in action; and we can still only call it a
property of the objects, by which they would exert a force on the
occurrence of a fresh collocation. The collocation, therefore, still
includes the force. The force said to be stored up, is simply a particular
property which the object has acquired. The cause we are in search of, is
a collocation of objects possessing that particular property. When,
indeed, we inquire further into the cause from which they derive that
property, the new conception introduced by the Conservation theory comes
in: the property is itself an effect, and its cause, according to the
theory, is a former motion of exactly equivalent amount, which has been
impressed on the particles of the body, perhaps at some very distant
period. But the case is simply one of those we have already considered, in
which the efficacy of a cause consists in its investing an object with a
property. The force said to be laid up, and merely potential, is no more a
really existing thing than any other properties of objects are really
existing things. The expression is a mere artifice of language, convenient
for describing the phenomena: it is unnecessary to suppose that any thing
has been in continuous existence except an abstract potentiality. A force
suspended in its operation, neither manifesting itself by motion nor by
pressure, is not an existing fact, but a name for our conviction that in
appropriate circumstances a fact would take place. We know that a pound
weight, were it to fall from the earth into the sun, would acquire in
falling a momentum equal to millions of pounds; but we do not credit the
pound weight with more of actually existing force than is equal to the
pressure it is now exerting on the earth, and that is exactly a pound. We
might as well say that a force of millions of pounds exists in a pound, as
that the force which will manifest itself when the coal is burned is a
real thing existing in the coal. What is fixed in the coal is only a
certain property: it has become fit to be the antecedent of an effect
called combustion, which partly consists in giving out, under certain
conditions, a given definite quantity of heat.

We thus see that no new general conception of Causation is introduced by
the Conservation theory. The indestructibility of Force no more interferes
with the theory of Causation than the indestructibility of Matter, meaning
by matter the element of resistance in the sensible world. It only enables
us to understand better than before the nature and laws of some of the
sequences.

This better understanding, however, enables us, with Mr. Bain, to admit,
as one of the tests for distinguishing causation from mere concomitance,
the expenditure or transfer of energy. If the effect, or any part of the
effect, to be accounted for, consists in putting matter in motion, then
any of the objects present which has lost motion has contributed to the
effect; and this is the true meaning of the proposition that the cause is
that one of the antecedents which exerts active force.

§ 11. It is proper in this place to advert to a rather ancient doctrine
respecting causation, which has been revived during the last few years in
many quarters, and at present gives more signs of life than any other
theory of causation at variance with that set forth in the preceding
pages.

According to the theory in question, Mind, or to speak move precisely,
Will, is the only cause of phenomena. The type of Causation, as well as
the exclusive source from which we derive the idea, is our own voluntary
agency. Here, and here only (it is said), we have direct evidence of
causation. We know that we can move our bodies. Respecting the phenomena
of inanimate nature, we have no other direct knowledge than that of
antecedence and sequence. But in the case of our voluntary actions, it is
affirmed that we are conscious of power before we have experience of
results. An act of volition, whether followed by an effect or not, is
accompanied by a consciousness of effort, “of force exerted, of power in
action, which is necessarily causal, or causative.” This feeling of energy
or force, inherent in an act of will, is knowledge _a priori_; assurance,
prior to experience, that we have the power of causing effects. Volition,
therefore, it is asserted, is something more than an unconditional
antecedent; it is a cause, in a different sense from that in which
physical phenomena are said to cause one another: it is an Efficient
Cause. From this the transition is easy to the further doctrine, that
Volition is the _sole_ Efficient Cause of all phenomena. “It is
inconceivable that dead force could continue unsupported for a moment
beyond its creation. We can not even conceive of change or phenomena
without the energy of a mind.” “The word _action_” itself, says another
writer of the same school, “has no real significance except when applied
to the doings of an intelligent agent. Let any one conceive, if he can, of
any power, energy, or force inherent in a lump of matter.” Phenomena may
have the semblance of being produced by physical causes, but they are in
reality produced, say these writers, by the immediate agency of mind. All
things which do not proceed from a human (or, I suppose, an animal) will
proceed, they say, directly from divine will. The earth is not moved by
the combination of a centripetal and a projectile force; this is but a
mode of speaking, which serves to facilitate our conceptions. It is moved
by the direct volition of an omnipotent Being, in a path coinciding with
that which we deduce from the hypothesis of these two forces.

As I have so often observed, the general question of the existence of
Efficient Causes does not fall within the limits of our subject; but a
theory which represents them as capable of being subjects of human
knowledge, and which passes off as efficient causes what are only physical
or phenomenal causes, belongs as much to Logic as to metaphysics, and is a
fit subject for discussion here.

To my apprehension, a volition is not an efficient, but simply a physical
cause. Our will causes our bodily actions in the same sense, and in no
other, in which cold causes ice, or a spark causes an explosion of
gunpowder. The volition, a state of our mind, is the antecedent; the
motion of our limbs in conformity to the volition, is the consequent. This
sequence I conceive to be not a subject of direct consciousness, in the
sense intended by the theory. The antecedent, indeed, and the consequent,
are subjects of consciousness. But the connection between them is a
subject of experience. I can not admit that our consciousness of the
volition contains in itself any _a priori_ knowledge that the muscular
motion will follow. If our nerves of motion were paralyzed, or our muscles
stiff and inflexible, and had been so all our lives, I do not see the
slightest ground for supposing that we should ever (unless by information
from other people) have known any thing of volition as a physical power,
or been conscious of any tendency in feelings of our mind to produce
motions of our body, or of other bodies. I will not undertake to say
whether we should in that case have had the physical feeling which I
suppose is meant when these writers speak of “consciousness of effort:” I
see no reason why we should not; since that physical feeling is probably a
state of nervous sensation beginning and ending in the brain, without
involving the motory apparatus: but we certainly should not have
designated it by any term equivalent to effort, since effort implies
consciously aiming at an end, which we should not only in that case have
had no reason to do, but could not even have had the idea of doing. If
conscious at all of this peculiar sensation, we should have been conscious
of it, I conceive, only as a kind of uneasiness, accompanying our feelings
of desire.

It is well argued by Sir William Hamilton against the theory in question,
that it “is refuted by the consideration that between the overt fact of
corporeal movement of which we are cognizant, and the internal act of
mental determination of which we are also cognizant, there intervenes a
numerous series of intermediate agencies of which we have no knowledge;
and, consequently, that we can have no consciousness of any causal
connection between the extreme links of this chain, the volition to move
and the limb moving, as this hypothesis asserts. No one is immediately
conscious, for example, of moving his arm through his volition. Previously
to this ultimate movement, muscles, nerves, a multitude of solid and fluid
parts, must be set in motion by the will, but of this motion we know, from
consciousness, absolutely nothing. A person struck with paralysis is
conscious of no inability in his limb to fulfill the determinations of his
will; and it is only after having willed, and finding that his limbs do
not obey his volition, that he learns by this experience, that the
external movement does not follow the internal act. But as the paralytic
learns after the volition that his limbs do not obey his mind; so it is
only after volition that the man in health learns, that his limbs do obey
the mandates of his will.”(123)

Those against whom I am contending have never produced, and do not pretend
to produce, any positive evidence(124) that the power of our will to move
our bodies would be known to us independently of experience. What they
have to say on the subject is, that the production of physical events by a
will seems to carry its own explanation with it, while the action of
matter upon matter seems to require something else to explain it; and is
even, according to them, “inconceivable” on any other supposition than
that some will intervenes between the apparent cause and its apparent
effect. They thus rest their case on an appeal to the inherent laws of our
conceptive faculty; mistaking, as I apprehend, for the laws of that
faculty its acquired habits, grounded on the spontaneous tendencies of its
uncultured state. The succession between the will to move a limb and the
actual motion is one of the most direct and instantaneous of all sequences
which come under our observation, and is familiar to every moment’s
experience from our earliest infancy; more familiar than any succession of
events exterior to our bodies, and especially more so than any other case
of the apparent origination (as distinguished from the mere communication)
of motion. Now, it is the natural tendency of the mind to be always
attempting to facilitate its conception of unfamiliar facts by
assimilating them to others which are familiar. Accordingly, our voluntary
acts, being the most familiar to us of all cases of causation, are, in the
infancy and early youth of the human race, spontaneously taken as the type
of causation in general, and all phenomena are supposed to be directly
produced by the will of some sentient being. This original Fetichism I
shall not characterize in the words of Hume, or of any follower of Hume,
but in those of a religious metaphysician, Dr. Reid, in order more
effectually to show the unanimity which exists on the subject among all
competent thinkers.

“When we turn our attention to external objects, and begin to exercise our
rational faculties about them, we find that there are some motions and
changes in them which we have power to produce, and that there are many
which must have some other cause. Either the objects must have life and
active power, as we have, or they must be moved or changed by something
that has life and active power, as external objects are moved by us.

“Our first thoughts seem to be, that the objects in which we perceive such
motion have understanding and active power as we have. ‘Savages,’ says the
Abbé Raynal, ‘wherever they see motion which they can not account for,
there they suppose a soul.’ All men may be considered as savages in this
respect, until they are capable of instruction, and of using their
faculties in a more perfect manner than savages do.

“The Abbé Raynal’s observation is sufficiently confirmed, both from fact,
and from the structure of all languages.

“Rude nations do really believe sun, moon, and stars, earth, sea, and air,
fountains, and lakes, to have understanding and active power. To pay
homage to them, and implore their favor, is a kind of idolatry natural to
savages.

“All languages carry in their structure the marks of their being formed
when this belief prevailed. The distinction of verbs and participles into
active and passive, which is found in all languages, must have been
originally intended to distinguish what is really active from what is
merely passive; and in all languages, we find active verbs applied to
those objects, in which, according to the Abbé Raynal’s observation,
savages suppose a soul.

“Thus we say the sun rises and sets, and comes to the meridian, the moon
changes, the sea ebbs and flows, the winds blow. Languages were formed by
men who believed these objects to have life and active power in
themselves. It was therefore proper and natural to express their motions
and changes by active verbs.

“There is no surer way of tracing the sentiments of nations before they
have records, than by the structure of their language, which,
notwithstanding the changes produced in it by time, will always retain
some signatures of the thoughts of those by whom it was invented. When we
find the same sentiments indicated in the structure of all languages,
those sentiments must have been common to the human species when languages
were invented.

“When a few, of superior intellectual abilities, find leisure for
speculation, they begin to philosophize, and soon discover, that many of
those objects which at first they believed to be intelligent and active
are really lifeless and passive. This is a very important discovery. It
elevates the mind, emancipates from many vulgar superstitions, and invites
to further discoveries of the same kind.

“As philosophy advances, life and activity in natural objects retires, and
leaves them dead and inactive. Instead of moving voluntarily, we find them
to be moved necessarily; instead of acting, we find them to be acted upon;
and Nature appears as one great machine, where one wheel is turned by
another, that by a third; and how far this necessary succession may reach,
the philosopher does not know.”(125)

There is, then, a spontaneous tendency of the intellect to account to
itself for all cases of causation by assimilating them to the intentional
acts of voluntary agents like itself. This is the instinctive philosophy
of the human mind in its earliest stage, before it has become familiar
with any other invariable sequences than those between its own volitions
or those of other human beings and their voluntary acts. As the notion of
fixed laws of succession among external phenomena gradually establishes
itself, the propensity to refer all phenomena to voluntary agency slowly
gives way before it. The suggestions, however, of daily life continuing to
be more powerful than those of scientific thought, the original
instinctive philosophy maintains its ground in the mind, underneath the
growths obtained by cultivation, and keeps up a constant resistance to
their throwing their roots deep into the soil. The theory against which I
am contending derives its nourishment from that substratum. Its strength
does not lie in argument, but in its affinity to an obstinate tendency of
the infancy of the human mind.

That this tendency, however, is not the result of an inherent mental law,
is proved by superabundant evidence. The history of science, from its
earliest dawn, shows that mankind have not been unanimous in thinking
either that the action of matter upon matter was not conceivable, or that
the action of mind upon matter was. To some thinkers, and some schools of
thinkers, both in ancient and in modern times, this last has appeared much
more inconceivable than the former. Sequences entirely physical and
material, as soon as they had become sufficiently familiar to the human
mind, came to be thought perfectly natural, and were regarded not only as
needing no explanation themselves, but as being capable of affording it to
others, and even of serving as the ultimate explanation of things in
general.

One of the ablest recent supporters of the Volitional theory has furnished
an explanation, at once historically true and philosophically acute, of
the failure of the Greek philosophers in physical inquiry, in which, as I
conceive, he unconsciously depicts his own state of mind. “Their
stumbling-block was one as to the nature of the evidence they had to
expect for their conviction.... They had not seized the idea that they
must not expect to understand the processes of outward causes, but only
their results; and consequently, the whole physical philosophy of the
Greeks was an attempt to identify mentally the effect with its cause, to
feel after some not only necessary but natural connection, where they
meant by natural that which would _per se_ carry some presumption to their
own mind.... They wanted to see some _reason_ why the physical antecedent
should produce this particular consequent, and their only attempts were in
directions where they could find such reasons.”(126) In other words, they
were not content merely to know that one phenomenon was always followed by
another; they thought that they had not attained the true aim of science,
unless they could perceive something in the nature of the one phenomenon
from which it might have been known or presumed _previous to trial_ that
it would be followed by the other: just what the writer, who has so
clearly pointed out their error, thinks that he perceives in the nature of
the phenomenon Volition. And to complete the statement of the case, he
should have added that these early speculators not only made this their
aim, but were quite satisfied with their success in it; not only sought
for causes which should carry in their mere statement evidence of their
efficiency, but fully believed that they had found such causes. The
reviewer can see plainly that this was an error, because _he_ does not
believe that there exist any relations between material phenomena which
can account for their producing one another; but the very fact of the
persistency of the Greeks in this error, shows that their minds were in a
very different state: they were able to derive from the assimilation of
physical facts to other physical facts, the kind of mental satisfaction
which we connect with the word explanation, and which the reviewer would
have us think can only be found in referring phenomena to a will. When
Thales and Hippo held that moisture was the universal cause, and external
element, of which all other things were but the infinitely various
sensible manifestations; when Anaximenes predicated the same thing of air,
Pythagoras of numbers, and the like, they all thought that they had found
a real explanation; and were content to rest in this explanation as
ultimate. The ordinary sequences of the external universe appeared to
them, no less than to their critic, to be inconceivable without the
supposition of some universal agency to connect the antecedents with the
consequents; but they did not think that Volition, exerted by minds, was
the only agency which fulfilled this requirement. Moisture, or air, or
numbers, carried to their minds a precisely similar impression of making
intelligible what was otherwise inconceivable, and gave the same full
satisfaction to the demands of their conceptive faculty.

It was not the Greeks alone, who “wanted to see some reason why the
physical antecedent should produce this particular consequent,” some
connection “which would _per se_ carry some presumption to their own
mind.” Among modern philosophers, Leibnitz laid it down as a self-evident
principle that all physical causes without exception must contain in their
own nature something which makes it intelligible that they should be able
to produce the effects which they do produce. Far from admitting Volition
as the only kind of cause which carried internal evidence of its own
power, and as the real bond of connection between physical antecedents and
their consequents, he demanded some naturally and _per se_ efficient
physical antecedent as the bond of connection between Volition itself and
its effects. He distinctly refused to admit the will of God as a
sufficient explanation of any thing except miracles; and insisted upon
finding something that would account _better_ for the phenomena of nature
than a mere reference to divine volition.(127)

Again, and conversely, the action of mind upon matter (which, we are now
told, not only needs no explanation itself, but is the explanation of all
other effects), has appeared to some thinkers to be itself the grand
inconceivability. It was to get over this very difficulty that the
Cartesians invented the system of Occasional Causes. They could not
conceive that thoughts in a mind could produce movements in a body, or
that bodily movements could produce thoughts. They could see no necessary
connection, no relation _a priori_, between a motion and a thought. And as
the Cartesians, more than any other school of philosophical speculation
before or since, made their own minds the measure of all things, and
refused, on principle, to believe that Nature had done what they were
unable to see any reason why she must do, they affirmed it to be
impossible that a material and a mental fact could be causes one of
another. They regarded them as mere Occasions on which the real agent,
God, thought fit to exert his power as a Cause. When a man wills to move
his foot, it is not his will that moves it, but God (they said) moves it
on the occasion of his will. God, according to this system, is the only
efficient cause, not _quâ_ mind, or _quâ_ endowed with volition, but _quâ_
omnipotent. This hypothesis was, as I said, originally suggested by the
supposed inconceivability of any real mutual action between Mind and
Matter; but it was afterward extended to the action of Matter upon Matter,
for on a nicer examination they found this inconceivable too, and
therefore, according to their logic, impossible. The _deus ex machinâ_ was
ultimately called in to produce a spark on the occasion of a flint and
steel coming together, or to break an egg on the occasion of its falling
on the ground.

All this, undoubtedly, shows that it is the disposition of mankind in
general, not to be satisfied with knowing that one fact is invariably
antecedent and another consequent, but to look out for something which may
seem to explain their being so. But we also see that this demand may be
completely satisfied by an agency purely physical, provided it be much
more familiar than that which it is invoked to explain. To Thales and
Anaximenes, it appeared inconceivable that the antecedents which we see in
nature should produce the consequents; but perfectly natural that water,
or air, should produce them. The writers whom I oppose declare this
inconceivable, but can conceive that mind, or volition, is _per se_ an
efficient cause: while the Cartesians could not conceive even that, but
peremptorily declared that no mode of production of any fact whatever was
conceivable, except the direct agency of an omnipotent being; thus giving
additional proof of what finds new confirmation in every stage of the
history of science: that both what persons can, and what they can not,
conceive, is very much an affair of accident, and depends altogether on
their experience, and their habits of thought; that by cultivating the
requisite associations of ideas, people may make themselves unable to
conceive any given thing; and may make themselves able to conceive most
things, however inconceivable these may at first appear; and the same
facts in each person’s mental history which determine what is or is not
conceivable to him, determine also which among the various sequences in
nature will appear to him so natural and plausible, as to need no other
proof of their existence; to be evident by their own light, independent
equally of experience and of explanation.

By what rule is any one to decide between one theory of this description
and another? The theorists do not direct us to any external evidence; they
appeal each to his own subjective feelings. One says, the succession C B
appears to me more natural, conceivable, and credible _per se_, than the
succession A B; you are therefore mistaken in thinking that B depends upon
A; I am certain, though I can give no other evidence of it, that C comes
in between A and B, and is the real and only cause of B. The other
answers, the successions C B and A B appear to me equally natural and
conceivable, or the latter more so than the former: A is quite capable of
producing B without any other intervention. A third agrees with the first
in being unable to conceive that A can produce B, but finds the sequence D
B still more natural than C B, or of nearer kin to the subject-matter, and
prefers his D theory to the C theory. It is plain that there is no
universal law operating here, except the law that each person’s
conceptions are governed and limited by his individual experiences and
habits of thought. We are warranted in saying of all three, what each of
them already believes of the other two, namely, that they exalt into an
original law of the human intellect and of outward nature one particular
sequence of phenomena, which appears to them more natural and more
conceivable than other sequences, only because it is more familiar. And
from this judgment I am unable to except the theory, that Volition is an
Efficient Cause.

I am unwilling to leave the subject without adverting to the additional
fallacy contained in the corollary from this theory; in the inference that
because Volition is an efficient cause, therefore it is the only cause,
and the direct agent in producing even what is apparently produced by
something else. Volitions are not known to produce any thing directly
except nervous action, for the will influences even the muscles only
through the nerves. Though it were granted, then, that every phenomenon
has an efficient, and not merely a phenomenal cause, and that volition, in
the case of the peculiar phenomena which are known to be produced by it,
is that efficient cause; are we therefore to say, with these writers, that
since we know of no other efficient cause, and ought not to assume one
without evidence, there _is_ no other, and volition is the direct cause of
all phenomena? A more outrageous stretch of inference could hardly be
made. Because among the infinite variety of the phenomena of nature there
is one, namely, a particular mode of action of certain nerves, which has
for its cause, and as we are now supposing for its efficient cause, a
state of our mind; and because this is the only efficient cause of which
we are conscious, being the only one of which in the nature of the case we
_can_ be conscious, since it is the only one which exists within
ourselves; does this justify us in concluding that all other phenomena
must have the same kind of efficient cause with that one eminently
special, narrow, and peculiarly human or animal, phenomenon? The nearest
parallel to this specimen of generalization is suggested by the recently
revived controversy on the old subject of Plurality of Worlds, in which
the contending parties have been so conspicuously successful in
overthrowing one another. Here also we have experience only of a single
case, that of the world in which we live, but that this is inhabited we
know absolutely, and without possibility of doubt. Now if on this evidence
any one were to infer that every heavenly body without exception, sun,
planet, satellite, comet, fixed star or nebula, is inhabited, and must be
so from the inherent constitution of things, his inference would exactly
resemble that of the writers who conclude that because volition is the
efficient cause of our own bodily motions, it must be the efficient cause
of every thing else in the universe. It is true there are cases in which,
with acknowledged propriety, we generalize from a single instance to a
multitude of instances. But they must be instances which resemble the one
known instance, and not such as have no circumstance in common with it
except that of being instances. I have, for example, no direct evidence
that any creature is alive except myself, yet I attribute, with full
assurance, life and sensation to other human beings and animals. But I do
not conclude that all other things are alive merely because I am. I
ascribe to certain other creatures a life like my own, because they
manifest it by the same sort of indications by which mine is manifested. I
find that their phenomena and mine conform to the same laws, and it is for
this reason that I believe both to arise from a similar cause. Accordingly
I do not extend the conclusion beyond the grounds for it. Earth, fire,
mountains, trees, are remarkable agencies, but their phenomena do not
conform to the same laws as my actions do, and I therefore do not believe
earth or fire, mountains or trees, to possess animal life. But the
supporters of the Volition Theory ask us to infer that volition causes
every thing, for no reason except that it causes one particular thing;
although that one phenomenon, far from being a type of all natural
phenomena, is eminently peculiar; its laws bearing scarcely any
resemblance to those of any other phenomenon, whether of inorganic or of
organic nature.

NOTE SUPPLEMENTARY TO THE PRECEDING CHAPTER.


    The author of the Second Burnett Prize Essay (Dr. Tulloch), who
    has employed a considerable number of pages in controverting the
    doctrines of the preceding chapter, has somewhat surprised me by
    denying a fact, which I imagined too well known to require
    proof—that there have been philosophers who found in physical
    explanations of phenomena the same complete mental satisfaction
    which we are told is only given by volitional explanation, and
    others who denied the Volitional Theory on the same ground of
    inconceivability on which it is defended. The assertion of the
    Essayist is countersigned still more positively by an able
    reviewer of the Essay:(128) “Two illustrations,” says the
    reviewer, “are advanced by Mr. Mill: the case of Thales and
    Anaximenes, stated by him to have maintained, the one Moisture and
    the other Air to be the origin of all things; and that of
    Descartes and Leibnitz, whom he asserts to have found the action
    of Mind upon Matter the grand inconceivability. In
    counter-statement as to the first of these cases the author
    shows—what we believe now hardly admits of doubt—that the Greek
    philosophers distinctly recognized as beyond and above their
    primal material source, the νοῦς, or Divine Intelligence, as the
    efficient and originating Source of all; and as to the second, by
    proof that it was the _mode_, not the _fact_, of that action on
    matter, which was represented as inconceivable.”

    A greater quantity of historical error has seldom been comprised
    in a single sentence. With regard to Thales, the assertion that he
    considered water as a mere material in the hands of νοῦς rests on
    a passage of Cicero _de Naturâ Deorum_; and whoever will refer to
    any of the accurate historians of philosophy, will find that they
    treat this as a mere fancy of Cicero, resting on no authority,
    opposed to all the evidence; and make surmises as to the manner in
    which Cicero may have been led into the error. (See Rutter, vol.
    i., p. 211, 2d ed.; Brandis, vol. i., pp. 118-9, 1st ed.; Preller,
    _Historia Philosophiæ Græco-Romanæ_, p. 10. “Schiefe Ansicht,
    durchaus zu verwerfen;” “augenscheinlich folgernd statt zu
    berichten;” “quibus vera sententia Thaletis plane detorquetur,”
    are the expressions of these writers.) As for Anaximenes, he even
    according to Cicero, maintained, not that air was the material out
    of which God made the world, but that the air was a god:
    “Anaximenes aëra deum statuit;” or, according to St. Augustine,
    that it was the material out of which the gods were made; “non
    tamen ab ipsis [Diis] aërem factum, sed ipsos ex aëre ortos
    credidit.” Those who are not familiar with the metaphysical
    terminology of antiquity, must not be misled by finding it stated
    that Anaximenes attributed ψυχὴ (translated _soul_, or _life_) to
    his universal element, the air. The Greek philosophers
    acknowledged several kinds of ψυχὴ, the nutritive, the sensitive,
    and the intellective.(129) Even the moderns, with admitted
    correctness, attribute life to plants. As far as we can make out
    the meaning of Anaximenes, he made choice of Air as the universal
    agent, on the ground that it is perpetually in motion, without any
    apparent cause external to itself: so that he conceived it as
    exercising spontaneous force, and as the principle of life and
    activity in all things, men and gods inclusive. If this be not
    representing it as the Efficient Cause the dispute altogether has
    no meaning.

    If either Anaximenes, or Thales, or any of their contemporaries,
    had held the doctrine that νοῦς was the Efficient Cause, that
    doctrine could not have been reputed, as it was throughout
    antiquity, to have originated with Anaxagoras. The testimony of
    Aristotle, in the first book of his Metaphysics, is perfectly
    decisive with respect to these early speculations. After
    enumerating four kinds of causes, or rather four different
    meanings of the word Cause, viz., the Essence of a thing, the
    Matter of it, the Origin of Motion (Efficient Cause), and the End
    or Final Cause, he proceeds to say, that most of the early
    philosophers recognized only the second kind of Cause, the Matter
    of a thing, τὰς ἐν ὕλης εἶδει μόνας ᾠήθησαν ἀρχὰς εἷναι πάντων. As
    his first example he specifies Thales, whom he describes as taking
    the lead in this view of the subject, ὁ τῆς τοιαύτης ἀρχηγὸς
    φιλοσοφίας, and goes on to Hippon, Anaximenes, Diogenes (of
    Apollonia), Hippasus of Metapontum, Heraclitus, and Empedocles.
    Anaxagoras, however (he proceeds to say), taught a different
    doctrine, as we _know_, and it is _alleged_ that Hermotimus of
    Clazomenæ taught it before him. Anaxagoras represented, that even
    if these various theories of the universal material were true,
    there would be need of some other cause to account for the
    transformations of the materials, since the material can not
    originate its own changes: οὐ γὰρ δὴ τό γε ὑποκείμενον αὐτὸ ποιεὶ
    μεταβάλλειν ἑαῦτο; λέγω δ᾽ οἰον οὐτε τὸ ξύλον οὔτε ὁ χαλκὸς αἴτιος
    τοῦ μεταβάλλειν ἑκάτερον αὐτῶν, οὐδὲ ποιεῖ τὸ μὲν ξύλον κλίνην ὁ
    δέ χαλκὸς ἀνδριάντα, ἀλλ᾽ ἑτερόν τι τῆς μεταβολῆς αἴτιον, viz.,
    the other kind of cause, ὄθεν ἡ ἀρχὴ τῆς κινήσεως—an Efficient
    Cause. Aristotle expresses great approbation of this doctrine
    (which he says made its author appear the only sober man among
    persons raving, οἰον νήφων ἐφάνη παρ᾽ εἰκῆ λέγοντας τοῦς
    πρότερον); but while describing the influence which it exercised
    over subsequent speculation, he remarks that the philosophers
    against whom this, as he thinks, insuperable difficulty was urged,
    had not felt it to be any difficulty: οὐδέν ἐδυσχεράναν ἐν
    ἑαυτοῖς. It is surely unnecessary to say more in proof of the
    matter of fact which Dr. Tulloch and his reviewer disbelieve.

    Having pointed out what he thinks the error of these early
    speculators in not recognizing the need of an efficient cause,
    Aristotle goes on to mention two other efficient causes to which
    they might have had recourse, instead of intelligence: τύχη,
    chance, and τὸ αὐτομάτον, spontaneity. He indeed puts these aside
    as not sufficiently worthy causes for the order in the universe,
    οὐδ᾽ αὑ τωῷ αὐτομάτῳ καὶ τῇ τύχῃ τοσοῦτον ἐπιτρέψαι πρᾶγμα καλῶς
    εἰχεν; but he does not reject them as incapable of producing _any_
    effect, but only as incapable of producing _that_ effect. He
    himself recognizes τύχη and τὸ αὐτομάτον as co-ordinate agents
    with Mind in producing the phenomena of the universe; the
    department allotted to them being composed of all the classes of
    phenomena which are not supposed to follow any uniform law. By
    thus including Chance among efficient causes, Aristotle fell into
    an error which philosophy has now outgrown, but which is by no
    means so alien to the spirit even of modern speculation as it may
    at first sight appear. Up to quite a recent period philosophers
    went on ascribing, and many of them have not yet ceased to
    ascribe, a real existence to the results of abstraction. Chance
    could make out as good a title to that dignity as many other of
    the mind’s abstract creations: it had had a name given to it, and
    why should it not be a reality? As for τὸ αὐτομάτον, it is
    recognized even yet as one of the modes of origination of
    phenomena by all those thinkers who maintain what is called the
    Freedom of the Will. The same self-determining power which that
    doctrine attributes to volitions, was supposed by the ancients to
    be possessed also by some other natural phenomena: a circumstance
    which throws considerable light on more than one of the supposed
    invincible necessities of belief. I have introduced it here,
    because this belief of Aristotle, or rather of the Greek
    philosophers generally, is as fatal as the doctrines of Thales and
    the Ionic school to the theory that the human mind is compelled by
    its constitution to conceive volition as the origin of all force,
    and the efficient cause of all phenomena.(130)

    With regard to the modern philosophers (Leibnitz and the
    Cartesians) whom I had cited as having maintained that the action
    of mind upon matter, so far from being the only conceivable origin
    of material phenomena, is itself inconceivable; the attempt to
    rebut this argument by asserting that the mode, not the fact, of
    the action of mind on matter was represented as inconceivable, is
    an abuse of the privilege of writing confidently about authors
    without reading them; for any knowledge whatever of Leibnitz would
    have taught those who thus speak of him, that the inconceivability
    of the mode, and the impossibility of the thing, were in his mind
    convertible expressions. What was his famous Principle of the
    Sufficient Reason, the very corner-stone of his Philosophy, from
    which the Pre-established Harmony, the doctrine of Monads, and all
    the opinions most characteristic of Leibnitz, were corollaries? It
    was, that nothing exists, the existence of which is not capable of
    being proved and explained _a priori_; the proof and explanation
    in the case of contingent facts being derived from the nature of
    their causes; which could not be the causes unless there was
    something in their nature showing them to be capable of producing
    those particular effects. And this “something” which accounts for
    the production of physical effects, he was able to find in many
    physical causes, but could not find it in any finite minds, which
    therefore he unhesitatingly asserted to be incapable of producing
    any physical effects whatever. “On ne saurait concevoir,” he says,
    “une action réciproque de la matière et de l’intelligence l’une
    sur l’autre,” and there is therefore (he contends) no choice but
    between the Occasional Causes of the Cartesians and his own
    Pre-established Harmony, according to which there is no more
    connection between our volitions and our muscular actions than
    there is between two clocks which are wound up to strike at the
    same instant. But he felt no similar difficulty as to physical
    causes; and throughout his speculations, as in the passage I have
    already cited respecting gravitation, he distinctly refuses to
    consider as part of the order of nature any fact which is not
    explicable from the nature of its physical cause.

    With regard to the Cartesians (not Descartes; I did not make that
    mistake, though the reviewer of Dr. Tulloch’s Essay attributes it
    to me) I take a passage almost at random from Malebranche, who is
    the best known of the Cartesians, and, though not the inventor of
    the system of Occasional Causes, is its principal expositor. In
    Part II., chap. iii., of his Sixth Book, having first said that
    matter can not have the power of moving itself, he proceeds to
    argue that neither can mind have the power of moving it. “Quand on
    examine l’idée que l’on a de tous les esprits finis, on ne voit
    point de liaison nécessaire entre leur volonté et le mouvement de
    quelque corps que ce soit, on voit au contraire qu’il n’y en a
    point, et qu’il n’y en peut avoir” (there is nothing in the idea
    of finite mind which can account for its causing the motion of a
    body); “on doit aussi conclure, si on vent raisonner selon ses
    lumières, qu’il n’y a aucun esprit créé qui puisse remuer quelque
    corps que ce soit comme cause véritable on principale, de même que
    l’on a dit qu’aucun corps ne se pouvait remuer soi-même:” thus the
    idea of Mind is according to him as incompatible as the idea of
    Matter with the exercise of active force. But when, he continues,
    we consider not a created but a Divine Mind, the case is altered;
    for the idea of a Divine Mind includes omnipotence; and the idea
    of omnipotence does contain the idea of being able to move bodies.
    Thus it is the nature of omnipotence which renders the motion of
    bodies even by the Divine Mind credible or conceivable, while, so
    far as depended on the mere nature of mind, it would have been
    inconceivable and incredible. If Malebranche had not believed in
    an omnipotent Being, he would have held all action of mind on body
    to be a demonstrated impossibility.(131)

    A doctrine more precisely the reverse of the Volitional theory of
    causation can not well be imagined. The Volitional theory is, that
    we know by intuition or by direct experience the action of our own
    mental volitions on matter; that we may hence infer all other
    action upon matter to be that of volition, and might thus know,
    without any other evidence, that matter is under the government of
    a Divine Mind. Leibnitz and the Cartesians, on the contrary,
    maintain that our volitions do not and can not act upon matter,
    and that it is only the existence of an all-governing Being, and
    that Being omnipotent, which can account for the sequence between
    our volitions and our bodily actions. When we consider that each
    of these two theories, which, as theories of causation, stand at
    the opposite extremes of possible divergence from one another,
    invokes not only as its evidence, but as its sole evidence, the
    absolute inconceivability of any theory but itself, we are enabled
    to measure the worth of this kind of evidence: and when we find
    the Volitional theory entirely built upon the assertion that by
    our mental constitution we are compelled to recognize our
    volitions as efficient causes, and then find other thinkers
    maintaining that we know that they are not and can not be such
    causes, and can not conceive them to be so, I think we have a
    right to say that this supposed law of our mental constitution
    does not exist.

    Dr. Tulloch (pp. 45-47) thinks it a sufficient answer to this,
    that Leibnitz and the Cartesians were Theists, and believed the
    will of God to be an efficient cause. Doubtless they did, and the
    Cartesians even believed (though Leibnitz did not) that it is the
    only such cause. Dr. Tulloch mistakes the nature of the question.
    I was not writing on Theism, as Dr. Tulloch is, but against a
    particular theory of causation, which, if it be unfounded, can
    give no effective support to Theism or to any thing else. I found
    it asserted that volition is the only efficient cause, on the
    ground that no other efficient cause is conceivable. To this
    assertion I oppose the instances of Leibnitz and of the
    Cartesians, who affirmed with equal positiveness that volition as
    an efficient cause is itself not conceivable, and that
    omnipotence, which renders all things conceivable, can alone take
    away the impossibility. This I thought, and think, a conclusive
    answer to the argument on which this theory of causation avowedly
    depends. But I certainly did not imagine that Theism was bound up
    with that theory; nor expected to be charged with denying Leibnitz
    and the Cartesians to be Theists because I denied that they held
    the theory.




                               Chapter VI.


On The Composition Of Causes.


§ 1. To complete the general notion of causation on which the rules of
experimental inquiry into the laws of nature must be founded, one
distinction still remains to be pointed out: a distinction so radical, and
of so much importance, as to require a chapter to itself.

The preceding discussions have rendered us familiar with the case in which
several agents, or causes, concur as conditions to the production of an
effect; a case, in truth, almost universal, there being very few effects
to the production of which no more than one agent contributes. Suppose,
then, that two different agents, operating jointly, are followed, under a
certain set of collateral conditions, by a given effect. If either of
these agents, instead of being joined with the other, had operated alone,
under the same set of conditions in all other respects, some effect would
probably have followed, which would have been different from the joint
effect of the two, and more or less dissimilar to it. Now, if we happen to
know what would be the effect of each cause when acting separately from
the other, we are often able to arrive deductively, or _a priori_, at a
correct prediction of what will arise from their conjunct agency. To
render this possible, it is only necessary that the same law which
expresses the effect of each cause acting by itself, shall also correctly
express the part due to that cause of the effect which follows from the
two together. This condition is realized in the extensive and important
class of phenomena commonly called mechanical, namely the phenomena of the
communication of motion (or of pressure, which is tendency to motion) from
one body to another. In this important class of cases of causation, one
cause never, properly speaking, defeats or frustrates another; both have
their full effect. If a body is propelled in two directions by two forces,
one tending to drive it to the north and the other to the east, it is
caused to move in a given time exactly as far in both directions as the
two forces would separately have carried it; and is left precisely where
it would have arrived if it had been acted upon first by one of the two
forces, and afterward by the other. This law of nature is called, in
dynamics, the principle of the Composition of Forces; and in imitation of
that well-chosen expression, I shall give the name of the Composition of
Causes to the principle which is exemplified in all cases in which the
joint effect of several causes is identical with the sum of their separate
effects.

This principle, however, by no means prevails in all departments of the
field of nature. The chemical combination of two substances produces, as
is well known, a third substance, with properties different from those of
either of the two substances separately, or of both of them taken
together. Not a trace of the properties of hydrogen or of oxygen is
observable in those of their compound, water. The taste of sugar of lead
is not the sum of the tastes of its component elements, acetic acid and
lead or its oxide; nor is the color of blue vitriol a mixture of the
colors of sulphuric acid and copper. This explains why mechanics is a
deductive or demonstrative science, and chemistry not. In the one, we can
compute the effects of combinations of causes, whether real or
hypothetical, from the laws which we know to govern those causes when
acting separately, because they continue to observe the same laws when in
combination which they observe when separate: whatever would have happened
in consequence of each cause taken by itself, happens when they are
together, and we have only to cast up the results. Not so in the phenomena
which are the peculiar subject of the science of chemistry. There most of
the uniformities to which the causes conform when separate, cease
altogether when they are conjoined; and we are not, at least in the
present state of our knowledge, able to foresee what result will follow
from any new combination until we have tried the specific experiment.

If this be true of chemical combinations, it is still more true of those
far more complex combinations of elements which constitute organized
bodies; and in which those extraordinary new uniformities arise which are
called the laws of life. All organized bodies are composed of parts
similar to those composing inorganic nature, and which have even
themselves existed in an inorganic state; but the phenomena of life, which
result from the juxtaposition of those parts in a certain manner, bear no
analogy to any of the effects which would be produced by the action of the
component substances considered as mere physical agents. To whatever
degree we might imagine our knowledge of the properties of the several
ingredients of a living body to be extended and perfected, it is certain
that no mere summing up of the separate actions of those elements will
ever amount to the action of the living body itself. The tongue, for
instance, is, like all other parts of the animal frame, composed of
gelatine, fibrine, and other products of the chemistry of digestion; but
from no knowledge of the properties of those substances could we ever
predict that it could taste, unless gelatine or fibrine could themselves
taste; for no elementary fact can be in the conclusion which was not in
the premises.

There are thus two different modes of the conjunct action of causes; from
which arise two modes of conflict, or mutual interference, between laws of
nature. Suppose, at a given point of time and space, two or more causes,
which, if they acted separately, would produce effects contrary, or at
least conflicting with each other; one of them tending to undo, wholly or
partially, what the other tends to do. Thus the expansive force of the
gases generated by the ignition of gunpowder tends to project a bullet
toward the sky, while its gravity tends to make it fall to the ground. A
stream running into a reservoir at one end tends to fill it higher and
higher, while a drain at the other extremity tends to empty it. Now, in
such cases as these, even if the two causes which are in joint action
exactly annul one another, still the laws of both are fulfilled; the
effect is the same as if the drain had been open for half an hour
first,(132) and the stream had flowed in for as long afterward. Each agent
produces the same amount of effect as if it had acted separately, though
the contrary effect which was taking place during the same time
obliterated it as fast as it was produced. Here, then, are two causes,
producing by their joint operations an effect which at first seems quite
dissimilar to those which they produce separately, but which on
examination proves to be really the sum of those separate effects. It will
be noticed that we here enlarge the idea of the sum of two effects, so as
to include what is commonly called their difference, but which is in
reality the result of the addition of opposites; a conception to which
mankind are indebted for that admirable extension of the algebraical
calculus, which has so vastly increased its powers as an instrument of
discovery, by introducing into its reasonings (with the sign of
subtraction prefixed, and under the name of Negative Quantities) every
description whatever of positive phenomena, provided they are of such a
quality in reference to those previously introduced, that to add the one
is equivalent to subtracting an equal quantity of the other.

There is, then, one mode of the mutual interference of laws of nature, in
which, even when the concurrent causes annihilate each other’s effects,
each exerts its full efficacy according to its own law—its law as a
separate agent. But in the other description of cases, the agencies which
are brought together cease entirely, and a totally different set of
phenomena arise: as in the experiment of two liquids which, when mixed in
certain proportions, instantly become, not a larger amount of liquid, but
a solid mass.

§ 2. This difference between the case in which the joint effect of causes
is the sum of their separate effects, and the case in which it is
heterogeneous to them—between laws which work together without alteration,
and laws which, when called upon to work together, cease and give place to
others—is one of the fundamental distinctions in nature. The former case,
that of the Composition of Causes, is the general one; the other is always
special and exceptional. There are no objects which do not, as to some of
their phenomena, obey the principle of the Composition of Causes; none
that have not some laws which are rigidly fulfilled in every combination
into which the objects enter. The weight of a body, for instance, is a
property which it retains in all the combinations in which it is placed.
The weight of a chemical compound, or of an organized body, is equal to
the sum of the weights of the elements which compose it. The weight either
of the elements or of the compound will vary, if they be carried farther
from their centre of attraction, or brought nearer to it; but whatever
effects the one effects the other. They always remain precisely equal. So,
again, the component parts of a vegetable or animal substance do not lose
their mechanical and chemical properties as separate agents, when, by a
peculiar mode of juxtaposition, they, as an aggregate whole, acquire
physiological or vital properties in addition. Those bodies continue, as
before, to obey mechanical and chemical laws, in so far as the operation
of those laws is not counteracted by the new laws which govern them as
organized beings; when, in short, a concurrence of causes takes place
which calls into action new laws bearing no analogy to any that we can
trace in the separate operation of the causes, the new laws, while they
supersede one portion of the previous laws, may co-exist with another
portion, and may even compound the effect of those previous laws with
their own.

Again, laws which were themselves generated in the second mode, may
generate others in the first. Though there are laws which, like those of
chemistry and physiology, owe their existence to a breach of the principle
of Composition of Causes, it does not follow that these peculiar, or, as
they might be termed, _heteropathic_ laws, are not capable of composition
with one another. The causes which by one combination have had their laws
altered, may carry their new laws with them unaltered into their ulterior
combinations. And hence there is no reason to despair of ultimately
raising chemistry and physiology to the condition of deductive sciences;
for though it is impossible to deduce all chemical and physiological
truths from the laws or properties of simple substances or elementary
agents, they may possibly be deducible from laws which commence when these
elementary agents are brought together into some moderate number of not
very complex combinations. The Laws of Life will never be deducible from
the mere laws of the ingredients, but the prodigiously complex Facts of
Life may all be deducible from comparatively simple laws of life; which
laws (depending indeed on combinations, but on comparatively simple
combinations, of antecedents) may, in more complex circumstances, be
strictly compounded with one another, and with the physical and chemical
laws of the ingredients. The details of the vital phenomena, even now,
afford innumerable exemplifications of the Composition of Causes; and in
proportion as these phenomena are more accurately studied, there appears
more reason to believe that the same laws which operate in the simpler
combinations of circumstances do, in fact, continue to be observed in the
more complex. This will be found equally true in the phenomena of mind;
and even in social and political phenomena, the results of the laws of
mind. It is in the case of chemical phenomena that the least progress has
yet been made in bringing the special laws under general ones from which
they may be deduced; but there are even in chemistry many circumstances to
encourage the hope that such general laws will hereafter be discovered.
The different actions of a chemical compound will never, undoubtedly, be
found to be the sums of the actions of its separate elements; but there
may exist, between the properties of the compound and those of its
elements, some constant relation, which, if discoverable by a sufficient
induction, would enable us to foresee the sort of compound which will
result from a new combination before we have actually tried it, and to
judge of what sort of elements some new substance is compounded before we
have analyzed it. The law of definite proportions, first discovered in its
full generality by Dalton, is a complete solution of this problem in one,
though but a secondary aspect, that of quantity; and in respect to
quality, we have already some partial generalizations, sufficient to
indicate the possibility of ultimately proceeding farther. We can
predicate some common properties of the kind of compounds which result
from the combination, in each of the small number of possible proportions,
of any acid whatever with any base. We have also the curious law,
discovered by Berthollet, that two soluble salts mutually decompose one
another whenever the new combinations which result produce an insoluble
compound, or one less soluble than the two former. Another uniformity is
that called the law of isomorphism; the identity of the crystalline forms
of substances which possess in common certain peculiarities of chemical
composition.(133) Thus it appears that even heteropathic laws, such laws
of combined agency as are not compounded of the laws of the separate
agencies, are yet, at least in some cases, derived from them according to
a fixed principle. There may, therefore, be laws of the generation of laws
from others dissimilar to them; and in chemistry, these undiscovered laws
of the dependence of the properties of the compound on the properties of
its elements, may, together with the laws of the elements themselves,
furnish the premises by which the science is perhaps destined one day to
be rendered deductive.

It would seem, therefore, that there is no class of phenomena in which the
Composition of Causes does not obtain: that as a general rule, causes in
combination produce exactly the same effects as when acting singly: but
that this rule, though general, is not universal: that in some instances,
at some particular points in the transition from separate to united
action, the laws change, and an entirely new set of effects are either
added to, or take the place of, those which arise from the separate agency
of the same causes: the laws of these new effects being again susceptible
of composition, to an indefinite extent, like the laws which they
superseded.

§ 3. That effects are proportional to their causes is laid down by some
writers as an axiom in the theory of causation; and great use is sometimes
made of this principle in reasonings respecting the laws of nature, though
it is encumbered with many difficulties and apparent exceptions, which
much ingenuity has been expended in showing not to be real ones. This
proposition, in so far as it is true, enters as a particular case into the
general principle of the Composition of Causes; the causes compounded
being, in this instance, homogeneous; in which case, if in any, their
joint effect might be expected to be identical with the sum of their
separate effects. If a force equal to one hundred weight will raise a
certain body along an inclined plane, a force equal to two hundred weight
will raise two bodies exactly similar, and thus the effect is proportional
to the cause. But does not a force equal to two hundred weight actually
contain in itself two forces each equal to one hundred weight, which, if
employed apart, would separately raise the two bodies in question? The
fact, therefore, that when exerted jointly they raise both bodies at once,
results from the Composition of Causes, and is a mere instance of the
general fact that mechanical forces are subject to the law of Composition.
And so in every other case which can be supposed. For the doctrine of the
proportionality of effects to their causes can not of course be applicable
to cases in which the augmentation of the cause alters the kind of effect;
that is, in which the surplus quantity superadded to the cause does not
become compounded with it, but the two together generate an altogether new
phenomenon. Suppose that the application of a certain quantity of heat to
a body merely increases its bulk, that a double quantity melts it, and a
triple quantity decomposes it: these three effects being heterogeneous, no
ratio, whether corresponding or not to that of the quantities of heat
applied, can be established between them. Thus the supposed axiom of the
proportionality of effects to their causes fails at the precise point
where the principle of the Composition of Causes also fails; viz., where
the concurrence of causes is such as to determine a change in the
properties of the body generally, and render it subject to new laws, more
or less dissimilar to those to which it conformed in its previous state.
The recognition, therefore, of any such law of proportionality is
superseded by the more comprehensive principle, in which as much of it as
is true is implicitly asserted.(134)

The general remarks on causation, which seemed necessary as an
introduction to the theory of the inductive process, may here terminate.
That process is essentially an inquiry into cases of causation. All the
uniformities which exist in the succession of phenomena, and most of the
uniformities in their co-existence, are either, as we have seen,
themselves laws of causation, or consequences resulting from, and
corollaries capable of being deduced from, such laws. If we could
determine what causes are correctly assigned to what effects, and what
effects to what causes, we should be virtually acquainted with the whole
course of nature. All those uniformities which are mere results of
causation might then be explained and accounted for; and every individual
fact or event might be predicted, provided we had the requisite data, that
is, the requisite knowledge of the circumstances which, in the particular
instance, preceded it.

To ascertain, therefore, what are the laws of causation which exist in
nature; to determine the effect of every cause, and the causes of all
effects, is the main business of Induction; and to point out how this is
done is the chief object of Inductive Logic.




                               Chapter VII.


On Observation And Experiment.


§ 1. It results from the preceding exposition, that the process of
ascertaining what consequents, in nature, are invariably connected with
what antecedents, or in other words what phenomena are related to each
other as causes and effects, is in some sort a process of analysis. That
every fact which begins to exist has a cause, and that this cause must be
found in some fact or concourse of facts which immediately preceded the
occurrence, may be taken for certain. The whole of the present facts are
the infallible result of all past facts, and more immediately of all the
facts which existed at the moment previous. Here, then, is a great
sequence, which we know to be uniform. If the whole prior state of the
entire universe could again recur, it would again be followed by the
present state. The question is, how to resolve this complex uniformity
into the simpler uniformities which compose it, and assign to each portion
of the vast antecedent the portion of the consequent which is attendant on
it.

This operation, which we have called analytical, inasmuch as it is the
resolution of a complex whole into the component elements, is more than a
merely mental analysis. No mere contemplation of the phenomena, and
partition of them by the intellect alone, will of itself accomplish the
end we have now in view. Nevertheless, such a mental partition is an
indispensable first step. The order of nature, as perceived at a first
glance, presents at every instant a chaos followed by another chaos. We
must decompose each chaos into single facts. We must learn to see in the
chaotic antecedent a multitude of distinct antecedents, in the chaotic
consequent a multitude of distinct consequents. This, supposing it done,
will not of itself tell us on which of the antecedents each consequent is
invariably attendant. To determine that point, we must endeavor to effect
a separation of the facts from one another, not in our minds only, but in
nature. The mental analysis, however, must take place first. And every one
knows that in the mode of performing it, one intellect differs immensely
from another. It is the essence of the act of observing; for the observer
is not he who merely sees the thing which is before his eyes, but he who
sees what parts that thing is composed of. To do this well is a rare
talent. One person, from inattention, or attending only in the wrong
place, overlooks half of what he sees; another sets down much more than he
sees, confounding it with what he imagines, or with what he infers;
another takes note of the _kind_ of all the circumstances, but being
inexpert in estimating their degree, leaves the quantity of each vague and
uncertain; another sees indeed the whole, but makes such an awkward
division of it into parts, throwing things into one mass which require to
be separated, and separating others which might more conveniently be
considered as one, that the result is much the same, sometimes even worse,
than if no analysis had been attempted at all. It would be possible to
point out what qualities of mind, and modes of mental culture, fit a
person for being a good observer: that, however, is a question not of
Logic, but of the Theory of Education, in the most enlarged sense of the
term. There is not properly an Art of Observing. There may be rules for
observing. But these, like rules for inventing, are properly instructions
for the preparation of one’s own mind; for putting it into the state in
which it will be most fitted to observe, or most likely to invent. They
are, therefore, essentially rules of self-education, which is a different
thing from Logic. They do not teach how to do the thing, but how to make
ourselves capable of doing it. They are an art of strengthening the limbs,
not an art of using them.

The extent and minuteness of observation which may be requisite, and the
degree of decomposition to which it may be necessary to carry the mental
analysis, depend on the particular purpose in view. To ascertain the state
of the whole universe at any particular moment is impossible, but would
also be useless. In making chemical experiments, we do not think it
necessary to note the position of the planets; because experience has
shown, as a very superficial experience is sufficient to show, that in
such cases that circumstance is not material to the result: and
accordingly, in the ages when men believed in the occult influences of the
heavenly bodies, it might have been unphilosophical to omit ascertaining
the precise condition of those bodies at the moment of the experiment. As
to the degree of minuteness of the mental subdivision, if we were obliged
to break down what we observe into its very simplest elements, that is,
literally into single facts, it would be difficult to say where we should
find them; we can hardly ever affirm that our divisions of any kind have
reached the ultimate unit. But this, too, is fortunately unnecessary. The
only object of the mental separation is to suggest the requisite physical
separation, so that we may either accomplish it ourselves, or seek for it
in nature; and we have done enough when we have carried the subdivision as
far as the point at which we are able to see what observations or
experiments we require. It is only essential, at whatever point our mental
decomposition of facts may for the present have stopped, that we should
hold ourselves ready and able to carry it further as occasion requires,
and should not allow the freedom of our discriminating faculty to be
imprisoned by the swathes and bands of ordinary classification; as was the
case with all early speculative inquirers, not excepting the Greeks, to
whom it seldom occurred that what was called by one abstract name might,
in reality, be several phenomena, or that there was a possibility of
decomposing the facts of the universe into any elements but those which
ordinary language already recognized.

§ 2. The different antecedents and consequents being, then, supposed to
be, so far as the case requires, ascertained and discriminated from one
another, we are to inquire which is connected with which. In every
instance which comes under our observation, there are many antecedents and
many consequents. If those antecedents could not be severed from one
another except in thought, or if those consequents never were found apart,
it would be impossible for us to distinguish (_a posteriori_ at least) the
real laws, or to assign to any cause its effect, or to any effect its
cause. To do so, we must be able to meet with some of the antecedents
apart from the rest, and observe what follows from them; or some of the
consequents, and observe by what they are preceded. We must, in short,
follow the Baconian rule of _varying the circumstances_. This is, indeed,
only the first rule of physical inquiry, and not, as some have thought,
the sole rule; but it is the foundation of all the rest.

For the purpose of varying the circumstances, we may have recourse
(according to a distinction commonly made) either to observation or to
experiment; we may either _find_ an instance in nature suited to our
purposes, or, by an artificial arrangement of circumstances, _make_ one.
The value of the instance depends on what it is in itself, not on the mode
in which it is obtained: its employment for the purposes of induction
depends on the same principles in the one case and in the other; as the
uses of money are the same whether it is inherited or acquired. There is,
in short, no difference in kind, no real logical distinction, between the
two processes of investigation. There are, however, practical distinctions
to which it is of considerable importance to advert.

§ 3. The first and most obvious distinction between Observation and
Experiment is, that the latter is an immense extension of the former. It
not only enables us to produce a much greater number of variations in the
circumstances than nature spontaneously offers, but also, in thousands of
cases, to produce the precise _sort_ of variation which we are in want of
for discovering the law of the phenomenon; a service which nature, being
constructed on a quite different scheme from that of facilitating our
studies, is seldom so friendly as to bestow upon us. For example, in order
to ascertain what principle in the atmosphere enables it to sustain life,
the variation we require is that a living animal should be immersed in
each component element of the atmosphere separately. But nature does not
supply either oxygen or azote in a separate state. We are indebted to
artificial experiment for our knowledge that it is the former, and not the
latter, which supports respiration; and for our knowledge of the very
existence of the two ingredients.

Thus far the advantage of experimentation over simple observation is
universally recognized: all are aware that it enables us to obtain
innumerable combinations of circumstances which are not to be found in
nature, and so add to nature’s experiments a multitude of experiments of
our own. But there is another superiority (or, as Bacon would have
expressed it, another prerogative) of instances artificially obtained over
spontaneous instances—of our own experiments over even the same
experiments when made by nature—which is not of less importance, and which
is far from being felt and acknowledged in the same degree.

When we can produce a phenomenon artificially, we can take it, as it were,
home with us, and observe it in the midst of circumstances with which in
all other respects we are accurately acquainted. If we desire to know what
are the effects of the cause A, and are able to produce A by means at our
disposal, we can generally determine at our own discretion, so far as is
compatible with the nature of the phenomenon A, the whole of the
circumstances which shall be present along with it: and thus, knowing
exactly the simultaneous state of every thing else which is within the
reach of A’s influence, we have only to observe what alteration is made in
that state by the presence of A.

For example, by the electric machine we can produce, in the midst of known
circumstances, the phenomena which nature exhibits on a grander scale in
the form of lightning and thunder. Now let any one consider what amount of
knowledge of the effects and laws of electric agency mankind could have
obtained from the mere observation of thunder-storms, and compare it with
that which they have gained, and may expect to gain, from electrical and
galvanic experiments. This example is the more striking, now that we have
reason to believe that electric action is of all natural phenomena (except
heat) the most pervading and universal, which, therefore, it might
antecedently have been supposed could stand least in need of artificial
means of production to enable it to be studied; while the fact is so much
the contrary, that without the electric machine, the Leyden jar, and the
voltaic battery, we probably should never have suspected the existence of
electricity as one of the great agents in nature; the few electric
phenomena we should have known of would have continued to be regarded
either as supernatural, or as a sort of anomalies and eccentricities in
the order of the universe.

When we have succeeded in insulating the phenomenon which is the subject
of inquiry, by placing it among known circumstances, we may produce
further variations of circumstances to any extent, and of such kinds as we
think best calculated to bring the laws of the phenomenon into a clear
light. By introducing one well-defined circumstance after another into the
experiment, we obtain assurance of the manner in which the phenomenon
behaves under an indefinite variety of possible circumstances. Thus,
chemists, after having obtained some newly-discovered substance in a pure
state (that is, having made sure that there is nothing present which can
interfere with and modify its agency), introduce various other substances,
one by one, to ascertain whether it will combine with them, or decompose
them, and with what result; and also apply heat, or electricity, or
pressure, to discover what will happen to the substance under each of
these circumstances.

But if, on the other hand, it is out of our power to produce the
phenomenon, and we have to seek for instances in which nature produces it,
the task before us is very different.

Instead of being able to choose what the concomitant circumstances shall
be, we now have to discover what they are; which, when we go beyond the
simplest and most accessible cases, it is next to impossible to do with
any precision and completeness. Let us take, as an exemplification of a
phenomenon which we have no means of fabricating artificially, a human
mind. Nature produces many; but the consequence of our not being able to
produce them by art is, that in every instance in which we see a human
mind developing itself, or acting upon other things, we see it surrounded
and obscured by an indefinite multitude of unascertainable circumstances,
rendering the use of the common experimental methods almost delusive. We
may conceive to what extent this is true, if we consider, among other
things, that whenever Nature produces a human mind, she produces, in close
connection with it, a body; that is, a vast complication of physical
facts, in no two cases perhaps exactly similar, and most of which (except
the mere structure, which we can examine in a sort of coarse way after it
has ceased to act), are radically out of the reach of our means of
exploration. If, instead of a human mind, we suppose the subject of
investigation to be a human society or State, all the same difficulties
recur in a greatly augmented degree.

We have thus already come within sight of a conclusion, which the progress
of the inquiry will, I think, bring before us with the clearest evidence:
namely, that in the sciences which deal with phenomena in which artificial
experiments are impossible (as in the case of astronomy), or in which they
have a very limited range (as in mental philosophy, social science, and
even physiology), induction from direct experience is practiced at a
disadvantage in most cases equivalent to impracticability; from which it
follows that the methods of those sciences, in order to accomplish any
thing worthy of attainment, must be to a great extent, if not principally,
deductive. This is already known to be the case with the first of the
sciences we have mentioned, astronomy; that it is not generally recognized
as true of the others, is probably one of the reasons why they are not in
a more advanced state.

§ 4. If what is called pure observation is at so great a disadvantage,
compared with artificial experimentation, in one department of the direct
exploration of phenomena, there is another branch in which the advantage
is all on the side of the former.

Inductive inquiry having for its object to ascertain what causes are
connected with what effects, we may begin this search at either end of the
road which leads from the one point to the other: we may either inquire
into the effects of a given cause or into the causes of a given effect.
The fact that light blackens chloride of silver might have been discovered
either by experiments on light, trying what effect it would produce on
various substances, or by observing that portions of the chloride had
repeatedly become black, and inquiring into the circumstances. The effect
of the urali poison might have become known either by administering it to
animals, or by examining how it happened that the wounds which the Indians
of Guiana inflict with their arrows prove so uniformly mortal. Now it is
manifest from the mere statement of the examples, without any theoretical
discussion, that artificial experimentation is applicable only to the
former of these modes of investigation. We can take a cause, and try what
it will produce; but we can not take an effect, and try what it will be
produced by. We can only watch till we see it produced, or are enabled to
produce it by accident.

This would be of little importance, if it always depended on our choice
from which of the two ends of the sequence we would undertake our
inquiries. But we have seldom any option. As we can only travel from the
known to the unknown, we are obliged to commence at whichever end we are
best acquainted with. If the agent is more familiar to us than its
effects, we watch for, or contrive, instances of the agent, under such
varieties of circumstances as are open to us, and observe the result. If,
on the contrary, the conditions on which a phenomenon depends are obscure,
but the phenomenon itself familiar, we must commence our inquiry from the
effect. If we are struck with the fact that chloride of silver has been
blackened, and have no suspicion of the cause, we have no resource but to
compare instances in which the fact has chanced to occur, until by that
comparison we discover that in all those instances the substances had been
exposed to light. If we knew nothing of the Indian arrows but their fatal
effect, accident alone could turn our attention to experiments on the
urali; in the regular course of investigation, we could only inquire, or
try to observe, what had been done to the arrows in particular instances.

Wherever, having nothing to guide us to the cause, we are obliged to set
out from the effect, and to apply the rule of varying the circumstances to
the consequents, not the antecedents, we are necessarily destitute of the
resource of artificial experimentation. We can not, at our choice, obtain
consequents, as we can antecedents, under any set of circumstances
compatible with their nature. There are no means of producing effects but
through their causes, and by the supposition the causes of the effect in
question are not known to us. We have, therefore, no expedient but to
study it where it offers itself spontaneously. If nature happens to
present us with instances sufficiently varied in their circumstances, and
if we are able to discover, either among the proximate antecedents or
among some other order of antecedents, something which is always found
when the effect is found, however various the circumstances, and never
found when it is not, we may discover, by mere observation without
experiment, a real uniformity in nature.

But though this is certainly the most favorable case for sciences of pure
observation, as contrasted with those in which artificial experiments are
possible, there is in reality no case which more strikingly illustrates
the inherent imperfection of direct induction when not founded on
experimentation. Suppose that, by a comparison of cases of the effect, we
have found an antecedent which appears to be, and perhaps is, invariably
connected with it: we have not yet proved that antecedent to be the cause
until we have reversed the process, and produced the effect by means of
that antecedent. If we can produce the antecedent artificially, and if,
when we do so, the effect follows, the induction is complete; that
antecedent is the cause of that consequent.(135) But we have then added
the evidence of experiment to that of simple observation. Until we had
done so, we had only proved _invariable_ antecedence within the limits of
experience, but not _unconditional_ antecedence, or causation. Until it
had been shown by the actual production of the antecedent under known
circumstances, and the occurrence thereupon of the consequent, that the
antecedent was really the condition on which it depended; the uniformity
of succession which was proved to exist between them might, for aught we
knew, be (like the succession of day and night) not a case of causation at
all; both antecedent and consequent might be successive stages of the
effect of an ulterior cause. Observation, in short, without experiment
(supposing no aid from deduction) can ascertain sequences and
co-existences, but can not prove causation.

In order to see these remarks verified by the actual state of the
sciences, we have only to think of the condition of natural history. In
zoology, for example, there is an immense number of uniformities
ascertained, some of co-existence, others of succession, to many of which,
notwithstanding considerable variations of the attendant circumstances, we
know not any exception: but the antecedents, for the most part, are such
as we can not artificially produce; or if we can, it is only by setting in
motion the exact process by which nature produces them; and this being to
us a mysterious process, of which the main circumstances are not only
unknown but unobservable, we do not succeed in obtaining the antecedents
under known circumstances. What is the result? That on this vast subject,
which affords so much and such varied scope for observation, we have made
most scanty progress in ascertaining any laws of causation. We know not
with certainty, in the case of most of the phenomena that we find
conjoined, which is the condition of the other; which is cause, and which
effect, or whether either of them is so, or they are not rather conjunct
effects of causes yet to be discovered, complex results of laws hitherto
unknown.

Although some of the foregoing observations may be, in technical
strictness of arrangement, premature in this place, it seemed that a few
general remarks on the difference between sciences of mere observation and
sciences of experimentation, and the extreme disadvantage under which
directly inductive inquiry is necessarily carried on in the former, were
the best preparation for discussing the methods of direct induction; a
preparation rendering superfluous much that must otherwise have been
introduced, with some inconvenience, into the heart of that discussion. To
the consideration of these methods we now proceed.




                              Chapter VIII.


Of The Four Methods Of Experimental Inquiry.


§ 1. The simplest and most obvious modes of singling out from among the
circumstances which precede or follow a phenomenon, those with which it is
really connected by an invariable law, are two in number. One is, by
comparing together different instances in which the phenomenon occurs. The
other is, by comparing instances in which the phenomenon does occur, with
instances in other respects similar in which it does not. These two
methods may be respectively denominated, the Method of Agreement, and the
Method of Difference.

In illustrating these methods, it will be necessary to bear in mind the
twofold character of inquiries into the laws of phenomena; which may be
either inquiries into the cause of a given effect, or into the effects or
properties of a given cause. We shall consider the methods in their
application to either order of investigation, and shall draw our examples
equally from both.

We shall denote antecedents by the large letters of the alphabet, and the
consequents corresponding to them by the small. Let A, then, be an agent
or cause, and let the object of our inquiry be to ascertain what are the
effects of this cause. If we can either find, or produce, the agent A in
such varieties of circumstances that the different cases have no
circumstance in common except A; then whatever effect we find to be
produced in all our trials, is indicated as the effect of A. Suppose, for
example, that A is tried along with B and C, and that the effect is _a b
c_; and suppose that A is next tried with D and E, but without B and C,
and that the effect is _a d e_. Then we may reason thus: _b_ and _c_ are
not effects of A, for they were not produced by it in the second
experiment; nor are _d_ and _e_, for they were not produced in the first.
Whatever is really the effect of A must have been produced in both
instances; now this condition is fulfilled by no circumstance except _a_.
The phenomenon _a_ can not have been the effect of B or C, since it was
produced where they were not; nor of D or E, since it was produced where
they were not. Therefore it is the effect of A.

For example, let the antecedent A be the contact of an alkaline substance
and an oil. This combination being tried under several varieties of
circumstances, resembling each other in nothing else, the results agree in
the production of a greasy and detersive or saponaceous substance: it is
therefore concluded that the combination of an oil and an alkali causes
the production of a soap. It is thus we inquire, by the Method of
Agreement, into the effect of a given cause.

In a similar manner we may inquire into the cause of a given effect. Let
_a_ be the effect. Here, as shown in the last chapter, we have only the
resource of observation without experiment: we can not take a phenomenon
of which we know not the origin, and try to find its mode of production by
producing it: if we succeeded in such a random trial it could only be by
accident. But if we can observe a in two different combinations, _a b c_
and _a d e_; and if we know, or can discover, that the antecedent
circumstances in these cases respectively were A B C and A D E, we may
conclude by a reasoning similar to that in the preceding example, that A
is the antecedent connected with the consequent _a_ by a law of causation.
B and C, we may say, can not be causes of _a_, since on its second
occurrence they were not present; nor are D and E, for they were not
present on its first occurrence. A, alone of the five circumstances, was
found among the antecedents of _a_ in both instances.

For example, let the effect _a_ be crystallization. We compare instances
in which bodies are known to assume crystalline structure, but which have
no other point of agreement; and we find them to have one, and as far as
we can observe, only one, antecedent in common: the deposition of a solid
matter from a liquid state, either a state of fusion or of solution. We
conclude, therefore, that the solidification of a substance from a liquid
state is an invariable antecedent of its crystallization.

In this example we may go further, and say, it is not only the invariable
antecedent but the cause; or at least the proximate event which completes
the cause. For in this case we are able, after detecting the antecedent A,
to produce it artificially, and by finding that _a_ follows it, verify the
result of our induction. The importance of thus reversing the proof was
strikingly manifested when, by keeping a phial of water charged with
siliceous particles undisturbed for years, a chemist (I believe Dr.
Wollaston) succeeded in obtaining crystals of quartz; and in the equally
interesting experiment in which Sir James Hall produced artificial marble
by the cooling of its materials from fusion under immense pressure: two
admirable examples of the light which may be thrown upon the most secret
processes of Nature by well-contrived interrogation of her.

But if we can not artificially produce the phenomenon A, the conclusion
that it is the cause of _a_ remains subject to very considerable doubt.
Though an invariable, it may not be the unconditional antecedent of _a_,
but may precede it as day precedes night or night day. This uncertainty
arises from the impossibility of assuring ourselves that A is the _only_
immediate antecedent common to both the instances. If we could be certain
of having ascertained all the invariable antecedents, we might be sure
that the unconditional invariable antecedent, or cause, must be found
somewhere among them. Unfortunately it is hardly ever possible to
ascertain all the antecedents, unless the phenomenon is one which we can
produce artificially. Even then, the difficulty is merely lightened, not
removed: men knew how to raise water in pumps long before they adverted to
what was really the operating circumstance in the means they employed,
namely, the pressure of the atmosphere on the open surface of the water.
It is, however, much easier to analyze completely a set of arrangements
made by ourselves, than the whole complex mass of the agencies which
nature happens to be exerting at the moment of the production of a given
phenomenon. We may overlook some of the material circumstances in an
experiment with an electrical machine; but we shall, at the worst, be
better acquainted with them than with those of a thunder-storm.

The mode of discovering and proving laws of nature, which we have now
examined, proceeds on the following axiom: Whatever circumstances can be
excluded, without prejudice to the phenomenon, or can be absent
notwithstanding its presence, is not connected with it in the way of
causation. The casual circumstances being thus eliminated, if only one
remains, that one is the cause which we are in search of: if more than
one, they either are, or contain among them, the cause; and so, _mutatis
mutandis_, of the effect. As this method proceeds by comparing different
instances to ascertain in what they agree, I have termed it the Method of
Agreement; and we may adopt as its regulating principal the following
canon:

FIRST CANON.

_If two or more instances of the phenomenon under investigation have only
one circumstance in common, the circumstance in which alone all the
instances agree, is the cause (or effect) of the given phenomenon._

Quitting for the present the Method of Agreement, to which we shall almost
immediately return, we proceed to a still more potent instrument of the
investigation of nature, the Method of Difference.

§ 2. In the Method of Agreement, we endeavored to obtain instances which
agreed in the given circumstance but differed in every other: in the
present method we require, on the contrary, two instances resembling one
another in every other respect, but differing in the presence or absence
of the phenomenon we wish to study. If our object be to discover the
effects of an agent A, we must procure A in some set of ascertained
circumstances, as A B C, and having noted the effects produced, compare
them with the effect of the remaining circumstances B C, when A is absent.
If the effect of A B C is _a b c_, and the effect of B C _b c_, it is
evident that the effect of A is _a_. So again, if we begin at the other
end, and desire to investigate the cause of an effect _a_, we must select
an instance, as _a b c_, in which the effect occurs, and in which the
antecedents were A B C, and we must look out for another instance in which
the remaining circumstances, _b c_, occur without _a_. If the antecedents,
in that instance, are B C, we know that the cause of _a_ must be A: either
A alone, or A in conjunction with some of the other circumstances present.

It is scarcely necessary to give examples of a logical process to which we
owe almost all the inductive conclusions we draw in daily life. When a man
is shot through the heart, it is by this method we know that it was the
gunshot which killed him: for he was in the fullness of life immediately
before, all circumstances being the same, except the wound.

The axioms implied in this method are evidently the following. Whatever
antecedent can not be excluded without preventing the phenomenon, is the
cause, or a condition, of that phenomenon: whatever consequent can be
excluded, with no other difference in the antecedents than the absence of
a particular one, is the effect of that one. Instead of comparing
different instances of a phenomenon, to discover in what they agree, this
method compares an instance of its occurrence with an instance of its
non-occurrence, to discover in what they differ. The canon which is the
regulating principle of the Method of Difference may be expressed as
follows:

SECOND CANON.

_If an instance in which the phenomenon under investigation occurs, and an
instance in which it does not occur, have every circumstance in common
save one, that one occurring only in the former; the circumstance in which
alone the two instances differ, is the effect, or the cause, or an
indispensable part of the cause, of the phenomenon._

§ 3. The two methods which we have now stated have many features of
resemblance, but there are also many distinctions between them. Both are
methods of _elimination_. This term (employed in the theory of equations
to denote the process by which one after another of the elements of a
question is excluded, and the solution made to depend on the relation
between the remaining elements only) is well suited to express the
operation, analogous to this, which has been understood since the time of
Bacon to be the foundation of experimental inquiry: namely, the successive
exclusion of the various circumstances which are found to accompany a
phenomenon in a given instance, in order to ascertain what are those among
them which can be absent consistently with the existence of the
phenomenon. The Method of Agreement stands on the ground that whatever can
be eliminated, is not connected with the phenomenon by any law. The Method
of Difference has for its foundation, that whatever can not be eliminated,
is connected with the phenomenon by a law.

Of these methods, that of Difference is more particularly a method of
artificial experiment; while that of Agreement is more especially the
resource employed where experimentation is impossible. A few reflections
will prove the fact, and point out the reason of it.

It is inherent in the peculiar character of the Method of Difference, that
the nature of the combinations which it requires is much more strictly
defined than in the Method of Agreement. The two instances which are to be
compared with one another must be exactly similar, in all circumstances
except the one which we are attempting to investigate: they must be in the
relation of A B C and B C, or of _a b c_ and _b c_. It is true that this
similarity of circumstances needs not extend to such as are already known
to be immaterial to the result. And in the case of most phenomena we learn
at once, from the commonest experience, that most of the co-existent
phenomena of the universe may be either present or absent without
affecting the given phenomenon; or, if present, are present indifferently
when the phenomenon does not happen and when it does. Still, even limiting
the identity which is required between the two instances, A B C and B C,
to such circumstances as are not already known to be indifferent, it is
very seldom that nature affords two instances, of which we can be assured
that they stand in this precise relation to one another. In the
spontaneous operations of nature there is generally such complication and
such obscurity, they are mostly either on so overwhelmingly large or on so
inaccessibly minute a scale, we are so ignorant of a great part of the
facts which really take place, and even those of which we are not ignorant
are so multitudinous, and therefore so seldom exactly alike in any two
cases, that a spontaneous experiment, of the kind required by the Method
of Difference, is commonly not to be found. When, on the contrary, we
obtain a phenomenon by an artificial experiment, a pair of instances such
as the method requires is obtained almost as a matter of course, provided
the process does not last a long time. A certain state of surrounding
circumstances existed before we commenced the experiment; this is B C. We
then introduce A; say, for instance, by merely bringing an object from
another part of the room, before there has been time for any change in the
other elements. It is, in short (as M. Comté observes), the very nature of
an experiment, to introduce into the pre-existing state of circumstances a
change perfectly definite. We choose a previous state of things with which
we are well acquainted, so that no unforeseen alteration in that state is
likely to pass unobserved; and into this we introduce, as rapidly as
possible, the phenomenon which we wish to study; so that in general we are
entitled to feel complete assurance that the pre-existing state, and the
state which we have produced, differ in nothing except the presence or
absence of that phenomenon. If a bird is taken from a cage, and instantly
plunged into carbonic acid gas, the experimentalist may be fully assured
(at all events after one or two repetitions) that no circumstance capable
of causing suffocation had supervened in the interim, except the change
from immersion in the atmosphere to immersion in carbonic acid gas. There
is one doubt, indeed, which may remain in some cases of this description;
the effect may have been produced not by the change, but by the means
employed to produce the change. The possibility, however, of this last
supposition generally admits of being conclusively tested by other
experiments. It thus appears that in the study of the various kinds of
phenomena which we can, by our voluntary agency, modify or control, we can
in general satisfy the requisitions of the Method of Difference; but that
by the spontaneous operations of nature those requisitions are seldom
fulfilled.

The reverse of this is the case with the Method of Agreement. We do not
here require instances of so special and determinate a kind. Any instances
whatever, in which nature presents us with a phenomenon, may be examined
for the purposes of this method; and if all such instances agree in any
thing, a conclusion of considerable value is already attained. We can
seldom, indeed, be sure that the one point of agreement is the only one;
but this ignorance does not, as in the Method of Difference, vitiate the
conclusion; the certainty of the result, as far as it goes, is not
affected. We have ascertained one invariable antecedent or consequent,
however many other invariable antecedents or consequents may still remain
unascertained. If A B C, A D E, A F G, are all equally followed by a, then
a is an invariable consequent of A. If _a b c_, _a d e_, _a f g_, all
number A among their antecedents, then A is connected as an antecedent, by
some invariable law, with _a_. But to determine whether this invariable
antecedent is a cause, or this invariable consequent an effect, we must be
able, in addition, to produce the one by means of the other; or, at least,
to obtain that which alone constitutes our assurance of having produced
any thing, namely, an instance in which the effect, _a_, has come into
existence, with no other change in the pre-existing circumstances than the
addition of A. And this, if we can do it, is an application of the Method
of Difference, not of the Method of Agreement.

It thus appears to be by the Method of Difference alone that we can ever,
in the way of direct experience, arrive with certainty at causes. The
Method of Agreement leads only to laws of phenomena (as some writers call
them, but improperly, since laws of causation are also laws of phenomena):
that is, to uniformities, which either are not laws of causation, or in
which the question of causation must for the present remain undecided. The
Method of Agreement is chiefly to be resorted to, as a means of suggesting
applications of the Method of Difference (as in the last example the
comparison of A B C, A D E, A F G, suggested that A was the antecedent on
which to try the experiment whether it could produce _a_); or as an
inferior resource, in case the Method of Difference is impracticable;
which, as we before showed, generally arises from the impossibility of
artificially producing the phenomena. And hence it is that the Method of
Agreement, though applicable in principle to either case, is more
emphatically the method of investigation on those subjects where
artificial experimentation is impossible; because on those it is,
generally, our only resource of a directly inductive nature; while, in the
phenomena which we can produce at pleasure, the Method of Difference
generally affords a more efficacious process, which will ascertain causes
as well as mere laws.

§ 4. There are, however, many cases in which, though our power of
producing the phenomenon is complete, the Method of Difference either can
not be made available at all, or not without a previous employment of the
Method of Agreement. This occurs when the agency by which we can produce
the phenomenon is not that of one single antecedent, but a combination of
antecedents, which we have no power of separating from each other, and
exhibiting apart. For instance, suppose the subject of inquiry to be the
cause of the double refraction of light. We can produce this phenomenon at
pleasure, by employing any one of the many substances which are known to
refract light in that peculiar manner. But if, taking one of those
substances, as Iceland spar, for example, we wish to determine on which of
the properties of Iceland spar this remarkable phenomenon depends, we can
make no use, for that purpose, of the Method of Difference; for we can not
find another substance precisely resembling Iceland spar except in some
one property. The only mode, therefore, of prosecuting this inquiry is
that afforded by the Method of Agreement; by which, in fact, through a
comparison of all the known substances which have the property of doubly
refracting light, it was ascertained that they agree in the circumstance
of being crystalline substances; and though the converse does not hold,
though all crystalline substances have not the property of double
refraction, it was concluded, with reason, that there is a real connection
between these two properties; that either crystalline structure, or the
cause which gives rise to that structure, is one of the conditions of
double refraction.

Out of this employment of the Method of Agreement arises a peculiar
modification of that method, which is sometimes of great avail in the
investigation of nature. In cases similar to the above, in which it is not
possible to obtain the precise pair of instances which our second canon
requires—instances agreeing in every antecedent except A, or in every
consequent except _a_, we may yet be able, by a double employment of the
Method of Agreement, to discover in what the instances which contain A or
_a_ differ from those which do not.

If we compare various instances in which _a_ occurs, and find that they
all have in common the circumstance A, and (as far as can be observed) no
other circumstance, the Method of Agreement, so far, bears testimony to a
connection between A and _a_. In order to convert this evidence of
connection into proof of causation by the direct Method of Difference, we
ought to be able, in some one of these instances, as for example, A B C,
to leave out A, and observe whether by doing so, _a_ is prevented. Now
supposing (what is often the case) that we are not able to try this
decisive experiment; yet, provided we can by any means discover what would
be its result if we could try it, the advantage will be the same. Suppose,
then, that as we previously examined a variety of instances in which _a_
occurred, and found them to agree in containing A, so we now observe a
variety of instances in which _a_ does not occur, and find them agree in
not containing A; which establishes, by the Method of Agreement, the same
connection between the absence of A and the absence of _a_, which was
before established between their presence. As, then, it had been shown
that whenever A is present _a_ is present, so, it being now shown that
when A is taken away a is removed along with it, we have by the one
proposition A B C, _a b c_, by the other B C, _b c_, the positive and
negative instances which the Method of Difference requires.

This method may be called the Indirect Method of Difference, or the Joint
Method of Agreement and Difference; and consists in a double employment of
the Method of Agreement, each proof being independent of the other, and
corroborating it. But it is not equivalent to a proof by the direct Method
of Difference. For the requisitions of the Method of Difference are not
satisfied, unless we can be quite sure either that the instances
affirmative of _a_ agree in no antecedent whatever but A, or that the
instances negative of _a_ agree in nothing but the negation of A. Now, if
it were possible, which it never is, to have this assurance, we should not
need the joint method; for either of the two sets of instances separately
would then be sufficient to prove causation. This indirect method,
therefore, can only be regarded as a great extension and improvement of
the Method of Agreement, but not as participating in the more cogent
nature of the Method of Difference. The following may be stated as its
canon:

THIRD CANON.

_If two or more instances in which the phenomenon occurs have only one
circumstance in common, while two or more instances in which it does not
occur have nothing in common save the absence of that circumstance, the
circumstance in which alone the two sets of instances differ, is the
effect, or the cause, or an indispensable part of the cause, of the
phenomenon._

We shall presently see that the Joint Method of Agreement and Difference
constitutes, in another respect not yet adverted to, an improvement upon
the common Method of Agreement, namely, in being unaffected by a
characteristic imperfection of that method, the nature of which still
remains to be pointed out. But as we can not enter into this exposition
without introducing a new element of complexity into this long and
intricate discussion, I shall postpone it to a subsequent chapter, and
shall at once proceed to a statement of two other methods, which will
complete the enumeration of the means which mankind possess for exploring
the laws of nature by specific observation and experience.

§ 5. The first of these has been aptly denominated the Method of Residues.
Its principle is very simple. Subducting from any given phenomenon all the
portions which, by virtue of preceding inductions, can be assigned to
known causes, the remainder will be the effect of the antecedents which
had been overlooked, or of which the effect was as yet an unknown
quantity.

Suppose, as before, that we have the antecedents A B C, followed by the
consequents _a b c_, and that by previous inductions (founded, we will
suppose, on the Method of Difference) we have ascertained the causes of
some of these effects, or the effects of some of these causes; and are
thence apprised that the effect of A is _a_, and that the effect of B is
_b_. Subtracting the sum of these effects from the total phenomenon, there
remains _c_, which now, without any fresh experiments, we may know to be
the effect of C. This Method of Residues is in truth a peculiar
modification of the Method of Difference. If the instance A B C, _a b c_,
could have been compared with a single instance A B, _a b_, we should have
proved C to be the cause of _c_, by the common process of the Method of
Difference. In the present case, however, instead of a single instance A
B, we have had to study separately the causes A and B, and to infer from
the effects which they produce separately what effect they must produce in
the case A B C, where they act together. Of the two instances, therefore,
which the Method of Difference requires—the one positive, the other
negative—the negative one, or that in which the given phenomenon is
absent, is not the direct result of observation and experiment, but has
been arrived at by deduction. As one of the forms of the Method of
Difference, the Method of Residues partakes of its rigorous certainty,
provided the previous inductions, those which gave the effects of A and B,
were obtained by the same infallible method, and provided we are certain
that C is the _only_ antecedent to which the residual phenomenon _c_ can
be referred; the only agent of which we had not already calculated and
subducted the effect. But as we can never be quite certain of this, the
evidence derived from the Method of Residues is not complete unless we can
obtain C artificially, and try it separately, or unless its agency, when
once suggested, can be accounted for, and proved deductively from known
laws.

Even with these reservations, the Method of Residues is one of the most
important among our instruments of discovery. Of all the methods of
investigating laws of nature, this is the most fertile in unexpected
results: often informing us of sequences in which neither the cause nor
the effect were sufficiently conspicuous to attract of themselves the
attention of observers. The agent C may be an obscure circumstance, not
likely to have been perceived unless sought for, nor likely to have been
sought for until attention had been awakened by the insufficiency of the
obvious causes to account for the whole of the effect. And _c_ may be so
disguised by its intermixture with _a_ and _b_, that it would scarcely
have presented itself spontaneously as a subject of separate study. Of
these uses of the method, we shall presently cite some remarkable
examples. The canon of the Method of Residues is as follows:

FOURTH CANON.

_Subduct from any phenomenon such part as is known by previous inductions
to be the effect of certain antecedents, and the residue of the phenomenon
is the effect of the remaining antecedents._

§ 6. There remains a class of laws which it is impracticable to ascertain
by any of the three methods which I have attempted to characterize:
namely, the laws of those Permanent Causes, or indestructible natural
agents, which it is impossible either to exclude or to isolate; which we
can neither hinder from being present, nor contrive that they shall be
present alone. It would appear at first sight that we could by no means
separate the effects of these agents from the effects of those other
phenomena with which they can not be prevented from co-existing. In
respect, indeed, to most of the permanent causes, no such difficulty
exists; since, though we can not eliminate them as co-existing facts, we
can eliminate them as influencing agents, by simply trying our experiment
in a local situation beyond the limits of their influence. The pendulum,
for example, has its oscillations disturbed by the vicinity of a mountain:
we remove the pendulum to a sufficient distance from the mountain, and the
disturbance ceases: from these data we can determine by the Method of
Difference, the amount of effect due to the mountain; and beyond a certain
distance every thing goes on precisely as it would do if the mountain
exercised no influence whatever, which, accordingly, we, with sufficient
reason, conclude to be the fact.

The difficulty, therefore, in applying the methods already treated of to
determine the effects of Permanent Causes, is confined to the cases in
which it is impossible for us to get out of the local limits of their
influence. The pendulum can be removed from the influence of the mountain,
but it can not be removed from the influence of the earth: we can not take
away the earth from the pendulum, nor the pendulum from the earth, to
ascertain whether it would continue to vibrate if the action which the
earth exerts upon it were withdrawn. On what evidence, then, do we ascribe
its vibrations to the earth’s influence? Not on any sanctioned by the
Method of Difference; for one of the two instances, the negative instance,
is wanting. Nor by the Method of Agreement; for though all pendulums agree
in this, that during their oscillations the earth is always present, why
may we not as well ascribe the phenomenon to the sun, which is equally a
co-existent fact in all the experiments? It is evident that to establish
even so simple a fact of causation as this, there was required some method
over and above those which we have yet examined.

As another example, let us take the phenomenon Heat. Independently of all
hypothesis as to the real nature of the agency so called, this fact is
certain, that we are unable to exhaust any body of the whole of its heat.
It is equally certain that no one ever perceived heat not emanating from a
body. Being unable, then, to separate Body and Heat, we can not effect
such a variation of circumstances as the foregoing three methods require;
we can not ascertain, by those methods, what portion of the phenomena
exhibited by any body is due to the heat contained in it. If we could
observe a body with its heat, and the same body entirely divested of heat,
the Method of Difference would show the effect due to the heat, apart from
that due to the body. If we could observe heat under circumstances
agreeing in nothing but heat, and therefore not characterized also by the
presence of a body, we could ascertain the effects of heat, from an
instance of heat with a body and an instance of heat without a body, by
the Method of Agreement; or we could determine by the Method of Difference
what effect was due to the body, when the remainder which was due to the
heat would be given by the Method of Residues. But we can do none of these
things; and without them the application of any of the three methods to
the solution of this problem would be illusory. It would be idle, for
instance, to attempt to ascertain the effect of heat by subtracting from
the phenomena exhibited by a body all that is due to its other properties;
for as we have never been able to observe any bodies without a portion of
heat in them, effects due to that heat might form a part of the very
results which we were affecting to subtract, in order that the effect of
heat might be shown by the residue.

If, therefore, there were no other methods of experimental investigation
than these three, we should be unable to determine the effects due to heat
as a cause. But we have still a resource. Though we can not exclude an
antecedent altogether, we may be able to produce, or nature may produce
for us some modification in it. By a modification is here meant, a change
in it not amounting to its total removal. If some modification in the
antecedent A is always followed by a change in the consequent _a_, the
other consequents _b_ and _c_ remaining the same; or _vicè versa_, if
every change in _a_ is found to have been preceded by some modification in
A, none being observable in any of the other antecedents, we may safely
conclude that _a_ is, wholly or in part, an effect traceable to A, or at
least in some way connected with it through causation. For example, in the
case of heat, though we can not expel it altogether from any body, we can
modify it in quantity, we can increase or diminish it; and doing so, we
find by the various methods of experimentation or observation already
treated of, that such increase or diminution of heat is followed by
expansion or contraction of the body. In this manner we arrive at the
conclusion, otherwise unattainable by us, that one of the effects of heat
is to enlarge the dimensions of bodies; or, what is the same thing in
other words, to widen the distances between their particles.

A change in a thing, not amounting to its total removal, that is, a change
which leaves it still the same thing it was, must be a change either in
its quantity, or in some of its variable relations to other things, of
which variable relations the principal is its position in space. In the
previous example, the modification which was produced in the antecedent
was an alteration in its quantity. Let us now suppose the question to be,
what influence the moon exerts on the surface of the earth. We can not try
an experiment in the absence of the moon, so as to observe what
terrestrial phenomena her annihilation would put an end to; but when we
find that all the variations in the _position_ of the moon are followed by
corresponding variations in the time and place of high water, the place
being always either the part of the earth which is nearest to, or that
which is most remote from, the moon, we have ample evidence that the moon
is, wholly or partially, the cause which determines the tides. It very
commonly happens, as it does in this instance, that the variations of an
effect are correspondent, or analogous, to those of its cause; as the moon
moves farther toward the east, the high-water point does the same: but
this is not an indispensable condition, as may be seen in the same
example, for along with that high-water point there is at the same instant
another high-water point diametrically opposite to it, and which,
therefore, of necessity, moves toward the west, as the moon, followed by
the nearer of the tide waves, advances toward the east: and yet both these
motions are equally effects of the moon’s motion.

That the oscillations of the pendulum are caused by the earth, is proved
by similar evidence. Those oscillations take place between equidistant
points on the two sides of a line, which, being perpendicular to the
earth, varies with every variation in the earth’s position, either in
space or relatively to the object. Speaking accurately, we only know by
the method now characterized, that all terrestrial bodies tend to the
earth, and not to some unknown fixed point lying in the same direction. In
every twenty-four hours, by the earth’s rotation, the line drawn from the
body at right angles to the earth coincides successively with all the
radii of a circle, and in the course of six months the place of that
circle varies by nearly two hundred millions of miles; yet in all these
changes of the earth’s position, the line in which bodies tend to fall
continues to be directed toward it: which proves that terrestrial gravity
is directed to the earth, and not, as was once fancied by some, to a fixed
point of space.

The method by which these results were obtained may be termed the Method
of Concomitant Variations; it is regulated by the following canon:

FIFTH CANON.

_Whatever phenomenon varies in any manner whenever another phenomenon
varies in some particular manner, is either a cause or an effect of that
phenomenon, or is connected with it through some fact of causation._

The last clause is subjoined, because it by no means follows when two
phenomena accompany each other in their variations, that the one is cause
and the other effect. The same thing may, and indeed must happen,
supposing them to be two different effects of a common cause: and by this
method alone it would never be possible to ascertain which of the
suppositions is the true one. The only way to solve the doubt would be
that which we have so often adverted to, viz., by endeavoring to ascertain
whether we can produce the one set of variations by means of the other. In
the case of heat, for example, by increasing the temperature of a body we
increase its bulk, but by increasing its bulk we do not increase its
temperature; on the contrary (as in the rarefaction of air under the
receiver of an air-pump), we generally diminish it: therefore heat is not
an effect, but a cause, of increase of bulk. If we can not ourselves
produce the variations, we must endeavor, though it is an attempt which is
seldom successful, to find them produced by nature in some case in which
the pre-*existing circumstances are perfectly known to us.

It is scarcely necessary to say, that in order to ascertain the uniform
concomitance of variations in the effect with variations in the cause, the
same precautions must be used as in any other case of the determination of
an invariable sequence. We must endeavor to retain all the other
antecedents unchanged, while that particular one is subjected to the
requisite series of variations; or, in other words, that we may be
warranted in inferring causation from concomitance of variations, the
concomitance itself must be proved by the Method of Difference.

It might at first appear that the Method of Concomitant Variations assumes
a new axiom, or law of causation in general, namely, that every
modification of the cause is followed by a change in the effect. And it
does usually happen that when a phenomenon A causes a phenomenon _a_, any
variation in the quantity or in the various relations of A, is uniformly
followed by a variation in the quantity or relations of _a_. To take a
familiar instance, that of gravitation. The sun causes a certain tendency
to motion in the earth; here we have cause and effect; but that tendency
is _toward_ the sun, and therefore varies in direction as the sun varies
in the relation of position; and, moreover, the tendency varies in
intensity, in a certain numerical correspondence to the sun’s distance
from the earth, that is, according to another relation of the sun. Thus we
see that there is not only an invariable connection between the sun and
the earth’s gravitation, but that two of the relations of the sun, its
position with respect to the earth and its distance from the earth, are
invariably connected as antecedents with the quantity and direction of the
earth’s gravitation. The cause of the earth’s gravitating at all, is
simply the sun; but the cause of its gravitating with a given intensity
and in a given direction, is the existence of the sun in a given direction
and at a given distance. It is not strange that a modified cause, which is
in truth a different cause, should produce a different effect.

Although it is for the most part true that a modification of the cause is
followed by a modification of the effect, the Method of Concomitant
Variations does not, however, presuppose this as an axiom. It only
requires the converse proposition: that any thing on whose modifications,
modifications of an effect are invariably consequent, must be the cause
(or connected with the cause) of that effect; a proposition, the truth of
which is evident; for if the thing itself had no influence on the effect,
neither could the modifications of the thing have any influence. If the
stars have no power over the fortunes of mankind, it is implied in the
very terms that the conjunctions or oppositions of different stars can
have no such power.

Although the most striking applications of the Method of Concomitant
Variations take place in the cases in which the Method of Difference,
strictly so called, is impossible, its use is not confined to those cases;
it may often usefully follow after the Method of Difference, to give
additional precision to a solution which that has found. When by the
Method of Difference it has first been ascertained that a certain object
produces a certain effect, the Method of Concomitant Variations may be
usefully called in, to determine according to what law the quantity or the
different relations of the effect follow those of the cause.

§ 7. The case in which this method admits of the most extensive
employment, is that in which the variations of the cause are variations of
quantity. Of such variations we may in general affirm with safety, that
they will be attended not only with variations, but with similar
variations, of the effect: the proposition that more of the cause is
followed by more of the effect, being a corollary from the principle of
the Composition of Causes, which, as we have seen, is the general rule of
causation; cases of the opposite description, in which causes change their
properties on being conjoined with one another, being, on the contrary,
special and exceptional. Suppose, then, that when A changes in quantity,
_a_ also changes in quantity, and in such a manner that we can trace the
numerical relation which the changes of the one bear to such changes of
the other as take place within our limits of observation. We may then,
with certain precautions, safely conclude that the same numerical relation
will hold beyond those limits. If, for instance, we find that when A is
double, _a_ is double; that when A is treble or quadruple, _a_ is treble
or quadruple; we may conclude that if A were a half or a third, _a_ would
be a half or a third, and finally, that if A were annihilated, _a_ would
be annihilated; and that _a_ is wholly the effect of A, or wholly the
effect of the same cause with A. And so with any other numerical relation
according to which A and _a_ would vanish simultaneously; as, for
instance, if _a_ were proportional to the square of A. If, on the other
hand, _a_ is not wholly the effect of A, but yet varies when A varies, it
is probably a mathematical function not of A alone, but of A and something
else: its changes, for example, may be such as would occur if part of it
remained constant, or varied on some other principle, and the remainder
varied in some numerical relations to the variations of A. In that case,
when A diminishes, _a_ will be seen to approach not toward zero, but
toward some other limit; and when the series of variations is such as to
indicate what that limit is, if constant, or the law of its variation, if
variable, the limit will exactly measure how much of _a_ is the effect of
some other and independent cause, and the remainder will be the effect of
A (or of the cause of A).

These conclusions, however, must not be drawn without certain precautions.
In the first place, the possibility of drawing them at all, manifestly
supposes that we are acquainted not only with the variations, but with the
absolute quantities both of A and _a_. If we do not know the total
quantities, we can not, of course, determine the real numerical relation
according to which those quantities vary. It is, therefore, an error to
conclude, as some have concluded, that because increase of heat expands
bodies, that is, increases the distance between their particles, therefore
the distance is wholly the effect of heat, and that if we could entirely
exhaust the body of its heat, the particles would be in complete contact.
This is no more than a guess, and of the most hazardous sort, not a
legitimate induction: for since we neither know how much heat there is in
any body, nor what is the real distance between any two of its particles,
we can not judge whether the contraction of the distance does or does not
follow the diminution of the quantity of heat according to such a
numerical relation that the two quantities would vanish simultaneously.

In contrast with this, let us consider a case in which the absolute
quantities are known; the case contemplated in the first law of motion:
viz., that all bodies in motion continue to move in a straight line with
uniform velocity until acted upon by some new force. This assertion is in
open opposition to first appearances; all terrestrial objects, when in
motion, gradually abate their velocity, and at last stop; which
accordingly the ancients, with their _inductio per enumerationem
simplicem_, imagined to be the law. Every moving body, however, encounters
various obstacles, as friction, the resistance of the atmosphere, etc.,
which we know by daily experience to be causes capable of destroying
motion. It was suggested that the whole of the retardation might be owing
to these causes. How was this inquired into? If the obstacles could have
been entirely removed, the case would have been amenable to the Method of
Difference. They could not be removed, they could only be diminished, and
the case, therefore, admitted only of the Method of Concomitant
Variations. This accordingly being employed, it was found that every
diminution of the obstacles diminished the retardation of the motion: and
inasmuch as in this case (unlike the case of heat) the total quantities
both of the antecedent and of the consequent were known, it was
practicable to estimate, with an approach to accuracy, both the amount of
the retardation and the amount of the retarding causes, or resistances,
and to judge how near they both were to being exhausted; and it appeared
that the effect dwindled as rapidly, and at each step was as far on the
road toward annihilation, as the cause was. The simple oscillation of a
weight suspended from a fixed point, and moved a little out of the
perpendicular, which in ordinary circumstances lasts but a few minutes,
was prolonged in Borda’s experiments to more than thirty hours, by
diminishing as much as possible the friction at the point of suspension,
and by making the body oscillate in a space exhausted as nearly as
possible of its air. There could therefore be no hesitation in assigning
the whole of the retardation of motion to the influence of the obstacles;
and since, after subducting this retardation from the total phenomenon,
the remainder was a uniform velocity, the result was the proposition known
as the first law of motion.

There is also another characteristic uncertainty affecting the inference
that the law of variation which the quantities observe within our limits
of observation, will hold beyond those limits. There is, of course, in the
first instance, the possibility that beyond the limits, and in
circumstances therefore of which we have no direct experience, some
counteracting cause might develop itself; either a new agent or a new
property of the agents concerned, which lies dormant in the circumstances
we are able to observe. This is an element of uncertainty which enters
largely into all our predictions of effects; but it is not peculiarly
applicable to the Method of Concomitant Variations. The uncertainty,
however, of which I am about to speak, is characteristic of that method;
especially in the cases in which the extreme limits of our observation are
very narrow, in comparison with the possible variations in the quantities
of the phenomena. Any one who has the slightest acquaintance with
mathematics, is aware that very different laws of variation may produce
numerical results which differ but slightly from one another within narrow
limits; and it is often only when the absolute amounts of variation are
considerable, that the difference between the results given by one law and
by another becomes appreciable. When, therefore, such variations in the
quantity of the antecedents as we have the means of observing are small in
comparison with the total quantities, there is much danger lest we should
mistake the numerical law, and be led to miscalculate the variations which
would take place beyond the limits; a miscalculation which would vitiate
any conclusion respecting the dependence of the effect upon the cause,
that could be founded on those variations. Examples are not wanting of
such mistakes. “The formulæ,” says Sir John Herschel,(136) “which have
been empirically deduced for the elasticity of steam (till very recently),
and those for the resistance of fluids, and other similar subjects,” when
relied on beyond the limits of the observations from which they were
deduced, "have almost invariably failed to support the theoretical
structures which have been erected on them."

In this uncertainty, the conclusion we may draw from the concomitant
variations of _a_ and A, to the existence of an invariable and exclusive
connection between them, or to the permanency of the same numerical
relation between their variations when the quantities are much greater or
smaller than those which we have had the means of observing, can not be
considered to rest on a complete induction. All that in such a case can be
regarded as proved on the subject of causation is, that there is some
connection between the two phenomena; that A, or something which can
influence A, must be _one_ of the causes which collectively determine _a_.
We may, however, feel assured that the relation which we have observed to
exist between the variations of A and _a_, will hold true in all cases
which fall between the same extreme limits; that is, wherever the utmost
increase or diminution in which the result has been found by observation
to coincide with the law, is not exceeded.

The four methods which it has now been attempted to describe, are the only
possible modes of experimental inquiry—of direct induction _a posteriori_,
as distinguished from deduction: at least, I know not, nor am able to
imagine any others. And even of these, the Method of Residues, as we have
seen, is not independent of deduction; though, as it also requires
specific experience, it may, without impropriety, be included among
methods of direct observation and experiment.

These, then, with such assistance as can be obtained from Deduction,
compose the available resources of the human mind for ascertaining the
laws of the succession of phenomena. Before proceeding to point out
certain circumstances by which the employment of these methods is
subjected to an immense increase of complication and of difficulty, it is
expedient to illustrate the use of the methods, by suitable examples drawn
from actual physical investigations. These, accordingly, will form the
subject of the succeeding chapter.




                               Chapter IX.


Miscellaneous Examples Of The Four Methods.


§ 1. I shall select, as a first example, an interesting speculation of one
of the most eminent of theoretical chemists, Baron Liebig. The object in
view is to ascertain the immediate cause of the death produced by metallic
poisons.

Arsenious acid, and the salts of lead, bismuth, copper, and mercury, if
introduced into the animal organism, except in the smallest doses, destroy
life. These facts have long been known, as insulated truths of the lowest
order of generalization; but it was reserved for Liebig, by an apt
employment of the first two of our methods of experimental inquiry, to
connect these truths together by a higher induction, pointing out what
property, common to all these deleterious substances, is the really
operating cause of their fatal effect.

When solutions of these substances are placed in sufficiently close
contact with many animal products, albumen, milk, muscular fibre, and
animal membranes, the acid or salt leaves the water in which it was
dissolved, and enters into combination with the animal substance, which
substance, after being thus acted upon, is found to have lost its tendency
to spontaneous decomposition, or putrefaction.

Observation also shows, in cases where death has been produced by these
poisons, that the parts of the body with which the poisonous substances
have been brought into contact, do not afterward putrefy.

And, finally, when the poison has been supplied in too small a quantity to
destroy life, eschars are produced, that is, certain superficial portions
of the tissues are destroyed, which are afterward thrown off by the
reparative process taking place in the healthy parts.

These three sets of instances admit of being treated according to the
Method of Agreement. In all of them the metallic compounds are brought
into contact with the substances which compose the human or animal body;
and the instances do not seem to agree in any other circumstance. The
remaining antecedents are as different, and even opposite, as they could
possibly be made; for in some the animal substances exposed to the action
of the poisons are in a state of life, in others only in a state of
organization, in others not even in that. And what is the result which
follows in all the cases? The conversion of the animal substance (by
combination with the poison) into a chemical compound, held together by so
powerful a force as to resist the subsequent action of the ordinary causes
of decomposition. Now, organic life (the necessary condition of sensitive
life) consisting in a continual state of decomposition and recomposition
of the different organs and tissues, whatever incapacitates them for this
decomposition destroys life. And thus the proximate cause of the death
produced by this description of poisons is ascertained, as far as the
Method of Agreement can ascertain it.

Let us now bring our conclusion to the test of the Method of Difference.
Setting out from the cases already mentioned, in which the antecedent is
the presence of substances forming with the tissues a compound incapable
of putrefaction, (and _a fortiori_ incapable of the chemical actions which
constitute life), and the consequent is death, either of the whole
organism, or of some portion of it; let us compare with these cases other
cases, as much resembling them as possible, but in which that effect is
not produced. And, first, “many insoluble basic salts of arsenious acid
are known not to be poisonous. The substance called alkargen, discovered
by Bunsen, which contains a very large quantity of arsenic, and approaches
very closely in composition to the organic arsenious compounds found in
the body, has not the slightest injurious action upon the organism.” Now
when these substances are brought into contact with the tissues in any
way, they do not combine with them; they do not arrest their progress to
decomposition. As far, therefore, as these instances go, it appears that
when the effect is absent, it is by reason of the absence of that
antecedent which we had already good ground for considering as the
proximate cause.

But the rigorous conditions of the Method of Difference are not yet
satisfied; for we can not be sure that these unpoisonous bodies agree with
the poisonous substances in every property, except the particular one of
entering into a difficultly decomposable compound with the animal tissues.
To render the method strictly applicable, we need an instance, not of a
different substance, but of one of the very same substances, in
circumstances which would prevent it from forming, with the tissues, the
sort of compound in question; and then, if death does not follow, our case
is made out. Now such instances are afforded by the antidotes to these
poisons. For example, in case of poisoning by arsenious acid, if hydrated
peroxide of iron is administered, the destructive agency is instantly
checked. Now this peroxide is known to combine with the acid, and form a
compound, which, being insoluble, can not act at all on animal tissues.
So, again, sugar is a well-known antidote to poisoning by salts of copper;
and sugar reduces those salts either into metallic copper, or into the red
sub-oxide, neither of which enters into combination with animal matter.
The disease called painter’s colic, so common in manufactories of
white-lead, is unknown where the workmen are accustomed to take, as a
preservative, sulphuric acid lemonade (a solution of sugar rendered acid
by sulphuric acid). Now diluted sulphuric acid has the property of
decomposing all compounds of lead with organic matter, or of preventing
them from being formed.

There is another class of instances, of the nature required by the Method
of Difference, which seem at first sight to conflict with the theory.
Soluble salts of silver, such for instance as the nitrate, have the same
stiffening antiseptic effect on decomposing animal substances as corrosive
sublimate and the most deadly metallic poisons; and when applied to the
external parts of the body, the nitrate is a powerful caustic, depriving
those parts of all active vitality, and causing them to be thrown off by
the neighboring living structures, in the form of an eschar. The nitrate
and the other salts of silver ought, then, it would seem, if the theory be
correct, to be poisonous; yet they may be administered internally with
perfect impunity. From this apparent exception arises the strongest
confirmation which the theory has yet received. Nitrate of silver, in
spite of its chemical properties, does not poison when introduced into the
stomach; but in the stomach, as in all animal liquids, there is common
salt; and in the stomach there is also free muriatic acid. These
substances operate as natural antidotes, combining with the nitrate, and
if its quantity is not too great, immediately converting it into chloride
of silver, a substance very slightly soluble, and therefore incapable of
combining with the tissues, although to the extent of its solubility it
has a medicinal influence, though an entirely different class of organic
actions.

The preceding instances have afforded an induction of a high order of
conclusiveness, illustrative of the two simplest of our four methods;
though not rising to the maximum of certainty which the Method of
Difference, in its most perfect exemplification, is capable of affording.
For (let us not forget) the positive instance and the negative one which
the rigor of that method requires, ought to differ only in the presence or
absence of one single circumstance. Now, in the preceding argument, they
differ in the presence or absence not of a single _circumstance_, but of a
single _substance_: and as every substance has innumerable properties,
there is no knowing what number of real differences are involved in what
is nominally and apparently only one difference. It is conceivable that
the antidote, the peroxide of iron for example, may counteract the poison
through some other of its properties than that of forming an insoluble
compound with it; and if so, the theory would fall to the ground, so far
as it is supported by that instance. This source of uncertainty, which is
a serious hinderance to all extensive generalizations in chemistry, is,
however, reduced in the present case to almost the lowest degree possible,
when we find that not only one substance, but many substances, possess the
capacity of acting as antidotes to metallic poisons, and that all these
agree in the property of forming insoluble compounds with the poisons,
while they can not be ascertained to agree in any other property
whatsoever. We have thus, in favor of the theory, all the evidence which
can be obtained by what we termed the Indirect Method of Difference, or
the Joint Method of Agreement and Difference; the evidence of which,
though it never can amount to that of the Method of Difference properly so
called, may approach indefinitely near to it.

§ 2. Let the object be(137) to ascertain the law of what is termed
_induced_ electricity; to find under what conditions any electrified body,
whether positively or negatively electrified, gives rise to a contrary
electric state in some other body adjacent to it.

The most familiar exemplification of the phenomenon to be investigated is
the following. Around the prime conductors of an electrical machine the
atmosphere to some distance, or any conducting surface suspended in that
atmosphere, is found to be in an electric condition opposite to that of
the prime conductor itself. Near and around the positive prime conductor
there is negative electricity, and near and around the negative prime
conductor there is positive electricity. When pith balls are brought near
to either of the conductors, they become electrified with the opposite
electricity to it; either receiving a share from the already electrified
atmosphere by conduction, or acted upon by the direct inductive influence
of the conductor itself: they are then attracted by the conductor to which
they are in opposition; or, if withdrawn in their electrified state, they
will be attracted by any other oppositely charged body. In like manner the
hand, if brought near enough to the conductor, receives or gives an
electric discharge; now we have no evidence that a charged conductor can
be suddenly discharged unless by the approach of a body oppositely
electrified. In the case, therefore, of the electric machine, it appears
that the accumulation of electricity in an insulated conductor is always
accompanied by the excitement of the contrary electricity in the
surrounding atmosphere, and in every conductor placed near the former
conductor. It does not seem possible, in this case, to produce one
electricity by itself.

Let us now examine all the other instances which we can obtain, resembling
this instance in the given consequent, namely, the evolution of an
opposite electricity in the neighborhood of an electrified body. As one
remarkable instance we have the Leyden jar; and after the splendid
experiments of Faraday in complete and final establishment of the
substantial identity of magnetism and electricity, we may cite the magnet,
both the natural and the electro-magnet, in neither of which it is
possible to produce one kind of electricity by itself, or to charge one
pole without charging an opposite pole with the contrary electricity at
the same time. We can not have a magnet with one pole: if we break a
natural loadstone into a thousand pieces, each piece will have its two
oppositely electrified poles complete within itself. In the voltaic
circuit, again, we can not have one current without its opposite. In the
ordinary electric machine, the glass cylinder or plate, and the rubber,
acquire opposite electricities.

From all these instances, treated by the Method of Agreement, a general
law appears to result. The instances embrace all the known modes in which
a body can become charged with electricity; and in all of them there is
found, as a concomitant or consequent, the excitement of the opposite
electric state in some other body or bodies. It seems to follow that the
two facts are invariably connected, and that the excitement of electricity
in any body has for one of its necessary conditions the possibility of a
simultaneous excitement of the opposite electricity in some neighboring
body.

As the two contrary electricities can only be produced together, so they
can only cease together. This may be shown by an application of the Method
of Difference to the example of the Leyden jar. It needs scarcely be here
remarked that in the Leyden jar, electricity can be accumulated and
retained in considerable quantity, by the contrivance of having two
conducting surfaces of equal extent, and parallel to each other through
the whole of that extent, with a non-conducting substance such as glass
between them. When one side of the jar is charged positively, the other is
charged negatively, and it was by virtue of this fact that the Leyden jar
served just now as an instance in our employment of the Method of
Agreement. Now it is impossible to discharge one of the coatings unless
the other can be discharged at the same time. A conductor held to the
positive side can not convey away any electricity unless an equal quantity
be allowed to pass from the negative side: if one coating be perfectly
insulated, the charge is safe. The dissipation of one must proceed _pari
passu_ with that of the other.

The law thus strongly indicated admits of corroboration by the Method of
Concomitant Variations. The Leyden jar is capable of receiving a much
higher charge than can ordinarily be given to the conductor of an
electrical machine. Now in the case of the Leyden jar, the metallic
surface which receives the induced electricity is a conductor exactly
similar to that which receives the primary charge, and is therefore as
susceptible of receiving and retaining the one electricity, as the
opposite surface of receiving and retaining the other; but in the machine,
the neighboring body which is to be oppositely electrified is the
surrounding atmosphere, or any body casually brought near to the
conductor; and as these are generally much inferior in their capacity of
becoming electrified, to the conductor itself, their limited power imposes
a corresponding limit to the capacity of the conductor for being charged.
As the capacity of the neighboring body for supporting the opposition
increases, a higher charge becomes possible: and to this appears to be
owing the great superiority of the Leyden jar.

A further and most decisive confirmation by the Method of Difference, is
to be found in one of Faraday’s experiments in the course of his
researches on the subject of Induced Electricity.

Since common or machine electricity, and voltaic electricity, may be
considered for the present purpose to be identical, Faraday wished to know
whether, as the prime conductor develops opposite electricity upon a
conductor in its vicinity, so a voltaic current running along a wire would
induce an opposite current upon another wire laid parallel to it at a
short distance. Now this case is similar to the cases previously examined,
in every circumstance except the one to which we have ascribed the effect.
We found in the former instances that whenever electricity of one kind was
excited in one body, electricity of the opposite kind must be excited in a
neighboring body. But in Faraday’s experiment this indispensable
opposition exists within the wire itself. From the nature of a voltaic
charge, the two opposite currents necessary to the existence of each other
are both accommodated in one wire; and there is no need of another wire
placed beside it to contain one of them, in the same way as the Leyden jar
must have a positive and a negative surface. The exciting cause can and
does produce all the effect which its laws require, independently of any
electric excitement of a neighboring body. Now the result of the
experiment with the second wire was, that no opposite current was
produced. There was an instantaneous effect at the closing and breaking of
the voltaic circuit; electric inductions appeared when the two wires were
moved to and from one another; but these are phenomena of a different
class. There was no induced electricity in the sense in which this is
predicated of the Leyden jar; there was no sustained current running up
the one wire while an opposite current ran down the neighboring wire; and
this alone would have been a true parallel case to the other.

It thus appears by the combined evidence of the Method of Agreement, the
Method of Concomitant Variations, and the most rigorous form of the Method
of Difference, that neither of the two kinds of electricity can be excited
without an equal excitement of the other and opposite kind: that both are
effects of the same cause; that the possibility of the one is a condition
of the possibility of the other, and the quantity of the one an impassable
limit to the quantity of the other. A scientific result of considerable
interest in itself, and illustrating those three methods in a manner both
characteristic and easily intelligible.(138)

§ 3. Our third example shall be extracted from Sir John Herschel’s
_Discourse __ course on the Study of Natural Philosophy_, a work replete
with happily-selected exemplifications of inductive processes from almost
every department of physical science, and in which alone, of all books
which I have met with, the four methods of induction are distinctly
recognized, though not so clearly characterized and defined, nor their
correlation so fully shown, as has appeared to me desirable. The present
example is described by Sir John Herschel as “one of the most beautiful
specimens” which can be cited “of inductive experimental inquiry lying
within a moderate compass;” the theory of dew, first promulgated by the
late Dr. Wells, and now universally adopted by scientific authorities. The
passages in inverted commas are extracted verbatim from the
Discourse.(139)

“Suppose _dew_ were the phenomenon proposed, whose cause we would know. In
the first place” we must determine precisely what we mean by dew: what the
fact really is whose cause we desire to investigate. “We must separate dew
from rain, and the moisture of fogs, and limit the application of the term
to what is really meant, which is the spontaneous appearance of moisture
on substances exposed in the open air when no rain or _visible_ wet is
falling.” This answers to a preliminary operation which will be
characterized in the ensuing book, treating of operations subsidiary to
induction.(140)

“Now, here we have analogous phenomena in the moisture which bedews a cold
metal or stone when we breathe upon it; that which appears on a glass of
water fresh from the well in hot weather; that which appears on the inside
of windows when sudden rain or hail chills the external air; that which
runs down our walls when, after a long frost, a warm, moist thaw comes
on.” Comparing these cases, we find that they all contain the phenomenon
which was proposed as the subject of investigation. Now “all these
instances agree in one point, the coldness of the object dewed, in
comparison with the air in contact with it.” But there still remains the
most important case of all, that of nocturnal dew: does the same
circumstance exist in this case? “Is it a fact that the object dewed _is_
colder than the air? Certainly not, one would at first be inclined to say;
for what is to _make_ it so? But ... the experiment is easy: we have only
to lay a thermometer in contact with the dewed substance, and hang one at
a little distance above it, out of reach of its influence. The experiment
has been therefore made, the question has been asked, and the answer has
been invariably in the affirmative. Whenever an object contracts dew, it
_is_ colder than the air.”

Here, then, is a complete application of the Method of Agreement,
establishing the fact of an invariable connection between the deposition
of dew on a surface, and the coldness of that surface compared with the
external air. But which of these is cause, and which effect? or are they
both effects of something else? On this subject the Method of Agreement
can afford us no light: we must call in a more potent method. “We must
collect more facts, or, which comes to the same thing, vary the
circumstances; since every instance in which the circumstances differ is a
fresh fact: and especially, we must note the contrary or negative cases,
_i.e._, where no dew is produced:” a comparison between instances of dew
and instances of no dew, being the condition necessary to bring the Method
of Difference into play.

“Now, first, no dew is produced on the surface of polished metals, but it
_is_ very copiously on glass, both exposed with their faces upward, and in
some cases the under side of a horizontal plate of glass is also dewed.”
Here is an instance in which the effect is produced, and another instance
in which it is not produced; but we can not yet pronounce, as the canon of
the Method of Difference requires, that the latter instance agrees with
the former in all its circumstances except one; for the differences
between glass and polished metals are manifold, and the only thing we can
as yet be sure of is, that the cause of dew will be found among the
circumstances by which the former substance is distinguished from the
latter. But if we could be sure that glass, and the various other
substances on which dew is deposited, have only one quality in common, and
that polished metals and the other substances on which dew is not
deposited, have also nothing in common but the one circumstance of not
having the one quality which the others have; the requisitions of the
Method of Difference would be completely satisfied, and we should
recognize, in that quality of the substances, the cause of dew. This,
accordingly, is the path of inquiry which is next to be pursued.

“In the cases of polished metal and polished glass, the contrast shows
evidently that the _substance_ has much to do with the phenomenon;
therefore let the substance _alone_ be diversified as much as possible, by
exposing polished surfaces of various kinds. This done, a _scale of
intensity_ becomes obvious. Those polished substances are found to be most
strongly dewed which conduct heat worst; while those which conduct heat
well, resist dew most effectually.” The complication increases; here is
the Method of Concomitant Variations called to our assistance; and no
other method was practicable on this occasion; for the quality of
conducting heat could not be excluded, since all substances conduct heat
in some degree. The conclusion obtained is, that _cæteris paribus_ the
deposition of dew is in some proportion to the power which the body
possesses of resisting the passage of heat; and that this, therefore (or
something connected with this), must be at least one of the causes which
assist in producing the deposition of dew on the surface.

“But if we expose rough surfaces instead of polished, we sometimes find
this law interfered with. Thus, roughened iron, especially if painted over
or blackened, becomes dewed sooner than varnished paper; the kind of
_surface_, therefore, has a great influence. Expose, then, the _same_
material in very diversified states, as to surface” (that is, employ the
Method of Difference to ascertain concomitance of variations), “and
another scale of intensity becomes at once apparent; those _surfaces_
which _part with their heat_ most readily by radiation are found to
contract dew most copiously.” Here, therefore, are the requisites for a
second employment of the Method of Concomitant Variations; which in this
case also is the only method available, since all substances radiate heat
in some degree or other. The conclusion obtained by this new application
of the method is, that _cæteris paribus_ the deposition of dew is also in
some proportion to the power of radiating heat; and that the quality of
doing this abundantly (or some cause on which that quality depends) is
another of the causes which promote the deposition of dew on the
substance.

“Again, the influence ascertained to exist of _substance_ and _surface_
leads us to consider that of _texture_: and here, again, we are presented
on trial with remarkable differences, and with a third scale of intensity,
pointing out substances of a close, firm texture, such as stones, metals,
etc., as unfavorable, but those of a loose one, as cloth, velvet, wool,
eider-down, cotton, etc., as eminently favorable to the contraction of
dew." The Method of Concomitant Variations is here, for the third time,
had recourse to; and, as before, from necessity, since the texture of no
substance is absolutely firm or absolutely loose. Looseness of texture,
therefore, or something which is the cause of that quality, is another
circumstance which promotes the deposition of dew; but this third course
resolves itself into the first, viz., the quality of resisting the passage
of heat: for substances of loose texture "are precisely those which are
best adapted for clothing, or for impeding the free passage of heat from
the skin into the air, so as to allow their outer surfaces to be very
cold, while they remain warm within;” and this last is, therefore, an
induction (from fresh instances) simply _corroborative_ of a former
induction.

It thus appears that the instances in which much dew is deposited, which
are very various, agree in this, and, so far as we are able to observe, in
this only, that they either radiate heat rapidly or conduct it slowly:
qualities between which there is no other circumstance of agreement than
that by virtue of either, the body tends to lose heat from the surface
more rapidly than it can be restored from within. The instances, on the
contrary, in which no dew, or but a small quantity of it, is formed, and
which are also extremely various, agree (as far as we can observe) in
nothing except in _not_ having this same property. We seem, therefore, to
have detected the characteristic difference between the substances on
which dew is produced and those on which it is not produced. And thus have
been realized the requisitions of what we have termed the Indirect Method
of Difference, or the Joint Method of Agreement and Difference. The
example afforded of this indirect method, and of the manner in which the
data are prepared for it by the Methods of Agreement and of Concomitant
Variations, is the most important of all the illustrations of induction
afforded by this interesting speculation.

We might now consider the question, on what the deposition of dew depends,
to be completely solved, if we could be quite sure that the substances on
which dew is produced differ from those on which it is not, in _nothing_
but in the property of losing heat from the surface faster than the loss
can be repaired from within. And though we never can have that complete
certainty, this is not of so much importance as might at first be
supposed; for we have, at all events, ascertained that even if there be
any other quality hitherto unobserved which is present in all the
substances which contract dew, and absent in those which do not, this
other property must be one which, in all that great number of substances,
is present or absent exactly where the property of being a better radiator
than conductor is present or absent; an extent of coincidence which
affords a strong presumption of a community of cause, and a consequent
invariable co-existence between the two properties; so that the property
of being a better radiator than conductor, if not itself the cause, almost
certainly always accompanies the cause, and for purposes of prediction, no
error is likely to be committed by treating it as if it were really such.

Reverting now to an earlier stage of the inquiry, let us remember that we
had ascertained that, in every instance where dew is formed, there is
actual coldness of the surface below the temperature of the surrounding
air; but we were not sure whether this coldness was the cause of dew, or
its effect. This doubt we are now able to resolve. We have found that, in
every such instance, the substance is one which, by its own properties or
laws, would, if exposed in the night, become colder than the surrounding
air. The coldness, therefore, being accounted for independently of the
dew, while it is proved that there is a connection between the two, it
must be the dew which depends on the coldness; or, in other words, the
coldness is the cause of the dew.

This law of causation, already so amply established, admits, however, of
efficient additional corroboration in no less than three ways. First, by
deduction from the known laws of aqueous vapor when diffused through air
or any other gas; and though we have not yet come to the Deductive Method,
we will not omit what is necessary to render this speculation complete. It
is known by direct experiment that only a limited quantity of water can
remain suspended in the state of vapor at each degree of temperature, and
that this maximum grows less and less as the temperature diminishes. From
this it follows, deductively, that if there is already as much vapor
suspended as the air will contain at its existing temperature, any
lowering of that temperature will cause a portion of the vapor to be
condensed, and become water. But again, we know deductively, from the laws
of heat, that the contact of the air with a body colder than itself will
necessarily lower the temperature of the stratum of air immediately
applied to its surface; and will, therefore, cause it to part with a
portion of its water, which accordingly will, by the ordinary laws of
gravitation or cohesion, attach itself to the surface of the body, thereby
constituting dew. This deductive proof, it will have been seen, has the
advantage of at once proving causation as well as co-existence; and it has
the additional advantage that it also accounts for the exceptions to the
occurrence of the phenomenon, the cases in which, although the body is
colder than the air, yet no dew is deposited; by showing that this will
necessarily be the case when the air is so under-supplied with aqueous
vapor, comparatively to its temperature, that even when somewhat cooled by
the contact of the colder body it can still continue to hold in suspension
all the vapor which was previously suspended in it: thus in a very dry
summer there are no dews, in a very dry winter no hoar-frost. Here,
therefore, is an additional condition of the production of dew, which the
methods we previously made use of failed to detect, and which might have
remained still undetected, if recourse had not been had to the plan of
deducing the effect from the ascertained properties of the agents known to
be present.

The second corroboration of the theory is by direct experiment, according
to the canon of the Method of Difference. We can, by cooling the surface
of any body, find in all cases some temperature (more or less inferior to
that of the surrounding air, according to its hygrometric condition) at
which dew will begin to be deposited. Here, too, therefore, the causation
is directly proved. We can, it is true, accomplish this only on a small
scale, but we have ample reason to conclude that the same operation, if
conducted in nature’s great laboratory, would equally produce the effect.

And, finally, even on that great scale we are able to verify the result.
The case is one of those rare cases, as we have shown them to be, in which
nature works the experiment for us in the same manner in which we
ourselves perform it; introducing into the previous state of things a
single and perfectly definite new circumstance, and manifesting the effect
so rapidly that there is not time for any other material change in the
pre-existing circumstances. “It is observed that dew is never copiously
deposited in situations much screened from the open sky, and not at all in
a cloudy night; but _if the clouds withdraw even for a few minutes, and
leave a clear opening, a deposition of dew presently begins_, and goes on
increasing... Dew formed in clear intervals will often even evaporate
again when the sky becomes thickly overcast.” The proof, therefore, is
complete, that the presence or absence of an uninterrupted communication
with the sky causes the deposition or non-deposition of dew. Now, since a
clear sky is nothing but the absence of clouds, and it is a known property
of clouds, as of all other bodies between which and any given object
nothing intervenes but an elastic fluid, that they tend to raise or keep
up the superficial temperature of the object by radiating heat to it, we
see at once that the disappearance of clouds will cause the surface to
cool; so that nature, in this case, produces a change in the antecedent by
definite and known means, and the consequent follows accordingly: a
natural experiment which satisfies the requisitions of the Method of
Difference.(141)

The accumulated proof of which the Theory of Dew has been found
susceptible, is a striking instance of the fullness of assurance which the
inductive evidence of laws of causation may attain, in cases in which the
invariable sequence is by no means obvious to a superficial view.

§ 4. The admirable physiological investigations of Dr. Brown-Séquard
afford brilliant examples of the application of the Inductive Methods to a
class of inquiries in which, for reasons which will presently be given,
direct induction takes place under peculiar difficulties and
disadvantages. As one of the most apt instances, I select his speculation
(in the proceedings of the Royal Society for May 16, 1861) on the
relations between muscular irritability, cadaveric rigidity, and
putrefaction.

The law which Dr. Brown-Séquard’s investigation tends to establish, is the
following: “The greater the degree of muscular irritability at the time of
death, the later the cadaveric rigidity sets in, and the longer it lasts,
and the later also putrefaction appears, and the slower it progresses.”
One would say at first sight that the method here required must be that of
Concomitant Variations. But this is a delusive appearance, arising from
the circumstance that the conclusion to be tested is itself a fact of
concomitant variations. For the establishment of that fact any of the
Methods may be put in requisition, and it will be found that the fourth
Method, though really employed, has only a subordinate place in this
particular investigation.

The evidences by which Dr. Brown-Séquard establishes the law may be
enumerated as follows:

1st. Paralyzed muscles have greater irritability than healthy muscles.
Now, paralyzed muscles are later in assuming the cadaveric rigidity than
healthy muscles, the rigidity lasts longer, and putrefaction sets in
later, and proceeds more slowly.

Both these propositions had to be proved by experiment; and for the
experiments which prove them, science is also indebted to Dr.
Brown-Séquard. The former of the two—that paralyzed muscles have greater
irritability than healthy muscles—he ascertained in various ways, but most
decisively by “comparing the duration of irritability in a paralyzed
muscle and in the corresponding healthy one of the opposite side, while
they are both submitted to the same excitation.” He “often found, in
experimenting in that way, that the paralyzed muscle remained irritable
twice, three times, or even four times as long as the healthy one.” This
is a case of induction by the Method of Difference. The two limbs, being
those of the same animal, were presumed to differ in no circumstance
material to the case except the paralysis, to the presence and absence of
which, therefore, the difference in the muscular irritability was to be
attributed. This assumption of complete resemblance in all material
circumstances save one, evidently could not be safely made in any one pair
of experiments, because the two legs of any given animal might be
accidentally in very different pathological conditions; but if, besides
taking pains to avoid any such difference, the experiment was repeated
sufficiently often in different animals to exclude the supposition that
any abnormal circumstance could be present in them all, the conditions of
the Method of Difference were adequately secured.

In the same manner in which Dr. Brown-Séquard proved that paralyzed
muscles have greater irritability, he also proved the correlative
proposition respecting cadaveric rigidity and putrefaction. Having, by
section of the roots of the sciatic nerve, and again of a lateral half of
the spinal cord, produced paralysis in one hind leg of an animal while the
other remained healthy, he found that not only did muscular irritability
last much longer in the paralyzed limb, but rigidity set in later and
ended later, and putrefaction began later and was less rapid than on the
healthy side. This is a common case of the Method of Difference, requiring
no comment. A further and very important corroboration was obtained by the
same method. When the animal was killed, not shortly after the section of
the nerve, but a month later, the effect was reversed; rigidity set in
sooner, and lasted a shorter time, than in the healthy muscles. But after
this lapse of time, the paralyzed muscles, having been kept by the
paralysis in a state of rest, had lost a great part of their irritability,
and instead of more, had become less irritable than those on the healthy
side. This gives the A B C, _a b c_, and B C, b c, of the Method of
Difference. One antecedent, increased irritability, being changed, and the
other circumstances being the same, the consequence did not follow; and,
moreover, when a new antecedent, contrary to the first, was supplied, it
was followed by a contrary consequent. This instance is attended with the
special advantage of proving that the retardation and prolongation of the
rigidity do not depend directly on the paralysis, since that was the same
in both the instances; but specifically on one effect of the paralysis,
namely, the increased irritability; since they ceased when it ceased, and
were reversed when it was reversed.

2d. Diminution of the temperature of muscles before death increases their
irritability. But diminution of their temperature also retards cadaveric
rigidity and putrefaction.

Both these truths were first made known by Dr. Brown-Séquard himself,
through experiments which conclude according to the Method of Difference.
There is nothing in the nature of the process requiring specific analysis.

3d. Muscular exercise, prolonged to exhaustion, diminishes the muscular
irritability. This is a well-known truth, dependent on the most general
laws of muscular action, and proved by experiments under the Method of
Difference, constantly repeated. Now, it has been shown by observation
that overdriven cattle, if killed before recovery from their fatigue,
become rigid and putrefy in a surprisingly short time. A similar fact has
been observed in the case of animals hunted to death; cocks killed during
or shortly after a fight; and soldiers slain in the field of battle. These
various cases agree in no circumstance, directly connected with the
muscles, except that these have just been subjected to exhausting
exercise. Under the canon, therefore, of the Method of Agreement, it may
be inferred that there is a connection between the two facts. The Method
of Agreement, indeed, as has been shown, is not competent to prove
causation. The present case, however, is already known to be a case of
causation, it being certain that the state of the body after death must
somehow depend upon its state at the time of death. We are, therefore,
warranted in concluding that the single circumstance in which all the
instances agree, is the part of the antecedent which is the cause of that
particular consequent.

4th. In proportion as the nutrition of muscles is in a good state, their
irritability is high. This fact also rests on the general evidence of the
laws of physiology, grounded on many familiar applications of the Method
of Difference. Now, in the case of those who die from accident or
violence, with their muscles in a good state of nutrition, the muscular
irritability continues long after death, rigidity sets in late, and
persists long without the putrefactive change. On the contrary, in cases
of disease in which nutrition has been diminished for a long time before
death, all these effects are reversed. These are the conditions of the
Joint Method of Agreement and Difference. The cases of retarded and long
continued rigidity here in question agree only in being preceded by a high
state of nutrition of the muscles; the cases of rapid and brief rigidity
agree only in being preceded by a low state of muscular nutrition; a
connection is, therefore, inductively proved between the degree of the
nutrition, and the slowness and prolongation of the rigidity.

5th. Convulsions, like exhausting exercise, but in a still greater degree,
diminish the muscular irritability. Now, when death follows violent and
prolonged convulsions, as in tetanus, hydrophobia, some cases of cholera,
and certain poisons, rigidity sets in very rapidly, and after a very brief
duration, gives place to putrefaction. This is another example of the
Method of Agreement, of the same character with No. 3.

6th. The series of instances which we shall take last, is of a more
complex character, and requires a more minute analysis.

It has long been observed that in some cases of death by lightning,
cadaveric rigidity either does not take place at all, or is of such
extremely brief duration as to escape notice, and that in these cases
putrefaction is very rapid. In other cases, however, the usual cadaveric
rigidity appears. There must be some difference in the cause, to account
for this difference in the effect. Now, “death by lightning may be the
result of, 1st, a syncope by fright, or in consequence of a direct or
reflex influence of lightning on the par vagum; 2d, hemorrhage in or
around the brain, or in the lungs, the pericardium, etc.; 3d, concussion,
or some other alteration in the brain;” none of which phenomena have any
known property capable of accounting for the suppression, or almost
suppression, of the cadaveric rigidity. But the cause of death may also be
that the lightning produces “a violent convulsion of every muscle in the
body,” of which, if of sufficient intensity, the known effect would be
that “muscular irritability ceases almost at once.” If Dr. Brown-Séquard’s
generalization is a true law, these will be the very cases in which
rigidity is so much abridged as to escape notice; and the cases in which,
on the contrary, rigidity takes place as usual, will be those in which the
stroke of lightning operates in some of the other modes which have been
enumerated. How, then, is this brought to the test? By experiments, not on
lightning, which can not be commanded at pleasure, but on the same natural
agency in a manageable form, that of artificial galvanism. Dr.
Brown-Séquard galvanized the entire bodies of animals immediately after
death. Galvanism can not operate in any of the modes in which the stroke
of lightning may have operated, except the single one of producing
muscular convulsions. If, therefore, after the bodies have been
galvanized, the duration of rigidity is much shortened and putrefaction
much accelerated, it is reasonable to ascribe the same effects when
produced by lightning to the property which galvanism shares with
lightning, and not to those which it does not. Now this Dr. Brown-Séquard
found to be the fact. The galvanic experiment was tried with charges of
very various degrees of strength; and the more powerful the charge, the
shorter was found to be the duration of rigidity, and the more speedy and
rapid the putrefaction. In the experiment in which the charge was
strongest, and the muscular irritability most promptly destroyed, the
rigidity only lasted fifteen minutes. On the principle, therefore, of the
Method of Concomitant Variations, it may be inferred that the duration of
the rigidity depends on the degree of the irritability; and that if the
charge had been as much stronger than Dr. Brown-Séquard’s strongest, as a
stroke of lightning must be stronger than any electric shock which we can
produce artificially, the rigidity would have been shortened in a
corresponding ratio, and might have disappeared altogether. This
conclusion having been arrived at, the case of an electric shock, whether
natural or artificial, becomes an instance, in addition to all those
already ascertained, of correspondence between the irritability of the
muscle and the duration of rigidity.

All these instances are summed up in the following statement: “That when
the degree of muscular irritability at the time of death is considerable,
either in consequence of a good state of nutrition, as in persons who die
in full health from an accidental cause, or in consequence of rest, as in
cases of paralysis, or on account of the influence of cold, cadaveric
rigidity in all these cases sets in late and lasts long, and putrefaction
appears late, and progresses slowly;” but “that when the degree of
muscular irritability at the time of death is slight, either in
consequence of a bad state of nutrition, or of exhaustion from
overexertion, or from convulsions caused by disease or poison, cadaveric
rigidity sets in and ceases soon, and putrefaction appears and progresses
quickly.” These facts present, in all their completeness, the conditions
of the Joint Method of Agreement and Difference. Early and brief rigidity
takes place in cases which agree only in the circumstance of a low state
of muscular irritability. Rigidity begins late and lasts long in cases
which agree only in the contrary circumstance, of a muscular irritability
high and unusually prolonged. It follows that there is a connection
through causation between the degree of muscular irritability after death,
and the tardiness and prolongation of the cadaveric rigidity.

This investigation places in a strong light the value and efficacy of the
Joint Method. For, as we have already seen, the defect of that Method is,
that like the Method of Agreement, of which it is only an improved form,
it can not prove causation. But in the present case (as in one of the
steps in the argument which led up to it) causation is already proved;
since there could never be any doubt that the rigidity altogether, and the
putrefaction which follows it, are caused by the fact of death: the
observations and experiments on which this rests are too familiar to need
analysis, and fall under the Method of Difference. It being, therefore,
beyond doubt that the aggregate antecedent, the death, is the actual cause
of the whole train of consequents, whatever of the circumstances attending
the death can be shown to be followed in all its variations by variations
in the effect under investigation, must be the particular feature of the
fact of death on which that effect depends. The degree of muscular
irritability at the time of death fulfills this condition. The only point
that could be brought into question, would be whether the effect depended
on the irritability itself, or on something which always accompanied the
irritability: and this doubt is set at rest by establishing, as the
instances do, that by whatever cause the high or low irritability is
produced, the effect equally follows; and can not, therefore, depend upon
the causes of irritability, nor upon the other effects of those causes,
which are as various as the causes themselves, but upon the irritability,
solely.

§ 5. The last two examples will have conveyed to any one by whom they have
been duly followed, so clear a conception of the use and practical
management of three of the four methods of experimental inquiry, as to
supersede the necessity of any further exemplification of them. The
remaining method, that of Residues, not having found a place in any of the
preceding investigations, I shall quote from Sir John Herschel some
examples of that method, with the remarks by which they are introduced.

“It is by this process, in fact, that science, in its present advanced
state, is chiefly promoted. Most of the phenomena which Nature presents
are very complicated; and when the effects of all known causes are
estimated with exactness, and subducted, the residual facts are constantly
appearing in the form of phenomena altogether new, and leading to the most
important conclusions.

“For example: the return of the comet predicted by Professor Eucke a great
many times in succession, and the general good agreement of its calculated
with its observed place during any one of its periods of visibility, would
lead us to say that its gravitation toward the sun and planets is the sole
and sufficient cause of all the phenomena of its orbitual motion; but when
the effect of this cause is strictly calculated and subducted from the
observed motion, there is found to remain behind a _residual phenomenon_,
which would never have been otherwise ascertained to exist, which is a
small anticipation of the time of its re-appearance, or a diminution of
its periodic time, which can not be accounted for by gravity, and whose
cause is therefore to be inquired into. Such an anticipation would be
caused by the resistance of a medium disseminated through the celestial
regions; and as there are other good reasons for believing this to be a
_vera causa_” (an actually existing antecedent), “it has therefore been
ascribed to such a resistance.(142)

“M. Arago, having suspended a magnetic needle by a silk thread, and set it
in vibration, observed, that it came much sooner to a state of rest when
suspended over a plate of copper, than when no such plate was beneath it.
Now, in both cases there were two _veræ causæ_” (antecedents known to
exist) “why it _should_ come at length to rest, viz., the resistance of
the air, which opposes, and at length destroys, all motions performed in
it; and the want of perfect mobility in the silk thread. But the effect of
these causes being exactly known by the observation made in the absence of
the copper, and being thus allowed for and subducted, a residual
phenomenon appeared, in the fact that a retarding influence was exerted by
the copper itself; and this fact, once ascertained, speedily led to the
knowledge of an entirely new and unexpected class of relations.” This
example belongs, however, not to the Method of Residues but to the Method
of Difference, the law being ascertained by a direct comparison of the
results of two experiments, which differed in nothing but the presence or
absence of the plate of copper. To have made it exemplify the Method of
Residues, the effect of the resistance of the air and that of the rigidity
of the silk should have been calculated _a priori_, from the laws obtained
by separate and foregone experiments.

“Unexpected and peculiarly striking confirmations of inductive laws
frequently occur in the form of residual phenomena, in the course of
investigations of a widely different nature from those which gave rise to
the inductions themselves. A very elegant example may be cited in the
unexpected confirmation of the law of the development of heat in elastic
fluids by compression, which is afforded by the phenomena of sound. The
inquiry into the cause of sound had led to conclusions respecting its mode
of propagation, from which its velocity in the air could be precisely
calculated. The calculations were performed; but, when compared with fact,
though the agreement was quite sufficient to show the general correctness
of the cause and mode of propagation assigned, yet the _whole_ velocity
could not be shown to arise from this theory. There was still a residual
velocity to be accounted for, which placed dynamical philosophers for a
long time in great dilemma. At length Laplace struck on the happy idea,
that this might arise from the _heat_ developed in the act of that
condensation which necessarily takes place at every vibration by which
sound is conveyed. The matter was subjected to exact calculation, and the
result was at once the complete explanation of the residual phenomenon,
and a striking confirmation of the general law of the development of heat
by compression, under circumstances beyond artificial imitation.”

“Many of the new elements of chemistry have been detected in the
investigation of residual phenomena. Thus Arfwedson discovered lithia by
perceiving an excess of weight in the sulphate produced from a small
portion of what he considered as magnesia present in a mineral he had
analyzed. It is on this principle, too, that the small concentrated
residues of great operations in the arts are almost sure to be the
lurking-places of new chemical ingredients: witness iodine, brome,
selenium, and the new metals accompanying platina in the experiments of
Wollaston and Tennant. It was a happy thought of Glauber to examine what
every body else threw away.”(143)

“Almost all the greatest discoveries in Astronomy,” says the same
author,(144) “have resulted from the consideration of residual phenomena
of a quantitative or numerical kind.... It was thus that the grand
discovery of the precession of the equinoxes resulted as a residual
phenomenon, from the imperfect explanation of the return of the seasons by
the return of the sun to the same apparent place among the fixed stars.
Thus, also, aberration and nutation resulted as residual phenomena from
that portion of the changes of the apparent places of the fixed stars
which was left unaccounted for by precession. And thus again the apparent
proper motions of the stars are the observed residues of their apparent
movements outstanding and unaccounted for by strict calculation of the
effects of precession, nutation, and aberration. The nearest approach
which human theories can make to perfection is to diminish this residue,
this _caput mortuum_ of observation, as it may be considered, as much as
practicable, and, if possible, to reduce it to nothing, either by showing
that something has been neglected in our estimation of known causes, or by
reasoning upon it as a new fact, and on the principle of the inductive
philosophy ascending from the effect to its cause or causes.”

The disturbing effects mutually produced by the earth and planets upon
each other’s motions were first brought to light as residual phenomena, by
the difference which appeared between the observed places of those bodies,
and the places calculated on a consideration solely of their gravitation
toward the sun. It was this which determined astronomers to consider the
law of gravitation as obtaining between all bodies whatever, and therefore
between all particles of matter; their first tendency having been to
regard it as a force acting only between each planet or satellite and the
central body to whose system it belonged. Again, the catastrophists, in
geology, be their opinion right or wrong, support it on the plea, that
after the effect of all causes now in operation has been allowed for,
there remains in the existing constitution of the earth a large residue of
facts, proving the existence at former periods either of other forces, or
of the same forces in a much greater degree of intensity. To add one more
example: those who assert, what no one has shown any real ground for
believing, that there is in one human individual, one sex, or one race of
mankind over another, an inherent and inexplicable superiority in mental
faculties, could only substantiate their proposition by subtracting from
the differences of intellect which we in fact see, all that can be traced
by known laws either to the ascertained differences of physical
organization, or to the differences which have existed in the outward
circumstances in which the subjects of the comparison have hitherto been
placed. What these causes might fail to account for would constitute a
residual phenomenon, which and which alone would be evidence of an
ulterior original distinction, and the measure of its amount. But the
asserters of such supposed differences have not provided themselves with
these necessary logical conditions of the establishment of their doctrine.

The spirit of the Method of Residues being, it is hoped, sufficiently
intelligible from these examples, and the other three methods having
already been so fully exemplified, we may here close our exposition of the
four methods, considered as employed in the investigation of the simpler
and more elementary order of the combinations of phenomena.

§ 6. Dr. Whewell has expressed a very unfavorable opinion of the utility
of the Four Methods, as well as of the aptness of the examples by which I
have attempted to illustrate them. His words are these:(145)

“Upon these methods, the obvious thing to remark is, that they take for
granted the very thing which is most difficult to discover, the reduction
of the phenomena to formulæ such as are here presented to us. When we have
any set of complex facts offered to us; for instance, those which were
offered in the cases of discovery which I have mentioned—the facts of the
planetary paths, of falling bodies, of refracted rays, of cosmical
motions, of chemical analysis; and when, in any of these cases, we would
discover the law of nature which governs them, or, if any one chooses so
to term it, the feature in which all the cases agree, where are we to look
for our A, B, C, and _a_, _b_, _c_? Nature does not present to us the
cases in this form; and how are we to reduce them to this form? You say
_when_ we find the combination of A B C with _a b c_ and A B D with _a b
d_, then we may draw our inference. Granted; but when and where are we to
find such combinations? Even now that the discoveries are made, who will
point out to us what are the A, B, C, and _a_, _b_, _c_, elements of the
cases which have just been enumerated? Who will tell us which of the
methods of inquiry those historically real and successful inquiries
exemplify? Who will carry these formulæ through the history of the
sciences, as they have really grown up, and show us that these four
methods have been operative in their formation; or that any light is
thrown upon the steps of their progress by reference to these formulæ?”

He adds that, in this work, the methods have not been applied “to a large
body of conspicuous and undoubted examples of discovery, extending along
the whole history of science;” which ought to have been done in order that
the methods might be shown to possess the “advantage” (which he claims as
belonging to his own) of being those “by which all great discoveries in
science have really been made.”—(P. 277.)

There is a striking similarity between the objections here made against
Canons of Induction, and what was alleged, in the last century, by as able
men as Dr. Whewell, against the acknowledged Canon of Ratiocination. Those
who protested against the Aristotelian Logic said of the Syllogism, what
Dr. Whewell says of the Inductive Methods, that it “takes for granted the
very thing which is most difficult to discover, the reduction of the
argument to formulæ such as are here presented to us.” The grand
difficulty, they said, is to obtain your syllogism, not to judge of its
correctness when obtained. On the matter of fact, both they and Dr.
Whewell are right. The greatest difficulty in both cases is, first, that
of obtaining the evidence, and next, of reducing it to the form which
tests its conclusiveness. But if we try to reduce it without knowing what
it is to be reduced to, we are not likely to make much progress. It is a
more difficult thing to solve a geometrical problem, than to judge whether
a proposed solution is correct: but if people were not able to judge of
the solution when found, they would have little chance of finding it. And
it can not be pretended that to judge of an induction when found is
perfectly easy, is a thing for which aids and instruments are superfluous;
for erroneous inductions, false inferences from experience, are quite as
common, on some subjects much commoner than true ones. The business of
Inductive Logic is to provide rules and models (such as the Syllogism and
its rules are for ratiocination) to which if inductive arguments conform,
those arguments are conclusive, and not otherwise. This is what the Four
Methods profess to be, and what I believe they are universally considered
to be by experimental philosophers, who had practiced all of them long
before any one sought to reduce the practice to theory.

The assailants of the Syllogism had also anticipated Dr. Whewell in the
other branch of his argument. They said that no discoveries were ever made
by syllogism; and Dr. Whewell says, or seems to say, that none were ever
made by the Four Methods of Induction. To the former objectors, Archbishop
Whately very pertinently answered, that their argument, if good at all,
was good against the reasoning process altogether; for whatever can not be
reduced to syllogism, is not reasoning. And Dr. Whewell’s argument, if
good at all, is good against all inferences from experience. In saying
that no discoveries were ever made by the Four Methods, he affirms that
none were ever made by observation and experiment; for assuredly if any
were, it was by processes reducible to one or other of those methods.

This difference between us accounts for the dissatisfaction which my
examples give him; for I did not select them with a view to satisfy any
one who required to be convinced that observation and experiment are modes
of acquiring knowledge: I confess that in the choice of them I thought
only of illustration, and of facilitating the _conception_ of the Methods
by concrete instances. If it had been my object to justify the processes
themselves as means of investigation, there would have been no need to
look far off, or make use of recondite or complicated instances. As a
specimen of a truth ascertained by the Method of Agreement, I might have
chosen the proposition, “Dogs bark.” This dog, and that dog, and the other
dog, answer to A B C, A D E, A F G. The circumstance of being a dog
answers to A. Barking answers to _a_. As a truth made known by the Method
of Difference, “Fire burns” might have sufficed. Before I touch the fire I
am not burned; this is B C: I touch it, and am burned; this is A B C, _a_
B C.

Such familiar experimental processes are not regarded as inductions by Dr.
Whewell; but they are perfectly homogeneous with those by which, even on
his own showing, the pyramid of science is supplied with its base. In vain
he attempts to escape from this conclusion by laying the most arbitrary
restrictions on the choice of examples admissible as instances of
Induction: they must neither be such as are still matter of discussion (p.
265), nor must any of them be drawn from mental and social subjects (p.
269), nor from ordinary observation and practical life (pp. 241-247). They
must be taken exclusively from the generalizations by which scientific
thinkers have ascended to great and comprehensive laws of natural
phenomena. Now it is seldom possible, in these complicated inquiries, to
go much beyond the initial steps, without calling in the instrument of
Deduction, and the temporary aid of hypothesis; as I myself, in common
with Dr. Whewell, have maintained against the purely empirical school.
Since, therefore, such cases could not conveniently be selected to
illustrate the principles of mere observation and experiment, Dr. Whewell
is misled by their absence into representing the Experimental Methods as
serving no purpose in scientific investigation; forgetting that if those
methods had not supplied the first generalizations, there would have been
no materials for his own conception of Induction to work upon.

His challenge, however, to point out which of the four methods are
exemplified in certain important cases of scientific inquiry, is easily
answered. “The planetary paths,” as far as they are a case of induction at
all,(146) fall under the Method of Agreement. The law of “falling bodies,”
namely, that they describe spaces proportional to the squares of the
times, was historically a deduction from the first law of motion; but the
experiments by which it was verified, and by which it might have been
discovered, were examples of the Method of Agreement; and the apparent
variation from the true law, caused by the resistance of the air, was
cleared up by experiments _in vacuo_, constituting an application of the
Method of Difference. The law of “refracted rays” (the constancy of the
ratio between the sines of incidence and of refraction for each refracting
substance) was ascertained by direct measurement, and therefore by the
Method of Agreement. The “cosmical motions” were determined by highly
complex processes of thought, in which Deduction was predominant, but the
Methods of Agreement and of Concomitant Variations had a large part in
establishing the empirical laws. Every case without exception of “chemical
analysis” constitutes a well-marked example of the Method of Difference.
To any one acquainted with the subjects—to Dr. Whewell himself, there
would not be the smallest difficulty in setting out “the A B C and _a b c_
elements” of these cases.

If discoveries are ever made by observation and experiment without
Deduction, the four methods are methods of discovery: but even if they
were not methods of discovery, it would not be the less true that they are
the sole methods of Proof; and in that character, even the results of
deduction are amenable to them. The great generalizations which begin as
Hypotheses, must end by being proved, and are in reality (as will be shown
hereafter) proved, by the Four Methods. Now it is with Proof, as such,
that Logic is principally concerned. This distinction has indeed no chance
of finding favor with Dr. Whewell; for it is the peculiarity of his
system, not to recognize, in cases of Induction, any necessity for proof.
If, after assuming an hypothesis and carefully collating it with facts,
nothing is brought to light inconsistent with it, that is, if experience
does not _dis_prove it, he is content: at least until a simpler
hypothesis, equally consistent with experience, presents itself. If this
be Induction, doubtless there is no necessity for the four methods. But to
suppose that it is so, appears to me a radical misconception of the nature
of the evidence of physical truths.

So real and practical is the need of a test for induction, similar to the
syllogistic test of ratiocination, that inferences which bid defiance to
the most elementary notions of inductive logic are put forth without
misgiving by persons eminent in physical science, as soon as they are off
the ground on which they are conversant with the facts, and not reduced to
judge only by the arguments; and as for educated persons in general, it
may be doubted if they are better judges of a good or a bad induction than
they were before Bacon wrote. The improvement in the results of thinking
has seldom extended to the processes; or has reached, if any process, that
of investigation only, not that of proof. A knowledge of many laws of
nature has doubtless been arrived at, by framing hypotheses and finding
that the facts corresponded to them; and many errors have been got rid of
by coming to a knowledge of facts which were inconsistent with them, but
not by discovering that the mode of thought which led to the errors was
itself faulty, and might have been known to be such independently of the
facts which disproved the specific conclusion. Hence it is, that while the
thoughts of mankind have on many subjects worked themselves practically
right, the thinking power remains as weak as ever: and on all subjects on
which the facts which would check the result are not accessible, as in
what relates to the invisible world, and even, as has been seen lately, to
the visible world of the planetary regions, men of the greatest scientific
acquirements argue as pitiably as the merest ignoramus. For though they
have made many sound inductions, they have not learned from them (and Dr.
Whewell thinks there is no necessity that they should learn) the
principles of inductive _evidence_.




                                Chapter X.


Of Plurality Of Causes, And Of The Intermixture Of Effects.


§ 1. In the preceding exposition of the four methods of observation and
experiment, by which we contrive to distinguish among a mass of
co-existent phenomena the particular effect due to a given cause, or the
particular cause which gave birth to a given effect, it has been necessary
to suppose, in the first instance, for the sake of simplification, that
this analytical operation is encumbered by no other difficulties than what
are essentially inherent in its nature; and to represent to ourselves,
therefore, every effect, on the one hand as connected exclusively with a
single cause, and on the other hand as incapable of being mixed and
confounded with any other co-existent effect. We have regarded _a b c d
e_, the aggregate of the phenomena existing at any moment, as consisting
of dissimilar facts, _a_, _b_, _c_, _d_, and _e_, for each of which one,
and only one, cause needs be sought; the difficulty being only that of
singling out this one cause from the multitude of antecedent
circumstances, A, B, C, D, and E. The cause indeed may not be simple; it
may consist of an assemblage of conditions; but we have supposed that
there was only one possible assemblage of conditions from which the given
effect could result.

If such were the fact, it would be comparatively an easy task to
investigate the laws of nature. But the supposition does not hold in
either of its parts. In the first place, it is not true that the same
phenomenon is always produced by the same cause: the effect _a_ may
sometimes arise from A, sometimes from B. And, secondly, the effects of
different causes are often not dissimilar, but homogeneous, and marked out
by no assignable boundaries from one another: A and B may produce not _a_
and _b_, but different portions of an effect _a_. The obscurity and
difficulty of the investigation of the laws of phenomena is singularly
increased by the necessity of adverting to these two circumstances:
Intermixture of Effects, and Plurality of Causes. To the latter, being the
simpler of the two considerations, we shall first direct our attention.

It is not true, then, that one effect must be connected with only one
cause, or assemblage of conditions; that each phenomenon can be produced
only in one way. There are often several independent modes in which the
same phenomenon could have originated. One fact may be the consequent in
several invariable sequences; it may follow, with equal uniformity, any
one of several antecedents, or collections of antecedents. Many causes may
produce mechanical motion; many causes may produce some kinds of
sensation; many causes may produce death. A given effect may really be
produced by a certain cause, and yet be perfectly capable of being
produced without it.

§ 2. One of the principal consequences of this fact of Plurality of Causes
is, to render the first of the inductive methods, that of Agreement,
uncertain. To illustrate that method, we supposed two instances, A B C
followed by _a b c_, and A D E followed by _a d e_. From these instances
it might apparently be concluded that A is an invariable antecedent of
_a_, and even that it is the unconditional invariable antecedent, or
cause, if we could be sure that there is no other antecedent common to the
two cases. That this difficulty may not stand in the way, let us suppose
the two cases positively ascertained to have no antecedent in common
except A. The moment, however, that we let in the possibility of a
plurality of causes, the conclusion fails. For it involves a tacit
supposition, that _a_ must have been produced in both instances by the
same cause. If there can possibly have been two causes, those two may, for
example, be C and E: the one may have been the cause of _a_ in the former
of the instances, the other in the latter, A having no influence in either
case.

Suppose, for example, that two great artists or great philosophers, that
two extremely selfish or extremely generous characters, were compared
together as to the circumstances of their education and history, and the
two cases were found to agree only in one circumstance: would it follow
that this one circumstance was the cause of the quality which
characterized both those individuals? Not at all; for the causes which may
produce any type of character are very numerous; and the two persons might
equally have agreed in their character, though there had been no manner of
resemblance in their previous history.

This, therefore, is a characteristic imperfection of the Method of
Agreement, from which imperfection the Method of Difference is free. For
if we have two instances, A B C and B C, of which B C gives _b c_, and A
being added converts it into _a b c_, it is certain that in this instance
at least, A was either the cause of _a_, or an indispensable portion of
its cause, even though the cause which produces it in other instances may
be altogether different. Plurality of Causes, therefore, not only does not
diminish the reliance due to the Method of Difference, but does not even
render a greater number of observations or experiments necessary: two
instances, the one positive and the other negative, are still sufficient
for the most complete and rigorous induction. Not so, however, with the
Method of Agreement. The conclusions which that yields, when the number of
instances compared is small, are of no real value, except as, in the
character of suggestions, they may lead either to experiments bringing
them to the test of the Method of Difference, or to reasonings which may
explain and verify them deductively.

It is only when the instances, being indefinitely multiplied and varied,
continue to suggest the same result, that this result acquires any high
degree of independent value. If there are but two instances, A B C and A D
E, though these instances have no antecedent in common except A, yet as
the effect may possibly have been produced in the two cases by different
causes, the result is at most only a slight probability in favor of A;
there may be causation, but it is almost equally probable that there was
only a coincidence. But the oftener we repeat the observation, varying the
circumstances, the more we advance toward a solution of this doubt. For if
we try A F G, A H K, etc., all unlike one another except in containing the
circumstance A, and if we find the effect _a_ entering into the result in
all these cases, we must suppose one of two things, either that it is
caused by A, or that it has as many different causes as there are
instances. With each addition, therefore, to the number of instances, the
presumption is strengthened in favor of A. The inquirer, of course, will
not neglect, if an opportunity present itself, to exclude A from some one
of these combinations, from A H K for instance, and by trying H K
separately, appeal to the Method of Difference in aid of the Method of
Agreement. By the Method of Difference alone can it be ascertained that A
is the cause of _a_; but that it is either the cause, or another effect of
the same cause, may be placed beyond any reasonable doubt by the Method of
Agreement, provided the instances are very numerous as well as
sufficiently various.

After how great a multiplication, then, of varied instances, all agreeing
in no other antecedent except A, is the supposition of a plurality of
causes sufficiently rebutted, and the conclusion that _a_ is connected
with A divested of the characteristic imperfection, and reduced to a
virtual certainty? This is a question which we can not be exempted from
answering: but the consideration of it belongs to what is called the
Theory of Probability, which will form the subject of a chapter hereafter.
It is seen, however, at once, that the conclusion does amount to a
practical certainty after a sufficient number of instances, and that the
method, therefore, is not radically vitiated by the characteristic
imperfection. The result of these considerations is only, in the first
place, to point out a new source of inferiority in the Method of Agreement
as compared with other modes of investigation, and new reasons for never
resting contented with the results obtained by it, without attempting to
confirm them either by the Method of Difference, or by connecting them
deductively with some law or laws already ascertained by that superior
method. And, in the second place, we learn from this the true theory of
the value of mere _number_ of instances in inductive inquiry. The
Plurality of Causes is the only reason why mere number is of any
importance. The tendency of unscientific inquirers is to rely too much on
number, without analyzing the instances; without looking closely enough
into their nature to ascertain what circumstances are or are not
eliminated by means of them. Most people hold their conclusions with a
degree of assurance proportioned to the mere _mass_ of the experience on
which they appear to rest; not considering that by the addition of
instances to instances, all of the same kind, that is, differing from one
another only in points already recognized as immaterial, nothing whatever
is added to the evidence of the conclusion. A single instance eliminating
some antecedent which existed in all the other cases, is of more value
than the greatest multitude of instances which are reckoned by their
number alone. It is necessary, no doubt, to assure ourselves, by
repetition of the observation or experiment, that no error has been
committed concerning the individual facts observed; and until we have
assured ourselves of this, instead of varying the circumstances, we can
not too scrupulously repeat the same experiment or observation without any
change. But when once this assurance has been obtained, the multiplication
of instances which do not exclude any more circumstances is entirely
useless, provided there have been already enough to exclude the
supposition of Plurality of Causes.

It is of importance to remark, that the peculiar modification of the
Method of Agreement, which, as partaking in some degree of the nature of
the Method of Difference, I have called the Joint Method of Agreement and
Difference, is not affected by the characteristic imperfection now pointed
out. For, in the joint method, it is supposed not only that the instances
in which _a_ is, agree only in containing A, but also that the instances
in which _a_ is not, agree only in not containing A. Now, if this be so, A
must be not only the cause of _a_, but the only possible cause: for if
there were another, as for example B, then in the instances in which _a_
is not, B must have been absent as well as A, and it would not be true
that these instances agree _only_ in not containing A. This, therefore,
constitutes an immense advantage of the joint method over the simple
Method of Agreement. It may seem, indeed, that the advantage does not
belong so much to the joint method, as to one of its two premises (if they
may be so called), the negative premise. The Method of Agreement, when
applied to negative instances, or those in which a phenomenon does _not_
take place, is certainly free from the characteristic imperfection which
affects it in the affirmative case. The negative premise, it might
therefore be supposed, could be worked as a simple case of the Method of
Agreement, without requiring an affirmative premise to be joined with it.
But though this is true in principle, it is generally altogether
impossible to work the Method of Agreement by negative instances without
positive ones; it is so much more difficult to exhaust the field of
negation than that of affirmation. For instance, let the question be what
is the cause of the transparency of bodies; with what prospect of success
could we set ourselves to inquire directly in what the multifarious
substances which are _not_ transparent agree? But we might hope much
sooner to seize some point of resemblance among the comparatively few and
definite species of objects which _are_ transparent; and this being
attained, we should quite naturally be put upon examining whether the
_absence_ of this one circumstance be not precisely the point in which all
opaque substances will be found to resemble.

The Joint Method of Agreement and Difference, therefore, or as I have
otherwise called it, the Indirect Method of Difference (because, like the
Method of Difference properly so-called, it proceeds by ascertaining how
and in what the cases where the phenomenon is present differ from those in
which it is absent) is, after the Direct Method of Difference, the most
powerful of the remaining instruments of inductive investigation; and in
the sciences which depend on pure observation, with little or no aid from
experiment, this method, so well exemplified in the speculation on the
cause of dew, is the primary resource, so far as direct appeals to
experience are concerned.

§ 3. We have thus far treated Plurality of Causes only as a possible
supposition, which, until removed, renders our inductions uncertain; and
have only considered by what means, where the plurality does not really
exist, we may be enabled to disprove it. But we must also consider it as a
case actually occurring in nature, and which, as often as it does occur,
our methods of induction ought to be capable of ascertaining and
establishing. For this, however, there is required no peculiar method.
When an effect is really producible by two or more causes, the process for
detecting them is in no way different from that by which we discover
single causes. They may (first) be discovered as separate sequences, by
separate sets of instances. One set of observations or experiments shows
that the sun is a cause of heat, another that friction is a source of it,
another that percussion, another that electricity, another that chemical
action is such a source. Or (secondly) the plurality may come to light in
the course of collating a number of instances, when we attempt to find
some circumstance in which they all agree, and fail in doing so. We find
it impossible to trace, in all the cases in which the effect is met with,
any common circumstance. We find that we can eliminate _all_ the
antecedents; that no one of them is present in all the instances, no one
of them indispensable to the effect. On closer scrutiny, however, it
appears that though no one is always present, one or other of several
always is. If, on further analysis, we can detect in these any common
element, we may be able to ascend from them to some one cause which is the
really operative circumstance in them all. Thus it is now thought that in
the production of heat by friction, percussion, chemical action, etc., the
ultimate source is one and the same. But if (as continually happens) we
can not take this ulterior step, the different antecedents must be set
down provisionally as distinct causes, each sufficient of itself to
produce the effect.

We here close our remarks on the Plurality of Causes, and proceed to the
still more peculiar and more complex case of the Intermixture of Effects,
and the interference of causes with one another: a case constituting the
principal part of the complication and difficulty of the study of nature;
and with which the four only possible methods of directly inductive
investigation by observation and experiment, are, for the most part, as
will appear presently, quite unequal to cope. The instrument of Deduction
alone is adequate to unravel the complexities proceeding from this source;
and the four methods have little more in their power than to supply
premises for, and a verification of, our deductions.

§ 4. A concurrence of two or more causes, not separately producing each
its own effect, but interfering with or modifying the effects of one
another, takes place, as has already been explained in two different ways.
In the one, which is exemplified by the joint operation of different
forces in mechanics, the separate effects of all the causes continue to be
produced, but are compounded with one another, and disappear in one total.
In the other, illustrated by the case of chemical action, the separate
effects cease entirely, and are succeeded by phenomena altogether
different, and governed by different laws.

Of these cases the former is by far the more frequent, and this case it is
which, for the most part, eludes the grasp of our experimental methods.
The other and exceptional case is essentially amenable to them. When the
laws of the original agents cease entirely, and a phenomenon makes its
appearance, which, with reference to those laws, is quite heterogeneous;
when, for example, two gaseous substances, hydrogen and oxygen, on being
brought together, throw off their peculiar properties, and produce the
substance called water; in such cases the new fact may be subjected to
experimental inquiry, like any other phenomenon; and the elements which
are said to compose it may be considered as the mere agents of its
production—the conditions on which it depends, the facts which make up its
cause.

The _effects_ of the new phenomenon, the _properties_ of water, for
instance, are as easily found by experiment as the effects of any other
cause. But to discover the _cause_ of it, that is, the particular
conjunction of agents from which it results, is often difficult enough. In
the first place, the origin and actual production of the phenomenon are
most frequently inaccessible to our observation. If we could not have
learned the composition of water until we found instances in which it was
actually produced from oxygen and hydrogen, we should have been forced to
wait until the casual thought struck some one of passing an electric spark
through a mixture of the two gases, or inserting a lighted taper into it,
merely to try what would happen. Besides, many substances, though they can
be analyzed, can not by any known artificial means be recompounded.
Further, even if we could have ascertained, by the Method of Agreement,
that oxygen and hydrogen were both present when water is produced, no
experimentation on oxygen and hydrogen separately, no knowledge of their
laws, could have enabled us deductively to infer that they would produce
water. We require a specific experiment on the two combined.

Under these difficulties, we should generally have been indebted for our
knowledge of the causes of this class of effects, not to any inquiry
directed specifically toward that end, but either to accident, or to the
gradual progress of experimentation on the different combinations of which
the producing agents are susceptible; if it were not for a peculiarity
belonging to effects of this description, that they often, under some
particular combination of circumstances, reproduce their causes. If water
results from the juxtaposition of hydrogen and oxygen whenever this can be
made sufficiently close and intimate, so, on the other hand, if water
itself be placed in certain situations, hydrogen and oxygen are reproduced
from it: an abrupt termination is put to the new laws, and the agents
re-appear separately with their own properties as at first. What is called
chemical analysis is the process of searching for the causes of a
phenomenon among its effects, or rather among the effects produced by the
action of some other causes upon it.

Lavoisier, by heating mercury to a high temperature in a close vessel
containing air, found that the mercury increased in weight, and became
what was then called red precipitate, while the air, on being examined
after the experiment, proved to have lost weight, and to have become
incapable of supporting life or combustion. When red precipitate was
exposed to a still greater heat, it became mercury again, and gave off a
gas which did support life and flame. Thus the agents which by their
combination produced red precipitate, namely, the mercury and the gas,
reappear as effects resulting from that precipitate when acted upon by
heat. So, if we decompose water by means of iron filings, we produce two
effects, rust and hydrogen. Now rust is already known, by experiments upon
the component substances, to be an effect of the union of iron and oxygen:
the iron we ourselves supplied, but the oxygen must have been produced
from the water. The result, therefore, is that water has disappeared, and
hydrogen and oxygen have appeared in its stead; or, in other words, the
original laws of these gaseous agents, which had been suspended by the
superinduction of the new laws called the properties of water, have again
started into existence, and the causes of water are found among its
effects.

Where two phenomena, between the laws or properties of which, considered
in themselves, no connection can be traced, are thus reciprocally cause
and effect, each capable in its turn of being produced from the other, and
each, when it produces the other, ceasing itself to exist (as water is
produced from oxygen and hydrogen, and oxygen and hydrogen are reproduced
from water); this causation of the two phenomena by one another, each
being generated by the other’s destruction, is properly transformation.
The idea of chemical composition is an idea of transformation, but of a
transformation which is incomplete; since we consider the oxygen and
hydrogen to be present in the water _as_ oxygen and hydrogen, and capable
of being discovered in it if our senses were sufficiently keen: a
supposition (for it is no more) grounded solely on the fact that the
weight of the water is the sum of the separate weights of the two
ingredients. If there had not been this exception to the entire
disappearance, in the compound, of the laws of the separate ingredients;
if the combined agents had not, in this one particular of weight,
preserved their own laws, and produced a joint result equal to the sum of
their separate results; we should never, probably, have had the notion now
implied by the words chemical composition; and, in the facts of water
produced from hydrogen and oxygen, and hydrogen and oxygen produced from
water, as the transformation would have been complete, we should have seen
only a transformation.

In these cases, where the heteropathic effect (as we called it in a former
chapter)(147) is but a transformation of its cause, or in other words,
where the effect and its cause are reciprocally such, and mutually
convertible into each other; the problem of finding the cause resolves
itself into the far easier one of finding an effect, which is the kind of
inquiry that admits of being prosecuted by direct experiment. But there
are other cases of heteropathic effects to which this mode of
investigation is not applicable. Take, for instance, the heteropathic laws
of mind; that portion of the phenomena of our mental nature which are
analogous to chemical rather than to dynamical phenomena; as when a
complex passion is formed by the coalition of several elementary impulses,
or a complex emotion by several simple pleasures or pains, of which it is
the result without being the aggregate, or in any respect homogeneous with
them. The product, in these cases, is generated by its various factors;
but the factors can not be reproduced from the product; just as a youth
can grow into an old man, but an old man can not grow into a youth. We can
not ascertain from what simple feelings any of our complex states of mind
are generated, as we ascertain the ingredients of a chemical compound, by
making it, in its turn, generate them. We can only, therefore, discover
these laws by the slow process of studying the simple feelings themselves,
and ascertaining synthetically, by experimenting on the various
combinations of which they are susceptible, what they, by their mutual
action upon one another, are capable of generating.

§ 5. It might have been supposed that the other, and apparently simpler
variety of the mutual interference of causes, where each cause continues
to produce its own proper effect according to the same laws to which it
conforms in its separate state, would have presented fewer difficulties to
the inductive inquirer than that of which we have just finished the
consideration. It presents, however, so far as direct induction apart from
deduction is concerned, infinitely greater difficulties. When a
concurrence of causes gives rise to a new effect, bearing no relation to
the separate effects of those causes, the resulting phenomenon stands
forth undisguised, inviting attention to its peculiarity, and presenting
no obstacle to our recognizing its presence or absence among any number of
surrounding phenomena. It admits, therefore, of being easily brought under
the canons of Induction, provided instances can be obtained such as those
canons require; and the non-occurrence of such instances, or the want of
means to produce them artificially, is the real and only difficulty in
such investigations; a difficulty not logical but in some sort physical.
It is otherwise with cases of what, in a preceding chapter, has been
denominated the Composition of Causes. There, the effects of the separate
causes do not terminate and give place to others, thereby ceasing to form
any part of the phenomenon to be investigated; on the contrary, they still
take place, but are intermingled with, and disguised by, the homogeneous
and closely allied effects of other causes. They are no longer _a_, _b_,
_c_, _d_, _e_, existing side by side, and continuing to be separately
discernible; they are +_a_, -_a_, ½_b_, _-b_, 2_b_, etc.; some of which
cancel one another, while many others do not appear distinguishably, but
merge in one sum; forming altogether a result, between which and the
causes whereby it was produced there is often an insurmountable difficulty
in tracing by observation any fixed relation whatever.

The general idea of the Composition of Causes has been seen to be, that
though two or more laws interfere with one another, and apparently
frustrate or modify one another’s operation, yet in reality all are
fulfilled, the collective effect being the exact sum of the effects of the
causes taken separately. A familiar instance is that of a body kept in
equilibrium by two equal and contrary forces. One of the forces if acting
alone would carry the body in a given time a certain distance to the west,
the other if acting alone would carry it exactly as far toward the east;
and the result is the same as if it had been first carried to the west as
far as the one force would carry it, and then back toward the east as far
as the other would carry it—that is, precisely the same distance; being
ultimately left where it was found at first.

All laws of causation are liable to be in this manner counteracted, and
seemingly frustrated, by coming into conflict with other laws, the
separate result of which is opposite to theirs, or more or less
inconsistent with it. And hence, with almost every law, many instances in
which it really is entirely fulfilled, do not, at first sight, appear to
be cases of its operation at all. It is so in the example just adduced: a
force in mechanics means neither more nor less than a cause of motion, yet
the sum of the effects of two causes of motion may be rest. Again, a body
solicited by two forces in directions making an angle with one another,
moves in the diagonal; and it seems a paradox to say that motion in the
diagonal is the sum of two motions in two other lines. Motion, however, is
but change of place, and at every instant the body is in the exact place
it would have been in if the forces had acted during alternate instants
instead of acting in the same instant (saving that if we suppose two
forces to act successively which are in truth simultaneous we must of
course allow them double the time). It is evident, therefore, that each
force has had, during each instant, all the effect which belonged to it;
and that the modifying influence which one of two concurrent causes is
said to exercise with respect to the other may be considered as exerted
not over the action of the cause itself, but over the effect after it is
completed. For all purposes of predicting, calculating, or explaining
their joint result, causes which compound their effects may be treated as
if they produced simultaneously each of them its own effect, and all these
effects co-existed visibly.

Since the laws of causes are as really fulfilled when the causes are said
to be counteracted by opposing causes, as when they are left to their own
undisturbed action, we must be cautious not to express the laws in such
terms as would render the assertion of their being fulfilled in those
cases a contradiction. If, for instance, it were stated as a law of nature
that a body to which a force is applied moves in the direction of the
force, with a velocity proportioned to the force directly, and to its own
mass inversely; when in point of fact some bodies to which a force is
applied do not move at all, and those which do move (at least in the
region of our earth) are, from the very first, retarded by the action of
gravity and other resisting forces, and at last stopped altogether; it is
clear that the general proposition, though it would be true under a
certain hypothesis, would not express the facts as they actually occur. To
accommodate the expression of the law to the real phenomena, we must say,
not that the object moves, but that it _tends_ to move, in the direction
and with the velocity specified. We might, indeed, guard our expression in
a different mode, by saying that the body moves in that manner unless
prevented, or except in so far as prevented, by some counteracting cause.
But the body does not only move in that manner unless counteracted; it
_tends_ to move in that manner even when counteracted; it still exerts, in
the original direction, the same energy of movement as if its first
impulse had been undisturbed, and produces, by that energy, an exactly
equivalent quantity of effect. This is true even when the force leaves the
body as it found it, in a state of absolute rest; as when we attempt to
raise a body of three tons’ weight with a force equal to one ton. For if,
while we are applying this force, wind or water or any other agent
supplies an additional force just exceeding two tons, the body will be
raised; thus proving that the force we applied exerted its full effect, by
neutralizing an equivalent portion of the weight which it was insufficient
altogether to overcome. And if, while we are exerting this force of one
ton upon the object in a direction contrary to that of gravity, it be put
into a scale and weighed, it will be found to have lost a ton of its
weight, or, in other words, to press downward with a force only equal to
the difference of the two forces.

These facts are correctly indicated by the expression _tendency_. All laws
of causation, in consequence of their liability to be counteracted,
require to be stated in words affirmative of tendencies only, and not of
actual results. In those sciences of causation which have an accurate
nomenclature, there are special words which signify a tendency to the
particular effect with which the science is conversant; thus _pressure_,
in mechanics, is synonymous with tendency to motion, and forces are not
reasoned on as causing actual motion, but as exerting pressure. A similar
improvement in terminology would be very salutary in many other branches
of science.

The habit of neglecting this necessary element in the precise expression
of the laws of nature, has given birth to the popular prejudice that all
general truths have exceptions; and much unmerited distrust has thence
accrued to the conclusions of science, when they have been submitted to
the judgment of minds insufficiently disciplined and cultivated. The rough
generalizations suggested by common observation usually have exceptions;
but principles of science, or, in other words, laws of causation, have
not. “What is thought to be an exception to a principle” (to quote words
used on a different occasion), “is always some other and distinct
principle cutting into the former; some other force which impinges(148)
against the first force, and deflects it from its direction. There are not
a law and an exception to that law, the law acting in ninety-nine cases,
and the exception in one. There are two laws, each possibly acting in the
whole hundred cases, and bringing about a common effect by their conjunct
operation. If the force which, being the less conspicuous of the two, is
called the _disturbing_ force, prevails sufficiently over the other force
in some one case, to constitute that case what is commonly called an
exception, the same disturbing force probably acts as a modifying cause in
many other cases which no one will call exceptions.

“Thus if it were stated to be a law of nature that all heavy bodies fall
to the ground, it would probably be said that the resistance of the
atmosphere, which prevents a balloon from falling, constitutes the balloon
an exception to that pretended law of nature. But the real law is, that
all heavy bodies _tend_ to fall; and to this there is no exception, not
even the sun and moon; for even they, as every astronomer knows, tend
toward the earth, with a force exactly equal to that with which the earth
tends toward them. The resistance of the atmosphere might, in the
particular case of the balloon, from a misapprehension of what the law of
gravitation is, be said to _prevail over_ the law; but its disturbing
effect is quite as real in every other case, since though it does not
prevent, it retards the fall of all bodies whatever. The rule, and the
so-called exception, do not divide the cases between them; each of them is
a comprehensive rule extending to all cases. To call one of these
concurrent principles an exception to the other, is superficial, and
contrary to the correct principles of nomenclature and arrangement. An
effect of precisely the same kind, and arising from the same cause, ought
not to be placed in two different categories, merely as there does or does
not exist another cause preponderating over it.”(149)

§ 6. We have now to consider according to what method these complex
effects, compounded of the effects of many causes, are to be studied; how
we are enabled to trace each effect to the concurrence of causes in which
it originated, and ascertain the conditions of its recurrence—the
circumstances in which it may be expected again to occur. The conditions
of a phenomenon which arises from a composition of causes, may be
investigated either deductively or experimentally.

The case, it is evident, is naturally susceptible of the deductive mode of
investigation. The law of an effect of this description is a result of the
laws of the separate causes on the combination of which it depends, and
is, therefore, in itself capable of being deduced from these laws. This is
called the method _a priori_. The other, or _a posteriori_ method,
professes to proceed according to the canons of experimental inquiry.
Considering the whole assemblage of concurrent causes which produced the
phenomenon, as one single cause, it attempts to ascertain the cause in the
ordinary manner, by a comparison of instances. This second method
subdivides itself into two different varieties. If it merely collates
instances of the effect, it is a method of pure observation. If it
operates upon the causes, and tries different combinations of them, in
hopes of ultimately hitting the precise combination which will produce the
given total effect, it is a method of experiment.

In order more completely to clear up the nature of each of these three
methods, and determine which of them deserves the preference, it will be
expedient (conformably to a favorite maxim of Lord Chancellor Eldon, to
which, though it has often incurred philosophical ridicule, a deeper
philosophy will not refuse its sanction) to “clothe them in
circumstances.” We shall select for this purpose a case which as yet
furnishes no very brilliant example of the success of any of the three
methods, but which is all the more suited to illustrate the difficulties
inherent in them. Let the subject of inquiry be, the conditions of health
and disease in the human body; or (for greater simplicity) the conditions
of recovery from a given disease; and in order to narrow the question
still more, let it be limited, in the first instance, to this one inquiry:
Is, or is not, some particular medicament (mercury, for instance) a remedy
for the given disease.

Now, the deductive method would set out from known properties of mercury,
and known laws of the human body, and by reasoning from these, would
attempt to discover whether mercury will act upon the body when in the
morbid condition supposed, in such a manner as would tend to restore
health. The experimental method would simply administer mercury in as many
cases as possible, noting the age, sex, temperament, and other
peculiarities of bodily constitution, the particular form or variety of
the disease, the particular stage of its progress, etc., remarking in
which of these cases it was attended with a salutary effect, and with what
circumstances it was on those occasions combined. The method of simple
observation would compare instances of recovery, to find whether they
agreed in having been preceded by the administration of mercury; or would
compare instances of recovery with instances of failure, to find cases
which, agreeing in all other respects, differed only in the fact that
mercury had been administered, or that it had not.

§ 7. That the last of these three modes of investigation is applicable to
the case, no one has ever seriously contended. No conclusions of value on
a subject of such intricacy ever were obtained in that way. The utmost
that could result would be a vague general impression for or against the
efficacy of mercury, of no avail for guidance unless confirmed by one of
the other two methods. Not that the results, which this method strives to
obtain, would not be of the utmost possible value if they could be
obtained. If all the cases of recovery which presented themselves, in an
examination extending to a great number of instances, were cases in which
mercury had been administered, we might generalize with confidence from
this experience, and should have obtained a conclusion of real value. But
no such basis for generalization can we, in a case of this description,
hope to obtain. The reason is that which we have spoken of as constituting
the characteristic imperfection of the Method of Agreement, Plurality of
Causes. Supposing even that mercury does tend to cure the disease, so many
other causes, both natural and artificial, also tend to cure it, that
there are sure to be abundant instances of recovery in which mercury has
not been administered, unless, indeed, the practice be to administer it in
all cases; on which supposition it will equally be found in the cases of
failure.

When an effect results from the union of many causes, the share which each
has in the determination of the effect can not in general be great, and
the effect is not likely, even in its presence or absence, still less in
its variations, to follow, even approximately, any one of the causes.
Recovery from a disease is an event to which, in every case, many
influences must concur. Mercury may be one such influence; but from the
very fact that there are many other such, it will necessarily happen that
although mercury is administered, the patient, for want of other
concurring influences, will often not recover, and that he often will
recover when it is not administered, the other favorable influences being
sufficiently powerful without it. Neither, therefore, will the instances
of recovery agree in the administration of mercury, nor will the instances
of failure agree in its non-administration. It is much if, by multiplied
and accurate returns from hospitals and the like, we can collect that
there are rather more recoveries and rather fewer failures when mercury is
administered than when it is not; a result of very secondary value even as
a guide to practice, and almost worthless as a contribution to the theory
of the subject.(150)

§ 8. The inapplicability of the method of simple observation to ascertain
the conditions of effects dependent on many concurring causes, being thus
recognized, we shall next inquire whether any greater benefit can be
expected from the other branch of the _a posteriori_ method, that which
proceeds by directly trying different combinations of causes, either
artificially produced or found in nature, and taking notice what is their
effect; as, for example, by actually trying the effect of mercury in as
many different circumstances as possible. This method differs from the one
which we have just examined in turning our attention directly to the
causes or agents, instead of turning it to the effect, recovery from the
disease. And since, as a general rule, the effects of causes are far more
accessible to our study than the causes of effects, it is natural to think
that this method has a much better chance of proving successful than the
former.

The method now under consideration is called the Empirical Method; and in
order to estimate it fairly, we must suppose it to be completely, not
incompletely, empirical. We must exclude from it every thing which
partakes of the nature not of an experimental but of a deductive
operation. If, for instance, we try experiments with mercury upon a person
in health, in order to ascertain the general laws of its action upon the
human body, and then reason from these laws to determine how it will act
upon persons affected with a particular disease, this may be a really
effectual method; but this is deduction. The experimental method does not
derive the law of a complex case from the simpler laws which conspire to
produce it, but makes its experiments directly upon the complex case. We
must make entire abstraction of all knowledge of the simpler tendencies,
the _modi operandi_ of mercury in detail. Our experimentation must aim at
obtaining a direct answer to the specific question, Does or does not
mercury tend to cure the particular disease?

Let us see, therefore, how far the case admits of the observance of those
rules of experimentation which it is found necessary to observe in other
cases. When we devise an experiment to ascertain the effect of a given
agent, there are certain precautions which we never, if we can help it,
omit. In the first place, we introduce the agent into the midst of a set
of circumstances which we have exactly ascertained. It needs hardly be
remarked how far this condition is from being realized in any case
connected with the phenomena of life; how far we are from knowing what are
all the circumstances which pre-exist in any instance in which mercury is
administered to a living being. This difficulty, however, though
insuperable in most cases, may not be so in all; there are sometimes
concurrences of many causes, in which we yet know accurately what the
causes are. Moreover, the difficulty may be attenuated by sufficient
multiplication of experiments, in circumstances rendering it improbable
that any of the unknown causes should exist in them all. But when we have
got clear of this obstacle, we encounter another still more serious. In
other cases, when we intend to try an experiment, we do not reckon it
enough that there be no circumstance in the case the presence of which is
unknown to us. We require, also, that none of the circumstances which we
do know shall have effects susceptible of being confounded with those of
the agents whose properties we wish to study. We take the utmost pains to
exclude all causes capable of composition with the given cause; or, if
forced to let in any such causes, we take care to make them such that we
can compute and allow for their influence, so that the effect of the given
cause may, after the subduction of those other effects, be apparent as a
residual phenomenon.

These precautions are inapplicable to such cases as we are now
considering. The mercury of our experiment being tried with an unknown
multitude (or even let it be a known multitude) of other influencing
circumstances, the mere fact of their being influencing circumstances
implies that they disguise the effect of the mercury, and preclude us from
knowing whether it has any effect or not. Unless we already knew what and
how much is owing to every other circumstance (that is, unless we suppose
the very problem solved which we are considering the means of solving), we
can not tell that those other circumstances may not have produced the
whole of the effect, independently or even in spite of the mercury. The
Method of Difference, in the ordinary mode of its use, namely, by
comparing the state of things following the experiment with the state
which preceded it, is thus, in the case of intermixture of effects,
entirely unavailing; because other causes than that whose effect we are
seeking to determine have been operating during the transition. As for the
other mode of employing the Method of Difference, namely, by comparing,
not the same case at two different periods, but different cases, this in
the present instance is quite chimerical. In phenomena so complicated it
is questionable if two cases, similar in all respects but one, ever
occurred; and were they to occur, we could not possibly know that they
were so exactly similar.

Any thing like a scientific use of the method of experiment, in these
complicated cases, is therefore out of the question. We can generally,
even in the most favorable cases, only discover by a succession of trials,
that a certain cause is _very often_ followed by a certain effect. For, in
one of these conjunct effects, the portion which is determined by any one
of the influencing agents, is usually, as we before remarked, but small;
and it must be a more potent cause than most, if even the tendency which
it really exerts is not thwarted by other tendencies in nearly as many
cases as it is fulfilled. Some causes indeed there are which are more
potent than any counteracting causes to which they are commonly exposed;
and accordingly there are some truths in medicine which are sufficiently
proved by direct experiment. Of these the most familiar are those that
relate to the efficacy of the substances known as Specifics for particular
diseases, “quinine, colchicum, lime-juice, cod-liver oil,”(151) and a few
others. Even these are not invariably followed by success; but they
succeed in so large a proportion of cases, and against such powerful
obstacles, that their _tendency_ to restore health in the disorders for
which they are prescribed may be regarded as an experimental truth.(152)

If so little can be done by the experimental method to determine the
conditions of an effect of many combined causes, in the case of medical
science; still less is this method applicable to a class of phenomena more
complicated than even those of physiology, the phenomena of politics and
history. There, Plurality of Causes exists in almost boundless excess, and
effects are, for the most part, inextricably interwoven with one another.
To add to the embarrassment, most of the inquiries in political science
relate to the production of effects of a most comprehensive description,
such as the public wealth, public security, public morality, and the like:
results liable to be affected directly or indirectly either in _plus_ or
in _minus_ by nearly every fact which exists, or event which occurs, in
human society. The vulgar notion, that the safe methods on political
subjects are those of Baconian induction—that the true guide is not
general reasoning, but specific experience—will one day be quoted as among
the most unequivocal marks of a low state of the speculative faculties in
any age in which it is accredited. Nothing can be more ludicrous than the
sort of parodies on experimental reasoning which one is accustomed to meet
with, not in popular discussion only, but in grave treatises, when the
affairs of nations are the theme. “How,” it is asked, “can an institution
be bad, when the country has prospered under it?” “How can such or such
causes have contributed to the prosperity of one country, when another has
prospered without them?” Whoever makes use of an argument of this kind,
not intending to deceive, should be sent back to learn the elements of
some one of the more easy physical sciences. Such reasoners ignore the
fact of Plurality of Causes in the very case which affords the most signal
example of it. So little could be concluded, in such a case, from any
possible collation of individual instances, that even the impossibility,
in social phenomena, of making artificial experiments, a circumstance
otherwise so prejudicial to directly inductive inquiry, hardly affords, in
this case, additional reason of regret. For even if we could try
experiments upon a nation or upon the human race, with as little scruple
as M. Magendie tried them on dogs and rabbits, we should never succeed in
making two instances identical in every respect except the presence or
absence of some one definite circumstance. The nearest approach to an
experiment in the philosophical sense, which takes place in politics, is
the introduction of a new operative element into national affairs by some
special and assignable measure of government, such as the enactment or
repeal of a particular law. But where there are so many influences at
work, it requires some time for the influence of any new cause upon
national phenomena to become apparent; and as the causes operating in so
extensive a sphere are not only infinitely numerous, but in a state of
perpetual alteration, it is always certain that before the effect of the
new cause becomes conspicuous enough to be a subject of induction, so many
of the other influencing circumstances will have changed as to vitiate the
experiment.(153)

Two, therefore, of the three possible methods for the study of phenomena
resulting from the composition of many causes, being, from the very nature
of the case, inefficient and illusory, there remains only the third—that
which considers the causes separately, and infers the effect from the
balance of the different tendencies which produce it: in short, the
deductive, or _a priori_ method. The more particular consideration of this
intellectual process requires a chapter to itself.




                               Chapter XI.


Of The Deductive Method.


§ 1. The mode of investigation which, from the proved inapplicability of
direct methods of observation and experiment, remains to us as the main
source of the knowledge we possess or can acquire respecting the
conditions and laws of recurrence, of the more complex phenomena, is
called, in its most general expression, the Deductive Method; and consists
of three operations: the first, one of direct induction; the second, of
ratiocination; the third, of verification.

I call the first step in the process an inductive operation, because there
must be a direct induction as the basis of the whole; though in many
particular investigations the place of the induction may be supplied by a
prior deduction; but the premises of this prior deduction must have been
derived from induction.

The problem of the Deductive Method is, to find the law of an effect, from
the laws of the different tendencies of which it is the joint result. The
first requisite, therefore, is to know the laws of those tendencies; the
law of each of the concurrent causes: and this supposes a previous process
of observation or experiment upon each cause separately; or else a
previous deduction, which also must depend for its ultimate premises on
observation or experiment. Thus, if the subject be social or historical
phenomena, the premises of the Deductive Method must be the laws of the
causes which determine that class of phenomena; and those causes are human
actions, together with the general outward circumstances under the
influence of which mankind are placed, and which constitute man’s position
on the earth. The Deductive Method, applied to social phenomena, must
begin, therefore, by investigating, or must suppose to have been already
investigated, the laws of human action, and those properties of outward
things by which the actions of human beings in society are determined.
Some of these general truths will naturally be obtained by observation and
experiment, others by deduction: the more complex laws of human action,
for example, may be deduced from the simpler ones; but the simple or
elementary laws will always, and necessarily, have been obtained by a
directly inductive process.

To ascertain, then, the laws of each separate cause which takes a share in
producing the effect, is the first desideratum of the Deductive Method. To
know what the causes are which must be subjected to this process of study,
may or may not be difficult. In the case last mentioned, this first
condition is of easy fulfillment. That social phenomena depend on the acts
and mental impressions of human beings, never could have been a matter of
any doubt, however imperfectly it may have been known either by what laws
those impressions and actions are governed, or to what social consequences
their laws naturally lead. Neither, again, after physical science had
attained a certain development, could there be any real doubt where to
look for the laws on which the phenomena of life depend, since they must
be the mechanical and chemical laws of the solid and fluid substances
composing the organized body and the medium in which it subsists, together
with the peculiar vital laws of the different tissues constituting the
organic structure. In other cases, really far more simple than these, it
was much less obvious in what quarter the causes were to be looked for: as
in the case of the celestial phenomena. Until, by combining the laws of
certain causes, it was found that those laws explained all the facts which
experience had proved concerning the heavenly motions, and led to
predictions which it always verified, mankind never knew that those _were_
the causes. But whether we are able to put the question before, or not
until after, we have become capable of answering it, in either case it
must be answered; the laws of the different causes must be ascertained,
before we can proceed to deduce from them the conditions of the effect.

The mode of ascertaining those laws neither is, nor can be any other than
the fourfold method of experimental inquiry, already discussed. A few
remarks on the application of that method to cases of the Composition of
Causes are all that is requisite.

It is obvious that we can not expect to find the law of a tendency by an
induction from cases in which the tendency is counteracted. The laws of
motion could never have been brought to light from the observation of
bodies kept at rest by the equilibrium of opposing forces. Even where the
tendency is not, in the ordinary sense of the word, counteracted, but only
modified, by having its effects compounded with the effects arising from
some other tendency or tendencies, we are still in an unfavorable position
for tracing, by means of such cases, the law of the tendency itself. It
would have been scarcely possible to discover the law that every body in
motion tends to continue moving in a straight line, by an induction from
instances in which the motion is deflected into a curve, by being
compounded with the effect of an accelerating force. Notwithstanding the
resources afforded in this description of cases by the Method of
Concomitant Variations, the principles of a judicious experimentation
prescribe that the law of each of the tendencies should be studied, if
possible, in cases in which that tendency operates alone, or in
combination with no agencies but those of which the effect can, from
previous knowledge, be calculated and allowed for.

Accordingly, in the cases, unfortunately very numerous and important, in
which the causes do not suffer themselves to be separated and observed
apart, there is much difficulty in laying down with due certainty the
inductive foundation necessary to support the deductive method. This
difficulty is most of all conspicuous in the case of physiological
phenomena; it being seldom possible to separate the different agencies
which collectively compose an organized body, without destroying the very
phenomena which it is our object to investigate:


    ——following life, in creatures we dissect,
    We lose it, in the moment we detect.


And for this reason I am inclined to the opinion that physiology (greatly
and rapidly progressive as it now is) is embarrassed by greater natural
difficulties, and is probably susceptible of a less degree of ultimate
perfection, than even the social science; inasmuch as it is possible to
study the laws and operations of one human mind apart from other minds,
much less imperfectly than we can study the laws of one organ or tissue of
the human body apart from the other organs or tissues.

It has been judiciously remarked that pathological facts, or, to speak in
common language, diseases in their different forms and degrees afford in
the case of physiological investigation the most valuable equivalent to
experimentation properly so called; inasmuch as they often exhibit to us a
definite disturbance in some one organ or organic function, the remaining
organs and functions being, in the first instance at least, unaffected. It
is true that from the perpetual actions and reactions which are going on
among all parts of the organic economy, there can be no prolonged
disturbance in any one function without ultimately involving many of the
others; and when once it has done so, the experiment for the most part
loses its scientific value. All depends on observing the early stages of
the derangement; which, unfortunately, are of necessity the least marked.
If, however, the organs and functions not disturbed in the first instance
become affected in a fixed order of succession, some light is thereby
thrown upon the action which one organ exercises over another: and we
occasionally obtain a series of effects which we can refer with some
confidence to the original local derangement; but for this it is necessary
that we should know that the original derangement _was_ local. If it was
what is termed constitutional; that is, if we do not know in what part of
the animal economy it took its rise, or the precise nature of the
disturbance which took place in that part, we are unable to determine
which of the various derangements was cause and which effect; which of
them were produced by one another, and which by the direct, though perhaps
tardy, action of the original cause.

Besides natural pathological facts, we can produce pathological facts
artificially: we can try experiments, even in the popular sense of the
term, by subjecting the living being to some external agent, such as the
mercury of our former example, or the section of a nerve to ascertain the
functions of different parts of the nervous system. As this
experimentation is not intended to obtain a direct solution of any
practical question, but to discover general laws, from which afterward the
conditions of any particular effect may be obtained by deduction, the best
cases to select are those of which the circumstances can be best
ascertained: and such are generally not those in which there is any
practical object in view. The experiments are best tried, not in a state
of disease, which is essentially a changeable state, but in the condition
of health, comparatively a fixed state. In the one, unusual agencies are
at work, the results of which we have no means of predicting: in the
other, the course of the accustomed physiological phenomena would, it may
generally be presumed, remain undisturbed, were it not for the disturbing
cause which we introduce.

Such, with the occasional aid of the Method of Concomitant Variations (the
latter not less encumbered than the more elementary methods by the
peculiar difficulties of the subject), are our inductive resources for
ascertaining the laws of the causes considered separately, when we have it
not in our power to make trial of them in a state of actual separation.
The insufficiency of these resources is so glaring, that no one can be
surprised at the backward state of the science of physiology; in which
indeed our knowledge of causes is so imperfect, that we can neither
explain, nor could without specific experience have predicted, many of the
facts which are certified to us by the most ordinary observation.
Fortunately, we are much better informed as to the empirical laws of the
phenomena, that is, the uniformities respecting which we can not yet
decide whether they are cases of causation, or mere results of it. Not
only has the order in which the facts of organization and life
successively manifest themselves, from the first germ of existence to
death, been found to be uniform, and very accurately ascertainable; but,
by a great application of the Method of Concomitant Variations to the
entire facts of comparative anatomy and physiology, the characteristic
organic structure corresponding to each class of functions has been
determined with considerable precision. Whether these organic conditions
are the whole of the conditions, and in many cases whether they are
conditions at all, or mere collateral effects of some common cause, we are
quite ignorant; nor are we ever likely to know, unless we could construct
an organized body and try whether it would live.

Under such disadvantages do we, in cases of this description, attempt the
initial, or inductive step, in the application of the Deductive Method to
complex phenomena. But such, fortunately, is not the common case. In
general, the laws of the causes on which the effect depends may be
obtained by an induction from comparatively simple instances, or, at the
worst, by deduction from the laws of simpler causes, so obtained. By
simple instances are meant, of course, those in which the action of each
cause was not intermixed or interfered with, or not to any great extent,
by other causes whose laws were unknown. And only when the induction which
furnished the premises to the Deductive method rested on such instances
has the application of such a method to the ascertainment of the laws of a
complex effect, been attended with brilliant results.

§ 2. When the laws of the causes have been ascertained, and the first
stage of the great logical operation now under discussion satisfactorily
accomplished, the second part follows; that of determining from the laws
of the causes what effect any given combination of those causes will
produce. This is a process of calculation, in the wider sense of the term;
and very often involves processes of calculation in the narrowest sense.
It is a ratiocination; and when our knowledge of the causes is so perfect
as to extend to the exact numerical laws which they observe in producing
their effects, the ratiocination may reckon among its premises the
theorems of the science of number, in the whole immense extent of that
science. Not only are the most advanced truths of mathematics often
required to enable us to compute an effect, the numerical law of which we
already know; but, even by the aid of those most advanced truths, we can
go but a little way. In so simple a case as the common problem of three
bodies gravitating toward one another, with a force directly as their mass
and inversely as the square of the distance, all the resources of the
calculus have not hitherto sufficed to obtain any general solution, but an
approximate one. In a case a little more complex, but still one of the
simplest which arise in practice, that of the motion of a projectile, the
causes which affect the velocity and range (for example) of a cannon-ball
may be all known and estimated: the force of the gunpowder, the angle of
elevation, the density of the air, the strength and direction of the wind;
but it is one of the most difficult of mathematical problems to combine
all these, so as to determine the effect resulting from their collective
action.

Besides the theorems of number, those of geometry also come in as
premises, where the effects take place in space, and involve motion and
extension, as in mechanics, optics, acoustics, astronomy. But when the
complication increases, and the effects are under the influence of so many
and such shifting causes as to give no room either for fixed numbers, or
for straight lines and regular curves (as in the case of physiological, to
say nothing of mental and social phenomena), the laws of number and
extension are applicable, if at all, only on that large scale on which
precision of details becomes unimportant. Although these laws play a
conspicuous part in the most striking examples of the investigation of
nature by the Deductive Method, as for example in the Newtonian theory of
the celestial motions, they are by no means an indispensable part of every
such process. All that is essential in it is reasoning from a general law
to a particular case, that is, determining by means of the particular
circumstances of that case, what result is required in that instance to
fulfill the law. Thus in the Torricellian experiment, if the fact that air
has weight had been previously known, it would have been easy, without any
numerical data, to deduce from the general law of equilibrium, that the
mercury would stand in the tube at such a height that the column of
mercury would exactly balance a column of the atmosphere of equal
diameter; because, otherwise, equilibrium would not exist.

By such ratiocinations from the separate laws of the causes, we may, to a
certain extent, succeed in answering either of the following questions:
Given a certain combination of causes, what effect will follow? and, What
combination of causes, if it existed, would produce a given effect? In the
one case, we determine the effect to be expected in any complex
circumstances of which the different elements are known: in the other case
we learn, according to what law—under what antecedent conditions—a given
complex effect will occur.

§ 3. But (it may here be asked) are not the same arguments by which the
methods of direct observation and experiment were set aside as illusory
when applied to the laws of complex phenomena, applicable with equal force
against the Method of Deduction? When in every single instance a
multitude, often an unknown multitude, of agencies, are clashing and
combining, what security have we that in our computation _a priori_ we
have taken all these into our reckoning? How many must we not generally be
ignorant of? Among those which we know, how probable that some have been
overlooked; and, even were all included, how vain the pretense of summing
up the effects of many causes, unless we know accurately the numerical law
of each—a condition in most cases not to be fulfilled; and even when it is
fulfilled, to make the calculation transcends, in any but very simple
cases, the utmost power of mathematical science with all its most modern
improvements.

These objections have real weight, and would be altogether unanswerable,
if there were no test by which, when we employ the Deductive Method, we
might judge whether an error of any of the above descriptions had been
committed or not. Such a test, however, there is: and its application
forms, under the name of Verification, the third essential component part
of the Deductive Method; without which all the results it can give have
little other value than that of conjecture. To warrant reliance on the
general conclusions arrived at by deduction, these conclusions must be
found, on careful comparison, to accord with the results of direct
observation wherever it can be had. If, when we have experience to compare
with them, this experience confirms them, we may safely trust to them in
other cases of which our specific experience is yet to come. But if our
deductions have led to the conclusion that from a particular combination
of causes a given effect would result, then in all known cases where that
combination can be shown to have existed, and where the effect has not
followed, we must be able to show (or at least to make a probable surmise)
what frustrated it: if we can not, the theory is imperfect, and not yet to
be relied upon. Nor is the verification complete, unless some of the cases
in which the theory is borne out by the observed result are of at least
equal complexity with any other cases in which its application could be
called for.

If direct observation and collation of instances have furnished us with
any empirical laws of the effect (whether true in all observed cases, or
only true for the most part), the most effectual verification of which the
theory could be susceptible, would be, that it led deductively to those
empirical laws; that the uniformities, whether complete or incomplete,
which were observed to exist among the phenomena, were accounted for by
the laws of the causes—were such as could not but exist if those be really
the causes by which the phenomena are produced. Thus it was very
reasonably deemed an essential requisite of any true theory of the causes
of the celestial motions, that it should lead by deduction to Kepler’s
laws; which, accordingly, the Newtonian theory did.

In order, therefore, to facilitate the verification of theories obtained
by deduction, it is important that as many as possible of the empirical
laws of the phenomena should be ascertained, by a comparison of instances,
conformably to the Method of Agreement: as well as (it must be added) that
the phenomena themselves should be described, in the most comprehensive as
well as accurate manner possible; by collecting from the observation of
parts, the simplest possible correct expressions for the corresponding
wholes: as when the series of the observed places of a planet was first
expressed by a circle, then by a system of epicycles, and subsequently by
an ellipse.

It is worth remarking, that complex instances which would have been of no
use for the discovery of the simple laws into which we ultimately analyze
their phenomena, nevertheless, when they have served to verify the
analysis, become additional evidence of the laws themselves. Although we
could not have got at the law from complex cases, still when the law, got
at otherwise, is found to be in accordance with the result of a complex
case, that case becomes a new experiment on the law, and helps to confirm
what it did not assist to discover. It is a new trial of the principle in
a different set of circumstances; and occasionally serves to eliminate
some circumstance not previously excluded, and the exclusion of which
might require an experiment impossible to be executed. This was strikingly
conspicuous in the example formerly quoted, in which the difference
between the observed and the calculated velocity of sound was ascertained
to result from the heat extricated by the condensation which takes place
in each sonorous vibration. This was a trial, in new circumstances, of the
law of the development of heat by compression; and it added materially to
the proof of the universality of that law. Accordingly, any law of nature
is deemed to have gained in point of certainty, by being found to explain
some complex case which had not previously been thought of in connection
with it; and this indeed is a consideration to which it is the habit of
scientific inquirers to attach rather too much value than too little.

To the Deductive Method, thus characterized in its three constituent
parts, Induction, Ratiocination, and Verification, the human mind is
indebted for its most conspicuous triumphs in the investigation of nature.
To it we owe all the theories by which vast and complicated phenomena are
embraced under a few simple laws, which, considered as the laws of those
great phenomena, could never have been detected by their direct study. We
may form some conception of what the method has done for us from the case
of the celestial motions: one of the simplest among the greater instances
of the Composition of Causes, since (except in a few cases not of primary
importance) each of the heavenly bodies may be considered, without
material inaccuracy, to be never at one time influenced by the attraction
of more than two bodies, the sun and one other planet or satellite;
making, with the reaction of the body itself, and the force generated by
the body’s own motion and acting in the direction of the tangent, only
four different agents on the concurrence of which the motions of that body
depend; a much smaller number, no doubt, than that by which any other of
the great phenomena of nature is determined or modified. Yet how could we
ever have ascertained the combination of forces on which the motions of
the earth and planets are dependent, by merely comparing the orbits or
velocities of different planets, or the different velocities or positions
of the same planet? Notwithstanding the regularity which manifests itself
in those motions, in a degree so rare among the effects of concurrence of
causes; and although the periodical recurrence of exactly the same effect,
affords positive proof that all the combinations of causes which occur at
all, recur periodically; we should not have known what the causes were, if
the existence of agencies precisely similar on our own earth had not,
fortunately, brought the causes themselves within the reach of
experimentation under simple circumstances. As we shall have occasion to
analyze, further on, this great example of the Method of Deduction, we
shall not occupy any time with it here, but shall proceed to that
secondary application of the Deductive Method, the result of which is not
to prove laws of phenomena, but to explain them.




                               Chapter XII.


Of The Explanation Of Laws Of Nature.


§ 1. The deductive operation by which we derive the law of an effect from
the laws of the causes, the concurrence of which gives rise to it, may be
undertaken either for the purpose of discovering the law, or of explaining
a law already discovered. The word _explanation_ occurs so continually,
and holds so important a place in philosophy, that a little time spent in
fixing the meaning of it will be profitably employed.

An individual fact is said to be explained, by pointing out its cause,
that is, by stating the law or laws of causation, of which its production
is an instance. Thus, a conflagration is explained, when it is proved to
have arisen from a spark falling into the midst of a heap of combustibles.
And in a similar manner, a law or uniformity in nature is said to be
explained, when another law or laws are pointed out, of which that law
itself is but a case, and from which it could be deduced.

§ 2. There are three distinguishable sets of circumstances in which a law
of causation may be explained from, or, as it also is often expressed,
resolved into, other laws.

The first is the case already so fully considered; an intermixture of
laws, producing a joint effect equal to the sum of the effects of the
causes taken separately. The law of the complex effect is explained, by
being resolved into the separate laws of the causes which contribute to
it. Thus, the law of the motion of a planet is resolved into the law of
the acquired force, which tends to produce a uniform motion in the
tangent, and the law of the centripetal force, which tends to produce an
accelerating motion toward the sun; the real motion being a compound of
the two.

It is necessary here to remark, that in this resolution of the law of a
complex effect, the laws of which it is compounded are not the only
elements. It is resolved into the laws of the separate causes, together
with the fact of their co-existence. The one is as essential an ingredient
as the other; whether the object be to discover the law of the effect, or
only to explain it. To deduce the laws of the heavenly motions, we require
not only to know the law of a rectilineal and that of a gravitative force,
but the existence of both these forces in the celestial regions, and even
their relative amount. The complex laws of causation are thus resolved
into two distinct kinds of elements: the one, simpler laws of causation,
the other (in the aptly selected expression of Dr. Chalmers) collocations;
the collocations consisting in the existence of certain agents or powers,
in certain circumstances of place and time. We shall hereafter have
occasion to return to this distinction, and to dwell on it at such length
as dispenses with the necessity of further insisting on it here. The first
mode, then, of the explanation of Laws of Causation, is when the law of an
effect is resolved into the various tendencies of which it is the result,
together with the laws of those tendencies.

§ 3. A second case is when, between what seemed the cause and what was
supposed to be its effect, further observation detects an intermediate
link; a fact caused by the antecedent, and in its turn causing the
consequent; so that the cause at first assigned is but the remote cause,
operating through the intermediate phenomenon. A seemed the cause of C,
but it subsequently appeared that A was only the cause of B, and that it
is B which was the cause of C. For example: mankind were aware that the
act of touching an outward object caused a sensation. It was subsequently
discovered that after we have touched the object, and before we experience
the sensation, some change takes place in a kind of thread called a nerve,
which extends from our outward organs to the brain. Touching the object,
therefore, is only the remote cause of our sensation; that is, not the
cause, properly speaking, but the cause of the cause; the real cause of
the sensation is the change in the state of the nerve. Future experience
may not only give us more knowledge than we now have of the particular
nature of this change, but may also interpolate another link: between the
contact (for example) of the object with our outward organs, and the
production of the change of state in the nerve, there may take place some
electric phenomenon, or some phenomenon of a nature not resembling the
effects of any known agency. Hitherto, however, no such intermediate link
has been discovered; and the touch of the object must be considered,
provisionally, as the proximate cause of the affection of the nerve. The
sequence, therefore, of a sensation of touch on contact with an object is
ascertained not to be an ultimate law; it is resolved, as the phrase is,
into two other laws—the law that contact with an object produces an
affection of the nerve, and the law that an affection of the nerve
produces sensation.

To take another example: the more powerful acids corrode or blacken
organic compounds. This is a case of causation, but of remote causation;
and is said to be explained when it is shown that there is an intermediate
link, namely, the separation of some of the chemical elements of the
organic structure from the rest, and their entering into combination with
the acid. The acid causes this separation of the elements, and the
separation of the elements causes the disorganization, and often the
charring of the structure. So, again, chlorine extracts coloring matters
(whence its efficacy in bleaching) and purifies the air from infection.
This law is resolved into the two following laws: Chlorine has a powerful
affinity for bases of all kinds, particularly metallic bases and hydrogen:
such bases are essential elements of coloring matters and contagious
compounds, which substances, therefore, are decomposed and destroyed by
chlorine.

§ 4. It is of importance to remark, that when a sequence of phenomena is
thus resolved into other laws, they are always laws more general than
itself. The law that A is followed by C, is less general than either of
the laws which connect B with C and A with B. This will appear from very
simple considerations.

All laws of causation are liable to be counteracted or frustrated, by the
non-fulfillment of some negative condition; the tendency, therefore, of B
to produce C may be defeated. Now the law that A produces B, is equally
fulfilled whether B is followed by C or not; but the law that A produces C
by means of B, is of course only fulfilled when B is really followed by C,
and is, therefore, less general than the law that A produces B. It is also
less general than the law that B produces C. For B may have other causes
besides A; and as A produces C only by means of B, while B produces C,
whether it has itself been produced by A or by any thing else, the second
law embraces a greater number of instances, covers as it were a greater
space of ground, than the first.

Thus, in our former example, the law that the contact of an object causes
a change in the state of the nerve, is more general than the law that
contact with an object causes sensation, since, for aught we know, the
change in the nerve may equally take place when, from a counteracting
cause, as, for instance, strong mental excitement, the sensation does not
follow; as in a battle, where wounds are sometimes received without any
consciousness of receiving them. And again, the law that change in the
state of a nerve produces sensation, is more general than the law that
contact with an object produces sensation; since the sensation equally
follows the change in the nerve when not produced by contact with an
object, but by some other cause; as in the well-known case, when a person
who has lost a limb feels the same sensation which he has been accustomed
to call a pain in the limb.

Not only are the laws of more immediate sequence into which the law of a
remote sequence is resolved, laws of greater generality than that law is,
but (as a consequence of, or rather as implied in, their greater
generality) they are more to be relied on; there are fewer chances of
their being ultimately found not to be universally true. From the moment
when the sequence of A and C is shown not to be immediate, but to depend
on an intervening phenomenon, then, however constant and invariable the
sequence of A and C has hitherto been found, possibilities arise of its
failure, exceeding those which can effect either of the more immediate
sequences, A, B, and B, C. The tendency of A to produce C may be defeated
by whatever is capable of defeating either the tendency of A to produce B,
or the tendency of B to produce C; it is, therefore, twice as liable to
failure as either of those more elementary tendencies; and the
generalization that A is always followed by C, is twice as likely to be
found erroneous. And so of the converse generalization, that C is always
preceded and caused by A; which will be erroneous not only if there should
happen to be a second immediate mode of production of C itself, but
moreover if there be a second mode of production of B, the immediate
antecedent of C in the sequence.

The resolution of the one generalization into the other two, not only
shows that there are possible limitations of the former, from which its
two elements are exempt, but shows also where these are to be looked for.
As soon as we know that B intervenes between A and C, we also know that if
there be cases in which the sequence of A and C does not hold, these are
most likely to be found by studying the effects or the conditions of the
phenomenon B.

It appears, then, that in the second of the three modes in which a law may
be resolved into other laws, the latter are more general, that is, extend
to more cases, and are also less likely to require limitation from
subsequent experience, than the law which they serve to explain. They are
more nearly unconditional; they are defeated by fewer contingencies; they
are a nearer approach to the universal truth of nature. The same
observations are still more evidently true with regard to the first of the
three modes of resolution. When the law of an effect of combined forces is
resolved into the separate laws of the causes, the nature of the case
implies that the law of the effect is less general than the law of any of
the causes, since it only holds when they are combined; while the law of
any one of the causes holds good both then, and also when that cause acts
apart from the rest.

It is also manifest that the complex law is liable to be oftener
unfulfilled than any one of the simpler laws of which it is the result,
since every contingency which defeats any of the laws prevents so much of
the effect as depends on it, and thereby defeats the complex law. The mere
rusting, for example, of some small part of a great machine, often
suffices entirely to prevent the effect which ought to result from the
joint action of all the parts. The law of the effect of a combination of
causes is always subject to the whole of the negative conditions which
attach to the action of all the causes severally.

There is another and an equally strong reason why the law of a complex
effect must be less general than the laws of the causes which conspire to
produce it. The same causes, acting according to the same laws, and
differing only in the proportions in which they are combined, often
produce effects which differ not merely in quantity, but in kind. The
combination of a centripetal with a projectile force, in the proportions
which obtain in all the planets and satellites of our solar system, gives
rise to an elliptical motion; but if the ratio of the two forces to each
other were slightly altered, it is demonstrated that the motion produced
would be in a circle, or a parabola, or an hyperbola; and it is thought
that in the case of some comets one of these is probably the fact. Yet the
law of the parabolic motion would be resolvable into the very same simple
laws into which that of the elliptical motion is resolved, namely, the law
of the permanence of rectilineal motion, and the law of gravitation. If,
therefore, in the course of ages, some circumstance were to manifest
itself which, without defeating the law of either of those forces, should
merely alter their proportion to one another (such as the shock of some
solid body, or even the accumulating effect of the resistance of the
medium in which astronomers have been led to surmise that the motions of
the heavenly bodies take place), the elliptical motion might be changed
into a motion in some other conic section; and the complex law, that the
planetary motions take place in ellipses, would be deprived of its
universality, though the discovery would not at all detract from the
universality of the simpler laws into which that complex law is resolved.
The law, in short, of each of the concurrent causes remains the same,
however their collocations may vary; but the law of their joint effect
varies with every difference in the collocations. There needs no more to
show how much more general the elementary laws must be than any of the
complex laws which are derived from them.

§ 5. Besides the two modes which have been treated of, there is a third
mode in which laws are resolved into one another; and in this it is
self-evident that they are resolved into laws more general than
themselves. This third mode is the _subsumption_ (as it has been called)
of one law under another; or (what comes to the same thing) the gathering
up of several laws into one more general law which includes them all. The
most splendid example of this operation was when terrestrial gravity and
the central force of the solar system were brought together under the
general law of gravitation. It had been proved antecedently that the earth
and the other planets tend to the sun; and it had been known from the
earliest times that terrestrial bodies tend toward the earth. These were
similar phenomena; and to enable them both to be subsumed under one law,
it was only necessary to prove that, as the effects were similar in
quality so also they, as to quantity, conform to the same rules. This was
first shown to be true of the moon, which agreed with terrestrial objects
not only in tending to a centre, but in the fact that this centre was the
earth. The tendency of the moon toward the earth being ascertained to vary
as the inverse square of the distance, it was deduced from this, by direct
calculation, that if the moon were as near to the earth as terrestrial
objects are, and the acquired force in the direction of the tangent were
suspended, the moon would fall toward the earth through exactly as many
feet in a second as those objects do by virtue of their weight. Hence the
inference was irresistible, that the moon also tends to the earth by
virtue of its weight: and that the two phenomena, the tendency of the moon
to the earth and the tendency of terrestrial objects to the earth, being
not only similar in quality, but, when in the same circumstances,
identical in quantity, are cases of one and the same law of causation. But
the tendency of the moon to the earth, and the tendency of the earth and
planets to the sun, were already known to be cases of the same law of
causation; and thus the law of all these tendencies, and the law of
terrestrial gravity, were recognized as identical, and were subsumed under
one general law, that of gravitation.

In a similar manner, the laws of magnetic phenomena have more recently
been subsumed under known laws of electricity. It is thus that the most
general laws of nature are usually arrived at: we mount to them by
successive steps. For, to arrive by correct induction at laws which hold
under such an immense variety of circumstances, laws so general as to be
independent of any varieties of space or time which we are able to
observe, requires for the most part many distinct sets of experiments or
observations, conducted at different times and by different people. One
part of the law is first ascertained, afterward another part: one set of
observations teaches us that the law holds good under some conditions,
another that it holds good under other conditions, by combining which
observations we find that it holds good under conditions much more
general, or even universally. The general law, in this case, is literally
the sum of all the partial ones; it is a recognition of the same sequence
in different sets of instances; and may, in fact, be regarded as merely
one step in the process of elimination. The tendency of bodies toward one
another, which we now call gravity, had at first been observed only on the
earth’s surface, where it manifested itself only as a tendency of all
bodies toward the earth, and might, therefore, be ascribed to a peculiar
property of the earth itself: one of the circumstances, namely, the
proximity of the earth, had not been eliminated. To eliminate this
circumstance required a fresh set of instances in other parts of the
universe: these we could not ourselves create; and though nature had
created them for us, we were placed in very unfavorable circumstances for
observing them. To make these observations, fell naturally to the lot of a
different set of persons from those who studied terrestrial phenomena; and
had, indeed, been a matter of great interest at a time when the idea of
explaining celestial facts by terrestrial laws was looked upon as the
confounding of an indefeasible distinction. When, however, the celestial
motions were accurately ascertained, and the deductive processes
performed, from which it appeared that their laws and those of terrestrial
gravity corresponded, those celestial observations became a set of
instances which exactly eliminated the circumstance of proximity to the
earth; and proved that in the original case, that of terrestrial objects,
it was not the earth, as such, that caused the motion or the pressure, but
the circumstance common to that case with the celestial instances, namely,
the presence of some great body within certain limits of distance.

§ 6. There are, then, three modes of explaining laws of causation, or,
which is the same thing, resolving them into other laws. First, when the
law of an effect of combined causes is resolved into the separate laws of
the causes, together with the fact of their combination. Secondly, when
the law which connects any two links, not proximate, in a chain of
causation, is resolved into the laws which connect each with the
intermediate links. Both of these are cases of resolving one law into two
or more; in the third, two or more are resolved into one: when, after the
law has been shown to hold good in several different classes of cases, we
decide that what is true in each of these classes of cases, is true under
some more general supposition, consisting of what all those classes of
cases have in common. We may here remark that this last operation involves
none of the uncertainties attendant on induction by the Method of
Agreement, since we need not suppose the result to be extended by way of
inference to any new class of cases different from those by the comparison
of which it was engendered.

In all these three processes, laws are, as we have seen, resolved into
laws more general than themselves; laws extending to all the cases which
the former extended to, and others besides. In the first two modes they
are also resolved into laws more certain, in other words, more universally
true than themselves; they are, in fact, proved not to be themselves laws
of nature, the character of which is to be universally true, but _results_
of laws of nature, which may be only true conditionally, and for the most
part. No difference of this sort exists in the third case; since here the
partial laws are, in fact, the very same law as the general one, and any
exception to them would be an exception to it too.

By all the three processes, the range of deductive science is extended;
since the laws, thus resolved, may be thenceforth deduced demonstratively
from the laws into which they are resolved. As already remarked, the same
deductive process which proves a law or fact of causation if unknown,
serves to explain it when known.

The word explanation is here used in its philosophical sense. What is
called explaining one law of nature by another, is but substituting one
mystery for another; and does nothing to render the general course of
nature other than mysterious: we can no more assign a _why_ for the more
extensive laws than for the partial ones. The explanation may substitute a
mystery which has become familiar, and has grown to _seem_ not mysterious,
for one which is still strange. And this is the meaning of explanation, in
common parlance. But the process with which we are here concerned often
does the very contrary: it resolves a phenomenon with which we are
familiar into one of which we previously knew little or nothing; as when
the common fact of the fall of heavy bodies was resolved into the tendency
of all particles of matter toward one another. It must be kept constantly
in view, therefore, that in science, those who speak of explaining any
phenomenon mean (or should mean) pointing out not some more familiar, but
merely some more general, phenomenon, of which it is a partial
exemplification; or some laws of causation which produce it by their joint
or successive action, and from which, therefore, its conditions may be
determined deductively. Every such operation brings us a step nearer
toward answering the question which was stated in a previous chapter as
comprehending the whole problem of the investigation of nature, viz.: what
are the fewest assumptions, which being granted, the order of nature as it
exists would be the result? What are the fewest, general propositions from
which all the uniformities existing in nature could be deduced?

The laws, thus explained or resolved, are sometimes said to be _accounted
for_; but the expression is incorrect, if taken to mean any thing more
than what has been already stated. In minds not habituated to accurate
thinking, there is often a confused notion that the general laws are the
_causes_ of the partial ones; that the law of general gravitation, for
example, causes the phenomenon of the fall of bodies to the earth. But to
assert this would be a misuse of the word cause: terrestrial gravity is
not an effect of general gravitation, but a _case_ of it; that is, one
kind of the particular instances in which that general law obtains. To
account for a law of nature means, and can mean, nothing more than to
assign other laws more general, together with collocations, which laws and
collocations being supposed, the partial law follows without any
additional supposition.




                              Chapter XIII.


Miscellaneous Examples Of The Explanation Of Laws Of Nature.


§ 1. The most striking example which the history of science presents, of
the explanation of laws of causation and other uniformities of sequence
among special phenomena, by resolving them into laws of greater simplicity
and generality, is the great Newtonian generalization; respecting which
typical instance, so much having already been said, it is sufficient to
call attention to the great number and variety of the special observed
uniformities, which are in this case accounted for, either as particular
cases, or as consequences, of one very simple law of universal nature. The
simple fact of a tendency of every particle of matter toward every other
particle, varying inversely as the square of the distance, explains the
fall of bodies to the earth, the revolutions of the planets and
satellites, the motions (so far as known) of comets, and all the various
regularities which have been observed in these special phenomena; such as
the elliptical orbits, and the variations from exact ellipses; the
relation between the solar distances of the planets and the duration of
their revolutions; the precession of the equinoxes; the tides, and a vast
number of minor astronomical truths.

Mention has also been made in the preceding chapter of the explanation of
the phenomena of magnetism from laws of electricity; the special laws of
magnetic agency having been affiliated by deduction to observed laws of
electric action, in which they have ever since been considered to be
included as special cases. An example not so complete in itself, but even
more fertile in consequences, having been the starting-point of the really
scientific study of physiology, is the affiliation, commenced by Bichat,
and carried on by subsequent biologists, of the properties of the bodily
organs, to the elementary properties of the tissues into which they are
anatomically decomposed.

Another striking instance is afforded by Dalton’s generalization, commonly
known as the atomic theory. It had been known from the very commencement
of accurate chemical observation, that any two bodies combine chemically
with one another in only a certain number of proportions; but those
proportions were in each case expressed by a percentage—so many parts (by
weight) of each ingredient, in 100 of the compound (say 35 and a fraction
of one element, 64 and a fraction of the other); in which mode of
statement no relation was perceived between the proportion in which a
given element combines with one substance, and that in which it combines
with others. The great step made by Dalton consisted in perceiving that a
unit of weight might be established for each substance, such that by
supposing the substance to enter into all its combinations in the ratio
either of that unit, or of some low multiple of that unit, all the
different proportions, previously expressed by percentages, were found to
result. Thus 1 being assumed as the unit of hydrogen, if 8 were then taken
as that of oxygen, the combination of one unit of hydrogen with one unit
of oxygen would produce the exact proportion of weight between the two
substances which is known to exist in water; the combination of one unit
of hydrogen with two units of oxygen would produce the proportion which
exists in the other compound of the same two elements, called peroxide of
hydrogen; and the combinations of hydrogen and of oxygen with all other
substances, would correspond with the supposition that those elements
enter into combination by single units, or twos, or threes, of the numbers
assigned to them, 1 and 8, and the other substances by ones or twos or
threes of other determinate numbers proper to each. The result is that a
table of the equivalent numbers, or, as they are called, atomic weights,
of all the elementary substances, comprises in itself, and scientifically
explains, all the proportions in which any substance, elementary or
compound, is found capable of entering into chemical combination with any
other substance whatever.

§ 2. Some interesting cases of the explanation of old uniformities by
newly ascertained laws are afforded by the researches of Professor Graham.
That eminent chemist was the first who drew attention to the distinction
which may be made of all substances into two classes, termed by him
crystalloids and colloids; or rather, of all states of matter into the
crystalloid and the colloidal states, for many substances are capable of
existing in either. When in the colloidal state, their sensible properties
are very different from those of the same substance when crystallized, or
when in a state easily susceptible of crystallization. Colloid substances
pass with extreme difficulty and slowness into the crystalline state, and
are extremely inert in all the ordinary chemical relations. Substances in
the colloid state are almost always, when combined with water, more or
less viscous or gelatinous. The most prominent examples of the state are
certain animal and vegetable substances, particularly gelatine, albumen,
starch, the gums, caramel, tannin, and some others. Among substances not
of organic origin, the most notable instances are hydrated silicic acid,
and hydrated alumina, with other metallic peroxides of the aluminous
class.

Now it is found, that while colloidal substances are easily penetrated by
water, and by the solutions of crystalloid substances, they are very
little penetrable by one another: which enabled Professor Graham to
introduce a highly effective process (termed dialysis) for separating the
crystalloid substances contained in any liquid mixture, by passing them
through a thin septum of colloidal matter, which does not suffer any thing
colloidal to pass, or suffers it only in very minute quantity. This
property of colloids enabled Mr. Graham to account for a number of special
results of observation, not previously explained.

For instance, “while soluble crystalloids are always highly sapid, soluble
colloids are singularly insipid,” as might be expected; for, as the
sentient extremities of the nerves of the palate “are probably protected
by a colloidal membrane,” impermeable to other colloids, a colloid, when
tasted, probably never reaches those nerves. Again, “it has been observed
that vegetable gum is not digested in the stomach; the coats of that organ
dialyse the soluble food, absorbing crystalloids, and rejecting all
colloids.” One of the mysterious processes accompanying digestion, the
secretion of free muriatic acid by the coats of the stomach, obtains a
probable hypothetical explanation through the same law. Finally, much
light is thrown upon the observed phenomena of osmose (the passage of
fluids outward and inward through animal membranes) by the fact that the
membranes are colloidal. In consequence, the water and saline solutions
contained in the animal body pass easily and rapidly through the
membranes, while the substances directly applicable to nutrition, which
are mostly colloidal, are detained by them.(154)

The property which salt possesses of preserving animal substances from
putrefaction is resolved by Liebig into two more general laws, the strong
attraction of salt for water, and the necessity of the presence of water
as a condition of putrefaction. The intermediate phenomenon which is
interpolated between the remote cause and the effect, can here be not
merely inferred but seen; for it is a familiar fact, that flesh upon which
salt has been thrown is speedily found swimming in brine.

The second of the two factors (as they may be termed) into which the
preceding law has been resolved, the necessity of water to putrefaction,
itself affords an additional example of the Resolution of Laws. The law
itself is proved by the Method of Difference, since flesh completely dried
and kept in a dry atmosphere does not putrefy; as we see in the case of
dried provisions and human bodies in very dry climates. A deductive
explanation of this same law results from Liebig’s speculations. The
putrefaction of animal and other azotized bodies is a chemical process, by
which they are gradually dissipated in a gaseous form, chiefly in that of
carbonic acid and ammonia; now to convert the carbon of the animal
substance into carbonic acid requires oxygen, and to convert the azote
into ammonia requires hydrogen, which are the elements of water. The
extreme rapidity of the putrefaction of azotized substances, compared with
the gradual decay of non-azotized bodies (such as wood and the like) by
the action of oxygen alone, he explains from the general law that
substances are much more easily decomposed by the action of two different
affinities upon two of their elements than by the action of only one.

§ 3. Among the many important properties of the nervous system which have
either been first discovered or strikingly illustrated by Dr.
Brown-Séquard, I select the reflex influence of the nervous system on
nutrition and secretion. By reflex nervous action is meant, action which
one part of the nervous system exerts over another part, without any
intermediate action on the brain, and consequently without consciousness;
or which, if it does pass through the brain, at least produces its effects
independently of the will. There are many experiments which prove that
irritation of a nerve in one part of the body may in this manner excite
powerful action in another part; for example, food injected into the
stomach through a divided œsophagus, nevertheless produces secretion of
saliva; warm water injected into the bowels, and various other irritations
of the lower intestines, have been found to excite secretion of the
gastric juice, and so forth. The reality of the power being thus proved,
its agency explains a great variety of apparently anomalous phenomena; of
which I select the following from Dr. Brown-Séquard’s _Lectures on the
Nervous System_:

The production of tears by irritation of the eye, or of the mucous
membrane of the nose;

The secretions of the eye and nose increased by exposure of other parts of
the body to cold;

Inflammation of the eye, especially when of traumatic origin, very
frequently excites a similar affection in the other eye, which may be
cured by section of the intervening nerve;

Loss of sight sometimes produced by neuralgia, and has been known to be at
once cured by the extirpation (for instance) of a carious tooth;

Even cataract has been produced in a healthy eye by cataract in the other
eye, or by neuralgia, or by a wound of the frontal nerve;

The well-known phenomenon of a sudden stoppage of the heart’s action, and
consequent death, produced by irritation of some of the nervous
extremities; _e.g._, by drinking very cold water, or by a blow on the
abdomen, or other sudden excitation of the abdominal sympathetic nerve,
though this nerve may be irritated to any extent without stopping the
heart’s action, if a section be made of the communicating nerves;

The extraordinary effects produced on the internal organs by an extensive
burn on the surface of the body, consisting in violent inflammation of the
tissues of the abdomen, chest, or head, which, when death ensues from this
kind of injury, is one of the most frequent causes of it;

Paralysis and anæsthesia of one part of the body from neuralgia in another
part; and muscular atrophy from neuralgia, even when there is no
paralysis;

Tetanus produced by the lesion of a nerve. Dr. Brown-Séquard thinks it
highly probable that hydrophobia is a phenomenon of a similar nature;

Morbid changes in the nutrition of the brain and spinal cord, manifesting
themselves by epilepsy, chorea, hysteria, and other diseases, occasioned
by lesion of some of the nervous extremities in remote places, as by
worms, calculi, tumors, carious bones, and in some cases even by very
slight irritations of the skin.

§ 4. From the foregoing and similar instances, we may see the importance,
when a law of nature previously unknown has been brought to light, or when
new light has been thrown upon a known law by experiment, of examining all
cases which present the conditions necessary for bringing that law into
action; a process fertile in demonstrations of special laws previously
unsuspected, and explanations of others already empirically known.

For instance, Faraday discovered by experiment, that voltaic electricity
could be evolved from a natural magnet, provided a conducting body were
set in motion at right angles to the direction of the magnet; and this he
found to hold not only of small magnets, but of that great magnet, the
earth. The law being thus established experimentally, that electricity is
evolved, by a magnet, and a conductor moving at right angles to the
direction of its poles, we may now look out for fresh instances in which
these conditions meet. Wherever a conductor moves or revolves at right
angles to the direction of the earth’s magnetic poles, there we may expect
an evolution of electricity. In the northern regions, where the polar
direction is nearly perpendicular to the horizon, all horizontal motions
of conductors will produce electricity; horizontal wheels, for example,
made of metal; likewise all running streams will evolve a current of
electricity, which will circulate round them; and the air thus charged
with electricity may be one of the causes of the Aurora Borealis. In the
equatorial regions, on the contrary, upright wheels placed parallel to the
equator will originate a voltaic circuit, and water-falls will naturally
become electric.

For a second example, it has been proved, chiefly by the researches of
Professor Graham, that gases have a strong tendency to permeate animal
membranes, and diffuse themselves through the spaces which such membranes
inclose, notwithstanding the presence of other gases in those spaces.
Proceeding from this general law, and reviewing a variety of cases in
which gases lie contiguous to membranes, we are enabled to demonstrate or
to explain the following more special laws: 1st. The human or animal body,
when surrounded with any gas not already contained within the body,
absorbs it rapidly; such, for instance, as the gases of putrefying
matters: which helps to explain malaria. 2d. The carbonic acid gas of
effervescing drinks, evolved in the stomach, permeates its membranes, and
rapidly spreads through the system. 3d. Alcohol taken into the stomach
passes into vapor, and spreads through the system with great rapidity
(which, combined with the high combustibility of alcohol, or in other
words its ready combination with oxygen, may perhaps help to explain the
bodily warmth immediately consequent on drinking spirituous liquors). 4th.
In any state of the body in which peculiar gases are formed within it,
these will rapidly exhale through all parts of the body; and hence the
rapidity with which, in certain states of disease, the surrounding
atmosphere becomes tainted. 5th. The putrefaction of the interior parts of
a carcass will proceed as rapidly as that of the exterior, from the ready
passage outward of the gaseous products. 6th. The exchange of oxygen and
carbonic acid in the lungs is not prevented, but rather promoted, by the
intervention of the membrane of the lungs and the coats of the
blood-vessels between the blood and the air. It is necessary, however,
that there should be a substance in the blood with which the oxygen of the
air may immediately combine; otherwise, instead of passing into the blood,
it would permeate the whole organism: and it is necessary that the
carbonic acid, as it is formed in the capillaries, should also find a
substance in the blood with which it can combine; otherwise it would leave
the body at all points, instead of being discharged through the lungs.

§ 5. The following is a deduction which confirms, by explaining, the
empirical generalization, that soda powders weaken the human system. These
powders, consisting of a mixture of tartaric acid with bicarbonate of
soda, from which the carbonic acid is set free, must pass into the stomach
as tartrate of soda. Now, neutral tartrates, citrates, and acetates of the
alkalis are found, in their passage through the system, to be changed into
carbonates; and to convert a tartrate into a carbonate requires an
additional quantity of oxygen, the abstraction of which must lessen the
oxygen destined for assimilation with the blood, on the quantity of which
the vigorous action of the human system partly depends.

The instances of new theories agreeing with and explaining old
empiricisms, are innumerable. All the just remarks made by experienced
persons on human character and conduct, are so many special laws, which
the general laws of the human mind explain and resolve. The empirical
generalizations on which the operations of the arts have usually been
founded, are continually justified and confirmed on the one hand, or
corrected and improved on the other, by the discovery of the simpler
scientific laws on which the efficacy of those operations depends. The
effects of the rotation of crops, of the various manures, and other
processes of improved agriculture, have been for the first time resolved
in our own day into known laws of chemical and organic action, by Davy,
Liebig, and others. The processes of the medical art are even now mostly
empirical: their efficacy is concluded, in each instance, from a special
and most precarious experimental generalization: but as science advances
in discovering the simple laws of chemistry and physiology, progress is
made in ascertaining the intermediate links in the series of phenomena,
and the more general laws on which they depend; and thus, while the old
processes are either exploded, or their efficacy, in so far as real,
explained, better processes, founded on the knowledge of proximate causes,
are continually suggested and brought into use.(155) Many even of the
truths of geometry were generalizations from experience before they were
deduced from first principles. The quadrature of the cycloid is said to
have been first effected by measurement, or rather by weighing a cycloidal
card, and comparing its weight with that of a piece of similar card of
known dimensions.

§ 6. To the foregoing examples from physical science, let us add another
from mental. The following is one of the simple laws of mind: Ideas of a
pleasurable or painful character form associations more easily and
strongly than other ideas, that is, they become associated after fewer
repetitions, and the association is more durable. This is an experimental
law, grounded on the Method of Difference. By deduction from this law,
many of the more special laws which experience shows to exist among
particular mental phenomena may be demonstrated and explained: the ease
and rapidity, for instance, with which thoughts connected with our
passions or our more cherished interests are excited, and the firm hold
which the facts relating to them have on our memory; the vivid
recollection we retain of minute circumstances which accompanied any
object or event that deeply interested us, and of the times and places in
which we have been very happy or very miserable; the horror with which we
view the accidental instrument of any occurrence which shocked us, or the
locality where it took place and the pleasure we derive from any memorial
of past enjoyment; all these effects being proportional to the sensibility
of the individual mind, and to the consequent intensity of the pain or
pleasure from which the association originated. It has been suggested by
the able writer of a biographical sketch of Dr. Priestley in a monthly
periodical,(156) that the same elementary law of our mental constitution,
suitably followed out, would explain a variety of mental phenomena
previously inexplicable, and in particular some of the fundamental
diversities of human character and genius. Associations being of two
sorts, either between synchronous, or between successive impressions; and
the influence of the law which renders associations stronger in proportion
to the pleasurable or painful character of the impressions, being felt
with peculiar force in the synchronous class of associations; it is
remarked by the writer referred to, that in minds of strong organic
sensibility synchronous associations will be likely to predominate,
producing a tendency to conceive things in pictures and in the concrete,
richly clothed in attributes and circumstances, a mental habit which is
commonly called Imagination, and is one of the peculiarities of the
painter and the poet; while persons of more moderate susceptibility to
pleasure and pain will have a tendency to associate facts chiefly in the
order of their succession, and such persons, if they possess mental
superiority, will addict themselves to history or science rather than to
creative art. This interesting speculation the author of the present work
has endeavored, on another occasion, to pursue further, and to examine how
far it will avail toward explaining the peculiarities of the poetical
temperament.(157) It is at least an example which may serve, instead of
many others, to show the extensive scope which exists for deductive
investigation in the important and hitherto so imperfect Science of Mind.

§ 7. The copiousness with which the discovery and explanation of special
laws of phenomena by deduction from simpler and more general ones has here
been exemplified, was prompted by a desire to characterize clearly, and
place in its due position of importance, the Deductive Method; which, in
the present state of knowledge, is destined henceforth irrevocably to
predominate in the course of scientific investigation. A revolution is
peaceably and progressively effecting itself in philosophy, the reverse of
that to which Bacon has attached his name. That great man changed the
method of the sciences from deductive to experimental, and it is now
rapidly reverting from experimental to deductive. But the deductions which
Bacon abolished were from premises hastily snatched up, or arbitrarily
assumed. The principles were neither established by legitimate canons of
experimental inquiry, nor the results tested by that indispensable element
of a rational Deductive Method, verification by specific experience.
Between the primitive method of Deduction and that which I have attempted
to characterize, there is all the difference which exists between the
Aristotelian physics and the Newtonian theory of the heavens.

It would, however, be a mistake to expect that those great
generalizations, from which the subordinate truths of the more backward
sciences will probably at some future period be deduced by reasoning (as
the truths of astronomy are deduced from the generalities of the Newtonian
theory), will be found in all, or even in most cases, among truths now
known and admitted. We may rest assured, that many of the most general
laws of nature are as yet entirely unthought of; and that many others,
destined hereafter to assume the same character, are known, if at all,
only as laws or properties of some limited class of phenomena; just as
electricity, now recognized as one of the most universal of natural
agencies, was once known only as a curious property which certain
substances acquired by friction, of first attracting and then repelling
light bodies. If the theories of heat, cohesion, crystallization, and
chemical action are destined, as there can be little doubt that they are,
to become deductive, the truths which will then be regarded as the
_principia_ of those sciences would probably, if now announced, appear
quite as novel(158) as the law of gravitation appeared to the
contemporaries of Newton; possibly even more so, since Newton’s law, after
all, was but an extension of the law of weight—that is, of a
generalization familiar from of old, and which already comprehended a not
inconsiderable body of natural phenomena. The general laws of a similarly
commanding character, which we still look forward to the discovery of, may
not always find so much of their foundations already laid.

These general truths will doubtless make their first appearance in the
character of hypotheses; not proved, nor even admitting of proof, in the
first instance, but assumed as premises for the purpose of deducing from
them the known laws of concrete phenomena. But this, though their initial,
can not be their final state. To entitle an hypothesis to be received as
one of the truths of nature, and not as a mere technical help to the human
faculties, it must be capable of being tested by the canons of legitimate
induction, and must actually have been submitted to that test. When this
shall have been done, and done successfully, premises will have been
obtained from which all the other propositions of the science will
thenceforth be presented as conclusions, and the science will, by means of
a new and unexpected Induction, be rendered Deductive.




                               Chapter XIV.


Of The Limits To The Explanation Of Laws Of Nature; And Of Hypotheses.


§ 1. The preceding considerations have led us to recognize a distinction
between two kinds of laws, or observed uniformities in nature: ultimate
laws, and what may be termed derivative laws. Derivative laws are such as
are deducible from, and may, in any of the modes which we have pointed
out, be resolved into, other and more general ones. Ultimate laws are
those which can not. We are not sure that any of the uniformities with
which we are yet acquainted are ultimate laws; but we know that there must
be ultimate laws; and that every resolution of a derivative law into more
general laws brings us nearer to them.

Since we are continually discovering that uniformities, not previously
known to be other than ultimate, are derivative, and resolvable into more
general laws; since (in other words) we are continually discovering the
explanation of some sequence which was previously known only as a fact; it
becomes an interesting question whether there are any necessary limits to
this philosophical operation, or whether it may proceed until all the
uniform sequences in nature are resolved into some one universal law. For
this seems, at first sight, to be the ultimatum toward which the progress
of induction by the Deductive Method, resting on a basis of observation
and experiment, is tending. Projects of this kind were universal in the
infancy of philosophy; any speculations which held out a less brilliant
prospect being in these early times deemed not worth pursuing. And the
idea receives so much apparent countenance from the nature of the most
remarkable achievements of modern science, that speculators are even now
frequently appearing, who profess either to have solved the problem, or to
suggest modes in which it may one day be solved. Even where pretensions of
this magnitude are not made, the character of the solutions which are
given or sought of particular classes of phenomena, often involves such
conceptions of what constitutes explanation, as would render the notion of
explaining all phenomena whatever by means of some one cause or law,
perfectly admissible.

§ 2. It is, therefore, useful to remark that the ultimate Laws of Nature
can not possibly be less numerous than the distinguishable sensations or
other feelings of our nature; those, I mean, which are distinguishable
from one another in quality, and not merely in quantity or degree. For
example: since there is a phenomenon _sui generis_, called color, which
our consciousness testifies to be not a particular degree of some other
phenomenon, as heat or odor or motion, but intrinsically unlike all
others, it follows that there are ultimate laws of color; that though the
facts of color may admit of explanation, they never can be explained from
laws of heat or odor alone, or of motion alone, but that, however far the
explanation may be carried, there will always remain in it a law of color.
I do not mean that it might not possibly be shown that some other
phenomenon, some chemical or mechanical action, for example, invariably
precedes, and is the cause of, every phenomenon of color. But though this,
if proved, would be an important extension of our knowledge of nature, it
would not explain how or why a motion, or a chemical action, can produce a
sensation of color; and, however diligent might be our scrutiny of the
phenomena, whatever number of hidden links we might detect in the chain of
causation terminating in the color, the last link would still be a law of
color, not a law of motion, nor of any other phenomenon whatever. Nor does
this observation apply only to color, as compared with any other of the
great classes of sensations; it applies to every particular color, as
compared with others. White color can in no manner be explained
exclusively by the laws of the production of red color. In any attempt to
explain it, we can not but introduce, as one element of the explanation,
the proposition that some antecedent or other produces the sensation of
white.

The ideal limit, therefore, of the explanation of natural phenomena
(toward which as toward other ideal limits we are constantly tending,
without the prospect of ever completely attaining it) would be to show
that each distinguishable variety of our sensations, or other states of
consciousness, has only one sort of cause; that, for example, whenever we
perceive a white color, there is some one condition or set of conditions
which is always present, and the presence of which always produces in us
that sensation. As long as there are several known modes of production of
a phenomenon (several different substances, for instance, which have the
property of whiteness, and between which we can not trace any other
resemblance) so long it is not impossible that one of these modes of
production may be resolved into another, or that all of them may be
resolved into some more general mode of production not hitherto
recognized. But when the modes of production are reduced to one, we can
not, in point of simplification, go any further. This one may not, after
all, be the ultimate mode; there may be other links to be discovered
between the supposed cause and the effect; but we can only further resolve
the known law, by introducing some other law hitherto unknown, which will
not diminish the number of ultimate laws.

In what cases, accordingly, has science been most successful in explaining
phenomena, by resolving their complex laws into laws of greater simplicity
and generality? Hitherto chiefly in cases of the propagation of various
phenomena through space; and, first and principally, the most extensive
and important of all facts of that description, mechanical motion. Now
this is exactly what might be expected from the principles here laid down.
Not only is motion one of the most universal of all phenomena, it is also
(as might be expected from that circumstance) one of those which,
apparently at least, are produced in the greatest number of ways; but the
phenomenon itself is always, to our sensations, the same in every respect
but degree. Differences of duration or of velocity, are evidently
differences in degree only; and differences of direction in space, which
alone has any semblance of being a distinction in kind, entirely disappear
(so far as our sensations are concerned) by a change in our own position;
indeed, the very same motion appears to us, according to our position, to
take place in every variety of direction, and motions in every different
direction to take place in the same. And again, motion in a straight line
and in a curve are no otherwise distinct than that the one is motion
continuing in the same direction, the other is motion which at each
instant changes its direction. There is, therefore, according to the
principles I have stated, no absurdity in supposing that all motion may be
produced in one and the same way, by the same kind of cause. Accordingly,
the greatest achievements in physical science have consisted in resolving
one observed law of the production of motion into the laws of other known
modes of production, or the laws of several such modes into one more
general mode; as when the fall of bodies to the earth, and the motions of
the planets, were brought under the one law of the mutual attraction of
all particles of matter; when the motions said to be produced by magnetism
were shown to be produced by electricity; when the motions of fluids in a
lateral direction, or even contrary to the direction of gravity, were
shown to be produced by gravity; and the like. There is an abundance of
distinct causes of motion still unresolved into one another: gravitation,
heat, electricity, chemical action, nervous action, and so forth; but
whether the efforts of the present generation of savants to resolve all
these different modes of production into one are ultimately successful or
not, the attempt so to resolve them is perfectly legitimate. For, though
these various causes produce, in other respects, sensations intrinsically
different, and are not, therefore, capable of being resolved into one
another, yet, in so far as they all produce motion, it is quite possible
that the immediate antecedent of the motion may in all these different
cases be the same; nor is it impossible that these various agencies
themselves may, as the new doctrines assert, all of them have for their
own immediate antecedent modes of molecular motion.

We need not extend our illustration to other cases, as, for instance, to
the propagation of light, sound, heat, electricity, etc., through space,
or any of the other phenomena which have been found susceptible of
explanation by the resolution of their observed laws into more general
laws. Enough has been said to display the difference between the kind of
explanation and resolution of laws which is chimerical, and that of which
the accomplishment is the great aim of science; and to show into what sort
of elements the resolution must be effected, if at all.(159)

§ 3. As, however, there is scarcely any one of the principles of a true
method of philosophizing which does not require to be guarded against
errors on both sides, I must enter a caveat against another
misapprehension, of a kind directly contrary to the preceding. M. Comte,
among other occasions on which he has condemned, with some asperity, any
attempt to explain phenomena which are “evidently primordial” (meaning,
apparently, no more than that every peculiar phenomenon must have at least
one peculiar and therefore inexplicable law), has spoken of the attempt to
furnish any explanation of the color belonging to each substance, “la
couleur élémentaire propre à chaque substance,” as essentially illusory.
“No one,” says he, “in our time attempts to explain the particular
specific gravity of each substance or of each structure. Why should it be
otherwise as to the specific color, the notion of which is undoubtedly no
less primordial?”(160)

Now although, as he elsewhere observes, a color must always remain a
different thing from a weight or a sound, varieties of color might
nevertheless follow, or correspond to, given varieties of weight, or
sound, or some other phenomenon as different as these are from color
itself. It is one question what a thing is, and another what it depends
on; and though to ascertain the conditions of an elementary phenomenon is
not to obtain any new insight into the nature of the phenomenon itself,
that is no reason against attempting to discover the conditions. The
interdict against endeavoring to reduce distinctions of color to any
common principle, would have held equally good against a like attempt on
the subject of distinctions of sound; which nevertheless have been found
to be immediately preceded and caused by distinguishable varieties in the
vibrations of elastic bodies; though a sound, no doubt, is quite as
different as a color is from any motion of particles, vibratory or
otherwise. We might add, that, in the case of colors, there are strong
positive indications that they are not ultimate properties of the
different kinds of substances, but depend on conditions capable of being
superinduced upon all substances; since there is no substance which can
not, according to the kind of light thrown upon it, be made to assume
almost any color; and since almost every change in the mode of aggregation
of the particles of the same substance is attended with alterations in its
color, and in its optical properties generally.

The really weak point in the attempts which have been made to account for
colors by the vibrations of a fluid, is not that the attempt itself is
unphilosophical, but that the existence of the fluid, and the fact of its
vibratory motion, are not proved, but are assumed, on no other ground than
the facility they are supposed to afford of explaining the phenomena. And
this consideration leads to the important question of the proper use of
scientific hypotheses, the connection of which with the subject of the
explanation of the phenomena of nature, and of the necessary limits to
that explanation, need not be pointed out.

§ 4. An hypothesis is any supposition which we make (either without actual
evidence, or on evidence avowedly insufficient) in order to endeavor to
deduce from it conclusions in accordance with facts which are known to be
real; under the idea that if the conclusions to which the hypothesis leads
are known truths, the hypothesis itself either must be, or at least is
likely to be, true. If the hypothesis relates to the cause or mode of
production of a phenomenon, it will serve, if admitted, to explain such
facts as are found capable of being deduced from it. And this explanation
is the purpose of many, if not most hypotheses. Since explaining, in the
scientific sense, means resolving a uniformity which is not a law of
causation, into the laws of causation from which it results, or a complex
law of causation into simpler and more general ones from which it is
capable of being deductively inferred, if there do not exist any known
laws which fulfill this requirement, we may feign or imagine some which
would fulfill it; and this is making an hypothesis.

An hypothesis being a mere supposition, there are no other limits to
hypotheses than those of the human imagination; we may, if we please,
imagine, by way of accounting for an effect, some cause of a kind utterly
unknown, and acting according to a law altogether fictitious. But as
hypotheses of this sort would not have any of the plausibility belonging
to those which ally themselves by analogy with known laws of nature, and
besides would not supply the want which arbitrary hypotheses are generally
invented to satisfy, by enabling the imagination to represent to itself an
obscure phenomenon in a familiar light, there is probably no hypothesis in
the history of science in which both the agent itself and the law of its
operation were fictitious. Either the phenomenon assigned as the cause is
real, but the law according to which it acts merely supposed; or the cause
is fictitious, but is supposed to produce its effects according to laws
similar to those of some known class of phenomena. An instance of the
first kind is afforded by the different suppositions made respecting the
law of the planetary central force, anterior to the discovery of the true
law, that the force varies as the inverse square of the distance; which
also suggested itself to Newton, in the first instance, as an hypothesis,
and was verified by proving that it led deductively to Kepler’s laws.
Hypotheses of the second kind are such as the vortices of Descartes, which
were fictitious, but were supposed to obey the known laws of rotatory
motion; or the two rival hypotheses respecting the nature of light, the
one ascribing the phenomena to a fluid emitted from all luminous bodies,
the other (now generally received) attributing them to vibratory motions
among the particles of an ether pervading all space. Of the existence of
either fluid there is no evidence, save the explanation they are
calculated to afford of some of the phenomena; but they are supposed to
produce their effects according to known laws: the ordinary laws of
continued locomotion in the one case, and in the other those of the
propagation of undulatory movements among the particles of an elastic
fluid.

According to the foregoing remarks, hypotheses are invented to enable the
Deductive Method to be earlier applied to phenomena. But(161) in order to
discover the cause of any phenomenon by the Deductive Method, the process
must consist of three parts: induction, ratiocination, and verification.
Induction (the place of which, however, may be supplied by a prior
deduction), to ascertain the laws of the causes; ratiocination, to compute
from those laws how the causes will operate in the particular combination
known to exist in the case in hand; verification, by comparing this
calculated effect with the actual phenomenon. No one of these three parts
of the process can be dispensed with. In the deduction which proves the
identity of gravity with the central force of the solar system, all the
three are found. First, it is proved from the moon’s motions, that the
earth attracts her with a force varying as the inverse square of the
distance. This (though partly dependent on prior deductions) corresponds
to the first, or purely inductive, step: the ascertainment of the law of
the cause. Secondly, from this law, and from the knowledge previously
obtained of the moon’s mean distance from the earth, and of the actual
amount of her deflection from the tangent, it is ascertained with what
rapidity the earth’s attraction would cause the moon to fall, if she were
no further off, and no more acted upon by extraneous forces, than
terrestrial bodies are: that is the second step, the ratiocination.
Finally, this calculated velocity being compared with the observed
velocity with which all heavy bodies fall, by mere gravity, toward the
surface of the earth (sixteen feet in the first second, forty-eight in the
second, and so forth, in the ratio of the odd numbers, 1, 3, 5, etc.), the
two quantities are found to agree. The order in which the steps are here
presented was not that of their discovery; but it is their correct logical
order, as portions of the proof that the same attraction of the earth
which causes the moon’s motion causes also the fall of heavy bodies to the
earth: a proof which is thus complete in all its parts.

Now, the Hypothetical Method suppresses the first of the three steps, the
induction to ascertain the law; and contents itself with the other two
operations, ratiocination and verification; the law which is reasoned from
being assumed instead of proved.

This process may evidently be legitimate on one supposition, namely, if
the nature of the case be such that the final step, the verification,
shall amount to, and fulfill the conditions of, a complete induction. We
want to be assured that the law we have hypothetically assumed is a true
one; and its leading deductively to true results will afford this
assurance, provided the case be such that a false law can not lead to a
true result; provided no law, except the very one which we have assumed,
can lead deductively to the same conclusions which that leads to. And this
proviso is often realized. For example, in the very complete specimen of
deduction which we just cited, the original major premise of the
ratiocination, the law of the attractive force, was ascertained in this
mode; by this legitimate employment of the Hypothetical Method. Newton
began by an assumption that the force which at each instant deflects a
planet from its rectilineal course, and makes it describe a curve round
the sun, is a force tending directly toward the sun. He then proved that
if this be so, the planet will describe, as we know by Kepler’s first law
that it does describe, equal areas in equal times; and, lastly, he proved
that if the force acted in any other direction whatever, the planet would
not describe equal areas in equal times. It being thus shown that no other
hypothesis would accord with the facts, the assumption was proved; the
hypothesis became an inductive truth. Not only did Newton ascertain by
this hypothetical process the direction of the deflecting force; he
proceeded in exactly the same manner to ascertain the law of variation of
the quantity of that force. He assumed that the force varied inversely as
the square of the distance; showed that from this assumption the remaining
two of Kepler’s laws might be deduced; and, finally, that any other law of
variation would give results inconsistent with those laws, and
inconsistent, therefore, with the real motions of the planets, of which
Kepler’s laws were known to be a correct expression.

I have said that in this case the verification fulfills the conditions of
an induction; but an induction of what sort? On examination we find that
it conforms to the canon of the Method of Difference. It affords the two
instances, A B C, _a b c_, and B C, _b c_. A represents central force; A B
C, the planets _plus_ a central force; B C, the planets apart from a
central force. The planets with a central force give _a_, areas
proportional to the times; the planets without a central force give _b c_
(a set of motions) without _a_, or with something else instead of _a_.
This is the Method of Difference in all its strictness. It is true, the
two instances which the method requires are obtained in this case, not by
experiment, but by a prior deduction. But that is of no consequence. It is
immaterial what is the nature of the evidence from which we derive the
assurance that A B C will produce _a b c_, and B C only _b c_; it is
enough that we have that assurance. In the present case, a process of
reasoning furnished Newton with the very instances which, if the nature of
the case had admitted of it, he would have sought by experiment.

It is thus perfectly possible, and indeed is a very common occurrence,
that what was an hypothesis at the beginning of the inquiry becomes a
proved law of nature before its close. But in order that this should
happen, we must be able, either by deduction or experiment, to obtain
_both_ the instances which the Method of Difference requires. That we are
able from the hypothesis to deduce the known facts, gives only the
affirmative instance, A B C, _a b c_. It is equally necessary that we
should be able to obtain, as Newton did, the negative instance B C, _b c_;
by showing that no antecedent, except the one assumed in the hypothesis,
would in conjunction with B C produce _a_.

Now it appears to me that this assurance can not be obtained, when the
cause assumed in the hypothesis is an unknown cause imagined solely to
account for _a_. When we are only seeking to determine the precise law of
a cause already ascertained, or to distinguish the particular agent which
is in fact the cause, among several agents of the same kind, one or other
of which it is already known to be, we may then obtain the negative
instance. An inquiry which of the bodies of the solar system causes by its
attraction some particular irregularity in the orbit or periodic time of
some satellite or comet, would be a case of the second description.
Newton’s was a case of the first. If it had not been previously known that
the planets were hindered from moving in straight lines by some force
tending toward the interior of their orbit, though the exact direction was
doubtful; or if it had not been known that the force increased in some
proportion or other as the distance diminished, and diminished as it
increased, Newton’s argument would not have proved his conclusion. These
facts, however, being already certain, the range of admissible
suppositions was limited to the various possible directions of a line, and
the various possible numerical relations between the variations of the
distance, and the variations of the attractive force. Now among these it
was easily shown that different suppositions could not lead to identical
consequences.

Accordingly, Newton could not have performed his second great scientific
operation: that of identifying terrestrial gravity with the central force
of the solar system by the same hypothetical method. When the law of the
moon’s attraction had been proved from the data of the moon itself, then,
on finding the same law to accord with the phenomena of terrestrial
gravity, he was warranted in adopting it as the law of those phenomena
likewise; but it would not have been allowable for him, without any lunar
data, to assume that the moon was attracted toward the earth with a force
as the inverse square of the distance, merely because that ratio would
enable him to account for terrestrial gravity; for it would have been
impossible for him to prove that the observed law of the fall of heavy
bodies to the earth could not result from any force, save one extending to
the moon, and proportional to the inverse square.

It appears, then, to be a condition of the most genuinely scientific
hypothesis, that it be not destined always to remain an hypothesis, but be
of such a nature as to be either proved or disproved by comparison with
observed facts. This condition is fulfilled when the effect is already
known to depend on the very cause supposed, and the hypothesis relates
only to the precise mode of dependence; the law of the variation of the
effect according to the variations in the quantity or in the relations of
the cause. With these may be classed the hypotheses which do not make any
supposition with regard to causation, but only with regard to the law of
correspondence between facts which accompany each other in their
variations, though there may be no relation of cause and effect between
them. Such were the different false hypotheses which Kepler made
respecting the law of the refraction of light. It was known that the
direction of the line of refraction varied with every variation in the
direction of the line of incidence, but it was not known how; that is,
what changes of the one corresponded to the different changes of the
other. In this case any law different from the true one must have led to
false results. And, lastly, we must add to these all hypothetical modes of
merely representing or _describing_ phenomena; such as the hypothesis of
the ancient astronomers that the heavenly bodies moved in circles; the
various hypotheses of eccentrics, deferents, and epicycles, which were
added to that original hypothesis; the nineteen false hypotheses which
Kepler made and abandoned respecting the form of the planetary orbits; and
even the doctrine in which he finally rested, that those orbits are
ellipses, which was but an hypothesis like the rest until verified by
facts.

In all these cases, verification is proof; if the supposition accords with
the phenomena there needs no other evidence of it. But in order that this
may be the case, I conceive it to be necessary, when the hypothesis
relates to causation, that the supposed cause should not only be a real
phenomenon, something actually existing in nature, but should be already
known to exercise, or at least to be capable of exercising, an influence
of some sort over the effect. In any other case, it is no sufficient
evidence of the truth of the hypothesis that we are able to deduce the
real phenomena from it.

Is it, then, never allowable, in a scientific hypothesis, to assume a
cause, but only to ascribe an assumed law to a known cause? I do not
assert this. I only say, that in the latter case alone can the hypothesis
be received as true merely because it explains the phenomena. In the
former case it may be very useful by suggesting a line of investigation
which may possibly terminate in obtaining real proof. But for this
purpose, as is justly remarked by M. Comte, it is indispensable that the
cause suggested by the hypothesis should be in its own nature susceptible
of being proved by other evidence. This seems to be the philosophical
import of Newton’s maxim, (so often cited with approbation by subsequent
writers), that the cause assigned for any phenomenon must not only be such
as if admitted would explain the phenomenon, but must also be a _vera
causa_. What he meant by a _vera causa_ Newton did not indeed very
explicitly define; and Dr. Whewell, who dissents from the propriety of any
such restriction upon the latitude of framing hypotheses, has had little
difficulty in showing(162) that his conception of it was neither precise
nor consistent with itself; accordingly his optical theory was a signal
instance of the violation of his own rule. It is certainly not necessary
that the cause assigned should be a cause already known; otherwise we
should sacrifice our best opportunities of becoming acquainted with new
causes. But what is true in the maxim is, that the cause, though not known
previously, should be capable of being known thereafter; that its
existence should be capable of being detected, and its connection with the
effect ascribed to it should be susceptible of being proved, by
independent evidence. The hypothesis, by suggesting observations and
experiments, puts us on the road to that independent evidence, if it be
really attainable; and till it be attained, the hypothesis ought only to
count for a more or less plausible conjecture.

§ 5. This function, however, of hypotheses, is one which must be reckoned
absolutely indispensable in science. When Newton said, “Hypotheses non
fingo,” he did not mean that he deprived himself of the facilities of
investigation afforded by assuming in the first instance what he hoped
ultimately to be able to prove. Without such assumptions, science could
never have attained its present state; they are necessary steps in the
progress to something more certain; and nearly every thing which is now
theory was once hypothesis. Even in purely experimental science, some
inducement is necessary for trying one experiment rather than another; and
though it is abstractedly possible that all the experiments which have
been tried, might have been produced by the mere desire to ascertain what
would happen in certain circumstances, without any previous conjecture as
to the result; yet, in point of fact, those unobvious, delicate, and often
cumbrous and tedious processes of experiment, which have thrown most light
upon the general constitution of nature, would hardly ever have been
undertaken by the persons or at the time they were, unless it had seemed
to depend on them whether some general doctrine or theory which had been
suggested, but not yet proved, should be admitted or not. If this be true
even of merely experimental inquiry, the conversion of experimental into
deductive truths could still less have been effected without large
temporary assistance from hypotheses. The process of tracing regularity in
any complicated, and at first sight confused, set of appearances, is
necessarily tentative; we begin by making any supposition, even a false
one, to see what consequences will follow from it; and by observing how
these differ from the real phenomena, we learn what corrections to make in
our assumption. The simplest supposition which accords with the more
obvious facts is the best to begin with; because its consequences are the
most easily traced. This rude hypothesis is then rudely corrected, and the
operation repeated; and the comparison of the consequences deducible from
the corrected hypothesis, with the observed facts, suggests still further
correction, until the deductive results are at last made to tally with the
phenomena. “Some fact is as yet little understood, or some law is unknown;
we frame on the subject an hypothesis as accordant as possible with the
whole of the data already possessed; and the science, being thus enabled
to move forward freely, always ends by leading to new consequences capable
of observation, which either confirm or refute, unequivocally, the first
supposition.” Neither induction nor deduction would enable us to
understand even the simplest phenomena, “if we did not often commence by
anticipating on the results; by making a provisional supposition, at first
essentially conjectural, as to some of the very notions which constitute
the final object of the inquiry.”(163) Let any one watch the manner in
which he himself unravels a complicated mass of evidence; let him observe
how, for instance, he elicits the true history of any occurrence from the
involved statements of one or of many witnesses; he will find that he does
not take all the items of evidence into his mind at once, and attempt to
weave them together; he extemporizes, from a few of the particulars, a
first rude theory of the mode in which the facts took place, and then
looks at the other statements one by one, to try whether they can be
reconciled with that provisional theory, or what alterations or additions
it requires to make it square with them. In this way, which has been
justly compared to the Methods of Approximation of mathematicians, we
arrive, by means of hypotheses, at conclusions not hypothetical.(164)

§ 6. It is perfectly consistent with the spirit of the method, to assume
in this provisional manner not only an hypothesis respecting the law of
what we already know to be the cause, but an hypothesis respecting the
cause itself. It is allowable, useful, and often even necessary, to begin
by asking ourselves what cause _may_ have produced the effect, in order
that we may know in what direction to look out for evidence to determine
whether it actually _did_. The vortices of Descartes would have been a
perfectly legitimate hypothesis, if it had been possible, by any mode of
exploration which we could entertain the hope of ever possessing, to bring
the reality of the vortices, as a fact in nature, conclusively to the test
of observation. The vice of the hypothesis was that it could not lead to
any course of investigation capable of converting it from an hypothesis
into a proved fact. It might chance to be _dis_proved, either by some want
of correspondence with the phenomena it purported to explain, or (as
actually happened) by some extraneous fact. “The free passage of comets
through the spaces in which these vortices should have been, convinced men
that these vortices did not exist.”(165) But the hypothesis would have
been false, though no such direct evidence of its falsity had been
procurable. Direct evidence of its truth there could not be.

The prevailing hypothesis of a luminiferous ether, in other respects not
without analogy to that of Descartes, is not in its own nature entirely
cut off from the possibility of direct evidence in its favor. It is well
known that the difference between the calculated and the observed times of
the periodical return of Encke’s comet, has led to a conjecture that a
medium capable of opposing resistance to motion is diffused through space.
If this surmise should be confirmed, in the course of ages, by the gradual
accumulation of a similar variance in the case of the other bodies of the
solar system, the luminiferous ether would have made a considerable
advance toward the character of a _vera causa_, since the existence would
have been ascertained of a great cosmical agent, possessing some of the
attributes which the hypothesis assumes; though there would still remain
many difficulties, and the identification of the ether with the resisting
medium would even, I imagine, give rise to new ones. At present, however,
this supposition can not be looked upon as more than a conjecture; the
existence of the ether still rests on the possibility of deducing from its
assumed laws a considerable number of actual phenomena; and this evidence
I can not regard as conclusive, because we can not have, in the case of
such an hypothesis, the assurance that if the hypothesis be false it must
lead to results at variance with the true facts.

Accordingly, most thinkers of any degree of sobriety allow that an
hypothesis of this kind is not to be received as probably true because it
accounts for all the known phenomena; since this is a condition sometimes
fulfilled tolerably well by two conflicting hypotheses; while there are
probably many others which are equally possible, but which, for want of
any thing analogous in our experience, our minds are unfitted to conceive.
But it seems to be thought that an hypothesis of the sort in question is
entitled to a more favorable reception, if, besides accounting for all the
facts previously known, it has led to the anticipation and prediction of
others which experience afterward verified; as the undulatory theory of
light led to the prediction, subsequently realized by experiment, that two
luminous rays might meet each other in such a manner as to produce
darkness. Such predictions and their fulfillment are, indeed, well
calculated to impress the uninformed, whose faith in science rests solely
on similar coincidences between its prophecies and what comes to pass. But
it is strange that any considerable stress should be laid upon such a
coincidence by persons of scientific attainments. If the laws of the
propagation of light accord with those of the vibrations of an elastic
fluid in as many respects as is necessary to make the hypothesis afford a
correct expression of all or most of the phenomena known at the time, it
is nothing strange that they should accord with each other in one respect
more. Though twenty such coincidences should occur, they would not prove
the reality of the undulatory ether; it would not follow that the
phenomena of light were results of the laws of elastic fluids, but at most
that they are governed by laws partially identical with these; which, we
may observe, is already certain, from the fact that the hypothesis in
question could be for a moment tenable.(166) Cases may be cited, even in
our imperfect acquaintance with nature, where agencies that we have good
reason to consider as radically distinct produce their effects, or some of
their effects, according to laws which are identical. The law, for
example, of the inverse square of the distance, is the measure of the
intensity not only of gravitation, but (it is believed) of illumination,
and of heat diffused from a centre. Yet no one looks upon this identity as
proving similarity in the mechanism by which the three kinds of phenomena
are produced.

According to Dr. Whewell, the coincidence of results predicted from an
hypothesis with facts afterward observed, amounts to a conclusive proof of
the truth of the theory. “If I copy a long series of letters, of which the
last half-dozen are concealed, and if I guess these aright, as is found to
be the case when they are afterward uncovered, this must be because I have
made out the import of the inscription. To say that because I have copied
all that I could see, it is nothing strange that I should guess those
which I can not see, would be absurd, without supposing such a ground for
guessing.”(167) If any one, from examining the greater part of a long
inscription, can interpret the characters so that the inscription gives a
rational meaning in a known language, there is a strong presumption that
his interpretation is correct; but I do not think the presumption much
increased by his being able to guess the few remaining letters without
seeing them; for we should naturally expect (when the nature of the case
excludes chance) that even an erroneous interpretation which accorded with
all the visible parts of the inscription would accord also with the small
remainder; as would be the case, for example, if the inscription had been
designedly so contrived as to admit of a double sense. I assume that the
uncovered characters afford an amount of coincidence too great to be
merely casual; otherwise the illustration is not a fair one. No one
supposes the agreement of the phenomena of light with the theory of
undulations to be merely fortuitous. It must arise from the actual
identity of some of the laws of undulations with some of those of light;
and if there be that identity, it is reasonable to suppose that its
consequences would not end with the phenomena which first suggested the
identification, nor be even confined to such phenomena as were known at
the time. But it does not follow, because some of the laws agree with
those of undulations, that there are any actual undulations; no more than
it followed because some (though not so many) of the same laws agreed with
those of the projection of particles, that there was actual emission of
particles. Even the undulatory hypothesis does not account for all the
phenomena of light. The natural colors of objects, the compound nature of
the solar ray, the absorption of light, and its chemical and vital action,
the hypothesis leaves as mysterious as it found them; and some of these
facts are, at least apparently, more reconcilable with the emission theory
than with that of Young and Fresnel. Who knows but that some third
hypothesis, including all these phenomena, may in time leave the
undulatory theory as far behind as that has left the theory of Newton and
his successors?

To the statement, that the condition of accounting for all the known
phenomena is often fulfilled equally well by two conflicting hypotheses,
Dr. Whewell makes answer that he knows “of no such case in the history of
science, where the phenomena are at all numerous and complicated.”(168)
Such an affirmation, by a writer of Dr. Whewell’s minute acquaintance with
the history of science, would carry great authority, if he had not, a few
pages before, taken pains to refute it,(169) by maintaining that even the
exploded scientific hypotheses might always, or almost always, have been
so modified as to make them correct representations of the phenomena. The
hypothesis of vortices, he tells us, was, by successive modifications,
brought to coincide in its results with the Newtonian theory and with the
facts. The vortices did not, indeed, explain all the phenomena which the
Newtonian theory was ultimately found to account for, such as the
precession of the equinoxes; but this phenomenon was not, at the time, in
the contemplation of either party, as one of the facts to be accounted
for. All the facts which they did contemplate, we may believe on Dr.
Whewell’s authority to have accorded as accurately with the Cartesian
hypothesis, in its finally improved state, as with Newton’s.

But it is not, I conceive, a valid reason for accepting any given
hypothesis, that we are unable to imagine any other which will account for
the facts. There is no necessity for supposing that the true explanation
must be one which, with only our present experience, we could imagine.
Among the natural agents with which we are acquainted, the vibrations of
an elastic fluid may be the only one whose laws bear a close resemblance
to those of light; but we can not tell that there does not exist an
unknown cause, other than an elastic ether diffused through space, yet
producing effects identical in some respects with those which would result
from the undulations of such an ether. To assume that no such cause can
exist, appears to me an extreme case of assumption without evidence. And
at the risk of being charged with want of modesty, I can not help
expressing astonishment that a philosopher of Dr. Whewell’s abilities and
attainments should have written an elaborate treatise on the philosophy of
induction, in which he recognizes absolutely no mode of induction except
that of trying hypothesis after hypothesis until one is found which fits
the phenomena; which one, when found, is to be assumed as true, with no
other reservation than that if, on re-examination, it should appear to
assume more than is needful for explaining the phenomena, the superfluous
part of the assumption should be cut off. And this without the slightest
distinction between the cases in which it may be known beforehand that two
different hypotheses can not lead to the same result, and those in which,
for aught we can ever know, the range of suppositions, all equally
consistent with the phenomena, may be infinite.(170)

Nevertheless, I do not agree with M. Comte in condemning those who employ
themselves in working out into detail the application of these hypotheses
to the explanation of ascertained facts, provided they bear in mind that
the utmost they can prove is, not that the hypothesis is, but that it
_may_ be true. The ether hypothesis has a very strong claim to be so
followed out, a claim greatly strengthened since it has been shown to
afford a mechanism which would explain the mode of production, not of
light only, but also of heat. Indeed, the speculation has a smaller
element of hypothesis in its application to heat, than in the case for
which it was originally framed. We have proof by our senses of the
existence of molecular movement among the particles of all heated bodies;
while we have no similar experience in the case of light. When, therefore,
heat is communicated from the sun to the earth across apparently empty
space, the chain of causation has molecular motion both at the beginning
and end. The hypothesis only makes the motion continuous by extending it
to the middle. Now, motion in a body is known to be capable of being
imparted to another body contiguous to it; and the intervention of a
hypothetical elastic fluid occupying the space between the sun and the
earth, supplies the contiguity which is the only condition wanting, and
which can be supplied by no supposition but that of an intervening medium.
The supposition, notwithstanding, is at best a probable conjecture, not a
proved truth. For there is no proof that contiguity is absolutely required
for the communication of motion from one body to another. Contiguity does
not always exist, to our senses at least, in the cases in which motion
produces motion. The forces which go under the name of attraction,
especially the greatest of all, gravitation, are examples of motion
producing motion without apparent contiguity. When a planet moves, its
distant satellites accompany its motion. The sun carries the whole solar
system along with it in the progress which it is ascertained to be
executing through space. And even if we were to accept as conclusive the
geometrical reasonings (strikingly similar to those by which the
Cartesians defended their vortices) by which it has been attempted to show
that the motions of the ether may account for gravitation itself, even
then it would only have been proved that the supposed mode of production
may be, but not that no other mode can be, the true one.

§ 7. It is necessary, before quitting the subject of hypotheses, to guard
against the appearance of reflecting upon the scientific value of several
branches of physical inquiry, which, though only in their infancy, I hold
to be strictly inductive. There is a great difference between inventing
agencies to account for classes of phenomena, and endeavoring, in
conformity with known laws, to conjecture what former collocations of
known agents may have given birth to individual facts still in existence.
The latter is the legitimate operation of inferring from an observed
effect the existence, in time past, of a cause similar to that by which we
know it to be produced in all cases in which we have actual experience of
its origin. This, for example, is the scope of the inquiries of geology;
and they are no more illogical or visionary than judicial inquiries, which
also aim at discovering a past event by inference from those of its
effects which still subsist. As we can ascertain whether a man was
murdered or died a natural death, from the indications exhibited by the
corpse, the presence or absence of signs of struggling on the ground or on
the adjacent objects, the marks of blood, the footsteps of the supposed
murderers, and so on, proceeding throughout on uniformities ascertained by
a perfect induction without any mixture of hypothesis; so if we find, on
and beneath the surface of our planet, masses exactly similar to deposits
from water, or to results of the cooling of matter melted by fire, we may
justly conclude that such has been their origin; and if the effects,
though similar in kind, are on a far larger scale than any which are now
produced, we may rationally, and without hypothesis, conclude either that
the causes existed formerly with greater intensity, or that they have
operated during an enormous length of time. Further than this no geologist
of authority has, since the rise of the present enlightened school of
geological speculation, attempted to go.

In many geological inquiries it doubtless happens that though the laws to
which the phenomena are ascribed are known laws, and the agents known
agents, those agents are not known to have been present in the particular
case. In the speculation respecting the igneous origin of trap or granite,
the fact does not admit of direct proof that those substances have been
actually subjected to intense heat. But the same thing might be said of
all judicial inquiries which proceed on circumstantial evidence. We can
conclude that a man was murdered, though it is not proved by the testimony
of eye-witnesses that some person who had the intention of murdering him
was present on the spot. It is enough for most purposes, if no other known
cause could have generated the effects shown to have been produced.

                  -------------------------------------

The celebrated speculation of Laplace concerning the origin of the earth
and planets, participates essentially in the inductive character of modern
geological theory. The speculation is, that the atmosphere of the sun
originally extended to the present limits of the solar system; from which,
by the process of cooling, it has contracted to its present dimensions;
and since, by the general principles of mechanics the rotation of the sun
and of its accompanying atmosphere must increase in rapidity as its volume
diminishes, the increased centrifugal force generated by the more rapid
rotation, overbalancing the action of gravitation, has caused the sun to
abandon successive rings of vaporous matter, which are supposed to have
condensed by cooling, and to have become the planets. There is in this
theory no unknown substance introduced on supposition, nor any unknown
property or law ascribed to a known substance. The known laws of matter
authorize us to suppose that a body which is constantly giving out so
large an amount of heat as the sun is, must be progressively cooling, and
that, by the process of cooling it must contract; if, therefore, we
endeavor, from the present state of that luminary, to infer its state in a
time long past, we must necessarily suppose that its atmosphere extended
much farther than at present, and we are entitled to suppose that it
extended as far as we can trace effects such as it might naturally leave
behind it on retiring; and such the planets are. These suppositions being
made, it follows from known laws that successive zones of the solar
atmosphere might be abandoned; that these would continue to revolve round
the sun with the same velocity as when they formed part of its substance;
and that they would cool down, long before the sun itself, to any given
temperature, and consequently to that at which the greater part of the
vaporous matter of which they consisted would become liquid or solid. The
known law of gravitation would then cause them to agglomerate in masses,
which would assume the shape our planets actually exhibit; would acquire,
each about its own axis, a rotatory movement; and would in that state
revolve, as the planets actually do, about the sun, in the same direction
with the sun’s rotation, but with less velocity, because in the same
periodic time which the sun’s rotation occupied when his atmosphere
extended to that point. There is thus, in Laplace’s theory, nothing,
strictly speaking, hypothetical; it is an example of legitimate reasoning
from a present effect to a possible past cause, according to the known
laws of that cause. The theory, therefore, is, as I have said, of a
similar character to the theories of geologists; but considerably inferior
to them in point of evidence. Even if it were proved (which it is not)
that the conditions necessary for determining the breaking off of
successive rings would certainly occur, there would still be a much
greater chance of error in assuming that the existing laws of nature are
the same which existed at the origin of the solar system, than in merely
presuming (with geologists) that those laws have lasted through a few
revolutions and transformations of a single one among the bodies of which
that system is composed.




                               Chapter XV.


Of Progressive Effects; And Of The Continued Action Of Causes.


§ 1. In the last four chapters we have traced the general outlines of the
theory of the generation of derivative laws from ultimate ones. In the
present chapter our attention will be directed to a particular case of the
derivation of laws from other laws, but a case so general, and so
important as not only to repay, but to require, a separate examination.
This is the case of a complex phenomenon resulting from one simple law, by
the continual addition of an effect to itself.

There are some phenomena, some bodily sensations, for example, which are
essentially instantaneous, and whose existence can only be prolonged by
the prolongation of the existence of the cause by which they are produced.
But most phenomena are in their own nature permanent; having begun to
exist, they would exist forever unless some cause intervened having a
tendency to alter or destroy them. Such, for example, are all the facts of
phenomena which we call bodies. Water, once produced, will not of itself
relapse into a state of hydrogen and oxygen; such a change requires some
agent having the power of decomposing the compound. Such, again, are the
positions in space and the movements of bodies. No object at rest alters
its position without the intervention of some conditions extraneous to
itself; and when once in motion, no object returns to a state of rest, or
alters either its direction or its velocity, unless some new external
conditions are superinduced. It, therefore, perpetually happens that a
temporary cause gives rise to a permanent effect. The contact of iron with
moist air for a few hours, produces a rust which may endure for centuries;
or a projectile force which launches a cannon-ball into space, produces a
motion which would continue forever unless some other force counteracted
it.

Between the two examples which we have here given, there is a difference
worth pointing out. In the former (in which the phenomenon produced is a
substance, and not a motion of a substance), since the rust remains
forever and unaltered unless some new cause supervenes, we may speak of
the contact of air a hundred years ago as even the proximate cause of the
rust which has existed from that time until now. But when the effect is
motion, which is itself a change, we must use a different language. The
permanency of the effect is now only the permanency of a series of
changes. The second foot, or inch, or mile of motion is not the mere
prolonged duration of the first foot, or inch, or mile, but another fact
which succeeds, and which may in some respects be very unlike the former,
since it carries the body through a different region of space. Now, the
original projectile force which set the body moving is the remote cause of
all its motion, however long continued, but the proximate cause of no
motion except that which took place at the first instant. The motion at
any subsequent instant is proximately caused by the motion which took
place at the instant preceding. It is on that, and not on the original
moving cause, that the motion at any given moment depends. For, suppose
that the body passes through some resisting medium, which partially
counteracts the effect of the original impulse, and retards the motion;
this counteraction (it need scarcely here be repeated) is as strict an
example of obedience to the law of the impulse, as if the body had gone on
moving with its original velocity; but the motion which results is
different, being now a compound of the effects of two causes acting in
contrary directions, instead of the single effect of one cause. Now, what
cause does the body obey in its subsequent motion? The original cause of
motion, or the actual motion at the preceding instant? The latter; for
when the object issues from the resisting medium, it continues moving, not
with its original, but with its retarded velocity. The motion having once
been diminished, all that which follows is diminished. The effect changes,
because the cause which it really obeys, the proximate cause, the real
cause in fact, has changed. This principle is recognized by mathematicians
when they enumerate among the causes by which the motion of a body is at
any instant determined the _force generated_ by the previous motion; an
expression which would be absurd if taken to imply that this “force” was
an intermediate link between the cause and the effect, but which really
means only the previous motion itself, considered as a cause of further
motion. We must, therefore, if we would speak with perfect precision,
consider each link in the succession of motions as the effect of the link
preceding it. But if, for the convenience of discourse, we speak of the
whole series as one effect, it must be as an effect produced by the
original impelling force; a permanent effect produced by an instantaneous
cause, and possessing the property of self-perpetuation.

Let us now suppose that the original agent or cause, instead of being
instantaneous, is permanent. Whatever effect has been produced up to a
given time, would (unless prevented by the intervention of some new cause)
subsist permanently, even if the cause were to perish. Since, however, the
cause does not perish, but continues to exist and to operate, it must go
on producing more and more of the effect; and instead of a uniform effect,
we have a progressive series of effects, arising from the accumulated
influence of a permanent cause. Thus, the contact of iron with the
atmosphere causes a portion of it to rust; and if the cause ceased, the
effect already produced would be permanent, but no further effect would be
added. If, however, the cause, namely, exposure to moist air, continues,
more and more of the iron becomes rusted, until all which is exposed is
converted into a red powder, when one of the conditions of the production
of rust, namely, the presence of unoxidized iron, has ceased, and the
effect can not any longer be produced. Again, the earth causes bodies to
fall toward it; that is, the existence of the earth at a given instant
causes an unsupported body to move toward it at the succeeding instant;
and if the earth were annihilated, as much of the effect as is already
produced would continue; the object would go on moving in the same
direction, with its acquired velocity, until intercepted by some body or
deflected by some other force. The earth, however, not being annihilated,
goes on producing in the second instant an effect similar and of equal
amount with the first, which two effects being added together, there
results an accelerated velocity; and this operation being repeated at each
successive instant, the mere permanence of the cause, though without
increase, gives rise to a constant progressive increase of the effect, so
long as all the conditions, negative and positive, of the production of
that effect continue to be realized.

It is obvious that this state of things is merely a case of the
Composition of Causes. A cause which continues in action must on a strict
analysis be considered as a number of causes exactly similar, successively
introduced, and producing by their combination the sum of the effects
which they would severally produce if they acted singly. The progressive
rusting of the iron is in strictness the sum of the effects of many
particles of air acting in succession upon corresponding particles of
iron. The continued action of the earth upon a falling body is equivalent
to a series of forces, applied in successive instants, each tending to
produce a certain constant quantity of motion; and the motion at each
instant is the sum of the effects of the new force applied at the
preceding instant, and the motion already acquired. In each instant a
fresh effect, of which gravity is the proximate cause, is added to the
effect of which it was the remote cause; or (to express the same thing in
another manner), the effect produced by the earth’s influence at the
instant last elapsed is added to the sum of the effects of which the
remote causes were the influences exerted by the earth at all the previous
instants since the motion began. The case, therefore, comes under the
principle of a concurrence of causes producing an effect equal to the sum
of their separate effects. But as the causes come into play not all at
once, but successively, and as the effect at each instant is the sum of
the effects of those causes only which have come into action up to that
instant, the result assumes the form of an ascending series; a succession
of sums, each greater than that which preceded it; and we have thus a
progressive effect from the continued action of a cause.

Since the continuance of the cause influences the effect only by adding to
its quantity, and since the addition takes place according to a fixed law
(equal quantities in equal times), the result is capable of being computed
on mathematical principles. In fact, this case, being that of
infinitesimal increments, is precisely the case which the differential
calculus was invented to meet. The questions, what effect will result from
the continual addition of a given cause to itself, and what amount of the
cause, being continually added to itself, will produce a given amount of
the effect, are evidently mathematical questions, and to be treated,
therefore, deductively. If, as we have seen, cases of the Composition of
Causes are seldom adapted for any other than deductive investigation, this
is especially true in the case now examined, the continual composition of
a cause with its own previous effects; since such a case is peculiarly
amenable to the deductive method, while the undistinguishable manner in
which the effects are blended with one another and with the causes, must
make the treatment of such an instance experimentally still more
chimerical than in any other case.

§ 2. We shall next advert to a rather more intricate operation of the same
principle, namely, when the cause does not merely continue in action, but
undergoes, during the same time, a progressive change in those of its
circumstances which contribute to determine the effect. In this case, as
in the former, the total effect goes on accumulating by the continual
addition of a fresh effect to that already produced, but it is no longer
by the addition of equal quantities in equal times; the quantities added
are unequal, and even the quality may now be different. If the change in
the state of the permanent cause be progressive, the effect will go
through a double series of changes, arising partly from the accumulated
action of the cause, and partly from the changes in its action. The effect
is still a progressive effect, produced, however, not by the mere
continuance of a cause, but by its continuance and its progressiveness
combined.

A familiar example is afforded by the increase of the temperature as
summer advances, that is, as the sun draws nearer to a vertical position,
and remains a greater number of hours above the horizon. This instance
exemplifies in a very interesting manner the twofold operation on the
effect, arising from the continuance of the cause, and from its
progressive change. When once the sun has come near enough to the zenith,
and remains above the horizon long enough, to give more warmth during one
diurnal rotation than the counteracting cause, the earth’s radiation, can
carry off, the mere continuance of the cause would progressively increase
the effect, even if the sun came no nearer and the days grew no longer;
but in addition to this, a change takes place in the accidents of the
cause (its series of diurnal positions), tending to increase the quantity
of the effect. When the summer solstice has passed, the progressive change
in the cause begins to take place the reverse way, but, for some time, the
accumulating effect of the mere continuance of the cause exceeds the
effect of the changes in it, and the temperature continues to increase.

Again, the motion of a planet is a progressive effect, produced by causes
at once permanent and progressive. The orbit of a planet is determined
(omitting perturbations) by two causes: first, the action of the central
body, a permanent cause, which alternately increases and diminishes as the
planet draws nearer to or goes farther from its perihelion, and which acts
at every point in a different direction; and, secondly, the tendency of
the planet to continue moving in the direction and with the velocity which
it has already acquired. This force also grows greater as the planet draws
nearer to its perihelion, because as it does so its velocity increases,
and less, as it recedes from its perihelion; and this force as well as the
other acts at each point in a different direction, because at every point
the action of the central force, by deflecting the planet from its
previous direction, alters the line in which it tends to continue moving.
The motion at each instant is determined by the amount and direction of
the motion, and the amount and direction of the sun’s action, at the
previous instant; and if we speak of the entire revolution of the planet
as one phenomenon (which, as it is periodical and similar to itself, we
often find it convenient to do), that phenomenon is the progressive effect
of two permanent and progressive causes, the central force and the
acquired motion. Those causes happening to be progressive in the
particular way which is called periodical, the effect necessarily is so
too; because the quantities to be added together returning in a regular
order, the same sums must also regularly return.

This example is worthy of consideration also in another respect. Though
the causes themselves are permanent, and independent of all conditions
known to us, the changes which take place in the quantities and relations
of the causes are actually caused by the periodical changes in the
effects. The causes, as they exist at any moment, having produced a
certain motion, that motion, becoming itself a cause, reacts upon the
causes, and produces a change in them. By altering the distance and
direction of the central body relatively to the planet, and the direction
and quantity of the force in the direction of the tangent, it alters the
elements which determine the motion at the next succeeding instant. This
change renders the next motion somewhat different; and this difference, by
a fresh reaction upon the causes, renders the next motion again different,
and so on. The original state of the causes might have been such that this
series of actions modified by reactions would not have been periodical.
The sun’s action, and the original impelling force, might have been in
such a ratio to one another, that the reaction of the effect would have
been such as to alter the causes more and more, without ever bringing them
back to what they were at any former time. The planet would then have
moved in a parabola, or an hyperbola, curves not returning into
themselves. The quantities of the two forces were, however, originally
such, that the successive reactions of the effect bring back the causes,
after a certain time, to what they were before; and from that time all the
variations continued to recur again and again in the same periodical
order, and must so continue while the causes subsist and are not
counteracted.

§ 3. In all cases of progressive effects, whether arising from the
accumulation of unchanging or of changing elements, there is a uniformity
of succession not merely between the cause and the effect, but between the
first stages of the effect and its subsequent stages. That a body _in
vacuo_ falls sixteen feet in the first second, forty-eight in the second,
and so on in the ratio of the odd numbers, is as much a uniform sequence
as that when the supports are removed the body falls. The sequence of
spring and summer is as regular and invariable as that of the approach of
the sun and spring; but we do not consider spring to be the cause of
summer; it is evident that both are successive effects of the heat
received from the sun, and that, considered merely in itself, spring might
continue forever without having the slightest tendency to produce summer.
As we have so often remarked, not the conditional, but the unconditional
invariable antecedent is termed the cause. That which would not be
followed by the effect unless something else had preceded, and which if
that something else had preceded, would not have been required, is not the
cause, however invaluable the sequence may in fact be.

It is in this way that most of those uniformities of succession are
generated, which are not cases of causation. When a phenomenon goes on
increasing, or periodically increases and diminishes, or goes through any
continued and unceasing process of variation reducible to a uniform rule
or law of succession, we do not on this account presume that any two
successive terms of the series are cause and effect. We presume the
contrary; we expect to find that the whole series originates either from
the continued action of fixed causes or from causes which go through a
corresponding process of continuous change. A tree grows from half an inch
high to a hundred feet; and some trees will generally grow to that height
unless prevented by some counteracting cause. But we do not call the
seedling the cause of the full-grown tree; the invariable antecedent it
certainly is, and we know very imperfectly on what other antecedents the
sequence is contingent, but we are convinced that it is contingent on
something; because the homogeneousness of the antecedent with the
consequent, the close resemblance of the seedling to the tree in all
respects except magnitude, and the graduality of the growth, so exactly
resembling the progressively accumulating effect produced by the long
action of some one cause, leave no possibility of doubting that the
seedling and the tree are two terms in a series of that description, the
first term of which is yet to seek. The conclusion is further confirmed by
this, that we are able to prove by strict induction the dependence of the
growth of the tree, and even of the continuance of its existence, upon the
continued repetition of certain processes of nutrition, the rise of the
sap, the absorptions and exhalations by the leaves, etc.; and the same
experiments would probably prove to us that the growth of the tree is the
accumulated sum of the effects of these continued processes, were we not,
for want of sufficiently microscopic eyes, unable to observe correctly and
in detail what those effects are.

This supposition by no means requires that the effect should not, during
its progress, undergo many modifications besides those of quantity, or
that it should not sometimes appear to undergo a very marked change of
character. This may be either because the unknown cause consists of
several component elements or agents, whose effects, accumulating
according to different laws, are compounded in different proportions at
different periods in the existence of the organized being; or because, at
certain points in its progress, fresh causes or agencies come in, or are
evolved, which intermix their laws with those of the prime agent.




                               Chapter XVI.


Of Empirical Laws.


§ 1. Scientific inquirers give the name of Empirical Laws to those
uniformities which observation or experiment has shown to exist, but on
which they hesitate to rely in cases varying much from those which have
been actually observed, for want of seeing any reason _why_ such a law
should exist. It is implied, therefore, in the notion of an empirical law,
that it is not an ultimate law; that if true at all, its truth is capable
of being, and requires to be, accounted for. It is a derivative law, the
derivation of which is not yet known. To state the explanation, the _why_,
of the empirical law, would be to state the laws from which it is
derived—the ultimate causes on which it is contingent. And if we knew
these, we should also know what are its limits; under what conditions it
would cease to be fulfilled.

The periodical return of eclipses, as originally ascertained by the
persevering observation of the early Eastern astronomers, was an empirical
law, until the general laws of the celestial motions had accounted for it.
The following are empirical laws still waiting to be resolved into the
simpler laws from which they are derived: the local laws of the flux and
reflux of the tides in different places; the succession of certain kinds
of weather to certain appearances of sky; the apparent exceptions to the
almost universal truth that bodies expand by increase of temperature; the
law that breeds, both animal and vegetable, are improved by crossing; that
gases have a strong tendency to permeate animal membranes; that substances
containing a very high proportion of nitrogen (such as hydrocyanic acid
and morphia) are powerful poisons; that when different metals are fused
together the alloy is harder than the various elements; that the number of
atoms of acid required to neutralize one atom of any base is equal to the
number of atoms of oxygen in the base; that the solubility of substances
in one another depends,(171) at least in some degree, on the similarity of
their elements.

An empirical law, then, is an observed uniformity, presumed to be
resolvable into simpler laws, but not yet resolved into them. The
ascertainment of the empirical laws of phenomena often precedes by a long
interval the explanation of those laws by the Deductive Method; and the
verification of a deduction usually consists in the comparison of its
results with empirical laws previously ascertained.

§ 2. From a limited number of ultimate laws of causation, there are
necessarily generated a vast number of derivative uniformities, both of
succession and co-existence. Some are laws of succession or of
co-existence between different effects of the same cause; of these we had
examples in the last chapter. Some are laws of succession between effects
and their remote causes, resolvable into the laws which connect each with
the intermediate link. Thirdly, when causes act together and compound
their effects, the laws of those causes generate the fundamental law of
the effect, namely, that it depends on the co-existence of those causes.
And, finally, the order of succession or of co-existence which obtains
among effects necessarily depends on their causes. If they are effects of
the same cause, it depends on the laws of that cause; if on different
causes, it depends on the laws of those causes severally, and on the
circumstances which determine their co-existence. If we inquire further
when and how the causes will co-exist, that, again, depends on _their_
causes; and we may thus trace back the phenomena higher and higher, until
the different series of effects meet in a point, and the whole is shown to
have depended ultimately on some common cause; or until, instead of
converging to one point, they terminate in different points, and the order
of the effects is proved to have arisen from the collocation of some of
the primeval causes, or natural agents. For example, the order of
succession and of co-existence among the heavenly motions, which is
expressed by Kepler’s laws, is derived from the co-existence of two
primeval causes, the sun, and the original impulse or projectile force
belonging to each planet.(172) Kepler’s laws are resolved into the laws of
these causes and the fact of their co-existence.

Derivative laws, therefore, do not depend solely on the ultimate laws into
which they are resolvable; they mostly depend on those ultimate laws, and
an ultimate fact; namely, the mode of co-existence of some of the
component elements of the universe. The ultimate laws of causation might
be the same as at present, and yet the derivative laws completely
different, if the causes co-existed in different proportions, or with any
difference in those of their relations by which the effects are
influenced. If, for example, the sun’s attraction, and the original
projectile force, had existed in some other ratio to one another than they
did (and we know of no reason why this should not have been the case), the
derivative laws of the heavenly motions might have been quite different
from what they are. The proportions which exist happen to be such as to
produce regular elliptical motions; any other proportions would have
produced different ellipses, or circular, or parabolic, or hyperbolic
motions, but still regular ones; because the effects of each of the agents
accumulate according to a uniform law; and two regular series of
quantities, when their corresponding terms are added, must produce a
regular series of some sort, whatever the quantities themselves are.

§ 3. Now this last-mentioned element in the resolution of a derivative
law, the element which is not a law of causation, but a collocation of
causes, can not itself be reduced to any law. There is, as formerly
remarked,(173) no uniformity, no _norma_, principle, or rule, perceivable
in the distribution of the primeval natural agents through the universe.
The different substances composing the earth, the powers that pervade the
universe, stand in no constant relation to one another. One substance is
more abundant than others, one power acts through a larger extent of space
than others, without any pervading analogy that we can discover. We not
only do not know of any reason why the sun’s attraction and the force in
the direction of the tangent co-exist in the exact proportion they do, but
we can trace no coincidence between it and the proportions in which any
other elementary powers in the universe are intermingled. The utmost
disorder is apparent in the combination of the causes, which is consistent
with the most regular order in their effects; for when each agent carries
on its own operations according to a uniform law, even the most capricious
combination of agencies will generate a regularity of some sort; as we see
in the kaleidoscope, where any casual arrangement of colored bits of glass
produces by the laws of reflection a beautiful regularity in the effect.

§ 4. In the above considerations lies the justification of the limited
degree of reliance which scientific inquirers are accustomed to place in
empirical laws.

A derivative law which results wholly from the operation of some one
cause, will be as universally true as the laws of the cause itself; that
is, it will always be true except where some one of those effects of the
cause, on which the derivative law depends, is defeated by a counteracting
cause. But when the derivative law results not from different effects of
one cause, but from effects of several causes, we can not be certain that
it will be true under any variation in the mode of co-existence of those
causes, or of the primitive natural agents on which the causes ultimately
depend. The proposition that coal-beds rest on certain descriptions of
strata exclusively, though true on the earth, so far as our observation
has reached, can not be extended to the moon or the other planets,
supposing coal to exist there; because we can not be assured that the
original constitution of any other planet was such as to produce the
different depositions in the same order as in our globe. The derivative
law in this case depends not solely on laws, but on a collocation; and
collocations can not be reduced to any law.

Now it is the very nature of a derivative law which has not yet been
resolved into its elements, in other words, an empirical law, that we do
not know whether it results from the different effects of one cause, or
from effects of different causes. We can not tell whether it depends
wholly on laws, or partly on laws and partly on a collocation. If it
depends on a collocation, it will be true in all the cases in which that
particular collocation exists. But, since we are entirely ignorant, in
case of its depending on a collocation, what the collocation is, we are
not safe in extending the law beyond the limits of time and place in which
we have actual experience of its truth. Since within those limits the law
has always been found true, we have evidence that the collocations,
whatever they are, on which it depends, do really exist within those
limits. But, knowing of no rule or principle to which the collocations
themselves conform, we can not conclude that because a collocation is
proved to exist within certain limits of place or time, it will exist
beyond those limits. Empirical laws, therefore, can only be received as
true within the limits of time and place in which they have been found
true by observation; and not merely the limits of time and place, but of
time, place, and circumstance; for, since it is the very meaning of an
empirical law that we do not know the ultimate laws of causation on which
it is dependent, we can not foresee, without actual trial, in what manner
or to what extent the introduction of any new circumstance may affect it.

§ 5. But how are we to know that a uniformity ascertained by experience is
only an empirical law? Since, by the supposition, we have not been able to
resolve it into any other laws, how do we know that it is not an ultimate
law of causation?

I answer that no generalization amounts to more than an empirical law when
the only proof on which it rests is that of the Method of Agreement. For
it has been seen that by that method alone we never can arrive at causes.
The utmost that the Method of Agreement can do is, to ascertain the whole
of the circumstances common to all cases in which a phenomenon is
produced; and this aggregate includes not only the cause of the
phenomenon, but all phenomena with which it is connected by any derivative
uniformity, whether as being collateral effects of the same cause, or
effects of any other cause which, in all the instances we have been able
to observe, co-existed with it. The method affords no means of determining
which of these uniformities are laws of causation, and which are merely
derivative laws, resulting from those laws of causation and from the
collocation of the causes. None of them, therefore, can be received in any
other character than that of derivative laws, the derivation of which has
not been traced; in other words, empirical laws: in which light all
results obtained by the Method of Agreement (and therefore almost all
truths obtained by simple observation without experiment) must be
considered, until either confirmed by the Method of Difference, or
explained deductively; in other words, accounted for _a priori_.

These empirical laws may be of greater or less authority, according as
there is reason to presume that they are resolvable into laws only, or
into laws and collocations together. The sequences which we observe in the
production and subsequent life of an animal or a vegetable, resting on the
Method of Agreement only, are mere empirical laws; but though the
antecedents in those sequences may not be the causes of the consequents,
both the one and the other are doubtless, in the main, successive stages
of a progressive effect originating in a common cause, and therefore
independent of collocations. The uniformities, on the other hand, in the
order of superposition of strata on the earth, are empirical laws of a
much weaker kind, since they not only are not laws of causation, but there
is no reason to believe that they depend on any common cause; all
appearances are in favor of their depending on the particular collocation
of natural agents which at some time or other existed on our globe, and
from which no inference can be drawn as to the collocation which exists or
has existed in any other portion of the universe.

§ 6. Our definition of an empirical law, including not only those
uniformities which are not known to be laws of causation, but also those
which are, provided there be reason to presume that they are not ultimate
laws; this is the proper place to consider by what signs we may judge that
even if an observed uniformity be a law of causation, it is not an
ultimate, but a derivative law.

The first sign is, if between the antecedent _a_ and the consequent _b_
there be evidence of some intermediate link; some phenomenon of which we
can surmise the existence, though from the imperfection of our senses or
of our instruments we are unable to ascertain its precise nature and laws.
If there be such a phenomenon (which may be denoted by the letter _x_), it
follows that even if _a_ be the cause of _b_, it is but the remote cause,
and that the law, _a_ causes _b_, is resolvable into at least two laws,
_a_ causes _x_, and _x_ causes _b_. This is a very frequent case, since
the operations of nature mostly take place on so minute a scale, that many
of the successive steps are either imperceptible, or very indistinctly
perceived.

Take, for example, the laws of the chemical composition of substances; as
that hydrogen and oxygen being combined, water is produced. All we see of
the process is, that the two gases being mixed in certain proportions, and
heat or electricity being applied, an explosion takes place, the gases
disappear, and water remains. There is no doubt about the law, or about
its being a law of causation. But between the antecedent (the gases in a
state of mechanical mixture, heated or electrified), and the consequent
(the production of water), there must be an intermediate process which we
do not see. For if we take any portion whatever of the water, and subject
it to analysis, we find that it always contains hydrogen and oxygen; nay,
the very same proportions of them, namely, two-thirds, in volume, of
hydrogen, and one-third oxygen. This is true of a single drop; it is true
of the minutest portion which our instruments are capable of appreciating.
Since, then, the smallest perceptible portion of the water contains both
those substances, portions of hydrogen and oxygen smaller than the
smallest perceptible must have come together in every such minute portion
of space; must have come closer together than when the gases were in a
state of mechanical mixture, since (to mention no other reasons) the water
occupies far less space than the gases. Now, as we can not see this
contact or close approach of the minute particles, we can not observe with
what circumstances it is attended, or according to what laws it produces
its effects. The production of water, that is, of the sensible phenomena
which characterize the compound, may be a very remote effect of those
laws. There may be innumerable intervening links; and we are sure that
there must be some. Having full proof that corpuscular action of some kind
takes place previous to any of the great transformations in the sensible
properties of substances, we can have no doubt that the laws of chemical
action, as at present known, are not ultimate, but derivative laws;
however ignorant we may be, and even though we should forever remain
ignorant, of the nature of the laws of corpuscular action from which they
are derived.

In like manner, all the processes of vegetative life, whether in the
vegetable properly so called or in the animal body, are corpuscular
processes. Nutrition is the addition of particles to one another,
sometimes merely replacing other particles separated and excreted,
sometimes occasioning an increase of bulk or weight so gradual that only
after a long continuance does it become perceptible. Various organs, by
means of peculiar vessels, secrete from the blood fluids, the component
particles of which must have been in the blood, but which differ from it
most widely both in mechanical properties and in chemical composition.
Here, then, are abundance of unknown links to be filled up; and there can
be no doubt that the laws of the phenomena of vegetative or organic life
are derivative laws, dependent on properties of the corpuscles, and of
those elementary tissues which are comparatively simple combinations of
corpuscles.

The first sign, then, from which a law of causation, though hitherto
unresolved, may be inferred to be a derivative law, is any indication of
the existence of an intermediate link or links between the antecedent and
the consequent. The second is, when the antecedent is an extremely complex
phenomenon, and its effects, therefore, probably in part at least,
compounded of the effects of its different elements; since we know that
the case in which the effect of the whole is not made up of the effects of
its parts is exceptional, the Composition of Causes being by far the more
ordinary case.

We will illustrate this by two examples, in one of which the antecedent is
the sum of many homogeneous, in the other of heterogeneous, parts. The
weight of a body is made up of the weights of its minute particles; a
truth which astronomers express in its most general terms when they say
that bodies, at equal distances, gravitate to one another in proportion to
their quantity of matter. All true propositions, therefore, which can be
made concerning gravity, are derivative laws; the ultimate law into which
they are all resolvable being, that every particle of matter attracts
every other. As our second example, we may take any of the sequences
observed in meteorology; for instance, a diminution of the pressure of the
atmosphere (indicated by a fall of the barometer) is followed by rain. The
antecedent is here a complex phenomenon, made up of heterogeneous
elements; the column of the atmosphere over any particular place
consisting of two parts, a column of air, and a column of aqueous vapor
mixed with it; and the change in the two together manifested by a fall of
the barometer, and followed by rain, must be either a change in one of
these, or in the other, or in both. We might, then, even in the absence of
any other evidence, form a reasonable presumption, from the invariable
presence of both these elements in the antecedent, that the sequence is
probably not an ultimate law, but a result of the laws of the two
different agents; a presumption only to be destroyed when we had made
ourselves so well acquainted with the laws of both, as to be able to
affirm that those laws could not by themselves produce the observed
result.

There are but few known cases of succession from very complex antecedents
which have not either been actually accounted for from simpler laws, or
inferred with great probability (from the ascertained existence of
intermediate links of causation not yet understood) to be capable of being
so accounted for. It is, therefore, highly probable that all sequences
from complex antecedents are thus resolvable, and that ultimate laws are
in all cases comparatively simple. If there were not the other reasons
already mentioned for believing that the laws of organized nature are
resolvable into simpler laws, it would be almost a sufficient reason that
the antecedents in most of the sequences are so very complex.

§ 7. In the preceding discussion we have recognized two kinds of empirical
laws: those known to be laws of causation, but presumed to be resolvable
into simpler laws; and those not known to be laws of causation at all.
Both these kinds of laws agree in the demand which they make for being
explained by deduction, and agree in being the appropriate means of
verifying such deduction, since they represent the experience with which
the result of the deduction must be compared. They agree, further, in
this, that until explained, and connected with the ultimate laws from
which they result, they have not attained the highest degree of certainty
of which laws are susceptible. It has been shown on a former occasion that
laws of causation which are derivative, and compounded of simpler laws,
are not only, as the nature of the case implies, less general, but even
less certain, than the simpler laws from which they result; not in the
same degree to be relied on as universally true. The inferiority of
evidence, however, which attaches to this class of laws, is trifling,
compared with that which is inherent in uniformities not known to be laws
of causation at all. So long as these are unresolved, we can not tell on
how many collocations, as well as laws, their truth may be dependent; we
can never, therefore, extend them with any confidence to cases in which we
have not assured ourselves, by trial, that the necessary collocation of
causes, whatever it may be, exists. It is to this class of laws alone that
the property, which philosophers usually consider as characteristic of
empirical laws, belongs in all its strictness—the property of being unfit
to be relied on beyond the limits of time, place, and circumstance in
which the observations have been made. These are empirical laws in a more
emphatic sense; and when I employ that term (except where the context
manifestly indicates the reverse) I shall generally mean to designate
those uniformities only, whether of succession or of co-existence, which
are not known to be laws of causation.




                              Chapter XVII.


Of Chance And Its Elimination.


§ 1. Considering, then, as empirical laws only those observed uniformities
respecting which the question whether they are laws of causation must
remain undecided until they can be explained deductively, or until some
means are found of applying the Method of Difference to the case, it has
been shown in the preceding chapter that until a uniformity can, in one or
the other of these modes, be taken out of the class of empirical laws, and
brought either into that of laws of causation or of the demonstrated
results of laws of causation, it can not with any assurance be pronounced
true beyond the local and other limits within which it has been found so
by actual observation. It remains to consider how we are to assure
ourselves of its truth even within those limits; after what quantity of
experience a generalization which rests solely on the Method of Agreement
can be considered sufficiently established, even as an empirical law. In a
former chapter, when treating of the Methods of Direct Induction, we
expressly reserved this question,(174) and the time is now come for
endeavoring to solve it.

We found that the Method of Agreement has the defect of not proving
causation, and can, therefore, only be employed for the ascertainment of
empirical laws. But we also found that besides this deficiency, it labors
under a characteristic imperfection, tending to render uncertain even such
conclusions as it is in itself adapted to prove. This imperfection arises
from Plurality of Causes. Although two or more cases in which the
phenomenon _a_ has been met with may have no common antecedent except A,
this does not prove that there is any connection between _a_ and A, since
_a_ may have many causes, and may have been produced, in these different
instances, not by any thing which the instances had in common, but by some
of those elements in them which were different. We nevertheless observed,
that in proportion to the multiplication of instances pointing to A as the
antecedent, the characteristic uncertainty of the method diminishes, and
the existence of a law of connection between A and _a_ more nearly
approaches to certainty. It is now to be determined after what amount of
experience this certainty may be deemed to be practically attained, and
the connection between A and _a_ may be received as an empirical law.

This question may be otherwise stated in more familiar terms: After how
many and what sort of instances may it be concluded that an observed
coincidence between two phenomena is not the effect of chance?

It is of the utmost importance for understanding the logic of induction,
that we should form a distinct conception of what is meant by chance, and
how the phenomena which common language ascribes to that abstraction are
really produced.

§ 2. Chance is usually spoken of in direct antithesis to law; whatever, it
is supposed, can not be ascribed to any law is attributed to chance. It
is, however, certain that whatever happens is the result of some law; is
an effect of causes, and could have been predicted from a knowledge of the
existence of those causes, and from their laws. If I turn up a particular
card, that is a consequence of its place in the pack. Its place in the
pack was a consequence of the manner in which the cards were shuffled, or
of the order in which they were played in the last game; which, again,
were effects of prior causes. At every stage, if we had possessed an
accurate knowledge of the causes in existence, it would have been
abstractedly possible to foretell the effect.

An event occurring by chance may be better described as a coincidence from
which we have no ground to infer a uniformity—the occurrence of a
phenomenon in certain circumstances, without our having reason on that
account to infer that it will happen again in those circumstances. This,
however, when looked closely into, implies that the enumeration of the
circumstances is not complete. Whatever the fact be, since it has occurred
once, we may be sure that if _all_ the same circumstances were repeated it
would occur again; and not only if all, but there is some particular
portion of those circumstances on which the phenomenon is invariably
consequent. With most of them, however, it is not connected in any
permanent manner; its conjunction with those is said to be the effect of
chance, to be merely casual. Facts casually conjoined are separately the
effects of causes, and therefore of laws; but of different causes, and
causes not connected by any law.

It is incorrect, then, to say that any phenomenon is produced by chance;
but we may say that two or more phenomena are conjoined by chance, that
they co-exist or succeed one another only by chance; meaning that they are
in no way related through causation; that they are neither cause and
effect, nor effects of the same cause, nor effects of causes between which
there subsists any law of co-existence, nor even effects of the same
collocation of primeval causes.

If the same casual coincidence never occurred a second time, we should
have an easy test for distinguishing such from the coincidences which are
the results of a law. As long as the phenomena had been found together
only once, so long, unless we knew some more general laws from which the
coincidence might have resulted, we could not distinguish it from a casual
one; but if it occurred twice, we should know that the phenomena so
conjoined must be in some way connected through their causes.

There is, however, no such test. A coincidence may occur again and again,
and yet be only casual. Nay, it would be inconsistent with what we know of
the order of nature to doubt that every casual coincidence will sooner or
later be repeated, as long as the phenomena between which it occurred do
not cease to exist, or to be reproduced. The recurrence, therefore, of the
same coincidence more than once, or even its frequent recurrence, does not
prove that it is an instance of any law; does not prove that it is not
casual, or, in common language, the effect of chance.

And yet, when a coincidence can not be deduced from known laws, nor proved
by experiment to be itself a case of causation, the frequency of its
occurrence is the only evidence from which we can infer that it is the
result of a law. Not, however, its absolute frequency. The question is not
whether the coincidence occurs often or seldom, in the ordinary sense of
those terms; but whether it occurs more often than chance will account
for; more often than might rationally be expected if the coincidence were
casual. We have to decide, therefore, what degree of frequency in a
coincidence chance will account for; and to this there can be no general
answer. We can only state the principle by which the answer must be
determined; the answer itself will be different in every different case.

Suppose that one of the phenomena, A, exists always, and the other
phenomenon, B, only occasionally; it follows that every instance of B will
be an instance of its coincidence with A, and yet the coincidence will be
merely casual, not the result of any connection between them. The fixed
stars have been constantly in existence since the beginning of human
experience, and all phenomena that have come under human observation have,
in every single instance, co-existed with them; yet this coincidence,
though equally invariable with that which exists between any of those
phenomena and its own cause, does not prove that the stars are its cause,
nor that they are in anywise connected with it. As strong a case of
coincidence, therefore, as can possibly exist, and a much stronger one in
point of mere frequency than most of those which prove laws, does not here
prove a law; why? because, since the stars exist always, they _must_
co-exist with every other phenomenon, whether connected with them by
causation or not. The uniformity, great though it be, is no greater than
would occur on the supposition that no such connection exists.

On the other hand, suppose that we were inquiring whether there be any
connection between rain and any particular wind. Rain, we know,
occasionally occurs with every wind; therefore, the connection, if it
exists, can not be an actual law; but still rain may be connected with
some particular wind through causation; that is, though they can not be
always effects of the same cause (for if so they would regularly
co-exist), there may be some causes common to the two, so that in so far
as either is produced by those common causes, they will, from the laws of
the causes, be found to co-exist. How, then, shall we ascertain this? The
obvious answer is, by observing whether rain occurs with one wind more
frequently than with any other. That, however, is not enough; for perhaps
that one wind blows more frequently than any other; so that its blowing
more frequently in rainy weather is no more than would happen, although it
had no connection with the causes of rain, provided it were not connected
with causes adverse to rain. In England, westerly winds blow during about
twice as great a portion of the year as easterly. If, therefore, it rains
only twice as often with a westerly as with an easterly wind, we have no
reason to infer that any law of nature is concerned in the coincidence. If
it rains more than twice as often, we may be sure that some law is
concerned; either there is some cause in nature which, in this climate,
tends to produce both rain and a westerly wind, or a westerly wind has
itself some tendency to produce rain. But if it rains less than twice as
often, we may draw a directly opposite inference: the one, instead of
being a cause, or connected with causes of the other, must be connected
with causes adverse to it, or with the absence of some cause which
produces it; and though it may still rain much oftener with a westerly
wind than with an easterly, so far would this be from proving any
connection between the phenomena, that the connection proved would be
between rain and an easterly wind, to which, in mere frequency of
coincidence, it is less allied.

Here, then, are two examples: in one, the greatest possible frequency of
coincidence, with no instance whatever to the contrary, does not prove
that there is any law; in the other, a much less frequency of coincidence,
even when non-coincidence is still more frequent, does prove that there is
a law. In both cases the principle is the same. In both we consider the
positive frequency of the phenomena themselves, and how great frequency of
coincidence that must of itself bring about, without supposing any
connection between them, provided there be no repugnance; provided neither
be connected with any cause tending to frustrate the other. If we find a
greater frequency of coincidence than this, we conclude that there is some
connection; if a less frequency, that there is some repugnance. In the
former case, we conclude that one of the phenomena can under some
circumstances cause the other, or that there exists something capable of
causing them both; in the latter, that one of them, or some cause which
produces one of them, is capable of counteracting the production of the
other. We have thus to deduct from the observed frequency of coincidence
as much as may be the effect of chance, that is, of the mere frequency of
the phenomena themselves; and if any thing remains, what does remain is
the residual fact which proves the existence of a law.

The frequency of the phenomena can only be ascertained within definite
limits of space and time; depending as it does on the quantity and
distribution of the primeval natural agents, of which we can know nothing
beyond the boundaries of human observation, since no law, no regularity,
can be traced in it, enabling us to infer the unknown from the known. But
for the present purpose this is no disadvantage, the question being
confined within the same limits as the data. The coincidences occurred in
certain places and times, and within those we can estimate the frequency
with which such coincidences would be produced by chance. If, then, we
find from observation that A exists in one case out of every two, and B in
one case out of every three; then, if there be neither connection nor
repugnance between them, or between any of their causes, the instances in
which A and B will both exist, that is to say will co-exist, will be one
case in every six. For A exists in three cases out of six; and B, existing
in one case out of every three without regard to the presence or absence
of A, will exist in one case out of those three. There will therefore be,
of the whole number of cases, two in which A exists without B; one case of
B without A; two in which neither B nor A exists, and one case out of six
in which they both exist. If, then, in point of fact, they are found to
co-exist oftener than in one case out of six; and, consequently, A does
not exist without B so often as twice in three times, nor B without A so
often as once in every twice, there is some cause in existence which tends
to produce a conjunction between A and B.

Generalizing the result, we may say that if A occurs in a larger
proportion of the cases where B is than of the cases where B is not, then
will B also occur in a larger proportion of the cases where A is than of
the cases where A is not; and there is some connection, through causation,
between A and B. If we could ascend to the causes of the two phenomena, we
should find, at some stage, either proximate or remote, some cause or
causes common to both; and if we could ascertain what these are, we could
frame a generalization which would be true without restriction of place or
time; but until we can do so, the fact of a connection between the two
phenomena remains an empirical law.

§ 3. Having considered in what manner it may be determined whether any
given conjunction of phenomena is casual, or the result of some law, to
complete the theory of chance it is necessary that we should now consider
those effects which are partly the result of chance and partly of law, or,
in other words, in which the effects of casual conjunctions of causes are
habitually blended in one result with the effects of a constant cause.

This is a case of Composition of Causes; and the peculiarity of it is,
that instead of two or more causes intermixing their effects in a regular
manner with those of one another, we have now one constant cause,
producing an effect which is successively modified by a series of variable
causes. Thus, as summer advances, the approach of the sun to a vertical
position tends to produce a constant increase of temperature; but with
this effect of a constant cause, there are blended the effects of many
variable causes, winds, clouds, evaporation, electric agencies and the
like, so that the temperature of any given day depends in part on these
fleeting causes, and only in part on the constant cause. If the effect of
the constant cause is always accompanied and disguised by effects of
variable causes, it is impossible to ascertain the law of the constant
cause in the ordinary manner by separating it from all other causes and
observing it apart. Hence arises the necessity of an additional rule of
experimental inquiry.

When the action of a cause A is liable to be interfered with, not steadily
by the same cause or causes, but by different causes at different times,
and when these are so frequent, or so indeterminate, that we can not
possibly exclude all of them from any experiment, though we may vary them;
our resource is, to endeavor to ascertain what is the effect of all the
variable causes taken together. In order to do this, we make as many
trials as possible, preserving A invariable. The results of these
different trials will naturally be different, since the indeterminate
modifying causes are different in each; if, then, we do not find these
results to be progressive, but, on the contrary, to oscillate about a
certain point, one experiment giving a result a little greater, another a
little less, one a result tending a little more in one direction, another
a little more in the contrary direction; while the average or middle point
does not vary, but different sets of experiments (taken in as great a
variety of circumstances as possible) yield the same mean, provided only
they be sufficiently numerous; then that mean, or average result, is the
part, in each experiment, which is due to the cause A, and is the effect
which would have been obtained if A could have acted alone; the variable
remainder is the effect of chance, that is, of causes the co-existence of
which with the cause A was merely casual. The test of the sufficiency of
the induction in this case is, when any increase of the number of trials
from which the average is struck does not materially alter the average.

This kind of elimination, in which we do not eliminate any one assignable
cause, but the multitude of floating unassignable ones, may be termed the
Elimination of Chance. We afford an example of it when we repeat an
experiment, in order, by taking the mean of different results, to get rid
of the effects of the unavoidable errors of each individual experiment.
When there is no permanent cause, such as would produce a tendency to
error peculiarly in one direction, we are warranted by experience in
assuming that the errors on one side will, in a certain number of
experiments, about balance the errors on the contrary side. We therefore
repeat the experiment, until any change which is produced in the average
of the whole by further repetition, falls within limits of error
consistent with the degree of accuracy required by the purpose we have in
view.(175)

§ 4. In the supposition hitherto made, the effect of the constant cause A
has been assumed to form so great and conspicuous a part of the general
result, that its existence never could be a matter of uncertainty, and the
object of the eliminating process was only to ascertain _how much_ is
attributable to that cause; what is its exact law. Cases, however, occur
in which the effect of a constant cause is so small, compared with that of
some of the changeable causes with which it is liable to be casually
conjoined, that of itself it escapes notice, and the very existence of any
effect arising from a constant cause is first learned by the process which
in general serves only for ascertaining the quantity of that effect. This
case of induction may be characterized as follows: A given effect is known
to be chiefly, and not known not to be wholly, determined by changeable
causes. If it be wholly so produced, then if the aggregate be taken of a
sufficient number of instances, the effects of these different causes will
cancel one another. If, therefore, we do not find this to be the case,
but, on the contrary, after such a number of trials has been made that no
further increase alters the average result, we find that average to be,
not zero, but some other quantity, about which, though small in comparison
with the total effect, the effect nevertheless oscillates, and which is
the middle point in its oscillation; we may conclude this to be the effect
of some constant cause; which cause, by some of the methods already
treated of, we may hope to detect. This may be called _the discovery of a
residual phenomenon by eliminating the effects of chance_.

It is in this manner, for example, that loaded dice may be discovered. Of
course no dice are so clumsily loaded that they must always throw certain
numbers; otherwise the fraud would be instantly detected. The loading, a
constant cause, mingles with the changeable causes which determine what
cast will be thrown in each individual instance. If the dice were not
loaded, and the throw were left to depend entirely on the changeable
causes, these in a sufficient number of instances would balance one
another, and there would be no preponderant number of throws of any one
kind. If, therefore, after such a number of trials that no further
increase of their number has any material effect upon the average, we find
a preponderance in favor of a particular throw; we may conclude with
assurance that there is some constant cause acting in favor of that throw,
or, in other words, that the dice are not fair; and the exact amount of
the unfairness. In a similar manner, what is called the diurnal variation
of the barometer, which is very small compared with the variations arising
from the irregular changes in the state of the atmosphere, was discovered
by comparing the average height of the barometer at different hours of the
day. When this comparison was made, it was found that there was a small
difference, which on the average was constant, however the absolute
quantities might vary, and which difference, therefore, must be the effect
of a constant cause. This cause was afterward ascertained, deductively, to
be the rarefaction of the air, occasioned by the increase of temperature
as the day advances.

§ 5. After these general remarks on the nature of chance, we are prepared
to consider in what manner assurance may be obtained that a conjunction
between two phenomena, which has been observed a certain number of times,
is not casual, but a result of causation, and to be received, therefore,
as one of the uniformities of nature, though (until accounted for _a
priori_) only as an empirical law.

We will suppose the strongest case, namely, that the phenomenon B has
never been observed except in conjunction with A. Even then, the
probability that they are connected is not measured by the total number of
instances in which they have been found together, but by the excess of
that number above the number due to the absolutely frequency of A. If, for
example, A exists always, and therefore co-exists with every thing, no
number of instances of its co-existence with B would prove a connection;
as in our example of the fixed stars. If A be a fact of such common
occurrence that it may be presumed to be present in half of all the cases
that occur, and therefore in half the cases in which B occurs, it is only
the proportional excess above half that is to be reckoned as evidence
toward proving a connection between A and B.

In addition to the question, What is the number of coincidences which, on
an average of a great multitude of trials, may be expected to arise from
chance alone? there is also another question, namely, Of what extent of
deviation from that average is the occurrence credible, from chance alone,
in some number of instances smaller than that required for striking a fair
average? It is not only to be considered what is the general result of the
chances in the long run, but also what are the extreme limits of variation
from the general result, which may occasionally be expected as the result
of some smaller number of instances.

The consideration of the latter question, and any consideration of the
former beyond that already given to it, belong to what mathematicians term
the doctrine of chances, or, in a phrase of greater pretension, the Theory
of Probabilities.




                              Chapter XVIII.


Of The Calculation Of Chances.


§ 1. “Probability,” says Laplace,(176) “has reference partly to our
ignorance, partly to our knowledge. We know that among three or more
events, one, and only one, must happen; but there is nothing leading us to
believe that any one of them will happen rather than the others. In this
state of indecision, it is impossible for us to pronounce with certainty
on their occurrence. It is, however, probable that any one of these
events, selected at pleasure, will not take place; because we perceive
several cases, all equally possible, which exclude its occurrence, and
only one which favors it.

“The theory of chances consists in reducing all events of the same kind to
a certain number of cases equally possible, that is, such that we are
_equally undecided_ as to their existence; and in determining the number
of these cases which are favorable to the event of which the probability
is sought. The ratio of that number to the number of all the possible
cases is the measure of the probability; which is thus a fraction, having
for its numerator the number of cases favorable to the event, and for its
denominator the number of all the cases which are possible.”

To a calculation of chances, then, according to Laplace, two things are
necessary; we must know that of several events some one will certainly
happen, and no more than one; and we must not know, nor have any reason to
expect, that it will be one of these events rather than another. It has
been contended that these are not the only requisites, and that Laplace
has overlooked, in the general theoretical statement, a necessary part of
the foundation of the doctrine of chances. To be able (it has been said)
to pronounce two events equally probable, it is not enough that we should
know that one or the other must happen, and should have no grounds for
conjecturing which. Experience must have shown that the two events are of
equally frequent occurrence. Why, in tossing up a half-penny, do we reckon
it equally probable that we shall throw cross or pile? Because we know
that in any great number of throws, cross and pile are thrown about
equally often; and that the more throws we make, the more nearly the
equality is perfect. We may know this if we please by actual experiment,
or by the daily experience which life affords of events of the same
general character, or, deductively, from the effect of mechanical laws on
a symmetrical body acted upon by forces varying indefinitely in quantity
and direction. We may know it, in short, either by specific experience, or
on the evidence of our general knowledge of nature. But, in one way or the
other, we must know it, to justify us in calling the two events equally
probable; and if we knew it not, we should proceed as much at hap-hazard
in staking equal sums on the result, as in laying odds.

This view of the subject was taken in the first edition of the present
work; but I have since become convinced that the theory of chances, as
conceived by Laplace and by mathematicians generally, has not the
fundamental fallacy which I had ascribed to it.

We must remember that the probability of an event is not a quality of the
event itself, but a mere name for the degree of ground which we, or some
one else, have for expecting it. The probability of an event to one person
is a different thing from the probability of the same event to another, or
to the same person after he has acquired additional evidence. The
probability to me, that an individual of whom I know nothing but his name
will die within the year, is totally altered by my being told the next
minute that he is in the last stage of a consumption. Yet this makes no
difference in the event itself, nor in any of the causes on which it
depends. Every event is in itself certain, not probable; if we knew all,
we should either know positively that it will happen, or positively that
it will not. But its probability to us means the degree of expectation of
its occurrence, which we are warranted in entertaining by our present
evidence.

Bearing this in mind, I think it must be admitted, that even when we have
no knowledge whatever to guide our expectations, except the knowledge that
what happens must be some one of a certain number of possibilities, we may
still reasonably judge, that one supposition is more probable _to us_ than
another supposition; and if we have any interest at stake, we shall best
provide for it by acting conformably to that judgment.

§ 2. Suppose that we are required to take a ball from a box, of which we
only know that it contains balls both black and white, and none of any
other color. We know that the ball we select will be either a black or a
white ball; but we have no ground for expecting black rather than white,
or white rather than black. In that case, if we are obliged to make a
choice, and to stake something on one or the other supposition, it will,
as a question of prudence, be perfectly indifferent which; and we shall
act precisely as we should have acted if we had known beforehand that the
box contained an equal number of black and white balls. But though our
conduct would be the same, it would not be founded on any surmise that the
balls were in fact thus equally divided; for we might, on the contrary,
know by authentic information that the box contained ninety-nine balls of
one color, and only one of the other; still, if we are not told which
color has only one, and which has ninety-nine, the drawing of a white and
of a black ball will be equally probable to us. We shall have no reason
for staking any thing on the one event rather than on the other; the
option between the two will be a matter of indifference; in other words,
it will be an even chance.

But let it now be supposed that instead of two there are three
colors—white, black, and red; and that we are entirely ignorant of the
proportion in which they are mingled. We should then have no reason for
expecting one more than another, and if obliged to bet, should venture our
stake on red, white, or black with equal indifference. But should we be
indifferent whether we betted for or against some one color, as, for
instance, white? Surely not. From the very fact that black and red are
each of them separately equally probable to us with white, the two
together must be twice as probable. We should in this case expect not
white rather than white, and so much rather that we would lay two to one
upon it. It is true, there might, for aught we knew, be more white balls
than black and red together; and if so, our bet would, if we knew more, be
seen to be a disadvantageous one. But so also, for aught we knew, might
there be more red balls than black and white, or more black balls than
white and red, and in such case the effect of additional knowledge would
be to prove to us that our bet was more advantageous than we had supposed
it to be. There is in the existing state of our knowledge a rational
probability of two to one against white; a probability fit to be made a
basis of conduct. No reasonable person would lay an even wager in favor of
white against black and red; though against black alone or red alone he
might do so without imprudence.

The common theory, therefore, of the calculation of chances, appears to be
tenable. Even when we know nothing except the number of the possible and
mutually excluding contingencies, and are entirely ignorant of their
comparative frequency, we may have grounds, and grounds numerically
appreciable, for acting on one supposition rather than on another; and
this is the meaning of Probability.

§ 3. The principle, however, on which the reasoning proceeds, is
sufficiently evident. It is the obvious one that when the cases which
exist are shared among several kinds, it is impossible that _each_ of
those kinds should be a majority of the whole: on the contrary, there must
be a majority against each kind, except one at most; and if any kind has
more than its share in proportion to the total number, the others
collectively must have less. Granting this axiom, and assuming that we
have no ground for selecting any one kind as more likely than the rest to
surpass the average proportion, it follows that we can not rationally
presume this of any, which we should do if we were to bet in favor of it,
receiving less odds than in the ratio of the number of the other kinds.
Even, therefore, in this extreme case of the calculation of probabilities,
which does not rest on special experience at all, the logical ground of
the process is our knowledge—such knowledge as we then have—of the laws
governing the frequency of occurrence of the different cases; but in this
case the knowledge is limited to that which, being universal and
axiomatic, does not require reference to specific experience, or to any
considerations arising out of the special nature of the problem under
discussion.

Except, however, in such cases as games of chance, where the very purpose
in view requires ignorance instead of knowledge, I can conceive no case in
which we ought to be satisfied with such an estimate of chances as this—an
estimate founded on the absolute minimum of knowledge respecting the
subject. It is plain that, in the case of the colored balls, a very slight
ground of surmise that the white balls were really more numerous than
either of the other colors, would suffice to vitiate the whole of the
calculations made in our previous state of indifference. It would place us
in that position of more advanced knowledge, in which the probabilities,
to us, would be different from what they were before; and in estimating
these new probabilities we should have to proceed on a totally different
set of data, furnished no longer by mere counting of possible
suppositions, but by specific knowledge of facts. Such data it should
always be our endeavor to obtain; and in all inquiries, unless on subjects
equally beyond the range of our means of knowledge and our practical uses,
they may be obtained, if not good, at least better than none at all.(177)

It is obvious, too, that even when the probabilities are derived from
observation and experiment, a very slight improvement in the data, by
better observations, or by taking into fuller consideration the special
circumstances of the case, is of more use than the most elaborate
application of the calculus to probabilities founded on the data in their
previous state of inferiority. The neglect of this obvious reflection has
given rise to misapplications of the calculus of probabilities which have
made it the real opprobrium of mathematics. It is sufficient to refer to
the applications made of it to the credibility of witnesses, and to the
correctness of the verdicts of juries. In regard to the first, common
sense would dictate that it is impossible to strike a general average of
the veracity and other qualifications for true testimony of mankind, or of
any class of them; and even if it were possible, the employment of it for
such a purpose implies a misapprehension of the use of averages, which
serve, indeed, to protect those whose interest is at stake, against
mistaking the general result of large masses of instances, but are of
extremely small value as grounds of expectation in any one individual
instance, unless the case be one of those in which the great majority of
individual instances do not differ much from the average. In the case of a
witness, persons of common sense would draw their conclusions from the
degree of consistency of his statements, his conduct under
cross-examination, and the relation of the case itself to his interests,
his partialities, and his mental capacity, instead of applying so rude a
standard (even if it were capable of being verified) as the ratio between
the number of true and the number of erroneous statements which he may be
supposed to make in the course of his life.

Again, on the subject of juries or other tribunals, some mathematicians
have set out from the proposition that the judgment of any one judge or
juryman is, at least in some small degree, more likely to be right than
wrong, and have concluded that the chance of a number of persons
concurring in a wrong verdict is diminished the more the number is
increased; so that if the judges are only made sufficiently numerous, the
correctness of the judgment may be reduced almost to certainty. I say
nothing of the disregard shown to the effect produced on the moral
position of the judges by multiplying their numbers, the virtual
destruction of their individual responsibility, and weakening of the
application of their minds to the subject. I remark only the fallacy of
reasoning from a wide average to cases necessarily differing greatly from
any average. It may be true that, taking all causes one with another, the
opinion of any one of the judges would be oftener right than wrong; but
the argument forgets that in all but the more simple cases, in all cases
in which it is really of much consequence what the tribunal is, the
proposition might probably be reversed; besides which, the cause of error,
whether arising from the intricacy of the case or from some common
prejudice or mental infirmity, if it acted upon one judge, would be
extremely likely to affect all the others in the same manner, or at least
a majority, and thus render a wrong instead of a right decision more
probable the more the number was increased.

These are but samples of the errors frequently committed by men who,
having made themselves familiar with the difficult formulæ which algebra
affords for the estimation of chances under suppositions of a complex
character, like better to employ those formulæ in computing what are the
probabilities to a person half informed about a case than to look out for
means of being better informed. Before applying the doctrine of chances to
any scientific purpose, the foundation must be laid for an evaluation of
the chances, by possessing ourselves of the utmost attainable amount of
positive knowledge. The knowledge required is that of the comparative
frequency with which the different events in fact occur. For the purposes,
therefore, of the present work, it is allowable to suppose that
conclusions respecting the probability of a fact of a particular kind rest
on our knowledge of the proportion between the cases in which facts of
that kind occur, and those in which they do not occur; this knowledge
being either derived from specific experiment, or deduced from our
knowledge of the causes in operation which tend to produce, compared with
those which tend to prevent, the fact in question.

Such calculation of chances is grounded on an induction; and to render the
calculation legitimate, the induction must be a valid one. It is not less
an induction, though it does not prove that the event occurs in all cases
of a given description, but only that out of a given number of such cases
it occurs in about so many. The fraction which mathematicians use to
designate the probability of an event is the ratio of these two numbers;
the ascertained proportion between the number of cases in which the event
occurs and the sum of all the cases, those in which it occurs and in which
it does not occur, taken together. In playing at cross and pile, the
description of cases concerned are throws, and the probability of cross is
one-half, because if we throw often enough cross is thrown about once in
every two throws. In the cast of a die, the probability of ace is
one-sixth; not simply because there are six possible throws, of which ace
is one, and because we do not know any reason why one should turn up
rather than another—though I have admitted the validity of this ground in
default of a better—but because we do actually know, either by reasoning
or by experience, that in a hundred or a million of throws ace is thrown
in about one-sixth of that number, or once in six times.

§ 4. I say, “either by reasoning or by experience,” meaning specific
experience. But in estimating probabilities, it is not a matter of
indifference from which of these two sources we derive our assurance. The
probability of events, as calculated from their mere frequency in past
experience, affords a less secure basis for practical guidance than their
probability as deduced from an equally accurate knowledge of the frequency
of occurrence of their causes.

The generalization that an event occurs in ten out of every hundred cases
of a given description, is as real an induction as if the generalization
were that it occurs in all cases. But when we arrive at the conclusion by
merely counting instances in actual experience, and comparing the number
of cases in which A has been present with the number in which it has been
absent, the evidence is only that of the Method of Agreement, and the
conclusion amounts only to an empirical law. We can make a step beyond
this when we can ascend to the causes on which the occurrence of A or its
non-occurrence will depend, and form an estimate of the comparative
frequency of the causes favorable and of those unfavorable to the
occurrence. These are data of a higher order, by which the empirical law
derived from a mere numerical comparison of affirmative and negative
instances will be either corrected or confirmed, and in either case we
shall obtain a more correct measure of probability than is given by that
numerical comparison. It has been well remarked that in the kind of
examples by which the doctrine of chances is usually illustrated, that of
balls in a box, the estimate of probabilities is supported by reasons of
causation, stronger than specific experience. “What is the reason that in
a box where there are nine black balls and one white, we expect to draw a
black ball nine times as much (in other words, nine times as often,
frequency being the gauge of intensity in expectation) as a white?
Obviously because the local conditions are nine times as favorable;
because the hand may alight in nine places and get a black ball, while it
can only alight in one place and find a white ball; just for the same
reason that we do not expect to succeed in finding a friend in a crowd,
the conditions in order that we and he should come together being many and
difficult. This of course would not hold to the same extent were the white
balls of smaller size than the black, neither would the probability remain
the same; the larger ball would be much more likely to meet the
hand.”(178)

It is, in fact, evident that when once causation is admitted as a
universal law, our expectation of events can only be rationally grounded
on that law. To a person who recognizes that every event depends on
causes, a thing’s having happened once is a reason for expecting it to
happen again, only because proving that there exists, or is liable to
exist, a cause adequate to produce it.(179) The frequency of the
particular event, apart from all surmise respecting its cause, can give
rise to no other induction than that _per enumerationem simplicem_; and
the precarious inferences derived from this are superseded, and disappear
from the field as soon as the principle of causation makes its appearance
there.

Notwithstanding, however, the abstract superiority of an estimate of
probability grounded on causes, it is a fact that in almost all cases in
which chances admit of estimation sufficiently precise to render their
numerical appreciation of any practical value, the numerical data are not
drawn from knowledge of the causes, but from experience of the events
themselves. The probabilities of life at different ages or in different
climates; the probabilities of recovery from a particular disease; the
chances of the birth of male or female offspring; the chances of the
destruction of houses or other property by fire; the chances of the loss
of a ship in a particular voyage, are deduced from bills of mortality,
returns from hospitals, registers of births, of shipwrecks, etc., that is,
from the observed frequency not of the causes, but of the effects. The
reason is, that in all these classes of facts the causes are either not
amenable to direct observation at all, or not with the requisite
precision, and we have no means of judging of their frequency except from
the empirical law afforded by the frequency of the effects. The inference
does not the less depend on causation alone. We reason from an effect to a
similar effect by passing through the cause. If the actuary of an
insurance office infers from his tables that among a hundred persons now
living of a particular age, five on the average will attain the age of
seventy, his inference is legitimate, not for the simple reason that this
is the proportion who have lived till seventy in times past, but because
the fact of their having so lived shows that this is the proportion
existing, at that place and time, between the causes which prolong life to
the age of seventy and those tending to bring it to an earlier close.(180)

§ 5. From the preceding principles it is easy to deduce the demonstration
of that theorem of the doctrine of probabilities which is the foundation
of its application to inquiries for ascertaining the occurrence of a given
event, or the reality of an individual fact. The signs or evidences by
which a fact is usually proved are some of its consequences; and the
inquiry hinges upon determining what cause is most likely to have produced
a given effect. The theorem applicable to such investigations is the Sixth
Principle in Laplace’s “_Essai Philosophique sur les Probabilités_,” which
is described by him as the “fundamental principle of that branch of the
Analysis of Chances which consists in ascending from events to their
causes.”(181)

Given an effect to be accounted for, and there being several causes which
might have produced it, but of the presence of which in the particular
case nothing is known; the probability that the effect was produced by any
one of these causes _is as the antecedent probability of the cause,
multiplied by the probability that the cause, if it existed, would have
produced the given effect_.

Let M be the effect, and A, B, two causes, by either of which it might
have been produced. To find the probability that it was produced by the
one and not by the other, ascertain which of the two is most likely to
have existed, and which of them, if it did exist, was most likely to
produce the effect M: the probability sought is a compound of these two
probabilities.

CASE I. Let the causes be both alike in the second respect: either A or B,
when it exists, being supposed equally likely (or equally certain) to
produce M; but let A be in itself twice as likely as B to exist, that is,
twice as frequent a phenomenon. Then it is twice as likely to have existed
in this case, and to have been the cause which produced M.

For, since A exists in nature twice as often as B, in any 300 cases in
which one or other existed, A has existed 200 times and B 100. But either
A or B must have existed wherever M is produced; therefore, in 300 times
that M is produced, A was the producing cause 200 times, B only 100, that
is, in the ratio of 2 to 1. Thus, then, if the causes are alike in their
capacity of producing the effect, the probability as to which actually
produced it is in the ratio of their antecedent probabilities.

CASE II. Reversing the last hypothesis, let us suppose that the causes are
equally frequent, equally likely to have existed, but not equally likely,
if they did exist, to produce M; that in three times in which A occurs, it
produces that effect twice, while B, in three times, produces it only
once. Since the two causes are equally frequent in their occurrence; in
every six times that either one or the other exists, A exists three times
and B three times. A, of its three times, produces M in two; B, of its
three times, produces M in one. Thus, in the whole six times, M is only
produced thrice; but of that thrice it is produced twice by A, once only
by B. Consequently, when the antecedent probabilities of the causes are
equal, the chances that the effect was produced by them are in the ratio
of the probabilities that if they did exist they would produce the effect.

CASE III. The third case, that in which the causes are unlike in both
respects, is solved by what has preceded. For, when a quantity depends on
two other quantities, in such a manner that while either of them remains
constant it is proportional to the other, it must necessarily be
proportional to the product of the two quantities, the product being the
only function of the two which obeys that law of variation. Therefore, the
probability that M was produced by either cause, is as the antecedent
probability of the cause, multiplied by the probability that if it existed
it would produce M. Which was to be demonstrated.

Or we may prove the third case as we proved the first and second. Let A be
twice as frequent as B, and let them also be unequally likely, when they
exist, to produce M; let A produce it twice in four times, B thrice in
four times. The antecedent probability of A is to that of B as 2 to 1; the
probabilities of their producing M are as 2 to 3; the product of these
ratios is the ratio of 4 to 3; and this will be the ratio of the
probabilities that A or B was the producing cause in the given instance.
For, since A is twice as frequent as B, out of twelve cases in which one
or other exists, A exists in 8 and B in 4. But of its eight cases, A, by
the supposition, produces M in only 4, while B of its four cases produces
M in 3. M, therefore, is only produced at all in seven of the twelve
cases; but in four of these it is produced by A, in three by B; hence the
probabilities of its being produced by A and by B are as 4 to 3, and are
expressed by the fractions 4/7 and 3/7. Which was to be demonstrated.

§ 6. It remains to examine the bearing of the doctrine of chances on the
peculiar problem which occupied us in the preceding chapter, namely, how
to distinguish coincidences which are casual from those which are the
result of law; from those in which the facts which accompany or follow one
another are somehow connected through causation.

The doctrine of chances affords means by which, if we knew the _average_
number of coincidences to be looked for between two phenomena connected
only casually, we could determine how often any given deviation from that
average will occur by chance. If the probability of any casual
coincidence, considered in itself, be 1/_m_, the probability that the same
coincidence will be repeated _n_ times in succession is 1/_m_n. For
example, in one throw of a die the probability of ace being 1/6; the
probability of throwing ace twice in succession will be 1 divided by the
square of 6, or 1/36. For ace is thrown at the first throw once in six, or
six in thirty-six times, and of those six, the die being cast again, ace
will be thrown but once; being altogether once in thirty-six times. The
chance of the same cast three times successively is, by a similar
reasoning, 1/63 or 1/216; that is, the event will happen, on a large
average, only once in two hundred and sixteen throws.

We have thus a rule by which to estimate the probability that any given
series of coincidences arises from chance, provided we can measure
correctly the probability of a single coincidence. If we can obtain an
equally precise expression for the probability that the same series of
coincidences arises from causation, we should only have to compare the
numbers. This, however, can rarely be done. Let us see what degree of
approximation can practically be made to the necessary precision.

The question falls within Laplace’s sixth principle, just demonstrated.
The given fact, that is to say, the series of coincidences, may have
originated either in a casual conjunction of causes or in a law of nature.
The probabilities, therefore, that the fact originated in these two modes,
are as their antecedent probabilities, multiplied by the probabilities
that if they existed they would produce the effect. But the particular
combination of chances, if it occurred, or the law of nature if real,
would certainly produce the series of coincidences. The probabilities,
therefore, that the coincidences are produced by the two causes in
question are as the antecedent probabilities of the causes. One of these,
the antecedent probability of the combination of mere chances which would
produce the given result, is an appreciable quantity. The antecedent
probability of the other supposition may be susceptible of a more or less
exact estimation, according to the nature of the case.

In some cases, the coincidence, supposing it to be the result of causation
at all, must be the result of a known cause; as the succession of aces, if
not accidental, must arise from the loading of the die. In such cases we
may be able to form a conjecture as to the antecedent probability of such
a circumstance from the characters of the parties concerned, or other such
evidence; but it would be impossible to estimate that probability with any
thing like numerical precision. The counter-probability, however, that of
the accidental origin of the coincidence, dwindling so rapidly as it does
at each new trial, the stage is soon reached at which the chance of
unfairness in the die, however small in itself, must be greater than that
of a casual coincidence; and on this ground, a practical decision can
generally be come to without much hesitation, if there be the power of
repeating the experiment.

When, however, the coincidence is one which can not be accounted for by
any known cause, and the connection between the two phenomena, if produced
by causation, must be the result of some law of nature hitherto unknown;
which is the case we had in view in the last chapter; then, though the
probability of a casual coincidence may be capable of appreciation, that
of the counter-supposition, the existence of an undiscovered law of
nature, is clearly unsusceptible of even an approximate valuation. In
order to have the data which such a case would require, it would be
necessary to know what proportion of all the individual sequences or
co-existences occurring in nature are the result of law, and what
proportion are mere casual coincidences. It being evident that we can not
form any plausible conjecture as to this proportion, much less appreciate
it numerically, we can not attempt any precise estimation of the
comparitive probabilities. But of this we are sure, that the detection of
an unknown law of nature—of some previously unrecognized constancy of
conjunction among phenomena—is no uncommon event. If, therefore, the
number of instances in which a coincidence is observed, over and above
that which would arise on the average from the mere concurrence of
chances, be such that so great an amount of coincidences from accident
alone would be an extremely uncommon event; we have reason to conclude
that the coincidence is the effect of causation, and may be received
(subject to correction from further experience) as an empirical law.
Further than this, in point of precision, we can not go; nor, in most
cases, is greater precision required, for the solution of any practical
doubt.(182)




                               Chapter XIX.


Of The Extension Of Derivative Laws To Adjacent Cases.


§ 1. We have had frequent occasion to notice the inferior generality of
derivative laws, compared with the ultimate laws from which they are
derived. This inferiority, which affects not only the extent of the
propositions themselves, but their degree of certainty within that extent,
is most conspicuous in the uniformities of co-existence and sequence
obtaining between effects which depend ultimately on different primeval
causes. Such uniformities will only obtain where there exists the same
collocation of those primeval causes. If the collocation varies, though
the laws themselves remain the same, a totally different set of derivative
uniformities may, and generally will, be the result.

Even where the derivative uniformity is between different effects of the
same cause, it will by no means obtain as universally as the law of the
cause itself. If _a_ and _b_ accompany or succeed one another as effects
of the cause A, it by no means follows that A is the only cause which can
produce them, or that if there be another cause, as B, capable of
producing _a_, it must produce _b_ likewise. The conjunction, therefore,
of _a_ and _b_ perhaps does not hold universally, but only in the
instances in which _a_ arises from A. When it is produced by _a_ cause
other than A, _a_ and _b_ may be dissevered. Day (for example) is always
in our experience followed by night; but day is not the cause of night;
both are successive effects of _a_ common cause, the periodical passage of
the spectator into and out of the earth’s shadow, consequent on the
earth’s rotation, and on the illuminating property of the sun. If,
therefore, day is ever produced by a different cause or set of causes from
this, day will not, or at least may not, be followed by night. On the
sun’s own surface, for instance, this may be the case.

Finally, even when the derivative uniformity is itself a law of causation
(resulting from the combination of several causes), it is not altogether
independent of collocations. If a cause supervenes, capable of wholly or
partially counteracting the effect of any one of the conjoined causes, the
effect will no longer conform to the derivative law. While, therefore,
each ultimate law is only liable to frustration from one set of
counteracting causes, the derivative law is liable to it from several.
Now, the possibility of the occurrence of counteracting causes which do
not arise from any of the conditions involved in the law itself depends on
the original collocations.

It is true that, as we formerly remarked, laws of causation, whether
ultimate or derivative, are, in most cases, fulfilled even when
counteracted; the cause produces its effect, though that effect is
destroyed by something else. That the effect may be frustrated, is,
therefore, no objection to the universality of laws of causation. But it
is fatal to the universality of the sequences or co-existences of effects,
which compose the greater part of the derivative laws flowing from laws of
causation. When, from the law of a certain combination of causes, there
results a certain order in the effects; as from the combination of a
single sun with the rotation of an opaque body round its axis, there
results, on the whole surface of that opaque body, an alternation of day
and night; then, if we suppose one of the combined causes counteracted,
the rotation stopped, the sun extinguished, or a second sun superadded,
the truth of that particular law of causation is in no way affected; it is
still true that one sun shining on an opaque revolving body will
alternately produce day and night; but since the sun no longer does shine
on such a body, the derivative uniformity, the succession of day and night
on the given planet, is no longer true. Those derivative uniformities,
therefore, which are not laws of causation, are (except in the rare case
of their depending on one cause alone, not on a combination of causes)
always more or less contingent on collocations; and are hence subject to
the characteristic infirmity of empirical laws—that of being admissible
only where the collocations are known by experience to be such as are
requisite for the truth of the law; that is, only within the conditions of
time and place confirmed by actual observation.

§ 2. This principle, when stated in general terms, seems clear and
indisputable; yet many of the ordinary judgments of mankind, the propriety
of which is not questioned, have at least the semblance of being
inconsistent with it. On what grounds, it may be asked, do we expect that
the sun will rise to-morrow? To-morrow is beyond the limits of time
comprehended in our observations. They have extended over some thousands
of years past, but they do not include the future. Yet we infer with
confidence that the sun will rise to-morrow; and nobody doubts that we are
entitled to do so. Let us consider what is the warrant for this
confidence.

In the example in question, we know the causes on which the derivative
uniformity depends. They are: the sun giving out light, the earth in a
state of rotation and intercepting light. The induction which shows these
to be the real causes, and not merely prior effects of a common cause,
being complete, the only circumstances which could defeat the derivative
law are such as would destroy or counteract one or other of the combined
causes. While the causes exist and are not counteracted, the effect will
continue. If they exist and are not counteracted to-morrow, the sun will
rise to-morrow.

Since the causes, namely, the sun and the earth, the one in the state of
giving out light, the other in a state of rotation, will exist until
something destroys them, all depends on the probabilities of their
destruction, or of their counteraction. We know by observation (omitting
the inferential proofs of an existence for thousands of ages anterior)
that these phenomena have continued for (say) five thousand years. Within
that time there has existed no cause sufficient to diminish them
appreciably, nor which has counteracted their effect in any appreciable
degree. The chance, therefore, that the sun may not rise to-morrow amounts
to the chance that some cause, which has not manifested itself in the
smallest degree during five thousand years, will exist to-morrow in such
intensity as to destroy the sun or the earth, the sun’s light or the
earth’s rotation, or to produce an immense disturbance in the effect
resulting from those causes.

Now, if such a cause will exist to-morrow, or at any future time, some
cause, proximate or remote, of that cause must exist now, and must have
existed during the whole of the five thousand years. If, therefore, the
sun do not rise to-morrow, it will be because some cause has existed, the
effects of which, though during five thousand years they have not amounted
to a perceptible quantity, will in one day become overwhelming. Since this
cause has not been recognized during such an interval of time by observers
stationed on our earth, it must, if it be a single agent, be either one
whose effects develop themselves gradually and very slowly, or one which
existed in regions beyond our observation, and is now on the point of
arriving in our part of the universe. Now all causes which we have
experience of act according to laws incompatible with the supposition that
their effects, after accumulating so slowly as to be imperceptible for
five thousand years, should start into immensity in a single day. No
mathematical law of proportion between an effect and the quantity or
relations of its cause could produce such contradictory results. The
sudden development of an effect of which there was no previous trace
always arises from the coming together of several distinct causes, not
previously conjoined; but if such sudden conjunction is destined to take
place, the causes, or _their_ causes, must have existed during the entire
five thousand years; and their not having once come together during that
period shows how rare that particular combination is. We have, therefore,
the warrant of a rigid induction for considering it probable, in a degree
undistinguishable from certainty, that the known conditions requisite for
the sun’s rising will exist to-morrow.

§ 3. But this extension of derivative laws, not causative, beyond the
limits of observation can only be to _adjacent_ cases. If, instead of
to-morrow, we had said this day twenty thousand years, the inductions
would have been any thing but conclusive. That a cause which, in
opposition to very powerful causes, produced no perceptible effect during
five thousand years, should produce a very considerable one by the end of
twenty thousand, has nothing in it which is not in conformity with our
experience of causes. We know many agents, the effect of which in a short
period does not amount to a perceptible quantity, but by accumulating for
a much longer period becomes considerable. Besides, looking at the immense
multitude of the heavenly bodies, their vast distances, and the rapidity
of the motion of such of them as are known to move, it is a supposition
not at all contradictory to experience that some body may be in motion
toward us, or we toward it, within the limits of whose influence we have
not come during five thousand years, but which in twenty thousand more may
be producing effects upon us of the most extraordinary kind. Or the fact
which is capable of preventing sunrise may be, not the cumulative effect
of one cause, but some new combination of causes; and the chances
favorable to that combination, though they have not produced it once in
five thousand years, may produce it once in twenty thousand. So that the
inductions which authorize us to expect future events, grow weaker and
weaker the further we look into the future, and at length become
inappreciable.

We have considered the probabilities of the sun’s rising to-morrow, as
derived from the real laws; that is, from the laws of the causes on which
that uniformity is dependent. Let us now consider how the matter would
have stood if the uniformity had been known only as an empirical law; if
we had not been aware that the sun’s light and the earth’s rotation (or
the sun’s motion) were the causes on which the periodical occurrence of
daylight depends. We could have extended this empirical law to cases
adjacent in time, though not to so great a distance of time as we can now.
Having evidence that the effects had remained unaltered and been
punctually conjoined for five thousand years, we could infer that the
unknown causes on which the conjunction is dependent had existed
undiminished and uncounteracted during the same period. The same
conclusions, therefore, would follow as in the preceding case, except that
we should only know that during five thousand years nothing had occurred
to defeat perceptibly this particular effect; while, when we know the
causes, we have the additional assurance that during that interval no such
change has been noticeable in the causes themselves as by any degree of
multiplication or length of continuance could defeat the effect.

To this must be added, that when we know the causes, we may be able to
judge whether there exists any known cause capable of counteracting them,
while as long as they are unknown, we can not be sure but that if we did
know them, we could predict their destruction from causes actually in
existence. A bed-ridden savage, who had never seen the cataract of
Niagara, but who lived within hearing of it, might imagine that the sound
he heard would endure forever; but if he knew it to be the effect of a
rush of waters over a barrier of rock which is progressively wearing away,
he would know that within a number of ages which may be calculated it will
be heard no more. In proportion, therefore, to our ignorance of the causes
on which the empirical law depends, we can be less assured that it will
continue to hold good; and the further we look into futurity, the less
improbable is it that some one of the causes, whose co-existence gives
rise to the derivative uniformity, may be destroyed or counteracted. With
every prolongation of time the chances multiply of such an event; that is
to say, its non-occurrence hitherto becomes a less guarantee of its not
occurring within the given time. If, then, it is only to cases which in
point of time are adjacent (or nearly adjacent) to those which we have
actually observed, that _any_ derivative law, not of causation, can be
extended with an assurance equivalent to certainty, much more is this true
of a merely empirical law. Happily, for the purposes of life it is to such
cases alone that we can almost ever have occasion to extend them.

In respect of place, it might seem that a merely empirical law could not
be extended even to adjacent cases; that we could have no assurance of its
being true in any place where it has not been specially observed. The past
duration of a cause is a guarantee for its future existence, unless
something occurs to destroy it; but the existence of a cause in one or any
number of places is no guarantee for its existence in any other place,
since there is no uniformity in the collocations of primeval causes. When,
therefore, an empirical law is extended beyond the local limits within
which it has been found true by observation, the cases to which it is thus
extended must be such as are presumably within the influence of the same
individual agents. If we discover a new planet within the known bounds of
the solar system (or even beyond those bounds, but indicating its
connection with the system by revolving round the sun), we may conclude,
with great probability, that it revolves on its axis. For all the known
planets do so; and this uniformity points to some common cause, antecedent
to the first records of astronomical observation; and though the nature of
this cause can only be matter of conjecture, yet if it be, as is not
unlikely, and as Laplace’s theory supposes, not merely the same kind of
cause, but the same individual cause (such as an impulse given to all the
bodies at once), that cause, acting at the extreme points of the space
occupied by the sun and planets, is likely, unless defeated by some
counteracting cause, to have acted at every intermediate point, and
probably somewhat beyond; and therefore acted, in all probability, upon
the supposed newly-discovered planet.

When, therefore, effects which are always found conjoined can be traced
with any probability to an identical (and not merely a similar) origin, we
may with the same probability extend the empirical law of their
conjunction to all places within the extreme local boundaries within which
the fact has been observed, subject to the possibility of counteracting
causes in some portion of the field. Still more confidently may we do so
when the law is not merely empirical; when the phenomena which we find
conjoined are effects of ascertained causes, from the laws of which the
conjunction of their effects is deducible. In that case, we may both
extend the derivative uniformity over a larger space, and with less
abatement for the chance of counteracting causes. The first, because
instead of the local boundaries of our observation of the fact itself, we
may include the extreme boundaries of the ascertained influence of its
causes. Thus the succession of day and night, we know, holds true of all
the bodies of the solar system except the sun itself; but we know this
only because we are acquainted with the causes. If we were not, we could
not extend the proposition beyond the orbits of the earth and moon, at
both extremities of which we have the evidence of observation for its
truth. With respect to the probability of counteracting causes, it has
been seen that this calls for a greater abatement of confidence, in
proportion to our ignorance of the causes on which the phenomena depend.
On both accounts, therefore, a derivative law which we know how to
resolve, is susceptible of a greater extension to cases adjacent in place,
than a merely empirical law.




                               Chapter XX.


Of Analogy.


§ 1. The word Analogy, as the name of a mode of reasoning, is generally
taken for some kind of argument supposed to be of an inductive nature, but
not amounting to a complete induction. There is no word, however, which is
used more loosely, or in a greater variety of senses, than Analogy. It
sometimes stands for arguments which may be examples of the most rigorous
induction. Archbishop Whately, for instance, following Ferguson and other
writers, defines Analogy conformably to its primitive acceptation, that
which was given to it by mathematicians: Resemblance of Relations. In this
sense, when a country which has sent out colonies is termed the mother
country, the expression is analogical, signifying that the colonies of a
country stand in the same _relation_ to her in which children stand to
their parents. And if any inference be drawn from this resemblance of
relations, as, for instance, that obedience or affection is due from
colonies to the mother country, this is called reasoning by analogy. Or,
if it be argued that a nation is most beneficially governed by an assembly
elected by the people, from the admitted fact that other associations for
a common purpose, such as joint-stock companies, are best managed by a
committee chosen by the parties interested; this, too, is an argument from
analogy in the preceding sense, because its foundation is, not that a
nation is like a joint-stock company, or Parliament like a board of
directors, but that Parliament stands in the same _relation_ to the nation
in which a board of directors stands to a joint-stock company. Now, in an
argument of this nature, there is no inherent inferiority of
conclusiveness. Like other arguments from resemblance, it may amount to
nothing, or it may be a perfect and conclusive induction. The circumstance
in which the two cases resemble, may be capable of being shown to be the
_material_ circumstance; to be that on which all the consequences,
necessary to be taken into account in the particular discussion, depend.
In the example last given, the resemblance is one of relation; the
_fundamentum relationis_ being the management, by a few persons, of
affairs in which a much greater number are interested along with them.
Now, some may contend that this circumstance which is common to the two
cases, and the various consequences which follow from it, have the chief
share in determining all the effects which make up what we term good or
bad administration. If they can establish this, their argument has the
force of a rigorous induction; if they can not, they are said to have
failed in proving the analogy between the two cases; a mode of speech
which implies that when the analogy can be proved, the argument founded on
it can not be resisted.

§ 2. It is on the whole more usual, however, to extend the name of
analogical evidence to arguments from any sort of resemblance, provided
they do not amount to a complete induction; without peculiarly
distinguishing resemblance of relations. Analogical reasoning, in this
sense, may be reduced to the following formula: Two things resemble each
other in one or more respects; a certain proposition is true of the one;
therefore it is true of the other. But we have nothing here by which to
discriminate analogy from induction, since this type will serve for all
reasoning from experience. In the strictest induction, equally with the
faintest analogy, we conclude because A resembles B in one or more
properties, that it does so in a certain other property. The difference
is, that in the case of a complete induction it has been previously shown,
by due comparison of instances, that there is an invariable conjunction
between the former property or properties and the latter property; but in
what is called analogical reasoning, no such conjunction has been made
out. There have been no opportunities of putting in practice the Method of
Difference, or even the Method of Agreement; but we conclude (and that is
all which the argument of analogy amounts to) that a fact _m_, known to be
true of A, is more likely to be true of B if B agrees with A in some of
its properties (even though no connection is known to exist between _m_
and those properties), than if no resemblance at all could be traced
between B and any other thing known to possess the attribute _m_.

To this argument it is of course requisite that the properties common to A
with B shall be merely not known to be connected with _m_; they must not
be properties known to be unconnected with it. If, either by processes of
elimination, or by deduction from previous knowledge of the laws of the
properties in question, it can be concluded that they have nothing to do
with _m_, the argument of analogy is put out of court. The supposition
must be that _m_ is an effect really dependent on some property of A, but
we know not on which. We can not point out any of the properties of A,
which is the cause of _m_, or united with it by any law. After rejecting
all which we know to have nothing to do with it, there remain several
between which we are unable to decide; of which remaining properties, B
possesses one or more. This, accordingly, we consider as affording
grounds, of more or less strength, for concluding by analogy that B
possesses the attribute _m_.

There can be no doubt that every such resemblance which can be pointed out
between B and A, affords some degree of probability, beyond what would
otherwise exist, in favor of the conclusion drawn from it. If B resembled
A in all its ultimate properties, its possessing the attribute _m_ would
be a certainty, not a probability; and every resemblance which can be
shown to exist between them, places it by so much the nearer to that
point. If the resemblance be in an ultimate property, there will be
resemblance in all the derivative properties dependent on that ultimate
property, and of these _m_ may be one. If the resemblance be in a
derivative property, there is reason to expect resemblance in the ultimate
property on which it depends, and in the other derivative properties
dependent on the same ultimate property. Every resemblance which can be
shown to exist, affords ground for expecting an indefinite number of other
resemblances; the particular resemblance sought will, therefore, be
oftener found among things thus known to resemble, than among things
between which we know of no resemblance.

For example, I might infer that there are probably inhabitants in the
moon, because there are inhabitants on the earth, in the sea, and in the
air: and this is the evidence of analogy. The circumstance of having
inhabitants is here assumed not to be an ultimate property, but (as is
reasonable to suppose) a consequence of other properties; and depending,
therefore, in the case of the earth, on some of its properties as a
portion of the universe, but on which of those properties we know not. Now
the moon resembles the earth in being a solid, opaque, nearly spherical
substance, appearing to contain, or to have contained, active volcanoes;
receiving heat and light from the sun, in about the same quantity as our
earth; revolving on its axis; composed of materials which gravitate, and
obeying all the various laws resulting from that property. And I think no
one will deny that if this were all that was known of the moon, the
existence of inhabitants in that luminary would derive from these various
resemblances to the earth, a greater degree of probability than it would
otherwise have; though the amount of the augmentation it would be useless
to attempt to estimate.

If, however, every resemblance proved between B and A, in any point not
known to be immaterial with respect to _m_, forms some additional reason
for presuming that B has the attribute _m_; it is clear, _è contra_, that
every dissimilarity which can be proved between them furnishes a
counter-probability of the same nature on the other side. It is not,
indeed, unusual that different ultimate properties should, in some
particular instances, produce the same derivative property; but on the
whole it is certain that things which differ in their ultimate properties,
will differ at least as much in the aggregate of their derivative
properties, and that the differences which are unknown will, on the
average of cases, bear some proportion to those which are known. There
will, therefore, be a competition between the known points of agreement
and the known points of difference in A and B; and according as the one or
the other may be deemed to preponderate, the probability derived from
analogy will be for or against B’s having the property _m_. The moon, for
instance, agrees with the earth in the circumstances already mentioned;
but differs in being smaller, in having its surface more unequal, and
apparently volcanic throughout, in having, at least on the side next the
earth, no atmosphere sufficient to refract light, no clouds, and (it is
therefore concluded) no water. These differences, considered merely as
such, might perhaps balance the resemblances, so that analogy would afford
no presumption either way. But considering that some of the circumstances
which are wanting on the moon are among those which, on the earth, are
found to be indispensable conditions of animal life, we may conclude that
if that phenomenon does exist in the moon (or at all events on the nearer
side), it must be as an effect of causes totally different from those on
which it depends here; as a consequence, therefore, of the moon’s
differences from the earth, not of the points of agreement. Viewed in this
light, all the resemblances which exist become presumptions against, not
in favor of, the moon’s being inhabited. Since life can not exist there in
the manner in which it exists here, the greater the resemblance of the
lunar world to the terrestrial in other respects, the less reason we have
to believe that it can contain life.

There are, however, other bodies in our system, between which and the
earth there is a much closer resemblance; which possess an atmosphere,
clouds, consequently water (or some fluid analogous to it), and even give
strong indications of snow in their polar regions; while the cold, or
heat, though differing greatly on the average from ours, is, in some parts
at least of those planets, possibly not more extreme than in some regions
of our own which are habitable. To balance these agreements, the
ascertained differences are chiefly in the average light and heat,
velocity of rotation, density of material, intensity of gravity, and
similar circumstances of a secondary kind. With regard to these planets,
therefore, the argument of analogy gives a decided preponderance in favor
of their resembling the earth in any of its derivative properties, such as
that of having inhabitants; though when we consider how immeasurably
multitudinous are those of their properties which we are entirely ignorant
of, compared with the few which we know, we can attach but trifling weight
to any considerations of resemblance in which the known elements bear so
inconsiderable a proportion to the unknown.

Besides the competition between analogy and diversity, there may be a
competition of conflicting analogies. The new case may be similar in some
of its circumstances to cases in which the fact _m_ exists, but in others
to cases in which it is known not to exist. Amber has some properties in
common with vegetable, others with mineral products. A painting of unknown
origin may resemble, in certain of its characters, known works of a
particular master, but in others it may as strikingly resemble those of
some other painter. A vase may bear some analogy to works of Grecian, and
some to those of Etruscan, or Egyptian art. We are of course supposing
that it does not possess any quality which has been ascertained, by a
sufficient induction, to be a conclusive mark either of the one or of the
other.

§ 3. Since the value of an analogical argument inferring one resemblance
from other resemblances without any antecedent evidence of a connection
between them, depends on the extent of ascertained resemblance, compared
first with the amount of ascertained difference, and next with the extent
of the unexplored region of unascertained properties; it follows that
where the resemblance is very great, the ascertained difference very
small, and our knowledge of the subject-matter tolerably extensive, the
argument from analogy may approach in strength very near to a valid
induction. If, after much observation of B, we find that it agrees with A
in nine out of ten of its known properties, we may conclude with a
probability of nine to one, that it will possess any given derivative
property of A. If we discover, for example, an unknown animal or plant,
resembling closely some known one in the greater number of the properties
we observe in it, but differing in some few, we may reasonably expect to
find in the unobserved remainder of its properties, a general agreement
with those of the former; but also a difference corresponding
proportionately to the amount of observed diversity.

It thus appears that the conclusions derived from analogy are only of any
considerable value, when the case to which we reason is an adjacent case;
adjacent, not as before, in place or time, but in circumstances. In the
case of effects of which the causes are imperfectly or not at all known,
when consequently the observed order of their occurrence amounts only to
an empirical law, it often happens that the conditions which have
co-existed whenever the effect was observed, have been very numerous. Now
if a new case presents itself, in which all these conditions do not exist,
but the far greater part of them do, some one or a few only being wanting,
the inference that the effect will occur, notwithstanding this deficiency
of complete resemblance to the cases in which it has been observed, may,
though of the nature of analogy, possess a high degree of probability. It
is hardly necessary to add that, however considerable this probability may
be, no competent inquirer into nature will rest satisfied with it when a
complete induction is attainable; but will consider the analogy as a mere
guide-post, pointing out the direction in which more rigorous
investigations should be prosecuted.

It is in this last respect that considerations of analogy have the highest
scientific value. The cases in which analogical evidence affords in itself
any very high degree of probability, are, as we have observed, only those
in which the resemblance is very close and extensive; but there is no
analogy, however faint, which may not be of the utmost value in suggesting
experiments or observations that may lead to more positive conclusions.
When the agents and their effects are out of the reach of further
observation and experiment, as in the speculations already alluded to
respecting the moon and planets, such slight probabilities are no more
than an interesting theme for the pleasant exercise of imagination; but
any suspicion, however slight, that sets an ingenious person at work to
contrive an experiment, or affords a reason for trying one experiment
rather than another, may be of the greatest benefit to science.

On this ground, though I can not accept as positive truths any of those
scientific hypotheses which are unsusceptible of being ultimately brought
to the test of actual induction, such, for instance, as the two theories
of light, the emission theory of the last century, and the undulatory
theory which predominates in the present, I am yet unable to agree with
those who consider such hypotheses to be worthy of entire disregard. As is
well said by Hartley (and concurred in by a thinker in general so
diametrically opposed to Hartley’s opinions as Dugald Stewart), “any
hypothesis which has so much plausibility as to explain a considerable
number of facts, helps us to digest these facts in proper order, to bring
new ones to light, and make _experimenta crucis_ for the sake of future
inquirers.”(183) If an hypothesis both explains known facts, and has led
to the prediction of others previously unknown, and since verified by
experience, the laws of the phenomenon which is the subject of inquiry
must bear at least a great similarity to those of the class of phenomena
to which the hypothesis assimilates it; and since the analogy which
extends so far may probably extend further, nothing is more likely to
suggest experiments tending to throw light upon the real properties of the
phenomenon, than the following out such an hypothesis. But to this end it
is by no means necessary that the hypothesis be mistaken for a scientific
truth. On the contrary, that illusion is in this respect, as in every
other, an impediment to the progress of real knowledge, by leading
inquirers to restrict themselves arbitrarily to the particular hypothesis
which is most accredited at the time, instead of looking out for every
class of phenomena between the laws of which and those of the given
phenomenon any analogy exists, and trying all such experiments as may tend
to the discovery of ulterior analogies pointing in the same direction.




                               Chapter XXI.


Of The Evidence Of The Law Of Universal Causation.


§ 1. We have now completed our review of the logical processes by which
the laws, or uniformities, of the sequence of phenomena, and those
uniformities in their co-existence which depend on the laws of their
sequence, are ascertained or tested. As we recognized in the commencement,
and have been enabled to see more clearly in the progress of the
investigation, the basis of all these logical operations is the law of
causation.

The validity of all the Inductive Methods depends on the assumption that
every event, or the beginning of every phenomenon, must have some cause;
some antecedent, on the existence of which it is invariably and
unconditionally consequent. In the Method of Agreement this is obvious;
that method avowedly proceeding on the supposition that we have found the
true cause as soon as we have negatived every other. The assertion is
equally true of the Method of Difference. That method authorizes us to
infer a general law from two instances; one, in which A exists together
with a multitude of other circumstances, and B follows; another, in which,
A being removed, and all other circumstances remaining the same, B is
prevented. What, however, does this prove? It proves that B, in the
particular instance, can not have had any other cause than A; but to
conclude from this that A was the cause, or that A will on other occasions
be followed by B, is only allowable on the assumption that B must have
some cause; that among its antecedents in any single instance in which it
occurs, there must be one which has the capacity of producing it at other
times. This being admitted, it is seen that in the case in question that
antecedent can be no other than A; but that if it be no other than A it
must be A, is not proved, by these instances at least, but taken for
granted. There is no need to spend time in proving that the same thing is
true of the other Inductive Methods. The universality of the law of
causation is assumed in them all.

But is this assumption warranted? Doubtless (it may be said) _most_
phenomena are connected as effects with some antecedent or cause, that is,
are never produced unless some assignable fact has preceded them; but the
very circumstance that complicated processes of induction are sometimes
necessary, shows that cases exist in which this regular order of
succession is not apparent to our unaided apprehension. If, then, the
processes which bring these cases within the same category with the rest,
require that we should assume the universality of the very law which they
do not at first sight appear to exemplify, is not this a _petitio
principii_? Can we prove a proposition, by an argument which takes it for
granted? And if not so proved, on what evidence does it rest?

For this difficulty, which I have purposely stated in the strongest terms
it will admit of, the school of metaphysicians who have long predominated
in this country find a ready salvo. They affirm, that the universality of
causation is a truth which we can not help believing; that the belief in
it is an instinct, one of the laws of our believing faculty. As the proof
of this, they say, and they have nothing else to say, that every body does
believe it; and they number it among the propositions, rather numerous in
their catalogue, which may be logically argued against, and perhaps can
not be logically proved, but which are of higher authority than logic, and
so essentially inherent in the human mind, that even he who denies them in
speculation, shows by his habitual practice that his arguments make no
impression upon himself.

Into the merits of this question, considered as one of psychology, it
would be foreign to my purpose to enter here; but I must protest against
adducing, as evidence of the truth of a fact in external nature, the
disposition, however strong or however general, of the human mind to
believe it. Belief is not proof, and does not dispense with the necessity
of proof. I am aware, that to ask for evidence of a proposition which we
are supposed to believe instinctively, is to expose one’s self to the
charge of rejecting the authority of the human faculties; which of course
no one can consistently do, since the human faculties are all which any
one has to judge by; and inasmuch as the meaning of the word evidence is
supposed to be, something which when laid before the mind, induces it to
believe; to demand evidence when the belief is insured by the mind’s own
laws, is supposed to be appealing to the intellect against the intellect.
But this, I apprehend, is a misunderstanding of the nature of evidence. By
evidence is not meant any thing and every thing which produces belief.
There are many things which generate belief besides evidence. A mere
strong association of ideas often causes a belief so intense as to be
unshakable by experience or argument. Evidence is not that which the mind
does or must yield to, but that which it ought to yield to, namely, that,
by yielding to which its belief is kept conformable to fact. There is no
appeal from the human faculties generally, but there is an appeal from one
human faculty to another; from the judging faculty, to those which take
cognizance of fact, the faculties of sense and consciousness. The
legitimacy of this appeal is admitted whenever it is allowed that our
judgments ought to be conformable to fact. To say that belief suffices for
its own justification is making opinion the test of opinion; it is denying
the existence of any outward standard, the conformity of an opinion to
which constitutes its truth. We call one mode of forming opinions right
and another wrong, because the one does, and the other does not, tend to
make the opinion agree with the fact—to make people believe what really
is, and expect what really will be. Now a mere disposition to believe,
even if supposed instinctive, is no guarantee for the truth of the thing
believed. If, indeed, the belief ever amounted to an irresistible
necessity, there would then be no _use_ in appealing from it, because
there would be no possibility of altering it. But even then the truth of
the belief would not follow; it would only follow that mankind were under
a permanent necessity of believing what might possibly not be true; in
other words, that a case might occur in which our senses or consciousness,
if they could be appealed to, might testify one thing, and our reason
believe another. But in fact there is no such permanent necessity. There
is no proposition of which it can be asserted that every human mind must
eternally and irrevocably believe it. Many of the propositions of which
this is most confidently stated, great numbers of human beings have
disbelieved. The things which it has been supposed that nobody could
possibly help believing, are innumerable; but no two generations would
make out the same catalogue of them. One age or nation believes implicitly
what to another seems incredible and inconceivable; one individual has not
a vestige of a belief which another deems to be absolutely inherent in
humanity. There is not one of these supposed instinctive beliefs which is
really inevitable. It is in the power of every one to cultivate habits of
thought which make him independent of them. The habit of philosophical
analysis (of which it is the surest effect to enable the mind to command,
instead of being commanded by, the laws of the merely passive part of its
own nature), by showing to us that things are not necessarily connected in
fact because their ideas are connected in our minds, is able to loosen
innumerable associations which reign despotically over the undisciplined
or early-prejudiced mind. And this habit is not without power even over
those associations which the school of which I have been speaking regard
as connate and instinctive. I am convinced that any one accustomed to
abstraction and analysis, who will fairly exert his faculties for the
purpose, will, when his imagination has once learned to entertain the
notion, find no difficulty in conceiving that in some one, for instance,
of the many firmaments into which sidereal astronomy now divides the
universe, events may succeed one another at random, without any fixed law;
nor can any thing in our experience, or in our mental nature, constitute a
sufficient, or indeed any, reason for believing that this is nowhere the
case.

Were we to suppose (what it is perfectly possible to imagine) that the
present order of the universe were brought to an end, and that a chaos
succeeded in which there was no fixed succession of events, and the past
gave no assurance of the future; if a human being were miraculously kept
alive to witness this change, he surely would soon cease to believe in any
uniformity, the uniformity itself no longer existing. If this be admitted,
the belief in uniformity either is not an instinct, or it is an instinct
conquerable, like all other instincts, by acquired knowledge.

But there is no need to speculate on what might be, when we have positive
and certain knowledge of what has been. It is not true, as a matter of
fact, that mankind have always believed that all the successions of events
were uniform and according to fixed laws. The Greek philosophers, not even
excepting Aristotle, recognized Chance and Spontaneity (τύχη and τὸ
αὐτομάτον) as among the agents in nature; in other words, they believed
that to that extent there was no guarantee that the past had been similar
to itself, or that the future would resemble the past. Even now a full
half of the philosophical world, including the very same metaphysicians
who contend most for the instinctive character of the belief in
uniformity, consider one important class of phenomena, volitions, to be an
exception to the uniformity, and not governed by a fixed law.(184)

§ 2. As was observed in a former place,(185) the belief we entertain in
the universality, throughout nature, of the law of cause and effect, is
itself an instance of induction; and by no means one of the earliest which
any of us, or which mankind in general, can have made. We arrive at this
universal law, by generalization from many laws of inferior generality. We
should never have had the notion of causation (in the philosophical
meaning of the term) as a condition of all phenomena, unless many cases of
causation, or in other words, many partial uniformities of sequence, had
previously become familiar. The more obvious of the particular
uniformities suggest, and give evidence of, the general uniformity, and
the general uniformity, once established, enables us to prove the
remainder of the particular uniformities of which it is made up. As,
however, all rigorous processes of induction presuppose the general
uniformity, our knowledge of the particular uniformities from which it was
first inferred was not, of course, derived from rigorous induction, but
from the loose and uncertain mode of induction _per enumerationem
simplicem_; and the law of universal causation, being collected from
results so obtained, can not itself rest on any better foundation.

It would seem, therefore, that induction _per enumerationem simplicem_ not
only is not necessarily an illicit logical process, but is in reality the
only kind of induction possible; since the more elaborate process depends
for its validity on a law, itself obtained in that inartificial mode. Is
there not then an inconsistency in contrasting the looseness of one method
with the rigidity of another, when that other is indebted to the looser
method for its own foundation?

The inconsistency, however, is only apparent. Assuredly, if induction by
simple enumeration were an invalid process, no process grounded on it
could be valid; just as no reliance could be placed on telescopes, if we
could not trust our eyes. But though a valid process, it is a fallible
one, and fallible in very different degrees: if, therefore, we can
substitute for the more fallible forms of the process, an operation
grounded on the same process in a less fallible form, we shall have
effected a very material improvement. And this is what scientific
induction does.

A mode of concluding from experience must be pronounced untrustworthy when
subsequent experience refuses to confirm it. According to this criterion,
induction by simple enumeration—in other words, generalization of an
observed fact from the mere absence of any known instance to the
contrary—affords in general a precarious and unsafe ground of assurance;
for such generalizations are incessantly discovered, on further
experience, to be false. Still, however, it affords some assurance,
sufficient, in many cases, for the ordinary guidance of conduct. It would
be absurd to say, that the generalizations arrived at by mankind in the
outset of their experience, such as these—food nourishes, fire burns,
water drowns—were unworthy of reliance.(186) There is a scale of
trustworthiness in the results of the original unscientific induction; and
on this diversity (as observed in the fourth chapter of the present book)
depend the rules for the improvement of the process. The improvement
consists in correcting one of these inartificial generalizations by means
of another. As has been already pointed out, this is all that art can do.
To test a generalization, by showing that it either follows from, or
conflicts with, some stronger induction, some generalization resting on a
broader foundation of experience, is the beginning and end of the logic of
induction.

§ 3. Now the precariousness of the method of simple enumeration is in an
inverse ratio to the largeness of the generalization. The process is
delusive and insufficient, exactly in proportion as the subject-matter of
the observation is special and limited in extent. As the sphere widens,
this unscientific method becomes less and less liable to mislead; and the
most universal class of truths, the law of causation, for instance, and
the principles of number and of geometry, are duly and satisfactorily
proved by that method alone, nor are they susceptible of any other proof.

With respect to the whole class of generalizations of which we have
recently treated, the uniformities which depend on causation, the truth of
the remark just made follows by obvious inference from the principles laid
down in the preceding chapters. When a fact has been observed a certain
number of times to be true, and is not in any instance known to be false,
if we at once affirm that fact as a universal truth or law of nature,
without either testing it by any of the four methods of induction, or
deducing it from other known laws, we shall in general err grossly; but we
are perfectly justified in affirming it as an empirical law, true within
certain limits of time, place, and circumstance, provided the number of
coincidences be greater than can with any probability be ascribed to
chance. The reason for not extending it beyond those limits is, that the
fact of its holding true within them may be a consequence of collocations,
which can not be concluded to exist in one place because they exist in
another; or may be dependent on the accidental absence of counteracting
agencies, which any variation of time, or the smallest change of
circumstances, may possibly bring into play. If we suppose, then, the
subject-matter of any generalization to be so widely diffused that there
is no time, no place, and no combination of circumstances, but must afford
an example either of its truth or of its falsity, and if it be never found
otherwise than true, its truth can not be contingent on any collocations,
unless such as exist at all times and places; nor can it be frustrated by
any counteracting agencies, unless by such as never actually occur. It is,
therefore, an empirical law co-extensive with all human experience; at
which point the distinction between empirical laws and laws of nature
vanishes, and the proposition takes its place among the most firmly
established as well as largest truths accessible to science.

Now, the most extensive in its subject-matter of all generalizations which
experience warrants, respecting the sequences and co-existences of
phenomena, is the law of causation. It stands at the head of all observed
uniformities, in point of universality, and therefore (if the preceding
observations are correct) in point of certainty. And if we consider, not
what mankind would have been justified in believing in the infancy of
their knowledge, but what may rationally be believed in its present more
advanced state, we shall find ourselves warranted in considering this
fundamental law, though itself obtained by induction from particular laws
of causation, as not less certain, but on the contrary, more so, than any
of those from which it was drawn. It adds to them as much proof as it
receives from them. For there is probably no one even of the best
established laws of causation which is not sometimes counteracted, and to
which, therefore, apparent exceptions do not present themselves, which
would have necessarily and justly shaken the confidence of mankind in the
universality of those laws, if inductive processes founded on the
universal law had not enabled us to refer those exceptions to the agency
of counteracting causes, and thereby reconcile them with the law with
which they apparently conflict. Errors, moreover, may have slipped into
the statement of any one of the special laws, through inattention to some
material circumstance: and instead of the true proposition, another may
have been enunciated, false as a universal law, though leading, in all
cases hitherto observed, to the same result. To the law of causation, on
the contrary, we not only do not know of any exception, but the exceptions
which limit or apparently invalidate the special laws, are so far from
contradicting the universal one, that they confirm it; since in all cases
which are sufficiently open to our observation, we are able to trace the
difference of result, either to the absence of a cause which had been
present in ordinary cases, or to the presence of one which had been
absent.

The law of cause and effect, being thus certain, is capable of imparting
its certainty to all other inductive propositions which can be deduced
from it; and the narrower inductions may be regarded as receiving their
ultimate sanction from that law, since there is no one of them which is
not rendered more certain than it was before, when we are able to connect
it with that larger induction, and to show that it can not be denied,
consistently with the law that every thing which begins to exist has a
cause. And hence we are justified in the seeming inconsistency, of holding
induction by simple enumeration to be good for proving this general truth,
the foundation of scientific induction, and yet refusing to rely on it for
any of the narrower inductions. I fully admit that if the law of causation
were unknown, generalization in the more obvious cases of uniformity in
phenomena would nevertheless be possible, and though in all cases more or
less precarious, and in some extremely so, would suffice to constitute a
certain measure of probability; but what the amount of this probability
might be, we are dispensed from estimating, since it never could amount to
the degree of assurance which the proposition acquires, when, by the
application to it of the Four Methods, the supposition of its falsity is
shown to be inconsistent with the Law of Causation. We are therefore
logically entitled, and, by the necessities of scientific induction,
required, to disregard the probabilities derived from the early rude
method of generalizing, and to consider no minor generalization as proved
except so far as the law of causation confirms it, nor probable except so
far as it may reasonably be expected to be so confirmed.

§ 4. The assertion, that our inductive processes assume the law of
causation, while the law of causation is itself a case of induction, is a
paradox, only on the old theory of reasoning, which supposes the universal
truth, or major premise, in a ratiocination, to be the real proof of the
particular truths which are ostensibly inferred from it. According to the
doctrine maintained in the present treatise,(187) the major premise is not
the proof of the conclusion, but is itself proved, along with the
conclusion from the same evidence. “All men are mortal” is not the proof
that Lord Palmerston is mortal; but our past experience of mortality
authorizes us to infer _both_ the general truth and the particular fact,
and the one with exactly the same degree of assurance as the other. The
mortality of Lord Palmerston is not an inference from the mortality of all
men, but from the experience which proves the mortality of all men; and is
a correct inference from experience, if that general truth is so too. This
relation between our general beliefs and their particular applications
holds equally true in the more comprehensive case which we are now
discussing. Any new fact of causation inferred by induction, is rightly
inferred, if no other objection can be made to the inference than can be
made to the general truth that every event has a cause. The utmost
certainty which can be given to a conclusion arrived at in the way of
inference, stops at this point. When we have ascertained that the
particular conclusion must stand or fall with the general uniformity of
the laws of nature—that it is liable to no doubt except the doubt whether
every event has a cause—we have done all that can be done for it. The
strongest assurance we can obtain of any theory respecting the cause of a
given phenomenon, is that the phenomenon has either that cause or none.

The latter supposition might have been an admissible one in a very early
period of our study of nature. But we have been able to perceive that in
the stage which mankind have now reached, the generalization which gives
the Law of Universal Causation has grown into a stronger and better
induction, one deserving of greater reliance, than any of the subordinate
generalizations. We may even, I think, go a step further than this, and
regard the certainty of that great induction as not merely comparative,
but, for all practical purposes, complete.

The considerations, which, as I apprehend, give, at the present day, to
the proof of the law of uniformity of succession as true of all phenomena
without exception, this character of completeness and conclusiveness, are
the following: First, that we now know it directly to be true of far the
greatest number of phenomena; that there are none of which we know it not
to be true, the utmost that can be said being, that of some we can not
positively from direct evidence affirm its truth; while phenomenon after
phenomenon, as they become better known to us, are constantly passing from
the latter class into the former; and in all cases in which that
transition has not yet taken place, the absence of direct proof is
accounted for by the rarity or the obscurity of the phenomena, our
deficient means of observing them, or the logical difficulties arising
from the complication of the circumstances in which they occur; insomuch
that, notwithstanding as rigid a dependence on given conditions as exists
in the case of any other phenomenon, it was not likely that we should be
better acquainted with those conditions than we are. Besides this first
class of considerations, there is a second, which still further
corroborates the conclusion. Although there are phenomena the production
and changes of which elude all our attempts to reduce them universally to
any ascertained law; yet in every such case, the phenomenon, or the
objects concerned in it, are found in some instances to obey the known
laws of nature. The wind, for example, is the type of uncertainty and
caprice, yet we find it in some cases obeying with as much constancy as
any phenomenon in nature the law of the tendency of fluids to distribute
themselves so as to equalize the pressure on every side of each of their
particles; as in the case of the trade-winds and the monsoons.

Lightning might once have been supposed to obey no laws; but since it has
been ascertained to be identical with electricity, we know that the very
same phenomenon in some of its manifestations is implicitly obedient to
the action of fixed causes. I do not believe that there is now one object
or event in all our experience of nature, within the bounds of the solar
system at least, which has not either been ascertained by direct
observation to follow laws of its own, or been proved to be closely
similar to objects and events which, in more familiar manifestations, or
on a more limited scale, follow strict laws; our inability to trace the
same laws on a larger scale and in the more recondite instances, being
accounted for by the number and complication of the modifying causes, or
by their inaccessibility to observation.

The progress of experience, therefore, has dissipated the doubt which must
have rested on the universality of the law of causation while there were
phenomena which seemed to be _sui generis_, not subject to the same laws
with any other class of phenomena, and not as yet ascertained to have
peculiar laws of their own. This great generalization, however, might
reasonably have been, as it in fact was, acted on as a probability of the
highest order, before there were sufficient grounds for receiving it as a
certainty. In matters of evidence, as in all other human things, we
neither require, nor can attain, the absolute. We must hold even our
strongest convictions with an opening left in our minds for the reception
of facts which contradict them; and only when we have taken this
precaution, have we earned the right to act upon our convictions with
complete confidence when no such contradiction appears. Whatever has been
found true in innumerable instances, and never found to be false after due
examination in any, we are safe in acting on as universal provisionally,
until an undoubted exception appears; provided the nature of the case be
such that a real exception could scarcely have escaped notice. When every
phenomenon that we ever knew sufficiently well to be able to answer the
question, had a cause on which it was invariably consequent, it was more
rational to suppose that our inability to assign the causes of other
phenomena arose from our ignorance, than that there were phenomena which
were uncaused, and which happened to be exactly those which we had
hitherto had no sufficient opportunity of studying.

It must, at the same time, be remarked, that the reasons for this reliance
do not hold in circumstances unknown to us, and beyond the possible range
of our experience. In distant parts of the stellar regions, where the
phenomena may be entirely unlike those with which we are acquainted, it
would be folly to affirm confidently that this general law prevails, any
more than those special ones which we have found to hold universally on
our own planet. The uniformity in the succession of events, otherwise
called the law of causation, must be received not as a law of the
universe, but of that portion of it only which is within the range of our
means of sure observation, with a reasonable degree of extension to
adjacent cases. To extend it further is to make a supposition without
evidence, and to which, in the absence of any ground from experience for
estimating its degree of probability, it would be idle to attempt to
assign any.(188)




                              Chapter XXII.


Of Uniformities Of Co-Existence Not Dependent On Causation.


§ 1. The order of the occurrence of phenomena in time, is either
successive or simultaneous; the uniformities, therefore, which obtain in
their occurrence, are either uniformities of succession or of
co-existence. Uniformities of succession are all comprehended under the
law of causation and its consequences. Every phenomenon has a cause, which
it invariably follows; and from this are derived other invariable
sequences among the successive stages of the same effect, as well as
between the effects resulting from causes which invariably succeed one
another.

In the same manner with these derivative uniformities of succession, a
great variety of uniformities of co-existence also take their rise.
Co-ordinate effects of the same cause naturally co-exist with one another.
High water at any point on the earth’s surface, and high water at the
point diametrically opposite to it, are effects uniformly simultaneous,
resulting from the direction in which the combined attractions of the sun
and moon act upon the waters of the ocean. An eclipse of the sun to us,
and an eclipse of the earth to a spectator situated in the moon, are in
like manner phenomena invariably co-existent; and their co-existence can
equally be deduced from the laws of their production.

It is an obvious question, therefore, whether all the uniformities of
co-existence among phenomena may not be accounted for in this manner. And
it can not be doubted that between phenomena which are themselves effects,
the co-existences must necessarily depend on the causes of those
phenomena. If they are effects immediately or remotely of the same cause,
they can not co-exist except by virtue of some laws or properties of that
cause; if they are effects of different causes, they can not co-exist
unless it be because their causes co-exist; and the uniformity of
co-existence, if such there be, between the effects, proves that those
particular causes, within the limits of our observation, have uniformly
been co-existent.

§ 2. But these same considerations compel us to recognize that there must
be one class of co-existences which can not depend on causation: the
co-existences between the ultimate properties of things—those properties
which are the causes of all phenomena, but are not themselves caused by
any phenomenon, and a cause for which could only be sought by ascending to
the origin of all things. Yet among these ultimate properties there are
not only co-existences, but uniformities of co-existence. General
propositions may be, and are, formed, which assert that whenever certain
properties are found, certain others are found along with them. We
perceive an object; say, for instance, water. We recognize it to be water,
of course by certain of its properties. Having recognized it, we are able
to affirm of it innumerable other properties; which we could not do unless
it were a general truth, a law or uniformity in nature, that the set of
properties by which we identify the substance as water always have those
other properties conjoined with them.

In a former place(189) it has been explained, in some detail, what is
meant by the Kinds of objects; those classes which differ from one another
not by a limited and definite, but by an indefinite and unknown, number of
distinctions. To this we have now to add, that every proposition by which
any thing is asserted of a Kind, affirms a uniformity of co-existence.
Since we know nothing of Kinds but their properties, the Kind, to us, _is_
the set of properties by which it is identified, and which must of course
be sufficient to distinguish it from every other kind.(190) In affirming
any thing, therefore, of a Kind, we are affirming something to be
uniformly co-existent with the properties by which the kind is recognized;
and that is the sole meaning of the assertion.

Among the uniformities of co-existence which exist in nature, may hence be
numbered all the properties of Kinds. The whole of these, however, are not
independent of causation, but only a portion of them. Some are ultimate
properties, others derivative: of some, no cause can be assigned, but
others are manifestly dependent on causes. Thus, pure oxygen gas is a
Kind, and one of its most unequivocal properties is its gaseous form; this
property, however, has for its cause the presence of a certain quantity of
latent heat; and if that heat could be taken away (as has been done from
so many gases in Faraday’s experiments), the gaseous form would doubtless
disappear, together with numerous other properties which depend on, or are
caused by, that property.

In regard to all substances which are chemical compounds, and which
therefore may be regarded as products of the juxtaposition of substances
different in Kind from themselves, there is considerable reason to presume
that the specific properties of the compound are consequent, as effects,
on some of the properties of the elements, though little progress has yet
been made in tracing any invariable relation between the latter and the
former. Still more strongly will a similar presumption exist, when the
object itself, as in the case of organized beings, is no primeval agent,
but an effect, which depends on a cause or causes for its very existence.
The Kinds, therefore, which are called in chemistry simple substances, or
elementary natural agents, are the only ones, any of whose properties can
with certainty be considered ultimate; and of these the ultimate
properties are probably much more numerous than we at present recognize,
since every successful instance of the resolution of the properties of
their compounds into simpler laws, generally leads to the recognition of
properties in the elements distinct from any previously known. The
resolution of the laws of the heavenly motions established the previously
unknown ultimate property of a mutual attraction between all bodies; the
resolution, so far as it has yet proceeded, of the laws of
crystallization, of chemical composition, electricity, magnetism, etc.,
points to various polarities, ultimately inherent in the particles of
which bodies are composed; the comparative atomic weights of different
kinds of bodies were ascertained by resolving into more general laws the
uniformities observed in the proportions in which substances combine with
one another, and so forth. Thus, although every resolution of a complex
uniformity into simpler and more elementary laws has an apparent tendency
to diminish the number of the ultimate properties, and really does remove
many properties from the list; yet (since the result of this simplifying
process is to trace up an ever greater variety of different effects to the
same agents) the further we advance in this direction, the greater number
of distinct properties we are forced to recognize in one and the same
object; the co-existences of which properties must accordingly be ranked
among the ultimate generalities of nature.

§ 3. There are, therefore, only two kinds of propositions which assert
uniformity of co-existence between properties. Either the properties
depend on causes or they do not. If they do, the proposition which affirms
them to be co-existent is a derivative law of co-existence between
effects, and, until resolved into the laws of causation on which it
depends, is an empirical law, and to be tried by the principles of
induction to which such laws are amenable. If, on the other hand, the
properties do not depend on causes, but are ultimate properties, then, if
it be true that they invariably co-exist, they must all be ultimate
properties of one and the same Kind; and it is of these only that the
co-existences can be classed as a peculiar sort of laws of nature.

When we affirm that all crows are black, or that all negroes have woolly
hair, we assert a uniformity of co-existence. We assert that the property
of blackness or of having woolly hair invariably co-exists with the
properties which, in common language, or in the scientific classification
that we adopt, are taken to constitute the class crow, or the class negro.
Now, supposing blackness to be an ultimate property of black objects, or
woolly hair an ultimate property of the animals which possess it;
supposing that these properties are not results of causation, are not
connected with antecedent phenomena by any law; then if all crows are
black, and all negroes have woolly hair, these must be ultimate properties
of the kind _crow_, or _negro_, or of some kind which includes them. If,
on the contrary, blackness or woolly hair be an effect depending on
causes, these general propositions are manifestly empirical laws; and all
that has already been said respecting that class of generalizations may be
applied without modification to these.

Now, we have seen that in the case of all compounds—of all things, in
short, except the elementary substances and primary powers of nature—the
presumption is, that the properties do really depend upon causes; and it
is impossible in any case whatever to be certain that they do not. We
therefore should not be safe in claiming for any generalization respecting
the co-existence of properties, a degree of certainty to which, if the
properties should happen to be the result of causes, it would have no
claim. A generalization respecting co-existence, or, in other words,
respecting the properties of kinds, may be an ultimate truth, but it may
also be merely a derivative one; and since, if so, it is one of those
derivative laws which are neither laws of causation nor have been resolved
into the laws of causation on which they depend, it can possess no higher
degree of evidence than belongs to an empirical law.

§ 4. This conclusion will be confirmed by the consideration of one great
deficiency, which precludes the application to the ultimate uniformities
of co-existence, of a system of rigorous scientific induction, such as the
uniformities in the succession of phenomena have been found to admit of.
The basis of such a system is wanting; there is no general axiom standing
in the same relation to the uniformities of co-existence as the law of
causation does to those of succession. The Methods of Induction applicable
to the ascertainment of causes and effects are grounded on the principle
that every thing which has a beginning must have some cause or other; that
among the circumstances which actually existed at the time of its
commencement, there is certainly some one combination, on which the effect
in question is unconditionally consequent, and on the repetition of which
it would certainly again recur. But in an inquiry whether some kind (as
crow) universally possesses a certain property (as blackness), there is no
room for any assumption analogous to this. We have no previous certainty
that the property must have something which constantly co-exists with it;
must have an invariable co-existent, in the same manner as an event must
have an invariable antecedent. When we feel pain, we must be in some
circumstances under which, if exactly repeated, we should always feel
pain. But when we are conscious of blackness, it does not follow that
there is something else present of which blackness is a constant
accompaniment. There is, therefore, no room for elimination; no method of
Agreement or Difference, or of Concomitant Variations (which is but a
modification either of the Method of Agreement or of the Method of
Difference). We can not conclude that the blackness we see in crows must
be an invariable property of crows merely because there is nothing else
present of which it can be an invariable property. We therefore inquire
into the truth of a proposition like “All crows are black,” under the same
disadvantage as if, in our inquiries into causation, we were compelled to
let in, as one of the possibilities, that the effect may in that
particular instance have arisen without any cause at all.

To overlook this grand distinction was, as it seems to me, the capital
error in Bacon’s view of inductive philosophy. The principle of
elimination, that great logical instrument which he had the immense merit
of first bringing into general use, he deemed applicable in the same
sense, and in as unqualified a manner, to the investigation of the
co-existences, as to that of the successions of phenomena. He seems to
have thought that as every event has a cause, or invariable antecedent, so
every property of an object has an invariable co-existent, which he called
its form; and the examples he chiefly selected for the application and
illustration of his method, were inquiries into such forms; attempts to
determine in what else all those objects resembled, which agreed in some
one general property, as hardness or softness, dryness or moistness, heat
or coldness. Such inquiries could lead to no result. The objects seldom
have any such circumstances in common. They usually agree in the one point
inquired into, and in nothing else. A great proportion of the properties
which, so far as we can conjecture, are the likeliest to be really
ultimate, would seem to be inherently properties of many different kinds
of things not allied in any other respect. And as for the properties
which, being effects of causes, we are able to give some account of, they
have generally nothing to do with the ultimate resemblances or diversities
in the objects themselves, but depend on some outward circumstances, under
the influence of which any objects whatever are capable of manifesting
those properties; as is emphatically the case with those favorite subjects
of Bacon’s scientific inquiries, hotness and coldness, as well as with
hardness and softness, solidity and fluidity, and many other conspicuous
qualities.

In the absence, then, of any universal law of co-existence similar to the
universal law of causation which regulates sequence, we are thrown back
upon the unscientific induction of the ancients, _per enumerationem
simplicem, ubi non reperitur instantia contradictoria_. The reason we have
for believing that all crows are black, is simply that we have seen and
heard of many black crows, and never one of any other color. It remains to
be considered how far this evidence can reach, and how we are to measure
its strength in any given case.

§ 5. It sometimes happens that a mere change in the mode of verbally
enunciating a question, though nothing is really added to the meaning
expressed, is of itself a considerable step toward its solution. This, I
think, happens in the present instance. The degree of certainty of any
generalization which rests on no other evidence than the agreement, so far
as it goes, of all past observation, is but another phrase for the degree
of improbability that an exception, if any existed, could have hitherto
remained unobserved. The reason for believing that all crows are black, is
measured by the improbability that crows of any other color should have
existed to the present time without our being aware of it. Let us state
the question in this last mode, and consider what is implied in the
supposition that there may be crows which are not black, and under what
conditions we can be justified in regarding this as incredible.

If there really exist crows which are not black, one of two things must be
the fact. Either the circumstance of blackness, in all crows hitherto
observed, must be, as it were, an accident, not connected with any
distinction of Kind; or if it be a property of Kind, the crows which are
not black must be a new Kind, a Kind hitherto overlooked, though coming
under the same general description by which crows have hitherto been
characterized. The first supposition would be proved true if we were to
discover casually a white crow among black ones, or if it were found that
black crows sometimes turn white. The second would be shown to be the fact
if in Australia or Central Africa a species or a race of white or gray
crows were found to exist.

§ 6. The former of these suppositions necessarily implies that the color
is an effect of causation. If blackness, in the crows in which it has been
observed, be not a property of Kind, but can be present or absent without
any difference generally in the properties of the object, then it is not
an ultimate fact in the individuals themselves, but is certainly dependent
on a cause. There are, no doubt, many properties which vary from
individual to individual of the same Kind, even the same _infima species_,
or lowest Kind. Some flowers may be either white or red, without differing
in any other respect. But these properties are not ultimate; they depend
on causes. So far as the properties of a thing belong to its own nature,
and do not arise from some cause extrinsic to it, they are always the same
in the same Kind. Take, for instance, all simple substances and elementary
powers; the only things of which we are certain that some at least of
their properties are really ultimate. Color is generally esteemed the most
variable of all properties: yet we do not find that sulphur is sometimes
yellow and sometimes white, or that it varies in color at all, except so
far as color is the effect of some extrinsic cause, as of the sort of
light thrown upon it, the mechanical arrangement of the particles (as
after fusion), etc. We do not find that iron is sometimes fluid and
sometimes solid at the same temperature; gold sometimes malleable and
sometimes brittle; that hydrogen will sometimes combine with oxygen and
sometimes not; or the like. If from simple substances we pass to any of
their definite compounds, as water, lime, or sulphuric acid, there is the
same constancy in their properties. When properties vary from individual
to individual, it is either in the case of miscellaneous aggregations,
such as atmospheric air or rock, composed of heterogeneous substances, and
not constituting or belonging to any real Kind,(191) or it is in the case
of organic beings. In them, indeed, there is variability in a high degree.
Animals of the same species and race, human beings of the same age, sex,
and country, will be most different, for example, in face and figure. But
organized beings (from the extreme complication of the laws by which they
are regulated) being more eminently modifiable, that is, liable to be
influenced by a greater number and variety of causes, than any other
phenomena whatever; having also themselves had a beginning, and therefore
a cause; there is reason to believe that none of their properties are
ultimate, but all of them derivative, and produced by causation. And the
presumption is confirmed, by the fact that the properties which vary from
one individual to another, also generally vary more or less at different
times in the same individual; which variation, like any other event,
supposes a cause, and implies, consequently, that the properties are not
independent of causation.

If, therefore, blackness be merely accidental in crows, and capable of
varying while the Kind remains the same, its presence or absence is
doubtless no ultimate fact, but the effect of some unknown cause: and in
that case the universality of the experience that all crows are black is
sufficient proof of a common cause, and establishes the generalization as
an empirical law. Since there are innumerable instances in the
affirmative, and hitherto none at all in the negative, the causes on which
the property depends must exist everywhere in the limits of the
observations which have been made; and the proposition may be received as
universal within those limits, and with the allowable degree of extension
to adjacent cases.

§ 7. If, in the second place, the property, in the instances in which it
has been observed, is not an effect of causation, it is a property of
Kind; and in that case the generalization can only be set aside by the
discovery of a new Kind of crow. That, however, a peculiar Kind not
hitherto discovered should exist in nature, is a supposition so often
realized that it can not be considered at all improbable. We have nothing
to authorize us in attempting to limit the Kinds of things which exist in
nature. The only unlikelihood would be that a new Kind should be
discovered in localities which there was previously reason to believe had
been thoroughly explored; and even this improbability depends on the
degree of conspicuousness of the difference between the newly-discovered
Kind and all others, since new kinds of minerals, plants, and even
animals, previously overlooked or confounded with known species, are still
continually detected in the most frequented situations. On this second
ground, therefore, as well as on the first, the observed uniformity of
co-existence can only hold good as an empirical law, within the limits not
only of actual observation, but of an observation as accurate as the
nature of the case required. And hence it is that (as remarked in an early
chapter of the present book) we so often give up generalizations of this
class at the first summons. If any credible witness stated that he had
seen a white crow, under circumstances which made it not incredible that
it should have escaped notice previously, we should give full credence to
the statement.

It appears, then, that the uniformities which obtain in the co-existence
of phenomena—those which we have reason to consider as ultimate, no less
than those which arise from the laws of causes yet undetected—are entitled
to reception only as empirical laws; are not to be presumed true except
within the limits of time, place, and circumstance, in which the
observations were made, or except in cases strictly adjacent.

§ 8. We have seen in the last chapter that there is a point of generality
at which empirical laws become as certain as laws of nature, or, rather,
at which there is no longer any distinction between empirical laws and
laws of nature. As empirical laws approach this point, in other words, as
they rise in their degree of generality, they become more certain; their
universality may be more strongly relied on. For, in the first place, if
they are results of causation (which, even in the class of uniformities
treated of in the present chapter, we never can be certain that they are
not) the more general they are, the greater is proved to be the space over
which the necessary collocations prevail, and within which no causes exist
capable of counteracting the unknown causes on which the empirical law
depends. To say that any thing is an invariable property of some very
limited class of objects, is to say that it invariably accompanies some
very numerous and complex group of distinguishing properties; which, if
causation be at all concerned in the matter, argues a combination of many
causes, and therefore a great liability to counteraction; while the
comparatively narrow range of the observations renders it impossible to
predict to what extent unknown counteracting causes may be distributed
throughout nature. But when a generalization has been found to hold good
of a very large proportion of all things whatever, it is already proved
that nearly all the causes which exist in nature have no power over it;
that very few changes in the combination of causes can affect it; since
the greater number of possible combinations must have already existed in
some one or other of the instances in which it has been found true. If,
therefore, any empirical law is a result of causation, the more general it
is, the more it may be depended on. And even if it be no result of
causation, but an ultimate co-existence, the more general it is, the
greater amount of experience it is derived from, and the greater therefore
is the probability that if exceptions had existed, some would already have
presented themselves.

For these reasons, it requires much more evidence to establish an
exception to one of the more general empirical laws than to the more
special ones. We should not have any difficulty in believing that there
might be a new Kind of crow; or a new kind of bird resembling a crow in
the properties hitherto considered distinctive of that Kind. But it would
require stronger proof to convince us of the existence of a Kind of crow
having properties at variance with any generally recognized universal
property of birds; and a still higher degree if the properties conflict
with any recognized universal property of animals. And this is conformable
to the mode of judgment recommended by the common sense and general
practice of mankind, who are more incredulous as to any novelties in
nature, according to the degree of generality of the experience which
these novelties seem to contradict.

§ 9. It is conceivable that the alleged properties might conflict with
some recognized universal property of all matter. In that case their
improbability would be at the highest, but would not even then amount to
incredibility. There are only two known properties common to all matter;
in other words, there is but one known uniformity of co-existence of
properties co-extensive with all physical nature, namely, that whatever
opposes resistance to movement gravitates, or, as Professor Bain expresses
it, Inertia and Gravity are co-existent through all matter, and
proportionate in their amount. These properties, as he truly says, are not
mutually implicated; from neither of them could we, on grounds of
causation, presume the other. But, for this very reason, we are never
certain that a Kind may not be discovered possessing one of the properties
without the other. The hypothetical ether, if it exists, may be such a
Kind. Our senses can not recognize in it either resistance or gravity; but
if the reality of a resisting medium should eventually be proved (by
alteration, for example, in the times of revolution of periodic comets,
combined with the evidences afforded by the phenomena of light and heat),
it would be rash to conclude from this alone, without other proofs, that
it must gravitate.

For even the greater generalizations, which embrace comprehensive Kinds
containing under them a great number and variety of _infimæ species_, are
only empirical laws, resting on induction by simple enumeration merely,
and not on any process of elimination—a process wholly inapplicable to
this sort of case. Such generalizations, therefore, ought to be grounded
on an examination of all the _infimæ species_ comprehended in them, and
not of a portion only. We can not conclude (where causation is not
concerned), because a proposition is true of a number of things resembling
one another only in being animals, that it is therefore true of all
animals. If, indeed, any thing be true of species which differ more from
one another than either differs from a third, especially if that third
species occupies in most of its known properties a position between the
two former, there is some probability that the same thing will also be
true of that intermediate species; for it is often, though by no means
universally, found, that there is a sort of parallelism in the properties
of different Kinds, and that their degree of unlikeness in one respect
bears some proportion to their unlikeness in others. We see this
parallelism in the properties of the different metals; in those of
sulphur, phosphorus, and carbon; of chlorine, iodine, and bromine; in the
natural orders of plants and animals, etc. But there are innumerable
anomalies and exceptions to this sort of conformity; if indeed the
conformity itself be any thing but an anomaly and an exception in nature.

Universal propositions, therefore, respecting the properties of superior
Kinds, unless grounded on proved or presumed connection by causation,
ought not to be hazarded except after separately examining every known
sub-kind included in the larger Kind. And even then such generalizations
must be held in readiness to be given up on the occurrence of some new
anomaly, which, when the uniformity is not derived from causation, can
never, even in the case of the most general of these empirical laws, be
considered very improbable. Thus, all the universal propositions which it
has been attempted to lay down respecting simple substances, or concerning
any of the classes which have been formed among simple substances (and the
attempt has been often made), have, with the progress of experience,
either faded into inanity, or been proved to be erroneous; and each Kind
of simple substance remains, with its own collection of properties apart
from the rest, saving a certain parallelism with a few other Kinds, the
most similar to itself. In organized beings, indeed, there are abundance
of propositions ascertained to be universally true of superior genera, to
many of which the discovery hereafter of any exceptions must be regarded
as extremely improbable. But these, as already observed, are, we have
every reason to believe, properties dependent on causation.(192)

Uniformities of co-existence, then, not only when they are consequences of
laws of succession, but also when they are ultimate truths, must be
ranked, for the purpose of logic, among empirical laws; and are amenable
in every respect to the same rules with those unresolved uniformities
which are known to be dependent on causation.(193)




                              Chapter XXIII.


Of Approximate Generalizations, And Probable Evidence.


§ 1. In our inquiries into the nature of the inductive process, we must
not confine our notice to such generalizations from experience as profess
to be universally true. There is a class of inductive truths avowedly not
universal; in which it is not pretended that the predicate is always true
of the subject; but the value of which, as generalizations, is
nevertheless extremely great. An important portion of the field of
inductive knowledge does not consist of universal truths, but of
approximations to such truths; and when a conclusion is said to rest on
probable evidence, the premises it is drawn from are usually
generalizations of this sort.

As every certain inference respecting a particular case implies that there
is ground for a general proposition of the form, every A is B; so does
every probable inference suppose that there is ground for a proposition of
the form, Most A are B; and the degree of probability of the inference in
an average case will depend on the proportion between the number of
instances existing in nature which accord with the generalization, and the
number of those which conflict with it.

§ 2. Propositions in the form, Most A are B, are of a very different
degree of importance in science, and in the practice of life. To the
scientific inquirer they are valuable chiefly as materials for, and steps
toward universal truths. The discovery of these is the proper end of
science; its work is not done if it stops at the proposition that a
majority of A are B, without circumscribing that majority by some common
character, fitted to distinguish them from the minority. Independently of
the inferior precision of such imperfect generalizations, and the inferior
assurance with which they can be applied to individual cases, it is plain
that, compared with exact generalizations, they are almost useless as
means of discovering ulterior truths by way of deduction. We may, it is
true, by combining the proposition Most A are B, with a universal
proposition, Every B is C, arrive at the conclusion that Most A are C. But
when a second proposition of the approximate kind is introduced—or even
when there is but one, if that one be the major premise—nothing can, in
general, be positively concluded. When the major is Most B are D, then,
even if the minor be Every A is B, we can not infer that most A are D, or
with any certainty that even some A are D. Though the majority of the
class B have the attribute signified by D, the whole of the sub-class A
may belong to the minority.(194)

Though so little use can be made, in science, of approximate
generalizations, except as a stage on the road to something better, for
practical guidance they are often all we have to rely on. Even when
science has really determined the universal laws of any phenomenon, not
only are those laws generally too much encumbered with conditions to be
adapted for everyday use, but the cases which present themselves in life
are too complicated, and our decisions require to be taken too rapidly, to
admit of waiting till the existence of a phenomenon can be proved by what
have been scientifically ascertained to be universal marks of it. To be
indecisive and reluctant to act, because we have not evidence of a
perfectly conclusive character to act on, is a defect sometimes incident
to scientific minds, but which, wherever it exists, renders them unfit for
practical emergencies. If we would succeed in action, we must judge by
indications which, though they do not generally mislead us, sometimes do,
and must make up, as far as possible, for the incomplete conclusiveness of
any one indication, by obtaining others to corroborate it. The principles
of induction applicable to approximate generalization are therefore a not
less important subject of inquiry than the rules for the investigation of
universal truths; and might reasonably be expected to detain us almost as
long, were it not that these principles are mere corollaries from those
which have been already treated of.

§ 3. There are two sorts of cases in which we are forced to guide
ourselves by generalizations of the imperfect form, Most A are B. The
first is, when we have no others; when we have not been able to carry our
investigation of the laws of the phenomena any further; as in the
following propositions—Most dark-eyed persons have dark hair; Most springs
contain mineral substances; Most stratified formations contain fossils.
The importance of this class of generalizations is not very great; for,
though it frequently happens that we see no reason why that which is true
of most individuals of a class is not true of the remainder, nor are able
to bring the former under any general description which can distinguish
them from the latter, yet if we are willing to be satisfied with
propositions of a less degree of generality, and to break down the class A
into sub-classes, we may generally obtain a collection of propositions
exactly true. We do not know why most wood is lighter than water, nor can
we point out any general property which discriminates wood that is lighter
than water from that which is heavier. But we know exactly what species
are the one and what the other. And if we meet with a specimen not
conformable to any known species (the only case in which our previous
knowledge affords no other guidance than the approximate generalization),
we can generally make a specific experiment, which is a surer resource.

It often happens, however, that the proposition, Most A are B, is not the
ultimatum of our scientific attainments, though the knowledge we possess
beyond it can not conveniently be brought to bear upon the particular
instance. We may know well enough what circumstances distinguish the
portion of A which has the attribute B from the portion which has it not,
but may have no means, or may not have time, to examine whether those
characteristic circumstances exist or not in the individual case. This is
the situation we are generally in when the inquiry is of the kind called
moral, that is, of the kind which has in view to predict human actions. To
enable us to affirm any thing universally concerning the actions of
classes of human beings, the classification must be grounded on the
circumstances of their mental culture and habits, which in an individual
case are seldom exactly known; and classes grounded on these distinctions
would never precisely accord with those into which mankind are divided for
social purposes. All propositions which can be framed respecting the
actions of human beings as ordinarily classified, or as classified
according to any kind of outward indications, are merely approximate. We
can only say, Most persons of a particular age, profession, country, or
rank in society, have such and such qualities; or, Most persons, when
placed in certain circumstances, act in such and such a way. Not that we
do not often know well enough on what causes the qualities depend, or what
sort of persons they are who act in that particular way; but we have
seldom the means of knowing whether any individual person has been under
the influence of those causes, or is a person of that particular sort. We
could replace the approximate generalizations by propositions universally
true; but these would hardly ever be capable of being applied to practice.
We should be sure of our majors, but we should not be able to get minors
to fit; we are forced, therefore, to draw our conclusions from coarser and
more fallible indications.

§ 4. Proceeding now to consider what is to be regarded as sufficient
evidence of an approximate generalization, we can have no difficulty in at
once recognizing that, when admissible at all, it is admissible only as an
empirical law. Propositions of the form, Every A is B, are not necessarily
laws of causation, or ultimate uniformities of co-existence; propositions
like Most A are B, _can not_ be so. Propositions hitherto found true in
every observed instance may yet be no necessary consequence of laws of
causation, or of ultimate uniformities, and unless they are so, may, for
aught we know, be false beyond the limits of actual observation; still
more evidently must this be the case with propositions which are only true
in a mere majority of the observed instances.

There is some difference, however, in the degree of certainty of the
proposition, Most A are B, according as that approximate generalization
composes the whole of our knowledge of the subject, or not. Suppose,
first, that the former is the case. We know only that most A are B, not
why they are so, nor in what respect those which are differ from those
which are not. How, then, did we learn that most A are B? Precisely in the
manner in which we should have learned, had such happened to be the fact
that all A are B. We collected a number of instances sufficient to
eliminate chance, and, having done so, compared the number of instances in
the affirmative with the number in the negative. The result, like other
unresolved derivative laws, can be relied on solely within the limits not
only of place and time, but also of circumstance, under which its truth
has been actually observed; for, as we are supposed to be ignorant of the
causes which make the proposition true, we can not tell in what manner any
new circumstance might perhaps affect it. The proposition, Most judges are
inaccessible to bribes, would probably be found true of Englishmen,
Frenchmen, Germans, North Americans, and so forth; but if on this evidence
alone we extended the assertion to Orientals, we should step beyond the
limits, not only of place but of circumstance, within which the fact had
been observed, and should let in possibilities of the absence of the
determining causes, or the presence of counteracting ones, which might be
fatal to the approximate generalization.

In the case where the approximate proposition is not the ultimatum of our
scientific knowledge, but only the most available form of it for practical
guidance; where we know, not only that most A have the attribute B, but
also the causes of B, or some properties by which the portion of A which
has that attribute is distinguished from the portion which has it not, we
are rather more favorably situated than in the preceding case. For we have
now a double mode of ascertaining whether it be true that most A are B;
the direct mode, as before, and an indirect one, that of examining whether
the proposition admits of being deduced from the known cause, or from any
known criterion, of B. Let the question, for example, be whether most
Scotchmen can read? We may not have observed, or received the testimony of
others respecting, a sufficient number and variety of Scotchmen to
ascertain this fact; but when we consider that the cause of being able to
read is the having been taught it, another mode of determining the
question presents itself, namely, by inquiring whether most Scotchmen have
been sent to schools where reading is effectually taught. Of these two
modes, sometimes one and sometimes the other is the more available. In
some cases, the frequency of the effect is the more accessible to that
extensive and varied observation which is indispensable to the
establishment of an empirical law; at other times, the frequency of the
causes, or of some collateral indications. It commonly happens that
neither is susceptible of so satisfactory an induction as could be
desired, and that the grounds on which the conclusion is received are
compounded of both. Thus a person may believe that most Scotchmen can
read, because, so far as his information extends, most Scotchmen have been
sent to school, and most Scotch schools teach reading effectually; and
also because most of the Scotchmen whom he has known or heard of could
read; though neither of these two sets of observations may by itself
fulfill the necessary conditions of extent and variety.

Although the approximate generalization may in most cases be indispensable
for our guidance, even when we know the cause, or some certain mark, of
the attribute predicated, it needs hardly be observed that we may always
replace the uncertain indication by a certain one, in any case in which we
can actually recognize the existence of the cause or mark. For example, an
assertion is made by a witness, and the question is whether to believe it.
If we do not look to any of the individual circumstances of the case, we
have nothing to direct us but the approximate generalization, that truth
is more common than falsehood, or, in other words, that most persons, on
most occasions, speak truth. But if we consider in what circumstances the
cases where truth is spoken differ from those in which it is not, we find,
for instance, the following: the witness’s being an honest person or not;
his being an accurate observer or not; his having an interest to serve in
the matter or not. Now, not only may we be able to obtain other
approximate generalizations respecting the degree of frequency of these
various possibilities, but we may know which of them is positively
realized in the individual case. That the witness has or has not an
interest to serve, we perhaps know directly; and the other two points
indirectly, by means of marks; as, for example, from his conduct on some
former occasion; or from his reputation, which, though a very uncertain
mark, affords an approximate generalization (as, for instance, Most
persons who are believed to be honest by those with whom they have had
frequent dealings, are really so), which approaches nearer to a universal
truth than the approximate general proposition with which we set out,
viz., Most persons on most occasions speak truth.

As it seems unnecessary to dwell further on the question of the evidence
of approximate generalizations, we shall proceed to a not less important
topic, that of the cautions to be observed in arguing from these
incompletely universal propositions to particular cases.

§ 5. So far as regards the direct application of an approximate
generalization to an individual instance, this question presents no
difficulty. If the proposition, Most A are B, has been established, by a
sufficient induction, as an empirical law, we may conclude that any
particular A is B with a probability proportioned to the preponderance of
the number of affirmative instances over the number of exceptions. If it
has been found practicable to attain numerical precision in the data, a
corresponding degree of precision may be given to the evaluation of the
chances of error in the conclusion. If it can be established as an
empirical law that nine out of every ten A are B, there will be one chance
in ten of error in assuming that any A, not individually known to us, is a
B: but this of course holds only within the limits of time, place, and
circumstance, embraced in the observations, and therefore can not be
counted on for any sub-class or variety of A (or for A in any set of
external circumstances) which were not included in the average. It must be
added, that we can guide ourselves by the proposition, Nine out of every
ten A are B, only in cases of which we know nothing except that they fall
within the class A. For if we know, of any particular instances _i_, not
only that it falls under A, but to what species or variety of A it
belongs, we shall generally err in applying to _i_ the average struck for
the whole genus, from which the average corresponding to that species
alone would, in all probability, materially differ. And so if _i_, instead
of being a particular sort of instance, is an instance known to be under
the influence of a particular set of circumstances, the presumption drawn
from the numerical proportions in the whole genus would probably, in such
a case, only mislead. A general average should only be applied to cases
which are neither known, nor can be presumed, to be other than average
cases. Such averages, therefore, are commonly of little use for the
practical guidance of any affairs but those which concern large numbers.
Tables of the chances of life are useful to insurance offices, but they go
a very little way toward informing any one of the chances of his own life,
or any other life in which he is interested, since almost every life is
either better or worse than the average. Such averages can only be
considered as supplying the first term in a series of approximations; the
subsequent terms proceeding on an appreciation of the circumstances
belonging to the particular case.

§ 6. From the application of a single approximate generalization to
individual cases, we proceed to the application of two or more of them
together to the same case.

When a judgment applied to an individual instance is grounded on two
approximate generalizations taken in conjunction, the propositions may
cooperate toward the result in two different ways. In the one, each
proposition is separately applicable to the case in hand, and our object
in combining them is to give to the conclusion in that particular case the
double probability arising from the two propositions separately. This may
be called joining two probabilities by way of Addition; and the result is
a probability greater than either. The other mode is, when only one of the
propositions is directly applicable to the case, the second being only
applicable to it by virtue of the application of the first. This is
joining two probabilities by way of Ratiocination or Deduction; the result
of which is a less probability than either. The type of the first argument
is, Most A are B; most C are B; this thing is both an A and a C; therefore
it is probably a B. The type of the second is, Most A are B; most C are A;
this is a C; therefore it is probably an A, therefore it is probably a B.
The first is exemplified when we prove a fact by the testimony of two
unconnected witnesses; the second, when we adduce only the testimony of
one witness that he has heard the thing asserted by another. Or again, in
the first mode it may be argued that the accused committed the crime,
because he concealed himself, and because his clothes were stained with
blood; in the second, that he committed it because he washed or destroyed
his clothes, which is supposed to render it probable that they were
stained with blood. Instead of only two links, as in these instances, we
may suppose chains of any length. A chain of the former kind was termed by
Bentham(195) a self-corroborative chain of evidence; the second, a
self-infirmative chain.

When approximate generalizations are joined by way of addition, we may
deduce from the theory of probabilities laid down in a former chapter, in
what manner each of them adds to the probability of a conclusion which has
the warrant of them all.

If, on an average, two of every three As are Bs, and three of every four
Cs are Bs, the probability that something which is both an A and a C is a
B, will be more than two in three, or than three in four. Of every twelve
things which are As, all except four are Bs by the supposition; and if the
whole twelve, and consequently those four, have the characters of C
likewise, three of these will be Bs on that ground. Therefore, out of
twelve which are both As and Cs, eleven are Bs. To state the argument in
another way; a thing which is both an A and a C, but which is not a B, is
found in only one of three sections of the class A, and in only one of
four sections of the class C; but this fourth of C being spread over the
whole of A indiscriminately, only one-third part of it (or one-twelfth of
the whole number) belongs to the third section of A; therefore a thing
which is not a B occurs only once, among twelve things which are both As
and Cs. The argument would, in the language of the doctrine of chances, be
thus expressed: the chance that an A is not a B is 1/3, the chance that a
C is not a B is 1/4; hence if the thing be both an A and a C, the chance
is 1/3 of 1/4 = 1/12.(196)

In this computation it is of course supposed that the probabilities
arising from A and C are independent of each other. There must not be any
such connection between A and C, that when a thing belongs to the one
class it will therefore belong to the other, or even have a greater chance
of doing so. Otherwise the not-Bs which are Cs may be, most or even all of
them, identical with the not-Bs which are As; in which last case the
probability arising from A and C together will be no greater than that
arising from A alone.

When approximate generalizations are joined together in the other mode,
that of deduction, the degree of probability of the inference, instead of
increasing, diminishes at each step. From two such premises as Most A are
B, Most B are C, we can not with certainty conclude that even a single A
is C; for the whole of the portion of A which in any way falls under B,
may perhaps be comprised in the exceptional part of it. Still, the two
propositions in question afford an appreciable probability that any given
A is C, provided the average on which the second proposition is grounded
was taken fairly with reference to the first; provided the proposition,
Most B are C, was arrived at in a manner leaving no suspicion that the
probability arising from it is otherwise than fairly distributed over the
section of B which belongs to A. For though the instances which are A
_may_ be all in the minority, they may, also, be all in the majority; and
the one possibility is to be set against the other. On the whole, the
probability arising from the two propositions taken together, will be
correctly measured by the probability arising from the one, abated in the
ratio of that arising from the other. If nine out of ten Swedes have light
hair, and eight out of nine inhabitants of Stockholm are Swedes, the
probability arising from these two propositions, that any given inhabitant
of Stockholm is light-haired, will amount to eight in ten; though it is
rigorously possible that the whole Swedish population of Stockholm might
belong to that tenth section of the people of Sweden who are an exception
to the rest.

If the premises are known to be true not of a bare majority, but of nearly
the whole, of their respective subjects, we may go on joining one such
proposition to another for several steps, before we reach a conclusion not
presumably true even of a majority. The error of the conclusion will
amount to the aggregate of the errors of all the premises. Let the
proposition, most A are B, be true of nine in ten; Most B are C, of eight
in nine; then not only will one A in ten not be C, because not B, but even
of the nine-tenths which are B, only eight-ninths will be C; that is, the
cases of A which are C will be only 8/9 of 9/10, or four-fifths. Let us
now add Most C are D, and suppose this to be true of seven cases out of
eight; the proportion of A which is D will be only 7/8 of 8/9 of 9/10, or
7/10. Thus the probability progressively dwindles. The experience,
however, on which our approximate generalizations are grounded, has so
rarely been subjected to, or admits of, accurate numerical estimation,
that we can not in general apply any measurement to the diminution of
probability which takes place at each illation; but must be content with
remembering that it does diminish at every step, and that unless the
premises approach very nearly indeed to being universally true, the
conclusion after a very few steps is worth nothing. A hearsay of a
hearsay, or an argument from presumptive evidence depending not on
immediate marks but on marks of marks, is worthless at a very few removes
from the first stage.

§ 7. There are, however, two cases in which reasonings depending on
approximate generalizations may be carried to any length we please with as
much assurance, and are as strictly scientific, as if they were composed
of universal laws of nature. But these cases are exceptions of the sort
which are currently said to prove the rule. The approximate
generalizations are as suitable, in the cases in question, for purposes of
ratiocination, as if they were complete generalizations, because they are
capable of being transformed into complete generalizations exactly
equivalent.

First: If the approximate generalization is of the class in which our
reason for stopping at the approximation is not the impossibility, but
only the inconvenience, of going further; if we are cognizant of the
character which distinguishes the cases that accord with the
generalization from those which are exceptions to it; we may then
substitute for the approximate proposition, a universal proposition with a
proviso. The proposition, Most persons who have uncontrolled power employ
it ill, is a generalization of this class, and may be transformed into the
following: All persons who have uncontrolled power employ it ill, provided
they are not persons of unusual strength of judgment and rectitude of
purpose. The proposition, carrying the hypothesis or proviso with it, may
then be dealt with no longer as an approximate, but as a universal
proposition; and to whatever number of steps the reasoning may reach, the
hypothesis, being carried forward to the conclusion, will exactly indicate
how far that conclusion is from being applicable universally. If in the
course of the argument other approximate generalizations are introduced,
each of them being in like manner expressed as a universal proposition
with a condition annexed, the sum of all the conditions will appear at the
end as the sum of all the errors which affect the conclusion. Thus, to the
proposition last cited, let us add the following: All absolute monarchs
have uncontrolled power, unless their position is such that they need the
active support of their subjects (as was the case with Queen Elizabeth,
Frederick of Prussia, and others). Combining these two propositions, we
can deduce from them a universal conclusion, which will be subject to both
the hypotheses in the premises; All absolute monarchs employ their power
ill, unless their position makes them need the active support of their
subjects, or unless they are persons of unusual strength of judgment and
rectitude of purpose. It is of no consequence how rapidly the errors in
our premises accumulate, if we are able in this manner to record each
error, and keep an account of the aggregate as it swells up.

Secondly: there is a case in which approximate propositions, even without
our taking note of the conditions under which they are not true of
individual cases, are yet, for the purposes of science, universal ones;
namely, in the inquiries which relate to the properties not of
individuals, but of multitudes. The principal of these is the science of
politics, or of human society. This science is principally concerned with
the actions not of solitary individuals, but of masses; with the fortunes
not of single persons, but of communities. For the statesman, therefore,
it is generally enough to know that _most_ persons act or are acted upon
in a particular way; since his speculations and his practical arrangements
refer almost exclusively to cases in which the whole community, or some
large portion of it, is acted upon at once, and in which, therefore, what
is done or felt by _most_ persons determines the result produced by or
upon the body at large. He can get on well enough with approximate
generalizations on human nature, since what is true approximately of all
individuals is true absolutely of all masses. And even when the operations
of individual men have a part to play in his deductions, as when he is
reasoning of kings, or other single rulers, still, as he is providing for
indefinite duration, involving an indefinite succession of such
individuals, he must in general both reason and act as if what is true of
most persons were true of all.

The two kinds of considerations above adduced are a sufficient refutation
of the popular error, that speculations on society and government, as
resting on merely probable evidence, must be inferior in certainty and
scientific accuracy to the conclusions of what are called the exact
sciences, and less to be relied on in practice. There are reasons enough
why the moral sciences must remain inferior to at least the more perfect
of the physical; why the laws of their more complicated phenomena can not
be so completely deciphered, nor the phenomena predicted with the same
degree of assurance. But though we can not attain to so many truths, there
is no reason that those we can attain should deserve less reliance, or
have less of a scientific character. Of this topic, however, I shall treat
more systematically in the concluding Book, to which place any further
consideration of it must be deferred.




                              Chapter XXIV.


Of The Remaining Laws Of Nature.


§ 1. In the First Book we found that all the assertions which can be
conveyed by language, express some one or more of five different things:
Existence; Order in Place; Order in Time; Causation; and Resemblance.(197)
Of these, Causation, in our view of the subject, not being fundamentally
different from Order in Time, the five species of possible assertions are
reduced to four. The propositions which affirm Order in Time in either of
its two modes, Co-existence and Succession, have formed, thus far, the
subject of the present Book. And we have now concluded the exposition, so
far as it falls within the limits assigned to this work, of the nature of
the evidence on which these propositions rest, and the processes of
investigation by which they are ascertained and proved. There remain three
classes of facts: Existence, Order in Place, and Resemblance; in regard to
which the same questions are now to be resolved.

Regarding the first of these, very little needs be said. Existence in
general, is a subject not for our science, but for metaphysics. To
determine what things can be recognized as really existing, independently
of our own sensible or other impressions, and in what meaning the term is,
in that case, predicated of them, belongs to the consideration of “Things
in themselves,” from which, throughout this work, we have as much as
possible kept aloof. Existence, so far as Logic is concerned about it, has
reference only to phenomena; to actual, or possible, states of external or
internal consciousness, in ourselves or others. Feelings of sensitive
beings, or possibilities of having such feelings, are the only things the
existence of which can be a subject of logical induction, because the only
things of which the existence in individual cases can be a subject of
experience.

It is true that a thing is said by us to exist, even when it is absent,
and therefore is not and can not be perceived. But even then, its
existence is to us only another word for our conviction that we should
perceive it on a certain supposition; namely, if we were in the needful
circumstances of time and place, and endowed with the needful perfection
of organs. My belief that the Emperor of China exists, is simply my belief
that if I were transported to the imperial palace or some other locality
in Pekin, I should see him. My belief that Julius Cæsar existed, is my
belief that I should have seen him if I had been present in the field of
Pharsalia, or in the senate-house at Rome. When I believe that stars exist
beyond the utmost range of my vision, though assisted by the most powerful
telescopes yet invented, my belief, philosophically expressed, is, that
with still better telescopes, if such existed, I could see them, or that
they may be perceived by beings less remote from them in space, or whose
capacities of perception are superior to mine.

The existence, therefore, of a phenomenon, is but another word for its
being perceived, or for the inferred possibility of perceiving it. When
the phenomenon is within the range of present observation, by present
observation we assure ourselves of its existence; when it is beyond that
range, and is therefore said to be absent, we infer its existence from
marks or evidences. But what can these evidences be? Other phenomena;
ascertained by induction to be connected with the given phenomenon, either
in the way of succession or of co-existence. The simple existence,
therefore, of an individual phenomenon, when not directly perceived, is
inferred from some inductive law of succession or co-existence; and is
consequently not amenable to any peculiar inductive principles. We prove
the existence of a thing, by proving that it is connected by succession or
co-existence with some known thing.

With respect to _general_ propositions of this class, that is, which
affirm the bare fact of existence, they have a peculiarity which renders
the logical treatment of them a very easy matter; they are generalizations
which are sufficiently proved by a single instance. That ghosts, or
unicorns, or sea-serpents exist, would be fully established if it could be
ascertained positively that such things had been even once seen. Whatever
has once happened, is capable of happening again; the only question
relates to the conditions under which it happens.

So far, therefore, as relates to simple existence, the Inductive Logic has
no knots to untie. And we may proceed to the remaining two of the great
classes into which facts have been divided; Resemblance, and Order in
Place.

§ 2. Resemblance and its opposite, except in the case in which they assume
the names of Equality and Inequality, are seldom regarded as subjects of
science; they are supposed to be perceived by simple apprehension; by
merely applying our senses or directing our attention to the two objects
at once, or in immediate succession. And this simultaneous, or virtually
simultaneous, application of our faculties to the two things which are to
be compared, does necessarily constitute the ultimate appeal, wherever
such application is practicable. But, in most cases, it is not
practicable: the objects can not be brought so close together that the
feeling of their resemblance (at least a complete feeling of it) directly
arises in the mind. We can only compare each of them with some third
object, capable of being transported from one to the other. And besides,
even when the objects can be brought into immediate juxtaposition, their
resemblance or difference is but imperfectly known to us, unless we have
compared them minutely, part by part. Until this has been done, things in
reality very dissimilar often appear undistinguishably alike. Two lines of
very unequal length will appear about equal when lying in different
directions; but place them parallel with their farther extremities even,
and if we look at the nearer extremities, their inequality becomes a
matter of direct perception.

To ascertain whether, and in what, two phenomena resemble or differ, is
not always, therefore, so easy a thing as it might at first appear. When
the two can not be brought into juxtaposition, or not so that the observer
is able to compare their several parts in detail, he must employ the
indirect means of reasoning and general propositions. When we can not
bring two straight lines together, to determine whether they are equal, we
do it by the physical aid of a foot-rule applied first to one and then to
the other, and the logical aid of the general proposition or formula,
“Things which are equal to the same thing are equal to one another.” The
comparison of two things through the intervention of a third thing, when
their direct comparison is impossible, is the appropriate scientific
process for ascertaining resemblances and dissimilarities, and is the sum
total of what Logic has to teach on the subject.

An undue extension of this remark induced Locke to consider reasoning
itself as nothing but the comparison of two ideas through the medium of a
third, and knowledge as the perception of the agreement or disagreement of
two ideas; doctrines which the Condillac school blindly adopted, without
the qualifications and distinctions with which they were studiously
guarded by their illustrious author. Where, indeed, the agreement or
disagreement (otherwise called resemblance or dissimilarity) of any two
things is the very matter to be determined, as is the case particularly in
the sciences of quantity and extension; there, the process by which a
solution, if not attainable by direct perception, must be indirectly
sought, consists in comparing these two things through the medium of a
third. But this is far from being true of all inquiries. The knowledge
that bodies fall to the ground is not a perception of agreement or
disagreement, but of a series of physical occurrences, a succession of
sensations. Locke’s definitions of knowledge and of reasoning required to
be limited to our knowledge of, and reasoning about, resemblances. Nor,
even when thus restricted, are the propositions strictly correct; since
the comparison is not made, as he represents, between the ideas of the two
phenomena, but between the phenomena themselves. This mistake has been
pointed out in an earlier part of our inquiry,(198) and we traced it to an
imperfect conception of what takes place in mathematics, where very often
the comparison is really made between the ideas, without any appeal to the
outward senses; only, however, because in mathematics a comparison of the
ideas is strictly equivalent to a comparison of the phenomena themselves.
Where, as in the case of numbers, lines, and figures, our idea of an
object is a complete picture of the object, so far as respects the matter
in hand; we can, of course, learn from the picture, whatever could be
learned from the object itself by mere contemplation of it as it exists at
the particular instant when the picture is taken. No mere contemplation of
gunpowder would ever teach us that a spark would make it explode, nor,
consequently, would the contemplation of the idea of gunpowder do so; but
the mere contemplation of a straight line shows that it can not inclose a
space; accordingly the contemplation of the idea of it will show the same.
What takes place in mathematics is thus no argument that the comparison is
between the ideas only. It is always, either indirectly or directly, a
comparison of the phenomena.

In cases in which we can not bring the phenomena to the test of direct
inspection at all, or not in a manner sufficiently precise, but must judge
of their resemblance by inference from other resemblances or
dissimilarities more accessible to observation, we of course require, as
in all cases of ratiocination, generalizations or formulæ applicable to
the subject. We must reason from laws of nature; from the uniformities
which are observable in the fact of likeness or unlikeness.

§ 3. Of these laws or uniformities, the most comprehensive are those
supplied by mathematics; the axioms relating to equality, inequality, and
proportionality, and the various theorems thereon founded. And these are
the only Laws of Resemblance which require to be, or which can be, treated
apart. It is true there are innumerable other theorems which affirm
resemblances among phenomena; as that the angle of the reflection of light
is _equal_ to its angle of incidence (equality being merely exact
resemblance in magnitude). Again, that the heavenly bodies describe
_equal_ areas in equal times; and that their periods of revolution are
_proportional_ (another species of resemblance) to the sesquiplicate
powers of their distances from the centre of force. These and similar
propositions affirm resemblances, of the same nature with those asserted
in the theorems of mathematics; but the distinction is, that the
propositions of mathematics are true of all phenomena whatever, or at
least without distinction of origin; while the truths in question are
affirmed only of special phenomena, which originate in a certain way; and
the equalities, proportionalities, or other resemblances, which exist
between such phenomena, must necessarily be either derived from, or
identical with, the law of their origin—the law of causation on which they
depend. The equality of the areas described in equal times by the planets,
is _derived_ from the laws of the causes; and, until its derivation was
shown, it was an empirical law. The equality of the angles of reflection
and incidence is _identical_ with the law of the cause; for the cause is
the incidence of a ray of light upon a reflecting surface, and the
equality in question is the very law according to which that cause
produces its effects. This class, therefore, of the uniformities of
resemblance between phenomena, are inseparable, in fact and in thought,
from the laws of the production of those phenomena; and the principles of
induction applicable to them are no other than those of which we have
treated in the preceding chapters of this Book.

It is otherwise with the truths of mathematics. The laws of equality and
inequality between spaces, or between numbers, have no connection with
laws of causation. That the angle of reflection is equal to the angle of
incidence, is a statement of the mode of action of a particular cause; but
that when two straight lines intersect each other the opposite angles are
equal, is true of all such lines and angles, by whatever cause produced.
That the squares of the periodic times of the planets are proportional to
the cubes of their distances from the sun, is a uniformity derived from
the laws of the causes (or forces) which produce the planetary motions;
but that the square of any number is four times the square of half the
number, is true independently of any cause. The only laws of resemblance,
therefore, which we are called upon to consider independently of
causation, belong to the province of mathematics.

§ 4. The same thing is evident with respect to the only one remaining of
our five categories, Order in Place. The order in place, of the effects of
a cause, is (like every thing else belonging to the effects) a consequence
of the laws of that cause. The order in place, or, as we have termed it,
the collocation, of the primeval causes, is (as well as their resemblance)
in each instance an ultimate fact, in which no laws or uniformities are
traceable. The only remaining general propositions respecting order in
place, and the only ones which have nothing to do with causation, are some
of the truths of geometry; laws through which we are able, from the order
in place of certain points, lines, or spaces, to infer the order in place
of others which are connected with the former in some known mode; quite
independently of the particular nature of those points, lines, or spaces,
in any other respect than position or magnitude, as well as independently
of the physical cause from which in any particular case they happen to
derive their origin.

It thus appears that mathematics is the only department of science into
the methods of which it still remains to inquire. And there is the less
necessity that this inquiry should occupy us long, as we have already, in
the Second Book, made considerable progress in it. We there remarked, that
the directly inductive truths of mathematics are few in number; consisting
of the axioms, together with certain propositions concerning existence,
tacitly involved in most of the so-called definitions. And we gave what
appeared conclusive reasons for affirming that these original premises,
from which the remaining truths of the science are deduced, are,
notwithstanding all appearances to the contrary, results of observation
and experience; founded, in short, on the evidence of the senses. That
things equal to the same thing are equal to one another, and that two
straight lines which have once intersected one another continue to
diverge, are inductive truths; resting, indeed, like the law of universal
causation, only on induction _per enumerationem simplicem_; on the fact
that they have been perpetually perceived to be true, and never once found
to be false. But, as we have seen in a recent chapter that this evidence,
in the case of a law so completely universal as the law of causation,
amounts to the fullest proof, so is this even more evidently true of the
general propositions to which we are now adverting; because, as a
perception of their truth in any individual case whatever, requires only
the simple act of looking at the objects in a proper position, there never
could have been in their case (what, for a long period, there were in the
case of the law of causation) instances which were apparently, though not
really, exceptions to them. Their infallible truth was recognized from the
very dawn of speculation; and as their extreme familiarity made it
impossible for the mind to conceive the objects under any other law, they
were, and still are, generally considered as truths recognized by their
own evidence, or by instinct.

§ 5. There is something which seems to require explanation, in the fact
that the immense multitude of truths (a multitude still as far from being
exhausted as ever) comprised in the mathematical sciences, can be elicited
from so small a number of elementary laws. One sees not, at first, how it
is that there can be room for such an infinite variety of true
propositions, on subjects apparently so limited.

To begin with the science of number. The elementary or ultimate truths of
this science are the common axioms concerning equality, namely, “Things
which are equal to the same thing are equal to one another,” and “Equals
added to equals make equal sums” (no other axioms are required),(199)
together with the definitions of the various numbers. Like other so-called
definitions, these are composed of two things, the explanation of a name,
and the assertion of a fact; of which the latter alone can form a first
principle or premise of a science. The fact asserted in the definition of
a number is a physical fact. Each of the numbers two, three, four, etc.,
denotes physical phenomena, and connotes a physical property of those
phenomena. Two, for instance, denotes all pairs of things, and twelve all
dozens of things, connoting what makes them pairs, or dozens; and that
which makes them so is something physical; since it can not be denied that
two apples are physically distinguishable from three apples, two horses
from one horse, and so forth; that they are a different visible and
tangible phenomenon. I am not undertaking to say what the difference is;
it is enough that there is a difference of which the senses can take
cognizance. And although a hundred and two horses are not so easily
distinguished from a hundred and three, as two horses are from
three—though in most positions the senses do not perceive any
difference—yet they may be so placed that a difference will be
perceptible, or else we should never have distinguished them, and given
them different names. Weight is confessedly a physical property of things;
yet small differences between great weights are as imperceptible to the
senses in most situations, as small differences between great numbers; and
are only put in evidence by placing the two objects in a peculiar
position—namely, in the opposite scales of a delicate balance.

What, then, is that which is connoted by a name of number? Of course, some
property belonging to the agglomeration of things which we call by the
name; and that property is, the characteristic manner in which the
agglomeration is made up of, and may be separated into, parts. I will
endeavor to make this more intelligible by a few explanations.

When we call a collection of objects _two_, _three_, or _four_, they are
not two, three, or four in the abstract; they are two, three, or four
things of some particular kind; pebbles, horses, inches, pounds’ weight.
What the name of number connotes is, the manner in which single objects of
the given kind must be put together, in order to produce that particular
aggregate. If the aggregate be of pebbles, and we call it _two_, the name
implies that, to compose the aggregate, one pebble must be joined to one
pebble. If we call it _three_, one and one and one pebble must be brought
together to produce it, or else one pebble must be joined to an aggregate
of the kind called _two_, already existing. The aggregate which we call
_four_, has a still greater number of characteristic modes of formation.
One and one and one and one pebble may be brought together; or two
aggregates of the kind called _two_ may be united; or one pebble may be
added to an aggregate of the kind called _three_. Every succeeding number
in the ascending series, may be formed by the junction of smaller numbers
in a progressively greater variety of ways. Even limiting the parts to
two, the number may be formed, and consequently may be divided, in as many
different ways as there are numbers smaller than itself; and, if we admit
of threes, fours, etc., in a still greater variety. Other modes of
arriving at the same aggregate present themselves, not by the union of
smaller, but by the dismemberment of larger aggregates. Thus, _three
pebbles_ may be formed by taking away one pebble from an aggregate of
four; _two pebbles_, by an equal division of a similar aggregate; and so
on.

Every arithmetical proposition; every statement of the result of an
arithmetical operation; is a statement of one of the modes of formation of
a given number. It affirms that a certain aggregate might have been formed
by putting together certain other aggregates, or by withdrawing certain
portions of some aggregate; and that, by consequence, we might reproduce
those aggregates from it, by reversing the process.

Thus, when we say that the cube of 12 is 1728, what we affirm is this:
that if, having a sufficient number of pebbles or of any other objects, we
put them together into the particular sort of parcels or aggregates called
twelves; and put together these twelves again into similar collections;
and, finally, make up twelve of these largest parcels; the aggregate thus
formed will be such a one as we call 1728; namely, that which (to take the
most familiar of its modes of formation) may be made by joining the parcel
called a thousand pebbles, the parcel called seven hundred pebbles, the
parcel called twenty pebbles, and the parcel called eight pebbles.

The converse proposition that the cube root of 1728 is 12, asserts that
this large aggregate may again be decomposed into the twelve twelves of
twelves of pebbles which it consists of.

The modes of formation of any number are innumerable; but when we know one
mode of formation of each, all the rest may be determined deductively. If
we know that _a_ is formed from _b_ and _c_, _b_ from _a_ and _e_, _c_
from _d_ and _f_, and so forth, until we have included all the numbers of
any scale we choose to select (taking care that for each number the mode
of formation be really a distinct one, not bringing us round again to the
former numbers, but introducing a new number), we have a set of
propositions from which we may reason to all the other modes of formation
of those numbers from one another. Having established a chain of inductive
truths connecting together all the numbers of the scale, we can ascertain
the formation of any one of those numbers from any other by merely
traveling from one to the other along the chain. Suppose that we know only
the following modes of formation: 6=4+2, 4=7-3, 7=5+2, 5=9-4. We could
determine how 6 may be formed from 9. For 6=4+2=7-3+2=5+2-3+2=9-4+2-3+2.
It may therefore be formed by taking away 4 and 3, and adding 2 and 2. If
we know besides that 2+2=4, we obtain 6 from 9 in a simpler mode, by
merely taking away 3.

It is sufficient, therefore, to select one of the various modes of
formation of each number, as a means of ascertaining all the rest. And
since things which are uniform, and therefore simple, are most easily
received and retained by the understanding, there is an obvious advantage
in selecting a mode of formation which shall be alike for all; in fixing
the connotation of names of number on one uniform principle. The mode in
which our existing numerical nomenclature is contrived possesses this
advantage, with the additional one, that it happily conveys to the mind
two of the modes of formation of every number. Each number is considered
as formed by the addition of a unit to the number next below it in
magnitude, and this mode of formation is conveyed by the place which it
occupies in the series. And each is also considered as formed by the
addition of a number of units less than ten, and a number of aggregates
each equal to one of the successive powers of ten; and this mode of its
formation is expressed by its spoken name, and by its numerical character.

What renders arithmetic the type of a deductive science, is the fortunate
applicability to it of a law so comprehensive as “The sums of equals are
equals:” or (to express the same principle in less familiar but more
characteristic language), Whatever is made up of parts, is made up of the
parts of those parts. This truth, obvious to the senses in all cases which
can be fairly referred to their decision, and so general as to be
co-extensive with nature itself, being true of all sorts of phenomena (for
all admit of being numbered), must be considered an inductive truth, or
law of nature, of the highest order. And every arithmetical operation is
an application of this law, or of other laws capable of being deduced from
it. This is our warrant for all calculations. We believe that five and two
are equal to seven, on the evidence of this inductive law, combined with
the definitions of those numbers. We arrive at that conclusion (as all
know who remember how they first learned it) by adding a single unit at a
time: 5 + 1=6, therefore 5+1+1=6+1=7; and again 2=1+1, therefore
5+2=5+1+1=7.

§ 6. Innumerable as are the true propositions which can be formed
concerning particular numbers, no adequate conception could be gained,
from these alone, of the extent of the truths composing the science of
number. Such propositions as we have spoken of are the least general of
all numerical truths. It is true that even these are co-extensive with all
nature; the properties of the number four are true of all objects that are
divisible into four equal parts, and all objects are either actually or
ideally so divisible. But the propositions which compose the science of
algebra are true, not of a particular number, but of all numbers; not of
all things under the condition of being divided in a particular way, but
of all things under the condition of being divided in any way—of being
designated by a number at all.

Since it is impossible for different numbers to have any of their modes of
formation completely in common, it is a kind of paradox to say, that all
propositions which can be made concerning numbers relate to their modes of
formation from other numbers, and yet that there are propositions which
are true of all numbers. But this very paradox leads to the real principle
of generalization concerning the properties of numbers. Two different
numbers can not be formed in the same manner from the same numbers; but
they may be formed in the same manner from different numbers; as nine is
formed from three by multiplying it into itself, and sixteen is formed
from four by the same process. Thus there arises a classification of modes
of formation, or in the language commonly used by mathematicians, a
classification of Functions. Any number, considered as formed from any
other number, is called a function of it; and there are as many kinds of
functions as there are modes of formation. The simple functions are by no
means numerous, most functions being formed by the combination of several
of the operations which form simple functions, or by successive
repetitions of some one of those operations. The simple functions of any
number _x_ are all reducible to the following forms: _x_+_a_, _x_-_a_,
_ax_, _x_/_a_, log. _x_ (to the base _a_), and the same expressions varied
by putting _x_ for _a_ and _a_ for _x_, wherever that substitution would
alter the value: to which, perhaps, ought to be added sin _x_, and arc
(sin=_x_). All other functions of _x_ are formed by putting some one or
more of the simple functions in the place of _x_ or _a_, and subjecting
them to the same elementary operations.

In order to carry on general reasonings on the subject of Functions, we
require a nomenclature enabling us to express any two numbers by names
which, without specifying what particular numbers they are, shall show
what function each is of the other; or, in other words, shall put in
evidence their mode of formation from one another. The system of general
language called algebraical notation does this. The expressions _a_ and
a2+3a denote, the one any number, the other the number formed from it in a
particular manner. The expressions _a_, _b_, _n_, and (_a+b_)n, denote any
three numbers, and a fourth which is formed from them in a certain mode.

The following may be stated as the general problem of the algebraical
calculus: F being a certain function of a given number, to find what
function F will be of any function of that number. For example, a binomial
_a + b_ is a function of its two parts _a_ and _b_, and the parts are, in
their turn, functions of _a + b_: now (_a + b_)n is a certain function of
the binomial; what function will this be of _a_ and _b_, the two parts?
The answer to this question is the binomial theorem. The formula _(a +
b)__n__ = a__n__ + n/1 a__n-1__ b + n.n-1/1.2 a__n-2__ b__2_, etc., shows
in what manner the number which is formed by multiplying _a + b_ into
itself _n_ times, might be formed without that process, directly from _a,
b_, and _n_. And of this nature are all the theorems of the science of
number. They assert the identity of the result of different modes of
formation. They affirm that some mode of formation from _x_, and some mode
of formation from a certain function of _x_, produce the same number.

Such, as above described, is the aim and end of the calculus. As for its
processes, every one knows that they are simply deductive. In
demonstrating an algebraical theorem, or in resolving an equation, we
travel from the _datum_ to the _quæsitum_ by pure ratiocination; in which
the only premises introduced, besides the original hypotheses, are the
fundamental axioms already mentioned—that things equal to the same thing
are equal to one another, and that the sums of equal things are equal. At
each step in the demonstration or in the calculation, we apply one or
other of these truths, or truths deducible from them, as, that the
differences, products, etc., of equal numbers are equal.

It would be inconsistent with the scale of this work, and not necessary to
its design, to carry the analysis of the truths and processes of algebra
any further; which is also the less needful, as the task has been, to a
very great extent, performed by other writers. Peacock’s Algebra, and Dr.
Whewell’s _Doctrine of Limits_, are full of instruction on the subject.
The profound treatises of a truly philosophical mathematician, Professor
De Morgan, should be studied by every one who desires to comprehend the
evidence of mathematical truths, and the meaning of the obscurer processes
of the calculus, and the speculations of M. Comte, in his _Cours de
Philosophie Positive_, on the philosophy of the higher branches of
mathematics, are among the many valuable gifts for which philosophy is
indebted to that eminent thinker.

§ 7. If the extreme generality, and remoteness not so much from sense as
from the visual and tactual imagination, of the laws of number, renders it
a somewhat difficult effort of abstraction to conceive those laws as being
in reality physical truths obtained by observation; the same difficulty
does not exist with regard to the laws of extension. The facts of which
those laws are expressions, are of a kind peculiarly accessible to the
senses, and suggesting eminently distinct images to the fancy. That
geometry is a strictly physical science would doubtless have been
recognized in all ages, had it not been for the illusions produced by two
circumstances. One of these is the characteristic property, already
noticed, of the facts of geometry, that they may be collected from our
ideas or mental pictures of objects as effectually as from the objects
themselves. The other is, the demonstrative character of geometrical
truths; which was at one time supposed to constitute a radical distinction
between them and physical truths; the latter, as resting on merely
probable evidence, being deemed essentially uncertain and unprecise. The
advance of knowledge has, however, made it manifest that physical science,
in its better understood branches, is quite as demonstrative as geometry.
The task of deducing its details from a few comparatively simple
principles is found to be any thing but the impossibility it was once
supposed to be; and the notion of the superior certainty of geometry is an
illusion, arising from the ancient prejudice which, in that science,
mistakes the ideal data from which we reason, for a peculiar class of
realities, while the corresponding ideal data of any deductive physical
science are recognized as what they really are, hypotheses.

Every theorem in geometry is a law of external nature, and might have been
ascertained by generalizing from observation and experiment, which in this
case resolve themselves into comparison and measurement. But it was found
practicable, and, being practicable, was desirable, to deduce these truths
by ratiocination from a small number of general laws of nature, the
certainty and universality of which are obvious to the most careless
observer, and which compose the first principles and ultimate premises of
the science. Among these general laws must be included the same two which
we have noticed as ultimate principles of the Science of Number also, and
which are applicable to every description of quantity; viz., The sums of
equals are equal, and Things which are equal to the same thing are equal
to one another; the latter of which may be expressed in a manner more
suggestive of the inexhaustible multitude of its consequences, by the
following terms: Whatever is equal to any one of a number of equal
magnitudes, is equal to any other of them. To these two must be added, in
geometry, a third law of equality, namely, that lines, surfaces, or solid
spaces, which can be so applied to one another as to coincide, are equal.
Some writers have asserted that this law of nature is a mere verbal
definition; that the expression “equal magnitudes” _means_ nothing but
magnitudes which can be so applied to one another as to coincide. But in
this opinion I can not agree. The equality of two geometrical magnitudes
can not differ fundamentally in its nature from the equality of two
weights, two degrees of heat, or two portions of duration, to none of
which would this definition of equality be suitable. None of these things
can be so applied to one another as to coincide, yet we perfectly
understand what we mean when we call them equal. Things are equal in
magnitude, as things are equal in weight, when they are felt to be exactly
similar in respect of the attribute in which we compare them: and the
application of the objects to each other in the one case, like the
balancing them with a pair of scales in the other, is but a mode of
bringing them into a position in which our senses can recognize
deficiencies of exact resemblance that would otherwise escape our notice.

Along with these three general principles or axioms, the remainder of the
premises of geometry consists of the so-called definitions: that is to
say, propositions asserting the real existence of the various objects
therein designated, together with some one property of each. In some cases
more than one property is commonly assumed, but in no case is more than
one necessary. It is assumed that there are such things in nature as
straight lines, and that any two of them setting out from the same point,
diverge more and more without limit. This assumption (which includes and
goes beyond Euclid’s axiom that two straight lines can not inclose a
space) is as indispensable in geometry, and as evident, resting on as
simple, familiar, and universal observation, as any of the other axioms.
It is also assumed that straight lines diverge from one another in
different degrees; in other words, that there are such things as angles,
and that they are capable of being equal or unequal. It is assumed that
there is such a thing as a circle, and that all its radii are equal; such
things as ellipses, and that the sums of the focal distances are equal for
every point in an ellipse; such things as parallel lines, and that those
lines are everywhere equally distant.(200)

§ 8. It is a matter of more than curiosity to consider, to what
peculiarity of the physical truths which are the subject of geometry, it
is owing that they can all be deduced from so small a number of original
premises; why it is that we can set out from only one characteristic
property of each kind of phenomenon, and with that and two or three
general truths relating to equality, can travel from mark to mark until we
obtain a vast body of derivative truths, to all appearance extremely
unlike those elementary ones.

The explanation of this remarkable fact seems to lie in the following
circumstances. In the first place, all questions of position and figure
may be resolved into questions of magnitude. The position and figure of
any object are determined by determining the position of a sufficient
number of points in it; and the position of any point may be determined by
the magnitude of three rectangular co-ordinates, that is, of the
perpendiculars drawn from the point to three planes at right angles to one
another, arbitrarily selected. By this transformation of all questions of
quality into questions only of quantity, geometry is reduced to the single
problem of the measurement of magnitudes, that is, the ascertainment of
the equalities which exist between them. Now when we consider that by one
of the general axioms, any equality, when ascertained, is proof of as many
other equalities as there are other things equal to either of the two
equals; and that by another of those axioms, any ascertained equality is
proof of the equality of as many pairs of magnitudes as can be formed by
the numerous operations which resolve themselves into the addition of the
equals to themselves or to other equals; we cease to wonder that in
proportion as a science is conversant about equality, it should afford a
more copious supply of marks of marks; and that the sciences of number and
extension, which are conversant with little else than equality, should be
the most deductive of all the sciences.

There are also two or three of the principal laws of space or extension
which are unusually fitted for rendering one position or magnitude a mark
of another, and thereby contributing to render the science largely
deductive. First, the magnitudes of inclosed spaces, whether superficial
or solid, are completely determined by the magnitudes of the lines and
angles which bound them. Secondly, the length of any line, whether
straight or curve, is measured (certain other things being given) by the
angle which it subtends, and _vicè versa_. Lastly, the angle which any two
straight lines make with each other at an inaccessible point, is measured
by the angles they severally make with any third line we choose to select.
By means of these general laws, the measurement of all lines, angles, and
spaces whatsoever might be accomplished by measuring a single straight
line and a sufficient number of angles; which is the plan actually pursued
in the trigonometrical survey of a country; and fortunate it is that this
is practicable, the exact measurement of long straight lines being always
difficult, and often impossible, but that of angles very easy. Three such
generalizations as the foregoing afford such facilities for the indirect
measurement of magnitudes (by supplying us with known lines or angles
which are marks of the magnitude of unknown ones, and thereby of the
spaces which they inclose), that it is easily intelligible how from a few
data we can go on to ascertain the magnitude of an indefinite multitude of
lines, angles, and spaces, which we could not easily, or could not at all,
measure by any more direct process.

§ 9. Such are the remarks which it seems necessary to make in this place,
respecting the laws of nature which are the peculiar subject of the
sciences of number and extension. The immense part which those laws take
in giving a deductive character to the other departments of physical
science, is well known; and is not surprising, when we consider that all
causes operate according to mathematical laws. The effect is always
dependent on, or is a function of, the quantity of the agent; and
generally of its position also. We can not, therefore, reason respecting
causation, without introducing considerations of quantity and extension at
every step; and if the nature of the phenomena admits of our obtaining
numerical data of sufficient accuracy, the laws of quantity become the
grand instrument for calculating forward to an effect, or backward to a
cause. That in all other sciences, as well as in geometry, questions of
quality are scarcely ever independent of questions of quantity, may be
seen from the most familiar phenomena. Even when several colors are mixed
on a painter’s palette, the comparative quantity of each entirely
determines the color of the mixture.

With this mere suggestion of the general causes which render mathematical
principles and processes so predominant in those deductive sciences which
afford precise numerical data, I must, on the present occasion, content
myself; referring the reader who desires a more thorough acquaintance with
the subject, to the first two volumes of M. Comte’s systematic work.

In the same work, and more particularly in the third volume, are also
fully discussed the limits of the applicability of mathematical principles
to the improvement of other sciences. Such principles are manifestly
inapplicable, where the causes on which any class of phenomena depend are
so imperfectly accessible to our observation, that we can not ascertain,
by a proper induction, their numerical laws; or where the causes are so
numerous, and intermixed in so complex a manner with one another, that
even supposing their laws known, the computation of the aggregate effect
transcends the powers of the calculus as it is, or is likely to be; or,
lastly, where the causes themselves are in a state of perpetual
fluctuation; as in physiology, and still more, if possible, in the social
science. The mathematical solutions of physical questions become
progressively more difficult and imperfect, in proportion as the questions
divest themselves of their abstract and hypothetical character, and
approach nearer to the degree of complication actually existing in nature;
insomuch that beyond the limits of astronomical phenomena, and of those
most nearly analogous to them, mathematical accuracy is generally obtained
“at the expense of the reality of the inquiry:” while even in astronomical
questions, “notwithstanding the admirable simplicity of their mathematical
elements, our feeble intelligence becomes incapable of following out
effectually the logical combinations of the laws on which the phenomena
are dependent, as soon as we attempt to take into simultaneous
consideration more than two or three essential influences.”(201) Of this,
the problem of the Three Bodies has already been cited, more than once, as
a remarkable instance; the complete solution of so comparatively simple a
question having vainly tried the skill of the most profound
mathematicians. We may conceive, then, how chimerical would be the hope
that mathematical principles could be advantageously applied to phenomena
dependent on the mutual action of the innumerable minute particles of
bodies, as those of chemistry, and still more, of physiology; and for
similar reasons those principles remain inapplicable to the still more
complex inquiries, the subjects of which are phenomena of society and
government.

The value of mathematical instruction as a preparation for those more
difficult investigations, consists in the applicability not of its
doctrines, but of its method. Mathematics will ever remain the most
perfect type of the Deductive Method in general; and the applications of
mathematics to the deductive branches of physics, furnish the only school
in which philosophers can effectually learn the most difficult and
important portion of their art, the employment of the laws of simpler
phenomena for explaining and predicting those of the more complex. These
grounds are quite sufficient for deeming mathematical training an
indispensable basis of real scientific education, and regarding (according
to the _dictum_ which an old but unauthentic tradition ascribes to Plato)
one who is ἀγεωμέτρητος, as wanting in one of the most essential
qualifications for the successful cultivation of the higher branches of
philosophy.




                               Chapter XXV.


Of The Grounds Of Disbelief.


§ 1. The method of arriving at general truths, or general propositions fit
to be believed, and the nature of the evidence on which they are grounded,
have been discussed, as far as space and the writer’s faculties permitted,
in the twenty-four preceding chapters. But the result of the examination
of evidence is not always belief, nor even suspension of judgment; it is
sometimes disbelief. The philosophy, therefore, of induction and
experimental inquiry is incomplete, unless the grounds not only of belief,
but of disbelief, are treated of; and to this topic we shall devote one,
and the final, chapter.

By disbelief is not here to be understood the mere absence of belief. The
ground for abstaining from belief is simply the absence or insufficiency
of proof; and in considering what is sufficient evidence to support any
given conclusion, we have already, by implication, considered what
evidence is not sufficient for the same purpose. By disbelief is here
meant, not the state of mind in which we form no opinion concerning a
subject, but that in which we are fully persuaded that some opinion is not
true; insomuch that if evidence, even of great apparent strength (whether
grounded on the testimony of others or on our own supposed perceptions),
were produced in favor of the opinion, we should believe that the
witnesses spoke falsely, or that they, or we ourselves if we were the
direct percipients, were mistaken.

That there are such cases, no one is likely to dispute. Assertions for
which there is abundant positive evidence are often disbelieved, on
account of what is called their improbability, or impossibility. And the
question for consideration is what, in the present case, these words mean,
and how far and in what circumstances the properties which they express
are sufficient grounds for disbelief.

§ 2. It is to be remarked, in the first place, that the positive evidence
produced in support of an assertion which is nevertheless rejected on the
score of impossibility or improbability, is never such as amounts to full
proof. It is always grounded on some approximate generalization. The fact
may have been asserted by a hundred witnesses; but there are many
exceptions to the universality of the generalization that what a hundred
witnesses affirm is true. We may seem to ourselves to have actually seen
the fact; but that we really see what we think we see, is by no means a
universal truth; our organs may have been in a morbid state; or we may
have inferred something, and imagined that we perceived it. The evidence,
then, in the affirmative being never more than an approximate
generalization, all will depend on what the evidence in the negative is.
If that also rests on an approximate generalization, it is a case for
comparison of probabilities. If the approximate generalizations leading to
the affirmative are, when added together, less strong, or, in other words,
farther from being universal, than the approximate generalizations which
support the negative side of the question, the proposition is said to be
improbable, and is to be disbelieved provisionally. If, however, an
alleged fact be in contradiction, not to any number of approximate
generalizations, but to a completed generalization grounded on a rigorous
induction, it is said to be impossible, and is to be disbelieved totally.

This last principle, simple and evident as it appears, is the doctrine
which, on the occasion of an attempt to apply it to the question of the
credibility of miracles, excited so violent a controversy. Hume’s
celebrated doctrine, that nothing is credible which is contradictory to
experience, or at variance with laws of nature, is merely this very plain
and harmless proposition, that whatever is contradictory to a complete
induction is incredible. That such a maxim as this should either be
accounted a dangerous heresy, or mistaken for a great and recondite truth,
speaks ill for the state of philosophical speculation on such subjects.

But does not (it may be asked) the very statement of the proposition imply
a contradiction? An alleged fact, according to this theory, is not to be
believed if it contradict a complete induction. But it is essential to the
completeness of an induction that it shall not contradict any known fact.
Is it not, then, a _petitio principii_ to say, that the fact ought to be
disbelieved because the induction opposed to it is complete? How can we
have a right to declare the induction complete, while facts, supported by
credible evidence, present themselves in opposition to it?

I answer, we have that right whenever the scientific canons of induction
give it to us; that is, whenever the induction _can_ be complete. We have
it, for example, in a case of causation in which there has been an
_experimentum crucis_. If an antecedent A, superadded to a set of
antecedents in all other respects unaltered, is followed by an effect B
which did not exist before, A is, in that instance at least, the cause of
B, or an indispensable part of its cause; and if A be tried again with
many totally different sets of antecedents and B still follows, then it is
the whole cause. If these observations or experiments have been repeated
so often, and by so many persons, as to exclude all supposition of error
in the observer, a law of nature is established; and so long as this law
is received as such, the assertion that on any particular occasion A took
place, and yet B did not follow, _without any counteracting cause_, must
be disbelieved. Such an assertion is not to be credited on any less
evidence than what would suffice to overturn the law. The general truths,
that whatever has a beginning has a cause, and that when none but the same
causes exist, the same effects follow, rest on the strongest inductive
evidence possible; the proposition that things affirmed by even a crowd of
respectable witnesses are true, is but an approximate generalization;
and—even if we fancy we actually saw or felt the fact which is in
contradiction to the law—what a human being can see is no more than a set
of appearances; from which the real nature of the phenomenon is merely an
inference, and in this inference approximate generalizations usually have
a large share. If, therefore, we make our election to hold by the law, no
quantity of evidence whatever ought to persuade us that there has occurred
any thing in contradiction to it. If, indeed, the evidence produced is
such that it is more likely that the set of observations and experiments
on which the law rests should have been inaccurately performed or
incorrectly interpreted, than that the evidence in question should be
false, we may believe the evidence; but then we must abandon the law. And
since the law was received on what seemed a complete induction, it can
only be rejected on evidence equivalent; namely, as being inconsistent not
with any number of approximate generalizations, but with some other and
better established law of nature. This extreme case, of a conflict between
two supposed laws of nature, has probably never actually occurred where,
in the process of investigating both the laws, the true canons of
scientific induction had been kept in view; but if it did occur, it must
terminate in the total rejection of one of the supposed laws. It would
prove that there must be a flaw in the logical process by which either one
or the other was established; and if there be so, that supposed general
truth is no truth at all. We can not admit a proposition as a law of
nature, and yet believe a fact in real contradiction to it. We must
disbelieve the alleged fact, or believe that we were mistaken in admitting
the supposed law.

But in order that any alleged fact should be contradictory to a law of
causation, the allegation must be, not simply that the cause existed
without being followed by the effect, for that would be no uncommon
occurrence; but that this happened in the absence of any adequate
counteracting cause. Now in the case of an alleged miracle, the assertion
is the exact opposite of this. It is, that the effect was defeated, not in
the absence, but in consequence of a counteracting cause, namely, a direct
interposition of an act of the will of some being who has power over
nature; and in particular of a Being, whose will being assumed to have
endowed all the causes with the powers by which they produce their
effects, may well be supposed able to counteract them. A miracle (as was
justly remarked by Brown)(202) is no contradiction to the law of cause and
effect; it is a new effect, supposed to be produced by the introduction of
a new cause. Of the adequacy of that cause, if present, there can be no
doubt; and the only antecedent improbability which can be ascribed to the
miracle, is the improbability that any such cause existed.

All, therefore, which Hume has made out, and this he must be considered to
have made out, is, that (at least in the imperfect state of our knowledge
of natural agencies, which leaves it always possible that some of the
physical antecedents may have been hidden from us) no evidence can prove a
miracle to any one who did not previously believe the existence of a being
or beings with supernatural power; or who believes himself to have full
proof that the character of the Being whom he recognizes is inconsistent
with his having seen fit to interfere on the occasion in question.

If we do not already believe in supernatural agencies, no miracle can
prove to us their existence. The miracle itself, considered merely as an
extraordinary fact, may be satisfactorily certified by our senses or by
testimony; but nothing can ever prove that it is a miracle; there is still
another possible hypothesis, that of its being the result of some unknown
natural cause; and this possibility can not be so completely shut out, as
to leave no alternative but that of admitting the existence and
intervention of a being superior to nature. Those, however, who already
believe in such a being have two hypotheses to choose from, a supernatural
and an unknown natural agency; and they have to judge which of the two is
the most probable in the particular case. In forming this judgment, an
important element of the question will be the conformity of the result to
the laws of the supposed agent, that is, to the character of the Deity as
they conceive it. But with the knowledge which we now possess of the
general uniformity of the course of nature, religion, following in the
wake of science, has been compelled to acknowledge the government of the
universe as being on the whole carried on by general laws, and not by
special interpositions. To whoever holds this belief, there is a general
presumption against any supposition of divine agency not operating through
general laws, or, in other words, there is an antecedent improbability in
every miracle, which, in order to outweigh it, requires an extraordinary
strength of antecedent probability derived from the special circumstances
of the case.

§ 3. It appears from what has been said, that the assertion that a cause
has been defeated of an effect which is connected with it by a completely
ascertained law of causation, is to be disbelieved or not, according to
the probability or improbability that there existed in the particular
instance an adequate counteracting cause. To form an estimate of this, is
not more difficult than of other probabilities. With regard to all _known_
causes capable of counteracting the given causes, we have generally some
previous knowledge of the frequency or rarity of their occurrence, from
which we may draw an inference as to the antecedent improbability of their
having been present in any particular case. And neither in respect to
known nor unknown causes are we required to pronounce on the probability
of their existing in nature, but only of their having existed at the time
and place at which the transaction is alleged to have happened. We are
seldom, therefore, without the means (when the circumstances of the case
are at all known to us) of judging how far it is likely that such a cause
should have existed at that time and place without manifesting its
presence by some other marks, and (in the case of an unknown cause)
without having hitherto manifested its existence in any other instance.
According as this circumstance, or the falsity of the testimony, appears
more improbable—that is, conflicts with an approximate generalization of a
higher order—we believe the testimony, or disbelieve it; with a stronger
or a weaker degree of conviction, according to the preponderance; at least
until we have sifted the matter further.

So much, then, for the case in which the alleged fact conflicts, or
appears to conflict, with a real law of causation. But a more common case,
perhaps, is that of its conflicting with uniformities of mere
co-existence, not proved to be dependent on causation; in other words,
with the properties of Kinds. It is with these uniformities principally
that the marvelous stories related by travelers are apt to be at variance;
as of men with tails, or with wings, and (until confirmed by experience)
of flying fish; or of ice, in the celebrated anecdote of the Dutch
travelers and the King of Siam. Facts of this description, facts
previously unheard of, but which could not from any known law of causation
be pronounced impossible, are what Hume characterizes as not contrary to
experience, but merely unconformable to it; and Bentham, in his treatise
on Evidence, denominates them facts disconformable _in specie_, as
distinguished from such as are disconformable _in toto_ or in _degree_

In a case of this description, the fact asserted is the existence of a new
Kind; which in itself is not in the slightest degree incredible, and only
to be rejected if the improbability that any variety of object existing at
the particular place and time should not have been discovered sooner, be
greater than that of error or mendacity in the witnesses. Accordingly,
such assertions, when made by credible persons, and of unexplored places,
are not disbelieved, but at most regarded as requiring confirmation from
subsequent observers; unless the alleged properties of the supposed new
Kind are at variance with known properties of some larger kind which
includes it; or, in other words, unless, in the new Kind which is asserted
to exist, some properties are said to have been found disjoined from
others which have always been known to accompany them; as in the case of
Pliny’s men, or any other kind of animal of a structure different from
that which has always been found to co-exist with animal life. On the mode
of dealing with any such case, little needs be added to what has been said
on the same topic in the twenty-second chapter.(203) When the uniformities
of co-existence which the alleged fact would violate, are such as to raise
a strong presumption of their being the result of causation, the fact
which conflicts with them is to be disbelieved; at least provisionally,
and subject to further investigation. When the presumption amounts to a
virtual certainty, as in the case of the general structure of organized
beings, the only question requiring consideration is whether, in phenomena
so little understood, there may not be liabilities to counteraction from
causes hitherto unknown; or whether the phenomena may not be capable of
originating in some other way, which would produce a different set of
derivative uniformities. Where (as in the case of the flying fish, or the
ornithorhynchus) the generalization to which the alleged fact would be an
exception is very special and of limited range, neither of the above
suppositions can be deemed very improbable; and it is generally, in the
case of such alleged anomalies, wise to suspend our judgment, pending the
subsequent inquiries which will not fail to confirm the assertion if it be
true. But when the generalization is very comprehensive, embracing a vast
number and variety of observations, and covering a considerable province
of the domain of nature; then, for reasons which have been fully
explained, such an empirical law comes near to the certainty of an
ascertained law of causation; and any alleged exception to it can not be
admitted, unless on the evidence of some law of causation proved by a
still more complete induction.

Such uniformities in the course of nature as do not bear marks of being
the results of causation are, as we have already seen, admissible as
universal truths with a degree of credence proportioned to their
generality. Those which are true of all things whatever, or at least which
are totally independent of the varieties of Kinds, namely, the laws of
number and extension, to which we may add the law of causation itself, are
probably the only ones, an exception to which is absolutely and
permanently incredible. Accordingly, it is to assertions supposed to be
contradictory to these laws, or to some others coming near to them in
generality, that the word impossibility (at least _total_ impossibility)
seems to be generally confined. Violations of other laws, of special laws
of causation, for instance, are said, by persons studious of accuracy in
expression, to be impossible _in the circumstances of the case_; or
impossible unless some cause had existed which did not exist in the
particular case.(204) Of no assertion, not in contradiction to some of
these very general laws, will more than improbability be asserted by any
cautious person; and improbability not of the highest degree, unless the
time and place in which the fact is said to have occurred, render it
almost certain that the anomaly, if real, could not have been overlooked
by other observers. Suspension of judgment is in all other cases the
resource of the judicious inquirer; provided the testimony in favor of the
anomaly presents, when well sifted, no suspicious circumstances.

But the testimony is scarcely ever found to stand that test, in cases in
which the anomaly is not real. In the instances on record in which a great
number of witnesses, of good reputation and scientific acquirements, have
testified to the truth of something which has turned out untrue, there
have almost always been circumstances which, to a keen observer who had
taken due pains to sift the matter, would have rendered the testimony
untrustworthy. There have generally been means of accounting for the
impression on the senses or minds of the alleged percipients, by
fallacious appearances; or some epidemic delusion, propagated by the
contagious influence of popular feeling, has been concerned in the case;
or some strong interest has been implicated—religious zeal, party feeling,
vanity, or at least the passion for the marvelous, in persons strongly
susceptible of it. When none of these or similar circumstances exist to
account for the apparent strength of the testimony; and where the
assertion is not in contradiction either to those universal laws which
know no counteraction or anomaly, or to the generalizations next in
comprehensiveness to them, but would only amount, if admitted, to the
existence of an unknown cause or an anomalous Kind, in circumstances not
so thoroughly explored but that it is credible that things hitherto
unknown may still come to light; a cautious person will neither admit nor
reject the testimony, but will wait for confirmation at other times and
from other unconnected sources. Such ought to have been the conduct of the
King of Siam when the Dutch travelers affirmed to him the existence of
ice. But an ignorant person is as obstinate in his contemptuous
incredulity as he is unreasonably credulous. Any thing unlike his own
narrow experience he disbelieves, if it flatters no propensity; any
nursery tale is swallowed implicitly by him if it does.

§ 4. I shall now advert to a very serious misapprehension of the
principles of the subject, which has been committed by some of the writers
against Hume’s Essay on Miracles, and by Bishop Butler before them, in
their anxiety to destroy what appeared to them a formidable weapon of
assault against the Christian religion; and the effect of which is
entirely to confound the doctrine of the Grounds of Disbelief. The mistake
consists in overlooking the distinction between (what may be called)
improbability before the fact and improbability after it; or (since, as
Mr. Venn remarks, the distinction of past and future is not the material
circumstance) between the improbability of a mere guess being right, and
the improbability of an alleged fact being true.

Many events are altogether improbable to us, before they have happened, or
before we are informed of their happening, which are not in the least
incredible when we are informed of them, because not contrary to any, even
approximate, induction. In the cast of a perfectly fair die, the chances
are five to one against throwing ace, that is, ace will be thrown on an
average only once in six throws. But this is no reason against believing
that ace was thrown on a given occasion, if any credible witness asserts
it; since though ace is only thrown once in six times, _some_ number which
is only thrown once in six times must have been thrown if the die was
thrown at all. The improbability, then, or, in other words, the
unusualness, of any fact, is no reason for disbelieving it, if the nature
of the case renders it certain that either that or something equally
improbable, that is, equally unusual, did happen. Nor is this all; for
even if the other five sides of the die were all twos, or all threes, yet
as ace would still, on the average, come up once in every six throws, its
coming up in a given throw would be not in any way contradictory to
experience. If we disbelieved all facts which had the chances against them
beforehand, we should believe hardly any thing. We are told that A. B.
died yesterday; the moment before we were so told, the chances against his
having died on that day may have been ten thousand to one; but since he
was certain to die at some time or other, and when he died must
necessarily die on some particular day, while the preponderance of chances
is very great against every day in particular, experience affords no
ground for discrediting any testimony which may be produced to the event’s
having taken place on a given day.

Yet it has been considered by Dr. Campbell and others, as a complete
answer to Hume’s doctrine (that things are incredible which are _contrary_
to the uniform course of experience), that we do not disbelieve, merely
because the chances were against them, things in strict _conformity_ to
the uniform course of experience; that we do not disbelieve an alleged
fact merely because the combination of causes on which it depends occurs
only once in a certain number of times. It is evident that whatever is
shown by observation, or can be proved from laws of nature, to occur in a
certain proportion (however small) of the whole number of possible cases,
is not contrary to experience; though we are right in disbelieving it, if
some other supposition respecting the matter in question involves, on the
whole, a less departure from the ordinary course of events. Yet on such
grounds as this have able writers been led to the extraordinary
conclusion, that nothing supported by credible testimony ought ever to be
disbelieved.

§ 5. We have considered two species of events, commonly said to be
improbable; one kind which are in no way extraordinary, but which, having
an immense preponderance of chances against them, are improbable until
they are affirmed, but no longer; another kind which, being contrary to
some recognized law of nature, are incredible on any amount of testimony
except such as would be sufficient to shake our belief in the law itself.
But between these two classes of events, there is an intermediate class,
consisting of what are commonly termed Coincidences: in other words, those
combinations of chances which present some peculiar and unexpected
regularity, assimilating them, in so far, to the results of law. As if,
for example, in a lottery of a thousand tickets, the numbers should be
drawn in the exact order of what are called the natural numbers, 1, 2, 3,
etc. We have still to consider the principles of evidence applicable to
this case: whether there is any difference between coincidences and
ordinary events, in the amount of testimony or other evidence necessary to
render them credible.

It is certain that on every rational principle of expectation, a
combination of this peculiar sort may be expected quite as often as any
other given series of a thousand numbers; that with perfectly fair dice,
sixes will be thrown twice, thrice, or any number of times in succession,
quite as often in a thousand or a million throws, as any other succession
of numbers fixed upon beforehand; and that no judicious player would give
greater odds against the one series than against the other.
Notwithstanding this, there is a general disposition to regard the one as
much more improbable than the other, and as requiring much stronger
evidence to make it credible. Such is the force of this impression, that
it has led some thinkers to the conclusion, that nature has greater
difficulty in producing regular combinations than irregular ones; or in
other words, that there is some general tendency of things, some law,
which prevents regular combinations from occurring, or at least from
occurring so often as others. Among these thinkers may be numbered
D’Alembert; who, in an Essay on Probabilities to be found in the fifth
volume of his _Mélanges_, contends that regular combinations, though
equally probable according to the mathematical theory with any others, are
physically less probable. He appeals to common sense, or, in other words,
to common impressions; saying, if dice thrown repeatedly in our presence
gave sixes every time, should we not, before the number of throws had
reached ten (not to speak of thousands of millions), be ready to affirm,
with the most positive conviction, that the dice were false?

The common and natural impression is in favor of D’Alembert: the regular
series would be thought much more unlikely than an irregular. But this
common impression is, I apprehend, merely grounded on the fact, that
scarcely any body remembers to have ever seen one of these peculiar
coincidences: the reason of which is simply that no one’s experience
extends to any thing like the number of trials, within which that or any
other given combination of events can be expected to happen. The chance of
sixes on a single throw of two dice being 1/36, the chance of sixes ten
times in succession is 1 divided by the tenth power of 36; in other words,
such a concurrence is only likely to happen once in 3,656,158,440,062,976
trials, a number which no dice-player’s experience comes up to a millionth
part of. But if, instead of sixes ten times, any other given succession of
ten throws had been fixed upon, it would have been exactly as unlikely
that in any individual’s experience that particular succession had ever
occurred; although this does not _seem_ equally improbable, because no one
would be likely to have remembered whether it had occurred or not, and
because the comparison is tacitly made, not between sixes ten times and
any one particular series of throws, but between all regular and all
irregular successions taken together.

That (as D’Alembert says) if the succession of sixes was actually thrown
before our eyes, we should ascribe it not to chance, but to unfairness in
the dice, is unquestionably true. But this arises from a totally different
principle. We should then be considering, not the probability of the fact
in itself, but the comparative probability with which, when it is known to
have happened, it may be referred to one or to another cause. The regular
series is not at all less likely than the irregular one to be brought
about by chance, but it is much more likely than the irregular one to be
produced by design; or by some general cause operating through the
structure of the dice. It is the nature of casual combinations to produce
a repetition of the same event, as often and no oftener than any other
series of events. But it is the nature of general causes to reproduce, in
the same circumstances, always the same event. Common sense and science
alike dictate that, all other things being the same, we should rather
attribute the effect to a cause which if real would be very likely to
produce it, than to a cause which would be very unlikely to produce it.
According to Laplace’s sixth theorem, which we demonstrated in a former
chapter, the difference of probability arising from the superior
_efficacy_ of the constant cause, unfairness in the dice, would after a
very few throws far outweigh any antecedent probability which there could
be against its existence.

D’Alembert should have put the question in another manner. He should have
supposed that we had ourselves previously tried the dice, and knew by
ample experience that they were fair. Another person then tries them in
our absence, and assures us that he threw sixes ten times in succession.
Is the assertion credible or not? Here the effect to be accounted for is
not the occurrence itself, but the fact of the witness’s asserting it.
This may arise either from its having really happened, or from some other
cause. What we have to estimate is the comparative probability of these
two suppositions.

If the witness affirmed that he had thrown any other series of numbers,
supposing him to be a person of veracity, and tolerable accuracy, and to
profess that he took particular notice, we should believe him. But the ten
sixes are exactly as likely to have been really thrown as the other
series. If, therefore, this assertion is less credible than the other, the
reason must be, not that it is less likely than the other to be made
truly, but that it is more likely than the other to be made falsely.

One reason obviously presents itself why what is called a coincidence,
should be oftener asserted falsely than an ordinary combination. It
excites wonder. It gratifies the love of the marvelous. The motives,
therefore, to falsehood, one of the most frequent of which is the desire
to astonish, operate more strongly in favor of this kind of assertion than
of the other kind. Thus far there is evidently more reason for
discrediting an alleged coincidence, than a statement in itself not more
probable, but which if made would not be thought remarkable. There are
cases, however, in which the presumption on this ground would be the other
way. There are some witnesses who, the more extraordinary an occurrence
might appear, would be the more anxious to verify it by the utmost
carefulness of observation before they would venture to believe it, and
still more before they would assert it to others.

§ 6. Independently, however, of any peculiar chances of mendacity arising
from the nature of the assertion, Laplace contends, that merely on the
general ground of the fallibility of testimony, a coincidence is not
credible on the same amount of testimony on which we should be warranted
in believing an ordinary combination of events. In order to do justice to
his argument, it is necessary to illustrate it by the example chosen by
himself.

If, says Laplace, there were one thousand tickets in a box, and one only
has been drawn out, then if an eye-witness affirms that the number drawn
was 79, this, though the chances were 999 in 1000 against it, is not on
that account the less credible; its credibility is equal to the antecedent
probability of the witness’s veracity. But if there were in the box 999
black balls and only one white, and the witness affirms that the white
ball was drawn, the case according to Laplace is very different: the
credibility of his assertion is but a small fraction of what it was in the
former case; the reason of the difference being as follows:

The witnesses of whom we are speaking must, from the nature of the case,
be of a kind whose credibility falls materially short of certainty; let us
suppose, then, the credibility of the witness in the case in question to
be 9/10; that is, let us suppose that in every ten statements which the
witness makes, nine on an average are correct, and one incorrect. Let us
now suppose that there have taken place a sufficient number of drawings to
exhaust all the possible combinations, the witness deposing in every one.
In one case out of every ten in all these drawings he will actually have
made a false announcement. But in the case of the thousand tickets these
false announcements will have been distributed impartially over all the
numbers, and of the 999 cases in which No. 79 was not drawn, there will
have been only one case in which it was announced. On the contrary, in the
case of the thousand balls (the announcement being always either “black”
or “white”), if white was not drawn, and there was a false announcement,
that false announcement _must_ have been white; and since by the
supposition there was a false announcement once in every ten times, white
will have been announced falsely in one-tenth part of all the cases in
which it was not drawn, that is, in one-tenth part of 999 cases out of
every thousand. White, then, is drawn, on an average, exactly as often as
No. 79, but it is announced, without having been really drawn, 999 times
as often as No. 79; the announcement, therefore, requires a much greater
amount of testimony to render it credible.(205)

To make this argument valid it must of course be supposed, that the
announcements made by the witness are average specimens of his general
veracity and accuracy; or, at least, that they are neither more nor less
so in the case of the black and white balls, than in the case of the
thousand tickets. This assumption, however, is not warranted. A person is
far less likely to mistake, who has only one form of error to guard
against, than if he had 999 different errors to avoid. For instance, in
the example chosen, a messenger who might make a mistake once in ten times
in reporting the number drawn in a lottery, might not err once in a
thousand times if sent simply to observe whether a ball was black or
white. Laplace’s argument, therefore, is faulty even as applied to his own
case. Still less can that case be received as completely representing all
cases of coincidence. Laplace has so contrived his example, that though
black answers to 999 distinct possibilities, and white only to one, the
witness has nevertheless no bias which can make him prefer black to white.
The witness did not know that there were 999 black balls in the box and
only one white; or if he did, Laplace has taken care to make all the 999
cases so undistinguishably alike, that there is hardly a possibility of
any cause of falsehood or error operating in favor of any of them, which
would not operate in the same manner if there were only one. Alter this
supposition, and the whole argument falls to the ground. Let the balls,
for instance, be numbered, and let the white ball be No. 79. Considered in
respect of their color, there are but two things which the witness can be
interested in asserting, or can have dreamed or hallucinated, or has to
choose from if he answers at random, viz., black and white; but considered
in respect of the numbers attached to them, there are a thousand; and if
his interest or error happens to be connected with the numbers, though the
only assertion he makes is about the color, the case becomes precisely
assimilated to that of the thousand tickets. Or instead of the balls
suppose a lottery, with 1000 tickets and but one prize, and that I hold
No. 79, and being interested only in that, ask the witness not what was
the number drawn, but whether it was 79 or some other. There are now only
two cases, as in Laplace’s example; yet he surely would not say that if
the witness answered 79, the assertion would be in an enormous proportion
less credible, than if he made the same answer to the same question asked
in the other way. If, for instance (to put a case supposed by Laplace
himself), he has staked a large sum on one of the chances, and thinks that
by announcing its occurrence he shall increase his credit; he is equally
likely to have betted on any one of the 999 numbers which are attached to
black balls, and so far as the chances of mendacity from this cause are
concerned, there will be 999 times as many chances of his announcing black
falsely as white.

Or suppose a regiment of 1000 men, 999 Englishmen and one Frenchman, and
that of these one man has been killed, and it is not known which. I ask
the question, and the witness answers, the Frenchman. This was not only as
improbable _a priori_, but is in itself as singular a circumstance, as
remarkable a coincidence, as the drawing of the white ball; yet we should
believe the statement as readily, as if the answer had been John Thompson.
Because, though the 999 Englishmen were all alike in the point in which
they differed from the Frenchman, they were not, like the 999 black balls,
undistinguishable in every other respect; but being all different, they
admitted as many chances of interest or error, as if each man had been of
a different nation; and if a lie was told or a mistake made, the
misstatement was as likely to fall on any Jones or Thompson of the set, as
on the Frenchman.

The example of a coincidence selected by D’Alembert, that of sixes thrown
on a pair of dice ten times in succession, belongs to this sort of cases
rather than to such as Laplace’s. The coincidence is here far more
remarkable, because of far rarer occurrence, than the drawing of the white
ball. But though the improbability of its really occurring is greater, the
superior probability of its being announced falsely can not be established
with the same evidence. The announcement “black” represented 999 cases,
but the witness may not have known this, and if he did, the 999 cases are
so exactly alike, that there is really only one set of possible causes of
mendacity corresponding to the whole. The announcement “sixes _not_ drawn
ten times,” represents, and is known by the witness to represent, a great
multitude of contingencies, every one of which being unlike every other,
there may be a different and a fresh set of causes of mendacity
corresponding to each.

It appears to me, therefore, that Laplace’s doctrine is not strictly true
of any coincidences, and is wholly inapplicable to most; and that to know
whether a coincidence does or does not require more evidence to render it
credible than an ordinary event, we must refer, in every instance, to
first principles, and estimate afresh what is the probability that the
given testimony would have been delivered in that instance, supposing the
fact which it asserts not to be true.

With these remarks we close the discussion of the Grounds of Disbelief;
and along with it, such exposition as space admits, and as the writer has
it in his power to furnish, of the Logic of Induction.





                                 Book IV.


OF OPERATIONS SUBSIDIARY TO INDUCTION.


    “Clear and distinct ideas are terms which, though familiar and
    frequent in men’s mouths, I have reason to think every one who
    uses does not perfectly understand. And possibly it is but here
    and there one who gives himself the trouble to consider them so
    far as to know what he himself or others precisely mean by them; I
    have, therefore, in most places, chose to put determinate or
    determined, instead of clear and distinct, as more likely to
    direct men’s thoughts to my meaning in this matter.”—LOCKE’S
    _Essay on the Human Understanding_; Epistle to the Reader.

    “Il ne peut y avoir qu’une méthode parfaite, qui est la _méthode
    naturelle_; on nomme ainsi un arrangement dans lequel les êtres du
    même genre seraient plus voisins entre eux que ceux de tous les
    autres genres; les genres du même ordre, plus que ceux de tous les
    autres ordres; et ainsi de suite. Cette méthode est l’idéal auquel
    l’histoire naturelle doit tendre; car il est évident que si l’on y
    parvenait, l’on aurait l’expression exacte et complète de la
    nature entière.”—CUVIER, _Règne Animal_, Introduction.

    “Deux grandes notions philosophiques dominent la théorie
    fondamentale de la méthode naturelle proprement dite, savoir la
    formation des groupes naturels, et ensuite leur succession
    hiérarchique.”—COMTE, _Cours de Philosophie Positive_, 42me leçon.




                                Chapter I.


Of Observation And Description.


§ 1. The inquiry which occupied us in the two preceding Books, has
conducted us to what appears a satisfactory solution of the principal
problem of Logic, according to the conception I have formed of the
science. We have found, that the mental process with which Logic is
conversant, the operation of ascertaining truths by means of evidence, is
always, even when appearances point to a different theory of it, a process
of induction. And we have particularized the various modes of induction,
and obtained a clear view of the principles to which it must conform, in
order to lead to results which can be relied on.

The consideration of Induction, however, does not end with the direct
rules for its performance. Something must be said of those other
operations of the mind, which are either necessarily presupposed in all
induction, or are instrumental to the more difficult and complicated
inductive processes. The present Book will be devoted to the consideration
of these subsidiary operations; among which our attention must first be
given to those, which are indispensable preliminaries to all induction
whatsoever.

Induction being merely the extension to a class of cases, of something
which has been observed to be true in certain individual instances of the
class; the first place among the operations subsidiary to induction, is
claimed by Observation. This is not, however, the place to lay down rules
for making good observers; nor is it within the competence of Logic to do
so, but of the art of intellectual Education. Our business with
observation is only in its connection with the appropriate problem of
logic, the estimation of evidence. We have to consider, not how or what to
observe, but under what conditions observation is to be relied on; what is
needful, in order that the fact, supposed to be observed, may safely be
received as true.

§ 2. The answer to this question is very simple, at least in its first
aspect. The sole condition is, that what is supposed to have been observed
shall really have been observed; that it be an observation, not an
inference. For in almost every act of our perceiving faculties,
observation and inference are intimately blended. What we are said to
observe is usually a compound result, of which one-tenth may be
observation, and the remaining nine-tenths inference.

I affirm, for example, that I hear a man’s voice. This would pass, in
common language, for a direct perception. All, however, which is really
perception, is that I hear a sound. That the sound is a voice, and that
voice the voice of a man, are not perceptions but inferences. I affirm,
again, that I saw my brother at a certain hour this morning. If any
proposition concerning a matter of fact would commonly be said to be known
by the direct testimony of the senses, this surely would be so. The truth,
however, is far otherwise. I only saw a certain colored surface; or rather
I had the kind of visual sensations which are usually produced by a
colored surface; and from these as marks, known to be such by previous
experience, I concluded that I saw my brother. I might have had sensations
precisely similar, when my brother was not there. I might have seen some
other person so nearly resembling him in appearance, as, at the distance,
and, with the degree of attention which I bestowed, to be mistaken for
him. I might have been asleep, and have dreamed that I saw him; or in a
state of nervous disorder, which brought his image before me in a waking
hallucination. In all these modes, many have been led to believe that they
saw persons well known to them, who were dead or far distant. If any of
these suppositions had been true, the affirmation that I saw my brother
would have been erroneous; but whatever was matter of direct perception,
namely the visual sensations, would have been real. The inference only
would have been ill grounded; I should have ascribed those sensations to a
wrong cause.

Innumerable instances might be given, and analyzed in the same manner, of
what are vulgarly called errors of sense. There are none of them properly
errors of sense; they are erroneous inferences from sense. When I look at
a candle through a multiplying glass, I see what seems a dozen candles
instead of one; and if the real circumstances of the case were skillfully
disguised, I might suppose that there were really that number; there would
be what is called an optical deception. In the kaleidoscope there really
is that deception; when I look through the instrument, instead of what is
actually there, namely a casual arrangement of colored fragments, the
appearance presented is that of the same combination several times
repeated in symmetrical arrangement round a point. The delusion is of
course effected by giving me the same sensations which I should have had
if such a symmetrical combination had really been presented to me. If I
cross two of my fingers, and bring any small object, a marble for
instance, into contact with both, at points not usually touched
simultaneously by one object, I can hardly, if my eyes are shut, help
believing that there are two marbles instead of one. But it is not my
touch in this case, nor my sight in the other, which is deceived; the
deception, whether durable or only momentary, is in my judgment. From my
senses I have only the sensations, and those are genuine. Being accustomed
to have those or similar sensations when, and only when, a certain
arrangement of outward objects is present to my organs, I have the habit
of instantly, when I experience the sensations, inferring the existence of
that state of outward things. This habit has become so powerful, that the
inference, performed with the speed and certainty of an instinct, is
confounded with intuitive perceptions. When it is correct, I am
unconscious that it ever needed proof; even when I know it to be
incorrect, I can not without considerable effort abstain from making it.
In order to be aware that it is not made by instinct but by an acquired
habit, I am obliged to reflect on the slow process through which I learned
to judge by the eye of many things which I now appear to perceive directly
by sight; and on the reverse operation performed by persons learning to
draw, who with difficulty and labor divest themselves of their acquired
perceptions, and learn afresh to see things as they appear to the eye.

It would be easy to prolong these illustrations, were there any need to
expatiate on a topic so copiously exemplified in various popular works.
From the examples already given, it is seen sufficiently, that the
individual facts from which we collect our inductive generalizations are
scarcely ever obtained by observation alone. Observation extends only to
the sensations by which we recognize objects; but the propositions which
we make use of, either in science or in common life, relate mostly to the
objects themselves. In every act of what is called observation, there is
at least one inference—from the sensations to the presence of the object;
from the marks or diagnostics, to the entire phenomenon. And hence, among
other consequences, follows the seeming paradox, that a general
proposition collected from particulars is often more certainly true than
any one of the particular propositions from which, by an act of induction,
it was inferred. For, each of those particular (or rather singular)
propositions involved an inference, from the impression on the senses to
the fact which caused that impression; and this inference may have been
erroneous in any one of the instances, but can not well have been
erroneous in all of them, provided their number was sufficient to
eliminate chance. The conclusion, therefore, that is, the general
proposition, may deserve more complete reliance than it would be safe to
repose in any one of the inductive premises.

The logic of observation, then, consists solely in a correct
discrimination between that, in a result of observation, which has really
been perceived, and that which is an inference from the perception.
Whatever portion is inference, is amenable to the rules of induction
already treated of, and requires no further notice here; the question for
us in this place is, when all which is inference is taken away what
remains? There remains, in the first place, the mind’s own feelings or
states of consciousness, namely, its outward feelings or sensations, and
its inward feelings—its thoughts, emotions, and volitions. Whether any
thing else remains, or all else is inference from this; whether the mind
is capable of directly perceiving or apprehending any thing except states
of its own consciousness—is a problem of metaphysics not to be discussed
in this place. But after excluding all questions on which metaphysicians
differ, it remains true, that for most purposes the discrimination we are
called upon practically to exercise is that between sensations or other
feelings, of our own or of other people, and inferences drawn from them.
And on the theory of Observation this is all which seems necessary to be
said for the purposes of the present work.

§ 3. If, in the simplest observation, or in what passes for such, there is
a large part which is not observation but something else; so in the
simplest description of an observation, there is, and must always be, much
more asserted than is contained in the perception itself. We can not
describe a fact, without implying more than the fact. The perception is
only of one individual thing; but to describe it is to affirm a connection
between it and every other thing which is either denoted or connoted by
any of the terms used. To begin with an example, than which none can be
conceived more elementary: I have a sensation of sight, and I endeavor to
describe it by saying that I see something white. In saying this, I do not
solely affirm my sensation; I also class it. I assert a resemblance
between the thing I see, and all things which I and others are accustomed
to call white. I assert that it resembles them in the circumstance in
which they all resemble one another, in that which is the ground of their
being called by the name. This is not merely one way of describing an
observation, but the only way. If I would either register my observation
for my own future use, or make it known for the benefit of others, I must
assert a resemblance between the fact which I have observed and something
else. It is inherent in a description, to be the statement of a
resemblance, or resemblances.

We thus see that it is impossible to express in words any result of
observation, without performing an act possessing what Dr. Whewell
considers to be characteristic of Induction. There is always something
introduced which was not included in the observation itself; some
conception common to the phenomenon with other phenomena to which it is
compared. An observation can not be spoken of in language at all without
declaring more than that one observation; without assimilating it to other
phenomena already observed and classified. But this identification of an
object—this recognition of it as possessing certain known
characteristics—has never been confounded with Induction. It is an
operation which precedes all induction, and supplies it with its
materials. It is a perception of resemblances, obtained by comparison.

These resemblances are not always apprehended directly, by merely
comparing the object observed with some other present object, or with our
recollection of an object which is absent. They are often ascertained
through intermediate marks, that is, deductively. In describing some new
kind of animal, suppose me to say that it measures ten feet in length,
from the forehead to the extremity of the tail. I did not ascertain this
by the unassisted eye. I had a two-foot rule which I applied to the
object, and, as we commonly say, measured it; an operation which was not
wholly manual, but partly also mathematical, involving the two
propositions, Five times two is ten, and Things which are equal to the
same thing are equal to one another. Hence, the fact that the animal is
ten feet long is not an immediate perception, but a conclusion from
reasoning; the minor premises alone being furnished by observation of the
object. Nevertheless, this is called an observation, or a description of
the animal, not an induction respecting it.

To pass at once from a very simple to a very complex example: I affirm
that the earth is globular. The assertion is not grounded on direct
perception; for the figure of the earth can not, by us, be directly
perceived, though the assertion would not be true unless circumstances
could be supposed under which its truth could be so perceived. That the
form of the earth is globular is inferred from certain marks, as for
instance from this, that its shadow thrown upon the moon is circular; or
this, that on the sea, or any extensive plain, our horizon is always a
circle; either of which marks is incompatible with any other than a
globular form. I assert further, that the earth is that particular kind of
a globe which is termed an oblate spheroid; because it is found by
measurement in the direction of the meridian, that the length on the
surface of the earth which subtends a given angle at its centre,
diminishes as we recede from the equator and approach the poles. But these
propositions, that the earth is globular, and that it is an oblate
spheroid, assert, each of them, an individual fact; in its own nature
capable of being perceived by the senses when the requisite organs and the
necessary position are supposed, and only not actually perceived because
those organs and that position are wanting. This identification of the
earth, first as a globe, and next as an oblate spheroid, which, if the
fact could have been seen, would have been called a description of the
figure of the earth, may without impropriety be so called when, instead of
being seen, it is inferred. But we could not without impropriety call
either of these assertions an induction from facts respecting the earth.
They are not general propositions collected from particular facts, but
particular facts deduced from general propositions. They are conclusions
obtained deductively, from premises originating in induction: but of these
premises some were not obtained by observation of the earth, nor had any
peculiar reference to it.

If, then, the truth respecting the figure of the earth is not an
induction, why should the truth respecting the figure of the earth’s orbit
be so? The two cases only differ in this, that the form of the orbit was
not, like the form of the earth itself, deduced by ratiocination from
facts which were marks of ellipticity, but was got at by boldly guessing
that the path was an ellipse, and finding afterward, on examination, that
the observations were in harmony with the hypothesis. According to Dr.
Whewell, however, this process of guessing and verifying our guesses is
not only induction, but the whole of induction: no other exposition can be
given of that logical operation. That he is wrong in the latter assertion,
the whole of the preceding book has, I hope, sufficiently proved; and that
the process by which the ellipticity of the planetary orbits was
ascertained, is not induction at all, was attempted to be shown in the
second chapter of the same Book.(206) We are now, however, prepared to go
more into the heart of the matter than at that earlier period of our
inquiry, and to show, not merely what the operation in question is not,
but what it is.

§ 4. We observed, in the second chapter, that the proposition “the earth
moves in an ellipse,” so far as it only serves for the colligation or
connecting together of actual observations (that is, as it only affirms
that the observed positions of the earth may be correctly represented by
as many points in the circumference of an imaginary ellipse), is not an
induction, but a description: it is an induction, only when it affirms
that the intermediate positions, of which there has been no direct
observation, would be found to correspond to the remaining points of the
same elliptic circumference. Now, though this real induction is one thing,
and the description another, we are in a very different condition for
making the induction before we have obtained the description, and after
it. For inasmuch as the description, like all other descriptions, contains
the assertion of a resemblance between the phenomenon described and
something else; in pointing out something which the series of observed
places of a planet resembles, it points out something in which the several
places themselves agree. If the series of places correspond to as many
points of an ellipse, the places themselves agree in being situated in
that ellipse. We have, therefore, by the same process which gave us the
description, obtained the requisites for an induction by the Method of
Agreement. The successive observed places of the earth being considered as
effects, and its motion as the cause which produces them, we find that
those effects, that is, those places, agree in the circumstance of being
in an ellipse. We conclude that the remaining effects, the places which
have not been observed, agree in the same circumstance, and that the _law_
of the motion of the earth is motion in an ellipse.

The Colligation of Facts, therefore, by means of hypotheses, or, as Dr.
Whewell prefers to say, by means of Conceptions, instead of being, as he
supposes, Induction itself, takes its proper place among operations
subsidiary to Induction. All Induction supposes that we have previously
compared the requisite number of individual instances, and ascertained in
what circumstances they agree. The Colligation of Facts is no other than
this preliminary operation. When Kepler, after vainly endeavoring to
connect the observed places of a planet by various hypotheses of circular
motion, at last tried the hypotheses of an ellipse and found it answer to
the phenomena; what he really attempted, first unsuccessfully and at last
successfully, was to discover the circumstance in which all the observed
positions of the planet agreed. And when he in like manner connected
another set of observed facts, the periodic times of the different
planets, by the proposition that the squares of the times are proportional
to the cubes of the distances, what he did was simply to ascertain the
property in which the periodic times of all the different planets agreed.

Since, therefore, all that is true and to the purpose in Dr. Whewell’s
doctrine of Conceptions might be fully expressed by the more familiar term
Hypothesis; and since his Colligation of Facts by means of appropriate
Conceptions, is but the ordinary process of finding by a comparison of
phenomena, in what consists their agreement or resemblance; I would
willingly have confined myself to those better understood expressions, and
persevered to the end in the same abstinence which I have hitherto
observed from ideological discussions; considering the mechanism of our
thoughts to be a topic distinct from and irrelevant to the principles and
rules by which the trustworthiness of the results of thinking is to be
estimated. Since, however, a work of such high pretensions, and, it must
also be said, of so much real merit, has rested the whole theory of
Induction upon such ideological considerations, it seems necessary for
others who follow to claim for themselves and their doctrines whatever
position may properly belong to them on the same metaphysical ground. And
this is the object of the succeeding chapter.




                               Chapter II.


Of Abstraction, Or The Formation Of Conceptions.


§ 1. The metaphysical inquiry into the nature and composition of what have
been called Abstract Ideas, or, in other words, of the notions which
answer in the mind to classes and to general names, belongs not to Logic,
but to a different science, and our purpose does not require that we
should enter upon it here. We are only concerned with the universally
acknowledged fact, that such notions or conceptions do exist. The mind can
conceive a multitude of individual things as one assemblage or class; and
general names do really suggest to us certain ideas or mental
representations, otherwise we could not use the names with consciousness
of a meaning. Whether the idea called up by a general name is composed of
the various circumstances in which all the individuals denoted by the name
agree, and of no others (which is the doctrine of Locke, Brown, and the
Conceptualists); or whether it be the idea of some one of those
individuals, clothed in its individualizing peculiarities, but with the
accompanying knowledge that those peculiarities are not properties of the
class (which is the doctrine of Berkeley, Mr. Bailey,(207) and the modern
Nominalists); or whether (as held by Mr. James Mill) the idea of the class
is that of a miscellaneous assemblage of individuals belonging to the
class; or whether, finally, it be any one or any other of all these,
according to the accidental circumstances of the case; certain it is, that
_some_ idea or mental conception is suggested by a general name, whenever
we either hear it or employ it with consciousness of a meaning. And this,
which we may call, if we please, a general idea, _represents_ in our minds
the whole class of things to which the name is applied. Whenever we think
or reason concerning the class, we do so by means of this idea. And the
voluntary power which the mind has, of attending to one part of what is
present to it at any moment, and neglecting another part, enables us to
keep our reasonings and conclusions respecting the class unaffected by any
thing in the idea or mental image which is not really, or at least which
we do not really believe to be common, to the whole class.(208)

There are, then, such things as general conceptions, or conceptions by
means of which we can think generally; and when we form a set of phenomena
into a class, that is, when we compare them with one another to ascertain
in what they agree, some general conception is implied in this mental
operation. And inasmuch as such a comparison is a necessary preliminary to
Induction, it is most true that Induction could not go on without general
conceptions.

§ 2. But it does not therefore follow that these general conceptions must
have existed in the mind previously to the comparison. It is not a law of
our intellect, that in comparing things with each other and taking note of
their agreement we merely recognize as realized in the outward world
something that we already had in our minds. The conception originally
found its way to us as the _result_ of such a comparison. It was obtained
(in metaphysical phrase) by _abstraction_ from individual things. These
things may be things which we perceived or thought of on former occasions,
but they may also be the things which we are perceiving or thinking of on
the very occasion. When Kepler compared the observed places of the planet
Mars, and found that they agreed in being points of an elliptic
circumference, he applied a general conception which was already in his
mind, having been derived from his former experience. But this is by no
means universally the case. When we compare several objects and find them
to agree in being white, or when we compare the various species of
ruminating animals and find them to agree in being cloven-footed, we have
just as much a general conception in our minds as Kepler had in his: we
have the conception of “a white thing,” or the conception of “a
cloven-footed animal.” But no one supposes that we necessarily bring these
conceptions with us, and _superinduce_ them (to adopt Dr. Whewell’s
expression) upon the facts: because in these simple cases every body sees
that the very act of comparison which ends in our connecting the facts by
means of the conception, may be the source from which we derive the
conception itself. If we had never seen any white object or had never seen
any cloven-footed animal before, we should at the same time and by the
same mental act acquire the idea, and employ it for the colligation of the
observed phenomena. Kepler, on the contrary, really had to bring the idea
with him, and superinduce it upon the facts; he could not evolve it out of
them: if he had not already had the idea, he would not have been able to
acquire it by a comparison of the planet’s positions. But this inability
was a mere accident; the idea of an ellipse could have been acquired from
the paths of the planets as effectually as from any thing else, if the
paths had not happened to be invisible. If the planet had left a visible
track, and we had been so placed that we could see it at the proper angle,
we might have abstracted our original idea of an ellipse from the
planetary orbit. Indeed, every conception which can be made the instrument
for connecting a set of facts, might have been originally evolved from
those very facts. The conception is a conception _of_ something; and that
which it is a conception of, is really _in_ the facts, and might, under
some supposable circumstances, or by some supposable extension of the
faculties which we actually possess, have been detected in them. And not
only is this always in itself possible, but it actually happens in almost
all cases in which the obtaining of the right conception is a matter of
any considerable difficulty. For if there be no new conception required;
if one of those already familiar to mankind will serve the purpose, the
accident of being the first to whom the right one occurs, may happen to
almost any body; at least in the case of a set of phenomena which the
whole scientific world are engaged in attempting to connect. The honor, in
Kepler’s case, was that of the accurate, patient, and toilsome
calculations by which he compared the results that followed from his
different guesses, with the observations of Tycho Brahe; but the merit was
very small of guessing an ellipse; the only wonder is that men had not
guessed it before, nor could they have failed to do so if there had not
existed an obstinate _a priori_ prejudice that the heavenly bodies must
move, if not in a circle, in some combination of circles.

The really difficult cases are those in which the conception destined to
create light and order out of darkness and confusion has to be sought for
among the very phenomena which it afterward serves to arrange. Why,
according to Dr. Whewell himself, did the ancients fail in discovering the
laws of mechanics, that is, of equilibrium and of the communication of
motion? Because they had not, or at least had not clearly, the ideas or
conceptions of pressure and resistance, momentum, and uniform and
accelerating force. And whence could they have obtained these ideas except
from the very facts of equilibrium and motion? The tardy development of
several of the physical sciences, for example, of optics, electricity,
magnetism, and the higher generalizations of chemistry, he ascribes to the
fact that mankind had not yet possessed themselves of the Idea of
Polarity, that is, the idea of opposite properties in opposite directions.
But what was there to suggest such an idea, until, by a separate
examination of several of these different branches of knowledge, it was
shown that the facts of each of them did present, in some instances at
least, the curious phenomenon of opposite properties in opposite
directions? The thing was superficially manifest only in two cases, those
of the magnet and of electrified bodies; and there the conception was
encumbered with the circumstance of material poles, or fixed points in the
body itself, in which points this opposition of properties seemed to be
inherent. The first comparison and abstraction had led only to this
conception of poles; and if any thing corresponding to that conception had
existed in the phenomena of chemistry or optics, the difficulty now justly
considered so great, would have been extremely small. The obscurity arose
from the fact, that the polarities in chemistry and optics were distinct
species, though of the same genus, with the polarities in electricity and
magnetism; and that in order to assimilate the phenomena to one another,
it was necessary to compare a polarity without poles, such for instance as
is exemplified in the polarization of light, and the polarity with
(apparent) poles, which we see in the magnet; and to recognize that these
polarities, while different in many other respects, agree in the one
character which is expressed by the phrase, opposite properties in
opposite directions. From the result of such a comparison it was that the
minds of scientific men formed this new general conception; between which,
and the first confused feeling of an analogy between some of the phenomena
of light and those of electricity and magnetism, there is a long interval,
filled up by the labors and more or less sagacious suggestions of many
superior minds.

The conceptions, then, which we employ for the colligation and
methodization of facts, do not develop themselves from within, but are
impressed upon the mind from without; they are never obtained otherwise
than by way of comparison and abstraction, and, in the most important and
the most numerous cases, are evolved by abstraction from the very
phenomena which it is their office to colligate. I am far, however, from
wishing to imply that it is not often a very difficult thing to perform
this process of abstraction well, or that the success of an inductive
operation does not, in many cases, principally depend on the skill with
which we perform it. Bacon was quite justified in designating as one of
the principal obstacles to good induction, general conceptions wrongly
formed, “notiones temerè à rebus abstractæ;” to which Dr. Whewell adds,
that not only does bad abstraction make bad induction, but that, in order
to perform induction well, we must have abstracted well; our general
conceptions must be “clear” and “appropriate” to the matter in hand.

§ 3. In attempting to show what the difficulty in this matter really is,
and how it is surmounted, I must beg the reader, once for all, to bear
this in mind; that although, in discussing the opinions of a different
school of philosophy, I am willing to adopt their language, and to speak,
therefore, of connecting facts through the instrumentality of a
conception, this technical phraseology means neither more nor less than
what is commonly called comparing the facts with one another and
determining in what they agree. Nor has the technical expression even the
advantage of being metaphysically correct. The facts are not _connected_,
except in a merely metaphorical acceptation of the term. The _ideas_ of
the facts may become connected, that is, we may be led to think of them
together; but this consequence is no more than what may be produced by any
casual association. What really takes place, is, I conceive, more
philosophically expressed by the common word Comparison, than by the
phrases “to connect” or “to superinduce.” For, as the general conception
is itself obtained by a comparison of particular phenomena, so, when
obtained, the mode in which we apply it to other phenomena is again by
comparison. We compare phenomena with each other to get the conception,
and we then compare those and other phenomena _with_ the conception. We
get the conception of an animal (for instance) by comparing different
animals, and when we afterward see a creature resembling an animal, we
compare it with our general conception of an animal; and if it agrees with
that general conception, we include it in the class. The conception
becomes the type of comparison.

And we need only consider what comparison is, to see that where the
objects are more than two, and still more when they are an indefinite
number, a type of some sort is an indispensable condition of the
comparison. When we have to arrange and classify a great number of objects
according to their agreements and differences, we do not make a confused
attempt to compare all with all. We know that two things are as much as
the mind can easily attend to at a time, and we therefore fix upon one of
the objects, either at hazard or because it offers in a peculiarly
striking manner some important character, and, taking this as our
standard, compare it with one object after another. If we find a second
object which presents a remarkable agreement with the first, inducing us
to class them together, the question instantly arises, in what particular
circumstances do they agree? and to take notice of these circumstances is
already a first stage of abstraction, giving rise to a general conception.
Having advanced thus far, when we now take in hand a third object we
naturally ask ourselves the question, not merely whether this third object
agrees with the first, but whether it agrees with it in the same
circumstances in which the second did? in other words, whether it agrees
with the general conception which has been obtained by abstraction from
the first and second? Thus we see the tendency of general conceptions, as
soon as formed, to substitute themselves as types, for whatever individual
objects previously answered that purpose in our comparisons. We may,
perhaps, find that no considerable number of other objects agree with this
first general conception; and that we must drop the conception, and
beginning again with a different individual case, proceed by fresh
comparisons to a different general conception. Sometimes, again, we find
that the same conception will serve, by merely leaving out some of its
circumstances; and by this higher effort of abstraction, we obtain a still
more general conception; as in the case formerly referred to, the
scientific world rose from the conception of poles to the general
conception of opposite properties in opposite directions; or as those
South-Sea islanders, whose conception of a quadruped had been abstracted
from hogs (the only animals of that description which they had seen), when
they afterward compared that conception with other quadrupeds, dropped
some of the circumstances, and arrived at the more general conception
which Europeans associate with the term.

These brief remarks contain, I believe, all that is well grounded in the
doctrine, that the conception by which the mind arranges and gives unity
to phenomena must be furnished by the mind itself, and that we find the
right conception by a tentative process, trying first one and then another
until we hit the mark. The conception is not furnished _by_ the mind until
it has been furnished _to_ the mind; and the facts which supply it are
sometimes extraneous facts, but more often the very facts which we are
attempting to arrange by it. It is quite true, however, that in
endeavoring to arrange the facts, at whatever point we begin, we never
advance three steps without forming a general conception, more or less
distinct and precise; and that this general conception becomes the clue
which we instantly endeavor to trace through the rest of the facts, or
rather, becomes the standard with which we thenceforth compare them. If we
are not satisfied with the agreements which we discover among the
phenomena by comparing them with this type, or with some still more
general conception which by an additional stage of abstraction we can form
from the type; we change our path, and look out for other agreements; we
recommence the comparison from a different starting-point, and so generate
a different set of general conceptions. This is the tentative process
which Dr. Whewell speaks of; and which has not unnaturally suggested the
theory, that the conception is supplied by the mind itself; since the
different conceptions which the mind successively tries, it either already
possessed from its previous experience, or they were supplied to it in the
first stage of the corresponding act of comparison; so that, in the
subsequent part of the process, the conception manifested itself as
something compared with the phenomena, not evolved from them.

§ 4. If this be a correct account of the instrumentality of general
conceptions in the comparison which necessarily precedes Induction, we are
now able to translate into our own language what Dr. Whewell means by
saying that conceptions, to be subservient to Induction, must be “clear”
and “appropriate.”

If the conception corresponds to a real agreement among the phenomena; if
the comparison which we have made of a set of objects has led us to class
them according to real resemblances and differences; the conception which
does this can not fail to be appropriate, for some purpose or other. The
question of appropriateness is relative to the particular object we have
in view. As soon as, by our comparison, we have ascertained some
agreement, something which can be predicated in common of a number of
objects; we have obtained a basis on which an inductive process is capable
of being founded. But the agreements, or the ulterior consequences to
which those agreements lead, may be of very different degrees of
importance. If, for instance, we only compare animals according to their
color, and class those together which are colored alike, we form the
general conceptions of a white animal, a black animal, etc., which are
conceptions legitimately formed; and if an induction were to be attempted
concerning the causes of the colors of animals, this comparison would be
the proper and necessary preparation for such an induction, but would not
help us toward a knowledge of the laws of any other of the properties of
animals; while if, with Cuvier, we compare and class them according to the
structure of the skeleton, or, with Blainville, according to the nature of
their outward integuments, the agreements and differences which are
observable in these respects are not only of much greater importance in
themselves, but are marks of agreements and differences in many other
important particulars of the structure and mode of life of the animals.
If, therefore, the study of their structure and habits be our object, the
conceptions generated by these last comparisons are far more “appropriate”
than those generated by the former. Nothing, other than this, can be meant
by the appropriateness of a conception.

When Dr. Whewell says that the ancients, or the school-men, or any modern
inquirers, missed discovering the real law of a phenomenon because they
applied to it an inappropriate instead of an appropriate conception; he
can only mean that in comparing various instances of the phenomenon, to
ascertain in what those instances agreed, they missed the important points
of agreement; and fastened upon such as were either imaginary, and not
agreements at all, or, if real agreements, were comparatively trifling,
and had no connection with the phenomenon, the law of which was sought.

Aristotle, philosophizing on the subject of motion, remarked that certain
motions apparently take place spontaneously; bodies fall to the ground,
flame ascends, bubbles of air rise in water, etc.; and these he called
natural motions; while others not only never take place without external
incitement, but even when such incitement is applied, tend spontaneously
to cease; which, to distinguish them from the former, he called violent
motions. Now, in comparing the so-called natural motions with one another,
it appeared to Aristotle that they agreed in one circumstance, namely,
that the body which moved (or seemed to move) spontaneously, was moving
_toward its own place_; meaning thereby the place from whence it
originally came, or the place where a great quantity of matter similar to
itself was assembled. In the other class of motions, as when bodies are
thrown up in the air, they are, on the contrary, moving _from_ their own
place. Now, this conception of a body moving toward its own place may
justly be considered inappropriate; because, though it expresses a
circumstance really found in some of the most familiar instances of motion
apparently spontaneous, yet, first, there are many other cases of such
motion, in which that circumstance is absent; the motion, for instance, of
the earth and planets. Secondly, even when it is present, the motion, on
closer examination, would often be seen not to be spontaneous; as, when
air rises in water, it does not rise by its own nature, but is pushed up
by the superior weight of the water which presses upon it. Finally, there
are many cases in which the spontaneous motion takes place in the contrary
direction to what the theory considers as the body’s own place; for
instance, when a fog rises from a lake, or when water dries up. The
agreement, therefore, which Aristotle selected as his principle of
classification, did not extend to all cases of the phenomenon he wanted to
study, spontaneous motion; while it did include cases of the absence of
the phenomenon, cases of motion not spontaneous. The conception was hence
“inappropriate.” We may add that, in the case in question, no conception
would be appropriate; there is no agreement which runs through all the
cases of spontaneous or apparently spontaneous motion and no others; they
can not be brought under one law; it is a case of Plurality of
Causes.(209)

§ 5. So much for the first of Dr. Whewell’s conditions, that conceptions
must be appropriate. The second is, that they shall be “clear:” and let us
consider what this implies. Unless the conception corresponds to a real
agreement, it has a worse defect than that of not being clear: it is not
applicable to the case at all. Among the phenomena, therefore, which we
are attempting to connect by means of the conception, we must suppose that
there really is an agreement, and that the conception is a conception of
that agreement. In order, then, that it may be clear, the only requisite
is, that we shall know exactly in what the agreement consists; that it
shall have been carefully observed, and accurately remembered. We are said
not to have a clear conception of the resemblance among a set of objects,
when we have only a general feeling that they resemble, without having
analyzed their resemblance, or perceived in what points it consists, and
fixed in our memory an exact recollection of those points. This want of
clearness, or, as it may be otherwise called, this vagueness in the
general conception, may be owing either to our having no accurate
knowledge of the objects themselves, or merely to our not having carefully
compared them. Thus a person may have no clear idea of a ship because he
has never seen one, or because he remembers but little, and that faintly,
of what he has seen. Or he may have a perfect knowledge and remembrance of
many ships of various kinds, frigates among the rest, but he may have no
clear but only a confused idea of a frigate, because he has never been
told, and has not compared them sufficiently to have remarked and
remembered, in what particular points a frigate differs from some other
kind of ship.

It is not, however, necessary, in order to have clear ideas, that we
should know all the common properties of the things which we class
together. That would be to have our conception of the class complete as
well as clear. It is sufficient if we never class things together without
knowing exactly why we do so—without having ascertained exactly what
agreements we are about to include in our conception; and if, after having
thus fixed our conception, we never vary from it, never include in the
class any thing which has not those common properties, nor exclude from it
any thing which has. A clear conception means a determinate conception;
one which does not fluctuate, which is not one thing to-day and another
to-morrow, but remains fixed and invariable, except when, from the
progress of our knowledge, or the correction of some error, we consciously
add to it or alter it. A person of clear ideas is a person who always
knows in virtue of what properties his classes are constituted; what
attributes are connoted by his general names.

The principal requisites, therefore, of clear conceptions, are habits of
attentive observation, an extensive experience, and a memory which
receives and retains an exact image of what is observed. And in proportion
as any one has the habit of observing minutely and comparing carefully a
particular class of phenomena, and an accurate memory for the results of
the observation and comparison, so will his conceptions of that class of
phenomena be clear; provided he has the indispensable habit (naturally,
however, resulting from those other endowments), of never using general
names without a precise connotation.

As the clearness of our conceptions chiefly depends on the _carefulness_
and _accuracy_ of our observing and comparing faculties, so their
appropriateness, or rather the chance we have of hitting upon the
appropriate conception in any case, mainly depends on the _activity_ of
the same faculties. He who by habit, grounded on sufficient natural
aptitude, has acquired a readiness in accurately observing and comparing
phenomena, will perceive so many more agreements, and will perceive them
so much more rapidly than other people, that the chances are much greater
of his perceiving, in any instance, the agreement on which the important
consequences depend.

§ 6. It is of so much importance that the part of the process of
investigating truth, discussed in this chapter, should be rightly
understood, that I think it is desirable to restate the results we have
arrived at, in a somewhat different mode of expression.

We can not ascertain general truths, that is, truths applicable to
classes, unless we have formed the classes in such a manner that general
truths can be affirmed of them. In the formation of any class, there is
involved a conception of it as a class, that is, a conception of certain
circumstances as being those which characterize the class, and distinguish
the objects composing it from all other things. When we know exactly what
these circumstances are, we have a clear idea (or conception) of the
class, and of the meaning of the general name which designates it. The
primary condition implied in having this clear idea, is that the class be
really a class; that it correspond to a real distinction; that the things
it includes really do agree with one another in certain particulars, and
differ, in those same particulars, from all other things. A person without
clear ideas is one who habitually classes together, under the same general
names, things which have no common properties, or none which are not
possessed also by other things; or who, if the usage of other people
prevents him from actually misclassing things, is unable to state to
himself the common properties in virtue of which he classes them rightly.

But is it not the sole requisite of classification that the classes should
be real classes, framed by a legitimate mental process? Some modes of
classing things are more valuable than others for human uses, whether of
speculation or of practice; and our classifications are not well made,
unless the things which they bring together not only agree with each other
in something which distinguishes them from all other things, but agree
with each other and differ from other things in the very circumstances
which are of primary importance for the purpose (theoretical or practical)
which we have in view, and which constitutes the problem before us. In
other words, our conceptions, though they may be clear, are not
_appropriate_ for our purpose, unless the properties we comprise in them
are those which will help us toward what we wish to understand—_i.e._,
either those which go deepest into the nature of the things, if our object
be to understand that, or those which are most closely connected with the
particular property which we are endeavoring to investigate.

We can not, therefore, frame good general conceptions beforehand. That the
conception we have obtained is the one we want, can only be known when we
have done the work for the sake of which we wanted it; when we completely
understand the general character of the phenomena, or the conditions of
the particular property with which we concern ourselves. General
conceptions formed without this thorough knowledge, are Bacon’s “notiones
temerè à rebus abstractæ.” Yet such premature conceptions we must be
continually making up, in our progress to something better. They are an
impediment to the progress of knowledge, only when they are permanently
acquiesced in. When it has become our habit to group things in wrong
classes—in groups which either are not really classes, having no
distinctive points of agreement (absence of _clear_ ideas), or which are
not classes of which any thing important to our purpose can be predicated
(absence of _appropriate_ ideas); and when, in the belief that these badly
made classes are those sanctioned by nature, we refuse to exchange them
for others, and can not or will not make up our general conceptions from
any other elements; in that case all the evils which Bacon ascribes to his
“notiones temerè abstractæ” really occur. This was what the ancients did
in physics, and what the world in general does in morals and politics to
the present day.

It would thus, in my view of the matter, be an inaccurate mode of
expression to say, that obtaining appropriate conceptions is a condition
precedent to generalization. Throughout the whole process of comparing
phenomena with one another for the purpose of generalization, the mind is
trying to make up a conception; but the conception which it is trying to
make up is that of the really important point of agreement in the
phenomena. As we obtain more knowledge of the phenomena themselves, and of
the conditions on which their important properties depend, our views on
this subject naturally alter; and thus we advance from a less to a more
"appropriate" general conception, in the progress of our investigations.

We ought not, at the same time, to forget that the really important
agreement can not always be discovered by mere comparison of the very
phenomena in question, without the aid of a conception acquired elsewhere;
as in the case, so often referred to, of the planetary orbits.

The search for the agreement of a set of phenomena is in truth very
similar to the search for a lost or hidden object. At first we place
ourselves in a sufficiently commanding position, and cast our eyes round
us, and if we can see the object it is well; if not, we ask ourselves
mentally what are the places in which it may be hid, in order that we may
there search for it: and so on, until we imagine the place where it really
is. And here too we require to have had a previous conception, or
knowledge, of those different places. As in this familiar process, so in
the philosophical operation which it illustrates, we first endeavor to
find the lost object or recognize the common attribute, without
conjecturally invoking the aid of any previously acquired conception, or,
in other words, of any hypothesis. Having failed in this, we call upon our
imagination for some hypothesis of a possible place, or a possible point
of resemblance, and then look to see whether the facts agree with the
conjecture.

For such cases something more is required than a mind accustomed to
accurate observation and comparison. It must be a mind stored with general
conceptions, previously acquired, of the sorts which bear affinity to the
subject of the particular inquiry. And much will also depend on the
natural strength and acquired culture of what has been termed the
scientific imagination; on the faculty possessed of mentally arranging
known elements into new combinations, such as have not yet been observed
in nature, though not contradictory to any known laws.

But the variety of intellectual habits, the purposes which they serve, and
the modes in which they may be fostered and cultivated, are considerations
belonging to the Art of Education: a subject far wider than Logic, and
which this treatise does not profess to discuss. Here, therefore, the
present chapter may properly close.




                               Chapter III.


Of Naming, As Subsidiary To Induction.


§ 1. It does not belong to the present undertaking to dwell on the
importance of language as a medium of human intercourse, whether for
purposes of sympathy or of information. Nor does our design admit of more
than a passing allusion to that great property of names, on which their
functions as an intellectual instrument are, in reality, ultimately
dependent; their potency as a means of forming, and of riveting,
associations among our other ideas; a subject on which an able
thinker(210) has thus written:

“Names are impressions of sense, and as such take the strongest hold on
the mind, and of all other impressions can be most easily recalled and
retained in view. They therefore serve to give a point of attachment to
all the more volatile objects of thought and feeling. Impressions that
when passed might be dissipated forever, are, by their connection with
language, always within reach. Thoughts, of themselves, are perpetually
slipping out of the field of immediate mental vision; but the name abides
with us, and the utterance of it restores them in a moment. Words are the
custodiers of every product of mind less impressive than themselves. All
extensions of human knowledge, all new generalizations, are fixed and
spread, even unintentionally, by the use of words. The child growing up
learns, along with the vocables of his mother-tongue, that things which he
would have believed to be different are, in important points, the same.
Without any formal instruction, the language in which we grow up teaches
us all the common philosophy of the age. It directs us to observe and know
things which we should have overlooked; it supplies us with
classifications ready made, by which things are arranged (as far as the
light of by-gone generations admits) with the objects to which they bear
the greatest total resemblance. The number of general names in a language,
and the degree of generality of those names, afford a test of the
knowledge of the era, and of the intellectual insight which is the
birthright of any one born into it.”

It is not, however, of the functions of Names, considered generally, that
we have here to treat, but only of the manner and degree in which they are
directly instrumental to the investigation of truth; in other words, to
the process of induction.

§ 2. Observation and Abstraction, the operations which formed the subject
of the two foregoing chapters, are conditions indispensable to induction;
there can be no induction where they are not. It has been imagined that
Naming is also a condition equally indispensable. There are thinkers who
have held that language is not solely, according to a phrase generally
current, _an_ instrument of thought, but _the_ instrument; that names, or
something equivalent to them, some species of artificial signs, are
necessary to reasoning; that there could be no inference, and consequently
no induction, without them. But if the nature of reasoning was correctly
explained in the earlier part of the present work, this opinion must be
held to be an exaggeration, though of an important truth. If reasoning be
from particulars to particulars, and if it consist in recognizing one fact
as a mark of another, or a mark of a mark of another, nothing is required
to render reasoning possible, except senses and association; senses to
perceive that two facts are conjoined; association, as the law by which
one of those two facts raises up the idea of the other.(211) For these
mental phenomena, as well as for the belief or expectation which follows,
and by which we recognize as having taken place, or as about to take
place, that of which we have perceived a mark, there is evidently no need
of language. And this inference of one particular fact from another is a
case of induction. It is of this sort of induction that brutes are
capable; it is in this shape that uncultivated minds make almost all their
inductions, and that we all do so in the cases in which familiar
experience forces our conclusions upon us without any active process of
inquiry on our part, and in which the belief or expectation follows the
suggestion of the evidence with the promptitude and certainty of an
instinct.(212)

§ 3. But though inference of an inductive character is possible without
the use of signs, it could never, without them, be carried much beyond the
very simple cases which we have just described, and which form, in all
probability, the limit of the reasonings of those animals to whom
conventional language is unknown. Without language, or something
equivalent to it, there could only be as much reasoning from experience as
can take place without the aid of general propositions. Now, though in
strictness we may reason from past experience to a fresh individual case
without the intermediate stage of a general proposition, yet without
general propositions we should seldom remember what past experience we
have had, and scarcely ever what conclusions that experience will warrant.
The division of the inductive process into two parts, the first
ascertaining what is a mark of the given fact, the second whether in the
new case that mark exists, is natural, and scientifically indispensable.
It is, indeed, in a majority of cases, rendered necessary by mere distance
of time. The experience by which we are to guide our judgments may be
other people’s experience, little of which can be communicated to us
otherwise than by language; when it is our own, it is generally experience
long past; unless, therefore, it were recorded by means of artificial
signs, little of it (except in cases involving our intenser sensations or
emotions, or the subjects of our daily and hourly contemplation) would be
retained in the memory. It is hardly necessary to add, that when the
inductive inference is of any but the most direct and obvious nature—when
it requires several observations or experiments, in varying circumstances,
and the comparison of one of these with another—it is impossible to
proceed a step, without the artificial memory which words bestow. Without
words, we should, if we had often seen A and B in immediate and obvious
conjunction, expect B whenever we saw A; but to discover their conjunction
when not obvious, or to determine whether it is really constant or only
casual, and whether there is reason to expect it under any given change of
circumstances, is a process far too complex to be performed without some
contrivance to make our remembrance of our own mental operations accurate.
Now, language is such a contrivance. When that instrument is called to our
aid, the difficulty is reduced to that of making our remembrance of the
meaning of words accurate. This being secured, whatever passes through our
minds may be remembered accurately, by putting it carefully into words,
and committing the words either to writing or to memory.

The function of Naming, and particularly of General Names, in Induction,
may be recapitulated as follows. Every inductive inference which is good
at all, is good for a whole class of cases; and, that the inference may
have any better warrant of its correctness than the mere clinging together
of two ideas, a process of experimentation and comparison is necessary; in
which the whole class of cases must be brought to view, and some
uniformity in the course of nature evolved and ascertained, since the
existence of such a uniformity is required as a justification for drawing
the inference in even a single case. This uniformity, therefore, may be
ascertained once for all; and if, being ascertained, it can be remembered,
it will serve as a formula for making, in particular cases, all such
inferences as the previous experience will warrant. But we can only secure
its being remembered, or give ourselves even a chance of carrying in our
memory any considerable number of such uniformities, by registering them
through the medium of permanent signs; which (being, from the nature of
the case, signs not of an individual fact, but of a uniformity, that is,
of an indefinite number of facts similar to one another) are general
signs; universals; general names, and general propositions.

§ 4. And here I can not omit to notice an oversight committed by some
eminent thinkers; who have said that the cause of our using general names
is the infinite multitude of individual objects, which, making it
impossible to have a name for each, compels us to make one name serve for
many.

This is a very limited view of the function of general names. Even if
there were a name for every individual object, we should require general
names as much as we now do. Without them we could not express the result
of a single comparison, nor record any one of the uniformities existing in
nature; and should be hardly better off in respect to Induction than if we
had no names at all. With none but names of individuals (or, in other
words, proper names), we might, by pronouncing the name, suggest the idea
of the object, but we could not assert any proposition; except the
unmeaning ones formed by predicating two proper names one of another. It
is only by means of general names that we can convey any information,
predicate any attribute, even of an individual, much more of a class.
Rigorously speaking, we could get on without any other general names than
the abstract names of attributes; all our propositions might be of the
form “such an individual object possesses such an attribute,” or “such an
attribute is always (or never) conjoined with such another attribute.” In
fact, however, mankind have always given general names to objects as well
as attributes, and indeed before attributes: but the general names given
to objects imply attributes, derive their whole meaning from attributes;
and are chiefly useful as the language by means of which we predicate the
attributes which they connote.

It remains to be considered what principles are to be adhered to in giving
general names, so that these names, and the general propositions in which
they fill a place, may conduce most to the purposes of Induction.




                               Chapter IV.


Of The Requisites Of A Philosophical Language, And The Principles Of
Definition.


§ 1. In order that we may possess a language perfectly suitable for the
investigation and expression of general truths, there are two principal,
and several minor requisites. The first is, that every general name should
have a meaning, steadily fixed, and precisely determined. When, by the
fulfillment of this condition, such names as we possess are fitted for the
due performance of their functions, the next requisite, and the second in
order of importance, is that we should possess a name wherever one is
needed; wherever there is any thing to be designated by it, which it is of
importance to express.

The former of these requisites is that to which our attention will be
exclusively directed in the present chapter.

§ 2. Every general name, then, must have a certain and knowable meaning.
Now the meaning (as has so often been explained) of a general connotative
name, resides in the connotation; in the attribute on account of which,
and to express which, the name is given. Thus, the name animal being given
to all things which possess the attributes of sensation and voluntary
motion, the word connotes those attributes exclusively, and they
constitute the whole of its meaning. If the name be abstract, its
denotation is the same with the connotation of the corresponding concrete;
it designates directly the attribute, which the concrete term implies. To
give a precise meaning to general names is, then, to fix with steadiness
the attribute or attributes connoted by each concrete general name, and
denoted by the corresponding abstract. Since abstract names, in the order
of their creation, do not precede but follow concrete ones, as is proved
by the etymological fact that they are almost always derived from them; we
may consider their meaning as determined by, and dependent on, the meaning
of their concrete; and thus the problem of giving a distinct meaning to
general language, is all included in that of giving a precise connotation
to all concrete general names.

This is not difficult in the case of new names; of the technical terms
created by scientific inquirers for the purposes of science or art. But
when a name is in common use, the difficulty is greater; the problem in
this case not being that of choosing a convenient connotation for the
name, but of ascertaining and fixing the connotation with which it is
already used. That this can ever be a matter of doubt, is a sort of
paradox. But the vulgar (including in that term all who have not accurate
habits of thought) seldom know exactly what assertion they intend to make,
what common property they mean to express, when they apply the same name
to a number of different things. All which the name expresses with them,
when they predicate it of an object, is a confused feeling of resemblance
between that object and some of the other things which they have been
accustomed to denote by the name. They have applied the name Stone to
various objects previously seen; they see a new object, which appears to
them somewhat like the former, and they call it a stone, without asking
themselves in what respect it is like, or what mode or degree of
resemblance the best authorities, or even they themselves, require as a
warrant for using the name. This rough general impression of resemblance
is, however, made up of particular circumstances of resemblance; and into
these it is the business of the logician to analyze it; to ascertain what
points of resemblance among the different things commonly called by the
name, have produced in the common mind this vague feeling of likeness;
have given to the things the similarity of aspect, which has made them a
class, and has caused the same name to be bestowed upon them.

But though general names are imposed by the vulgar without any more
definite connotation than that of a vague resemblance; general
propositions come in time to be made, in which predicates are applied to
those names, that is, general assertions are made concerning the _whole_
of the things which are denoted by the name. And since by each of these
propositions some attribute, more or less precisely conceived, is of
course predicated, the ideas of these various attributes thus become
associated with the name, and in a sort of uncertain way it comes to
connote them; there is a hesitation to apply the name in any new case in
which any of the attributes familiarly predicated of the class do not
exist. And thus, to common minds, the propositions which they are in the
habit of hearing or uttering concerning a class make up in a loose way a
sort of connotation for the class name. Let us take, for instance, the
word Civilized. How few could be found, even among the most educated
persons, who would undertake to say exactly what the term Civilized
connotes. Yet there is a feeling in the minds of all who use it, that they
are using it with a meaning; and this meaning is made up, in a confused
manner, of every thing which they have heard or read that civilized men or
civilized communities are, or may be expected to be.

It is at this stage, probably, in the progress of a concrete name, that
the corresponding abstract name generally comes into use. Under the notion
that the concrete name must of course convey a meaning, or, in other
words, that there is some property common to all things which it denotes,
people give a name to this common property; from the concrete Civilized,
they form the abstract Civilization. But since most people have never
compared the different things which are called by the concrete name, in
such a manner as to ascertain what properties these things have in common,
or whether they have any; each is thrown back upon the marks by which he
himself has been accustomed to be guided in his application of the term;
and these, being merely vague hearsays and current phrases, are not the
same in any two persons, nor in the same person at different times. Hence
the word (as Civilization, for example) which professes to be the
designation of the unknown common property, conveys scarcely to any two
minds the same idea. No two persons agree in the things they predicate of
it; and when it is itself predicated of any thing, no other person knows,
nor does the speaker himself know with precision, what he means to assert.
Many other words which could be named, as the word _honor_, or the word
_gentleman_, exemplify this uncertainty still more strikingly.

It needs scarcely be observed, that general propositions of which no one
can tell exactly what they assert, can not possibly have been brought to
the test of a correct induction. Whether a name is to be used as an
instrument of thinking, or as a means of communicating the result of
thought, it is imperative to determine exactly the attribute or attributes
which it is to express; to give it, in short, a fixed and ascertained
connotation.

§ 3. It would, however, be a complete misunderstanding of the proper
office of a logician in dealing with terms already in use, if we were to
think that because a name has not at present an ascertained connotation,
it is competent to any one to give it such a connotation at his own
choice. The meaning of a term actually in use is not an arbitrary quantity
to be fixed, but an unknown quantity to be sought.

In the first place, it is obviously desirable to avail ourselves, as far
as possible, of the associations already connected with the name; not
enjoining the employment of it in a manner which conflicts with all
previous habits, and especially not so as to require the rupture of those
strongest of all associations between names, which are created by
familiarity with propositions in which they are predicated of one another.
A philosopher would have little chance of having his example followed, if
he were to give such a meaning to his terms as should require us to call
the North American Indians a civilized people, or the higher classes in
Europe savages; or to say that civilized people live by hunting, and
savages by agriculture. Were there no other reason, the extreme difficulty
of effecting so complete a revolution in speech would be more than a
sufficient one. The endeavor should be, that all generally received
propositions into which the term enters, should be at least as true after
its meaning is fixed, as they were before; and that the concrete name,
therefore, should not receive such a connotation as shall prevent it from
denoting things which, in common language, it is currently affirmed of.
The fixed and precise connotation which it receives should not be in
deviation from, but in agreement (as far as it goes) with, the vague and
fluctuating connotation which the term already had.

To fix the connotation of a concrete name, or the denotation of the
corresponding abstract, is to define the name. When this can be done
without rendering any received assertions inadmissible, the name can be
defined in accordance with its received use, which is vulgarly called
defining not the name but the thing. What is meant by the improper
expression of defining a thing (or rather a class of things—for nobody
talks of defining an individual), is to define the name, subject to the
condition that it shall denote those things. This, of course, supposes a
comparison of the things, feature by feature and property by property, to
ascertain what attributes they agree in; and not unfrequently an operation
strictly inductive, for the purpose of ascertaining some unobvious
agreement, which is the cause of the obvious agreements.

For, in order to give a connotation to a name, consistently with its
denoting certain objects, we have to make our selection from among the
various attributes in which those objects agree. To ascertain in what they
do agree is, therefore, the first logical operation requisite. When this
has been done as far as is necessary or practicable, the question arises,
which of these common attributes shall be selected to be associated with
the name. For if the class which the name denotes be a Kind, the common
properties are innumerable; and even if not, they are often extremely
numerous. Our choice is first limited by the preference to be given to
properties which are well known, and familiarly predicated of the class;
but even these are often too numerous to be all included in the
definition, and, besides, the properties most generally known may not be
those which serve best to mark out the class from all others. We should
therefore select from among the common properties (if among them any such
are to be found) those on which it has been ascertained by experience, or
proved by deduction, that many others depend; or at least which are sure
marks of them, and from whence, therefore, many others will follow by
inference. We thus see that to frame a good definition of a name already
in use, is not a matter of choice but of discussion, and discussion not
merely respecting the usage of language, but respecting the properties of
things, and even the origin of those properties. And hence every
enlargement of our knowledge of the objects to which the name is applied,
is liable to suggest an improvement in the definition. It is impossible to
frame a perfect set of definitions on any subject, until the theory of the
subject is perfect; and as science makes progress, its definitions are
also progressive.

§ 4. The discussion of Definitions, in so far as it does not turn on the
use of words but on the properties of things, Dr. Whewell calls the
Explication of Conceptions. The act of ascertaining, better than before,
in what particulars any phenomena which are classed together agree, he
calls in his technical phraseology, unfolding the general conception in
virtue of which they are so classed. Making allowance for what appears to
me the darkening and misleading tendency of this mode of expression,
several of his remarks are so much to the purpose, that I shall take the
liberty of transcribing them.

He observes,(213) that many of the controversies which have had an
important share in the formation of the existing body of science, have
“assumed the form of a battle of Definitions. For example, the inquiry
concerning the laws of falling bodies led to the question whether the
proper definition of a _uniform force_ is that it generates a velocity
proportional to the _space_ from rest, or to the _time_. The controversy
of the _vis viva_ was what was the proper definition of the _measure of
force_. A principal question in the classification of minerals is, what is
the definition of a _mineral species_. Physiologists have endeavored to
throw light on their subject by defining _organization_, or some similar
term.” Questions of the same nature were long open and are not yet
completely closed, respecting the definitions of Specific Heat, Latent
Heat, Chemical Combination, and Solution.

“It is very important for us to observe, that these controversies have
never been questions of insulated and _arbitrary_ definitions, as men seem
often tempted to imagine them to have been. In all cases there is a tacit
assumption of some proposition which is to be expressed by means of the
definition, and which gives it its importance. The dispute concerning the
definition thus acquires a real value, and becomes a question concerning
true and false. Thus, in the discussion of the question, What is a uniform
force? it was taken for granted that gravity is a uniform force. In the
debate of the _vis viva_, it was assumed that in the mutual action of
bodies the whole effect of the force is unchanged. In the zoological
definition of species (that it consists of individuals which have, or may
have, sprung from the same parents), it is presumed that individuals so
related resemble each other more than those which are excluded by such a
definition; or, perhaps, that species so defined have permanent and
definite differences. A definition of organization, or of some other term
which was not employed to express some principle, would be of no value.

“The establishment, therefore, of a right definition of a term, may be a
useful step in the explication of our conceptions; but this will be the
case then only when we have under our consideration some proposition in
which the term is employed. For then the question really is, how the
conception shall be understood and defined in order that the proposition
may be true.

“To unfold our conceptions by means of definitions has never been
serviceable to science, except when it has been associated with an
immediate use of the definitions. The endeavor to define a Uniform Force
was combined with the assertion that gravity is a uniform force; the
attempt to define Accelerating Force was immediately followed by the
doctrine that accelerating forces may be compounded; the process of
defining Momentum was connected with the principle that momenta gained and
lost are equal; naturalists would have given in vain the definition of
Species which we have quoted, if they had not also given the characters of
species so separated.... Definition may be the best mode of explaining our
conception, but that which alone makes it worth while to explain it in any
mode, is the opportunity of using it in the expression of truth. When a
definition is propounded to us as a useful step in knowledge, we are
always entitled to ask what principle it serves to enunciate.”

In giving, then, an exact connotation to the phrase, “a uniform force,”
the condition was understood, that the phrase should continue to denote
gravity. The discussion, therefore, respecting the definition, resolved
itself into this question, What is there of a uniform nature in the
motions produced by gravity? By observations and comparisons, it was found
that what was uniform in those motions was the ratio of the velocity
acquired to the time elapsed; equal velocities being added in equal times.
A uniform force, therefore, was defined a force which adds equal
velocities in equal times. So, again, in defining momentum. It was already
a received doctrine that, when two objects impinge upon one another, the
momentum lost by the one is equal to that gained by the other. This
proposition it was deemed necessary to preserve, not from the motive
(which operates in many other cases) that it was firmly fixed in popular
belief; for the proposition in question had never been heard of by any but
the scientifically instructed. But it was felt to contain a truth; even a
superficial observation of the phenomena left no doubt that in the
propagation of motion from one body to another, there was something of
which the one body gained precisely what the other lost; and the word
momentum had been invented to express this unknown something. The
settlement, therefore, of the definition of momentum, involved the
determination of the question, What is that of which a body, when it sets
another body in motion, loses exactly as much as it communicates? And when
experiment had shown that this _something_ was the product of the velocity
of the body by its mass, or quantity of matter, this became the definition
of momentum.

The following remarks,(214) therefore, are perfectly just: “The business
of definition is part of the business of discovery.... To define, so that
our definition shall have any scientific value, requires no small portion
of that sagacity by which truth is detected.... When it has been clearly
seen what ought to be our definition, it must be pretty well known what
truth we have to state. The definition, as well as the discovery, supposes
a decided step in our knowledge to have been made. The writers on Logic,
in the Middle Ages, made Definition the last stage in the progress of
knowledge; and in this arrangement at least, the history of science, and
the philosophy derived from the history, confirm their speculative views.”
For in order to judge finally how the name which denotes a class may best
be defined, we must know all the properties common to the class, and all
the relations of causation or dependence among those properties.

If the properties which are fittest to be selected as marks of other
common properties are also obvious and familiar, and especially if they
bear a great part in producing that general air of resemblance which was
the original inducement to the formation of the class, the definition will
then be most felicitous. But it is often necessary to define the class by
some property not familiarly known, provided that property be the best
mark of those which are known. M. De Blainville, for instance, founded his
definition of life on the process of decomposition and recomposition which
incessantly takes place in every living body, so that the particles
composing it are never for two instants the same. This is by no means one
of the most obvious properties of living bodies; it might escape
altogether the notice of an unscientific observer. Yet great authorities
(independently of M. De Blainville, who is himself a first-rate authority)
have thought that no other property so well answers the conditions
required for the definition.

§ 5. Having laid down the principles which ought for the most part to be
observed in attempting to give a precise connotation to a term in use, I
must now add, that it is not always practicable to adhere to those
principles, and that even when practicable, it is occasionally not
desirable.

Cases in which it is impossible to comply with all the conditions of a
precise definition of a name in agreement with usage, occur very
frequently. There is often no one connotation capable of being given to a
word, so that it shall still denote every thing it is accustomed to
denote; or that all the propositions into which it is accustomed to enter,
and which have any foundation in truth, shall remain true. Independently
of accidental ambiguities, in which the different meanings have no
connection with one another; it continually happens that a word is used in
two or more senses derived from each other, but yet radically distinct. So
long as a term is vague, that is, so long as its connotation is not
ascertained and permanently fixed, it is constantly liable to be applied
by _extension_ from one thing to another, until it reaches things which
have little, or even no, resemblance to those which were first designated
by it.

“Suppose,” says Dugald Stewart, in his _Philosophical Essays_,(215) “that
the letters A, B, C, D, E, denote a series of objects; that A possesses
some one quality in common with B; B a quality in common with C; C a
quality in common with D; D a quality in common with E; while at the same
time, no quality can be found which belongs in common to any _three_
objects in the series. Is it not conceivable, that the affinity between A
and B may produce a transference of the name of the first to the second;
and that, in consequence of the other affinities which connect the
remaining objects together, the same name may pass in succession from B to
C; from C to D; and from D to E? In this manner, a common appellation will
arise between A and E, although the two objects may, in their nature and
properties, be so widely distant from each other, that no stretch of
imagination can conceive how the thoughts were led from the former to the
latter. The transitions, nevertheless, may have been all so easy and
gradual, that, were they successfully detected by the fortunate ingenuity
of a theorist, we should instantly recognize, not only the verisimilitude,
but the truth of the conjecture: in the same way as we admit, with the
confidence of intuitive conviction, the certainty of the well-known
etymological process which connects the Latin preposition _e_ or _ex_ with
the English substantive _stranger_, the moment that the intermediate links
of the chain are submitted to our examination.”(216)

The applications which a word acquires by this gradual extension of it
from one set of objects to another, Stewart, adopting an expression from
Mr. Payne Knight, calls its _transitive_ applications; and after briefly
illustrating such of them as are the result of local or casual
associations, he proceeds as follows:(217)

“But although by far the greater part of the transitive or derivative
applications of words depend on casual and unaccountable caprices of the
feelings or the fancy, there are certain cases in which they open a very
interesting field of philosophical speculation. Such are those, in which
an analogous transference of the corresponding term may be remarked
universally, or very generally, in other languages; and in which, of
course, the uniformity of the result must be ascribed to the essential
principles of the human frame. Even in such cases, however, it will by no
means be always found, on examination, that the various applications of
the same term have arisen from any common quality or qualities in the
objects to which they relate. In the greater number of instances, they may
be traced to some natural and universal associations of ideas, founded in
the common faculties, common organs, and common condition of the human
race.... According to the different degrees of intimacy and strength in
the associations on which the _transitions_ of language are founded, very
different effects may be expected to arise. Where the association is
slight and casual, the several meanings will remain distinct from each
other, and will often, in process of time, assume the appearance of
capricious varieties in the use of the same arbitrary sign. _Where the
association is so natural and habitual as to become virtually
indissoluble, the transitive meanings will coalesce in one complex
conception; and every new transition will become a more comprehensive
generalization of the term in question._”

I solicit particular attention to the law of mind expressed in the last
sentence, and which is the source of the perplexity so often experienced
in detecting these transitions of meaning. Ignorance of that law is the
shoal on which some of the most powerful intellects which have adorned the
human race have been stranded. The inquiries of Plato into the definitions
of some of the most general terms of moral speculation are characterized
by Bacon as a far nearer approach to a true inductive method than is
elsewhere to be found among the ancients, and are, indeed, almost perfect
examples of the preparatory process of comparison and abstraction; but,
from being unaware of the law just mentioned, he often wasted the powers
of this great logical instrument on inquiries in which it could realize no
result, since the phenomena, whose common properties he so elaborately
endeavored to detect, had not really any common properties. Bacon himself
fell into the same error in his speculations on the nature of heat, in
which he evidently confounded under the name hot, classes of phenomena
which have no property in common. Stewart certainly overstates the matter
when he speaks of “a prejudice which has descended to modern times from
the scholastic ages, that when a word admits of a variety of
significations, these different significations must all be species of the
same genus, and must consequently include some essential idea common to
every individual to which the generic term can be applied;”(218) for both
Aristotle and his followers were well aware that there are such things as
ambiguities of language, and delighted in distinguishing them. But they
never suspected ambiguity in the cases where (as Stewart remarks) the
association on which the transition of meaning was founded is so natural
and habitual, that the two meanings blend together in the mind, and a real
transition becomes an apparent generalization. Accordingly they wasted
infinite pains in endeavoring to find a definition which would serve for
several distinct meanings at once; as in an instance noticed by Stewart
himself, that of “causation; the ambiguity of the word which, in the Greek
language corresponds to the English word _cause_, having suggested to them
the vain attempt of tracing the common idea which, in the case of any
_effect_, belongs to the _efficient_, to the _matter_, to the _form_, and
to the _end_. The idle generalities” (he adds) “we meet with in other
philosophers, about the ideas of the _good_, the _fit_, and the
_becoming_, have taken their rise from the same undue influence of popular
epithets on the speculations of the learned.”(219)

Among the words which have undergone so many successive transitions of
meaning that every trace of a property common to all the things they are
applied to, or at least common and also peculiar to those things, has been
lost, Stewart considers the word Beautiful to be one. And (without
attempting to decide a question which in no respect belongs to logic) I
can not but feel, with him, considerable doubt whether the word beautiful
connotes the same property when we speak of a beautiful color, a beautiful
face, a beautiful scene, a beautiful character, and a beautiful poem. The
word was doubtless extended from one of these objects to another on
account of a resemblance between them, or, more probably, between the
emotions they excited; and, by this progressive extension, it has at last
reached things very remote from those objects of sight to which there is
no doubt that it was first appropriated; and it is at least questionable
whether there is now any property common to all the things which,
consistently with usage, may be called beautiful, except the property of
agreeableness, which the term certainly does connote, but which can not be
all that people usually intend to express by it, since there are many
agreeable things which are never called beautiful. If such be the case, it
is impossible to give to the word Beautiful any fixed connotation, such
that it shall denote all the objects which in common use it now denotes,
but no others. A fixed connotation, however, it ought to have; for, so
long as it has not, it is unfit to be used as a scientific term, and is a
perpetual source of false analogies and erroneous generalizations.

This, then, constitutes a case in exemplification of our remark, that even
when there is a property common to all the things denoted by a name, to
erect that property into the definition and exclusive connotation of the
name is not always desirable. The various things called beautiful
unquestionably resemble one another in being agreeable; but to make this
the definition of beauty, and so extend the word Beautiful to all
agreeable things, would be to drop altogether a portion of meaning which
the word really, though indistinctly, conveys, and to do what depends on
us toward causing those qualities of the objects which the word
previously, though vaguely, pointed at, to be overlooked and forgotten. It
is better, in such a case, to give a fixed connotation to the term by
restricting, than by extending its use; rather excluding from the epithet
Beautiful some things to which it is commonly considered applicable, than
leaving out of its connotation any of the qualities by which, though
occasionally lost sight of, the general mind may have been habitually
guided in the commonest and most interesting applications of the term. For
there is no question that when people call any thing beautiful, they think
they are asserting more than that it is merely agreeable. They think they
are ascribing a peculiar _sort_ of agreeableness, analogous to that which
they find in some other of the things to which they are accustomed to
apply the same name. If, therefore, there be any peculiar sort of
agreeableness which is common though not to all, yet to the principal
things which are called beautiful, it is better to limit the denotation of
the term to those things, than to leave that kind of quality without a
term to connote it, and thereby divert attention from its peculiarities.

§ 6. The last remark exemplifies a rule of terminology, which is of great
importance, and which has hardly yet been recognized as a rule, but by a
few thinkers of the present century. In attempting to rectify the use of a
vague term by giving it a fixed connotation, we must take care not to
discard (unless advisedly, and on the ground of a deeper knowledge of the
subject) any portion of the connotation which the word, in however
indistinct a manner, previously carried with it. For otherwise language
loses one of its inherent and most valuable properties, that of being the
conservator of ancient experience; the keeper-alive of those thoughts and
observations of former ages, which may be alien to the tendencies of the
passing time. This function of language is so often overlooked or
undervalued, that a few observations on it appear to be extremely
required.

Even when the connotation of a term has been accurately fixed, and still
more if it has been left in the state of a vague unanalyzed feeling of
resemblance; there is a constant tendency in the word, through familiar
use, to part with a portion of its connotation. It is a well-known law of
the mind, that a word originally associated with a very complex cluster of
ideas, is far from calling up all those ideas in the mind, every time the
word is used; it calls up only one or two, from which the mind runs on by
fresh associations to another set of ideas, without waiting for the
suggestion of the remainder of the complex cluster. If this were not the
case, processes of thought could not take place with any thing like the
rapidity which we know they possess. Very often, indeed, when we are
employing a word in our mental operations, we are so far from waiting
until the complex idea which corresponds to the meaning of the word is
consciously brought before us in all its parts, that we run on to new
trains of ideas by the other associations which the mere word excites,
without having realized in our imagination any part whatever of the
meaning; thus using the word, and even using it well and accurately, and
carrying on important processes of reasoning by means of it, in an almost
mechanical manner; so much so, that some metaphysicians, generalizing from
an extreme case, have fancied that all reasoning is but the mechanical use
of a set of terms according to