Chance, Love, and Logic




                  International Library of Psychology

                    Philosophy and Scientific Method


                        Chance, Love, and Logic




International Library of Psychology

Philosophy and Scientific Method

GENERAL EDITOR: C. K. OGDEN, M.A.


_VOLUMES ALREADY PUBLISHED_

    PHILOSOPHICAL STUDIES, _by_ G. E. MOORE, Litt.D.

    THE MISUSE OF MIND, _by_ KARIN STEPHEN. _Prefatory note by Henri
    Bergson_

    CONFLICT AND DREAM, _by_ W. H. R. RIVERS, F.R.S.

    PSYCHOLOGY AND POLITICS, _by_ W. H. R. RIVERS, F.R.S.

    TRACTATUS LOGICO-PHILOSOPHICUS, _by_ L. WITTGENSTEIN. _Introduction
    by Bertrand Russell_

    THE MEASUREMENT OF EMOTION, _by_ W. WHATELY SMITH. _Introduction by
    William Brown_

    PSYCHOLOGICAL TYPES, _by_ C. G. JUNG, M.D., LL.D.

    SCIENTIFIC THOUGHT, _by_ C. D. BROAD, Litt.D.

    THE MEANING OF MEANING, _by_ C. K. OGDEN _and_ I. A. RICHARDS

    CHARACTER AND THE UNCONSCIOUS, _by_ J. H. VAN DER HOOP


IN PREPARATION

    SCIENTIFIC METHOD, _by_ A. D. RITCHIE

    THE ANALYSIS OF MATTER, _by_ BERTRAND RUSSELL, F.R.S.

    PSYCHOLOGY AND ETHNOLOGY, _by_ W. H. R. RIVERS, F.R.S.

    INDIVIDUAL PSYCHOLOGY, _by_ ALFRED ADLER

    MATHEMATICS FOR PHILOSOPHERS, _by_ G. H. HARDY, F.R.S.

    THE PSYCHOLOGY OF MYTHS, _by_ G. ELLIOT SMITH, F.R.S.

    THE PHILOSOPHY OF THE UNCONSCIOUS _by_ E. VON HARTMANN.
    _Introduction by Prof. G. Elliot Smith_

    THE THEORY OF MEDICAL DIAGNOSIS, _by_ F. G. CROOKSHANK, M.D.,
    F.R.C.P.

    THE ELEMENTS OF PSYCHOTHERAPY, _by_ WILLIAM BROWN, M.D., D.Sc.

    EMOTION AND INSANITY, _by_ S. THALBITZER. _Introduction by Prof. H.
    Höffding_

    THE LAWS OF FEELING, _by_ F. PAULHAN

    THE PSYCHOLOGY OF MUSIC, _by_ EDWARD J. DENT

    COLOUR-HARMONY, _by_ JAMES WOOD

    THE DEVELOPMENT OF CHINESE THOUGHT, _by_ LIANG CHE CHIAO

    THE HISTORY OF MATERIALISM, _by_ F. A. LANGE

    PSYCHE, _by_ E. ROHDE

    THE PRIMITIVE MIND, _by_ P. RADIN, Ph.D.

    THE PSYCHOLOGY OF PRIMITIVE PEOPLES, _by_ B. MALINOWSKI, Ph.D.,
    D.Sc.

    THE STATISTICAL METHOD IN ECONOMICS, _by_ P. SARGANT FLORENCE

    THE PRINCIPLES OF CRITICISM, _by_ I. A. RICHARDS

    THE PHILOSOPHY OF ‘AS IF’ _by_ H. VAIHINGER




                        CHANCE, LOVE, AND LOGIC

                          PHILOSOPHICAL ESSAYS

                              BY THE LATE
                           CHARLES S. PEIRCE
                       THE FOUNDER OF PRAGMATISM

                      EDITED WITH AN INTRODUCTION
                                   BY
                            MORRIS R. COHEN

                     WITH A SUPPLEMENTARY ESSAY ON
                        THE PRAGMATISM OF PEIRCE

                                   BY
                               JOHN DEWEY

                                NEW YORK
                    HARCOURT, BRACE & COMPANY, INC.
             LONDON: KEGAN PAUL TRENCH, TRUBNER & CO., LTD.
                                  1923




                          COPYRIGHT, 1923, BY
                   HARCOURT, BRACE AND COMPANY, INC.


                         PRINTED IN THE U.S.A.




                                PREFACE


In the essays gathered together in this volume we have the most
developed and coherent available account of the philosophy of Charles S.
Peirce, whom James, Royce, Dewey, and leading thinkers in England,
France, Germany and Italy have placed in the forefront of the great
seminal minds of recent times. Besides their inherent value as the
expression of a highly original and fruitful mind, unusually well
trained and informed in the exact sciences, these essays are also
important as giving us the sources of a great deal of contemporary
American philosophy. Because of this historical importance no omissions
or changes have been made in the text beyond the correction of some
obvious slips and the recasting of a few expressions in the interest of
intelligibility.

In a subject which bristles with suggestions and difficulties the
temptation to add notes of explanation or dissent is almost insuperable.
But as such notes might easily have doubled the size of this volume I
have refrained from all comment on the text except in a few footnotes
(indicated, as usual, in brackets). The introduction is intended (and I
hope it will) help the reader to concatenate the various lines of
thought contained in these essays. I cannot pretend to have adequately
indicated their significance. Great minds like those of James and Royce
have been nourished by these writings and I am persuaded that they still
offer mines of fruitful suggestion. Prof. Dewey’s supplementary essay
indicates their value for the fundamental question of metaphysics, viz.
the nature of reality.

Grateful acknowledgment is here made to Mrs. Paul Carus and to the Open
Court Publishing Co. for permission to reprint the essays of Part II
from the _Monist_. The late Paul Carus was one of the very few who not
only gave Peirce an opportunity to publish, but publicly recognized the
importance of his writings.

I must also acknowledge my obligation to Professor Dewey for kind
permission to reprint his essay on the Pragmatism of Peirce from the
Journal of Philosophy, and to the editors of that Journal, Professors
Woodbridge and Bush, for permission to reprint some material of my own.
Part V of the Bibliography was compiled by Mr. Irving Smith.

MORRIS R. COHEN

THE COLLEGE OF THE CITY OF NEW YORK.




                           TABLE OF CONTENTS


INTRODUCTION vii

PROEM. THE RULES OF PHILOSOPHY 1

PART I. CHANCE AND LOGIC (Illustrations of the Logic of Science.)

1. The Fixation of Belief 7

2. How to Make Our Ideas Clear 32

3. The Doctrine of Chances 61

4. The Probability of Induction 82

5. The Order of Nature 106

6. Deduction, Induction and Hypothesis 131


PART II. LOVE AND CHANCE

1. The Architecture of Theories 157

2. The Doctrine of Necessity Examined 179

3. The Law of Mind 202

4. Man’s Glassy Essence 238

5. Evolutionary Love 267


SUPPLEMENTARY ESSAY—The Pragmatism of Peirce, by John Dewey 301




                              INTRODUCTION


Many and diverse are the minds that form the philosophic community.
There are, first and foremost, the great masters, the system builders
who rear their stately palaces towering to the moon. These architectonic
minds are served by a varied host of followers and auxiliaries. Some
provide the furnishings to make these mystic mansions of the mind more
commodious, while others are engaged in making their façades more
imposing. Some are busy strengthening weak places or building
much-needed additions, while many more are engaged in defending these
structures against the impetuous army of critics who are ever eager and
ready to pounce down upon and destroy all that is new or bears the
mortal mark of human imperfection. There are also the philologists,
those who are in a more narrow sense scholars, who dig not only for
facts or roots, but also for the stones which may serve either for
building or as weapons of destruction. Remote from all these, however,
are the intellectual rovers who, in their search for new fields, venture
into the thick jungle that surrounds the little patch of cultivated
science. They are not gregarious creatures, these lonely pioneers; and
in their wanderings they often completely lose touch with those who
tread the beaten paths. Those that return to the community often speak
strangely of strange things; and it is not always that they arouse
sufficient faith for others to follow them and change their trails into
high roads.

Few nowadays question the great value of these pioneer minds; and it is
often claimed that universities are established to facilitate their
work, and to prevent it from being lost. But universities, like other
well-managed institutions, can find place only for those who work well
in harness. The restless, impatient minds, like the socially or
conventionally unacceptable, are thus kept out, no matter how fruitful
their originality. Charles S. Peirce was certainly one of these restless
pioneer souls with the fatal gift of genuine originality. In his early
papers, in the _Journal of Speculative Philosophy_, and later, in the
_Monist_ papers reprinted as Part II of this volume, we get glimpses of
a vast philosophic system on which he was working with an unusual wealth
of material and apparatus. To a rich imagination and extraordinary
learning he added one of the most essential gifts of successful system
builders, the power to coin an apt and striking terminology. But the
admitted incompleteness of these preliminary sketches of his philosophic
system is not altogether due to the inherent difficulty of the task and
to external causes such as neglect and poverty. A certain inner
instability or lack of self-mastery is reflected in the outer moral or
conventional waywardness which, except for a few years at Johns Hopkins,
caused him to be excluded from a university career, and thus deprived
him of much needed stimulus to ordinary consistency and intelligibility.
As the years advanced, bringing little general interest in, or
recognition of, the brilliant logical studies of his early years, Peirce
became more and more fragmentary, cryptic, and involved; so that James,
the intellectual companion of his youth, later found his lectures on
pragmatism, “flashes of brilliant light relieved against Cimmerian
darkness”—a statement not to be entirely discounted by the fact that
James had no interest in or aptitude for formal logical or mathematical
considerations.

Despite these limitations, however, Peirce stands out as one of the
great founders of modern scientific logic; and in the realm of general
philosophy the development of some of his pregnant ideas has led to the
pragmatism and radical empiricism of James, as well as to the
mathematical idealism of Royce, and to the anti-nominalism which
characterizes the philosophic movement known as Neo-Realism. At any
rate, the work of James, Royce, and Russell, as well as that of
logicians like Schroeder, brings us of the present generation into a
better position to appreciate the significance of Peirce’s work, than
were his contemporaries.


                                   I


Peirce was by antecedents, training, and occupation a scientist. He was
a son of Benjamin Peirce, the great Harvard mathematician, and his early
environment, together with his training in the Lawrence Scientific
School, justified his favorite claim that he was brought up in a
laboratory. He made important contributions not only in mathematical
logic but also in photometric astronomy, geodesy, and psychophysics, as
well as in philology. For many years Peirce worked on the problems of
geodesy, and his contribution to the subject, his researches on the
pendulum, was at once recognized by European investigators in this
field. The International Geodetic Congress, to which he was the first
American representative, gave unusual attention to his paper, and men
like Cellerier and Plantamour acknowledged their obligations to him.[1]

This and other scientific work involving fine measurement, with the
correlative investigations into the theory of probable error, seem to
have been a decisive influence in the development of Peirce’s philosophy
of chance. Philosophers inexperienced in actual scientific measurement
may naïvely accept as absolute truth such statements as “every particle
of matter attracts every other particle directly as the product of their
masses and inversely as the square of the distance,” or “when hydrogen
and oxygen combine to form water the ratio of their weights is 1 : 8.”
But to those who are actually engaged in measuring natural phenomena
with instruments of precision, nature shows no such absolute constancy
or simplicity. As every laboratory worker knows, no two observers, and
no one observer in successive experiments, get absolutely identical
results. To the men of the heroic period of science this was no
difficulty. They held unquestioningly the Platonic faith that nature was
created on simple geometric lines, and all the minute variations were
attributable to the fault of the observer or the crudity of his
instruments. This heroic faith was, and still is, a most powerful
stimulus to scientific research and a protection against the incursions
of supernaturalism. But few would defend it to-day in its explicit form,
and there is little empirical evidence to show that while the observer
and his instruments are always varying, the objects which he measures
never deviate in the slightest from the simple law. Doubtless, as one
becomes more expert in the manipulation of physical instruments, there
is a noticeable diminution of the range of the personal “error,” but no
amount of skill and no refinement of our instruments have ever succeeded
in eliminating irregular, though small, variations. “Try to verify any
law of nature and you will find that the more precise your observations,
the more certain they will be to show irregular departure from the
law.”[2] There is certainly nothing in our empirical information to
prevent us from saying that all the so-called constants of nature are
merely instances of variation between limits so near each other that
their differences may be neglected for certain purposes. Moreover, the
approach to constancy is observed only in mass phenomena, when we are
dealing with very large numbers of particles; but social statistics also
approach constant ratios when the numbers are very large. Hence, without
denying discrepancies due solely to errors of observation, Peirce
contends that “we must suppose far more minute discrepancies to exist
owing to the imperfect cogency of the law itself, to a certain swerving
of the facts from any definite formula.”[3]

It is usual to associate disbelief in absolute laws of nature with
sentimental claims for freedom or theological miracles. It is,
therefore, well to insist that Peirce’s attack is entirely in the
interests of exact logic and a rational account of the physical
universe. As a rigorous logician familiar with the actual procedures by
which our knowledge of the various laws of nature is obtained, he could
not admit that experience could prove their claim to absoluteness. All
the physical laws actually known, like Boyle’s law or the law of
gravitation, involve excessive simplification of the phenomenal course
of events, and thus a large element of empirical inaccuracy. But a more
positive objection against the traditional assumption of absolute or
invariable laws of nature, is the fact that such assumption makes the
regularities of the universe ultimate, and thus cuts us off from the
possibility of ever explaining them or how there comes to be as much
regularity in the universe as there is. But in ordinary affairs, the
occurrence of any regularity is the very thing to be explained.
Moreover, modern statistical mechanics and thermodynamics (theory of
gases, entropy, etc.) suggest that the regularity in the universe is a
matter of gradual growth; that the whole of physical nature is a growth
from a chaos of diversity to a maximum of uniformity or entropy. A
leading physicist of the 19th Century, Boltzmann, has suggested that the
process of the whole physical universe is like that of a continuous
shaking up of a hap-hazard or chance mixture of things, which thus
gradually results in a progressively more uniform distribution. Since
Duns Scotus, students of logic have known that every real entity has its
individual character (its _haecceitas_ or _thisness_) which cannot be
explained or deduced from that which is uniform. Every explanation, for
example, of the moon’s path must take particular existences for granted.
Such original or underived individuality and diversity is precisely what
Peirce means by chance; and from this point of view chance is prior to
law.

All that is necessary to visualize this is to suppose that there is an
infinitesimal tendency in things to acquire habits, a tendency which is
itself an accidental variation grown habitual. We shall then be on the
road to explain the evolution and existence of the limited uniformities
actually prevailing in the physical world.

A good deal of the foregoing may sound somewhat mythologic. But even if
it were so it would have the merit of offering a rational alternative to
the mechanical mythology according to which all the atoms in the
universe are to-day precisely in the same condition in which they were
on the day of creation, a mythology which is forced to regard all the
empirical facts of spontaneity and novelty as illusory, or devoid of
substantial truth.

The doctrine of the primacy of chance naturally suggests the primacy of
mind. Just as law is a chance habit so is matter inert mind. The
principal law of mind is that ideas literally spread themselves
continuously and become more and more general or inclusive, so that
people who form communities of any sort develop general ideas in common.
When this continuous reaching-out of feeling becomes nurturing love,
such, e.g., which parents have for their offspring or thinkers for their
ideas, we have creative evolution.

James and Royce have called attention to the similarity between Peirce’s
doctrine of tychistic-agapism (chance and love) and the creative
evolution of Bergson. But while both philosophies aim to restore life
and growth in their account of the nature of things, Peirce’s approach
seems to me to have marked advantages, owing to its being in closer
touch with modern physics. Bergson’s procedure is largely based on the
contention that mechanics cannot explain certain empirical facts, such
as the supposed identity of the vertebrate eye and the eye of the
scallop. But the fact here is merely one of a certain resemblance of
pattern, which may well be explained by the mechanical principles of
convergent evolution. Peirce’s account involves no rejection of the
possibility of mechanical explanations. Indeed, by carrying chance into
the laws of mechanics he is enabled to elaborate a positive and highly
suggestive theory of protoplasm to explain the facts of plasticity and
habit.[4] Instead of postulating with Spencer and Bergson a continuous
growth of diversity, Peirce allows for growth of habits both in
diversity and in uniformity. The Spencerian mechanical philosophy
reduces all diversity to mere spatial differences. There can be no
substantial novelty; only new forms or combinations can arise in time.
The creative evolution of Bergson though intended to support the claims
of spontaneity is still like the Spencerian in assuming all evolution as
proceeding from the simple to the complex. Peirce allows for diversity
and specificity as part of the original character or endowment of
things, which in the course of time may increase in some respects and
diminish in others. Mind acquires the habit both of taking on, and also
of laying aside, habits. Evolution may thus lead to homogeneity or
uniformity as well as to greater heterogeneity.

Not only has Peirce a greater regard than even Bergson for the actual
diversity and spontaneity of things, but he is in a much better position
than any other modern philosopher to explain the order and coherence of
the world. This he effects by uniting the medieval regard for the
reality of universals with the modern scientific use of the concept of
continuity. The unfortunate war between the pioneers of modern science
and the adherents of the scholastic doctrine of substantial forms, has
been one of the great misfortunes of human thought, in that it made
absolute atomism and nominalism the professed _creed_ of physical
science. Now, extreme nominalism, the insistence on the reality of the
particular, leaves no room for the genuine reality of law. It leaves, as
Hume had the courage to admit, nothing whereby the present can determine
the future; so that anything is as likely to happen as not. From such a
chaotic world, the _procedure_ of modern natural and mathematical
science has saved us by the persistent use of the principle of
continuity; and no one has indicated this more clearly than Peirce who
was uniquely qualified to do so by being a close student both of Duns
Scotus and of modern scientific methods.

It is instructive in this respect to contrast the views of Peirce and
James. James, who so generously indicated his indebtedness to Peirce for
his pragmatism, was also largely indebted to Peirce for his doctrine of
radical empiricism.[5] The latter doctrine seeks to rescue the
continuity and fluidity of experience from the traditional British
empiricism or nominalism, which had resolved everything into a number of
mutually exclusive mental states. It is curious, however, that while in
his psychology James made extensive use of the principle of continuity,
he could not free himself from British nominalism in his
philosophy—witness the extreme individualism of his social philosophy or
the equally extreme anthropomorphism of his religion. Certain of
Peirce’s suggestions as to the use of continuity in social philosophy
have been developed by Royce in his theory of social consciousness and
the nature of the community;[6] but much remains to be worked out and we
can but repeat Peirce’s own hope: “May some future student go over this
ground again and have the leisure to give his results to the world.”

It is well to note, however, that after writing the papers included in
this volume Peirce continued to be occupied with the issues here raised.
This he most significantly indicated in the articles on logical topics
contributed to Baldwin’s Dictionary of Philosophy.[7]

In these articles it is naturally the logical bearing of the principles
of tychism (chance), synechism (continuity), and agapism (love) that is
stressed. To use the Kantian terminology, almost native to Peirce, the
regulative rather than the constitutive aspect of these principles is
emphasized. Thus the doctrine of chance is not only what it was for
James’ radical empiricism, a release from the blind necessity of a
“block universe,” but also a method of keeping open a possible
explanation of the genesis of the laws of nature and an interpretation
of them in accordance with the theorems of probability, so fruitful in
physical science as well as in practical life. So the doctrine of love
is not only a cosmologic one, showing how chance feeling generates order
or rational diversity through the habit of generality or continuity, but
it also gives us the meaning of truth in social terms, in showing that
the test as to whether any proposition is true postulates an indefinite
number of co-operating investigators. On its logical side the doctrine
of love (agapism) also recognized the important fact that general ideas
have a certain attraction which makes us divine their nature even though
we cannot clearly determine their precise meaning before developing
their possible consequences.

Of the doctrine of continuity we are told expressly[8] that “synechism
is not an ultimate absolute metaphysical doctrine. It is a regulative
principle of logic,” seeking the thread of identity in diverse cases and
avoiding hypotheses that this or that is ultimate and, therefore,
inexplicable. (Examples of such hypotheses are: the existence of
absolutely accurate or uniform laws of nature, the eternity and absolute
likeness of all atoms, etc.) To be sure, the synechist cannot deny that
there is an element of the inexplicable or ultimate, since it is
directly forced upon him. But he cannot regard it as a source of
explanation. The assumption of an inexplicability is a barrier on the
road to science. “The form under which alone anything can be understood
is the form of generality which is the same thing as continuity.”[9]
This insistence on the generality of intelligible form is perfectly
consistent with due emphases on the reality of the individual, which to
a Scotist realist connotes an element of will or will-resistence, but in
logical procedure means that the test of the truth or falsity of any
proposition refers us to particular perceptions.[10] But as no multitude
of individuals can exhaust the meaning of a continuum, which includes
also organizing relations of order, the full meaning of a concept cannot
be in any individual reaction, but is rather to be sought in the manner
in which all such reactions contribute to the development of the
concrete reasonableness of the whole evolutionary process. In scientific
procedure this means that integrity of belief in general is more
important than, because it is the condition of, particular true beliefs.


                                   II


This insistence on the continuity so effectually used as a heuristic
principle in natural and mathematical science, distinguishes the
pragmatism of Peirce from that of his follower James. Prof. Dewey has
developed this point authoritatively in the supplementary essay; but in
view of the general ignorance as to the sources of pragmatism which
prevails in this incurious age, some remarks on the actual historical
origin of pragmatism may be in order.

There can be little doubt that Peirce was led to the formulation of the
principle of pragmatism through the influence of Chauncey Wright.[11]
Wright who had first hand acquaintance with creative scientific work in
mathematics, physics, and botany was led by the study of Mill and Bain
to reflect on the characteristics of scientific method. This reflection
led him to draw a distinction between the use of popular scientific
material, by men like Spencer, to construct a myth or picture of the
world, and the scientific use of laws by men like Newton as means for
extending our knowledge of phenomena. Gravitation as a general fact had
interested metaphysicians long before Newton. What made Newton’s
contribution scientific was the formulation of a mathematical law which
has enabled us to deduce all the then known facts of the solar system
and to anticipate or predict many more facts the existence of which
would not otherwise be even suspected, e.g., the existence of the planet
Neptune. Wright insists, therefore, that the principles of modern
mathematical and physical science are the means through which nature is
discovered, that scientific laws are the finders rather than merely the
summaries of factual truths. This conception of the experimental
scientist as translating general propositions into prescriptions for
attaining new experimental truths, is the starting point of Peirce’s
pragmatism. The latter is embodied in the principle that the meaning of
a concept is to be found in “all the conceivable experimental phenomena
which the affirmation or denial of the concept could imply.”[12]

In the earlier statement of the pragmatic maxim,[13] Peirce emphasized
the consequences for conduct that follow from the acceptance or
rejection of an idea; but the stoical maxim that the end of man is
action did not appeal to him as much at sixty as it did at thirty.[14]
Naturally also Peirce could not follow the development of pragmatism by
Wm. James who, like almost all modern psychologists, was a thorough
nominalist and always emphasized particular sensible experience.[15] It
seemed to Peirce that such emphasis on particular experiences endangered
the principle of continuity which in the hands of men like Weierstrass
had reformed modern mathematics. For this reason he began to call his
own doctrine pragmaticism, a sufficiently unattractive name, he thought,
to save it from kidnappers and from popularity. He never, however,
abandoned the principle of pragmatism, that the meaning of an idea is
clarified (because constituted) by its conceivable experimental
consequences. Indeed, if we want to clarify the meaning of the idea of
pragmatism, let us apply the pragmatic test to it. What will be the
effect of accepting it? Obviously it will be to develop certain general
ideas or habits of looking at things.

Peirce’s pragmatism has, therefore, a decidedly intellectual cast. The
meaning of an idea or proposition is found not by an intuition of it but
by working out its implications. It admits that thought does not
constitute reality. Categories can have no concrete being without action
or immediate feeling. But thought is none the less an essential
ingredient of reality; thought is “the melody running through the
succession of our sensations.” Pragmatism, according to Peirce, seeks to
define the rational purport, not the sensuous quality. It is interested
not in the effect of our practical occupations or desires on our ideas,
but in the function of ideas as guides of action. Whether a man is to
pay damages in a certain lawsuit may depend, in fact, on a term in the
Aristotelian logic such as proximate cause.

It is of interest to observe that though Peirce is an ardent admirer of
Darwin’s method, his scientific caution makes him refuse to apply the
analogy of biologic natural selection to the realm of ideas, in the
wholesale and uncritical manner that has lately become fashionable.
Natural selection may well favor the triumph of views which directly
influence biologic survival. But the pleasure of entertaining congenial
illusions may overbalance the inconvenience resulting from their
deceptive character. Thus rhetorical appeals may long prevail over
scientific evidence.


                                  III


Peirce preferred to call himself a logician, and his contributions to
logic have so far proved his most generally recognized achievement. For
a right perspective of these contributions we may well begin with the
observation that though few branches of philosophy have been cultivated
as continuously as logic, Kant was able to affirm that the science of
logic had made no substantial progress since the time of Aristotle. The
reason for this is that Aristotle’s logic, the logic of classes, was
based on his own scientific procedure as a zoologist, and is still in
essence a valid method so far as classification is part of all rational
procedure. But when we come to describe the mathematical method of
physical science, we cannot cast it into the Aristotelian form without
involving ourselves in such complicated artificialities as to reduce
almost to nil the value of Aristotle’s logic as an organon. Aristotle’s
logic enables us to make a single inference from two premises. But the
vast multitude of theorems that modern mathematics has derived from a
few premises as to the nature of number, shows the need of formulating a
logic or theory of inference that shall correspond to the modern, more
complicated, practice as Aristotle’s logic did to simple classificatory
zoology. To do this effectively would require the highest constructive
logical genius, together with an intimate knowledge of the methods of
the great variety of modern sciences. This is in the nature of the case
a very rare combination, since great investigators are not as critical
in examining their own procedure as they are in examining the subject
matter which is their primary scientific interest. Hence, when great
investigators like Poincaré come to describe their own work, they fall
back on the uncritical assumptions of the traditional logic which they
learned in their school days. Moreover, “For the last three centuries
thought has been conducted in laboratories, in the field, or otherwise
in the face of the facts, while chairs of logic have been filled by men
who breathe the air of the seminary.”[16] The great Leibnitz had the
qualifications, but here, as elsewhere, his worldly occupations left him
no opportunity except for very fragmentary contributions. It was not
until the middle of the 19th century that two mathematicians, Boole and
DeMorgan, laid the foundations for a more generalized logic. Boole
developed a general logical algorithm or calculus, while DeMorgan called
attention to non-syllogistic inference and especially to the importance
of the logic of relations. Peirce’s great achievement is to have
recognized the possibilities of both and to have generalized and
developed them into a general theory of scientific inference. The extent
and thoroughness of his achievement has been obscured by his fragmentary
way of writing and by a rather unwieldy symbolism. Still, modern
mathematical logic, such as that of Russell’s _Principles of
Mathematics_, is but a development of Peirce’s logic of relatives.

This phase of Peirce’s work is highly technical and an account of it is
out of place here. Such an account will be found in Lewis’ _Survey of
Symbolic Logic_.[17] I refer to it here only to remind the reader that
the _Illustrations of the Logic of the Sciences_ (Part I of this volume)
have a background of patient detailed work which is still being
developed to-day.

Symbolic logic has been held in rather low esteem by the followers of
the old classical methods in philosophy. Their stated objection to it
has been mainly that it is concerned with the minutiae of an artificial
language and is of no value as a guide to the interpretation of reality.
Now it should be readily admitted that preoccupation with symbolic logic
is rather apt to retard the irresponsible flight of philosophic fancy.
Yet this is by no means always an evil. By insisting on an accuracy that
is painful to those impatient to obtain sweeping and comforting, though
hasty, conclusions, symbolic logic is well calculated to remove the
great scandal of traditional philosophy—the claim of absolutely certain
results in fields where there is the greatest conflict of opinion. This
scandalous situation arises in part from the fact that in popular
exposition we do not have to make our premises or assumptions explicit;
hence all sorts of dubious prejudices are implicitly appealed to as
absolutely necessary principles. Also, by the use of popular terms which
have a variety of meanings, one easily slides from one meaning to
another, so that the most improbable conclusions are thus derived from
seeming truisms. By making assumptions and rules explicit, and by using
technical terms that do not drag wide penumbras of meaning with them,
the method of symbolic logic may cruelly reduce the sweeping pretensions
of philosophy. But there is no reason for supposing that pretentiousness
rather than humility is the way to philosophic salvation. Man is bound
to speculate about the universe beyond the range of his knowledge, but
he is not bound to indulge the vanity of setting up such speculations as
absolutely certain dogmas.

There is, however, no reason for denying that greater rigor and accuracy
of exposition can really help us to discern new truth. Modern
mathematics since Gauss and Weierstrass has actually been led to greater
fruitfulness by increased rigor which makes such procedure as the old
proofs of Taylor’s theorem no longer possible. The substitution of
rigorous analytic procedures for the old Euclidean proofs based on
intuition, has opened up vast fields of geometry. Nor has this been
without any effect on philosophy. Where formerly concepts like infinity
and continuity were objects of gaping awe or the recurrent occasions for
intellectual violence,[18] we are now beginning to use them, thanks to
Peirce and Royce, in accurate and definable senses. Consider, for
instance, the amount of a priori nonsense which Peirce eliminates by
pointing out that the application of the concept of continuity to a span
of consciousness removes the necessity for assuming a first or last
moment; so likewise the range of vision on a large unobstructed ground
has no line between the visible and the invisible. These considerations
will be found utterly destructive of the force of the old arguments
(fundamental to Kant and others) as to the necessary infinity of time
and space. Similar enlightenment is soon likely to result from the more
careful use of terms like relative and absolute, which are bones of
contention in philosophy but Ariadne threads of exploration in
theoretical physics, because of the definite symbolism of mathematics.
Other important truths made clear by symbolic logic is the hypothetical
character of universal propositions and the consequent insight that no
particulars can be deduced from universals alone, since no number of
hypotheses can without given data establish an existing fact.

There is, however, an even more positive direction in which symbolic
logic serves the interest of philosophy, and that is in throwing light
on the nature of symbols and on the relation of meaning. Philosophers
have light-heartedly dismissed questions as to the nature of significant
signs as ‘merely’ (most fatal word!) a matter of language. But Peirce in
the paper on Man’s Glassy [Shakespearian for Mirror-Like] Essence,
endeavors to exhibit man’s whole nature as symbolic.[19] This is closely
connected with his logical doctrine which regards signs or symbols as
one of the fundamental categories or aspects of the universe (Thoughts
and things are the other two). Independently of Peirce but in line with
his thought another great and neglected thinker, Santayana, has shown
that the whole life of man that is bound up with the institutions of
civilization, is concerned with symbols.

It is not altogether accidental that, since Boole and DeMorgan, those
who have occupied themselves with symbolic logic have felt called upon
to deal with the problem of probability. The reason is indicated by
Peirce when he formulates the problem of probable inference in such a
way as to make the old classic logic of absolutely true or false
conclusions, a limiting case (i.e., of values 1 and 0) of the logic of
probable inference whose values range all the way between these two
limits. This technical device is itself the result of applying the
principle of continuity to throw two hitherto distinct types of
reasoning into the same class. The result is philosophically
significant.

Where the classical logic spoke of major and minor premises without
establishing any really important difference between the two, Peirce
draws a distinction between the premises and the guiding principle of
our argument. All reasoning is from some concrete situation to another.
The propositions which represent the first are the premises in the
strict sense of the word. But the feeling that certain conclusions
follow from these premises is conditioned by an implicit or explicit
belief in some guiding principle which connects the premises and the
conclusions. When such a leading principle results in true conclusions
in all cases of true premises, we have logical deduction of the orthodox
type. If, however, such a principle brings about a true conclusion only
in a certain proportion of cases, then we have probability.

This reduction of probability to the relative frequency of true
propositions in a class of propositions, was suggested to Peirce by
Venn’s _Logic of Chance_. Peirce uses it to establish some truths of
greatest importance to logic and philosophy.

He eliminates the difficulties of the old conceptualist view, which made
probability a measure of our ignorance and yet had to admit that almost
all fruitfulness of our practical and scientific reasoning depended on
the theorems of probability. How could we safely predict phenomena by
measuring our ignorance?

Probability being reduced to a matter of the relative frequency of a
class in a larger class or genus, it becomes, strictly speaking,
inapplicable to single cases by themselves. A single penny will fall
head or it will fall tail every time; to-morrow it will rain, or it will
not rain at all. The probability of 1/2 or any other fraction means
nothing in the single case. It is only because we feel the single event
as representative of a class, as something which repeats itself, that we
speak elliptically of the probability of a single event. Hence follows
the important corollary that reasoning with respect to the probability
of this or that arrangement of the universe would be valid only if
universes were as plentiful as blackberries.

To be useful at all, theories must be simpler than the complex facts
which they seek to explain. Hence, it is often convenient to employ a
principle of certainty where the facts justify only a principle of some
degree of probability. In such cases we must be cautious in accepting
any extreme consequence of these principles, and also be on guard
against apparent refutations based on such extreme consequences.

Finally I should like to emphasize the value of Peirce’s theory of
inference for a philosophy of civilization. To the old argument that
logic is of no importance because people learn to reason, as to walk, by
instinct and habit and not by scientific instruction, Peirce admits[20]
that “all human knowledge up to the highest flights of science is but
the development of our inborn animal instincts.” But though logical
rules are first felt implicitly, bringing them into explicit
consciousness helps the process of analysis and thus makes possible the
recognition of old principles in novel situations. This increases our
range of adaptability to such an extent as to justify a general
distinction between the slave of routine or habit and the freeman who
can anticipate and control nature through knowledge of principles.
Peirce’s analysis of the method of science as a method of attaining
stability of beliefs by free inquiry inviting all possible doubt, in
contrast with the methods of iteration (“will to believe”) and social
authority, is one of the best introductions to a theory of liberal or
Hellenic civilization, as opposed to those of despotic societies.
Authority has its roots in the force of habit, but it cannot prevent new
and unorthodox ideas from arising; and in the effort to defend
authoritative social views men are apt to be far more ruthless than in
defending their own personal convictions.


                                   IV


Not only the pragmatism and the radical empiricism of James, but the
idealism of Royce and the more recent movement of neo-realism are
largely indebted to Peirce.

It may seem strange that the same thinker should be claimed as
foster-father of both recent idealism and realism, and some may take it
as another sign of his lack of consistency. But this seeming strangeness
is really due to the looseness with which the antithesis between realism
and idealism has generally been put. If by idealism we denote the
nominalistic doctrine of Berkeley, then Peirce is clearly not an
idealist; and his work in logic as a study of types of order (in which
Royce followed him) is fundamental for a logical realism. But if
idealism means the old Platonic doctrine that “ideas,” genera, or forms
are not merely mental but the real conditions of existence, we need not
wonder that Peirce was both idealist and realist.

Royce’s indebtedness to Peirce is principally in the use of modern
mathematical material, such as the recent development of the concepts of
infinity and continuity, to throw light on fundamental questions of
philosophy, such as relation of the individual to God or the Universe.
At the end of the nineteenth century mathematics had almost disappeared
from the repertory of philosophy (cf. Külpe’s _Introduction to
Philosophy_), and Peirce’s essay on the _Law of Mind_ opened a new way
which Royce followed in his _World and the Individual_, to the great
surprise of his idealistic brethren. In his _Problem of Christianity_
Royce has also indicated his indebtedness to Peirce for his doctrine of
social consciousness, the mind of the community, and the process of
interpretation. It may be that a great deal of the similarity between
the thoughts of these two men is due to common sources, such as the
works of Kant and Schelling; but it is well to note that not only in his
later writings but also in his lectures and seminars Royce continually
referred to Peirce’s views.

The ground for the neo-realist movement in American philosophy was
largely prepared by the mathematical work of Russell and by the
utilization of mathematics to which Royce was led by Peirce. The logic
of Mr. Russell is based, as he himself has pointed out, on a combination
of the work of Peirce and Peano. In this combination the notation of
Peano has proved of greater technical fluency, but all of Peano’s
results can also be obtained by Peirce’s method as developed by
Schroeder and Mrs. Ladd-Franklin. But philosophically Peirce’s influence
is far greater in insisting that logic is not a branch of psychology,
that it is not concerned with merely mental processes, but with
objective relations. To the view that the laws of logic represent “the
necessities of thought,” that propositions are true because “we can not
help thinking so,” he answers: “Exact logic will say that _C_’s
following logically from _A_ is a state of things which no impotence of
thought alone can bring about.”[21] “The question of validity is purely
one of fact and not of thinking.... It is not in the least the question
whether, when the premises are accepted by the mind, we feel an impulse
to accept the conclusion also. The true conclusion would remain true if
we had no impulse to accept it, and the false one would remain false
though we could not resist the tendency to believe in it.”[22]

Since the days of Locke modern philosophy has been almost entirely
dominated by the assumption that one must study the process of knowing
before one can find out the nature of things known; in other words, that
psychology is _the_ central philosophic science. The result of this has
been an almost complete identification of philosophy with mental
science. Nor did the influence of biologic studies of the middle of the
nineteenth century shake the belief in that banal dictum of philosophic
mediocrity: “The proper study of mankind is man.” The recent renaissance
of logical studies, and the remarkable progress of physics in our own
day bid fair to remind us that while the Lockian way has brought some
gains to philosophy, the more ancient way of philosophy is by no means
exhausted of promise. Man cannot lose his interest in the great cosmic
play. Those who have faith in the ancient and fruitful approach to
philosophy through the doors of mathematics and physics will find the
writings of Charles S. Peirce full of suggestions. That such an approach
can also throw light on the vexed problem of knowledge needs no
assurance to those acquainted with Plato and Aristotle. But I may
conclude by referring to Peirce’s doctrine of ideal as opposed to
sensible experiment,[23] and to his treatment of the question how it is
that in spite of an infinity of possible hypotheses, mankind has managed
to make so many successful inductions.[24] And for the bearing of
mathematical studies on the wisdom of life, the following is certainly
worth serious reflection: “All human affairs rest upon probabilities. If
man were immortal [on earth] he could be perfectly sure of seeing the
day when everything in which he had trusted should betray his trust. He
would break down, at last, as every great fortune, as every dynasty, as
every civilization does. In place of this we have death.” The
recognition that the death of the individual does not destroy the
logical meaning of his utterances, that this meaning involves the ideal
of an unlimited community, carries us into the heart of pure religion.

Footnote 1:

  See Plantamour’s “_Recherches Experimentales sur le mouvement
  simultané d’un pendule et de ses supports_,” Geneva, 1878, pp. 3-4.

Footnote 2:

  P. 190.

Footnote 3:

  Pp. 162-163.

Footnote 4:

  Pp. 249 ff.

Footnote 5:

  James, _Pluralistic Universe_, pp. 398-400.

Footnote 6:

  Royce, _Studies in Good and Evil_, and _The Problem of Christianity_,
  esp. Vol. 2. Baldwin (_Mental Development_) is heavily indebted to
  Royce in this respect.

Footnote 7:

  These articles are by-products or fragments of a comprehensive work on
  _Logic_ on which Peirce was engaged for many years. For the writing of
  this book, Royce declared, no greater mind or greater erudition has
  appeared in America. Only several chapters seem to have been finished,
  and will doubtless be included with other hitherto unpublished
  manuscripts in the complete edition of Peirce’s writings that is now
  being prepared by Harvard University.

Footnote 8:

  Baldwin’s _Dictionary_, article Synechism.

Footnote 9:

  _Ib._

Footnote 10:

  Baldwin’s _Dictionary_, art. Individual: “Everything whose identity
  consists in a continuity of reactions will be a single logical
  individual.”

Footnote 11:

  The personal relations between Peirce and Wright were thus described
  by Peirce in a letter to Mrs. Ladd-Franklin (_Journal of Philosophy_,
  Vol. 13, p. 719): “It must have been about 1857 when I first made the
  acquaintance of Chauncey Wright, a mind about on the level of J. S.
  Mill. He was a thorough mathematician. He had a most penetrating
  intellect.—He and I used to have long and very lively and close
  disputations lasting two or three hours daily for many years. In the
  sixties I started a little club called ‘The Metaphysical Club.’—Wright
  was the strongest member and probably I was next.—Then there were
  Frank Abbott, William James and others.” “It was there that the name
  and the doctrine of pragmatism saw the light.” It might be added that
  Peirce’s tychism is indebted to Wright’s doctrine of accidents and
  “cosmic weather,” a doctrine which maintained against LaPlace that a
  mind knowing nature from moment to moment is bound to encounter
  genuine novelty in phenomena, which no amount of knowledge would
  enable us to foresee. See Wright’s _Philosophical Discussions_—1876,
  also Cambridge _Hist. of American Literature_, Vol. 3, p. 234.

Footnote 12:

  _Monist_, Vol. 15, p. 180.

Footnote 13:

  This volume, pp. 43-45.

Footnote 14:

  “To say that we live for the sake of action would be to say that there
  is no such thing as a rational purport.” _Monist_, Vol. XV, p. 175.

Footnote 15:

  The letter to Mrs. Ladd-Franklin quoted before, explains why James,
  though always loyal to Peirce and anxious to give him credit whenever
  possible, could not understand the latter’s lectures on pragmatism.
  Peirce’s incidental judgments on others is worth quoting here:

  “Modern psychologists are so soaked with sensationalism that they
  cannot understand anything that does not mean that. How can I, to whom
  nothing seems so thoroughly real as generals, and who regards Truth
  and Justice as _literally_ the most powerful powers in the world,
  expect to be understood by the thoroughgoing Wundtian? But the curious
  thing is to see absolute idealists tainted with this disease,—or men
  who, like John Dewey, hover between Absolute Idealism and
  Sensationalism. Royce’s opinions as developed in his _World and
  Individualism_ are extremely near to mine. His insistence on the
  elements of purpose in intellectual concepts is essentially the
  pragmatic position.”

Footnote 16:

  Baldwin’s _Dictionary_, art. Method.

Footnote 17:

  “Peirce anticipated the most important procedures of his successors
  even when he did not work them out himself. Again and again one finds
  the clue to the most recent developments in the writings of Peirce,”
  Lewis’ _Survey of Symbolic Logic_, p. 79.

Footnote 18:

  Hans Breitmann is symbolic of those who “solved the infinite as one
  eternal sphere.”

Footnote 19:

  See _Journal of Speculative Philosophy_, Vol. 2, pp. 155-157, article
  on A New List of Categories in the Proceedings of the American Academy
  of Arts and Sciences, Vol. 7, 287-298 and article on _Sign_, in
  Baldwin’s _Dictionary_.

Footnote 20:

  _Studies in Logic_, p. 181.

Footnote 21:

  _Monist_, Vol. 7, p. 27. _Cf._ _Journal of Speculative Philosophy_,
  Vol. 2, p. 207; _Popular Science Monthly_, Vol. 58, pp. 305-306.

Footnote 22:

  This vol., p. 15.

Footnote 23:

  Suggestive for a theory of the metaphysics of fictions is the
  suggestion (p. 46) “that the question of what would occur under
  circumstances which do not actually arise, is not a question of fact,
  but only of the most perspicuous arrangement of them.” This
  arrangement is, of course, not merely subjective.

Footnote 24:

  Pp. 128-129, _cf._ _Monist_, Vol. 7, p. 206, and _Logical Studies_,
  pp. 175 ff.




                                 PROEM
                      THE RULES OF PHILOSOPHY[25]


Descartes is the father of modern philosophy, and the spirit of
Cartesianism—that which principally distinguishes it from the
scholasticism which it displaced—may be compendiously stated as follows:

1. It teaches that philosophy must begin with universal doubt; whereas
scholasticism had never questioned fundamentals.

2. It teaches that the ultimate test of certainty is to be found in the
individual consciousness; whereas scholasticism had rested on the
testimony of sages and of the Catholic Church.

3. The multiform argumentation of the middle ages is replaced by a
single thread of inference depending often upon inconspicuous premises.

4. Scholasticism had its mysteries of faith, but undertook to explain
all created things. But there are many facts which Cartesianism not only
does not explain but renders absolutely inexplicable, unless to say that
“God makes them so” is to be regarded as an explanation.

In some, or all of these respects, most modern philosophers have been,
in effect, Cartesians. Now without wishing to return to scholasticism,
it seems to me that modern science and modern logic require us to stand
upon a very different platform from this.

1. We cannot begin with complete doubt. We must begin with all the
prejudices which we actually have when we enter upon the study of
philosophy. These prejudices are not to be dispelled by a maxim, for
they are things which it does not occur to us can be questioned. Hence
this initial skepticism will be a mere self-deception, and not real
doubt; and no one who follows the Cartesian method will ever be
satisfied until he has formally recovered all those beliefs which in
form he has given up. It is, therefore, as useless a preliminary as
going to the North Pole would be in order to get to Constantinople by
coming down regularly upon a meridian. A person may, it is true, in the
course of his studies, find reason to doubt what he began by believing;
but in that case he doubts because he has a positive reason for it, and
not on account of the Cartesian maxim. Let us not pretend to doubt in
philosophy what we do not doubt in our hearts.

2. The same formalism appears in the Cartesian criterion, which amounts
to this: “Whatever I am clearly convinced of, is true.” If I were really
convinced, I should have done with reasoning and should require no test
of certainty. But then to make single individuals absolute judges of
truth is most pernicious. The result is that metaphysics has reached a
pitch of certainty far beyond that of the physical sciences;—only they
can agree upon nothing else. In sciences in which men come to agreement,
when a theory has been broached it is considered to be on probation
until this agreement is reached. After it is reached, the question of
certainty becomes an idle one, because there is no one left who doubts
it. We individually cannot reasonably hope to attain the ultimate
philosophy which we pursue; we can only seek it, therefore, for the
community of philosophers. Hence, if disciplined and candid minds
carefully examine a theory and refuse to accept it, this ought to create
doubts in the mind of the author of the theory himself.

3. Philosophy ought to imitate the successful sciences in its methods,
so far as to proceed only from tangible premises which can be subjected
to careful scrutiny, and to trust rather to the multitude and variety of
its arguments than to the conclusiveness of any one. Its reasoning
should not form a chain which is no stronger than its weakest link, but
a cable whose fibers may be ever so slender, provided they are
sufficiently numerous and intimately connected.

4. Every unidealistic philosophy supposes some absolutely inexplicable,
unanalyzable ultimate; in short, something resulting from mediation
itself not susceptible of mediation. Now that anything is thus
inexplicable, can only be known by reasoning from signs. But the only
justification of an inference from signs is that the conclusion explains
the fact. To suppose the fact absolutely inexplicable, is not to explain
it, and hence this supposition is never allowable.

Footnote 25:

  From the _Journal of Speculative Philosophy_, vol. 2, p. 140.




                                 PART I
                            CHANCE AND LOGIC
                (ILLUSTRATIONS OF THE LOGIC OF SCIENCE)




                            CHANCE AND LOGIC
                              FIRST PAPER
                       THE FIXATION OF BELIEF[26]


                                   I


Few persons care to study logic, because everybody conceives himself to
be proficient enough in the art of reasoning already. But I observe that
this satisfaction is limited to one’s own ratiocination, and does not
extend to that of other men.

We come to the full possession of our power of drawing inferences the
last of all our faculties, for it is not so much a natural gift as a
long and difficult art. The history of its practice would make a grand
subject for a book. The medieval schoolman, following the Romans, made
logic the earliest of a boy’s studies after grammar, as being very easy.
So it was as they understood it. Its fundamental principle, according to
them, was, that all knowledge rests on either authority or reason; but
that whatever is deduced by reason depends ultimately on a premise
derived from authority. Accordingly, as soon as a boy was perfect in the
syllogistic procedure, his intellectual kit of tools was held to be
complete.

To Roger Bacon, that remarkable mind who in the middle of the thirteenth
century was almost a scientific man, the schoolmen’s conception of
reasoning appeared only an obstacle to truth. He saw that experience
alone teaches anything—a proposition which to us seems easy to
understand, because a distinct conception of experience has been handed
down to us from former generations; which to him also seemed perfectly
clear, because its difficulties had not yet unfolded themselves. Of all
kinds of experience, the best, he thought, was interior illumination,
which teaches many things about Nature which the external senses could
never discover, such as the transubstantiation of bread.

Four centuries later, the more celebrated Bacon, in the first book of
his “Novum Organum,” gave his clear account of experience as something
which must be open to verification and reëxamination. But, superior as
Lord Bacon’s conception is to earlier notions, a modern reader who is
not in awe of his grandiloquence is chiefly struck by the inadequacy of
his view of scientific procedure. That we have only to make some crude
experiments, to draw up briefs of the results in certain blank forms, to
go through these by rule, checking off everything disproved and setting
down the alternatives, and that thus in a few years physical science
would be finished up—what an idea! “He wrote on science like a Lord
Chancellor,”[27] indeed.

The early scientists, Copernicus, Tycho Brahe, Kepler, Galileo and
Gilbert, had methods more like those of their modern brethren. Kepler
undertook to draw a curve through the places of Mars;[28] and his
greatest service to science was in impressing on men’s minds that this
was the thing to be done if they wished to improve astronomy; that they
were not to content themselves with inquiring whether one system of
epicycles was better than another but that they were to sit down by the
figures and find out what the curve, in truth, was. He accomplished this
by his incomparable energy and courage, blundering along in the most
inconceivable way (to us), from one irrational hypothesis to another,
until, after trying twenty-two of these, he fell, by the mere exhaustion
of his invention, upon the orbit which a mind well furnished with the
weapons of modern logic would have tried almost at the outset.[29]

In the same way, every work of science great enough to be remembered for
a few generations affords some exemplification of the defective state of
the art of reasoning of the time when it was written; and each chief
step in science has been a lesson in logic. It was so when Lavoisier and
his contemporaries took up the study of Chemistry. The old chemist’s
maxim had been, “Lege, lege, lege, labora, ora, et relege.” Lavoisier’s
method was not to read and pray, not to dream that some long and
complicated chemical process would have a certain effect, to put it into
practice with dull patience, after its inevitable failure to dream that
with some modification it would have another result, and to end by
publishing the last dream as a fact: his way was to carry his mind into
his laboratory, and to make of his alembics and cucurbits instruments of
thought, giving a new conception of reasoning as something which was to
be done with one’s eyes open, by manipulating real things instead of
words and fancies.

The Darwinian controversy is, in large part, a question of logic. Mr.
Darwin proposed to apply the statistical method to biology. The same
thing has been done in a widely different branch of science, the theory
of gases. Though unable to say what the movement of any particular
molecule of gas would be on a certain hypothesis regarding the
constitution of this class of bodies, Clausius and Maxwell were yet
able, by the application of the doctrine of probabilities, to predict
that in the long run such and such a proportion of the molecules would,
under given circumstances, acquire such and such velocities; that there
would take place, every second, such and such a number of collisions,
etc.; and from these propositions they were able to deduce certain
properties of gases, especially in regard to their heat-relations. In
like manner, Darwin, while unable to say what the operation of variation
and natural selection in every individual case will be, demonstrates
that in the long run they will adapt animals to their circumstances.
Whether or not existing animal forms are due to such action, or what
position the theory ought to take, forms the subject of a discussion in
which questions of fact and questions of logic are curiously interlaced.


                                   II


The object of reasoning is to find out, from the consideration of what
we already know, something else which we do not know. Consequently,
reasoning is good if it be such as to give a true conclusion from true
premises, and not otherwise. Thus, the question of validity is purely
one of fact and not of thinking. A being the premises and B being the
conclusion, the question is, whether these facts are really so related
that if A is B is. If so, the inference is valid; if not, not. It is not
in the least the question whether, when the premises are accepted by the
mind, we feel an impulse to accept the conclusion also. It is true that
we do generally reason correctly by nature. But that is an accident; the
true conclusion would remain true if we had no impulse to accept it; and
the false one would remain false, though we could not resist the
tendency to believe in it.

We are, doubtless, in the main logical animals, but we are not perfectly
so. Most of us, for example, are naturally more sanguine and hopeful
than logic would justify. We seem to be so constituted that in the
absence of any facts to go upon we are happy and self-satisfied; so that
the effect of experience is continually to counteract our hopes and
aspirations. Yet a lifetime of the application of this corrective does
not usually eradicate our sanguine disposition. Where hope is unchecked
by any experience, it is likely that our optimism is extravagant.
Logicality in regard to practical matters is the most useful quality an
animal can possess, and might, therefore, result from the action of
natural selection; but outside of these it is probably of more advantage
to the animal to have his mind filled with pleasing and encouraging
visions, independently of their truth; and thus, upon unpractical
subjects, natural selection might occasion a fallacious tendency of
thought.

That which determines us, from given premises, to draw one inference
rather than another, is some habit of mind, whether it be constitutional
or acquired. The habit is good or otherwise, according as it produces
true conclusions from true premises or not; and an inference is regarded
as valid or not, without reference to the truth or falsity of its
conclusion specially, but according as the habit which determines it is
such as to produce true conclusions in general or not. The particular
habit of mind which governs this or that inference may be formulated in
a proposition whose truth depends on the validity of the inferences
which the habit determines; and such a formula is called a _guiding
principle_ of inference. Suppose, for example, that we observe that a
rotating disk of copper quickly comes to rest when placed between the
poles of a magnet, and we infer that this will happen with every disk of
copper. The guiding principle is, that what is true of one piece of
copper is true of another. Such a guiding principle with regard to
copper would be much safer than with regard to many other
substances—brass, for example.

A book might be written to signalize all the most important of these
guiding principles of reasoning. It would probably be, we must confess,
of no service to a person whose thought is directed wholly to practical
subjects, and whose activity moves along thoroughly beaten paths. The
problems which present themselves to such a mind are matters of routine
which he has learned once for all to handle in learning his business.
But let a man venture into an unfamiliar field, or where his results are
not continually checked by experience, and all history shows that the
most masculine intellect will ofttimes lose his orientation and waste
his efforts in directions which bring him no nearer to his goal, or even
carry him entirely astray. He is like a ship on the open sea, with no
one on board who understands the rules of navigation. And in such a case
some general study of the guiding principles of reasoning would be sure
to be found useful.

The subject could hardly be treated, however, without being first
limited; since almost any fact may serve as a guiding principle. But it
so happens that there exists a division among facts, such that in one
class are all those which are absolutely essential as guiding
principles, while in the other are all those which have any other
interest as objects of research. This division is between those which
are necessarily taken for granted in asking whether a certain conclusion
follows from certain premises, and those which are not implied in that
question. A moment’s thought will show that a variety of facts are
already assumed when the logical question is first asked. It is implied,
for instance, that there are such states of mind as doubt and
belief—that a passage from one to the other is possible, the object of
thought remaining the same, and that this transition is subject to some
rules which all minds are alike bound by. As these are facts which we
must already know before we can have any clear conception of reasoning
at all, it cannot be supposed to be any longer of much interest to
inquire into their truth or falsity. On the other hand, it is easy to
believe that those rules of reasoning which are deduced from the very
idea of the process are the ones which are the most essential; and,
indeed, that so long as it conforms to these it will, at least, not lead
to false conclusions from true premises. In point of fact, the
importance of what may be deduced from the assumptions involved in the
logical question turns out to be greater than might be supposed, and
this for reasons which it is difficult to exhibit at the outset. The
only one which I shall here mention is, that conceptions which are
really products of logical reflections, without being readily seen to be
so, mingle with our ordinary thoughts, and are frequently the causes of
great confusion. This is the case, for example, with the conception of
quality. A quality as such is never an object of observation. We can see
that a thing is blue or green, but the quality of being blue and the
quality of being green are not things which we see; they are products of
logical reflections. The truth is, that common-sense, or thought as it
first emerges above the level of the narrowly practical, is deeply
imbued with that bad logical quality to which the epithet _metaphysical_
is commonly applied; and nothing can clear it up but a severe course of
logic.


                                  III


We generally know when we wish to ask a question and when we wish to
pronounce a judgment, for there is a dissimilarity between the sensation
of doubting and that of believing.

But this is not all which distinguishes doubt from belief. There is a
practical difference. Our beliefs guide our desires and shape our
actions. The Assassins, or followers of the Old Man of the Mountain,
used to rush into death at his least command, because they believed that
obedience to him would insure everlasting felicity. Had they doubted
this, they would not have acted as they did. So it is with every belief,
according to its degree. The feeling of believing is a more or less sure
indication of there being established in our nature some habit which
will determine our actions. Doubt never has such an effect.

Nor must we overlook a third point of difference. Doubt is an uneasy and
dissatisfied state from which we struggle to free ourselves and pass
into the state of belief; while the latter is a calm and satisfactory
state which we do not wish to avoid, or to change to a belief in
anything else.[30] On the contrary, we cling tenaciously, not merely to
believing, but to believing just what we do believe.

Thus, both doubt and belief have positive effects upon us, though very
different ones. Belief does not make us act at once, but puts us into
such a condition that we shall behave in a certain way, when the
occasion arises. Doubt has not the least effect of this sort, but
stimulates us to action until it is destroyed. This reminds us of the
irritation of a nerve and the reflex action produced thereby; while for
the analogue of belief, in the nervous system, we must look to what are
called nervous associations—for example, to that habit of the nerves in
consequence of which the smell of a peach will make the mouth water.


                                   IV


The irritation of doubt causes a struggle to attain a state of belief. I
shall term this struggle _inquiry_, though it must be admitted that this
is sometimes not a very apt designation.

The irritation of doubt is the only immediate motive for the struggle to
attain belief. It is certainly best for us that our beliefs should be
such as may truly guide our actions so as to satisfy our desires; and
this reflection will make us reject any belief which does not seem to
have been so formed as to insure this result. But it will only do so by
creating a doubt in the place of that belief. With the doubt, therefore,
the struggle begins, and with the cessation of doubt it ends. Hence, the
sole object of inquiry is the settlement of opinion. We may fancy that
this is not enough for us, and that we seek not merely an opinion, but a
true opinion. But put this fancy to the test, and it proves groundless;
for as soon as a firm belief is reached we are entirely satisfied,
whether the belief be false or true. And it is clear that nothing out of
the sphere of our knowledge can be our object, for nothing which does
not affect the mind can be a motive for a mental effort. The most that
can be maintained is, that we seek for a belief that we shall _think_ to
be true. But we think each one of our beliefs to be true, and, indeed,
it is mere tautology to say so.

That the settlement of opinion is the sole end of inquiry is a very
important proposition. It sweeps away, at once, various vague and
erroneous conceptions of proof. A few of these may be noticed here.

1. Some philosophers have imagined that to start an inquiry it was only
necessary to utter or question or set it down on paper, and have even
recommended us to begin our studies with questioning everything! But the
mere putting of a proposition into the interrogative form does not
stimulate the mind to any struggle after belief. There must be a real
and living doubt, and without all this discussion is idle.

2. It is a very common idea that a demonstration must rest on some
ultimate and absolutely indubitable propositions. These, according to
one school, are first principles of a general nature; according to
another, are first sensations. But, in point of fact, an inquiry, to
have that completely satisfactory result called demonstration, has only
to start with propositions perfectly free from all actual doubt. If the
premises are not in fact doubted at all, they cannot be more
satisfactory than they are.

3. Some people seem to love to argue a point after all the world is
fully convinced of it. But no further advance can be made. When doubt
ceases, mental action on the subject comes to an end; and, if it did go
on, it would be without a purpose.


                                   V


If the settlement of opinion is the sole object of inquiry, and if
belief is of the nature of a habit, why should we not attain the desired
end, by taking any answer to a question, which we may fancy, and
constantly reiterating it to ourselves, dwelling on all which may
conduce to that belief, and learning to turn with contempt and hatred
from anything which might disturb it? This simple and direct method is
really pursued by many men. I remember once being entreated not to read
a certain newspaper lest it might change my opinion upon free-trade.
“Lest I might be entrapped by its fallacies and misstatements,” was the
form of expression. “You are not,” my friend said, “a special student of
political economy. You might, therefore, easily be deceived by
fallacious arguments upon the subject. You might, then, if you read this
paper, be led to believe in protection. But you admit that free-trade is
the true doctrine; and you do not wish to believe what is not true.” I
have often known this system to be deliberately adopted. Still oftener,
the instinctive dislike of an undecided state of mind, exaggerated into
a vague dread of doubt, makes men cling spasmodically to the views they
already take. The man feels that, if he only holds to his belief without
wavering, it will be entirely satisfactory. Nor can it be denied that a
steady and immovable faith yields great peace of mind. It may, indeed,
give rise to inconveniences, as if a man should resolutely continue to
believe that fire would not burn him, or that he would be eternally
damned if he received his _ingesta_ otherwise than through a
stomach-pump. But then the man who adopts this method will not allow
that its inconveniences are greater than its advantages. He will say, “I
hold steadfastly to the truth and the truth is always wholesome.” And in
many cases it may very well be that the pleasure he derives from his
calm faith overbalances any inconveniences resulting from its deceptive
character. Thus, if it be true that death is annihilation, then the man
who believes that he will certainly go straight to heaven when he dies,
provided he have fulfilled certain simple observances in this life, has
a cheap pleasure which will not be followed by the least disappointment.
A similar consideration seems to have weight with many persons in
religious topics, for we frequently hear it said, “Oh, I could not
believe so-and-so, because I should be wretched if I did.” When an
ostrich buries its head in the sand as danger approaches, it very likely
takes the happiest course. It hides the danger, and then calmly says
there is no danger; and, if it feels perfectly sure there is none, why
should it raise its head to see? A man may go through life,
systematically keeping out of view all that might cause a change in his
opinions, and if he only succeeds—basing his method, as he does, on two
fundamental psychological laws—I do not see what can be said against his
doing so. It would be an egotistical impertinence to object that his
procedure is irrational, for that only amounts to saying that his method
of settling belief is not ours. He does not propose to himself to be
rational, and indeed, will often talk with scorn of man’s weak and
illusive reason. So let him think as he pleases.

But this method of fixing belief, which may be called the method of
tenacity, will be unable to hold its ground in practice. The social
impulse is against it. The man who adopts it will find that other men
think differently from him, and it will be apt to occur to him in some
saner moment that their opinions are quite as good as his own, and this
will shake his confidence in his belief. This conception, that another
man’s thought or sentiment may be equivalent to one’s own, is a
distinctly new step, and a highly important one. It arises from an
impulse too strong in man to be suppressed, without danger of destroying
the human species. Unless we make ourselves hermits, we shall
necessarily influence each other’s opinions; so that the problem becomes
how to fix belief, not in the individual merely, but in the community.

Let the will of the state act, then, instead of that of the individual.
Let an institution be created which shall have for its object to keep
correct doctrines before the attention of the people, to reiterate them
perpetually, and to teach them to the young; having at the same time
power to prevent contrary doctrines from being taught, advocated, or
expressed. Let all possible causes of a change of mind be removed from
men’s apprehensions. Let them be kept ignorant, lest they should learn
of some reason to think otherwise than they do. Let their passions be
enlisted, so that they may regard private and unusual opinions with
hatred and horror. Then, let all men who reject the established belief
be terrified into silence. Let the people turn out and tar-and-feather
such men, or let inquisitions be made into the manner of thinking of
suspected persons, and, when they are found guilty of forbidden beliefs,
let them be subjected to some signal punishment. When complete agreement
could not otherwise be reached, a general massacre of all who have not
thought in a certain way has proved a very effective means of settling
opinion in a country. If the power to do this be wanting, let a list of
opinions be drawn up, to which no man of the least independence of
thought can assent, and let the faithful be required to accept all these
propositions, in order to segregate them as radically as possible from
the influence of the rest of the world.

This method has, from the earliest times, been one of the chief means of
upholding correct theological and political doctrines, and of preserving
their universal or catholic character. In Rome, especially, it has been
practiced from the days of Numa Pompilius to those of Pius Nonus. This
is the most perfect example in history; but wherever there is a
priesthood—and no religion has been without one—this method has been
more or less made use of. Wherever there is aristocracy, or a guild, or
any association of a class of men whose interests depend or are supposed
to depend on certain propositions, there will be inevitably found some
traces of this natural product of social feeling. Cruelties always
accompany this system; and when it is consistently carried out, they
become atrocities of the most horrible kind in the eyes of any rational
man. Nor should this occasion surprise, for the officer of a society
does not feel justified in surrendering the interests of that society
for the sake of mercy, as he might his own private interests. It is
natural, therefore, that sympathy and fellowship should thus produce a
most ruthless power.

In judging this method of fixing belief, which may be called the method
of authority, we must in the first place, allow its immeasurable mental
and moral superiority to the method of tenacity. Its success is
proportionally greater; and in fact it has over and over again worked
the most majestic results. The mere structures of stone which it has
caused to be put together—in Siam, for example, in Egypt, and in
Europe—have many of them a sublimity hardly more than rivaled by the
greatest works of Nature. And, except the geological epochs, there are
no periods of time so vast as those which are measured by some of these
organized faiths. If we scrutinize the matter closely, we shall find
that there has not been one of their creeds which has remained always
the same; yet the change is so slow as to be imperceptible during one
person’s life, so that individual belief remains sensibly fixed. For the
mass of mankind, then, there is perhaps no better method than this. If
it is their highest impulse to be intellectual slaves, then slaves they
ought to remain.

But no institution can undertake to regulate opinions upon every
subject. Only the most important ones can be attended to, and on the
rest men’s minds must be left to the action of natural causes. This
imperfection will be no source of weakness so long as men are in such a
state of culture that one opinion does not influence another—that is, so
long as they cannot put two and two together. But in the most
priest-ridden states some individuals will be found who are raised above
that condition. These men possess a wider sort of social feeling; they
see that men in other countries and in other ages have held to very
different doctrines from those which they themselves have been brought
up to believe; and they cannot help seeing that it is the mere accident
of their having been taught as they have, and of their having been
surrounded with the manners and associations they have, that has caused
them to believe as they do and not far differently. And their candor
cannot resist the reflection that there is no reason to rate their own
views at a higher value than those of other nations and other centuries;
and this gives rise to doubts in their minds.

They will further perceive that such doubts as these must exist in their
minds with reference to every belief which seems to be determined by the
caprice either of themselves or of those who originated the popular
opinions. The willful adherence to a belief, and the arbitrary forcing
of it upon others, must, therefore, both be given up and a new method of
settling opinions must be adopted, which shall not only produce an
impulse to believe, but shall also decide what proposition it is which
is to be believed. Let the action of natural preferences be unimpeded,
then, and under their influence let men conversing together and
regarding matters in different lights, gradually develop beliefs in
harmony with natural causes. This method resembles that by which
conceptions of art have been brought to maturity. The most perfect
example of it is to be found in the history of metaphysical philosophy.
Systems of this sort have not usually rested upon observed facts, at
least not in any great degree. They have been chiefly adopted because
their fundamental propositions seemed “agreeable to reason.” This is an
apt expression; it does not mean that which agrees with experience, but
that which we find ourselves inclined to believe. Plato, for example,
finds it agreeable to reason that the distances of the celestial spheres
from one another should be proportional to the different lengths of
strings which produce harmonious chords. Many philosophers have been led
to their main conclusions by considerations like this; but this is the
lowest and least developed form which the method takes, for it is clear
that another man might find Kepler’s [earlier] theory, that the
celestial spheres are proportional to the inscribed and circumscribed
spheres of the different regular solids, more agreeable to _his_ reason.
But the shock of opinions will soon lead men to rest on preferences of a
far more universal nature. Take, for example, the doctrine that man only
acts selfishly—that is, from the consideration that acting in one way
will afford him more pleasure than acting in another. This rests on no
fact in the world, but it has had a wide acceptance as being the only
reasonable theory.

This method is far more intellectual and respectable from the point of
view of reason than either of the others which we have noticed. But its
failure has been the most manifest. It makes of inquiry something
similar to the development of taste; but taste, unfortunately, is always
more or less a matter of fashion, and accordingly, meta-physicians have
never come to any fixed agreement, but the pendulum has swung backward
and forward between a more material and a more spiritual philosophy,
from the earliest times to the latest. And so from this, which has been
called the _a priori_ method, we are driven, in Lord Bacon’s phrase, to
a true induction. We have examined into this _a priori_ method as
something which promised to deliver our opinions from their accidental
and capricious element. But development, while it is a process which
eliminates the effect of some casual circumstances, only magnifies that
of others. This method, therefore, does not differ in a very essential
way from that of authority. The government may not have lifted its
finger to influence my convictions; I may have been left outwardly quite
free to choose, we will say, between monogamy and polygamy, and
appealing to my conscience only, I may have concluded that the latter
practice is in itself licentious. But when I come to see that the chief
obstacle to the spread of Christianity among a people of as high culture
as the Hindoos has been a conviction of the immorality of our way of
treating women, I cannot help seeing that, though governments do not
interfere, sentiments in their development will be very greatly
determined by accidental causes. Now, there are some people, among whom
I must suppose that my reader is to be found, who, when they see that
any belief of theirs is determined by any circumstance extraneous to the
facts, will from that moment not merely admit in words that that belief
is doubtful, but will experience a real doubt of it, so that it ceases
to be a belief.

To satisfy our doubts, therefore, it is necessary that a method should
be found by which our beliefs may be caused by nothing human, but by
some external permanency—by something upon which our thinking has no
effect. Some mystics imagine that they have such a method in a private
inspiration from on high. But that is only a form of the method of
tenacity, in which the conception of truth as something public is not
yet developed. Our external permanency would not be external, in our
sense, if it was restricted in its influence to one individual. It must
be something which affects, or might affect, every man. And, though
these affections are necessarily as various as are individual
conditions, yet the method must be such that the ultimate conclusion of
every man shall be the same. Such is the method of science. Its
fundamental hypothesis, restated in more familiar language, is this:
There are real things, whose characters are entirely independent of our
opinions about them; whose realities affect our senses according to
regular laws, and, though our sensations are as different as our
relations to the objects, yet, by taking advantage of the laws of
perception, we can ascertain by reasoning how things really are, and any
man, if he have sufficient experience and reason enough about it, will
be led to the one true conclusion. The new conception here involved is
that of reality. It may be asked how I know that there are any
realities. If this hypothesis is the sole support of my method of
inquiry, my method of inquiry must not be used to support my hypothesis.
The reply is this: 1. If investigation cannot be regarded as proving
that there are real things, it at least does not lead to a contrary
conclusion; but the method and the conception on which it is based
remain ever in harmony. No doubts of the method, therefore, necessarily
arise from its practice, as is the case with all the others. 2. The
feeling which gives rise to any method of fixing belief is a
dissatisfaction at two repugnant propositions. But here already is a
vague concession that there is some _one_ thing to which a proposition
should conform. Nobody, therefore, can really doubt that there are
realities, or, if he did, doubt would not be a source of
dissatisfaction. The hypothesis, therefore, is one which every mind
admits. So that the social impulse does not cause me to doubt it. 3.
Everybody uses the scientific method about a great many things, and only
ceases to use it when he does not know how to apply it. 4. Experience of
the method has not led me to doubt it, but, on the contrary, scientific
investigation has had the most wonderful triumphs in the way of settling
opinion. These afford the explanation of my not doubting the method or
the hypothesis which it supposes; and not having any doubt, nor
believing that anybody else whom I could influence has, it would be the
merest babble for me to say more about it. If there be anybody with a
living doubt upon the subject, let him consider it.

To describe the method of scientific investigation is the object of this
series of papers. At present I have only room to notice some points of
contrast between it and other methods of fixing belief.

This is the only one of the four methods which presents any distinction
of a right and a wrong way. If I adopt the method of tenacity and shut
myself out from all influences, whatever I think necessary to doing this
is necessary according to that method. So with the method of authority:
the state may try to put down heresy by means which, from a scientific
point of view, seems very ill-calculated to accomplish its purposes; but
the only test _on that method_ is what the state thinks, so that it
cannot pursue the method wrongly. So with the _a priori_ method. The
very essence of it is to think as one is inclined to think. All
metaphysicians will be sure to do that, however they may be inclined to
judge each other to be perversely wrong. The Hegelian system recognizes
every natural tendency of thought as logical, although it is certain to
be abolished by counter-tendencies. Hegel thinks there is a regular
system in the succession of these tendencies, in consequence of which,
after drifting one way and the other for a long time, opinion will at
last go right. And it is true that metaphysicians get the right ideas at
last; Hegel’s system of Nature represents tolerably the science of that
day; and one may be sure that whatever scientific investigation has put
out of doubt will presently receive _a priori_ demonstration on the part
of the metaphysicians. But with the scientific method the case is
different. I may start with known and observed facts to proceed to the
unknown; and yet the rules which I follow in doing so may not be such as
investigation would approve. The test of whether I am truly following
the method is not an immediate appeal to my feelings and purposes, but,
on the contrary, itself involves the application of the method. Hence it
is that bad reasoning as well as good reasoning is possible; and this
fact is the foundation of the practical side of logic.

It is not to be supposed that the first three methods of settling
opinion present no advantage whatever over the scientific method. On the
contrary, each has some peculiar convenience of its own. The _a priori_
method is distinguished for its comfortable conclusions. It is the
nature of the process to adopt whatever belief we are inclined to, and
there are certain flatteries to one’s vanities which we all believe by
nature, until we are awakened from our pleasing dream by rough facts.
The method of authority will always govern the mass of mankind; and
those who wield the various forms of organized force in the state will
never be convinced that dangerous reasoning ought not to be suppressed
in some way. If liberty of speech is to be untrammeled from the grosser
forms of constraint, then uniformity of opinion will be secured by a
moral terrorism to which the respectability of society will give its
thorough approval. Following the method of authority is the path of
peace. Certain non-conformities are permitted; certain others
(considered unsafe) are forbidden. These are different in different
countries and in different ages; but, wherever you are let it be known
that you seriously hold a tabooed belief, and you may be perfectly sure
of being treated with a cruelty no less brutal but more refined than
hunting you like a wolf. Thus, the greatest intellectual benefactors of
mankind have never dared, and dare not now, to utter the whole of their
thought; and thus a shade of _prima facie_ doubt is cast upon every
proposition which is considered essential to the security of society.
Singularly enough, the persecution does not all come from without; but a
man torments himself and is oftentimes most distressed at finding
himself believing propositions which he has been brought up to regard
with aversion. The peaceful and sympathetic man will, therefore, find it
hard to resist the temptation to submit his opinions to authority. But
most of all I admire the method of tenacity for its strength,
simplicity, and directness. Men who pursue it are distinguished for
their decision of character, which becomes very easy with such a mental
rule. They do not waste time in trying to make up their minds to what
they want, but, fastening like lightning upon whatever alternative comes
first, they hold to it to the end, whatever happens, without an
instant’s irresolution. This is one of the splendid qualities which
generally accompany brilliant, unlasting success. It is impossible not
to envy the man who can dismiss reason, although we know how it must
turn out at last.

Such are the advantages which the other methods of settling opinions
have over scientific investigation. A man should consider well of them;
and then he should consider that, after all, he wishes his opinions to
coincide with the fact, and that there is no reason why the results of
these three methods should do so. To bring about this effect is the
prerogative of the method of science. Upon such considerations he has to
make his choice—a choice which is far more than the adoption of any
intellectual opinion, which is one of the ruling decisions of his life,
to which when once made he is bound to adhere. The force of habit will
sometimes cause a man to hold on to old beliefs, after he is in a
condition to see that they have no sound basis. But reflection upon the
state of the case will overcome these habits, and he ought to allow
reflection full weight. People sometimes shrink from doing this, having
an idea that beliefs are wholesome which they cannot help feeling rest
on nothing. But let such persons suppose an analogous though different
case from their own. Let them ask themselves what they would say to a
reformed Mussulman who should hesitate to give up his old notions in
regard to the relations of the sexes; or to a reformed Catholic who
should still shrink from the Bible. Would they not say that these
persons ought to consider the matter fully, and clearly understand the
new doctrine, and then ought to embrace it in its entirety? But, above
all, let it be considered that what is more wholesome than any
particular belief, is integrity of belief; and that to avoid looking
into the support of any belief from a fear that it may turn out rotten
is quite as immoral as it is disadvantageous. The person who confesses
that there is such a thing as truth, which is distinguished from
falsehood simply by this, that if acted on it will carry us to the point
we aim at and not astray, and then though convinced of this, dares not
know the truth and seeks to avoid it, is in a sorry state of mind,
indeed.

Yes, the other methods do have their merits: a clear logical conscience
does cost something—just as any virtue, just as all that we cherish,
costs us dear. But, we should not desire it to be otherwise. The genius
of a man’s logical method should be loved and reverenced as his bride,
whom he has chosen from all the world. He need not condemn the others;
on the contrary, he may honor them deeply, and in doing so he only
honors her the more. But she is the one that he has chosen, and he knows
that he was right in making that choice. And having made it, he will
work and fight for her, and will not complain that there are blows to
take, hoping that there may be as many and as hard to give, and will
strive to be the worthy knight and champion of her from the blaze of
whose splendors he draws his inspiration and his courage.

Footnote 26:

  _Popular Science Monthly_, November, 1877.

Footnote 27:

  [This is substantially the dictum of Harvey to John Aubrey. See the
  latter’s _Brief Lives_ (Oxford ed. 1898) I 299.]

Footnote 28:

  Not quite so, but as nearly so as can be told in a few words.

Footnote 29:

  [This modern logic, however, is largely the outcome of Kepler’s work.]

Footnote 30:

  I am not speaking of secondary effects occasionally produced by the
  interference of other impulses.




                              SECOND PAPER
                    HOW TO MAKE OUR IDEAS CLEAR[31]


                                   I


Whoever has looked into a modern treatise on logic of the common sort,
will doubtless remember the two distinctions between _clear_ and
_obscure_ conceptions, and between _distinct_ and _confused_
conceptions. They have lain in the books now for nigh two centuries,
unimproved and unmodified, and are generally reckoned by logicians as
among the gems of their doctrine.

A clear idea is defined as one which is so apprehended that it will be
recognized wherever it is met with, and so that no other will be
mistaken for it. If it fails of this clearness, it is said to be
obscure.

This is rather a neat bit of philosophical terminology; yet, since it is
clearness that they were defining, I wish the logicians had made their
definition a little more plain. Never to fail to recognize an idea, and
under no circumstances to mistake another for it, let it come in how
recondite a form it may, would indeed imply such prodigious force and
clearness of intellect as is seldom met with in this world. On the other
hand, merely to have such an acquaintance with the idea as to have
become familiar with it, and to have lost all hesitancy in recognizing
it in ordinary cases, hardly seems to deserve the name of clearness of
apprehension, since after all it only amounts to a subjective feeling of
mastery which may be entirely mistaken. I take it, however, that when
the logicians speak of “clearness,” they mean nothing more than such a
familiarity with an idea, since they regard the quality as but a small
merit, which needs to be supplemented by another, which they call
_distinctness_.

A distinct idea is defined as one which contains nothing which is not
clear. This is technical language; by the _contents_ of an idea
logicians understand whatever is contained in its definition. So that an
idea is _distinctly_ apprehended, according to them, when we can give a
precise definition of it, in abstract terms. Here the professional
logicians leave the subject; and I would not have troubled the reader
with what they have to say, if it were not such a striking example of
how they have been slumbering through ages of intellectual activity,
listlessly disregarding the enginery of modern thought, and never
dreaming of applying its lessons to the improvement of logic. It is easy
to show that the doctrine that familiar use and abstract distinctness
make the perfection of apprehension, has its only true place in
philosophies which have long been extinct; and it is now time to
formulate the method of attaining to a more perfect clearness of
thought, such as we see and admire in the thinkers of our own time.

When Descartes set about the reconstruction of philosophy, his first
step was to (theoretically) permit skepticism and to discard the
practice of the schoolmen of looking to authority as the ultimate source
of truth. That done, he sought a more natural fountain of true
principles, and professed to find it in the human mind; thus passing, in
the directest way, from the method of authority to that of apriority, as
described in my first paper. Self-consciousness was to furnish us with
our fundamental truths, and to decide what was agreeable to reason. But
since, evidently, not all ideas are true, he was led to note, as the
first condition of infallibility, that they must be clear. The
distinction between an idea _seeming_ clear and really being so, never
occurred to him. Trusting to introspection, as he did, even for a
knowledge of external things, why should he question its testimony in
respect to the contents of our own minds? But then, I suppose, seeing
men, who seemed to be quite clear and positive, holding opposite
opinions upon fundamental principles, he was further led to say that
clearness of ideas is not sufficient, but that they need also to be
distinct, i.e., to have nothing unclear about them. What he probably
meant by this (for he did not explain himself with precision) was, that
they must sustain the test of dialectical examination; that they must
not only seem clear at the outset, but that discussion must never be
able to bring to light points of obscurity connected with them.

Such was the distinction of Descartes, and one sees that it was
precisely on the level of his philosophy. It was somewhat developed by
Leibnitz. This great and singular genius was as remarkable for what he
failed to see as for what he saw. That a piece of mechanism could not do
work perpetually without being fed with power in some form, was a thing
perfectly apparent to him; yet he did not understand that the machinery
of the mind can only transform knowledge, but never originate it, unless
it be fed with facts of observation. He thus missed the most essential
point of the Cartesian philosophy, which is, that to accept propositions
which seem perfectly evident to us is a thing which, whether it be
logical or illogical, we cannot help doing. Instead of regarding the
matter in this way, he sought to reduce the first principles of science
to formulas which cannot be denied without self-contradiction, and was
apparently unaware of the great difference between his position and that
of Descartes. So he reverted to the old formalities of logic, and, above
all, abstract definitions played a great part in his philosophy. It was
quite natural, therefore, that on observing that the method of Descartes
labored under the difficulty that we may seem to ourselves to have clear
apprehensions of ideas which in truth are very hazy, no better remedy
occurred to him than to require an abstract definition of every
important term. Accordingly, in adopting the distinction of _clear_ and
_distinct_ notions, he described the latter quality as the clear
apprehension of everything contained in the definition; and the books
have ever since copied his words. There is no danger that his chimerical
scheme will ever again be over-valued. Nothing new can ever be learned
by analyzing definitions. Nevertheless, our existing beliefs can be set
in order by this process, and order is an essential element of
intellectual economy, as of every other. It may be acknowledged,
therefore, that the books are right in making familiarity with a notion
the first step toward clearness of apprehension, and the defining of it
the second. But in omitting all mention of any higher perspicuity of
thought, they simply mirror a philosophy which was exploded a hundred
years ago. That much-admired “ornament of logic”—the doctrine of
clearness and distinctness—may be pretty enough, but it is high time to
relegate to our cabinet of curiosities the antique _bijou_, and to wear
about us something better adapted to modern uses.

The very first lesson that we have a right to demand that logic shall
teach us is, how to make our ideas clear; and a most important one it
is, depreciated only by minds who stand in need of it. To know what we
think, to be masters of our own meaning, will make a solid foundation
for great and weighty thought. It is most easily learned by those whose
ideas are meagre and restricted; and far happier they than such as
wallow helplessly in a rich mud of conceptions. A nation, it is true,
may, in the course of generations, overcome the disadvantage of an
excessive wealth of language and its natural concomitant, a vast,
unfathomable deep of ideas. We may see it in history, slowly perfecting
its literary forms, sloughing at length its metaphysics, and, by virtue
of the untirable patience which is often a compensation, attaining great
excellence in every branch of mental acquirement. The page of history is
not yet unrolled which is to tell us whether such a people will or will
not in the long run prevail over one whose ideas (like the words of
their language) are few, but which possesses a wonderful mastery over
those which it has. For an individual, however, there can be no question
that a few clear ideas are worth more than many confused ones. A young
man would hardly be persuaded to sacrifice the greater part of his
thoughts to save the rest; and the muddled head is the least apt to see
the necessity of such a sacrifice. Him we can usually only commiserate,
as a person with a congenital defect. Time will help him, but
intellectual maturity with regard to clearness comes rather late, an
unfortunate arrangement of Nature, inasmuch as clearness is of less use
to a man settled in life, whose errors have in great measure had their
effect, than it would be to one whose path lies before him. It is
terrible to see how a single unclear idea, a single formula without
meaning, lurking in a young man’s head, will sometimes act like an
obstruction of inert matter in an artery, hindering the nutrition of the
brain, and condemning its victim to pine away in the fullness of his
intellectual vigor and in the midst of intellectual plenty. Many a man
has cherished for years as his hobby some vague shadow of an idea, too
meaningless to be positively false; he has, nevertheless, passionately
loved it, has made it his companion by day and by night, and has given
to it his strength and his life, leaving all other occupations for its
sake, and in short has lived with it and for it, until it has become, as
it were, flesh of his flesh and bone of his bone; and then he has waked
up some bright morning to find it gone, clean vanished away like the
beautiful Melusina of the fable, and the essence of his life gone with
it. I have myself known such a man; and who can tell how many histories
of circle-squarers, metaphysicians, astrologers, and what not, may not
be told in the old German story?


                                   II


The principles set forth in the first of these papers lead, at once, to
a method of reaching a clearness of thought of a far higher grade than
the “distinctness” of the logicians. We have there found that the action
of thought is excited by the irritation of doubt, and ceases when belief
is attained; so that the production of belief is the sole function of
thought. All these words, however, are too strong for my purpose. It is
as if I had described the phenomena as they appear under a mental
microscope. Doubt and Belief, as the words are commonly employed, relate
to religious or other grave discussions. But here I use them to
designate the starting of any question, no matter how small or how
great, and the resolution of it. If, for instance, in a horse-car, I
pull out my purse and find a five-cent nickel and five coppers, I
decide, while my hand is going to the purse, in which way I will pay my
fare. To call such a question Doubt, and my decision Belief, is
certainly to use words very disproportionate to the occasion. To speak
of such a doubt as causing an irritation which needs to be appeased,
suggests a temper which is uncomfortable to the verge of insanity. Yet,
looking at the matter minutely, it must be admitted that, if there is
the least hesitation as to whether I shall pay the five coppers or the
nickel (as there will be sure to be, unless I act from some previously
contracted habit in the matter), though irritation is too strong a word,
yet I am excited to such small mental activity as may be necessary to
deciding how I shall act. Most frequently doubts arise from some
indecision, however momentary, in our action. Sometimes it is not so. I
have, for example, to wait in a railway-station, and to pass the time I
read the advertisements on the walls, I compare the advantages of
different trains and different routes which I never expect to take,
merely fancying myself to be in a state of hesitancy, because I am bored
with having nothing to trouble me. Feigned hesitancy, whether feigned
for mere amusement or with a lofty purpose, plays a great part in the
production of scientific inquiry. However the doubt may originate, it
stimulates the mind to an activity which may be slight or energetic,
calm or turbulent. Images pass rapidly through consciousness, one
incessantly melting into another, until at last, when all is over—it may
be in a fraction of a second, in an hour, or after long years—we find
ourselves decided as to how we should act under such circumstances as
those which occasioned our hesitation. In other words, we have attained
belief.

In this process we observe two sorts of elements of consciousness, the
distinction between which may best be made clear by means of an
illustration. In a piece of music there are the separate notes, and
there is the air. A single tone may be prolonged for an hour or a day,
and it exists as perfectly in each second of that time as in the whole
taken together; so that, as long as it is sounding, it might be present
to a sense from which everything in the past was as completely absent as
the future itself. But it is different with the air, the performance of
which occupies a certain time, during the portions of which only
portions of it are played. It consists in an orderliness in the
succession of sounds which strike the ear at different times; and to
perceive it there must be some continuity of consciousness which makes
the events of a lapse of time present to us. We certainly only perceive
the air by hearing the separate notes; yet we cannot be said to directly
hear it, for we hear only what is present at the instant, and an
orderliness of succession cannot exist in an instant. These two sorts of
objects, what we are _immediately_ conscious of and what we are
_mediately_ conscious of, are found in all consciousness. Some elements
(the sensations) are completely present at every instant so long as they
last, while others (like thought) are actions having beginning, middle,
and end, and consist in a congruence in the succession of sensations
which flow through the mind. They cannot be immediately present to us,
but must cover some portion of the past or future. Thought is a thread
of melody running through the succession of our sensations.

We may add that just as a piece of music may be written in parts, each
part having its own air, so various systems of relationship of
succession subsist together between the same sensations. These different
systems are distinguished by having different motives, ideas, or
functions. Thought is only one such system; for its sole motive, idea,
and function is to produce belief, and whatever does not concern that
purpose belongs to some other system of relations. The action of
thinking may incidentally have other results. It may serve to amuse us,
for example, and among _dilettanti_ it is not rare to find those who
have so perverted thought to the purposes of pleasure that it seems to
vex them to think that the questions upon which they delight to exercise
it may ever get finally settled; and a positive discovery which takes a
favorite subject out of the arena of literary debate is met with
ill-concealed dislike. This disposition is the very debauchery of
thought. But the soul and meaning of thought, abstracted from the other
elements which accompany it, though it may be voluntarily thwarted, can
never be made to direct itself toward anything but the production of
belief. Thought in action has for its only possible motive the
attainment of thought at rest; and whatever does not refer to belief is
no part of the thought itself.

And what, then, is belief? It is the demi-cadence which closes a musical
phrase in the symphony of our intellectual life. We have seen that it
has just three properties: First, it is something that we are aware of;
second, it appeases the irritation of doubt; and, third, it involves the
establishment in our nature of a rule of action, or, say for short, a
_habit_. As it appeases the irritation of doubt, which is the motive for
thinking, thought relaxes, and comes to rest for a moment when belief is
reached. But, since belief is a rule for action, the application of
which involves further doubt and further thought, at the same time that
it is a stopping-place, it is also a new starting-place for thought.
That is why I have permitted myself to call it thought at rest, although
thought is essentially an action. The _final_ upshot of thinking is the
exercise of volition, and of this thought no longer forms a part; but
belief is only a stadium of mental action, an effect upon our nature due
to thought, which will influence future thinking.

[Illustration: Figure 1.]

[Illustration: Figure 2.]

The essence of belief is the establishment of a habit, and different
beliefs are distinguished by the different modes of action to which they
give rise. If beliefs do not differ in this respect, if they appease the
same doubt by producing the same rule of action, then no mere
differences in the manner of consciousness of them can make them
different beliefs, any more than playing a tune in different keys is
playing different tunes. Imaginary distinctions are often drawn between
beliefs which differ only in their mode of expression;—the wrangling
which ensues is real enough, however. To believe that any objects are
arranged as in Fig. 1, and to believe that they are arranged as in Fig.
2, are one and the same belief; yet it is conceivable that a man should
assert one proposition and deny the other. Such false distinctions do as
much harm as the confusion of beliefs really different, and are among
the pitfalls of which we ought constantly to beware, especially when we
are upon metaphysical ground. One singular deception of this sort, which
often occurs, is to mistake the sensation produced by our own
unclearness of thought for a character of the object we are thinking.
Instead of perceiving that the obscurity is purely subjective, we fancy
that we contemplate a quality of the object which is essentially
mysterious; and if our conception be afterward presented to us in a
clear form we do not recognize it as the same, owing to the absence of
the feeling of unintelligibility. So long as this deception lasts, it
obviously puts an impassable barrier in the way of perspicuous thinking;
so that it equally interests the opponents of rational thought to
perpetuate it, and its adherents to guard against it.

Another such deception is to mistake a mere difference in the
grammatical construction of two words for a distinction between the
ideas they express. In this pedantic age, when the general mob of
writers attend so much more to words than to things, this error is
common enough. When I just said that thought is an _action_, and that it
consists in a _relation_, although a person performs an action but not a
relation, which can only be the result of an action, yet there was no
inconsistency in what I said, but only a grammatical vagueness.

From all these sophisms we shall be perfectly safe so long as we reflect
that the whole function of thought is to produce habits of action; and
that whatever there is connected with a thought, but irrelevant to its
purpose, is an accretion to it, but no part of it. If there be a unity
among our sensations which has no reference to how we shall act on a
given occasion, as when we listen to a piece of music, why we do not
call that thinking. To develop its meaning, we have, therefore, simply
to determine what habits it produces, for what a thing means is simply
what habits it involves. Now, the identity of a habit depends on how it
might lead us to act, not merely under such circumstances as are likely
to arise, but under such as might possibly occur, no matter how
improbable they may be. What the habit is depends on _when_ and _how_ it
causes us to act. As for the _when_, every stimulus to action is derived
from perception; as for the _how_, every purpose of action is to produce
some sensible result. Thus, we come down to what is tangible and
practical, as the root of every real distinction of thought, no matter
how subtile it may be; and there is no distinction of meaning so fine as
to consist in anything but a possible difference of practice.

To see what this principle leads to, consider in the light of it such a
doctrine as that of transubstantiation. The Protestant churches
generally hold that the elements of the sacrament are flesh and blood
only in a tropical sense; they nourish our souls as meat and the juice
of it would our bodies. But the Catholics maintain that they are
literally just that; although they possess all the sensible qualities of
wafer-cakes and diluted wine. But we can have no conception of wine
except what may enter into a belief, either—

1. That this, that, or the other, is wine; or,

2. That wine possesses certain properties.

Such beliefs are nothing but self-notifications that we should, upon
occasion, act in regard to such things as we believe to be wine
according to the qualities which we believe wine to possess. The
occasion of such action would be some sensible perception, the motive of
it to produce some sensible result. Thus our action has exclusive
reference to what affects the senses, our habit has the same bearing as
our action, our belief the same as our habit, our conception the same as
our belief; and we can consequently mean nothing by wine but what has
certain effects, direct or indirect, upon our senses; and to talk of
something as having all the sensible characters of wine, yet being in
reality blood, is senseless jargon. Now, it is not my object to pursue
the theological question; and having used it as a logical example I drop
it, without caring to anticipate the theologian’s reply. I only desire
to point out how impossible it is that we should have an idea in our
minds which relates to anything but conceived sensible effects of
things. Our idea of anything _is_ our idea of its sensible effects; and
if we fancy that we have any other we deceive ourselves, and mistake a
mere sensation accompanying the thought for a part of the thought
itself. It is absurd to say that thought has any meaning unrelated to
its only function. It is foolish for Catholics and Protestants to fancy
themselves in disagreement about the elements of the sacrament, if they
agree in regard to all their sensible effects, here or hereafter.

It appears, then, that the rule for attaining the third grade of
clearness of apprehension is as follows: Consider what effects, which
might conceivably have practical bearings, we conceive the object of our
conception to have. Then, our conception of these effects is the whole
of our conception of the object.


                                  III


Let us illustrate this rule by some examples; and, to begin with the
simplest one possible, let us ask what we mean by calling a thing
_hard_. Evidently that it will not be scratched by many other
substances. The whole conception of this quality, as of every other,
lies in its conceived effects. There is absolutely no difference between
a hard thing and a soft thing so long as they are not brought to the
test. Suppose, then, that a diamond could be crystallized in the midst
of a cushion of soft cotton, and should remain there until it was
finally burned up. Would it be false to say that that diamond was soft?
This seems a foolish question, and would be so, in fact, except in the
realm of logic. There such questions are often of the greatest utility
as serving to bring logical principles into sharper relief than real
discussions ever could. In studying logic we must not put them aside
with hasty answers, but must consider them with attentive care, in order
to make out the principles involved. We may, in the present case, modify
our question, and ask what prevents us from saying that all hard bodies
remain perfectly soft until they are touched, when their hardness
increases with the pressure until they are scratched. Reflection will
show that the reply is this: there would be no _falsity_ in such modes
of speech. They would involve a modification of our present usage of
speech with regard to the words hard and soft, but not of their
meanings. For they represent no fact to be different from what it is;
only they involve arrangements of facts which would be exceedingly
maladroit. This leads us to remark that the question of what would occur
under circumstances which do not actually arise is not a question of
fact, but only of the most perspicuous arrangement of them. For example,
the question of free-will and fate in its simplest form, stripped of
verbiage, is something like this: I have done something of which I am
ashamed; could I, by an effort of the will, have resisted the
temptation, and done otherwise? The philosophical reply is, that this is
not a question of fact, but only of the arrangement of facts. Arranging
them so as to exhibit what is particularly pertinent to my
question—namely, that I ought to blame myself for having done wrong—it
is perfectly true to say that, if I had willed to do otherwise than I
did, I should have done otherwise. On the other hand, arranging the
facts so as to exhibit another important consideration, it is equally
true that, when a temptation has once been allowed to work, it will, if
it has a certain force, produce its effect, let me struggle how I may.
There is no objection to a contradiction in what would result from a
false supposition. The _reductio ad absurdum_ consists in showing that
contradictory results would follow from a hypothesis which is
consequently judged to be false. Many questions are involved in the
free-will discussion, and I am far from desiring to say that both sides
are equally right. On the contrary, I am of opinion that one side denies
important facts, and that the other does not. But what I do say is, that
the above single question was the origin of the whole doubt; that, had
it not been for this question, the controversy would never have arisen;
and that this question is perfectly solved in the manner which I have
indicated.

Let us next seek a clear idea of Weight. This is another very easy case.
To say that a body is heavy means simply that, in the absence of
opposing force, it will fall. This (neglecting certain specifications of
how it will fall, etc., which exist in the mind of the physicist who
uses the word) is evidently the whole conception of weight. It is a fair
question whether some particular facts may not _account_ for gravity;
but what we mean by the force itself is completely involved in its
effects.

This leads us to undertake an account of the idea of Force in general.
This is the great conception which, developed in the early part of the
seventeenth century from the rude idea of a cause, and constantly
improved upon since, has shown us how to explain all the changes of
motion which bodies experience, and how to think about all physical
phenomena; which has given birth to modern science, and changed the face
of the globe; and which, aside from its more special uses, has played a
principal part in directing the course of modern thought, and in
furthering modern social development. It is, therefore, worth some pains
to comprehend it. According to our rule, we must begin by asking what is
the immediate use of thinking about force; and the answer is, that we
thus account for changes of motion. If bodies were left to themselves,
without the intervention of forces, every motion would continue
unchanged both in velocity and in direction. Furthermore, change of
motion never takes place abruptly; if its direction is changed, it is
always through a curve without angles; if its velocity alters, it is by
degrees. The gradual changes which are constantly taking place are
conceived by geometers to be compounded together according to the rules
of the parallelogram of forces. If the reader does not already know what
this is, he will find it, I hope, to his advantage to endeavor to follow
the following explanation; but if mathematics are insupportable to him,
pray let him skip three paragraphs rather than that we should part
company here.

A _path_ is a line whose beginning and end are distinguished. Two paths
are considered to be equivalent, which, beginning at the same point,
lead to the same point. Thus the two paths, _A B C D E_ and _A F G H E_
(Fig. 3), are equivalent. Paths which do _not_ begin at the same point
are considered to be equivalent, provided that, on moving either of them
without turning it, but keeping it always parallel to its original
position, [so that] when its beginning coincides with that of the other
path, the ends also coincide. Paths are considered as geometrically
added together, when one begins where the other ends; thus the path _A
E_ is conceived to be a sum of _A B_, _B C_, _C D_, and _D E_. In the
parallelogram of Fig. 4 the diagonal _A C_ is the sum of _A B_ and _B
C_; or, since _A D_ is geometrically equivalent to _B C_, _A C_ is the
geometrical sum of _A B_ and _A D_.

[Illustration: Figure 3.]

[Illustration: Figure 4.]

All this is purely conventional. It simply amounts to this: that we
choose to call paths having the relations I have described equal or
added. But, though it is a convention, it is a convention with a good
reason. The rule for geometrical addition may be applied not only to
paths, but to any other things which can be represented by paths. Now,
as a path is determined by the varying direction and distance of the
point which moves over it from the starting-point, it follows that
anything which from its beginning to its end is determined by a varying
direction and a varying magnitude is capable of being represented by a
line. Accordingly, _velocities_ may be represented by lines, for they
have only directions and rates. The same thing is true of
_accelerations_, or changes of velocities. This is evident enough in the
case of velocities; and it becomes evident for accelerations if we
consider that precisely what velocities are to positions—namely, states
of change of them—that accelerations are to velocities.

[Illustration: Figure 5.]

The so-called “parallelogram of forces” is simply a rule for compounding
accelerations. The rule is, to represent the accelerations by paths, and
then to geometrically add the paths. The geometers, however, not only
use the “parallelogram of forces” to compound different accelerations,
but also to resolve one acceleration into a sum of several. Let _A B_
(Fig. 5) be the path which represents a certain acceleration—say, such a
change in the motion of a body that at the end of one second the body
will, under the influence of that change, be in a position different
from what it would have had if its motion had continued unchanged, such
that a path equivalent to _A B_ would lead from the latter position to
the former. This acceleration may be considered as the sum of the
accelerations represented by _A C_ and _C B_. It may also be considered
as the sum of the very different accelerations represented by _A D_ and
_D B_, where _A D_ is almost the opposite of _A C_. And it is clear that
there is an immense variety of ways in which _A B_ might be resolved
into the sum of two accelerations.

After this tedious explanation, which I hope, in view of the
extraordinary interest of the conception of force, may not have
exhausted the reader’s patience, we are prepared at last to state the
grand fact which this conception embodies. This fact is that if the
actual changes of motion which the different particles of bodies
experience are each resolved in its appropriate way, each component
acceleration is precisely such as is prescribed by a certain law of
Nature, according to which bodies in the relative positions which the
bodies in question actually have at the moment,[32] always receive
certain accelerations, which, being compounded by geometrical addition,
give the acceleration which the body actually experiences.

This is the only fact which the idea of force represents, and whoever
will take the trouble clearly to apprehend what this fact is, perfectly
comprehends what force is. Whether we ought to say that a force _is_ an
acceleration, or that it _causes_ an acceleration, is a mere question of
propriety of language, which has no more to do with our real meaning
than the difference between the French idiom “_Il fait froid_” and its
English equivalent “_It is cold_.” Yet it is surprising to see how this
simple affair has muddled men’s minds. In how many profound treatises is
not force spoken of as a “mysterious entity,” which seems to be only a
way of confessing that the author despairs of ever getting a clear
notion of what the word means! In a recent admired work on _Analytic
Mechanics_ it is stated that we understand precisely the effect of
force, but what force itself is we do not understand! This is simply a
self-contradiction. The idea which the word force excites in our minds
has no other function than to affect our actions, and these actions can
have no reference to force otherwise than through its effects.
Consequently, if we know what the effects of force are, we are
acquainted with every fact which is implied in saying that a force
exists, and there is nothing more to know. The truth is, there is some
vague notion afloat that a question may mean something which the mind
cannot conceive; and when some hair-splitting philosophers have been
confronted with the absurdity of such a view, they have invented an
empty distinction between positive and negative conceptions, in the
attempt to give their non-idea a form not obviously nonsensical. The
nullity of it is sufficiently plain from the considerations given a few
pages back; and, apart from those considerations, the quibbling
character of the distinction must have struck every mind accustomed to
real thinking.


                                   IV


Let us now approach the subject of logic, and consider a conception
which particularly concerns it, that of _reality_. Taking clearness in
the sense of familiarity, no idea could be clearer than this. Every
child uses it with perfect confidence, never dreaming that he does not
understand it. As for clearness in its second grade, however, it would
probably puzzle most men, even among those of a reflective turn of mind,
to give an abstract definition of the real. Yet such a definition may
perhaps be reached by considering the points of difference between
reality and its opposite, fiction. A figment is a product of somebody’s
imagination; it has such characters as his thought impresses upon it.
That those characters are independent of how you or I think is an
external reality. There are, however, phenomena within our own minds,
dependent upon our thought, which are at the same time real in the sense
that we really think them. But though their characters depend on how we
think, they do not depend on what we think those characters to be. Thus,
a dream has a real existence as a mental phenomenon, if somebody has
really dreamt it; that he dreamt so and so, does not depend on what
anybody thinks was dreamt, but is completely independent of all opinion
on the subject. On the other hand, considering, not the fact of
dreaming, but the thing dreamt, it retains its peculiarities by virtue
of no other fact than that it was dreamt to possess them. Thus we may
define the real as that whose characters are independent of what anybody
may think them to be.

But, however satisfactory such a definition may be found, it would be a
great mistake to suppose that it makes the idea of reality perfectly
clear. Here, then, let us apply our rules. According to them, reality,
like every other quality, consists in the peculiar sensible effects
which things partaking of it produce. The only effect which real things
have is to cause belief, for all the sensations which they excite emerge
into consciousness in the form of beliefs. The question, therefore, is,
how is true belief (or belief in the real) distinguished from false
belief (or belief in fiction). Now, as we have seen in the former paper,
the ideas of truth and falsehood, in their full development, appertain
exclusively to the scientific method of settling opinion. A person who
arbitrarily chooses the propositions which he will adopt can use the
word truth only to emphasize the expression of his determination to hold
on to his choice. Of course, the method of tenacity never prevailed
exclusively; reason is too natural to men for that. But in the
literature of the dark ages we find some fine examples of it. When
Scotus Erigena is commenting upon a poetical passage in which hellebore
is spoken of as having caused the death of Socrates, he does not
hesitate to inform the inquiring reader that Helleborus and Socrates
were two eminent Greek philosophers, and that the latter having been
overcome in argument by the former took the matter to heart and died of
it! What sort of an idea of truth could a man have who could adopt and
teach, without the qualification of a perhaps, an opinion taken so
entirely at random? The real spirit of Socrates, who I hope would have
been delighted to have been “overcome in argument,” because he would
have learned something by it, is in curious contrast with the naïve idea
of the glossist, for whom discussion would seem to have been simply a
struggle. When philosophy began to awake from its long slumber, and
before theology completely dominated it, the practice seems to have been
for each professor to seize upon any philosophical position he found
unoccupied and which seemed a strong one, to intrench himself in it, and
to sally forth from time to time to give battle to the others. Thus,
even the scanty records we possess of those disputes enable us to make
out a dozen or more opinions held by different teachers at one time
concerning the question of nominalism and realism. Read the opening part
of the _Historia Calamitatum_ of Abelard, who was certainly as
philosophical as any of his contemporaries, and see the spirit of combat
which it breathes. For him, the truth is simply his particular
stronghold. When the method of authority prevailed, the truth meant
little more than the Catholic faith. All the efforts of the scholastic
doctors are directed toward harmonizing their faith in Aristotle and
their faith in the Church, and one may search their ponderous folios
through without finding an argument which goes any further. It is
noticeable that where different faiths flourish side by side, renegades
are looked upon with contempt even by the party whose belief they adopt;
so completely has the idea of loyalty replaced that of truth-seeking.
Since the time of Descartes, the defect in the conception of truth has
been less apparent. Still, it will sometimes strike a scientific man
that the philosophers have been less intent on finding out what the
facts are, than on inquiring what belief is most in harmony with their
system. It is hard to convince a follower of the _a priori_ method by
adducing facts; but show him that an opinion he is defending is
inconsistent with what he has laid down elsewhere, and he will be very
apt to retract it. These minds do not seem to believe that disputation
is ever to cease; they seem to think that the opinion which is natural
for one man is not so for another, and that belief will, consequently,
never be settled. In contenting themselves with fixing their own
opinions by a method which would lead another man to a different result,
they betray their feeble hold of the conception of what truth is.

On the other hand, all the followers of science are fully persuaded that
the processes of investigation, if only pushed far enough, will give one
certain solution to every question to which they can be applied. One man
may investigate the velocity of light by studying the transits of Venus
and the aberration of the stars; another by the oppositions of Mars and
the eclipses of Jupiter’s satellites; a third by the method of Fizeau; a
fourth by that of Foucault; a fifth by the motions of the curves of
Lissajoux; a sixth, a seventh, an eighth, and a ninth, may follow the
different methods of comparing the measures of statical and dynamical
electricity. They may at first obtain different results, but, as each
perfects his method and his processes, the results will move steadily
together toward a destined center. So with all scientific research.
Different minds may set out with the most antagonistic views, but the
progress of investigation carries them by a force outside of themselves
to one and the same conclusion. This activity of thought by which we are
carried, not where we wish, but to a fore-ordained goal, is like the
operation of destiny. No modification of the point of view taken, no
selection of other facts for study, no natural bent of mind even, can
enable a man to escape the predestinate opinion. This great law is
embodied in the conception of truth and reality. The opinion which is
fated[33] to be ultimately agreed to by all who investigate, is what we
mean by the truth, and the object represented in this opinion is the
real. That is the way I would explain reality.

But it may be said that this view is directly opposed to the abstract
definition which we have given of reality, inasmuch as it makes the
characters of the real depend on what is ultimately thought about them.
But the answer to this is that, on the one hand, reality is independent,
not necessarily of thought in general, but only of what you or I or any
finite number of men may think about it; and that, on the other hand,
though the object of the final opinion depends on what that opinion is,
yet what that opinion is does not depend on what you or I or any man
thinks. Our perversity and that of others may indefinitely postpone the
settlement of opinion; it might even conceivably cause an arbitrary
proposition to be universally accepted as long as the human race should
last. Yet even that would not change the nature of the belief, which
alone could be the result of investigation carried sufficiently far; and
if, after the extinction of our race, another should arise with
faculties and disposition for investigation, that true opinion must be
the one which they would ultimately come to. “Truth crushed to earth
shall rise again,” and the opinion which would finally result from
investigation does not depend on how anybody may actually think. But the
reality of that which is real does depend on the real fact that
investigation is destined to lead, at last, if continued long enough, to
a belief in it.

But I may be asked what I have to say to all the minute facts of
history, forgotten never to be recovered, to the lost books of the
ancients, to the buried secrets.

               “Full many a gem of purest ray serene
                 The dark, unfathomed caves of ocean bear;
               Full many a flower is born to blush unseen,
                 And waste its sweetness on the desert air.”

Do these things not really exist because they are hopelessly beyond the
reach of our knowledge? And then, after the universe is dead (according
to the prediction of some scientists), and all life has ceased forever,
will not the shock of atoms continue though there will be no mind to
know it? To this I reply that, though in no possible state of knowledge
can any number be great enough to express the relation between the
amount of what rests unknown to the amount of the known, yet it is
unphilosophical to suppose that, with regard to any given question
(which has any clear meaning), investigation would not bring forth a
solution of it, if it were carried far enough. Who would have said, a
few years ago, that we could ever know of what substances stars are made
whose light may have been longer in reaching us than the human race has
existed? Who can be sure of what we shall not know in a few hundred
years? Who can guess what would be the result of continuing the pursuit
of science for ten thousand years, with the activity of the last
hundred? And if it were to go on for a million, or a billion, or any
number of years you please, how is it possible to say that there is any
question which might not ultimately be solved?

But it may be objected, “Why make so much of these remote
considerations, especially when it is your principle that only practical
distinctions have a meaning?” Well, I must confess that it makes very
little difference whether we say that a stone on the bottom of the
ocean, in complete darkness, is brilliant or not—that is to say, that it
_probably_ makes no difference, remembering always that that stone _may_
be fished up to-morrow. But that there are gems at the bottom of the
sea, flowers in the untraveled desert, etc., are propositions which,
like that about a diamond being hard when it is not pressed, concern
much more the arrangement of our language than they do the meaning of
our ideas.

It seems to me, however, that we have, by the application of our rule,
reached so clear an apprehension of what we mean by reality, and of the
fact which the idea rests on, that we should not, perhaps, be making a
pretension so presumptuous as it would be singular, if we were to offer
a metaphysical theory of existence for universal acceptance among those
who employ the scientific method of fixing belief. However, as
metaphysics is a subject much more curious than useful, the knowledge of
which, like that of a sunken reef, serves chiefly to enable us to keep
clear of it, I will not trouble the reader with any more Ontology at
this moment. I have already been led much further into that path than I
should have desired; and I have given the reader such a dose of
mathematics, psychology, and all that is most abstruse, that I fear he
may already have left me, and that what I am now writing is for the
compositor and proofreader exclusively. I trusted to the importance of
the subject. There is no royal road to logic, and really valuable ideas
can only be had at the price of close attention. But I know that in the
matter of ideas the public prefer the cheap and nasty; and in my next
paper I am going to return to the easily intelligible, and not wander
from it again. The reader who has been at the pains of wading through
this paper, shall be rewarded in the next one by seeing how beautifully
what has been developed in this tedious way can be applied to the
ascertainment of the rules of scientific reasoning.

We have, hitherto, not crossed the threshold of scientific logic. It is
certainly important to know how to make our ideas clear, but they may be
ever so clear without being true. How to make them so, we have next to
study. How to give birth to those vital and procreative ideas which
multiply into a thousand forms and diffuse themselves everywhere,
advancing civilization and making the dignity of man, is an art not yet
reduced to rules, but of the secret of which the history of science
affords some hints.

Footnote 31:

  _Popular Science Monthly_, January, 1878.

Footnote 32:

  Possibly the velocities also have to be taken into account.

Footnote 33:

  Fate means merely that which is sure to come true, and can nohow be
  avoided. It is a superstition to suppose that a certain sort of events
  are ever fated, and it is another to suppose that the word fate can
  never be freed from its superstitious taint. We are all fated to die.




                              THIRD PAPER
                      THE DOCTRINE OF CHANCES[34]


                                   I


It is a common observation that a science first begins to be exact when
it is quantitatively treated. What are called the exact sciences are no
others than the mathematical ones. Chemists reasoned vaguely until
Lavoisier showed them how to apply the balance to the verification of
their theories, when chemistry leaped suddenly into the position of the
most perfect of the classificatory sciences. It has thus become so
precise and certain that we usually think of it along with optics,
thermotics, and electrics. But these are studies of general laws, while
chemistry considers merely the relations and classification of certain
objects; and belongs, in reality, in the same category as systematic
botany and zoölogy. Compare it with these last, however, and the
advantage that it derives from its quantitative treatment is very
evident.

The rudest numerical scales, such as that by which the mineralogists
distinguish the different degrees of hardness, are found useful. The
mere counting of pistils and stamens sufficed to bring botany out of
total chaos into some kind of form. It is not, however, so much from
_counting_ as from _measuring_, not so much from the conception of
number as from that of continuous quantity, that the advantage of
mathematical treatment comes. Number, after all, only serves to pin us
down to a precision in our thoughts which, however beneficial, can
seldom lead to lofty conceptions, and frequently descends to pettiness.
Of those two faculties of which Bacon speaks, that which marks
differences and that which notes resemblances, the employment of number
can only aid the lesser one; and the excessive use of it must tend to
narrow the powers of the mind. But the conception of continuous quantity
has a great office to fulfill, independently of any attempt at
precision. Far from tending to the exaggeration of differences, it is
the direct instrument of the finest generalizations. When a naturalist
wishes to study a species, he collects a considerable number of
specimens more or less similar. In contemplating them, he observes
certain ones which are more or less alike in some particular respect.
They all have, for instance, a certain S-shaped marking. He observes
that they are not _precisely_ alike, in this respect; the S has not
precisely the same shape, but the differences are such as to lead him to
believe that forms could be found intermediate between any two of those
he possesses. He, now, finds other forms apparently quite dissimilar—say
a marking in the form of a C—and the question is, whether he can find
intermediate ones which will connect these latter with the others. This
he often succeeds in doing in cases where it would at first be thought
impossible; whereas he sometimes finds those which differ, at first
glance, much less, to be separated in Nature by the non-occurrence of
intermediaries. In this way, he builds up from the study of Nature a new
general conception of the character in question. He obtains, for
example, an idea of a leaf which includes every part of the flower, and
an idea of a vertebra which includes the skull. I surely need not say
much to show what a logical engine there is here. It is the essence of
the method of the naturalist.[35] How he applies it first to one
character, and then to another, and finally obtains a notion of a
species of animals, the differences between whose members, however
great, are confined within limits, is a matter which does not here
concern us. The whole method of classification must be considered later;
but, at present, I only desire to point out that it is by taking
advantage of the idea of continuity, or the passage from one form to
another by insensible degrees, that the naturalist builds his
conceptions. Now, the naturalists are the great builders of conceptions;
there is no other branch of science where so much of this work is done
as in theirs; and we must, in great measure, take them for our teachers
in this important part of logic. And it will be found everywhere that
the idea of continuity is a powerful aid to the formation of true and
fruitful conceptions. By means of it, the greatest differences are
broken down and resolved into differences of degree, and the incessant
application of it is of the greatest value in broadening our
conceptions. I propose to make a great use of this idea in the present
series of papers; and the particular series of important fallacies,
which, arising from a neglect of it, have desolated philosophy, must
further on be closely studied. At present, I simply call the reader’s
attention to the utility of this conception.

In studies of numbers, the idea of continuity is so indispensable, that
it is perpetually introduced even where there is no continuity in fact,
as where we say that there are in the United States 10.7 inhabitants per
square mile, or that in New York 14.72 persons live in the average
house.[36] Another example is that law of the distribution of errors
which Quetelet, Galton, and others, have applied with so much success to
the study of biological and social matters. This application of
continuity to cases where it does not really exist illustrates, also,
another point which will hereafter demand a separate study, namely, the
great utility which fictions sometimes have in science.


                                   II


The theory of probabilities is simply the science of logic
quantitatively treated. There are two conceivable certainties with
reference to any hypothesis, the certainty of its truth and the
certainty of its falsity. The numbers _one_ and _zero_ are appropriated,
in this calculus, to marking these extremes of knowledge; while
fractions having values intermediate between them indicate, as we may
vaguely say, the degrees in which the evidence leans toward one or the
other. The general problem of probabilities is, from a given state of
facts, to determine the numerical probability of a possible fact. This
is the same as to inquire how much the given facts are worth, considered
as evidence to prove the possible fact. Thus the problem of
probabilities is simply the general problem of logic.

Probability is a continuous quantity, so that great advantages may be
expected from this mode of studying logic. Some writers have gone so far
as to maintain that, by means of the calculus of chances, every solid
inference may be represented by legitimate arithmetical operations upon
the numbers given in the premises. If this be, indeed, true, the great
problem of logic, how it is that the observation of one fact can give us
knowledge of another independent fact, is reduced to a mere question of
arithmetic. It seems proper to examine this pretension before
undertaking any more recondite solution of the paradox.

But, unfortunately, writers on probabilities are not agreed in regard to
this result. This branch of mathematics is the only one, I believe, in
which good writers frequently get results entirely erroneous. In
elementary geometry the reasoning is frequently fallacious, but
erroneous conclusions are avoided; but it may be doubted if there is a
single extensive treatise on probabilities in existence which does not
contain solutions absolutely indefensible. This is partly owing to the
want of any regular method of procedure; for the subject involves too
many subtilties to make it easy to put its problems into equations
without such an aid. But, beyond this, the fundamental principles of its
calculus are more or less in dispute. In regard to that class of
questions to which it is chiefly applied for practical purposes, there
is comparatively little doubt; but in regard to others to which it has
been sought to extend it, opinion is somewhat unsettled.

This last class of difficulties can only be entirely overcome by making
the idea of probability perfectly clear in our minds in the way set
forth in our last paper.


                                  III


To get a clear idea of what we mean by probability, we have to consider
what real and sensible difference there is between one degree of
probability and another.

The character of probability belongs primarily, without doubt, to
certain inferences. Locke explains it as follows: After remarking that
the mathematician positively knows that the sum of the three angles of a
triangle is equal to two right angles because he apprehends the
geometrical proof, he thus continues: “But another man who never took
the pains to observe the demonstration, hearing a mathematician, a man
of credit, affirm the three angles of a triangle to be equal to two
right ones, _assents_ to it; i.e., receives it for true. In which case
the foundation of his assent is the probability of the thing, the proof
being such as, for the most part, carries truth with it; the man on
whose testimony he receives it not being wont to affirm anything
contrary to, or besides his knowledge, especially in matters of this
kind.” The celebrated _Essay concerning Human Understanding_ contains
many passages which, like this one, make the first steps in profound
analyses which are not further developed. It was shown in the first of
these papers that the validity of an inference does not depend on any
tendency of the mind to accept it, however strong such tendency may be;
but consists in the real fact that, when premises like those of the
argument in question are true, conclusions related to them like that of
this argument are also true. It was remarked that in a logical mind an
argument is always conceived as a member of a _genus_ of arguments all
constructed in the same way, and such that, when their premises are real
facts, their conclusions are so also. If the argument is demonstrative,
then this is always so; if it is only probable, then it is for the most
part so. As Locke says, the probable argument is “_such as_ for the most
part carries truth with it.”

According to this, that real and sensible difference between one degree
of probability and another, in which the meaning of the distinction
lies, is that in the frequent employment of two different modes of
inference, one will carry truth with it oftener than the other. It is
evident that this is the only difference there is in the existing fact.
Having certain premises, a man draws a certain conclusion, and as far as
this inference alone is concerned the only possible practical question
is whether that conclusion is true or not, and between existence and
non-existence there is no middle term. “Being only is and nothing is
altogether not,” said Parmenides; and this is in strict accordance with
the analysis of the conception of reality given in the last paper. For
we found that the distinction of reality and fiction depends on the
supposition that sufficient investigation would cause one opinion to be
universally received and all others to be rejected. That presupposition,
involved in the very conceptions of reality and figment, involves a
complete sundering of the two. It is the heaven-and-hell idea in the
domain of thought. But, in the long run, there is a real fact which
corresponds to the idea of probability, and it is that a given mode of
inference sometimes proves successful and sometimes not, and that in a
ratio ultimately fixed. As we go on drawing inference after inference of
the given kind, during the first ten or hundred cases the ratio of
successes may be expected to show considerable fluctuations; but when we
come into the thousands and millions, these fluctuations become less and
less; and if we continue long enough, the ratio will approximate toward
a fixed limit. We may, therefore, define the probability of a mode of
argument as the proportion of cases in which it carries truth with it.

The inference from the premise, A, to the conclusion, B, depends, as we
have seen, on the guiding principle, that if a fact of the class A is
true, a fact of the class B is true. The probability consists of the
fraction whose numerator is the number of times in which both A and B
are true, and whose denominator is the total number of times in which A
is true, whether B is so or not. Instead of speaking of this as the
probability of the inference, there is not the slightest objection to
calling it the probability that, if A happens, B happens. But to speak
of the probability of the event B, without naming the condition, really
has no meaning at all. It is true that when it is perfectly obvious what
condition is meant, the ellipsis may be permitted. But we should avoid
contracting the habit of using language in this way (universal as the
habit is), because it gives rise to a vague way of thinking, as if the
action of causation might either determine an event to happen or
determine it not to happen, or leave it more or less free to happen or
not, so as to give rise to an _inherent_ chance in regard to its
occurrence.[37] It is quite clear to me that some of the worst and most
persistent errors in the use of the doctrine of chances have arisen from
this vicious mode of expression.[38]


                                   IV


But there remains an important point to be cleared up. According to what
has been said, the idea of probability essentially belongs to a kind of
inference which is repeated indefinitely. An individual inference must
be either true or false, and can show no effect of probability; and,
therefore, in reference to a single case considered in itself,
probability can have no meaning. Yet if a man had to choose between
drawing a card from a pack containing twenty-five red cards and a black
one, or from a pack containing twenty-five black cards and a red one,
and if the drawing of a red card were destined to transport him to
eternal felicity, and that of a black one to consign him to everlasting
woe, it would be folly to deny that he ought to prefer the pack
containing the larger portion of red cards, although, from the nature of
the risk, it could not be repeated. It is not easy to reconcile this
with our analysis of the conception of chance. But suppose he should
choose the red pack, and should draw the wrong card, what consolation
would he have? He might say that he had acted in accordance with reason,
but that would only show that his reason was absolutely worthless. And
if he should choose the right card, how could he regard it as anything
but a happy accident? He could not say that if he had drawn from the
other pack, he might have drawn the wrong one, because an hypothetical
proposition such as, “if A, then B,” means nothing with reference to a
single case. Truth consists in the existence of a real fact
corresponding to the true proposition. Corresponding to the proposition,
“if A, then B,” there may be the fact that _whenever_ such an event as A
happens such an event as B happens. But in the case supposed, which has
no parallel as far as this man is concerned, there would be no real fact
whose existence could give any truth to the statement that, if he had
drawn from the other pack, he might have drawn a black card. Indeed,
since the validity of an inference consists in the truth of the
hypothetical proposition that _if_ the premises be true the conclusion
will also be true, and since the only real fact which can correspond to
such a proposition is that whenever the antecedent is true the
consequent is so also, it follows that there can be no sense in
reasoning in an isolated case, at all.

These considerations appear, at first sight, to dispose of the
difficulty mentioned. Yet the case of the other side is not yet
exhausted. Although probability will probably manifest its effect in,
say, a thousand risks, by a certain proportion between the numbers of
successes and failures, yet this, as we have seen, is only to say that
it certainly will, at length, do so. Now the number of risks, the number
of probable inferences, which a man draws in his whole life, is a finite
one, and he cannot be absolutely _certain_ that the mean result will
accord with the probabilities at all. Taking all his risks collectively,
then, it cannot be certain that they will not fail, and his case does
not differ, except in degree, from the one last supposed. It is an
indubitable result of the theory of probabilities that every gambler, if
he continues long enough, must ultimately be ruined. Suppose he tries
the martingale, which some believe infallible, and which is, as I am
informed, disallowed in the gambling-houses. In this method of playing,
he first bets say $1; if he loses it he bets $2; if he loses that he
bets $4; if he loses that he bets $8; if he then gains he has lost 1 + 2
+ 4 = 7, and he has gained $1 more; and no matter how many bets he
loses, the first one he gains will make him $1 richer than he was in the
beginning. In that way, he will probably gain at first; but, at last,
the time will come when the run of luck is so against him that he will
not have money enough to double, and must, therefore, let his bet go.
This will _probably_ happen before he has won as much as he had in the
first place, so that this run against him will leave him poorer than he
began; some time or other it will be sure to happen. It is true that
there is always a possibility of his winning any sum the bank can pay,
and we thus come upon a celebrated paradox that, though he is certain to
be ruined, the value of his expectation calculated according to the
usual rules (which omit this consideration) is large. But, whether a
gambler plays in this way or any other, the same thing is true, namely,
that if he plays long enough he will be sure some time to have such a
run against him as to exhaust his entire fortune. The same thing is true
of an insurance company. Let the directors take the utmost pains to be
independent of great conflagrations and pestilences, their actuaries can
tell them that, according to the doctrine of chances, the time must
come, at last, when their losses will bring them to a stop. They may
tide over such a crisis by extraordinary means, but then they will start
again in a weakened state, and the same thing will happen again all the
sooner. An actuary might be inclined to deny this, because he knows that
the expectation of his company is large, or perhaps (neglecting the
interest upon money) is infinite. But calculations of expectations leave
out of account the circumstance now under consideration, which reverses
the whole thing. However, I must not be understood as saying that
insurance is on this account unsound, more than other kinds of business.
All human affairs rest upon probabilities, and the same thing is true
everywhere. If man were immortal he could be perfectly sure of seeing
the day when everything in which he had trusted should betray his trust,
and, in short, of coming eventually to hopeless misery. He would break
down, at last, as every good fortune, as every dynasty, as every
civilization does. In place of this we have death.

But what, without death, would happen to every man, with death must
happen to some man. At the same time, death makes the number of our
risks, of our inferences, finite, and so makes their mean result
uncertain. The very idea of probability and of reasoning rests on the
assumption that this number is indefinitely great. We are thus landed in
the same difficulty as before, and I can see but one solution of it. It
seems to me that we are driven to this, that logicality inexorably
requires that our interests shall _not_ be limited. They must not stop
at our own fate, but must embrace the whole community. This community,
again, must not be limited, but must extend to all races of beings with
whom we can come into immediate or mediate intellectual relation. It
must reach, however vaguely, beyond this geological epoch, beyond all
bounds. He who would not sacrifice his own soul to save the whole world,
is, as it seems to me, illogical in all his inferences, collectively.
Logic is rooted in the social principle.

To be logical men should not be selfish; and, in point of fact, they are
not so selfish as they are thought. The willful prosecution of one’s
desires is a different thing from selfishness. The miser is not selfish;
his money does him no good, and he cares for what shall become of it
after his death. We are constantly speaking of _our_ possessions on the
Pacific, and of _our_ destiny as a republic, where no personal interests
are involved, in a way which shows that we have wider ones. We discuss
with anxiety the possible exhaustion of coal in some hundreds of years,
or the cooling-off of the sun in some millions, and show in the most
popular of all religious tenets that we can conceive the possibility of
a man’s descending into hell for the salvation of his fellows.

Now, it is not necessary for logicality that a man should himself be
capable of the heroism of self-sacrifice. It is sufficient that he
should recognize the possibility of it, should perceive that only that
man’s inferences who has it are really logical, and should consequently
regard his own as being only so far valid as they would be accepted by
the hero. So far as he thus refers his inferences to that standard, he
becomes identified with such a mind.

This makes logicality attainable enough. Sometimes we can personally
attain to heroism. The soldier who runs to scale a wall knows that he
will probably be shot, but that is not all he cares for. He also knows
that if all the regiment, with whom in feeling he identifies himself,
rush forward at once, the fort will be taken. In other cases we can only
imitate the virtue. The man whom we have supposed as having to draw from
the two packs, who if he is not a logician will draw from the red pack
from mere habit, will see, if he is logician enough, that he cannot be
logical so long as he is concerned only with his own fate, but that that
man who should care equally for what was to happen in all possible cases
of the sort could act logically, and would draw from the pack with the
most red cards, and thus, though incapable himself of such sublimity,
our logician would imitate the effect of that man’s courage in order to
share his logicality.

But all this requires a conceived identification of one’s interests with
those of an unlimited community. Now, there exist no reasons, and a
later discussion will show that there can be no reasons, for thinking
that the human race, or any intellectual race, will exist forever. On
the other hand, there can be no reason against it;[39] and, fortunately,
as the whole requirement is that we should have certain sentiments,
there is nothing in the facts to forbid our having a _hope_, or calm and
cheerful wish, that the community may last beyond any assignable date.

It may seem strange that I should put forward three sentiments, namely,
interest in an indefinite community, recognition of the possibility of
this interest being made supreme, and hope in the unlimited continuance
of intellectual activity, as indispensable requirements of logic. Yet,
when we consider that logic depends on a mere struggle to escape doubt,
which, as it terminates in action, must begin in emotion, and that,
furthermore, the only cause of our planting ourselves on reason is that
other methods of escaping doubt fail on account of the social impulse,
why should we wonder to find social sentiment presupposed in reasoning?
As for the other two sentiments which I find necessary, they are so only
as supports and accessories of that. It interests me to notice that
these three sentiments seem to be pretty much the same as that famous
trio of Charity, Faith, and Hope, which, in the estimation of St. Paul,
are the finest and greatest of spiritual gifts. Neither Old nor New
Testament is a textbook of the logic of science, but the latter is
certainly the highest existing authority in regard to the dispositions
of heart which a man ought to have.


                                   V


Such average statistical numbers as the number of inhabitants per square
mile, the average number of deaths per week, the number of convictions
per indictment, or, generally speaking, the numbers of _x_’s per _y_,
where the _x_’s are a class of things some or all of which are connected
with another class of things, their _y_’s, I term _relative numbers_. Of
the two classes of things to which a relative number refers, that one of
which it is a number may be called its _relate_, and that one _per_
which the numeration is made may be called its _correlate_.

Probability is a kind of relative number; namely, it is the ratio of the
number of arguments of a certain genus which carry truth with them to
the total number of arguments of that genus, and the rules for the
calculation of probabilities are very easily derived from this
consideration. They may all be given here, since they are extremely
simple, and it is sometimes convenient to know something of the
elementary rules of calculation of chances.


RULE I. _Direct Calculation._—To calculate, directly, any relative
number, say for instance the number of passengers in the average trip of
a street-car, we must proceed as follows:

Count the number of passengers for each trip; add all these numbers, and
divide by the number of trips. There are cases in which this rule may be
simplified. Suppose we wish to know the number of inhabitants to a
dwelling in New York. The same person cannot inhabit two dwellings. If
he divide his time between two dwellings he ought to be counted a
half-inhabitant of each. In this case we have only to divide the total
number of the inhabitants of New York by the number of their dwellings,
without the necessity of counting separately those which inhabit each
one. A similar proceeding will apply wherever each individual relate
belongs to one individual correlate exclusively. If we want the number
of _x_’s per _y_, and no _x_ belongs to more than one _y_, we have only
to divide the whole number of _x_’s of _y_’s by the number of _y_’s.
Such a method would, of course, fail if applied to finding the average
number of street-car passengers per trip. We could not divide the total
number of travelers by the number of trips, since many of them would
have made many passages.

To find the probability that from a given class of premises, A, a given
class of conclusions, B, follow, it is simply necessary to ascertain
what proportion of the times in which premises of that class are true,
the appropriate conclusions are also true. In other words, it is the
number of cases of the occurrence of both the events A and B, divided by
the total number of cases of the occurrence of the event A.


RULE II. _Addition of Relative Numbers._—Given two relative numbers
having the same correlate, say the number of _x_’s per _y_, and the
number of _z_’s per _y_; it is required to find the number of _x_’s and
_z_’s together per _y_. If there is nothing which is at once an _x_ and
a _z_ to the same _y_, the sum of the two given numbers would give the
required number. Suppose, for example, that we had given the average
number of friends that men have, and the average number of enemies, the
sum of these two is the average number of persons interested in a man.
On the other hand, it plainly would not do to add the average number of
persons having constitutional diseases and over military age, to the
average number exempted by each special cause from military service, in
order to get the average number exempt in any way, since many are exempt
in two or more ways at once.

This rule applies directly to probabilities, given the probability that
two different and mutually exclusive events will happen under the same
supposed set of circumstances. Given, for instance, the probability that
if A then B, and also the probability that if A then C, then the sum of
these two probabilities is the probability that if A then either B or C,
so long as there is no event which belongs at once to the two classes B
and C.


RULE III. _Multiplication of Relative Numbers._—Suppose that we have
given the relative number of _x_’s per _y_; also the relative number of
_z_’s per _x_ of _y_; or, to take a concrete example, suppose that we
have given, first, the average number of children in families living in
New York; and, second, the average number of teeth in the head of a New
York child—then the product of these two numbers would give the average
number of children’s teeth in a New York family. But this mode of
reckoning will only apply in general under two restrictions. In the
first place, it would not be true if the same child could belong to
different families, for in that case those children who belonged to
several different families might have an exceptionally large or small
number of teeth, which would affect the average number of children’s
teeth in a family more than it would affect the average number of teeth
in a child’s head. In the second place, the rule would not be true if
different children could share the same teeth, the average number of
children’s teeth being in that case evidently something different from
the average number of teeth belonging to a child.

In order to apply this rule to probabilities, we must proceed as
follows: Suppose that we have given the probability that the conclusion
B follows from the premise A, B and A representing as usual certain
classes of propositions. Suppose that we also knew the probability of an
inference in which B should be the premise, and a proposition of a third
kind, C, the conclusion. Here, then, we have the materials for the
application of this rule. We have, first, the relative number of B’s per
A. We next should have the relative number of C’s per B following from
A. But the classes of propositions being so selected that the
probability of C following from any B in general is just the same as the
probability of C’s following from one of those B’s which is deducible
from an A, the two probabilities may be multiplied together, in order to
give the probability of C following from A. The same restrictions exist
as before. It might happen that the probability that B follows from A
was affected by certain propositions of the class B following from
several different propositions of the class A. But, practically
speaking, all these restrictions are of very little consequence, and it
is usually recognized as a principle universally true that the
probability that, if A is true, B is, multiplied by the probability
that, if B is true, C is, gives the probability that, if A is true, C
is.

There is a rule supplementary to this, of which great use is made. It is
not universally valid, and the greatest caution has to be exercised in
making use of it—a double care, first, never to use it when it will
involve serious error; and, second, never to fail to take advantage of
it in cases in which it can be employed. This rule depends upon the fact
that in very many cases the probability that C is true if B is, is
substantially the same as the probability that C is true if A is.
Suppose, for example, we have the average number of males among the
children born in New York; suppose that we also have the average number
of children born in the winter months among those born in New York. Now,
we may assume without doubt, at least as a closely approximate
proposition (and no very nice calculation would be in place in regard to
probabilities), that the proportion of males among all the children born
in New York is the same as the proportion of males born in summer in New
York; and, therefore, if the names of all the children born during a
year were put into an urn, we might multiply the probability that any
name drawn would be the name of a male child by the probability that it
would be the name of a child born in summer, in order to obtain the
probability that it would be the name of a male child born in summer.
The questions of probability, in the treatises upon the subject, have
usually been such as relate to balls drawn from urns, and games of
cards, and so on, in which the question of the _independence_ of events,
as it is called—that is to say, the question of whether the probability
of C, under the hypothesis B, is the same as its probability under the
hypothesis A, has been very simple; but, in the application of
probabilities to the ordinary questions of life, it is often an
exceedingly nice question whether two events may be considered as
independent with sufficient accuracy or not. In all calculations about
cards it is assumed that the cards are thoroughly shuffled, which makes
one deal quite independent of another. In point of fact the cards seldom
are, in practice, shuffled sufficiently to make this true; thus, in a
game of whist, in which the cards have fallen in suits of four of the
same suit, and are so gathered up, they will lie more or less in sets of
four of the same suit, and this will be true even after they are
shuffled. At least some traces of this arrangement will remain, in
consequence of which the number of “short suits,” as they are
called—that is to say, the number of hands in which the cards are very
unequally divided in regard to suits—is smaller than the calculation
would make it to be; so that, when there is a misdeal, where the cards,
being thrown about the table, get very thoroughly shuffled, it is a
common saying that in the hands next dealt out there are generally short
suits. A few years ago a friend of mine, who plays whist a great deal,
was so good as to count the number of spades dealt to him in 165 hands,
in which the cards had been, if anything, shuffled better than usual.
According to calculation, there should have been 85 of these hands in
which my friend held either three or four spades, but in point of fact
there were 94, showing the influence of imperfect shuffling.

According to the view here taken, these are the only fundamental rules
for the calculation of chances. An additional one, derived from a
different conception of probability, is given in some treatises, which
if it be sound might be made the basis of a theory of reasoning. Being,
as I believe it is, absolutely absurd, the consideration of it serves to
bring us to the true theory; and it is for the sake of this discussion,
which must be postponed to the next number, that I have brought the
doctrine of chances to the reader’s attention at this early stage of our
studies of the logic of science.

Footnote 34:

  _Popular Science Monthly_, March, 1878.

Footnote 35:

  [Later, pp. 170 ff. and 215 ff., it is shown that continuity is also
  at the basis of mathematical generalization. See also article on
  Synechism in _Baldwin’s Dictionary of Philosophy_.]

Footnote 36:

  This mode of thought is so familiarly associated with all exact
  numerical consideration, that the phrase appropriate to it is imitated
  by shallow writers in order to produce the appearance of exactitude
  where none exists. Certain newspapers which affect a learned tone talk
  of “the average man,” when they simply mean _most men_, and have no
  idea of striking an average.

Footnote 37:

  _Cf._ pp. 179 ff. below.

Footnote 38:

  The conception of probability here set forth is substantially that
  first developed by Mr. Venn, in his _Logic of Chance_. Of course, a
  vague apprehension of the idea had always existed, but the problem was
  to make it perfectly clear, and to him belongs the credit of first
  doing this.

Footnote 39:

  I do not here admit an absolutely unknowable. Evidence could show us
  what would probably be the case after any given lapse of time; and
  though a subsequent time might be assigned which that evidence might
  not cover, yet further evidence would cover it.




                              FOURTH PAPER
                    THE PROBABILITY OF INDUCTION[40]


                                   I


We have found that every argument derives its force from the general
truth of the class of inferences to which it belongs; and that
probability is the proportion of arguments carrying truth with them
among those of any _genus_. This is most conveniently expressed in the
nomenclature of the medieval logicians. They called the fact expressed
by a premise an _antecedent_, and that which follows from it its
_consequent_; while the leading principle, that every (or almost every)
such antecedent is followed by such a consequent, they termed the
_consequence_. Using this language, we may say that probability belongs
exclusively to _consequences_, and the probability of any consequence is
the number of times in which antecedent and consequent both occur
divided by the number of all the times in which the antecedent occurs.
From this definition are deduced the following rules for the addition
and multiplication of probabilities:

_Rule for the Addition of Probabilities._—Given the separate
probabilities of two consequences having the same antecedent and
incompatible consequents. Then the sum of these two numbers is the
probability of the consequence, that from the same antecedent one or
other of those consequents follows.

_Rule for the Multiplication of Probabilities._—Given the separate
probabilities of the two consequences, “If A then B,” and “If both A and
B, then C.” Then the product of these two numbers is the probability of
the consequence, “If A, then both B and C.”

_Special Rule for the Multiplication of Independent
Probabilities._—Given the separate probabilities of two consequences
having the same antecedents, “If A, then B,” and “If A, then C.” Suppose
that these consequences are such that the probability of the second is
equal to the probability of the consequence, “If both A and B, then C.”
Then the product of the two given numbers is equal to the probability of
the consequence, “If A, then both B and C.”

To show the working of these rules we may examine the probabilities in
regard to throwing dice. What is the probability of throwing a six with
one die? The antecedent here is the event of throwing a die; the
consequent, its turning up a six. As the die has six sides, all of which
are turned up with equal frequency, the probability of turning up any
one is 1/6. Suppose two dice are thrown, what is the probability of
throwing sixes? The probability of either coming up six is obviously the
same when both are thrown as when one is thrown—namely, 1/6. The
probability that either will come up six when the other does is also the
same as that of its coming up six whether the other does or not. The
probabilities are, therefore, independent; and, by our rule, the
probability that both events will happen together is the product of
their several probabilities, or 1/6 x 1/6. What is the probability of
throwing deuce-ace? The probability that the first die will turn up ace
and the second deuce is the same as the probability that both will turn
up sixes—namely, 1/36; the probability that the _second_ will turn up
ace and the _first_ deuce is likewise 1/36; these two events—first, ace;
second, deuce; and, second, ace; first, deuce—are incompatible. Hence
the rule for addition holds, and the probability that either will come
up ace and the other deuce is 1/36 + 1/36, or 1/18.

In this way all problems about dice, etc., may be solved. When the
number of dice thrown is supposed very large, mathematics (which may be
defined as the art of making groups to facilitate numeration) comes to
our aid with certain devices to reduce the difficulties.


                                   II


The conception of probability as a matter of _fact_, i.e., as the
proportion of times in which an occurrence of one kind is accompanied by
an occurrence of another kind, is termed by Mr. Venn the materialistic
view of the subject. But probability has often been regarded as being
simply the degree of belief which ought to attach to a proposition, and
this mode of explaining the idea is termed by Venn the conceptualistic
view. Most writers have mixed the two conceptions together. They, first,
define the probability of an event as the reason we have to believe that
it has taken place, which is conceptualistic; but shortly after they
state that it is the ratio of the number of cases favorable to the event
to the total number of cases favorable or contrary, and all equally
possible. Except that this introduces the thoroughly unclear idea of
cases equally possible in place of cases equally frequent, this is a
tolerable statement of the materialistic view. The pure conceptualistic
theory has been best expounded by Mr. De Morgan in his _Formal Logic_:
or, the _Calculus of Inference, Necessary and Probable._

The great difference between the two analyses is, that the
conceptualists refer probability to an event, while the materialists
make it the ratio of frequency of events of a _species_ to those of a
_genus_ over that _species_, thus _giving it two terms instead of one_.
The opposition may be made to appear as follows:

Suppose that we have two rules of inference, such that, of all the
questions to the solution of which both can be applied, the first yields
correct answers to 81/100, and incorrect answers to the remaining
19/100; while the second yields correct answers to 93/100, and incorrect
answers to the remaining 7/100. Suppose, further, that the two rules are
entirely independent as to their truth, so that the second answers
correctly 93/100 of the questions which the first answers correctly, and
also 93/100 of the questions which the first answers incorrectly, and
answers incorrectly the remaining 7/100 of the questions which the first
answers correctly, and also the remaining 7/100 of the questions which
the first answers incorrectly. Then, of all the questions to the
solution of which both rules can be applied—

    both answer correctly 93/100 of 81/100 or 93/100 x 81/100;

    the second answers correctly and the first incorrectly 93/100 of
    19/100 or 93/100 x 19/100;

    the second answers incorrectly and the first correctly 7/100 of
    81/100 or 7/100 x 81/100;

    and both answer incorrectly 7/100 of 19/100 or 7/100 x 19/100;

Suppose, now, that, in reference to any question, both give the same
answer. Then (the questions being always such as are to be answered by
_yes_ or _no_), those in reference to which their answers agree are the
same as those which both answer correctly together with those which both
answer falsely, or 93/100 x 81/100 + 7/100 x 19/100 of all. The
proportion of those which both answer correctly out of those their
answers to which agree is, therefore—

    ((93 × 81)/(100 × 100))/((93 × 81)/(100 × 100)) + ((7 × 19)/(100 ×
    100)) or (93 × 81)/((93 × 81) + (7 × 19)).

This is, therefore, the probability that, if both modes of inference
yield the same result, that result is correct. We may here conveniently
make use of another mode of expression. _Probability_ is the ratio of
the favorable cases to all the cases. Instead of expressing our result
in terms of this ratio, we may make use of another—the ratio of
favorable to unfavorable cases. This last ratio may be called the
_chance_ of an event. Then the chance of a true answer by the first mode
of inference is 81/19 and by the second is 93/7; and the chance of a
correct answer from both, when they agree, is—

    (81 × 93)/(19 × 7) or 81/19 × 93/7,

or the product of the chances of each singly yielding a true answer.

It will be seen that a chance is a quantity which may have any
magnitude, however great. An event in whose favor there is an even
chance, or 1/1, has a probability of 1/2. An argument having an even
chance can do nothing toward re-enforcing others, since according to the
rule its combination with another would only multiply the chance of the
latter by 1.

Probability and chance undoubtedly belong primarily to consequences, and
are relative to premises; but we may, nevertheless, speak of the chance
of an event absolutely, meaning by that the chance of the combination of
all arguments in reference to it which exist for us in the given state
of our knowledge. Taken in this sense it is incontestable that the
chance of an event has an intimate connection with the degree of our
belief in it. Belief is certainly something more than a mere feeling;
yet there is a feeling of believing, and this feeling does and ought to
vary with the chance of the thing believed, as deduced from all the
arguments. Any quantity which varies with the chance might, therefore,
it would seem, serve as a thermometer for the proper intensity of
belief. Among all such quantities there is one which is peculiarly
appropriate. When there is a very great chance, the feeling of belief
ought to be very intense. Absolute certainty, or an infinite chance, can
never be attained by mortals, and this may be represented appropriately
by an infinite belief. As the chance diminishes the feeling of believing
should diminish, until an even chance is reached, where it should
completely vanish and not incline either toward or away from the
proposition. When the chance becomes less, then a contrary belief should
spring up and should increase in intensity as the chance diminishes, and
as the chance almost vanishes (which it can never quite do) the contrary
belief should tend toward an infinite intensity. Now, there is one
quantity which, more simply than any other, fulfills these conditions;
it is the _logarithm_ of the chance. But there is another consideration
which must, if admitted, fix us to this choice for our thermometer. It
is that our belief ought to be proportional to the weight of evidence,
in this sense, that two arguments which are entirely independent,
neither weakening nor strengthening each other, ought, when they concur,
to produce a belief equal to the sum of the intensities of belief which
either would produce separately. Now, we have seen that the chances of
independent concurrent arguments are to be multiplied together to get
the chance of their combination, and, therefore, the quantities which
best express the intensities of belief should be such that they are to
be _added_ when the _chances_ are multiplied in order to produce the
quantity which corresponds to the combined chance. Now, the logarithm is
the only quantity which fulfills this condition. There is a general law
of sensibility, called Fechner’s psychophysical law. It is that the
intensity of any sensation is proportional to the logarithm of the
external force which produces it. It is entirely in harmony with this
law that the feeling of belief should be as the logarithm of the chance,
this latter being the expression of the state of facts which produces
the belief.

The rule for the combination of independent concurrent arguments takes a
very simple form when expressed in terms of the intensity of belief,
measured in the proposed way. It is this: Take the sum of all the
feelings of belief which would be produced separately by all the
arguments _pro_, subtract from that the similar sum for arguments _con_,
and the remainder is the feeling of belief which we ought to have on the
whole. This is a proceeding which men often resort to, under the name of
_balancing reasons_.

These considerations constitute an argument in favor of the
conceptualistic view. The kernel of it is that the conjoint probability
of all the arguments in our possession, with reference to any fact, must
be intimately connected with the just degree of our belief in that fact;
and this point is supplemented by various others showing the consistency
of the theory with itself and with the rest of our knowledge.

But probability, to have any value at all, must express a fact. It is,
therefore, a thing to be inferred upon evidence. Let us, then, consider
for a moment the formation of a belief of probability. Suppose we have a
large bag of beans from which one has been secretly taken at random and
hidden under a thimble. We are now to form a probable judgment of the
color of that bean, by drawing others singly from the bag and looking at
them, each one to be thrown back, and the whole well mixed up after each
drawing. Suppose the first drawing is white and the next black. We
conclude that there is not an immense preponderance of either color, and
that there is something like an even chance that the bean under the
thimble is black. But this judgment may be altered by the next few
drawings. When we have drawn ten times, if 4, 5, or 6, are white, we
have more confidence that the chance is even. When we have drawn a
thousand times, if about half have been white, we have great confidence
in this result. We now feel pretty sure that, if we were to make a large
number of bets upon the color of single beans drawn from the bag, we
could approximately insure ourselves in the long run by betting each
time upon the white, a confidence which would be entirely wanting if,
instead of sampling the bag by 1,000 drawings, we had done so by only
two. Now, as the whole utility of probability is to insure us in the
long run, and as that assurance depends, not merely on the value of the
chance, but also on the accuracy of the evaluation, it follows that we
ought not to have the same feeling of belief in reference to all events
of which the chance is even. In short, to express the proper state of
our belief, not _one_ number but _two_ are requisite, the first
depending on the inferred probability, the second on the amount of
knowledge on which that probability is based.[41] It is true that when
our knowledge is very precise, when we have made many drawings from the
bag, or, as in most of the examples in the books, when the total
contents of the bag are absolutely known, the number which expresses the
uncertainty of the assumed probability and its liability to be changed
by further experience may become insignificant, or utterly vanish. But,
when our knowledge is very slight, this number may be even more
important than the probability itself; and when we have no knowledge at
all this completely overwhelms the other, so that there is no sense in
saying that the chance of the totally unknown event is even (for what
expresses absolutely no fact has absolutely no meaning), and what ought
to be said is that the chance is entirely indefinite. We thus perceive
that the conceptualistic view, though answering well enough in some
cases, is quite inadequate.

Suppose that the first bean which we drew from our bag were black. That
would constitute an argument, no matter how slender, that the bean under
the thimble was also black. If the second bean were also to turn out
black, that would be a second independent argument reënforcing the
first. If the whole of the first twenty beans drawn should prove black,
our confidence that the hidden bean was black would justly attain
considerable strength. But suppose the twenty-first bean were to be
white and that we were to go on drawing until we found that we had drawn
1,010 black beans and 990 white ones. We should conclude that our first
twenty beans being black was simply an extraordinary accident, and that
in fact the proportion of white beans to black was sensibly equal, and
that it was an even chance that the hidden bean was black. Yet according
to the rule of _balancing reasons_, since all the drawings of black
beans are so many independent arguments in favor of the one under the
thimble being black, and all the white drawings so many against it, an
excess of twenty black beans ought to produce the same degree of belief
that the hidden bean was black, whatever the total number drawn.

In the conceptualistic view of probability, complete ignorance, where
the judgment ought not to swerve either toward or away from the
hypothesis, is represented by the probability 1/2.[42]

But let us suppose that we are totally ignorant what colored hair the
inhabitants of Saturn have. Let us, then, take a color-chart in which
all possible colors are shown shading into one another by imperceptible
degrees. In such a chart the relative areas occupied by different
classes of colors are perfectly arbitrary. Let us inclose such an area
with a closed line, and ask what is the chance on conceptualistic
principles that the color of the hair of the inhabitants of Saturn falls
within that area? The answer cannot be indeterminate because we must be
in some state of belief; and, indeed, conceptualistic writers do not
admit indeterminate probabilities. As there is no certainty in the
matter, the answer lies between _zero_ and _unity_. As no numerical
value is afforded by the data, the number must be determined by the
nature of the scale of probability itself, and not by calculation from
the data. The answer can, therefore, only be one-half, since the
judgment should neither favor nor oppose the hypothesis. What is true of
this area is true of any other one; and it will equally be true of a
third area which embraces the other two. But the probability for each of
the smaller areas being one-half, that for the larger should be at least
unity, which is absurd.


                                  III


All our reasonings are of two kinds: 1. _Explicative_, _analytic_, or
_deductive_; 2. _Amplifiative_, _synthetic_, or (loosely speaking)
_inductive_. In explicative reasoning, certain facts are first laid down
in the premises. These facts are, in every case, an inexhaustible
multitude, but they may often be summed up in one simple proposition by
means of some regularity which runs through them all. Thus, take the
proposition that Socrates was a man; this implies (to go no further)
that during every fraction of a second of his whole life (or, if you
please, during the greater part of them) he was a man. He did not at one
instant appear as a tree and at another as a dog; he did not flow into
water, or appear in two places at once; you could not put your finger
through him as if he were an optical image, etc. Now, the facts being
thus laid down, some order among some of them, not particularly made use
of for the purpose of stating them, may perhaps be discovered; and this
will enable us to throw part or all of them into a new statement, the
possibility of which might have escaped attention. Such a statement will
be the conclusion of an analytic inference. Of this sort are all
mathematical demonstrations. But synthetic reasoning is of another kind.
In this case the facts summed up in the conclusion are not among those
stated in the premises. They are different facts, as when one sees that
the tide rises _m_ times and concludes that it will rise the next time.
These are the only inferences which increase our real knowledge, however
useful the others may be.

In any problem in probabilities, we have given the relative frequency of
certain events, and we perceive that in these facts the relative
frequency of another event is given in a hidden way. This being stated
makes the solution. This is, therefore, mere explicative reasoning, and
is evidently entirely inadequate to the representation of synthetic
reasoning, which goes out beyond the facts given in the premises. There
is, therefore, a manifest impossibility in so tracing out any
probability for a synthetic conclusion.

Most treatises on probability contain a very different doctrine. They
state, for example, that if one of the ancient denizens of the shores of
the Mediterranean, who had never heard of tides, had gone to the bay of
Biscay, and had there seen the tide rise, say _m_ times, he could know
that there was a probability equal to

    (m + 1)/(m + 2)

that it would rise the next time. In a well-known work by Quetelet, much
stress is laid on this, and it is made the foundation of a theory of
inductive reasoning.

But this solution betrays its origin if we apply it to the case in which
the man has never seen the tide rise at all; that is, if we put _m_ = 0.
In this case, the probability that it will rise the next time comes out
1/2, or, in other words, the solution involves the conceptualistic
principle that there is an even chance of a totally unknown event. The
manner in which it has been reached has been by considering a number of
urns all containing the same number of balls, part white and part black.
One urn contains all white balls, another one black and the rest white,
a third two black and the rest white, and so on, one urn for each
proportion, until an urn is reached containing only black balls. But the
only possible reason for drawing any analogy between such an arrangement
and that of Nature is the principle that alternatives of which we know
nothing must be considered as equally probable. But this principle is
absurd. There is an indefinite variety of ways of enumerating the
different possibilities, which, on the application of this principle,
would give different results. If there be any way of enumerating the
possibilities so as to make them all equal, it is not that from which
this solution is derived, but is the following: Suppose we had an
immense granary filled with black and white balls well mixed up; and
suppose each urn were filled by taking a fixed number of balls from this
granary quite at random. The relative number of white balls in the
granary might be anything, say one in three. Then in one-third of the
urns the first ball would be white, and in two-thirds black. In
one-third of those urns of which the first ball was white, and also in
one-third of those in which the first ball was black, the second ball
would be white. In this way, we should have a distribution like that
shown in the following table, where _w_ stands for a white ball and _b_
for a black one. The reader can, if he chooses, verify the table for
himself.

    wwww.

    wwwb.   wwbw.   wbww.   bwww.
    wwwb.   wwbw.   wbww.   bwww.

    wwbb.   wbwb.   bwwb.   wbbw.   bwbw.   bbww.
    wwbb.   wbwb.   bwwb.   wbbw.   bwbw.   bbww.
    wwbb.   wbwb.   bwwb.   wbbw.   bwbw.   bbww.
    wwbb.   wbwb.   bwwb.   wbbw.   bwbw.   bbww.

    wbbb.   bwbb.   bbwb.   bbbw.
    wbbb.   bwbb.   bbwb.   bbbw.
    wbbb.   bwbb.   bbwb.   bbbw.
    wbbb.   bwbb.   bbwb.   bbbw.
    wbbb.   bwbb.   bbwb.   bbbw.
    wbbb.   bwbb.   bbwb.   bbbw.
    wbbb.   bwbb.   bbwb.   bbbw.
    wbbb.   bwbb.   bbwb.   bbbw.

    bbbb.
    bbbb.
    bbbb.
    bbbb.
    bbbb.
    bbbb.
    bbbb.
    bbbb.
    bbbb.
    bbbb.
    bbbb.
    bbbb.
    bbbb.
    bbbb.
    bbbb.
    bbbb.

In the second group, where there is one b, there are two sets just
alike; in the third there are 4, in the fourth 8, and in the fifth 16,
doubling every time. This is because we have supposed twice as many
black balls in the granary as white ones; had we supposed 10 times as
many, instead of

           1, 2, 4, 8, 16

sets we should have had

           1, 10, 100, 1000, 10000

sets; on the other hand, had the numbers of black and white balls in the
granary been even, there would have been but one set in each group. Now
suppose two balls were drawn from one of these urns and were found to be
both white, what would be the probability of the next one being white?
If the two drawn out were the first two put into the urns, and the next
to be drawn out were the third put in, then the probability of this
third being white would be the same whatever the colors of the first
two, for it has been supposed that just the same proportion of urns has
the third ball white among those which have the first two _white-white_,
_white-black_, _black-white_, and _black-black_. Thus, in this case, the
chance of the third ball being white would be the same whatever the
first two were. But, by inspecting the table, the reader can see that in
each group all orders of the balls occur with equal frequency, so that
it makes no difference whether they are drawn out in the order they were
put in or not. Hence the colors of the balls already drawn have no
influence on the probability of any other being white or black.

Now, if there be any way of enumerating the possibilities of Nature so
as to make them equally probable, it is clearly one which should make
one arrangement or combination of the elements of Nature as probable as
another, that is, a distribution like that we have supposed, and it,
therefore, appears that the assumption that any such thing can be done,
leads simply to the conclusion that reasoning from past to future
experience is absolutely worthless. In fact, the moment that you assume
that the chances in favor of that of which we are totally ignorant are
even, the problem about the tides does not differ, in any arithmetical
particular, from the case in which a penny (known to be equally likely
to come up heads and tails) should turn up heads _m_ times successively.
In short, it would be to assume that Nature is a pure chaos, or chance
combination of independent elements, in which reasoning from one fact to
another would be impossible; and since, as we shall hereafter see, there
is no judgment of pure observation without reasoning, it would be to
suppose all human cognition illusory and no real knowledge possible. It
would be to suppose that if we have found the order of Nature more or
less regular in the past, this has been by a pure run of luck which we
may expect is now at an end. Now, it may be we have no scintilla of
proof to the contrary, but reason is unnecessary in reference to that
belief which is of all the most settled, which nobody doubts or can
doubt, and which he who should deny would stultify himself in so doing.

The relative probability of this or that arrangement of Nature is
something which we should have a right to talk about if universes were
as plenty as blackberries, if we could put a quantity of them in a bag,
shake them well up, draw out a sample, and examine them to see what
proportion of them had one arrangement and what proportion another. But,
even in that case, a higher universe would contain us, in regard to
whose arrangements the conception of probability could have no
applicability.


                                   IV


We have examined the problem proposed by the conceptualists, which,
translated into clear language, is this: Given a synthetic conclusion;
required to know out of all possible states of things how many will
accord, to any assigned extent, with this conclusion; and we have found
that it is only an absurd attempt to reduce synthetic to analytic
reason, and that no definite solution is possible.

But there is another problem in connection with this subject. It is
this: Given a certain state of things, required to know what proportion
of all synthetic inferences relating to it will be true within a given
degree of approximation. Now, there is no difficulty about this problem
(except for its mathematical complication); it has been much studied,
and the answer is perfectly well known. And is not this, after all, what
we want to know much rather than the other? Why should we want to know
the probability that the fact will accord with our conclusion? That
implies that we are interested in all possible worlds, and not merely
the one in which we find ourselves placed. Why is it not much more to
the purpose to know the probability that our conclusion will accord with
the fact? One of these questions is the first above stated and the other
the second, and I ask the reader whether, if people, instead of using
the word probability without any clear apprehension of their own
meaning, had always spoken of relative frequency, they could have failed
to see that what they wanted was not to follow along the synthetic
procedure with an analytic one, in order to find the probability of the
conclusion; but, on the contrary, to begin with the fact at which the
synthetic inference aims, and follow back to the facts it uses for
premises in order to see the probability of their being such as will
yield the truth.

As we cannot have an urn with an infinite number of balls to represent
the inexhaustibleness of Nature, let us suppose one with a finite
number, each ball being thrown back into the urn after being drawn out,
so that there is no exhaustion of them. Suppose one ball out of three is
white and the rest black, and that four balls are drawn. Then the table
on pages 95-96 represents the relative frequency of the different ways
in which these balls might be drawn. It will be seen that if we should
judge by these four balls of the proportion in the urn, 32 times out of
81 we should find it 1/4, and 24 times out of 81 we should find it 1/2,
the truth being 1/3. To extend this table to high numbers would be great
labor, but the mathematicians have found some ingenious ways of
reckoning what the numbers would be. It is found that, if the true
proportion of white balls is _p_, and _s_ balls are drawn, then the
error of the proportion obtained by the induction will be—

    half the time within 0.477 √((2p(1-p))/s)
    9 times out of 10 within 1.163 √((2p(1-p))/s)
    99 times out of 100 within 1.821 √((2p(1-p))/s)
    999 times out of 1,000 within 2.328 √((2p(1-p))/s)
    9,999 times out of 10,000 within 2.751 √((2p(1-p))/s)
    9,999,999,999 times out of 10,000,000,000 within 4.77 √((2p(1-p))/s)

The use of this may be illustrated by an example. By the census of 1870,
it appears that the proportion of males among native white children
under one year old was 0.5082, while among colored children of the same
age the proportion was only 0.4977. The difference between these is
0.0105, or about one in a 100. Can this be attributed to chance, or
would the difference always exist among a great number of white and
colored children under like circumstances? Here _p_ may be taken at 1/2;
hence 2_p_(1-_p_) is also 1/2. The number of white children counted was
near 1,000,000; hence the fraction whose square-root is to be taken is
about 1/2000000. The root is about 1/1400, and this multiplied by 0.477
gives about 0.0003 as the probable error in the ratio of males among the
whites as obtained from the induction. The number of black children was
about 150,000, which gives 0.0008 for the probable error. We see that
the actual discrepancy is ten times the sum of these, and such a result
would happen, according to our table, only once out of 10,000,000,000
censuses, in the long run.

It may be remarked that when the real value of the probability sought
inductively is either very large or very small, the reasoning is more
secure. Thus, suppose there were in reality one white ball in 100 in a
certain urn, and we were to judge of the number by 100 drawings. The
probability of drawing no white ball would be 366/1000; that of drawing
one white ball would be 370/1000; that of drawing two would be 185/1000;
that of drawing three would be 61/1000; that of drawing four would be
15/1000; that of drawing five would be only 3/1000, etc. Thus we should
be tolerably certain of not being in error by more than one ball in 100.

It appears, then, that in one sense we can, and in another we cannot,
determine the probability of synthetic inference. When I reason in this
way:

                Ninety-nine Cretans in a hundred are liars;
                But Epimenides is a Cretan;
                Therefore, Epimenides is a liar:—

I know that reasoning similar to that would carry truth 99 times in 100.
But when I reason in the opposite direction:

         Minos, Sarpedon, Rhadamanthus, Deucalion, and Epimenides,
         are all the Cretans I can think of;
         But these were all atrocious liars,
         Therefore, pretty much all Cretans must have been liars;

I do not in the least know how often such reasoning would carry me
right. On the other hand, what I do know is that some definite
proportion of Cretans must have been liars, and that this proportion can
be probably approximated to by an induction from five or six instances.
Even in the worst case for the probability of such an inference, that in
which about half the Cretans are liars, the ratio so obtained would
probably not be in error by more than 1/6. So much I know; but, then, in
the present case the inference is that pretty much all Cretans are
liars, and whether there may not be a special improbability in that I do
not know.


                                   V


Late in the last century, Immanuel Kant asked the question, “How are
synthetical judgments _a priori_ possible?” By synthetical judgments he
meant such as assert positive fact and are not mere affairs of
arrangement; in short, judgments of the kind which synthetical reasoning
produces, and which analytic reasoning cannot yield. By _a priori_
judgments he meant such as that all outward objects are in space, every
event has a cause, etc., propositions which according to him can never
be inferred from experience. Not so much by his answer to this question
as by the mere asking of it, the current philosophy of that time was
shattered and destroyed, and a new epoch in its history was begun. But
before asking _that_ question he ought to have asked the more general
one, “How are any synthetical judgments at all possible?” How is it that
a man can observe one fact and straightway pronounce judgment concerning
another different fact not involved in the first? Such reasoning, as we
have seen, has, at least in the usual sense of the phrase, no definite
probability; how, then, can it add to our knowledge? This is a strange
paradox; the Abbé Gratry says it is a miracle, and that every true
induction is an immediate inspiration from on high.[43] I respect this
explanation far more than many a pedantic attempt to solve the question
by some juggle with probabilities, with the forms of syllogism, or what
not. I respect it because it shows an appreciation of the depth of the
problem, because it assigns an adequate cause, and because it is
intimately connected—as the true account should be—with a general
philosophy of the universe. At the same time, I do not accept this
explanation, because an explanation should tell _how_ a thing is done,
and to assert a perpetual miracle seems to be an abandonment of all hope
of doing that, without sufficient justification.

It will be interesting to see how the answer which Kant gave to his
question about synthetical judgments _a priori_ will appear if extended
to the question of synthetical judgments in general. That answer is,
that synthetical judgments _a priori_ are possible because whatever is
universally true is involved in the conditions of experience. Let us
apply this to a general synthetical reasoning. I take from a bag a
handful of beans; they are all purple, and I infer that all the beans in
the bag are purple. How can I do that? Why, upon the principle that
whatever is universally true of my experience (which is here the
appearance of these different beans) is involved in the condition of
experience. The condition of this special experience is that all these
beans were taken from that bag. According to Kant’s principle, then,
whatever is found true of all the beans drawn from the bag must find its
explanation in some peculiarity of the contents of the bag. This is a
satisfactory statement of the principle of induction.

When we draw a deductive or analytic conclusion, our rule of inference
is that facts of a certain general character are either invariably or in
a certain proportion of cases accompanied by facts of another general
character. Then our premise being a fact of the former class, we infer
with certainty or with the appropriate degree of probability the
existence of a fact of the second class. But the rule for synthetic
inference is of a different kind. When we sample a bag of beans we do
not in the least assume that the fact of some beans being purple
involves the necessity or even the probability of other beans being so.
On the contrary, the conceptualistic method of treating probabilities,
which really amounts simply to the deductive treatment of them, when
rightly carried out leads to the result that a synthetic inference has
just an even chance in its favor, or in other words is absolutely
worthless. The color of one bean is entirely independent of that of
another. But synthetic inference is founded upon a classification of
facts, not according to their characters, but according to the manner of
obtaining them. Its rule is, that a number of facts obtained in a given
way will in general more or less resemble other facts obtained in the
same way; or, _experiences whose conditions are the same will have the
same general characters_.

In the former case, we know that premises precisely similar in form to
those of the given ones will yield true conclusions, just once in a
calculable number of times. In the latter case, we only know that
premises obtained under circumstances similar to the given ones (though
perhaps themselves very different) will yield true conclusions, at least
once in a calculable number of times. We may express this by saying that
in the case of analytic inference we know the probability of our
conclusion (if the premises are true), but in the case of synthetic
inferences we only know the degree of trustworthiness of our proceeding.
As all knowledge comes from synthetic inference, we must equally infer
that all human certainty consists merely in our knowing that the
processes by which our knowledge has been derived are such as must
generally have led to true conclusions.

Though a synthetic inference cannot by any means be reduced to
deduction, yet that the rule of induction will hold good in the long run
may be deduced from the principle that reality is only the object of the
final opinion to which sufficient investigation would lead. That belief
gradually tends to fix itself under the influence of inquiry is, indeed,
one of the facts with which logic sets out.

Footnote 40:

  _Popular Science Monthly_, April, 1878.

Footnote 41:

  Strictly we should need an infinite series of numbers each depending
  on the probable error of the last.

Footnote 42:

  “Perfect indecision, belief inclining neither way, an even chance.”—DE
  MORGAN, p. 182.

Footnote 43:

  _Logique_. The same is true, according to him, of every performance of
  a differentiation, but not of integration. He does not tell us whether
  it is the supernatural assistance which makes the former process so
  much the easier.




                              FIFTH PAPER
                        THE ORDER OF NATURE[44]


                                   I


Any proposition whatever concerning the order of Nature must touch more
or less upon religion. In our day, belief, even in these matters,
depends more and more upon the observation of facts. If a remarkable and
universal orderliness be found in the universe, there must be some cause
for this regularity, and science has to consider what hypotheses might
account for the phenomenon. One way of accounting for it, certainly,
would be to suppose that the world is ordered by a superior power. But
if there is nothing in the universal subjection of phenomena to laws,
nor in the character of those laws themselves (as being benevolent,
beautiful, economical, etc.), which goes to prove the existence of a
governor of the universe, it is hardly to be anticipated that any other
sort of evidence will be found to weigh very much with minds emancipated
from the tyranny of tradition.

Nevertheless, it cannot truly be said that even an absolutely negative
decision of that question could altogether destroy religion, inasmuch as
there are faiths in which, however much they differ from our own, we
recognize those essential characters which make them worthy to be called
religions, and which, nevertheless, do not postulate an actually
existing Deity. That one, for instance, which has had the most numerous
and by no means the least intelligent following of any on earth, teaches
that the Divinity in his highest perfection is wrapped away from the
world in a state of profound and eternal sleep, which really does not
differ from non-existence, whether it be called by that name or not. No
candid mind who has followed the writings of M. Vacherot can well deny
that his religion is as earnest as can be. He worships the Perfect, the
Supreme Ideal; but he conceives that the very notion of the Ideal is
repugnant to its real existence.[45] In fact, M. Vacherot finds it
agreeable to his reason to assert that non-existence is an essential
character of the perfect, just as St. Anselm and Descartes found it
agreeable to theirs to assert the extreme opposite. I confess that there
is one respect in which either of these positions seems to me more
congruous with the religious attitude than that of a theology which
stands upon evidences; for as soon as the Deity presents himself to
either Anselm or Vacherot, and manifests his glorious attributes,
whether it be in a vision of the night or day, either of them recognizes
his adorable God, and sinks upon his knees at once; whereas the
theologian of evidences will first demand that the divine apparition
shall identify himself, and only after having scrutinized his
credentials and weighed the probabilities of his being found among the
totality of existences, will he finally render his circumspect homage,
thinking that no characters can be adorable but those which belong to a
real thing.

If we could find out any general characteristic of the universe, any
mannerism in the ways of Nature, any law everywhere applicable and
universally valid, such a discovery would be of such singular assistance
to us in all our future reasoning, that it would deserve a place almost
at the head of the principles of logic. On the other hand, if it can be
shown that there is nothing of the sort to find out, but that every
discoverable regularity is of limited range, this again will be of
logical importance. What sort of a conception we ought to have of the
universe, how to think of the _ensemble_ of things, is a fundamental
problem in the theory of reasoning.


                                   II


It is the legitimate endeavor of scientific men now, as it was
twenty-three hundred years ago, to account for the formation of the
solar system and of the cluster of stars which forms the galaxy, by the
fortuitous concourse of atoms. The greatest expounder of this theory,
when asked how he could write an immense book on the system of the world
without one mention of its author, replied, very logically, “Je n’avais
pas besoin de cette hypothèse-là.” But, in truth, there is nothing
atheistical in the theory, any more than there was in this answer.
Matter is supposed to be composed of molecules which obey the laws of
mechanics and exert certain attractions upon one another; and it is to
these regularities (which there is no attempt to account for) that
general arrangement of the solar system would be due, and not to hazard.

If any one has ever maintained that the universe is a pure throw of the
dice, the theologians have abundantly refuted him. “How often,” says
Archbishop Tillotson, “might a man, after he had jumbled a set of
letters in a bag, fling them out upon the ground before they would fall
into an exact poem, yea, or so much as make a good discourse in prose!
And may not a little book be as easily made by chance as this great
volume of the world?” The chance world here shown to be so different
from that in which we live would be one in which there were no laws, the
characters of different things being entirely independent; so that,
should a sample of any kind of objects ever show a prevalent character,
it could only be by accident, and no general proposition could ever be
established. Whatever further conclusions we may come to in regard to
the order of the universe, thus much may be regarded as solidly
established, that the world is not a mere chance-medley.

But whether the world makes an exact poem or not, is another question.
When we look up at the heavens at night, we readily perceive that the
stars are not simply splashed on to the celestial vault; but there does
not seem to be any precise system in their arrangement either. It will
be worth our while, then, to inquire into the degree of orderliness in
the universe; and, to begin, let us ask whether the world we live in is
any more orderly than a purely chance-world would be.

Any uniformity, or law of Nature, may be stated in the form, “Every A is
B”; as, every ray of light is a non-curved line, every body is
accelerated toward the earth’s center, etc. This is the same as to say,
“There does not exist any A which is not B”; there is no curved ray;
there is no body not accelerated toward the earth; so that the
uniformity consists in the non-occurrence in Nature of a certain
combination of characters (in this case, the combination of being A with
being non-B).[46] And, conversely, every case of the non-occurrence of a
combination of characters would constitute a uniformity in Nature. Thus,
suppose the quality A is never found in combination with the quality C:
for example, suppose the quality of idiocy is never found in combination
with that of having a well-developed brain. Then nothing of the sort A
is of the sort C, or everything of the sort A is of the sort non-C (or
say, every idiot has an ill-developed brain), which, being something
universally true of the A’s, is a uniformity in the world. Thus we see
that, in a world where there were no uniformities, no logically possible
combination of characters would be excluded, but every combination would
exist in some object. But two objects not identical must differ in some
of their characters, though it be only in the character of being in
such-and-such a place. Hence, precisely the same combination of
characters could not be found in two different objects; and,
consequently, in a chance-world every combination involving either the
positive or negative of every character would belong to just one thing.
Thus, if there were but five simple characters in such a world,[47] we
might denote them by A, B, C, D, E, and their negatives by a, b, c, d,
e; and then, as there would be 2^5 or 32 different combinations of these
characters, completely determinate in reference to each of them, that
world would have just 32 objects in it, their characters being as in the
following table:


TABLE I.

    ABCDE   AbCDE   aBCDE   abCDE
    ABCDe   AbCDe   aBCDe   abCDe
    ABCdE   AbCdE   aBCdE   abCdE
    ABCde   AbCde   aBCde   abCde
    ABcDE   AbcDE   aBcDE   abcDE
    ABcDe   AbcDe   aBcDe   abcDe
    ABcdE   AbcdE   aBcdE   abcdE
    ABcde   Abcde   aBcde   abcde

For example, if the five primary characters were _hard_, _sweet_,
_fragrant_, _green_, _bright_, there would be one object which reunited
all these qualities, one which was hard, sweet, fragrant, and green, but
not bright; one which was hard, sweet, fragrant, and bright, but not
green; one which was hard, sweet, and fragrant, but neither green nor
bright; and so on through all the combinations.

This is what a thoroughly chance-world would be like, and certainly
nothing could be imagined more systematic. When a quantity of letters
are poured out of a bag, the appearance of disorder is due to the
circumstance that the phenomena are only partly fortuitous. The laws of
space are supposed, in that case, to be rigidly preserved, and there is
also a certain amount of regularity in the formation of the letters. The
result is that some elements are orderly and some are disorderly, which
is precisely what we observe in the actual world. Tillotson, in the
passage of which a part has been quoted, goes on to ask, “How long might
20,000 blind men which should be sent out from the several remote parts
of England, wander up and down before they would all meet upon Salisbury
Plains, and fall into rank and file in the exact order of an army? And
yet this is much more easy to be imagined than how the innumerable blind
parts of matter should rendezvous themselves into a world.” This is very
true, but in the actual world the _blind men_ are, as far as we can see,
_not_ drawn up in any particular order at all. And, in short, while a
certain amount of order exists in the world, it would seem that the
world is not so orderly as it might be, and, for instance, not so much
so as a world of pure chance would be.

But we can never get to the bottom of this question until we take
account of a highly-important logical principle[48] which I now proceed
to enounce. This principle is that any plurality or lot of objects
whatever have some character in common (no matter how insignificant)
which is peculiar to them and not shared by anything else. The word
“character” here is taken in such a sense as to include negative
characters, such as incivility, inequality, etc., as well as their
positives, civility, equality, etc. To prove the theorem, I will show
what character any two things, A and B, have in common, not shared by
anything else. The things, A and B, are each distinguished from all
other things by the possession of certain characters which may be named
A-ness and B-ness. Corresponding to these positive characters, are the
negative characters un-A-ness, which is possessed by everything except
A, and un-B-ness, which is possessed by everything except B. These two
characters are united in everything except A and B; and this union of
the characters un-A-ness and un-B-ness makes a compound character which
may be termed A-B-lessness. This is not possessed by either A or B, but
it is possessed by everything else. This character, like every other,
has its corresponding negative un-A-B-lessness, and this last is the
character possessed by both A and B, and by nothing else. It is obvious
that what has thus been shown true of two things is _mutatis mutandis_,
true of any number of things. Q. E. D.

In any world whatever, then, there must be a character peculiar to each
possible group of objects. If, as a matter of nomenclature, characters
peculiar to the same group be regarded as only different aspects of the
same character, then we may say that there will be precisely one
character for each possible group of objects. Thus, suppose a world to
contain five things, α, β, γ, δ, ε. Then it will have a separate
character for each of the 31 groups (with _non-existence_ making up 32
or 2^5) shown in the following table:


TABLE II.

         αβ    αβγ    αβγδ    αβγδε
    α    αγ    αβδ    αβγε
    β    αδ    αβε    αβδε
    γ    αε    αγδ    αγδε
    δ    βγ    αγε    βγδε
    ε    βδ    αδε
         βε    βγδ
         γδ    βγε
         γε    βδε
         δε    γδε

This shows that a contradiction is involved in the very idea[49] of a
chance-world, for in a world of 32 things, instead of there being only
3^5 or 243 characters, as we have seen that the notion of a chance-world
requires, there would, in fact, be no less than 2^{32}, or 4,294,967,296
characters, which would not be all independent, but would have all
possible relations with one another.

We further see that so long as we regard characters abstractly, without
regard to their relative importance, etc., there is no possibility of a
more or less degree of orderliness in the world, the whole system of
relationship between the different characters being given by mere logic;
that is, being implied in those facts which are tacitly admitted as soon
as we admit that there is any such thing as reasoning.

In order to descend from this abstract point of view, it is requisite to
consider the characters of things as relative to the perceptions and
active powers of living beings. Instead, then, of attempting to imagine
a world in which there should be no uniformities, let us suppose one in
which none of the uniformities should have reference to characters
interesting or important to us. In the first place, there would be
nothing to puzzle us in such a world. The small number of qualities
which would directly meet the senses would be the ones which would
afford the key to everything which could possibly interest us. The whole
universe would have such an air of system and perfect regularity that
there would be nothing to ask. In the next place, no action of ours, and
no event of Nature, would have important consequences in such a world.
We should be perfectly free from all responsibility, and there would be
nothing to do but to enjoy or suffer whatever happened to come along.
Thus there would be nothing to stimulate or develop either the mind or
the will, and we consequently should neither act nor think. We should
have no memory, because that depends on a law of our organization. Even
if we had any senses, we should be situated toward such a world
precisely as inanimate objects are toward the present one, provided we
suppose that these objects have an absolutely transitory and
instantaneous consciousness without memory—a supposition which is a mere
mode of speech, for that would be no consciousness at all. We may,
therefore, say that a world of chance is simply our actual world viewed
from the standpoint of an animal at the very vanishing-point of
intelligence. The actual world is almost a chance-medley to the mind of
a polyp. The interest which the uniformities of Nature have for an
animal measures his place in the scale of intelligence.

Thus, nothing can be made out from the orderliness of Nature in regard
to the existence of a God, unless it be maintained that the existence of
a finite mind proves the existence of an infinite one.


                                  III


In the last of these papers we examined the nature of inductive or
synthetic reasoning. We found it to be a process of sampling. A number
of specimens of a class are taken, not by selection within that class,
but at random. These specimens will agree in a great number of respects.
If, now, it were likely that a second lot would agree with the first in
the majority of these respects, we might base on this consideration an
inference in regard to any one of these characters. But such an
inference would neither be of the nature of induction, nor would it
(except in special cases) be valid, because the vast majority of points
of agreement in the first sample drawn would generally be entirely
accidental, as well as insignificant. To illustrate this, I take the
ages at death of the first five poets given in Wheeler’s _Biographical
Dictionary_. They are:

                               Aagard, 48.
                               Abeille, 70.
                               Abulola, 84.
                               Abunowas, 48.
                               Accords, 45.

These five ages have the following characters in common:

1. The difference of the two digits composing the number, divided by
three, leaves a remainder of _one_.

2. The first digit raised to the power indicated by the second, and
divided by three, leaves a remainder of _one_.

3. The sum of the prime factors of each age, including one, is divisible
by three.

It is easy to see that the number of accidental agreements of this sort
would be quite endless. But suppose that, instead of considering a
character because of its prevalence in the sample, we designate a
character before taking the sample, selecting it for its importance,
obviousness, or other point of interest. Then two considerable samples
drawn at random are extremely likely to agree approximately in regard to
the proportion of occurrences of a character so chosen. _The inference
that a previously designated character has nearly the same frequency of
occurrence in the whole of a class that it has in a sample drawn at
random out of that class is induction._ If the character be not
previously designated, then a sample in which it is found to be
prevalent can only serve to suggest that it _may be_ prevalent in the
whole class. We may consider this surmise as an inference if we
please—an inference of possibility; but a second sample must be drawn to
test the question of whether the character actually is prevalent.
Instead of designating beforehand a single character in reference to
which we will examine a sample, we may designate two, and use the same
sample to determine the relative frequencies of both. This will be
making two inductive inferences at once; and, of course, we are less
certain that both will yield correct conclusions than we should be that
either separately would do so. What is true of two characters is true of
any limited number. Now, the number of characters which have any
considerable interest for us in reference to any class of objects is
more moderate than might be supposed. As we shall be sure to examine any
sample with reference to these characters, they may be regarded not
exactly as predesignated, but as predetermined (which amounts to the
same thing); and we may infer that the sample represents the class in
all these respects if we please, remembering only that this is not so
secure an inference as if the particular quality to be looked for had
been fixed upon beforehand.

The demonstration of this theory of induction rests upon principles and
follows methods which are accepted by all those who display in other
matters the particular knowledge and force of mind which qualify them to
judge of this. The theory itself, however, quite unaccountably seems
never to have occurred to any of the writers who have undertaken to
explain synthetic reasoning. The most widely-spread opinion in the
matter is one which was much promoted by Mr. John Stuart Mill—namely,
that induction depends for its validity upon the uniformity of
Nature—that is, on the principle that what happens once will, under a
sufficient degree of similarity of circumstances, happen again as often
as the same circumstances recur. The application is this: The fact that
different things belong to the same class constitutes the similarity of
circumstances, and the induction is good, provided this similarity is
“sufficient.” What happens once is, that a number of these things are
found to have a certain character; what may be expected, then, to happen
again as often as the circumstances recur consists in this, that all
things belonging to the same class should have the same character.

This analysis of induction has, I venture to think, various
imperfections, to some of which it may be useful to call attention. In
the first place, when I put my hand in a bag and draw out a handful of
beans, and, finding three-quarters of them black, infer that about
three-quarters of all in the bag are black, my inference is obviously of
the same kind as if I had found any larger proportion, or the whole, of
the sample black, and had assumed that it represented in that respect
the rest of the contents of the bag. But the analysis in question hardly
seems adapted to the explanation of this _proportionate_ induction,
where the conclusion, instead of being that a certain event uniformly
happens under certain circumstances, is precisely that it does not
uniformly occur, but only happens in a certain proportion of cases. It
is true that the whole sample may be regarded as a single object, and
the inference may be brought under the formula proposed by considering
the conclusion to be that any similar sample will show a similar
proportion among its constituents. But this is to treat the induction as
if it rested on a single instance, which gives a very false idea of its
probability.

In the second place, if the uniformity of Nature were the sole warrant
of induction, we should have no right to draw one in regard to a
character whose constancy we knew nothing about. Accordingly, Mr. Mill
says that, though none but white swans were known to Europeans for
thousands of years, yet the inference that all swans were white was “not
a good induction,” because it was not known that color was a usual
generic character (it, in fact, not being so by any means). But it is
mathematically demonstrable that an inductive inference may have as high
a degree of probability as you please independent of any antecedent
knowledge of the constancy of the character inferred. Before it was
known that color is not usually a character of _genera_, there was
certainly a considerable probability that all swans were white. But the
further study of the _genera_ of animals led to the induction of their
non-uniformity in regard to color. A deductive application of this
general proposition would have gone far to overcome the probability of
the universal whiteness of swans before the black species was
discovered. When we do know anything in regard to the general constancy
or inconstancy of a character, the application of that general knowledge
to the particular class to which any induction relates, though it serves
to increase or diminish the force of the induction, is, like every
application of general knowledge to particular cases, deductive in its
nature and not inductive.

In the third place, to say that inductions are true because similar
events happen in similar circumstances—or, what is the same thing,
because objects similar in some respects are likely to be similar in
others—is to overlook those conditions which really are essential to the
validity of inductions. When we take all the characters into account,
any pair of objects resemble one another in just as many particulars as
any other pair. If we limit ourselves to such characters as have for us
any importance, interest, or obviousness, then a synthetic conclusion
may be drawn, but only on condition that the specimens by which we judge
have been taken at random from the class in regard to which we are to
form a judgment, and not selected as belonging to any sub-class. The
induction only has its full force when the character concerned has been
designated before examining the sample. These are the essentials of
induction, and they are not recognized in attributing the validity of
induction to the uniformity of Nature. The explanation of induction by
the doctrine of probabilities, given in the last of these papers, is not
a mere metaphysical formula, but is one from which all the rules of
synthetic reasoning can be deduced systematically and with mathematical
cogency. But the account of the matter by a principle of Nature, even if
it were in other respects satisfactory, presents the fatal disadvantage
of leaving us quite as much afloat as before in regard to the proper
method of induction. It does not surprise me, therefore, that those who
adopt this theory have given erroneous rules for the conduct of
reasoning, nor that the greater number of examples put forward by Mr.
Mill in his first edition, as models of what inductions should be,
proved in the light of further scientific progress so particularly
unfortunate that they had to be replaced by others in later editions.
One would have supposed that Mr. Mill might have based an induction on
_this_ circumstance, especially as it is his avowed principle that, if
the conclusion of an induction turns out false, it cannot have been a
good induction. Nevertheless, neither he nor any of his scholars seem to
have been led to suspect, in the least, the perfect solidity of the
framework which he devised for securely supporting the mind in its
passage from the known to the unknown, although at its first trial it
did not answer quite so well as had been expected.


                                   IV


When we have drawn any statistical induction—such, for instance, as that
one-half of all births are of male children—it is always possible to
discover, by investigation sufficiently prolonged, a class of which the
same predicate may be affirmed universally; to find out, for instance,
_what sort of_ births are of male children. The truth of this principle
follows immediately from the theorem that there is a character peculiar
to every possible group of objects. The form in which the principle is
usually stated is, that _every event must have a cause_.

But, though there exists a cause for every event, and that of a kind
which is capable of being discovered, yet if there be nothing to guide
us to the discovery; if we have to hunt among all the events in the
world without any scent; if, for instance, the sex of a child might
equally be supposed to depend on the configuration of the planets, on
what was going on at the antipodes, or on anything else—then the
discovery would have no chance of ever getting made.

That we ever do discover the precise causes of things, that any
induction whatever is absolutely without exception, is what we have no
right to assume. On the contrary, it is an easy corollary, from the
theorem just referred to, that every empirical rule has an
exception.[50] But there are certain of our inductions which present an
approach to universality so extraordinary that, even if we are to
suppose that they are not strictly universal truths, we cannot possibly
think that they have been reached merely by accident. The most
remarkable laws of this kind are those of _time_ and _space_. With
reference to space, Bishop Berkeley first showed, in a very conclusive
manner, that it was not a thing _seen_, but a thing _inferred_. Berkeley
chiefly insists on the impossibility of directly seeing the third
dimension of space, since the retina of the eye is a surface. But, in
point of fact, the retina is not even a surface; it is a conglomeration
of nerve-needles directed toward the light and having only their extreme
points sensitive, these points lying at considerable distances from one
another compared with their areas. Now, of these points, certainly the
excitation of no one singly can produce the perception of a surface, and
consequently not the aggregate of all the sensations can amount to this.
But certain relations subsist between the excitations of different
nerve-points, and these constitute the premises upon which the
hypothesis of space is founded, and from which it is inferred. That
space is not immediately perceived is now universally admitted; and a
mediate cognition is what is called an inference, and is subject to the
criticism of logic. But what are we to say to the fact of every chicken
as soon as it is hatched solving a problem whose data are of a
complexity sufficient to try the greatest mathematical powers? It would
be insane to deny that the tendency to light upon the conception of
space is inborn in the mind of the chicken and of every animal. The same
thing is equally true of time. That time is not directly perceived is
evident, since no lapse of time is present, and we only perceive what is
present. That, not having the idea of time, we should never be able to
perceive the flow in our sensations without some particular aptitude for
it, will probably also be admitted. The idea of force—at least, in its
rudiments—is another conception so early arrived at, and found in
animals so low in the scale of intelligence, that it must be supposed
innate. But the innateness of an idea admits of degree, for it consists
in the tendency of that idea to present itself to the mind. Some ideas,
like that of space, do so present themselves irresistibly at the very
dawn of intelligence, and take possession of the mind on small
provocation, while of other conceptions we are prepossessed, indeed, but
not so strongly, down a scale which is greatly extended. The tendency to
personify every thing, and to attribute human characters to it, may be
said to be innate; but it is a tendency which is very soon overcome by
civilized man in regard to the greater part of the objects about him.
Take such a conception as that of gravitation varying inversely as the
square of the distance. It is a very simple law. But to say that it is
simple is merely to say that it is one which the mind is particularly
adapted to apprehend with facility. Suppose the idea of a quantity
multiplied into another had been no more easy to the mind than that of a
quantity raised to the power indicated by itself—should we ever have
discovered the law of the solar system?

It seems incontestable, therefore, that the mind of man is strongly
adapted to the comprehension of the world; at least, so far as this
goes, that certain conceptions, highly important for such a
comprehension, naturally arise in his mind; and, without such a
tendency, the mind could never have had any development at all.

How are we to explain this adaptation? The great utility and
indispensableness of the conceptions of time, space, and force, even to
the lowest intelligence, are such as to suggest that they are the
results of natural selection. Without something like geometrical,
kinetical, and mechanical conceptions, no animal could seize his food or
do anything which might be necessary for the preservation of the
species. He might, it is true, be provided with an instinct which would
generally have the same effect; that is to say, he might have
conceptions different from those of time, space, and force, but which
coincided with them in regard to the ordinary cases of the animal’s
experience. But, as that animal would have an immense advantage in the
struggle for life whose mechanical conceptions did not break down in a
novel situation (such as development must bring about), there would be a
constant selection in favor of more and more correct ideas of these
matters. Thus would be attained the knowledge of that fundamental law
upon which all science rolls; namely, that forces depend upon relations
of time, space, and mass. When this idea was once sufficiently clear, it
would require no more than a comprehensible degree of genius to discover
the exact nature of these relations. Such an hypothesis naturally
suggests itself, but it must be admitted that it does not seem
sufficient to account for the extraordinary accuracy with which these
conceptions apply to the phenomena of Nature, and it is probable that
there is some secret here which remains to be discovered.


                                   V


Some important questions of logic depend upon whether we are to consider
the material universe as of limited extent and finite age, or quite
boundless in space and in time. In the former case, it is conceivable
that a general plan or design embracing the whole universe should be
discovered, and it would be proper to be on the alert for some traces of
such a unity. In the latter case, since the proportion of the world of
which we can have any experience is less than the smallest assignable
fraction, it follows that we never could discover any _pattern_ in the
universe except a repeating one; any design embracing the whole would be
beyond our powers to discern, and beyond the united powers of all
intellects during all time. Now, what is absolutely incapable of being
known is, as we have seen in a former paper, not real at all. An
absolutely incognizable existence is a nonsensical phrase. If,
therefore, the universe is infinite, the attempt to find in it any
design embracing it as a whole is futile, and involves a false way of
looking at the subject. If the universe never had any beginning, and if
in space world stretches beyond world without limit, there is no _whole_
of material things, and consequently no general character to the
universe, and no need or possibility of any governor for it. But if
there was a time before which absolutely no matter existed, if there are
certain absolute bounds to the region of things outside of which there
is a mere void, then we naturally seek for an explanation of it, and,
since we cannot look for it among material things, the hypothesis of a
great disembodied animal, the creator and governor of the world, is
natural enough.

The actual state of the evidence as to the limitation of the universe is
as follows: As to time, we find on our earth a constant progress of
development since the planet was a red-hot ball; the solar system seems
to have resulted from the condensation of a nebula, and the process
appears to be still going on. We sometimes see stars (presumably with
systems of worlds) destroyed and apparently resolved back into the
nebulous condition, but we have no evidence of any existence of the
world previous to the nebulous stage from which it seems to have been
evolved. All this rather favors the idea of a beginning than otherwise.
As for limits in space, we cannot be sure that we see anything outside
of the system of the Milky Way. Minds of theological predilections have
therefore no need of distorting the facts to reconcile them with their
views.

But the only scientific presumption is, that the unknown parts of space
and time are like the known parts, occupied; that, as we see cycles of
life and death in all development which we can trace out to the end, the
same holds good in regard to solar systems; that as enormous distances
lie between the different planets of our solar system, relatively to
their diameters, and as still more enormous distances lie between our
system relatively to its diameter and other systems, so it may be
supposed that other galactic clusters exist so remote from ours as not
to be recognized as such with certainty. I do not say that these are
strong inductions; I only say that they are the presumptions which, in
our ignorance of the facts, should be preferred to hypotheses which
involve conceptions of things and occurrences totally different in their
character from any of which we have had any experience, such as
disembodied spirits, the creation of matter, infringements of the laws
of mechanics, etc.

The universe ought to be presumed too vast to have any character. When
it is claimed that the arrangements of Nature are benevolent, or just,
or wise, or of any other peculiar kind, we ought to be prejudiced
against such opinions, as being the offspring of an ill-founded notion
of the finitude of the world. And examination has hitherto shown that
such beneficences, justice, etc., are of a most limited kind—limited in
degree and limited in range.

In like manner, if any one claims to have discovered a plan in the
structure of organized beings, or a scheme in their classification, or a
regular arrangement among natural objects, or a system of
proportionality in the human form, or an order of development, or a
correspondence between conjunctions of the planets and human events, or
a significance in numbers, or a key to dreams, the first thing we have
to ask is whether such relations are susceptible of explanation on
mechanical principles, and if not they should be looked upon with
disfavor as having already a strong presumption against them; and
examination has generally exploded all such theories.

There are minds to whom every prejudice, every presumption, seems
unfair. It is easy to say what minds these are. They are those who never
have known what it is to draw a well-grounded induction, and who imagine
that other people’s knowledge is as nebulous as their own. That all
science rolls upon presumption (not of a formal but of a real kind) is
no argument with them, because they cannot imagine that there is
anything solid in human knowledge. These are the people who waste their
time and money upon perpetual motions and other such rubbish.

But there are better minds who take up mystical theories (by which I
mean all those which have no possibility of being mechanically
explained). These are persons who are strongly prejudiced in favor of
such theories. We all have natural tendencies to believe in such things;
our education often strengthens this tendency; and the result is, that
to many minds nothing seems so antecedently probable as a theory of this
kind. Such persons find evidence enough in favor of their views, and in
the absence of any recognized logic of induction they cannot be driven
from their belief.

But to the mind of a physicist there ought to be a strong presumption
against every mystical theory; and, therefore, it seems to me that those
scientific men who have sought to make out that science was not hostile
to theology have not been so clear-sighted as their opponents.

It would be extravagant to say that science can at present disprove
religion; but it does seem to me that the spirit of science is hostile
to any religion except such a one as that of M. Vacherot. Our appointed
teachers inform us that Buddhism is a miserable and atheistical faith,
shorn of the most glorious and needful attributes of a religion; that
its priests can be of no use to agriculture by praying for rain, nor to
war by commanding the sun to stand still. We also hear the remonstrances
of those who warn us that to shake the general belief in the living God
would be to shake the general morals, public and private. This, too,
must be admitted; such a revolution of thought could no more be
accomplished without waste and desolation than a plantation of trees
could be transferred to new ground, however wholesome in itself, without
all of them languishing for a time, and many of them dying. Nor is it,
by-the-way, a thing to be presumed that a man would have taken part in a
movement having a possible atheistical issue without having taken
serious and adequate counsel in regard to that responsibility. But, let
the consequences of such a belief be as dire as they may, one thing is
certain: that the state of the facts, whatever it may be, will surely
get found out, and no human prudence can long arrest the triumphal car
of truth—no, not if the discovery were such as to drive every individual
of our race to suicide!

But it would be folly to suppose that any metaphysical theory in regard
to the mode of being of the perfect is to destroy that aspiration toward
the perfect which constitutes the essence of religion. It is true that,
if the priests of any particular form of religion succeed in making it
generally believed that religion cannot exist without the acceptance of
certain formulas, or if they succeed in so interweaving certain dogmas
with the popular religion that the people can see no essential analogy
between a religion which accepts these points of faith and one which
rejects them, the result may very well be to render those who cannot
believe these things irreligious. Nor can we ever hope that any body of
priests should consider themselves more teachers of religion in general
than of the particular system of theology advocated by their own party.
But no man need be excluded from participation in the common feelings,
nor from so much of the public expression of them as is open to all the
laity, by the unphilosophical narrowness of those who guard the
mysteries of worship. Am I to be prevented from joining in that common
joy at the revelation of enlightened principles of religion, which we
celebrate at Easter and Christmas, because I think that certain
scientific, logical, and metaphysical ideas which have been mixed up
with these principles are untenable? No; to do so would be to estimate
those errors as of more consequence than the truth—an opinion which few
would admit. People who do not believe what are really the fundamental
principles of Christianity are rare to find, and all but these few ought
to feel at home in the churches.

Footnote 44:

  _Popular Science Monthly_, June, 1878.

Footnote 45:

  [See Santayana, _Reason in Religion_.]

Footnote 46:

  For the present purpose, the negative of a character is to be
  considered as much a character as the positive, for a uniformity may
  either be affirmative or negative. I do not say that no distinction
  can be drawn between positive and negative uniformities.

Footnote 47:

  There being 5 simple characters, with their negatives, they could be
  compounded in various ways so as to make 241 characters in all,
  without counting the characters _existence_ and _non-existence_, which
  make up 243 or 3^5.

Footnote 48:

  This principle was, I believe, first stated by Mr. De Morgan.

Footnote 49:

  Not in every idea but only in the one so formulated.

Footnote 50:

  [Note that this corollary is itself a theoretical inference and not an
  empirical rule.]




                              SIXTH PAPER
                DEDUCTION, INDUCTION, AND HYPOTHESIS[51]


                                   I


The chief business of the logician is to classify arguments; for all
testing clearly depends on classification. The classes of the logicians
are defined by certain typical forms called syllogisms. For example, the
syllogism called _Barbara_ is as follows:

                              S is M; M is P:
                              Hence, S is P.

Or, to put words for letters—

                  Enoch and Elijah were men; all men die:
                  Hence, Enoch and Elijah must have died.

The “is P” of the logicians stands for any verb, active or neuter. It is
capable of strict proof (with which, however, I will not trouble the
reader) that all arguments whatever can be put into this form; but only
under the condition that the _is_ shall mean “_is_ for the purposes of
the argument” or “is represented by.” Thus, an induction will appear in
this form something like this:

These beans are two-thirds white;

But, the beans in this bag are (represented by) these beans;

∴ The beans in the bag are two-thirds white.

But, because all inference may be reduced in some way to _Barbara_, it
does not follow that this is the most appropriate form in which to
represent every kind of inference. On the contrary, to show the
distinctive characters of different sorts of inference, they must
clearly be exhibited in different forms peculiar to each. _Barbara_
particularly typifies deductive reasoning; and so long as the _is_ is
taken literally, no inductive reasoning can be put into this form.
_Barbara_ is, in fact, nothing but the application of a rule. The
so-called major premise lays down this rule; as, for example, _All men
are mortal._ The other or minor premise states a case under the rule;
as, _Enoch was a man._ The conclusion applies the rule to the case and
states the result: _Enoch is mortal._ All deduction is of this
character; it is merely the application of general rules to particular
cases. Sometimes this is not very evident, as in the following:

                 All quadrangles are figures,
                 But no triangle is a quadrangle;
                 Therefore, some figures are not triangles.

But here the reasoning is really this:

             _Rule._—Every quadrangle is other than a triangle.
             _Case._—Some figures are quadrangles.
             _Result._—Some figures are not triangles.

Inductive or synthetic reasoning, being something more than the mere
application of a general rule to a particular case, can never be reduced
to this form.

If, from a bag of beans of which we know that 2/3 are white, we take one
at random, it is a deductive inference that this bean is probably white,
the probability being 2/3. We have, in effect, the following syllogism:

_Rule._—The beans in this bag are 2/3 white.

_Case._—This bean has been drawn in such a way that in the long run the
relative number of white beans so drawn would be equal to the relative
number in the bag.

_Result._—This bean has been drawn in such a way that in the long run it
would turn out white 2/3 of the time.

If instead of drawing one bean we draw a handful at random and conclude
that about 2/3 of the handful are probably white, the reasoning is of
the same sort. If, however, not knowing what proportion of white beans
there are in the bag, we draw a handful at random and, finding 2/3 of
the beans in the handful white, conclude that about 2/3 of those in the
bag are white, we are rowing up the current of deductive sequence, and
are concluding a rule from the observation of a result in a certain
case. This is particularly clear when all the handful turn out one
color. The induction then is:

              These beans were in this bag.———————-
              These beans are white.—————————
              All the beans in the bag were white.             | |
                                                             | | |
          Which is but an inversion of the deductive         | | |
            syllogism.                                       | | |
                                                             | | |
              _Rule._—All the beans in the bag were white.—+ | |
              _Case._—These beans were in the bag.——————+-+
              _Result._—These beans are white.————————+

So that induction is the inference of the _rule_ from the _case_ and
_result_.

But this is not the only way of inverting a deductive syllogism so as to
produce a synthetic inference. Suppose I enter a room and there find a
number of bags, containing different kinds of beans. On the table there
is a handful of white beans; and, after some searching, I find one of
the bags contains white beans only. I at once infer as a probability, or
as a fair guess, that this handful was taken out of that bag. This sort
of inference is called _making an hypothesis_.[52] It is the inference
of a _case_ from a _rule_ and _result_. We have, then—

               DEDUCTION.

               _Rule._—All the beans from this bag are white.

               _Case._—These beans are from this bag.

               ∴ _Result._—These beans are white.

              INDUCTION.

              _Case._—These beans are from this bag.

              _Result._—These beans are white.

              ∴ _Rule._—All the beans from this bag are white.

               HYPOTHESIS.

               _Rule._—All the beans from this bag are white.

               _Result._—These beans are white.

               ∴ _Case._—These beans are from this bag.

We, accordingly, classify all inference as follows:

                              Inference.
                        /———————^———————-|
             Deductive or Analytic.       Synthetic.
                                        /————^—————|
                                   Induction.      Hypothesis.

Induction is where we generalize from a number of cases of which
something is true, and infer that the same thing is true of a whole
class. Or, where we find a certain thing to be true of a certain
proportion of cases and infer that it is true of the same proportion of
the whole class. Hypothesis is where we find some very curious
circumstance, which would be explained by the supposition that it was a
case of a certain general rule, and thereupon adopt that supposition.
Or, where we find that in certain respects two objects have a strong
resemblance, and infer that they resemble one another strongly in other
respects.

I once landed at a seaport in a Turkish province; and, as I was walking
up to the house which I was to visit, I met a man upon horseback,
surrounded by four horsemen holding a canopy over his head. As the
governor of the province was the only personage I could think of who
would be so greatly honored, I inferred that this was he. This was an
hypothesis.

Fossils are found; say, remains like those of fishes, but far in the
interior of the country. To explain the phenomenon, we suppose the sea
once washed over this land. This is another hypothesis.

Numberless documents and monuments refer to a conqueror called Napoleon
Bonaparte. Though we have not seen the man, yet we cannot explain what
we have seen, namely, all these documents and monuments, without
supposing that he really existed. Hypothesis again.

As a general rule, hypothesis is a weak kind of argument. It often
inclines our judgment so slightly toward its conclusion that we cannot
say that we believe the latter to be true; we only surmise that it may
be so. But there is no difference except one of degree between such an
inference and that by which we are led to believe that we remember the
occurrences of yesterday from our feeling as if we did so.


                                   II


Besides the way just pointed out of inverting a deductive syllogism to
produce an induction or hypothesis, there is another. If from the truth
of a certain premise the truth of a certain conclusion would necessarily
follow, then from the falsity of the conclusion the falsity of the
premise would follow. Thus, take the following syllogism in _Barbara_:

                 _Rule._—All men are mortal.

                 _Case._—Enoch and Elijah were men.

                 ∴ _Result._—Enoch and Elijah were mortal.

Now, a person who denies this result may admit the rule, and, in that
case, he must deny the case. Thus:

           _Denial of Result._—Enoch and Elijah were not mortal.

           _Rule._—All men are mortal.

           ∴ _Denial of Case._—Enoch and Elijah were not men.

This kind of syllogism is called _Baroco_, which is the typical mood of
the second figure. On the other hand, the person who denies the result
may admit the case, and in that case he must deny the rule. Thus:

         _Denial of the Result._—Enoch and Elijah were not mortal.

         _Case._—Enoch and Elijah were men.

         ∴ _Denial of the Rule._—Some men are not mortal.

This kind of syllogism is called _Bocardo_, which is the typical mood of
the third figure.

_Baroco_ and _Bocardo_ are, of course, deductive syllogisms; but of a
very peculiar kind. They are called by logicians indirect moods, because
they need some transformation to appear as the application of a rule to
a particular case. But if, instead of setting out as we have here done
with a necessary deduction in _Barbara_, we take a probable deduction of
similar form, the indirect moods which we shall obtain will be—

                    Corresponding to _Baroco_, an hypothesis;
               and, Corresponding to _Bocardo_, an induction.

For example, let us begin with this probable deduction in _Barbara_:

       _Rule._—Most of the beans in this bag are white.

       _Case._—This handful of beans are from this bag.

       ∴ _Result._—Probably, most of this handful of beans are white.

Now, deny the result, but accept the rule:

    _Denial of Result._—Few beans of this handful are white.

    _Rule._—Most beans in this bag are white.

    ∴ _Denial of Case._—Probably, these beans were taken from another
       bag.

This is an hypothetical inference. Next, deny the result, but accept the
case:

       _Denial of Result._—Few beans of this handful are white.

       _Case._—These beans came from this bag.

       ∴ _Denial of Rule._—Probably, few beans in the bag are white.

This is an induction.

The relation thus exhibited between synthetic and deductive reasoning is
not without its importance. When we adopt a certain hypothesis, it is
not alone because it will explain the observed facts, but also because
the contrary hypothesis would probably lead to results contrary to those
observed. So, when we make an induction, it is drawn not only because it
explains the distribution of characters in the sample, but also because
a different rule would probably have led to the sample being other than
it is.

But the advantage of this way of considering the subject might easily be
overrated. An induction is really the inference of a rule, and to
consider it as the denial of a rule is an artificial conception, only
admissible because, when statistical or proportional propositions are
considered as rules, the denial of a rule is itself a rule. So, an
hypothesis is really a subsumption of a case under a class and not the
denial of it, except for this, that to deny a subsumption under one
class is to admit a subsumption under another.

_Bocardo_ may be considered as an induction, so timid as to lose its
amplificative character entirely. Enoch and Elijah are specimens of a
certain kind of men. All that kind of men are shown by these instances
to be immortal. But instead of boldly concluding that all very pious
men, or all men favorites of the Almighty, etc., are immortal, we
refrain from specifying the description of men, and rest in the merely
explicative inference that _some_ men are immortal. So _Baroco_ might be
considered as a very timid hypothesis. Enoch and Elijah are not mortal.
Now, we might boldly suppose them to be gods or something of that sort,
but instead of that we limit ourselves to the inference that they are of
_some_ nature different from that of man.

But, after all, there is an immense difference between the relation of
_Baroco_ and _Bocardo_ to _Barbara_ and that of Induction and Hypothesis
to Deduction. _Baroco_ and _Bocardo_ are based upon the fact that if the
truth of a conclusion necessarily follows from the truth of a premise,
then the falsity of the premise follows from the falsity of the
conclusion. This is always true. It is different when the inference is
only probable. It by no means follows that, because the truth of a
certain premise would render the truth of a conclusion probable,
therefore the falsity of the conclusion renders the falsity of the
premise probable. At least, this is only true, as we have seen in a
former paper, when the word probable is used in one sense in the
antecedent and in another in the consequent.


                                  III


A certain anonymous writing is upon a torn piece of paper. It is
suspected that the author is a certain person. His desk, to which only
he has had access, is searched, and in it is found a piece of paper, the
torn edge of which exactly fits, in all its irregularities, that of the
paper in question. It is a fair hypothetic inference that the suspected
man was actually the author. The ground of this inference evidently is
that two torn pieces of paper are extremely unlikely to fit together by
accident. Therefore, of a great number of inferences of this sort, but a
very small proportion would be deceptive. The analogy of hypothesis with
induction is so strong that some logicians have confounded them.
Hypothesis has been called an induction of characters. A number of
characters belonging to a certain class are found in a certain object;
whence it is inferred that all the characters of that class belong to
the object in question. This certainly involves the same principle as
induction; yet in a modified form. In the first place, characters are
not susceptible of simple enumeration like objects; in the next place,
characters run in categories. When we make an hypothesis like that about
the piece of paper, we only examine a single line of characters, or
perhaps two or three, and we take no specimen at all of others. If the
hypothesis were nothing but an induction, all that we should be
justified in concluding, in the example above, would be that the two
pieces of paper which matched in such irregularities as have been
examined would be found to match in other, say slighter, irregularities.
The inference from the shape of the paper to its ownership is precisely
what distinguishes hypothesis from induction, and makes it a bolder and
more perilous step.

The same warnings that have been given against imagining that induction
rests upon the uniformity of Nature might be repeated in regard to
hypothesis. Here, as there, such a theory not only utterly fails to
account for the validity of the inference, but it also gives rise to
methods of conducting it which are absolutely vicious. There are, no
doubt, certain uniformities in Nature, the knowledge of which will
fortify an hypothesis very much. For example, we suppose that iron,
titanium, and other metals exist in the sun, because we find in the
solar spectrum many lines coincident in position with those which these
metals would produce; and this hypothesis is greatly strengthened by our
knowledge of the remarkable distinctiveness of the particular line of
characters observed. But such a fortification of hypothesis is of a
deductive kind, and hypothesis may still be probable when such
reënforcement is wanting.

There is no greater nor more frequent mistake in practical logic than to
suppose that things which resemble one another strongly in some respects
are any the more likely for that to be alike in others. That this is
absolutely false, admits of rigid demonstration; but, inasmuch as the
reasoning is somewhat severe and complicated (requiring, like all such
reasoning, the use of A, B, C, etc., to set it forth), the reader would
probably find it distasteful, and I omit it. An example, however, may
illustrate the proposition: The comparative mythologists occupy
themselves with finding points of resemblance between solar phenomena
and the careers of the heroes of all sorts of traditional stories; and
upon the basis of such resemblances they infer that these heroes are
impersonations of the sun. If there be anything more in their
reasonings, it has never been made clear to me. An ingenious logician,
to show how futile all that is, wrote a little book, in which he
pretended to prove, in the same manner, that Napoleon Bonaparte is only
an impersonation of the sun. It was really wonderful to see how many
points of resemblance he made out. The truth is, that any two things
resemble one another just as strongly as any two others, if recondite
resemblances are admitted. But, in order that the process of making an
hypothesis should lead to a probable result, the following rules must be
followed:

1. The hypothesis should be distinctly put as a question, before making
the observations which are to test its truth. In other words, we must
try to see what the result of predictions from the hypothesis will be.

2. The respect in regard to which the resemblances are noted must be
taken at random. We must not take a particular kind of predictions for
which the hypothesis is known to be good.

3. The failures as well as the successes of the predictions must be
honestly noted. The whole proceeding must be fair and unbiased.

Some persons fancy that bias and counter-bias are favorable to the
extraction of truth—that hot and partisan debate is the way to
investigate. This is the theory of our atrocious legal procedure. But
Logic puts its heel upon this suggestion. It irrefragably demonstrates
that knowledge can only be furthered by the real desire for it, and that
the methods of obstinacy, of authority, and every mode of trying to
reach a foregone conclusion, are absolutely of no value. These things
are proved. The reader is at liberty to think so or not as long as the
proof is not set forth, or as long as he refrains from examining it.
Just so, he can preserve, if he likes, his freedom of opinion in regard
to the propositions of geometry; only, in that case, if he takes a fancy
to read Euclid, he will do well to skip whatever he finds with A, B, C,
etc., for, if he reads attentively that disagreeable matter, the freedom
of his opinion about geometry may unhappily be lost forever.

How many people there are who are incapable of putting to their own
consciences this question, “Do I want to know how the fact stands, or
not?”

The rules which have thus far been laid down for induction and
hypothesis are such as are absolutely essential. There are many other
maxims expressing particular contrivances for making synthetic
inferences strong, which are extremely valuable and should not be
neglected. Such are, for example, Mr. Mill’s four methods. Nevertheless,
in the total neglect of these, inductions and hypotheses may and
sometimes do attain the greatest force.


                                   IV


Classifications in all cases perfectly satisfactory hardly exist. Even
in regard to the great distinction between explicative and ampliative
inferences, examples could be found which seem to lie upon the border
between the two classes, and to partake in some respects of the
characters of either. The same thing is true of the distinction between
induction and hypothesis. In the main, it is broad and decided. By
induction, we conclude that facts, similar to observed facts, are true
in cases not examined. By hypothesis, we conclude the existence of a
fact quite different from anything observed, from which, according to
known laws, something observed would necessarily result. The former, is
reasoning from particulars to the general law; the latter, from effect
to cause. The former classifies, the latter explains. It is only in some
special cases that there can be more than a momentary doubt to which
category a given inference belongs. One exception is where we observe,
not facts similar under similar circumstances, but facts different under
different circumstances—the difference of the former having, however, a
definite relation to the difference of the latter. Such inferences,
which are really inductions, sometimes present nevertheless some
indubitable resemblances to hypotheses.

Knowing that water expands by heat, we make a number of observations of
the volume of a constant mass of water at different temperatures. The
scrutiny of a few of these suggests a form of algebraical formula which
will approximately express the relation of the volume to the
temperature. It may be, for instance, that _v_ being the relative
volume, and _t_ the temperature, a few observations examined indicate a
relation of the form—

                     _v_ = 1 + _at_ + _bt_^2 + _ct_^3.

Upon examining observations at other temperatures taken at random, this
idea is confirmed; and we draw the inductive conclusion that all
observations within the limits of temperature from which we have drawn
our observations could equally be so satisfied. Having once ascertained
that such a formula is possible, it is a mere affair of arithmetic to
find the values of _a_, _b_, and _c_, which will make the formula
satisfy the observations best. This is what physicists call an empirical
formula, because it rests upon mere induction, and is not explained by
any hypothesis.

Such formulæ, though very useful as means of describing in general terms
the results of observations, do not take any high rank among scientific
discoveries. The induction which they embody, that expansion by heat (or
whatever other phenomenon is referred to) takes place in a perfectly
gradual manner without sudden leaps or inummerable fluctuations,
although really important, attracts no attention, because it is what we
naturally anticipate. But the defects of such expressions are very
serious. In the first place, as long as the observations are subject to
error, as all observations are, the formula cannot be expected to
satisfy the observations exactly. But the discrepancies cannot be due
solely to the errors of the observations, but must be partly owing to
the error of the formula which has been deducted from erroneous
observations. Moreover, we have no right to suppose that the real facts,
if they could be had free from error, could be expressed by such a
formula at all. They might, perhaps, be expressed by a similar formula
with an infinite number of terms; but of what use would that be to us,
since it would require an infinite number of coefficients to be written
down? When one quantity varies with another, if the corresponding values
are exactly known, it is a mere matter of mathematical ingenuity to find
some way of expressing their relation in a simple manner. If one
quantity is of one kind—say, a specific gravity—and the other of another
kind—say, a temperature—we do not desire to find an expression for their
relation which is wholly free from numerical constants, since if it were
free from them when, say, specific gravity as compared with water, and
temperature as expressed by the Centigrade thermometer, were in
question, numbers would have to be introduced when the scales of
measurement were changed. We may, however, and do desire to find
formulas expressing the relations of physical phenomena which shall
contain no more arbitrary numbers than changes in the scales of
measurement might require.

When a formula of this kind is discovered, it is no longer called an
empirical formula, but a law of Nature; and is sooner or later made the
basis of an hypothesis which is to explain it. These simple formulæ are
not usually, if ever, exactly true, but they are none the less important
for that; and the great triumph of the hypothesis comes when it explains
not only the formula, but also the deviations from the formula. In the
current language of the physicists, an hypothesis of this importance is
called a theory, while the term hypothesis is restricted to suggestions
which have little evidence in their favor. There is some justice in the
contempt which clings to the word hypothesis. To think that we can
strike out of our own minds a true preconception of how Nature acts, in
a vain fancy. As Lord Bacon well says: “The subtlety of Nature far
exceeds the subtlety of sense and intellect: so that these fine
meditations, and speculations, and reasonings of men are a sort of
insanity, only there is no one at hand to remark it.” The successful
theories are not pure guesses, but are guided by reasons.

The kinetical theory of gases is a good example of this. This theory is
intended to explain certain simple formulæ, the chief of which is called
the law of Boyle. It is, that if air or any other gas be placed in a
cylinder with a piston, and if its volume be measured under the pressure
of the atmosphere, say fifteen pounds on the square inch, and if then
another fifteen pounds per square inch be placed on the piston, the gas
will be compressed to one-half its bulk, and in similar inverse ratio
for other pressures. The hypothesis which has been adopted to account
for this law is that the molecules of a gas are small, solid particles
at great distances from each other (relatively to their dimensions), and
moving with great velocity, without sensible attractions or repulsions,
until they happen to approach one another very closely. Admit this, and
it follows that when a gas is under pressure what prevents it from
collapsing is not the incompressibility of the separate molecules, which
are under no pressure at all, since they do not touch, but the pounding
of the molecules against the piston. The more the piston falls, and the
more the gas is compressed, the nearer together the molecules will be;
the greater number there will be at any moment within a given distance
of the piston, the shorter the distance which any one will go before its
course is changed by the influence of another, the greater number of new
courses of each in a given time, and the oftener each, within a given
distance of the piston, will strike it. This explains Boyle’s law. The
law is not exact; but the hypothesis does not lead us to it exactly.
For, in the first place, if the molecules are large, they will strike
each other oftener when their mean distances are diminished, and will
consequently strike the piston oftener, and will produce more pressure
upon it. On the other hand, if the molecules have an attraction for one
another, they will remain for a sensible time within one another’s
influence, and consequently they will not strike the wall so often as
they otherwise would, and the pressure will be less increased by
compression.

When the kinetical theory of gases was first proposed by Daniel
Bernoulli, in 1738, it rested only on the law of Boyle, and was
therefore pure hypothesis. It was accordingly quite naturally and
deservedly neglected. But, at present, the theory presents quite another
aspect; for, not to speak of the considerable number of observed facts
of different kinds with which it has been brought into relation, it is
supported by the mechanical theory of heat. That bringing together
bodies which attract one another, or separating bodies which repel one
another, when sensible motion is not produced nor destroyed, is always
accompanied by the evolution of heat, is little more than an induction.
Now, it has been shown by experiment that, when a gas is allowed to
expand without doing work, a very small amount of heat disappears. This
proves that the particles of the gas attract one another slightly, and
but very slightly. It follows that, when a gas is under pressure, what
prevents it from collapsing is not any repulsion between the particles,
since there is none. Now, there are only two modes of force known to us,
force of position or attractions and repulsions, and force of motion.
Since, therefore, it is not the force of position which gives a gas its
expansive force, it must be the force of motion. In this point of view,
the kinetical theory of gases appears as a deduction from the mechanical
theory of heat. It is to be observed, however, that it supposes the same
law of mechanics (that there are only those two modes of force) which
holds in regard to bodies such as we can see and examine, to hold also
for what are very different, the molecules of bodies. Such a supposition
has but a slender support from induction. Our belief in it is greatly
strengthened by its connection with the law of Boyle, and it is,
therefore, to be considered as an hypothetical inference. Yet it must be
admitted that the kinetical theory of gases would deserve little
credence if it had not been connected with the principles of mechanics.

The great difference between induction and hypothesis is, that the
former infers the existence of phenomena such as we have observed in
cases which are similar, while hypothesis supposes something of a
different kind from what we have directly observed, and frequently
something which it would be impossible for us to observe directly.
Accordingly, when we stretch an induction quite beyond the limits of our
observation, the inference partakes of the nature of hypothesis. It
would be absurd to say that we have no inductive warrant for a
generalization extending a little beyond the limits of experience, and
there is no line to be drawn beyond which we cannot push our inference;
only it becomes weaker the further it is pushed. Yet, if an induction be
pushed very far, we cannot give it much credence unless we find that
such an extension explains some fact which we can and do observe. Here,
then, we have a kind of mixture of induction and hypothesis supporting
one another; and of this kind are most of the theories of physics.


                                   V


That synthetic inferences may be divided into induction and hypothesis
in the manner here proposed,[53] admits of no question. The utility and
value of the distinction are to be tested by their applications.

Induction is, plainly, a much stronger kind of inference than
hypothesis; and this is the first reason for distinguishing between
them. Hypotheses are sometimes regarded as provisional resorts, which in
the progress of science are to be replaced by inductions. But this is a
false view of the subject. Hypothetic reasoning infers very frequently a
fact not capable of direct observation. It is an hypothesis that
Napoleon Bonaparte once existed. How is that hypothesis ever to be
replaced by an induction? It may be said that from the premise that such
facts as we have observed are as they would be if Napoleon existed, we
are to infer by induction that _all_ facts that are hereafter to be
observed will be of the same character. There is no doubt that every
hypothetic inference may be distorted into the appearance of an
induction in this way. But the essence of an induction is that it infers
from one set of facts another set of similar facts, whereas hypothesis
infers from facts of one kind to facts of another. Now, the facts which
serve as grounds for our belief in the historic reality of Napoleon are
not by any means necessarily the only kind of facts which are explained
by his existence. It may be that, at the time of his career, events were
being recorded in some way not now dreamed of, that some ingenious
creature on a neighboring planet was photographing the earth, and that
these pictures on a sufficiently large scale may some time come into our
possession, or that some mirror upon a distant star will, when the light
reaches it, reflect the whole story back to earth. Never mind how
improbable these suppositions are; everything which happens is
infinitely improbable. I am not saying that _these_ things are likely to
occur, but that _some_ effect of Napoleon’s existence which now seems
impossible is certain nevertheless to be brought about. The hypothesis
asserts that such facts, when they do occur, will be of a nature to
confirm, and not to refute, the existence of the man. We have, in the
impossibility of inductively inferring hypothetical conclusions, a
second reason for distinguishing between the two kinds of inference.

A third merit of the distinction is, that it is associated with an
important psychological or rather physiological difference in the mode
of apprehending facts. Induction infers a rule. Now, the belief of a
rule is a habit. That a habit is a rule active in us, is evident. That
every belief is of the nature of a habit, in so far as it is of a
general character, has been shown in the earlier papers of this series.
Induction, therefore, is the logical formula which expresses the
physiological process of formation of a habit. Hypothesis substitutes,
for a complicated tangle of predicates attached to one subject, a single
conception. Now, there is a peculiar sensation belonging to the act of
thinking that each of these predicates inheres in the subject. In
hypothetic inference this complicated feeling so produced is replaced by
a single feeling of greater intensity, that belonging to the act of
thinking the hypothetic conclusion. Now, when our nervous system is
excited in a complicated way, there being a relation between the
elements of the excitation, the result is a single harmonious
disturbance which I call an emotion. Thus, the various sounds made by
the instruments of an orchestra strike upon the ear, and the result is a
peculiar musical emotion, quite distinct from the sounds themselves.
This emotion is essentially the same thing as an hypothetic inference,
and every hypothetic inference involves the formation of such an
emotion. We may say, therefore, that hypothesis produces the _sensuous_
element of thought, and induction the _habitual_ element. As for
deduction, which adds nothing to the premises, but only out of the
various facts represented in the premises selects one and brings the
attention down to it, this may be considered as the logical formula for
paying attention, which is the _volitional_ element of thought, and
corresponds to nervous discharge in the sphere of physiology.

Another merit of the distinction between induction and hypothesis is,
that it leads to a very natural classification of the sciences and of
the minds which prosecute them. What must separate different kinds of
scientific men more than anything else are the differences of their
_techniques_. We cannot expect men who work with books chiefly to have
much in common with men whose lives are passed in laboratories. But,
after differences of this kind, the next most important are differences
in the modes of reasoning. Of the natural sciences, we have, first, the
classificatory sciences, which are purely inductive—systematic botany
and zoölogy, mineralogy, and chemistry. Then, we have the sciences of
theory, as above explained—astronomy, pure physics, etc. Then, we have
sciences of hypothesis—geology, biology, etc.

There are many other advantages of the distinction in question which I
shall leave the reader to find out by experience. If he will only take
the custom of considering whether a given inference belongs to one or
other of the two forms of synthetic inference given on page 134, I can
promise him that he will find his advantage in it, in various ways.

Footnote 51:

  _Popular Science Monthly_, August, 1878.

Footnote 52:

  [Later Pierce called it _presumptive inference_. See Baldwin’s
  _Dictionary_ art. _Probable Inference_.]

Footnote 53:

  This division was first made in a course of lectures by the author
  before the Lowell Institute, Boston, in 1866, and was printed in the
  _Proceedings of the American Academy of Arts and Sciences_, for April
  9, 1867.




                                PART II
                            LOVE AND CHANCE




                  I. THE ARCHITECTURE OF THEORIES[54]


Of the fifty or hundred systems of philosophy that have been advanced at
different times of the world’s history, perhaps the larger number have
been, not so much results of historical evolution, as happy thoughts
which have accidently occurred to their authors. An idea which has been
found interesting and fruitful has been adopted, developed, and forced
to yield explanations of all sorts of phenomena. The English have been
particularly given to this way of philosophizing; witness, Hobbes,
Hartley, Berkeley, James Mill. Nor has it been by any means useless
labor; it shows us what the true nature and value of the ideas developed
are, and in that way affords serviceable materials for philosophy. Just
as if a man, being seized with the conviction that paper was a good
material to make things of, were to go to work to build a _papier mâché_
house, with roof of roofing-paper, foundations of pasteboard, windows of
paraffined paper, chimneys, bath tubs, locks, etc., all of different
forms of paper, his experiment would probably afford valuable lessons to
builders, while it would certainly make a detestable house, so those
one-idea’d philosophies are exceedingly interesting and instructive, and
yet are quite unsound.

The remaining systems of philosophy have been of the nature of reforms,
sometimes amounting to radical revolutions, suggested by certain
difficulties which have been found to beset systems previously in vogue;
and such ought certainly to be in large part the motive of any new
theory. This is like partially rebuilding a house. The faults that have
been committed are, first, that the repairs of the dilapidations have
generally not been sufficiently thorough-going, and second, that not
sufficient pains had been taken to bring the additions into deep harmony
with the really sound parts of the old structure.

When a man is about to build a house, what a power of thinking he has to
do, before he can safely break ground! With what pains he has to
excogitate the precise wants that are to be supplied! What a study to
ascertain the most available and suitable materials, to determine the
mode of construction to which those materials are best adapted, and to
answer a hundred such questions! Now without riding the metaphor too
far, I think we may safely say that the studies preliminary to the
construction of a great theory should be at least as deliberate and
thorough as those that are preliminary to the building of a
dwelling-house.

That systems ought to be constructed architectonically has been preached
since Kant, but I do not think the full import of the maxim has by any
means been apprehended. What I would recommend is that every person who
wishes to form an opinion concerning fundamental problems, should first
of all make a complete survey of human knowledge, should take note of
all the valuable ideas in each branch of science, should observe in just
what respect each has been successful and where it has failed, in order
that in the light of the thorough acquaintance so attained of the
available materials for a philosophical theory and of the nature and
strength of each, he may proceed to the study of what the problem of
philosophy consists in, and of the proper way of solving it. I must not
be understood as endeavoring to state fully all that these preparatory
studies should embrace; on the contrary, I purposely slur over many
points, in order to give emphasis to one special recommendation, namely,
to make a systematic study of the conceptions out of which a
philosophical theory may be built, in order to ascertain what place each
conception may fitly occupy in such a theory, and to what uses it is
adapted.

The adequate treatment of this single point would fill a volume, but I
shall endeavor to illustrate my meaning by glancing at several sciences
and indicating conceptions in them serviceable for philosophy. As to the
results to which long studies thus commenced have led me, I shall just
give a hint at their nature.

We may begin with dynamics,—field in our day of perhaps the grandest
conquest human science has ever made,—I mean the law of the conservation
of energy. But let us revert to the first step taken by modern
scientific thought,—and a great stride it was,—the inauguration of
dynamics by Galileo. A modern physicist on examining Galileo’s works is
surprised to find how little experiment had to do with the establishment
of the foundations of mechanics. His principal appeal is to common sense
and _il lume naturale_. He always assumes that the true theory will be
found to be a simple and natural one. And we can see why it should
indeed be so in dynamics. For instance, a body left to its own inertia,
moves in a straight line, and a straight line appears to us the simplest
of curves. In _itself_, no curve is simpler than another. A system of
straight lines has intersections precisely corresponding to those of a
system of like parabolas similarly placed, or to those of any one of an
infinity of systems of curves. But the straight line appears to us
simple, because, as Euclid says, it lies evenly between its extremities;
that is, because viewed endwise it appears as a point. That is, again,
because light moves in straight lines. Now, light moves in straight
lines because of the part which the straight line plays in the laws of
dynamics. Thus it is that our minds having been formed under the
influence of phenomena governed by the laws of mechanics, certain
conceptions entering into those laws become implanted in our minds, so
that we readily guess at what the laws are. Without such a natural
prompting, having to search blindfold for a law which would suit the
phenomena, our chance of finding it would be as one to infinity. The
further physical studies depart from phenomena which have directly
influenced the growth of the mind, the less we can expect to find the
laws which govern them “simple,” that is, composed of a few conceptions
natural to our minds.

The researches of Galileo, followed up by Huygens and others, led to
those modern conceptions of _Force_ and _Law_, which have revolutionized
the intellectual world. The great attention given to mechanics in the
seventeenth century soon so emphasized these conceptions as to give rise
to the Mechanical Philosophy, or doctrine that all the phenomena of the
physical universe are to be explained upon mechanical principles.
Newton’s great discovery imparted a new impetus to this tendency. The
old notion that heat consists in an agitation of corpuscles was now
applied to the explanation of the chief properties of gases. The first
suggestion in this direction was that the pressure of gases is explained
by the battering of the particles against the walls of the containing
vessel, which explained Boyle’s law of the compressibility of air.
Later, the expansion of gases, Avogadro’s chemical law, the diffusion
and viscosity of gases, and the action of Crookes’s radiometer were
shown to be consequences of the same kinetical theory; but other
phenomena, such as the ratio of the specific heat at constant volume to
that at constant pressure, require additional hypotheses, which we have
little reason to suppose are simple, so that we find ourselves quite
afloat. In like manner with regard to light. That it consists of
vibrations was almost proved by the phenomena of diffraction, while
those of polarization showed the excursions of the particles to be
perpendicular to the line of propagation; but the phenomena of
dispersion, etc., require additional hypotheses which may be very
complicated. Thus, the further progress of molecular speculation appears
quite uncertain. If hypotheses are to be tried haphazard, or simply
because they will suit certain phenomena, it will occupy the
mathematical physicists of the world say half a century on the average
to bring each theory to the test, and since the number of possible
theories may go up into the trillions, only one of which can be true, we
have little prospect of making further solid additions to the subject in
our time. When we come to atoms, the presumption in favor of a simple
law seems very slender. There is room for serious doubt whether the
fundamental laws of mechanics hold good for single atoms, and it seems
quite likely that they are capable of motion in more than three
dimensions.

To find out much more about molecules and atoms, we must search out a
natural history of laws of nature, which may fulfil that function which
the presumption in favor of simple laws fulfilled in the early days of
dynamics, by showing us what kind of laws we have to expect and by
answering such questions as this: Can we with reasonable prospect of not
wasting time, try the supposition that atoms attract one another
inversely as the seventh power of their distances, or can we not? To
suppose universal laws of nature capable of being apprehended by the
mind and yet having no reason for their special forms, but standing
inexplicable and irrational, is hardly a justifiable position.
Uniformities are precisely the sort of facts that need to be accounted
for. That a pitched coin should sometimes turn up heads and sometimes
tails calls for no particular explanation; but if it shows heads every
time, we wish to know how this result has been brought about. Law is
_par excellence_ the thing that wants a reason.

Now the only possible way of accounting for the laws of nature and for
uniformity in general is to suppose them results of evolution. This
supposes them not to be absolute, not to be obeyed precisely. It makes
an element of indeterminacy, spontaneity, or absolute chance in nature.
Just as, when we attempt to verify any physical law, we find our
observations cannot be precisely satisfied by it, and rightly attribute
the discrepancy to errors of observation, so we must suppose far more
minute discrepancies to exist owing to the imperfect cogency of the law
itself, to a certain swerving of the facts from any definite formula.

Mr. Herbert Spencer wishes to explain evolution upon mechanical
principles. This is illogical, for four reasons. First, because the
principle of evolution requires no extraneous cause; since the tendency
to growth can be supposed itself to have grown from an infinitesimal
germ accidentally started. Second, because law ought more than anything
else to be supposed a result of evolution. Third, because exact law
obviously never can produce heterogeneity out of homogeneity; and
arbitrary heterogeneity is the feature of the universe the most manifest
and characteristic. Fourth, because the law of the conservation of
energy is equivalent to the proposition that all operations governed by
mechanical laws are reversible; so that an immediate corollary from it
is that growth is not explicable by those laws, even if they be not
violated in the process of growth. In short, Spencer is not a
philosophical evolutionist, but only a half-evolutionist,—or, if you
will, only a semi-Spencerian. Now philosophy requires thoroughgoing
evolutionism or none.

The theory of Darwin was that evolution had been brought about by the
action of two factors: first, heredity, as a principle making offspring
nearly resemble their parents, while yet giving room for “sporting,” or
accidental variations,—for very slight variations often, for wider ones
rarely; and, second, the destruction of breeds or races that are unable
to keep the birth rate up to the death rate. This Darwinian principle is
plainly capable of great generalization. Wherever there are large
numbers of objects, having a tendency to retain certain characters
unaltered, this tendency, however, not being absolute but giving room
for chance variations, then, if the amount of variation is absolutely
limited in certain directions by the destruction of everything which
reaches those limits, there will be a gradual tendency to change in
directions of departure from them. Thus, if a million players sit down
to bet at an even game, since one after another will get ruined, the
average wealth of those who remain will perpetually increase. Here is
indubitably a genuine formula of possible evolution, whether its
operation accounts for much or little in the development of animal and
vegetable species.

The Lamarckian theory also supposes that the development of species has
taken place by a long series of insensible changes, but it supposes that
those changes have taken place during the lives of the individuals, in
consequence of effort and exercise, and that reproduction plays no part
in the process except in preserving these modifications. Thus, the
Lamarckian theory only explains the development of characters for which
individuals strive, while the Darwinian theory only explains the
production of characters really beneficial to the race, though these may
be fatal to individuals.[55] But more broadly and philosophically
conceived, Darwinian evolution is evolution by the operation of chance,
and the destruction of bad results, while Lamarckian evolution is
evolution by the effect of habit and effort.

A third theory of evolution is that of Mr. Clarence King. The testimony
of monuments and of rocks is that species are unmodified or scarcely
modified, under ordinary circumstances, but are rapidly altered after
cataclysms or rapid geological changes. Under novel circumstances, we
often see animals and plants sporting excessively in reproduction, and
sometimes even undergoing transformations during individual life,
phenomena no doubt due partly to the enfeeblement of vitality from the
breaking up of habitual modes of life, partly to changed food, partly to
direct specific influence of the element in which the organism is
immersed. If evolution has been brought about in this way, not only have
its single steps not been insensible, as both Darwinians and Lamarckians
suppose, but they are furthermore neither haphazard on the one hand, nor
yet determined by an inward striving on the other, but on the contrary
are effects of the changed environment, and have a positive general
tendency to adapt the organism to that environment, since variation will
particularly affect organs at once enfeebled and stimulated. This mode
of evolution, by external forces and the breaking up of habits, seems to
be called for by some of the broadest and most important facts of
biology and paleontology; while it certainly has been the chief factor
in the historical evolution of institutions as in that of ideas; and
cannot possibly be refused a very prominent place in the process of
evolution of the universe in general.

Passing to psychology, we find the elementary phenomena of mind fall
into three categories. First, we have Feelings, comprising all that is
immediately present, such as pain, blue, cheerfulness, the feeling that
arises when we contemplate a consistent theory, etc. A feeling is a
state of mind having its own living quality, independent of any other
state of mind. Or, a feeling is an element of consciousness which might
conceivably override every other state until it monopolized the mind,
although such a rudimentary state cannot actually be realized, and would
not properly be consciousness. Still, it is conceivable, or supposable,
that the quality of blue should usurp the whole mind, to the exclusion
of the ideas of shape, extension, contrast, commencement and cessation,
and all other ideas, whatsoever. A feeling is necessarily perfectly
simple, _in itself_, for if it had parts these would also be in the
mind, whenever the whole was present, and thus the whole could not
monopolize the mind.[56]

Besides Feelings, we have Sensations of reaction; as when a person
blindfold suddenly runs against a post, when we make a muscular effort,
or when any feeling gives way to a new feeling. Suppose I had nothing in
my mind but a feeling of blue, which were suddenly to give place to a
feeling of red; then, at the instant of transition there would be a
shock, a sense of reaction, my blue life being transmuted into red life.
If I were further endowed with a memory, that sense would continue for
some time, and there would also be a peculiar feeling or sentiment
connected with it. This last feeling might endure (conceivably I mean)
after the memory of the occurrence and the feelings of blue and red had
passed away. But the _sensation_ of reaction cannot exist except in the
actual presence of the two feelings blue and red to which it relates.
Wherever we have two feelings and pay attention to a relation between
them of whatever kind, there is the sensation of which I am speaking.
But the sense of action and reaction has two types: it may either be a
perception of relation between two ideas, or it may be a sense of action
and reaction between feeling and something out of feeling. And this
sense of external reaction again has two forms; for it is either a sense
of something happening to us, by no act of ours, we being passive in the
matter, or it is a sense of resistance, that is, of our expending
feeling upon something without. The sense of reaction is thus a sense of
connection or comparison between feelings, either, _A_, between one
feeling and another, or _B_, between feeling and its absence or lower
degree; and under _B_ we have, First, the sense of the access of
feeling, and Second, the sense of remission of feeling.

Very different both from feelings and from reaction-sensations or
disturbances of feeling are general conceptions. When we think, we are
conscious that a connection between feelings is determined by a general
rule, we are aware of being governed by a habit. Intellectual power is
nothing but facility in taking habits and in following them in cases
essentially analogous to, but in non-essentials widely remote from, the
normal cases of connections of feelings under which those habits were
formed.

The one primary and fundamental law of mental action consists in a
tendency to generalization. Feeling tends to spread; connections between
feelings awaken feelings; neighboring feelings become assimilated; ideas
are apt to reproduce themselves. These are so many formulations of the
one law of the growth of mind. When a disturbance of feeling takes
place, we have a consciousness of gain, the gain of experience; and a
new disturbance will be apt to assimilate itself to the one that
preceded it. Feelings, by being excited, become more easily excited,
especially in the ways in which they have previously been excited. The
consciousness of such a habit constitutes a general conception.

The cloudiness of psychological notions may be corrected by connecting
them with physiological conceptions. Feeling may be supposed to exist,
wherever a nerve-cell is in an excited condition. The disturbance of
feeling, or sense of reaction, accompanies the transmission of
disturbance between nerve-cells or from a nerve-cell to a muscle-cell or
the external stimulation of a nerve-cell. General conceptions arise upon
the formation of habits in the nerve-matter, which are molecular changes
consequent upon its activity and probably connected with its nutrition.

The law of habit exhibits a striking contrast to all physical laws in
the character of its commands. A physical law is absolute. What it
requires is an exact relation. Thus, a physical force introduces into a
motion a component motion to be combined with the rest by the
parallelogram of forces; but the component motion must actually take
place exactly as required by the law of force. On the other hand, no
exact conformity is required by the mental law. Nay, exact conformity
would be in downright conflict with the law; since it would instantly
crystallize thought and prevent all further formation of habit. The law
of mind only makes a given feeling _more likely_ to arise. It thus
resembles the “non-conservative” forces of physics, such as viscosity
and the like, which are due to statistical uniformities in the chance
encounters of trillions of molecules.

The old dualistic notion of mind and matter, so prominent in
Cartesianism, as two radically different kinds of substance, will hardly
find defenders to-day. Rejecting this, we are driven to some form of
hylopathy, otherwise called monism. Then the question arises whether
physical laws on the one hand, and the psychical law on the other are to
be taken—

(_A_) as independent, a doctrine often called _monism_, but which I
would name _neutralism_; or,

(_B_) the psychical law as derived and special, the physical law alone
as primordial, which is _materialism_; or,

(_C_) the physical law as derived and special, the psychical law alone
as primordial, which is _idealism_.

The materialistic doctrine seems to me quite as repugnant to scientific
logic as to common sense; since it requires us to suppose that a certain
kind of mechanism will feel, which would be a hypothesis absolutely
irreducible to reason,—an ultimate, inexplicable regularity; while the
only possible justification of any theory is that it should make things
clear and reasonable.

Neutralism is sufficiently condemned by the logical maxim known as
Ockham’s razor, i.e., that not more independent elements are to be
supposed than necessary. By placing the inward and outward aspects of
substance on a par, it seems to render both primordial.

The one intelligible theory of the universe is that of objective
idealism, that matter is effete mind, inveterate habits becoming
physical laws. But before this can be accepted it must show itself
capable of explaining the tridimensionality of space, the laws of
motion, and the general characteristics of the universe, with
mathematical clearness and precision; for no less should be demanded of
every Philosophy.

[Illustration: Figure 6.]

Modern mathematics is replete with ideas which may be applied to
philosophy. I can only notice one or two. The manner in which
mathematicians generalize is very instructive. Thus, painters are
accustomed to think of a picture as consisting geometrically of the
intersections of its plane by rays of light from the natural objects to
the eye. But geometers use a generalized perspective.[57] For instance
in the figure let _O_ be the eye, let _A_ _B_ _C_ _D_ _E_ be the
edgewise view of any plane, and let _a_ _f_ _e_ _D_ _c_ be the edgewise
view of another plane. The geometers draw rays through _O_ cutting both
these planes, and treat the points of intersection of each ray with one
plane as representing the point of intersection of the same ray with the
other plane. Thus, _e_ represents _E_, in the painter’s way. _D_
represents itself. _C_ is represented by _c_, which is further from the
eye; and _A_ is represented by _a_ which is on the other side of the
eye. Such generalization is not bound down to sensuous images. Further,
according to this mode of representation every point on one plane
represents a point on the other, and every point on the latter is
represented by a point on the former. But how about the point _f_ which
is in a direction from _O_ parallel to the represented plane, and how
about the point _B_ which is in a direction parallel to the representing
plane? Some will say that these are exceptions; but modern mathematics
does not allow exceptions which can be annulled by generalization.[58]
As a point moves from _C_ to _D_ and thence to _E_ and off toward
infinity, the corresponding point on the other plane moves from _c_ to
_D_ and thence to _e_ and toward _f_. But this second point can pass
through _f_ to _a_; and when it is there the first point has arrived at
_A_. We therefore say that the first point has passed _through
infinity_, and that every line joins in to itself somewhat like an oval.
Geometers talk of the parts of lines at an infinite distance as points.
This is a kind of generalization very efficient in mathematics.

Modern views of measurement have a philosophical aspect. There is an
indefinite number of systems of measuring along a line; thus, a
perspective representation of a scale on one line may be taken to
measure another, although of course such measurements will not agree
with what we call the distances of points on the latter line. To
establish a system of measurement on a line we must assign a distinct
number to each point of it, and for this purpose we shall plainly have
to suppose the numbers carried out into an infinite number of places of
decimals. These numbers must be ranged along the line in unbroken
sequence. Further, in order that such a scale of numbers should be of
any use, it must be capable of being shifted into new positions, each
number continuing to be attached to a single distinct point. Now it is
found that if this is true for “imaginary” as well as for real points
(an expression which I cannot stop to elucidate), any such shifting will
necessarily leave two numbers attached to the same points as before. So
that when the scale is moved over the line by any continuous series of
shiftings of one kind, there are two points which no numbers on the
scale can ever reach, except the numbers fixed there. This pair of
points, thus unattainable in measurement, is called the Absolute. These
two points may be distinct and real, or they may coincide, or they may
be both imaginary. As an example of a linear quantity with a double
absolute we may take probability, which ranges from an unattainable
absolute certainty _against_ a proposition to an equally unattainable
absolute certainty _for_ it. A line, according to ordinary notions, we
have seen is a linear quantity where the two points at infinity
coincide. A velocity is another example. A train going with infinite
velocity from Chicago to New York would be at all the points on the line
at the very same instant, and if the time of transit were reduced to
less than nothing it would be moving in the other direction. An angle is
a familiar example of a mode of magnitude with no real immeasurable
values. One of the questions philosophy has to consider is whether the
development of the universe is like the increase of an angle, so that it
proceeds forever without tending toward anything unattained, which I
take to be the Epicurean view, or whether the universe sprang from a
chaos in the infinitely distant past to tend toward something different
in the infinitely distant future, or whether the universe sprang from
nothing in the past to go on indefinitely toward a point in the
infinitely distant future, which, were it attained, would be the mere
nothing from which it set out.

The doctrine of the absolute applied to space comes to this, that
either—

First, space is, as Euclid teaches, both _unlimited_ and _immeasurable_,
so that the infinitely distant parts of any plane seen in perspective
appear as a straight line, in which case the sum of the three angles of
a triangle amounts to 180°; or,

Second, space is _immeasurable_ but _limited_, so that the infinitely
distant parts of any plane seen in perspective appear as a circle,
beyond which all is blackness, and in this case the sum of the three
angles of a triangle is less than 180° by an amount proportional to the
area of the triangle; or,

Third, space is _unlimited_ but _finite_, (like the surface of a
sphere), so that it has no infinitely distant parts; but a finite
journey along any straight line would bring one back to his original
position, and looking off with an unobstructed view one would see the
back of his own head enormously magnified, in which case the sum of the
three angles of a triangle exceeds 180° by an amount proportional to the
area.

Which of these three hypotheses is true we know not. The largest
triangles we can measure are such as have the earth’s orbit for base,
and the distance of a fixed star for altitude. The angular magnitude
resulting from subtracting the sum of the two angles at the base of such
a triangle from 180° is called the star’s _parallax_. The parallaxes of
only about forty stars have been measured as yet. Two of them come out
negative, that of Arided (α Cycni), a star of magnitude 1-1/2, which is
—0.“082, according to C. A. F. Peters, and that of a star of magnitude
7-3/4, known as Piazzi III 422, which is —0.”045, according to R. S.
Ball. But these negative parallaxes are undoubtedly to be attributed to
errors of observation; for the probable error of such a determination is
about ± 0.“075, and it would be strange indeed if we were to be able to
see, as it were, more than half way round space, without being able to
see stars with larger negative parallaxes. Indeed, the very fact that of
all the parallaxes measured only two come out negative would be a strong
argument that the smallest parallaxes really amount to +0.”1, were it
not for the reflection that the publication of other negative parallaxes
may have been suppressed. I think we may feel confident that the
parallax of the furthest star lies somewhere between -0.”05 and +0.”15,
and within another century our grandchildren will surely know whether
the three angles of a triangle are greater or less than 180°,—that they
are _exactly_ that amount is what nobody ever can be justified in
concluding. It is true that according to the axioms of geometry the sum
of the three sides of a triangle are precisely 180°; but these axioms
are now exploded, and geometers confess that they, as geometers, know
not the slightest reason for supposing them to be precisely true. They
are expressions of our inborn conception of space, and as such are
entitled to credit, so far as their truth could have influenced the
formation of the mind. But that affords not the slightest reason for
supposing them exact.

Now, metaphysics has always been the ape of mathematics. Geometry
suggested the idea of a demonstrative system of absolutely certain
philosophical principles; and the ideas of the metaphysicians have at
all times been in large part drawn from mathematics. The metaphysical
axioms are imitations of the geometrical axioms; and now that the latter
have been thrown overboard, without doubt the former will be sent after
them. It is evident, for instance, that we can have no reason to think
that every phenomenon in all its minutest details is precisely
determined by law. That there is an arbitrary element in the universe we
see,—namely, its variety. This variety must be attributed to spontaneity
in some form.

Had I more space, I now ought to show how important for philosophy is
the mathematical conception of continuity. Most of what is true in Hegel
is a darkling glimmer of a conception which the mathematicians had long
before made pretty clear, and which recent researches have still further
illustrated.

Among the many principles of Logic which find their application in
Philosophy, I can here only mention one. Three conceptions are
perpetually turning up at every point in every theory of logic, and in
the most rounded systems they occur in connection with one another. They
are conceptions so very broad and consequently indefinite that they are
hard to seize and may be easily overlooked. I call them the conceptions
of First, Second, Third. First is the conception of being or existing
independent of anything else. Second is the conception of being relative
to, the conception of reaction with, something else. Third is the
conception of mediation, whereby a first and second are brought into
relation. To illustrate these ideas, I will show how they enter into
those we have been considering. The origin of things, considered not as
leading to anything, but in itself, contains the idea of First, the end
of things that of Second, the process mediating between them that of
Third. A philosophy which emphasizes the idea of the One, is generally a
dualistic philosophy in which the conception of Second receives
exaggerated attention; for this One (though of course involving the idea
of First) is always the other of a manifold which is not one. The idea
of the Many, because variety is arbitrariness and arbitrariness is
repudiation of any Secondness, has for its principal component the
conception of First. In psychology Feeling is First, Sense of reaction
Second, General conception Third, or mediation. In biology, the idea of
arbitrary sporting is First, heredity is Second, the process whereby the
accidental characters become fixed is Third. Chance is First, Law is
Second, the tendency to take habits is Third. Mind is First, Matter is
Second, Evolution is Third.

Such are the materials out of which chiefly a philosophical theory ought
to be built, in order to represent the state of knowledge to which the
nineteenth century has brought us. Without going into other important
questions of philosophical architectonic, we can readily foresee what
sort of a metaphysics would appropriately be constructed from those
conceptions. Like some of the most ancient and some of the most recent
speculations it would be a Cosmogonic Philosophy. It would suppose that
in the beginning,—infinitely remote,—there was a chaos of unpersonalized
feeling, which being without connection or regularity would properly be
without existence. This feeling, sporting here and there in pure
arbitrariness, would have started the germ of a generalizing tendency.
Its other sportings would be evanescent, but this would have a growing
virtue. Thus, the tendency to habit would be started; and from this with
the other principles of evolution all the regularities of the universe
would be evolved. At any time, however, an element of pure chance
survives and will remain until the world becomes an absolutely perfect,
rational, and symmetrical system, in which mind is at last crystallized
in the infinitely distant future.

That idea has been worked out by me with elaboration. It accounts for
the main features of the universe as we know it,—the characters of time,
space, matter, force, gravitation, electricity, etc. It predicts many
more things which new observations can alone bring to the test. May some
future student go over this ground again, and have the leisure to give
his results to the world.

Footnote 54:

  _The Monist_, January, 1891.

Footnote 55:

  The neo-Darwinian, Weismann, has shown that mortality would almost
  necessarily result from the action of the Darwinian principle.

Footnote 56:

  A feeling may certainly be compound, but only in virtue of a
  perception which is not that feeling nor any feeling at all.

Footnote 57:

  [The reader will find further light on the following illustration in
  any text-book of projective geometry, e.g., Reye, _Geometry of
  Position_, I, pp. 17-24, or _Encyc. Britannica_, XI, p. 689.]

Footnote 58:

  [A more familiar example of this is the introduction of irrational or
  absurd numbers like √2. After it was proved that no ratio of two
  integers could possibly equal √2 the idea of number was generalized to
  include the latter. Fractions and the so-called imaginary numbers
  illustrate the same process of generalization for the sake of making
  certain operations (i.e. division and finding the root) continuously
  applicable.]




               II. THE DOCTRINE OF NECESSITY EXAMINED[59]


In _The Monist_ for January, 1891, I endeavored to show what elementary
ideas ought to enter into our view of the universe. I may mention that
on those considerations I had already grounded a cosmical theory, and
from it had deduced a considerable number of consequences capable of
being compared with experience. This comparison is now in progress, but
under existing circumstances must occupy many years.

I propose here to examine the common belief that every single fact in
the universe is precisely determined by law. It must not be supposed
that this is a doctrine accepted everywhere and at all times by all
rational men. Its first advocate appears to have been Democritus, the
atomist, who was led to it, as we are informed, by reflecting upon the
“impenetrability, translation, and impact of matter (ἀντιτυπία καὶ φορὰ
καὶ πληγὴ τῆς ὕλης).” That is to say, having restricted his attention to
a field where no influence other than mechanical constraint could
possibly come before his notice, he straightway jumped to the conclusion
that throughout the universe that was the sole principle of action,—a
style of reasoning so usual in our day with men not unreflecting as to
be more than excusable in the infancy of thought. But Epicurus, in
revising the atomic doctrine and repairing its defences, found himself
obliged to suppose that atoms swerve from their courses by spontaneous
chance; and thereby he conferred upon the theory life and entelechy. For
we now see clearly that the peculiar function of the molecular
hypothesis in physics is to open an entry for the calculus of
probabilities. Already, the prince of philosophers had repeatedly and
emphatically condemned the dictum of Democritus (especially in the
“Physics,” Book II, chapters iv, v, vi), holding that events come to
pass in three ways, namely, (1) by external compulsion, or the action of
efficient causes, (2) by virtue of an inward nature, or the influence of
final causes, and (3) irregularly without definite cause, but just by
absolute chance; and this doctrine is of the inmost essence of
Aristotelianism. It affords, at any rate, a valuable enumeration of the
possible ways in which anything can be supposed to have come about. The
freedom of the will, too, was admitted both by Aristotle and by
Epicurus. But the Stoa, which in every department seized upon the most
tangible, hard, and lifeless element, and blindly denied the existence
of every other, which, for example, impugned the validity of the
inductive method and wished to fill its place with the _reductio ad
absurdum_, very naturally became the one school of ancient philosophy to
stand by a strict necessitarianism, thus returning to a single principle
of Democritus that Epicurus had been unable to swallow. Necessitarianism
and materialism with the Stoics went hand in hand, as by affinity they
should. At the revival of learning, Stoicism met with considerable
favor, partly because it departed just enough from Aristotle to give it
the spice of novelty, and partly because its superficialities well
adapted it for acceptance by students of literature and art who wanted
their philosophy drawn mild. Afterwards, the great discoveries in
mechanics inspired the hope that mechanical principles might suffice to
explain the universe; and though without logical justification, this
hope has since been continually stimulated by subsequent advances in
physics. Nevertheless, the doctrine was in too evident conflict with the
freedom of the will and with miracles to be generally acceptable, at
first. But meantime there arose that most widely spread of philosophical
blunders, the notion that associationalism belongs intrinsically to the
materialistic family of doctrines; and thus was evolved the theory of
motives; and libertarianism became weakened. At present, historical
criticism has almost exploded the miracles, great and small; so that the
doctrine of necessity has never been in so great vogue as now.

The proposition in question is that the state of things existing at any
time, together with certain immutable laws, completely determine the
state of things at every other time (for a limitation to _future_ time
is indefensible). Thus, given the state of the universe in the original
nebula, and given the laws of mechanics, a sufficiently powerful mind
could deduce from these data the precise form of every curlicue of every
letter I am now writing.

Whoever holds that every act of the will as well as every idea of the
mind is under the rigid governance of a necessity co-ordinated with that
of the physical world, will logically be carried to the proposition that
minds are part of the physical world in such a sense that the laws of
mechanics determine everything that happens according to immutable
attractions and repulsions. In that case, that instantaneous state of
things from which every other state of things is calculable consists in
the positions and velocities of all the particles at any instant. This,
the usual and most logical form of necessitarianism, is called the
mechanical philosophy.

When I have asked thinking men what reason they had to believe that
every fact in the universe is precisely determined by law, the first
answer has usually been that the proposition is a “presupposition” or
postulate of scientific reasoning. Well, if that is the best that can be
said for it, the belief is doomed. Suppose it be “postulated”: that does
not make it true, nor so much as afford the slightest rational motive
for yielding it any credence. It is as if a man should come to borrow
money, and when asked for his security, should reply he “postulated” the
loan. To “postulate” a proposition is no more than to hope it is true.
There are, indeed, practical emergencies in which we act upon
assumptions of certain propositions as true, because if they are not so,
it can make no difference how we act. But all such propositions I take
to be hypotheses of individual facts. For it is manifest that no
universal principle can in its universality be comprised in a special
case or can be requisite for the validity of any ordinary inference. To
say, for instance, that the demonstration by Archimedes of the property
of the lever would fall to the ground if men were endowed with
free-will, is extravagant; yet this is implied by those who make a
proposition incompatible with the freedom of the will the postulate of
all inference. Considering, too, that the conclusions of science make no
pretence to being more than probable, and considering that a probable
inference can at most only suppose something to be most frequently, or
otherwise approximately, true, but never that anything is precisely true
without exception throughout the universe, we see how far this
proposition in truth is from being so postulated.

But the whole notion of a postulate being involved in reasoning
appertains to a by-gone and false conception of logic. Non-deductive, or
ampliative inference, is of three kinds: induction, hypothesis, and
analogy. If there be any other modes, they must be extremely unusual and
highly complicated, and may be assumed with little doubt to be of the
same nature as those enumerated. For induction, hypothesis, and analogy,
as far as their ampliative character goes, that is, so far as they
conclude something not implied in the premises, depend upon one
principle and involve the same procedure. All are essentially inferences
from sampling. Suppose a ship arrives at Liverpool laden with wheat in
bulk. Suppose that by some machinery the whole cargo be stirred up with
great thoroughness. Suppose that twenty-seven thimblefuls be taken
equally from the forward, midships, and aft parts, from the starboard,
center, and larboard parts, and from the top, half depth, and lower
parts of her hold, and that these being mixed and the grains counted,
four-fifths of the latter are found to be of quality _A_. Then we infer,
experientially and provisionally, that approximately four-fifths of all
the grain in the cargo is of the same quality. I say we infer this
_experientially_ and _provisionally_. By saying that we infer it
_experientially_, I mean that our conclusion makes no pretension to
knowledge of wheat-in-itself, our ἀλήθεια, as the derivation of that
word implies, has nothing to do with _latent_ wheat. We are dealing only
with the matter of possible experience,—experience in the full
acceptation of the term as something not merely affecting the senses but
also as the subject of thought. If there be any wheat hidden on the
ship, so that it can neither turn up in the sample nor be heard of
subsequently from purchasers,—or if it be half-hidden, so that it may,
indeed, turn up, but is less likely to do so than the rest,—or if it can
affect our senses and our pockets, but from some strange cause or
causelessness cannot be reasoned about,—all such wheat is to be excluded
(or have only its proportional weight) in calculating that true
proportion of quality _A_, to which our inference seeks to approximate.
By saying that we draw the inference _provisionally_, I mean that we do
not hold that we have reached any assigned degree of approximation as
yet, but only hold that if our experience be indefinitely extended, and
if every fact of whatever nature, as fast as it presents itself, be duly
applied, according to the inductive method, in correcting the inferred
ratio, then our approximation will become indefinitely close in the long
run; that is to say, close to the experience _to come_ (not merely close
by the exhaustion of a finite collection) so that if experience in
general is to fluctuate irregularly to and fro, in a manner to deprive
the ratio sought of all definite value, we shall be able to find out
approximately within what limits it fluctuates, and if, after having one
definite value, it changes and assumes another, we shall be able to find
that out, and in short, whatever may be the variations of this ratio in
experience, experience indefinitely extended will enable us to detect
them, so as to predict rightly, at last, what its ultimate value may be,
if it have any ultimate value, or what the ultimate law of succession of
values may be, if there be any such ultimate law, or that it ultimately
fluctuates irregularly within certain limits, if it do so ultimately
fluctuate. Now our inference, claiming to be no more than thus
experiential and provisional, manifestly involves no postulate whatever.

For what is a postulate? It is the formulation of a material fact which
we are not entitled to assume as a premise, but the truth of which is
requisite to the validity of an inference. Any fact, then, which might
be supposed postulated, must either be such that it would ultimately
present itself in experience, or not. If it will present itself, we need
not postulate it now in our provisional inference, since we shall
ultimately be entitled to use it as a premise. But if it never would
present itself in experience, our conclusion is valid but for the
possibility of this fact being otherwise than assumed, that is, it is
valid as far as possible experience goes, and that is all that we claim.
Thus, every postulate is cut off, either by the provisionality or by the
experientiality of our inference. For instance, it has been said that
induction postulates that, if an indefinite succession of samples be
drawn, examined, and thrown back each before the next is drawn, then in
the long run every grain will be drawn as often as any other, that is to
say, postulates that the ratio of the numbers of times in which any two
are drawn will indefinitely approximate to unity. But no such postulate
is made; for if, on the one hand, we are to have no other experience of
the wheat than from such drawings, it is the ratio that presents itself
in those drawings and not the ratio which belongs to the wheat in its
latent existence that we are endeavoring to determine; while if, on the
other hand, there is some other mode by which the wheat is to come under
our knowledge, equivalent to another kind of sampling, so that after all
our care in stirring up the wheat, some experiential grains will present
themselves in the first sampling operation more often than others in the
long run, this very singular fact will be sure to get discovered by the
inductive method, which must avail itself of every sort of experience;
and our inference, which was only provisional, corrects itself at last.
Again, it has been said, that induction postulates that under like
circumstances like events will happen, and that this postulate is at
bottom the same as the principle of universal causation. But this is a
blunder, or _bevue_, due to thinking exclusively of inductions where the
concluded ratio is either 1 or 0. If any such proposition were
postulated, it would be that under like circumstances (the circumstances
of drawing the different samples) different events occur in the same
proportions in all the different sets,—a proposition which is false and
even absurd. But in truth no such thing is postulated, the experiential
character of the inference reducing the condition of validity to this,
that if a certain result does not occur, the opposite result will be
manifested, a condition assured by the provisionality of the inference.
But it may be asked whether it is not conceivable that every instance of
a certain class destined to be ever employed as a datum of induction
should have one character, while every instance destined not to be so
employed should have the opposite character. The answer is that in that
case, the instances excluded from being subjects of reasoning would not
be experienced in the full sense of the word, but would be among these
_latent_ individuals of which our conclusion does not pretend to speak.

To this account of the rationale of induction I know of but one
objection worth mention: it is that I thus fail to deduce the full
degree of force which this mode of inference in fact possesses; that
according to my view, no matter how thorough and elaborate the stirring
and mixing process had been, the examination of a single handful of
grain would not give me any assurance, sufficient to risk money upon
that the next handful would not greatly modify the concluded value of
the ratio under inquiry, while, in fact, the assurance would be very
high that this ratio was not greatly in error. If the true ratio of
grains of quality _A_ were 0.80 and the handful contained a thousand
grains, nine such handfuls out of every ten would contain from 780 to
820 grains of quality _A_. The answer to this is that the calculation
given is correct when we know that the units of this handful and the
quality inquired into have the normal independence of one another, if
for instance the stirring has been complete and the character sampled
for has been settled upon in advance of the examination of the sample.
But in so far as these conditions are not known to be complied with, the
above figures cease to be applicable. Random sampling and predesignation
of the character sampled for should always be striven after in inductive
reasoning, but when they cannot be attained, so long as it is conducted
honestly, the inference retains some value. When we cannot ascertain how
the sampling has been done or the sample-character selected, induction
still has the essential validity which my present account of it shows it
to have.

I do not think a man who combines a willingness to be convinced with a
power of appreciating an argument upon a difficult subject can resist
the reasons which have been given to show that the principle of
universal necessity cannot be defended as being a postulate of
reasoning. But then the question immediately arises whether it is not
proved to be true, or at least rendered highly probable, by observation
of nature.

Still, this question ought not long to arrest a person accustomed to
reflect upon the force of scientific reasoning. For the essence of the
necessitarian position is that certain continuous quantities have
certain exact values. Now, how can observation determine the value of
such a quantity with a probable error absolutely _nil_? To one who is
behind the scenes, and knows that the most refined comparisons of
masses, lengths, and angles, far surpassing in precision all other
measurements, yet fall behind the accuracy of bank-accounts, and that
the ordinary determinations of physical constants, such as appear from
month to month in the journals, are about on a par with an upholsterer’s
measurements of carpets and curtains, the idea of mathematical
exactitude being demonstrated in the laboratory will appear simply
ridiculous. There is a recognized method of estimating the probable
magnitudes of errors in physics,—the method of least squares. It is
universally admitted that this method makes the errors smaller than they
really are; yet even according to that theory an error indefinitely
small is indefinitely improbable; so that any statement to the effect
that a certain continuous quantity has a certain exact value, if
well-founded at all, must be founded on something other than
observation.

Still, I am obliged to admit that this rule is subject to a certain
qualification. Namely, it only applies to continuous[60] quantity. Now,
certain kinds of continuous quantity are discontinuous at one or at two
limits, and for such limits the rule must be modified. Thus, the length
of a line cannot be less than zero. Suppose, then, the question arises
how long a line a certain person had drawn from a marked point on a
piece of paper. If no line at all can be seen, the observed length is
zero; and the only conclusion this observation warrants is that the
length of the line is less than the smallest length visible with the
optical power employed. But indirect observations,—for example, that the
person supposed to have drawn the line was never within fifty feet of
the paper,—may make it probable that no line at all was made, so that
the concluded length will be strictly zero. In like manner, experience
no doubt would warrant the conclusion that there is absolutely _no_
indigo in a given ear of wheat, and absolutely _no_ attar in a given
lichen. But such inferences can only be rendered valid by positive
experiential evidence, direct or remote, and cannot rest upon a mere
inability to detect the quantity in question. We have reason to think
there is no indigo in the wheat, because we have remarked that wherever
indigo is produced it is produced in considerable quantities, to mention
only one argument. We have reason to think there is no attar in the
lichen, because essential oils seem to be in general peculiar to single
species. If the question had been whether there was iron in the wheat or
the lichen, though chemical analysis should fail to detect its presence,
we should think some of it probably was there, since iron is almost
everywhere. Without any such information, one way or the other, we could
only abstain from any opinion as to the presence of the substance in
question. It cannot, I conceive, be maintained that we are in any
_better_ position than this in regard to the presence of the element of
chance or spontaneous departures from law in nature.

Those observations which are generally adduced in favor of mechanical
causation simply prove that there is an element of regularity in nature,
and have no bearing whatever upon the question of whether such
regularity is exact and universal, or not. Nay, in regard to this
_exactitude_, all observation is directly _opposed_ to it; and the most
that can be said is that a good deal of this observation can be
explained away. Try to verify any law of nature, and you will find that
the more precise your observations, the more certain they will be to
show irregular departures from the law. We are accustomed to ascribe
these, and I do not say wrongly, to errors of observation; yet we cannot
usually account for such errors in any antecedently probable way. Trace
their causes back far enough, and you will be forced to admit they are
always due to arbitrary determination, or chance.

But it may be asked whether if there were an element of real chance in
the universe it must not occasionally be productive of signal effects
such as could not pass unobserved. In answer to this question, without
stopping to point out that there is an abundance of great events which
one might be tempted to suppose were of that nature, it will be simplest
to remark that physicists hold that the particles of gases are moving
about irregularly, substantially as if by real chance, and that by the
principles of probabilities there must occasionally happen to be
concentrations of heat in the gases contrary to the second law of
thermodynamics, and these concentrations, occurring in explosive
mixtures, must sometimes have tremendous effects. Here, then, is in
substance the very situation supposed; yet no phenomena ever have
resulted which we are forced to attribute to such chance concentration
of heat, or which anybody, wise or foolish, has ever dreamed of
accounting for in that manner.

In view of all these considerations, I do not believe that anybody, not
in a state of case-hardened ignorance respecting the logic of science,
can maintain that the precise and universal conformity of facts to law
is clearly proved, or even rendered particularly probable, by any
observations hitherto made. In this way, the determined advocate of
exact regularity will soon find himself driven to _a priori_ reasons to
support his thesis. These received such a socdolager from Stuart Mill in
his Examination of Hamilton, that holding to them now seems to me to
denote a high degree of imperviousness to reason; so that I shall pass
them by with little notice.

To say that we cannot help believing a given proposition is no argument,
but it is a conclusive fact if it be true; and with the substitution of
“I” for “we,” it is true in the mouths of several classes of minds, the
blindly passionate, the unreflecting and ignorant, and the person who
has overwhelming evidence before his eyes. But that which has been
inconceivable to-day has often turned out indisputable on the morrow.
Inability to conceive is only a stage through which every man must pass
in regard to a number of beliefs,—unless endowed with extraordinary
obstinacy and obtuseness. His understanding is enslaved to some blind
compulsion which a vigorous mind is pretty sure soon to cast off.

Some seek to back up the _a priori_ position with empirical arguments.
They say that the exact regularity of the world is a natural belief, and
that natural beliefs have generally been confirmed by experience. There
is some reason in this. Natural beliefs, however, if they generally have
a foundation of truth, also require correction and purification from
natural illusions. The principles of mechanics are undoubtedly natural
beliefs; but, for all that, the early formulations of them were
exceedingly erroneous. The general approximation to truth in natural
beliefs is, in fact, a case of the general adaptation of genetic
products to recognizable utilities or ends. Now, the adaptations of
nature, beautiful and often marvelous as they verily are, are never
found to be quite perfect; so that the argument is quite _against_ the
absolute exactitude of any natural belief, including that of the
principle of causation.

Another argument, or convenient commonplace, is that absolute chance is
_inconceivable_. (This word has eight current significations. The
_Century Dictionary_ enumerates six.) Those who talk like this will
hardly be persuaded to say in what sense they mean that chance is
inconceivable. Should they do so, it would easily be shown either that
they have no sufficient reason for the statement or that the
inconceivability is of a kind which does not prove that chance is
non-existent.

Another _a priori_ argument is that chance is unintelligible; that is to
say, while it may perhaps be conceivable, it does not disclose to the
eye of reason the how or why of things; and since a hypothesis can only
be justified so far as it renders some phenomenon intelligible, we never
can have any right to suppose absolute chance to enter into the
production of anything in nature. This argument may be considered in
connection with two others. Namely, instead of going so far as to say
that the supposition of chance can _never_ properly be used to explain
any observed fact, it may be alleged merely that no facts are known
which such a supposition could in any way help in explaining. Or again,
the allegation being still further weakened, it may be said that since
departures from law are not unmistakably observed, chance is not a _vera
causa_, and ought not unnecessarily to be introduced into a hypothesis.

These are no mean arguments, and require us to examine the matter a
little more closely. Come, my superior opponent, let me learn from your
wisdom. It seems to me that every throw of sixes with a pair of dice is
a manifest instance of chance.

“While you would hold a throw of deuce-ace to be brought about by
necessity?” (The opponent’s supposed remarks are placed in quotation
marks.)

Clearly one throw is as much chance as another.

“Do you think throws of dice are of a different nature from other
events?”

I see that I must say that _all_ the diversity and specificalness of
events is attributable to chance.

“Would you, then, deny that there is any regularity in the world?”

That is clearly undeniable. I must acknowledge there is an approximate
regularity, and that every event is influenced by it. But the
diversification, specificalness, and irregularity of things I suppose is
chance. A throw of sixes appears to me a case in which this element is
particularly obtrusive.

“If you reflect more deeply, you will come to see that _chance_ is only
a name for a cause that is unknown to us.”

Do you mean that we have no idea whatever what kind of causes could
bring about a throw of sixes?

“On the contrary, each die moves under the influence of precise
mechanical laws.”

But it appears to me that it is not these _laws_ which made the die turn
up sixes; for these laws act just the same when other throws come up.
The chance lies in the diversity of throws; and this diversity cannot be
due to laws which are immutable.

“The diversity is due to the diverse circumstances under which the laws
act. The dice lie differently in the box, and the motion given to the
box is different. These are the unknown causes which produce the throws,
and to which we give the name of chance; not the mechanical law which
regulates the operation of these causes. You see you are already
beginning to think more clearly about this subject.”

Does the operation of mechanical law not increase the diversity?

“Properly not. You must know that the instantaneous state of a system of
particles is defined by six times as many numbers as there are
particles, three for the co-ordinates of each particle’s position, and
three more for the components of its velocity. This number of numbers,
which expresses the amount of diversity in the system, remains the same
at all times. There may be, to be sure, some kind of relation between
the co-ordinates and component velocities of the different particles, by
means of which the state of the system might be expressed by a smaller
number of numbers. But, if this is the case, a precisely corresponding
relationship must exist between the co-ordinates and component
velocities at any other time, though it may doubtless be a relation less
obvious to us. Thus, the intrinsic complexity of the system is the same
at all times.”

Very well, my obliging opponent, we have now reached an issue. You think
all the arbitrary specifications of the universe were introduced in one
dose, in the beginning, if there was a beginning, and that the variety
and complication of nature has always been just as much as it is now.
But I, for my part, think that the diversification, the specification,
has been continually taking place. Should you condescend to ask me why I
so think, I should give my reasons as follows:

(1) Question any science which deals with the course of time. Consider
the life of an individual animal or plant, or of a mind. Glance at the
history of states, of institutions, of language, of ideas. Examine the
successions of forms shown by paleontology, the history of the globe as
set forth in geology, of what the astronomer is able to make out
concerning the changes of stellar systems. Everywhere the main fact is
growth and increasing complexity. Death and corruption are mere
accidents or secondary phenomena. Among some of the lower organisms, it
is a moot point with biologists whether there be anything which ought to
be called death. Races, at any rate, do not die out except under
unfavorable circumstances. From these broad and ubiquitous facts we may
fairly infer, by the most unexceptionable logic, that there is probably
in nature some agency by which the complexity and diversity of things
can be increased; and that consequently the rule of mechanical necessity
meets in some way with interference.

(2) By thus admitting pure spontaneity or life as a character of the
universe, acting always and everywhere though restrained within narrow
bounds by law, producing infinitesimal departures from law continually,
and great ones with infinite infrequency, I account for all the variety
and diversity of the universe, in the only sense in which the really
_sui generis_ and new can be said to be accounted for. The ordinary view
has to admit the inexhaustible multitudinous variety of the world, has
to admit that its mechanical law cannot account for this in the least,
that variety can spring only from spontaneity, and yet denies without
any evidence or reason the existence of this spontaneity, or else shoves
it back to the beginning of time and supposes it dead ever since. The
superior logic of my view appears to me not easily controverted.

(3) When I ask the necessitarian how he would explain the diversity and
irregularity of the universe, he replies to me out of the treasury of
his wisdom that irregularity is something which from the nature of
things we must not seek to explain. Abashed at this, I seek to cover my
confusion by asking how he would explain the uniformity and regularity
of the universe, whereupon he tells me that the laws of nature are
immutable and ultimate facts, and no account is to be given of them. But
my hypothesis of spontaneity does explain irregularity, in a certain
sense; that is, it explains the general fact of irregularity, though
not, of course, what each lawless event is to be. At the same time, by
thus loosening the bond of necessity, it gives room for the influence of
another kind of causation, such as seems to be operative in the mind in
the formation of associations, and enables us to understand how the
uniformity of nature could have been brought about. That single events
should be hard and unintelligible, logic will permit without difficulty:
we do not expect to make the shock of a personally experienced
earthquake appear natural and reasonable by any amount of cogitation.
But logic does expect things _general_ to be understandable. To say that
there is a universal law, and that it is a hard, ultimate,
unintelligible fact, the why and wherefore of which can never be
inquired into, at this a sound logic will revolt; and will pass over at
once to a method of philosophizing which does not thus barricade the
road of discovery.

(4) Necessitarianism cannot logically stop short of making the whole
action of the mind a part of the physical universe. Our notion that we
decide what we are going to do, if as the necessitarian says, it has
been calculable since the earliest times, is reduced to illusion.
Indeed, consciousness in general thus becomes a mere illusory aspect of
a material system. What we call red, green, and violet are in reality
only different rates of vibration. The sole reality is the distribution
of qualities of matter in space and time. Brain-matter is protoplasm in
a certain degree and kind of complication,—a certain arrangement of
mechanical particles. Its feeling is but an inward aspect, a phantom.
For, from the positions and velocities of the particles at any one
instant, and the knowledge of the immutable forces, the positions at all
other times are calculable; so that the universe of space, time, and
matter is a rounded system uninterfered with from elsewhere. But from
the state of feeling at any instant, there is no reason to suppose the
states of feeling at all other instants are thus exactly calculable; so
that feeling is, as I said, a mere fragmentary and illusive aspect of
the universe. This is the way, then, that necessitarianism has to make
up its accounts. It enters consciousness under the head of sundries, as
a forgotten trifle; its scheme of the universe would be more
satisfactory if this little fact could be dropped out of sight. On the
other hand, by supposing the rigid exactitude of causation to yield, I
care not how little,—be it but by a strictly infinitesimal amount,—we
gain room to insert mind into our scheme, and to put it into the place
where it is needed, into the position which, as the sole
self-intelligible thing, it is entitled to occupy, that of the fountain
of existence; and in so doing we resolve the problem of the connection
of soul and body.

(5) But I must leave undeveloped the chief of my reasons, and can only
adumbrate it. The hypothesis of chance-spontaneity is one whose
inevitable consequences are capable of being traced out with
mathematical precision into considerable detail. Much of this I have
done and find the consequences to agree with observed facts to an extent
which seems to me remarkable. But the matter and methods of reasoning
are novel, and I have no right to promise that other mathematicians
shall find my deductions as satisfactory as I myself do, so that the
strongest reason for my belief must for the present remain a private
reason of my own, and cannot influence others. I mention it to explain
my own position; and partly to indicate to future mathematical
speculators a veritable goldmine, should time and circumstances and the
abridger of all joys prevent my opening it to the world.

If now I, in my turn, inquire of the necessitarian why he prefers to
suppose that all specification goes back to the beginning of things, he
will answer me with one of those last three arguments which I left
unanswered.

First, he may say that chance is a thing absolutely unintelligible, and,
therefore, that we never can be entitled to make such a supposition. But
does not this objection smack of naïve impudence? It is not mine, it is
his own conception of the universe which leads abruptly up to hard,
ultimate, inexplicable, immutable law, on the one hand, and to
inexplicable specification and diversification of circumstances on the
other. My view, on the contrary, hypothetises nothing at all, unless it
be hypothesis to say that all specification came about in some sense,
and is not to be accepted as unaccountable. To undertake to account for
anything by saying boldly that it is due to chance would, indeed, be
futile. But this I do not do. I make use of chance chiefly to make room
for a principle of generalization, or tendency to form habits, which I
hold has produced all regularities. The mechanical philosopher leaves
the whole specification of the world utterly unaccounted for, which is
pretty nearly as bad as to boldly attribute it to chance. I attribute it
altogether to chance, it is true, but to chance in the form of a
spontaneity which is to some degree regular. It seems to me clear at any
rate that one of these two positions must be taken, or else
specification must be supposed due to a spontaneity which develops
itself in a certain and not in a chance way, by an objective logic like
that of Hegel. This last way I leave as an open possibility, for the
present; for it is as much opposed to the necessitarian scheme of
existence as my own theory is.

Secondly, the necessitarian may say there are, at any rate, no observed
phenomena which the hypothesis of chance could aid in explaining. In
reply, I point first to the phenomenon of growth and developing
complexity, which appears to be universal, and which though it may
possibly be an affair of mechanism perhaps, certainly presents all the
appearance of increasing diversification. Then, there is variety itself,
beyond comparison the most obtrusive character of the universe: no
mechanism can account for this. Then, there is the very fact the
necessitarian most insists upon, the regularity of the universe which
for him serves only to block the road of inquiry. Then, there are the
regular relationships between the laws of nature,—similarities and
comparative characters, which appeal to our intelligence as its cousins,
and call upon us for a reason. Finally, there is consciousness, feeling,
a patent fact enough, but a very inconvenient one to the mechanical
philosopher.

Thirdly, the necessitarian may say that chance is not a _vera causa_,
that we cannot know positively there is any such element in the
universe. But the doctrine of the _vera causa_ has nothing to do with
elementary conceptions. Pushed to that extreme, it at once cuts off
belief in the existence of a material universe; and without that
necessitarianism could hardly maintain its ground. Besides, variety is a
fact which must be admitted; and the theory of chance merely consists in
supposing this diversification does not antedate all time. Moreover, the
avoidance of hypotheses involving causes nowhere positively known to
act—is only a recommendation of logic, not a positive command. It cannot
be formulated in any precise terms without at once betraying its
untenable character,—I mean as rigid rule, for as a recommendation it is
wholesome enough.

I believe I have thus subjected to fair examination all the important
reasons for adhering to the theory of universal necessity, and have
shown their nullity. I earnestly beg that whoever may detect any flaw in
my reasoning will point it out to me, either privately or publicly; for
if I am wrong, it much concerns me to be set right speedily. If my
argument remains unrefuted, it will be time, I think, to doubt the
absolute truth of the principle of universal law; and when once such a
doubt has obtained a living root in any man’s mind, my cause with him, I
am persuaded, is gained.

Footnote 59:

  _The Monist_, April, 1892.

Footnote 60:

  _Continuous_ is not exactly the right word, but I let it go to avoid a
  long and irrelevant discussion.




                        III. THE LAW OF MIND[61]


In an article published in _The Monist_ for January, 1891, I endeavored
to show what ideas ought to form the warp of a system of philosophy, and
particularly emphasized that of absolute chance. In the number of April,
1892, I argued further in favor of that way of thinking, which it will
be convenient to christen _tychism_ (from τύχη, chance). A serious
student of philosophy will be in no haste to accept or reject this
doctrine; but he will see in it one of the chief attitudes which
speculative thought may take, feeling that it is not for an individual,
nor for an age, to pronounce upon a fundamental question of philosophy.
That is a task for a whole era to work out. I have begun by showing that
_tychism_ must give birth to an evolutionary cosmology, in which all the
regularities of nature and of mind are regarded as products of growth,
and to a Schelling-fashioned idealism which holds matter to be mere
specialized and partially deadened mind. I may mention, for the benefit
of those who are curious in studying mental biographies, that I was born
and reared in the neighborhood of Concord,—I mean in Cambridge,—at the
time when Emerson, Hedge, and their friends were disseminating the ideas
that they had caught from Schelling, and Schelling from Plotinus, from
Boehm, or from God knows what minds stricken with the monstrous
mysticism of the East. But the atmosphere of Cambridge held many an
antiseptic against Concord transcendentalism; and I am not conscious of
having contracted any of that virus. Nevertheless, it is probable that
some cultured bacilli, some benignant form of the disease was implanted
in my soul, unawares, and that now, after long incubation, it comes to
the surface, modified by mathematical conceptions and by training in
physical investigations.

The next step in the study of cosmology must be to examine the general
law of mental action. In doing this, I shall for the time drop my
tychism out of view, in order to allow a free and independent expansion
to another conception signalized in my first _Monist_ paper as one of
the most indispensable to philosophy, though it was not there dwelt
upon; I mean the idea of continuity. The tendency to regard continuity,
in the sense in which I shall define it, as an idea of prime importance
in philosophy may conveniently be termed _synechism_. The present paper
is intended chiefly to show what synechism is, and what it leads to. I
attempted, a good many years ago, to develop this doctrine in the
_Journal of Speculative Philosophy_ (Vol. II.); but I am able now to
improve upon that exposition, in which I was a little blinded by
nominalistic prepossessions. I refer to it, because students may
possibly find that some points not sufficiently explained in the present
paper are cleared up in those earlier ones.


                            WHAT THE LAW IS


Logical analysis applied to mental phenomena shows that there is but one
law of mind, namely, that ideas tend to spread continuously and to
affect certain others which stand to them in a peculiar relation of
affectibility. In this spreading they lose intensity, and especially the
power of affecting others, but gain generality and become welded with
other ideas.

I set down this formula at the beginning, for convenience; and now
proceed to comment upon it.


                         INDIVIDUALITY OF IDEAS


We are accustomed to speak of ideas as reproduced, as passed from mind
to mind, as similar or dissimilar to one another, and, in short, as if
they were substantial things; nor can any reasonable objection be raised
to such expressions. But taking the word “idea” in the sense of an event
in an individual consciousness, it is clear that an idea once past is
gone forever, and any supposed recurrence of it is another idea. These
two ideas are not present in the same state of consciousness, and
therefore cannot possibly be compared. To say, therefore, that they are
similar can only mean that an occult power from the depths of the soul
forces us to connect them in our thoughts after they are both no more.
We may note, here, in passing, that of the two generally recognized
principles of association, contiguity and similarity, the former is a
connection due to a power without, the latter a connection due to a
power within.

But what can it mean to say that ideas wholly past are thought of at
all, any longer? They are utterly unknowable. What distinct meaning can
attach to saying that an idea in the past in any way affects an idea in
the future, from which it is completely detached? A phrase between the
assertion and the denial of which there can in no case be any sensible
difference is mere gibberish.

I will not dwell further upon this point, because it is a commonplace of
philosophy.


                          CONTINUITY OF IDEAS


We have here before us a question of difficulty, analogous to the
question of nominalism and realism. But when once it has been clearly
formulated, logic leaves room for one answer only. How can a past idea
be present? Can it be present vicariously? To a certain extent, perhaps;
but not merely so; for then the question would arise how the past idea
can be related to its vicarious representation. The relation, being
between ideas, can only exist in some consciousness: now that past idea
was in no consciousness but that past consciousness that alone contained
it; and that did not embrace the vicarious idea.

Some minds will here jump to the conclusion that a past idea cannot in
any sense be present. But that is hasty and illogical. How extravagant,
too, to pronounce our whole knowledge of the past to be mere delusion!
Yet it would seem that the past is as completely beyond the bounds of
possible experience as a Kantian thing-in-itself.

How can a past idea be present? Not vicariously. Then, only by direct
perception. In other words, to be present, it must be _ipso facto_
present. That is, it cannot be wholly past; it can only be going,
infinitesimally past, less past than any assignable past date. We are
thus brought to the conclusion that the present is connected with the
past by a series of real infinitesimal steps.

It has already been suggested by psychologists that consciousness
necessarily embraces an interval of time. But if a finite time be meant,
the opinion is not tenable. If the sensation that precedes the present
by half a second were still immediately before me, then, on the same
principle the sensation preceding that would be immediately present, and
so on _ad infinitum_. Now, since there is a time, say a year, at the end
of which an idea is no longer _ipso facto_ present, it follows that this
is true of any finite interval, however short.

But yet consciousness must essentially cover an interval of time; for if
it did not, we could gain no knowledge of time, and not merely no
veracious cognition of it, but no conception whatever. We are,
therefore, forced to say that we are immediately conscious through an
infinitesimal interval of time.

This is all that is requisite. For, in this infinitesimal interval, not
only is consciousness continuous in a subjective sense, that is,
considered as a subject or substance having the attribute of duration;
but also, because it is immediate consciousness, its object is _ipso
facto_ continuous. In fact, this infinitesimally spread-out
consciousness is a direct feeling of its contents as spread out. This
will be further elucidated below. In an infinitesimal interval we
directly perceive the temporal sequence of its beginning, middle, and
end,—not, of course, in the way of recognition, for recognition is only
of the past, but in the way of immediate feeling. Now upon this interval
follows another, whose beginning is the middle of the former, and whose
middle is the end of the former. Here, we have an immediate perception
of the temporal sequence of its beginning, middle, and end, or say of
the second, third, and fourth instants. From these two immediate
perceptions, we gain a mediate, or inferential, perception of the
relation of all four instants. This mediate perception is objectively,
or as to the object represented, spread over the four instants; but
subjectively, or as itself the subject of duration, it is completely
embraced in the second moment. (The reader will observe that I use the
word _instant_ to mean a point of time, and _moment_ to mean an
infinitesimal duration.) If it is objected that, upon the theory
proposed, we must have more than a mediate perception of the succession
of the four instants, I grant it; for the sum of the two infinitesimal
intervals is itself infinitesimal, so that it is immediately perceived.
It is immediately perceived in the whole interval, but only mediately
perceived in the last two-thirds of the interval. Now, let there be an
indefinite succession of these inferential acts of comparative
perception; and it is plain that the last moment will contain
objectively the whole series. Let there be, not merely an indefinite
succession, but a continuous flow of inference through a finite time;
and the result will be a mediate objective consciousness of the whole
time in the last moment. In this last moment, the whole series will be
recognized, or known as known before, except only the last moment, which
of course will be absolutely unrecognizable to itself. Indeed, even this
last moment will be recognized like the rest, or, at least, be just
beginning to be so. There is a little _elenchus_, or appearance of
contradiction, here, which the ordinary logic of reflection quite
suffices to resolve.


                  INFINITY AND CONTINUITY, IN GENERAL


Most of the mathematicians who during the last two generations have
treated the differential calculus have been of the opinion that an
infinitesimal quantity is an absurdity; although, with their habitual
caution, they have often added “or, at any rate, the conception of an
infinitesimal is so difficult, that we practically cannot reason about
it with confidence and security.” Accordingly, the doctrine of limits
has been invented to evade the difficulty, or, as some say, to explain
the signification of the word “infinitesimal.” This doctrine, in one
form or another, is taught in all the text-books, though in some of them
only as an alternative view of the matter; it answers well enough the
purposes of calculation, though even in that application it has its
difficulties.

The illumination of the subject by a strict notation for the logic of
relatives had shown me clearly and evidently that the idea of an
infinitesimal involves no contradiction, before I became acquainted with
the writings of Dr. Georg Cantor (though many of these had already
appeared in the _Mathematische Annalen_ and in _Borchardt’s Journal_, if
not yet in the _Acta Mathematica_, all mathematical journals of the
first distinction), in which the same view is defended with
extraordinary genius and penetrating logic.

The prevalent opinion is that finite numbers are the only ones that we
can reason about, at least, in any ordinary mode of reasoning, or, as
some authors express it, they are the only numbers that can be reasoned
about mathematically. But this is an irrational prejudice. I long ago
showed that finite collections are distinguished from infinite ones only
by one circumstance and its consequences, namely, that to them is
applicable a peculiar and unusual mode of reasoning called by its
discoverer, De Morgan, the “syllogism of transposed quantity.”

Balzac, in the introduction of his _Physiologie du mariage_, remarks
that every young Frenchman boasts of having seduced some Frenchwoman.
Now, as a woman can only be seduced once, and there are no more
Frenchwomen than Frenchmen, it follows, if these boasts are true, that
no French women escape seduction. If their number be finite, the
reasoning holds. But since the population is continually increasing, and
the seduced are on the average younger than the seducers, the conclusion
need not be true. In like manner, De Morgan, as an actuary, might have
argued that if an insurance company pays to its insured on an average
more than they have ever paid it, including interest, it must lose
money. But every modern actuary would see a fallacy in that, since the
business is continually on the increase. But should war, or other
cataclysm, cause the class of insured to be a finite one, the conclusion
would turn out painfully correct, after all. The above two reasonings
are examples of the syllogism of transposed quantity.

The proposition that finite and infinite collections are distinguished
by the applicability to the former of the syllogism of transposed
quantity ought to be regarded as the basal one of scientific arithmetic.

If a person does not know how to reason logically, and I must say that a
great many fairly good mathematicians,—yea, distinguished ones,—fall
under this category, but simply uses a rule of thumb in blindly drawing
inferences like other inferences that have turned out well, he will, of
course, be continually falling into error about infinite numbers. The
truth is such people do not reason, at all. But for the few who do
reason, reasoning about infinite numbers is easier than about finite
numbers, because the complicated syllogism of transposed quantity is not
called for. For example, that the whole is greater than its part is not
an axiom, as that eminently bad reasoner, Euclid, made it to be. It is a
theorem readily proved by means of a syllogism of transposed quantity,
but not otherwise. Of finite collections it is true, of infinite
collections false. Thus, a part of the whole numbers are even numbers.
Yet the even numbers are no fewer than all the numbers; an evident
proposition since if every number in the whole series of whole numbers
be doubled, the result will be the series of even numbers.

                          1, 2, 3, 4, 5, 6, etc.
                          2, 4, 6, 8, 10, 12, etc.

So for every number there is a distinct even number. In fact, there are
as many distinct doubles of numbers as there are of distinct numbers.
But the doubles of numbers are all even numbers.

In truth, of infinite collections there are but two grades of magnitude,
the _endless_ and the _innumerable_. Just as a finite collection is
distinguished from an infinite one by the applicability to it of a
special mode of reasoning, the syllogism of transposed quantity, so, as
I showed in the paper last referred to, a numerable collection is
distinguished from an innumerable one by the applicability to it of a
certain mode of reasoning, the Fermatian inference, or, as it is
sometimes improperly termed, “mathematical induction.”

As an example of this reasoning, Euler’s demonstration of the binomial
theorem for integral powers may be given. The theorem is that (_x_ +
_y_)^n, where _n_ is a whole number, may be expanded into the sum of a
series of terms of which the first is _x_^n_y_^o and each of the others
is derived from the next preceding by diminishing the exponent of _x_ by
1 and multiplying by that exponent and at the same time increasing the
exponent of _y_ by 1 and dividing by that increased exponent. Now,
suppose this proposition to be true for a certain exponent, _n_ = _M_,
then it must also be true for _n_ = _M_ + 1. For let one of the terms in
the expansion of (_x_ + _y_)^M be written A_x^p__y^q_. Then, this term
with the two following will be

    A_x^p__y^q_ + A _p_/(_q_ + 1) _x_^{_p_ - 1} _y_^{_q_ + 1} + A
       _p_/(_q_ + 1) (_p_ - 1)/(_q_ + 2) _x_^{_p_ - 2} _y_^{_q_ + 2}

Now, when (_x_ + _y_)^M is multiplied by _x_ + _y_ to give (_x_ +
_y_)^{M + 1}, we multiply first by _x_ and then by _y_ instead of by _x_
and add the two results. When we multiply by _x_, the second of the
above three terms will be the only one giving a term involving
_x^p__y_^{_q_ + 1} and the third will be the only one giving a term in
_x_^{_p_ - 1}_y_^{_q_ + 2}; and when we multiply by y the first will be
the only term giving a term in _x^p__y_^{_q_ + 1}, and the second will
be the only term giving a term in _x_^{_p_ - 1}_y_^{_q_ + 2}. Hence,
adding like terms, we find that the coefficient of _x^p__y_^{_q_ + 1} in
the expansion of (_x_ + _y_)^{M + 1} will be the sum of the coefficients
of the first two of the above three terms, and that the coefficient of
_x_^{_p_ - 1}_y_^{_q_ + 2} will be the sum of the coefficients of the
last two terms. Hence, two successive terms in the expansion of (_x_ +
_y_)^{M + 1} will be

    A[1 + (_p_/(_q_ + 1))]_x^p__y_^{_q_+1} + A(_p_/(_q_ + 1))[1+ ((_p_ -
       1)/(_q_ + 2))]_x_^{_p_-1}_y_^{_q_+2}
    = A((_p_ + _q_ + 1)/(_q_ + 1))_x^p__y_^{_q_+1} + A((_p_ + _q_ +
       1)/(_q_ + 1))(_p_/(_q_ + 2))_x_^{_p_-1}_y_{_q_+2}

It is, thus, seen that the succession of terms follows the rule. Thus if
any integral power follows the rule, so also does the next higher power.
But the first power obviously follows the rule. Hence, all powers do so.

Such reasoning holds good of any collection of objects capable of being
ranged in a series which though it may be endless, can be numbered so
that each member of it receives a definite integral number. For
instance, all the whole numbers constitute such a numerable collection.
Again, all numbers resulting from operating according to any definite
rule with any finite number of whole numbers form such a collection. For
they may be arranged in a series thus. Let F be the symbol of operation.
First operate on 1, giving F(1). Then, operate on a second 1, giving
F(1,1). Next, introduce 2, giving 3rd, F(2); 4th F(2,1); 5th, F(1,2);
6th, F(2,2). Next use a third variable giving 7th, F(1,1,1); 8th,
F(2,1,1); 9th, F(1,2,1); 10th, F(2,2,1); 11th, F(1,1,2); 12th, F(2,1,2);
13th, F(1,2,2); 14th, F(2,2,2). Next introduce 3, and so on, alternately
introducing new variables and new figures; and in this way it is plain
that every arrangement of integral values of the variables will receive
a numbered place in the series.[62]

The class of endless but numerable collections (so called because they
can be so ranged that to each one corresponds a distinct whole number)
is very large. But there are collections which are certainly
innumerable. Such is the collection of all numbers to which endless
series of decimals are capable of approximating. It has been recognized
since the time of Euclid that certain numbers are surd or
incommensurable, and are not exactly expressible by any finite series of
decimals, nor by a circulating decimal. Such is the ratio of the
circumference of a circle to its diameter, which we know is nearly
3.1415926. The calculation of this number has been carried to over 700
figures without the slightest appearance of regularity in their
sequence. The demonstrations that this and many other numbers are
incommensurable are perfect. That the entire collection of
incommensurable numbers is innumerable has been clearly proved by
Cantor. I omit the demonstration; but it is easy to see that to
discriminate one from some other would, in general, require the use of
an endless series of numbers. Now if they cannot be exactly expressed
and discriminated, clearly they cannot be ranged in a linear series.

It is evident that there are as many points on a line or in an interval
of time as there are of real numbers in all. These are, therefore,
innumerable collections. Many mathematicians have incautiously assumed
that the points on a surface or in a solid are more than those on a
line. But this has been refuted by Cantor. Indeed, it is obvious that
for every set of values of coördinates there is a single distinct
number. Suppose, for instance, the values of the coordinates all lie
between 0 and + 1. Then if we compose a number by putting in the first
decimal place the first figure of the first coördinate, in the second
the first figure of the second coördinate, and so on, and when the first
figures are all dealt out go on to the second figures in like manner, it
is plain that the values of the coördinates can be read off from the
single resulting number, so that a triad or tetrad of numbers, each
having innumerable values, has no more values than a single
incommensurable number.

Were the number of dimensions infinite, this would fail; and the
collection of infinite sets of numbers having each innumerable
variations, might, therefore, be greater than the simple innumerable
collection, and might be called _endlessly infinite_. The single
individuals of such a collection could not, however, be designated, even
approximately, so that this is indeed a magnitude concerning which it
would be possible to reason only in the most general way, if at all.

Although there are but two grades of magnitudes of infinite collections,
yet when certain conditions are imposed upon the order in which
individuals are taken, distinctions of magnitude arise from that cause.
Thus, if a simply endless series be doubled by separating each unit into
two parts, the successive first parts and also the second parts being
taken in the same order as the units from which they are derived, this
double endless series will, so long as it is taken in that order, appear
as twice as large as the original series. In like manner the product of
two innumerable collections, that is, the collection of possible pairs
composed of one individual of each, if the order of continuity is to be
maintained, is, by virtue of that order, infinitely greater than either
of the component collections.

We now come to the difficult question. What is continuity? Kant
confounds it with infinite divisibility, saying that the essential
character of a continuous series is that between any two members of it a
third can always be found. This is an analysis beautifully clear and
definite; but unfortunately, it breaks down under the first test. For
according to this, the entire series of rational fractions arranged in
the order of their magnitude, would be an infinite series, although the
rational fractions are numerable, while the points of a line are
innumerable. Nay, worse yet, if from that series of fractions any two
with all that lie between them be excised, and any number of such finite
gaps be made, Kant’s definition is still true of the series, though it
has lost all appearance of continuity.

Cantor defines a continuous series as one which is _concatenated_ and
_perfect_. By a concatenated series, he means such a one that if any two
points are given in it, and any finite distance, however small, it is
possible to proceed from the first point to the second through a
succession of points of the series each at a distance from the preceding
one less than the given distance. This is true of the series of rational
fractions ranged in the order of their magnitude. By a perfect series,
he means one which contains every point such that there is no distance
so small that this point has not an infinity of points of the series
within that distance of it. This is true of the series of numbers
between 0 and 1 capable of being expressed by decimals in which only the
digits 0 and 1 occur.

It must be granted that Cantor’s definition includes every series that
is continuous; nor can it be objected that it includes any important or
indubitable case of a series not continuous. Nevertheless, it has some
serious defects. In the first place, it turns upon metrical
considerations; while the distinction between a continuous and a
discontinuous series is manifestly non-metrical. In the next place, a
perfect series is defined as one containing “every point” of a certain
description. But no positive idea is conveyed of what all the points
are: that is definition by negation, and cannot be admitted. If that
sort of thing were allowed, it would be very easy to say, at once, that
the continuous linear series of points is one which contains every point
of the line between its extremities. Finally, Cantor’s definition does
not convey a distinct notion of what the components of the conception of
continuity are. It ingeniously wraps up its properties in two separate
parcels, but does not display them to our intelligence.

Kant’s definition expresses one simple property of a continuum; but it
allows of gaps in the series. To mend the definition, it is only
necessary to notice how these gaps can occur. Let us suppose, then, a
linear series of points extending from a point, _A_, to a point, _B_,
having a gap from _B_ to a third point, _C_, and thence extending to a
final limit, _D_; and let us suppose this series conforms to Kant’s
definition. Then, of the two points, _B_ and _C_, one or both must be
excluded from the series; for otherwise, by the definition, there would
be points between them. That is, if the series contains _C_, though it
contains all the points up to _B_, it cannot contain _B_. What is
required, therefore, is to state in non-metrical terms that if a series
of points up to a limit is included in a continuum the limit is
included. It may be remarked that this is the property of a continuum to
which Aristotle’s attention seems to have been directed when he defines
a continuum as something whose parts have a common limit. The property
may be exactly stated as follows: If a linear series of points is
continuous between two points, _A_ and _D_, and if an endless series of
points be taken, the first of them between _A_ and _D_ and each of the
others between the last preceding one and _D_, then there is a point of
the continuous series between all that endless series of points and _D_,
and such that every other point of which this is true lies between this
point and _D_. For example, take any number between 0 and 1, as 0.1;
then, any number between 0.1 and 1, as 0.11; then any number between
0.11 and 1, as 0.111; and so on, without end. Then, because the series
of real numbers between 0 and 1 is continuous, there must be a _least_
real number, greater than every number of that endless series. This
property, which may be called the Aristotelicity of the series, together
with Kant’s property, or its Kanticity, completes the definition of a
continuous series.

The property of Aristotelicity may be roughly stated thus: a continuum
contains the end point belonging to every endless series of points which
it contains. An obvious corollary is that every continuum contains its
limits. But in using this principle it is necessary to observe that a
series may be continuous except in this, that it omits one or both of
the limits.

Our ideas will find expression more conveniently if, instead of points
upon a line, we speak of real numbers. Every real number is, in one
sense, the limit of a series, for it can be indefinitely approximated
to. Whether every real number is a limit of a _regular_ series may
perhaps be open to doubt. But the series referred to in the definition
of Aristotelicity must be understood as including all series whether
regular or not. Consequently, it is implied that between any two points
an innumerable series of points can be taken.

Every number whose expression in decimals requires but a finite number
of places of decimals is commensurable. Therefore, incommensurable
numbers suppose an infinitieth place of decimals. The word infinitesimal
is simply the Latin form of infinitieth; that is, it is an ordinal
formed from _infinitum_, as centesimal from _centum_. Thus, continuity
supposes infinitesimal quantities. There is nothing contradictory about
the idea of such quantities. In adding and multiplying them the
continuity must not be broken up, and consequently they are precisely
like any other quantities, except that neither the syllogism of
transposed quantity, nor the Fermatian inference applies to them.

If A is a finite quantity and _i_ an infinitesimal, then in a certain
sense we may write A + _i_ = A. That is to say, this is so for all
purposes of measurement. But this principle must not be applied except
to get rid of _all_ the terms in the highest order of infinitesimals
present. As a mathematician, I prefer the method of infinitesimals to
that of limits, as far easier and less infested with snares. Indeed, the
latter, as stated in some books, involves propositions that are false;
but this is not the case with the forms of the method used by Cauchy,
Duhamel, and others. As they understand the doctrine of limits, it
involves the notion of continuity, and, therefore, contains in another
shape the very same ideas as the doctrine of infinitesimals.

Let us now consider an aspect of the Aristotelical principle which is
particularly important in philosophy. Suppose a surface to be part red
and part blue; so that every point on it is either red or blue, and, of
course, no part can be both red and blue. What, then, is the color of
the boundary line between the red and the blue? The answer is that red
or blue, to exist at all, must be spread over a surface; and the color
of the surface is the color of the surface in the immediate neighborhood
of the point. I purposely use a vague form of expression. Now, as the
parts of the surface in the immediate neighborhood of any ordinary point
upon a curved boundary are half of them red and half blue, it follows
that the boundary is half red and half blue. In like manner, we find it
necessary to hold that consciousness essentially occupies time; and what
is present to the mind at any ordinary instant, is what is present
during a moment in which that instant occurs. Thus, the present is half
past and half to come. Again, the color of the parts of a surface at any
finite distance from a point, has nothing to do with its color just at
that point; and, in the parallel, the feeling at any finite interval
from the present has nothing to do with the present feeling, except
vicariously. Take another case: the velocity of a particle at any
instant of time is its mean velocity during an infinitesimal instant in
which that time is contained. Just so my immediate feeling is my feeling
through an infinitesimal duration containing the present instant.


                            ANALYSIS OF TIME


One of the most marked features about the law of mind is that it makes
time to have a definite direction of flow from past to future. The
relation of past to future is, in reference to the law of mind,
different from the relation of future to past. This makes one of the
great contrasts between the law of mind and the law of physical force,
where there is no more distinction between the two opposite directions
in time than between moving northward and moving southward.

In order, therefore, to analyze the law of mind, we must begin by asking
what the flow of time consists in. Now, we find that in reference to any
individual state of feeling, all others are of two classes, those which
affect this one (or have a tendency to affect it, and what this means we
shall inquire shortly), and those which do not. The present is
affectible by the past but not by the future.

Moreover, if state _A_ is affected by state _B_, and state _B_ by state
_C_, then _A_ is affected by state _C_, though not so much so. It
follows, that if _A_ is affectible by _B_, _B_ is not affectible by _A_.

If, of two states, each is absolutely unaffectible by the other, they
are to be regarded as parts of the same state. They are contemporaneous.

To say that a state is _between_ two states means that it affects one
and is affected by the other. Between any two states in this sense lies
an innumerable series of states affecting one another; and if a state
lies between a given state and any other state which can be reached by
inserting states between this state and any third state, these inserted
states not immediately affecting or being affected by either, then the
second rate mentioned, immediately affects or is affected by the first,
in the sense that in the one the other is _ipso facto_ present in a
reduced degree.

These propositions involve a definition of time and of its flow. Over
and above this definition they involve a doctrine, namely, that every
state of feeling is affectible by every earlier state.


                THAT FEELINGS HAVE INTENSIVE CONTINUITY


Time with its continuity logically involves some other kind of
continuity than its own. Time, as the universal form of change, cannot
exist unless there is something to undergo change, and to undergo a
change continuous in time, there must be a continuity of changeable
qualities. Of the continuity of intrinsic qualities of feeling we can
now form but a feeble conception. The development of the human mind has
practically extinguished all feelings, except a few sporadic kinds,
sound, colors, smells, warmth, etc., which now appear to be disconnected
and disparate. In the case of colors, there is a tridimensional spread
of feelings. Originally, all feelings may have been connected in the
same way, and the presumption is that the number of dimensions was
endless. For development essentially involves a limitation of
possibilities. But given a number of dimensions of feeling, all possible
varieties are obtainable by varying the intensities of the different
elements. Accordingly, time logically supposes a continuous range of
intensity in feeling. It follows, then, from the definition of
continuity, that when any particular kind of feeling is present, an
infinitesimal continuum of all feelings differing infinitesimally from
that is present.


                  THAT FEELINGS HAVE SPATIAL EXTENSION


Consider a gob of protoplasm, say an amœba or a slime-mould. It does not
differ in any radical way from the contents of a nerve-cell, though its
functions may be less specialized. There is no doubt that this
slime-mould, or this amœba, or at any rate some similar mass of
protoplasm feels. That is to say, it feels when it is in its excited
condition. But note how it behaves. When the whole is quiescent and
rigid, a place upon it is irritated. Just at this point, an active
motion is set up, and this gradually spreads to other parts. In this
action, no unity nor relation to a nucleus, or other unitary organ can
be discerned. It is a mere amorphous continuum of protoplasm, with
feeling passing from one part to another. Nor is there anything like a
wave-motion. The activity does not advance to new parts, just as fast as
it leaves old parts. Rather, in the beginning, it dies out at a slower
rate than that at which it spreads. And while the process is going on,
by exciting the mass at another point, a second quite independent state
of excitation will be set up. In some places, neither excitation will
exist, in others each separately, in still other places, both effects
will be added together. Whatever there is in the whole phenomenon to
make us think there is feeling in such a mass of protoplasm,—_feeling_,
but plainly no _personality_,—goes logically to show that that feeling
has a subjective, or substantial, spatial extension, as the excited
state has. This is, no doubt, a difficult idea to seize, for the reason
that it is a subjective, not an objective, extension. It is not that we
have a feeling of bigness; though Professor James, perhaps rightly,
teaches that we have. It is that the feeling, as a subject of inhesion,
is big. Moreover, our own feelings are focused in attention to such a
degree that we are not aware that ideas are not brought to an absolute
unity; just as nobody not instructed by special experiment has any idea
how very, very little of the field of vision is distinct. Still, we all
know how the attention wanders about among our feelings; and this fact
shows that those feelings that are not co-ordinated in attention have a
reciprocal externality, although they are present at the same time. But
we must not tax introspection to make a phenomenon manifest which
essentially involves externality.

Since space is continuous, it follows that there must be an immediate
community of feeling between parts of mind infinitesimally near
together. Without this, I believe it would have been impossible for
minds external to one another, ever to become co-ordinated, and equally
impossible for any coördination to be established in the action of the
nerve-matter of one brain.


                          AFFECTIONS OF IDEAS


But we are met by the question what is meant by saying that one idea
affects another. The unravelment of this problem requires us to trace
out phenomena a little further.

Three elements go to make up an idea. The first is its intrinsic quality
as a feeling. The second is the energy with which it affects other
ideas, an energy which is infinite in the here-and-nowness of immediate
sensation, finite and relative in the recency of the past. The third
element is the tendency of an idea to bring along other ideas with it.

As an idea spreads, its power of affecting other ideas gets rapidly
reduced; but its intrinsic quality remains nearly unchanged. It is long
years now since I last saw a cardinal in his robes; and my memory of
their color has become much dimmed. The color itself, however, is not
remembered as dim. I have no inclination to call it a dull red. Thus,
the intrinsic quality remains little changed; yet more accurate
observation will show a slight reduction of it. The third element, on
the other hand, has increased. As well as I can recollect, it seems to
me the cardinals I used to see wore robes more scarlet than vermillion
is, and highly luminous. Still, I know the color commonly called
cardinal is on the crimson side of vermillion and of quite moderate
luminosity, and the original idea calls up so many other hues with it,
and asserts itself so feebly, that I am unable any longer to isolate it.

A finite interval of time generally contains an innumerable series of
feelings; and when these become welded together in association, the
result is a general idea. For we have just seen how by continuous
spreading an idea becomes generalised.

The first character of a general idea so resulting is that it is living
feeling. A continuum of this feeling, infinitesimal in duration, but
still embracing innumerable parts, and also, though infinitesimal,
entirely unlimited, is immediately present. And in its absence of
boundedness a vague possibility of more than is present is directly
felt.

Second, in the presence of this continuity of feeling, nominalistic
maxims appear futile. There is no doubt about one idea affecting
another, when we can directly perceive the one gradually modified and
shaping itself into the other. Nor can there any longer be any
difficulty about one idea resembling another, when we can pass along the
continuous field of quality from one to the other and back again to the
point which we had marked.

[Illustration: Figure 7.]

Third, consider the insistency of an idea. The insistency of a past idea
with reference to the present is a quantity which is less the further
back that past idea is, and rises to infinity as the past idea is
brought up into coincidence with the present. Here we must make one of
those inductive applications of the law of continuity which have
produced such great results in all the positive sciences. We must extend
the law of insistency into the future. Plainly, the insistency of a
future idea with reference to the present is a quantity affected by the
minus sign; for it is the present that affects the future, if there be
any effect, not the future that affects the present. Accordingly, the
curve of insistency is a sort of equilateral hyperbola. (See the
figure.) Such a conception is none the less mathematical, that its
quantification cannot now be exactly specified.

Now consider the induction which we have here been led into. This curve
says that feeling which has not yet emerged into immediate consciousness
is already affectible and already affected. In fact, this is habit, by
virtue of which an idea is brought up into present consciousness by a
bond that had already been established between it and another idea while
it was still _in futuro_.

We can now see what the affection of one idea by another consists in. It
is that the affected idea is attached as a logical predicate to the
affecting idea as subject. So when a feeling emerges into immediate
consciousness, it always appears as a modification of a more or less
general object already in the mind. The word suggestion is well adapted
to expressing this relation. The future is suggested by, or rather is
influenced by the suggestions of, the past.


             IDEAS CANNOT BE CONNECTED EXCEPT BY CONTINUITY


That ideas can nowise be connected without continuity is sufficiently
evident to one who reflects upon the matter. But still the opinion may
be entertained that after continuity has once made the connection of
ideas possible, then they may get to be connected in other modes than
through continuity. Certainly, I cannot see how anyone can deny that the
infinite diversity of the universe, which we call chance, may bring
ideas into proximity which are not associated in one general idea. It
may do this many times. But then the law of continuous spreading will
produce a mental association; and this I suppose is an abridged
statement of the way the universe has been evolved. But if I am asked
whether a blind ἀνάγκη cannot bring ideas together, first I point out
that it would not remain blind. There being a continuous connection
between the ideas, they would infallibly become associated in a living,
feeling, and perceiving general idea. Next, I cannot see what the
mustness or necessity of this ἁνάγκη would consist in. In the absolute
uniformity of the phenomenon, says the nominalist. Absolute is well put
in; for if it merely happened so three times in succession, or three
million times in succession, in the absence of any reason, the
coincidence could only be attributed to chance. But absolute uniformity
must extend over the whole infinite future; and it is idle to talk of
that except as an idea. No; I think we can only hold that wherever ideas
come together they tend to weld into general ideas; and wherever they
are generally connected, general ideas govern the connection; and these
general ideas are living feelings spread out.


                 MENTAL LAW FOLLOWS THE FORMS OF LOGIC


The three main classes of logical inference are Deduction, Induction,
and Hypothesis. These correspond to three chief modes of action of the
human soul. In deduction the mind is under the dominion of a habit or
association by virtue of which a general idea suggests in each case a
corresponding reaction. But a certain sensation is seen to involve that
idea. Consequently, that sensation is followed by that reaction. That is
the way the hind legs of a frog, separated from the rest of the body,
reason, when you pinch them. It is the lowest form of psychical
manifestation.

By induction, a habit becomes established. Certain sensations, all
involving one general idea, are followed each by the same reaction; and
an association becomes established, whereby that general idea gets to be
followed uniformly by that reaction.

Habit is that specialization of the law of mind whereby a general idea
gains the power of exciting reactions. But in order that the general
idea should attain all its functionality, it is necessary, also, that it
should become suggestible by sensations. That is accomplished by a
psychical process having the form of hypothetic inference. By hypothetic
inference, I mean, as I have explained in other writings, an induction
from qualities. For example, I know that the kind of man known and
classed as a “mugwump” has certain characteristics. He has a high
self-respect and places great value upon social distinction. He laments
the great part that rowdyism and unrefined good-fellowship play in the
dealings of American politicians with their constituency. He thinks that
the reform which would follow from the abandonment of the system by
which the distribution of offices is made to strengthen party
organizations and a return to the original and essential conception of
office-filling would be found an unmixed good. He holds that monetary
considerations should usually be the decisive ones in questions of
public policy. He respects the principle of individualism and of
_laissez-faire_ as the greatest agency of civilization. These views,
among others, I know to be obtrusive marks of a “mugwump.” Now, suppose
I casually meet a man in a railway-train, and falling into conversation
find that he holds opinions of this sort; I am naturally led to suppose
that he is a “mugwump.” That is hypothetic inference. That is to say, a
number of readily verifiable marks of a mugwump being selected, I find
this man has these, and infer that he has all the other characters which
go to make a thinker of that stripe. Or let us suppose that I meet a man
of a semi-clerical appearance and a sub-pharisaical sniff, who appears
to look at things from the point of view of a rather wooden dualism. He
cites several texts of scripture and always with particular attention to
their logical implications; and he exhibits a sternness, almost
amounting to vindictiveness, toward evil-doers, in general. I readily
conclude that he is a minister of a certain denomination. Now the mind
acts in a way similar to this, every time we acquire a power of
co-ordinating reactions in a peculiar way, as in performing any act
requiring skill. Thus, most persons have a difficulty in moving the two
hands simultaneously and in opposite directions through two parallel
circles nearly in the medial plane of the body. To learn to do this, it
is necessary to attend, first, to the different actions in different
parts of the motion, when suddenly a general conception of the action
springs up and it becomes perfectly easy. We think the motion we are
trying to do involves this action, and this, and this. Then, the general
idea comes which unites all those actions, and thereupon the desire to
perform the motion calls up the general idea. The same mental process is
many times employed whenever we are learning to speak a language or are
acquiring any sort of skill.

Thus, by induction, a number of sensations followed by one reaction
become united under one general idea followed by the same reaction;
while by the hypothetic process, a number of reactions called for by one
occasion get united in a general idea which is called out by the same
occasion. By deduction, the habit fulfils its function of calling out
certain reactions on certain occasions.


                      UNCERTAINTY OF MENTAL ACTION


The inductive and hypothetic forms of inference are essentially probable
inferences, not necessary; while deduction may be either necessary or
probable.

But no mental action seems to be necessary or invariable in its
character. In whatever manner the mind has reacted under a given
sensation, in that manner it is the more likely to react again; were
this, however, an absolute necessity, habits would become wooden and
ineradicable, and no room being left for the formation of new habits,
intellectual life would come to a speedy close. Thus, the uncertainty of
the mental law is no mere defect of it, but is on the contrary of its
essence. The truth is, the mind is not subject to “law,” in the same
rigid sense that matter is. It only experiences gentle forces which
merely render it more likely to act in a given way than it otherwise
would be. There always remains a certain amount of arbitrary spontaneity
in its action, without which it would be dead.

Some psychologists think to reconcile the uncertainty of reactions with
the principle of necessary causation by means of the law of fatigue.
Truly for a _law_, this law of fatigue is a little lawless. I think it
is merely a case of the general principle that an idea in spreading
loses its insistency. Put me tarragon into my salad, when I have not
tasted it for years, and I exclaim “What nectar is this!” But add it to
every dish I taste for week after week, and a habit of expectation has
been created; and in thus spreading into habit, the sensation makes
hardly any more impression upon me; or, if it be noticed, it is on a new
side from which it appears as rather a bore. The doctrine that fatigue
is one of the primordial phenomena of mind I am much disposed to doubt.
It seems a somewhat little thing to be allowed as an exception to the
great principle of mental uniformization. For this reason, I prefer to
explain it in the manner here indicated, as a special case of that great
principle. To consider it as something distinct in its nature, certainly
somewhat strengthens the necessitarian position; but even if it be
distinct, the hypothesis that all the variety and apparent arbitrariness
of mental action ought to be explained away in favor of absolute
determinism does not seem to me to recommend itself to a sober and sound
judgment, which seeks the guidance of observed facts and not that of
prepossessions.


                         RESTATEMENT OF THE LAW


Let me now try to gather up all these odds and ends of commentary and
restate the law of mind, in a unitary way.

First, then, we find that when we regard ideas from a nominalistic,
individualistic, sensualistic way, the simplest facts of mind become
utterly meaningless. That one idea should resemble another or influence
another, or that one state of mind should so much as be thought of in
another is, from that standpoint, sheer nonsense.

Second, by this and other means we are driven to perceive, what is quite
evident of itself, that instantaneous feelings flow together into a
continuum of feeling, which has in a modified degree the peculiar
vivacity of feeling and has gained generality. And in reference to such
general ideas, or continua of feeling, the difficulties about
resemblance and suggestion and reference to the external, cease to have
any force.

Third, these general ideas are not mere words, nor do they consist in
this, that certain concrete facts will every time happen under certain
descriptions of conditions; but they are just as much, or rather far
more, living realities than the feelings themselves out of which they
are concreted. And to say that mental phenomena are governed by law does
not mean merely that they are describable by a general formula; but that
there is a living idea, a conscious continuum of feeling, which pervades
them, and to which they are docile.

Fourth, this supreme law, which is the celestial and living harmony,
does not so much as demand that the special ideas shall surrender their
peculiar arbitrariness and caprice entirely; for that would be
self-destructive. It only requires that they shall influence and be
influenced by one another.

Fifth, in what measure this unification acts, seems to be regulated only
by special rules; or, at least, we cannot in our present knowledge say
how far it goes. But it may be said that, judging by appearances, the
amount of arbitrariness in the phenomena of human minds is neither
altogether trifling nor very prominent.


                              PERSONALITY


Having thus endeavored to state the law of mind, in general, I descend
to the consideration of a particular phenomenon which is remarkably
prominent in our own consciousnesses, that of personality. A strong
light is thrown upon this subject by recent observations of double and
multiple personality. The theory which at one time seemed plausible that
two persons in one body corresponded to the two halves of the brain
will, I take it, now be universally acknowledged to be insufficient. But
that which these cases make quite manifest is that personality is some
kind of co-ordination or connection of ideas. Not much to say, this,
perhaps. Yet when we consider that, according to the principle which we
are tracing out, a connection between ideas is itself a general idea,
and that a general idea is a living feeling, it is plain that we have at
least taken an appreciable step toward the understanding of personality.
This personality, like any general idea, is not a thing to be
apprehended in an instant. It has to be lived in time; nor can any
finite time embrace it in all its fullness. Yet in each infinitesimal
interval it is present and living, though specially colored by the
immediate feelings of that moment. Personality, so far as it is
apprehended in a moment, is immediate self-consciousness.

But the word co-ordination implies somewhat more than this; it implies a
teleological harmony in ideas, and in the case of personality this
teleology is more than a mere purposive pursuit of a predeterminate end;
it is a developmental teleology. This is personal character. A general
idea, living and conscious now, it is already determinative of acts in
the future to an extent to which it is not now conscious.

This reference to the future is an essential element of personality.
Were the ends of a person already explicit, there would be no room for
development, for growth, for life; and consequently there would be no
personality. The mere carrying out of predetermined purposes is
mechanical. This remark has an application to the philosophy of
religion. It is that a genuine evolutionary philosophy, that is, one
that makes the principle of growth a primordial element of the universe,
is so far from being antagonistic to the idea of a personal creator,
that it is really inseparable from that idea; while a necessitarian
religion is in an altogether false position and is destined to become
disintegrated. But a pseudo-evolutionism which enthrones mechanical law
above the principle of growth, is at once scientifically unsatisfactory,
as giving no possible hint of how the universe has come about, and
hostile to all hopes of personal relations to God.


                             COMMUNICATION


Consistently with the doctrine laid down in the beginning of this paper,
I am bound to maintain that an idea can only be affected by an idea in
continuous connection with it. By anything but an idea, it cannot be
affected at all. This obliges me to say, as I do say, on other grounds,
that what we call matter is not completely dead, but is merely mind
hide-bound with habits. It still retains the element of diversification;
and in that diversification there is life. When an idea is conveyed from
one mind to another, it is by forms of combination of the diverse
elements of nature, say by some curious symmetry, or by some union of a
tender color with a refined odor. To such forms the law of mechanical
energy has no application. If they are eternal, it is in the spirit they
embody; and their origin cannot be accounted for by any mechanical
necessity. They are embodied ideas; and so only can they convey ideas.
Precisely how primary sensations, as colors and tones, are excited, we
cannot tell, in the present state of psychology. But in our ignorance, I
think that we are at liberty to suppose that they arise in essentially
the same manner as the other feelings, called secondary. As far as sight
and hearing are in question, we know that they are only excited by
vibrations of inconceivable complexity; and the chemical senses are
probably not more simple. Even the least psychical of peripheral
sensations, that of pressure, has in its excitation conditions which,
though apparently simple, are seen to be complicated enough when we
consider the molecules and their attractions. The principle with which I
set out requires me to maintain that these feelings are communicated to
the nerves by continuity, so that there must be something like them in
the excitants themselves. If this seems extravagant, it is to be
remembered that it is the sole possible way of reaching any explanation
of sensation, which otherwise must be pronounced a general fact,
absolutely inexplicable and ultimate. Now absolute inexplicability is a
hypothesis which sound logic refuses under any circumstances to justify.

I may be asked whether my theory would be favorable or otherwise to
telepathy. I have no decided answer to give to this. At first sight, it
seems unfavorable. Yet there may be other modes of continuous connection
between minds other than those of time and space.

The recognition by one person of another’s personality takes place by
means to some extent identical with the means by which he is conscious
of his own personality. The idea of the second personality, which is as
much as to say that second personality itself, enters within the field
of direct consciousness of the first person, and is as immediately
perceived as his ego, though less strongly. At the same time, the
opposition between the two persons is perceived, so that the externality
of the second is recognized.

The psychological phenomena of intercommunication between two minds have
been unfortunately little studied. So that it is impossible to say, for
certain, whether they are favorable to this theory or not. But the very
extraordinary insight which some persons are able to gain of others from
indications so slight that it is difficult to ascertain what they are,
is certainly rendered more comprehensible by the view here taken.

A difficulty which confronts the synechistic philosophy is this. In
considering personality, that philosophy is forced to accept the
doctrine of a personal God; but in considering communication, it cannot
but admit that if there is a personal God, we must have a direct
perception of that person and indeed be in personal communication with
him. Now, if that be the case, the question arises how it is possible
that the existence of this being should ever have been doubted by
anybody. The only answer that I can at present make is that facts that
stand before our face and eyes and stare us in the face are far from
being, in all cases, the ones most easily discerned. That has been
remarked from time immemorial.


                               CONCLUSION


I have thus developed as well as I could in a little space the
_synechistic_ philosophy, as applied to mind. I think that I have
succeeded in making it clear that this doctrine gives room for
explanations of many facts which without it are absolutely and
hopelessly inexplicable; and further that it carries along with it the
following doctrines: 1st, a logical realism of the most pronounced type;
2nd, objective idealism; 3rd, tychism, with its consequent thoroughgoing
evolutionism. We also notice that the doctrine presents no hindrances to
spiritual influences, such as some philosophies are felt to do.

Footnote 61:

  _The Monist_, July, 1892.

Footnote 62:

  This proposition is substantially the same as a theorem of Cantor,
  though it is enunciated in a much more general form.




                      IV. MAN’S GLASSY ESSENCE[63]


In _The Monist_ for January, 1891, I tried to show what conceptions
ought to form the brick and mortar of a philosophical system. Chief
among these was that of absolute chance for which I argued again in last
April’s number.[64] In July, I applied another fundamental idea, that of
continuity, to the law of mind. Next in order, I have to elucidate, from
the point of view chosen, the relation between the psychical and
physical aspects of a substance.

The first step towards this ought, I think, to be the framing of a
molecular theory of protoplasm. But before doing that, it seems
indispensable to glance at the constitution of matter, in general. We
shall, thus, unavoidably make a long detour; but, after all, our pains
will not be wasted, for the problems of the papers that are to follow in
the series will call for the consideration of the same question.

All physicists are rightly agreed the evidence is overwhelming which
shows all sensible matter is composed of molecules in swift motion and
exerting enormous mutual attractions, and perhaps repulsions, too. Even
Sir William Thomson, Lord Kelvin, who wishes to explode action at a
distance and return to the doctrine of a plenum, not only speaks of
molecules, but undertakes to assign definite magnitudes to them. The
brilliant Judge Stallo, a man who did not always rightly estimate his
own qualities in accepting tasks for himself, declared war upon the
atomic theory in a book well worth careful perusal. To the old arguments
in favor of atoms which he found in Fechner’s monograph, he was able to
make replies of considerable force, though they were not sufficient to
destroy those arguments. But against modern proofs he made no headway at
all. These set out from the mechanical theory of heat. Rumford’s
experiments showed that heat is not a substance. Joule demonstrated that
it was a form of energy. The heating of gases under constant volume, and
other facts instanced by Rankine, proved that it could not be an energy
of strain. This drove physicists to the conclusion that it was a mode of
motion. Then it was remembered that John Bernoulli had shown that the
pressure of gases could be accounted for by assuming their molecules to
be moving uniformly in rectilinear paths. The same hypothesis was now
seen to account for Avogadro’s law, that in equal volumes of different
kinds of gases exposed to the same pressure and temperature are
contained equal numbers of molecules. Shortly after, it was found to
account for the laws of diffusion and viscosity of gases, and for the
numerical relation between these properties. Finally, Crookes’s
radiometer furnished the last link in the strongest chain of evidence
which supports any physical hypothesis.

Such being the constitution of gases, liquids must clearly be bodies in
which the molecules wander in curvilinear paths, while in solids they
move in orbits or quasi-orbits. (See my definition _solid_ II, 1, in the
_Century Dictionary_.)

We see that the resistance to compression and to inter-penetration
between sensible bodies is, by one of the prime propositions of the
molecular theory, due in large measure to the kinetical energy of the
particles, which must be supposed to be quite remote from one another,
on the average, even in solids. This resistance is no doubt influenced
by finite attractions and repulsions between the molecules. All the
impenetrability of bodies which we can observe is, therefore, a limited
impenetrability due to kinetic and positional energy. This being the
case, we have no logical right to suppose that absolute impenetrability,
or the exclusive occupancy of space, belongs to molecules or to atoms.
It is an unwarranted hypothesis, not a _vera causa_.[65] Unless we are
to give up the theory of energy, finite positional attractions and
repulsions between molecules must be admitted. Absolute impenetrability
would amount to an infinite repulsion at a certain distance. No analogy
of known phenomena exists to excuse such a wanton violation of the
principle of continuity as such a hypothesis is. In short, we are
logically bound to adopt the Boscovichian idea that an atom is simply a
distribution of component potential energy throughout space (this
distribution being absolutely rigid), combined with inertia. The
potential energy belongs to two molecules, and is to be conceived as
different between molecules _A_ and _B_ from what it is between
molecules _A_ and _C_. The distribution of energy is not necessarily
spherical. Nay, a molecule may conceivably have more than one center; it
may even have a central curve, returning into itself. But I do not think
there are any observed facts pointing to such multiple or linear
centers. On the other hand, many facts relating to crystals, especially
those observed by Voigt,[66] go to show that the distribution of energy
is harmonical but not concentric. We can easily calculate the forces
which such atoms must exert upon one another by considering[67] that
they are equivalent to aggregations of pairs of electrically positive
and negative points infinitely near to one another. About such an atom
there would be regions of positive and of negative potential, and the
number and distribution of such regions would determine the valency of
the atom, a number which it is easy to see would in many cases be
somewhat indeterminate. I must not dwell further upon this hypothesis,
at present. In another paper, its consequences will be further
considered.

I cannot assume that the students of philosophy who read this magazine
are thoroughly versed in modern molecular physics, and, therefore, it is
proper to mention that the governing principle in this branch of science
is Clausius’s law of the virial. I will first state the law, and then
explain the peculiar terms of the statement. This statement is that the
total kinetic energy of the particles of a system in stationary motion
is equal to the total virial. By a _system_ is here meant a number of
particles acting upon one another.[68] Stationary motion is a
quasi-orbital motion among a system of particles so that none of them
are removed to indefinitely great distances nor acquire indefinitely
great velocities. The kinetic energy of a particle is the work which
would be required to bring it to rest, independently of any forces which
may be acting upon it. The virial of a pair of particles is half the
work which the force which actually operates between them would do if,
being independent of the distance, it were to bring them together. The
equation of the virial is

                          1/2∑_mv_^2 = 1/2∑∑_Rr_.

Here _m_ is the mass of a particle, _v_ its velocity, _R_ is the
attraction between two particles, and _r_ is the distance between them.
The sign ∑ on the left hand side signifies that the values of _mv_^2 are
to be summed for all the particles, and ∑∑ on the right hand side
signifies that the values of _Rr_ are to be summed for all the pairs of
particles. If there is an external pressure _P_ (as from the atmosphere)
upon the system, and the volume of vacant space within the boundary of
that pressure is _V_, then the virial must be understood as including
3/2_PV_, so that the equation is

                     1/2∑_mv_^2 = 3/2_PV_ + 1/2∑∑_Rr_.

There is strong (if not demonstrative) reason for thinking that the
temperature of any body above the absolute zero (-273° C.), is
proportional to the average kinetic energy of its molecules, or say
_a_θ, where _a_ is a constant and θ is the absolute temperature. Hence,
we may write the equation

       _a_θ = (1/2)avg(_mv_^2) = (3/2)_P_ avg(_V_) + (1/2)∑ avg(_Rr_)

where the heavy lines above the different expressions signify that the
average values for single molecules are to be taken. In 1872, a student
in the University of Leyden, Van der Waals, propounded in his thesis for
the doctorate a specialization of the equation of the virial which has
since attracted great attention. Namely, he writes it

                    _a_θ = (_P_ + _c_/_V_^2)(_V_ - _b_.)

The quantity _b_ is the volume of a molecule, which he supposes to be an
impenetrable body, and all the virtue of the equation lies in this term
which makes the equation a cubic in _V_, which is required to account
for the shape of certain isothermal curves.[69] But if the idea of an
impenetrable atom is illogical, that of an impenetrable molecule is
almost absurd. For the kinetical theory of matter teaches us that a
molecule is like a solar system or star-cluster in miniature. Unless we
suppose that in all heating of gases and vapors internal work is
performed upon the molecules, implying that their atoms are at
considerable distances, the whole kinetical theory of gases falls to the
ground. As for the term added to _P_, there is no more than a partial
and roughly approximative justification for it. Namely, let us imagine
two spheres described round a particle as their center, the radius of
the larger being so great as to include all the particles whose action
upon the center is sensible, while the radius of the smaller is so large
that a good many molecules are included within it. The possibility of
describing such a sphere as the outer one implies that the attraction of
the particles varies at some distances inversely as some higher power of
the distance than the cube, or, to speak more clearly, that the
attraction multiplied by the cube of the distance diminishes as the
distance increases; for the number of particles at a given distance from
any one particle is proportionate to the square of that distance and
each of these gives a term of the virial which is the product of the
attraction into the distance. Consequently, unless the attraction
multiplied by the cube of the distance diminished so rapidly with the
distance as soon to become insensible, no such outer sphere as is
supposed could be described. However, ordinary experience shows that
such a sphere is possible; and consequently there must be distances at
which the attraction does thus rapidly diminish as the distance
increases. The two spheres, then, being so drawn, consider the virial of
the central particle due to the particles between them. Let the density
of the substance be increased, say, _N_ times. Then, for every turn,
_Rr_, of the virial before the condensation, there will be _N_ terms of
the same magnitude after the condensation. Hence, the virial of each
particle will be proportional to the density, and the equation of the
virial becomes

                    _a_θ = _P_ avg(_V_) + _c_/avg(_V_).

This omits the virial within the inner sphere, the radius of which is so
taken that within that distance the number of particles is not
proportional to the number in a large sphere. For Van der Waals this
radius is the diameter of his hard molecules, which assumption gives his
equation. But it is plain that the attraction between the molecules must
to a certain extent modify their distribution, unless some peculiar
conditions are fulfilled. The equation of Van der Waals can be
approximately true, therefore, only for a gas. In a solid or liquid
condition, in which the removal of a small amount of pressure has little
effect on the volume, and where consequently the virial must be much
greater than _P_ avg(_V_), the virial must increase with the volume. For
suppose we had a substance in a critical condition in which an increase
of the volume would diminish the virial more than it would increase
(3/2)_P_ avg(_V_). If we were forcibly to diminish the volume of such a
substance, when the temperature became equalized, the pressure which it
could withstand would be less than before, and it would be still further
condensed, and this would go on indefinitely until a condition were
reached in which an increase of volume would increase (3/2)_P_ avg(_V_)
more than it would decrease the virial. In the case of solids, at least,
_P_ may be zero; so that the state reached would be one in which the
virial increases with the volume, or the attraction between the
particles does not increase so fast with a diminution of their distance
as it would if the attraction were inversely as the distance.

Almost contemporaneously with Van der Waals’s paper, another remarkable
thesis for the doctorate was presented at Paris by Amagat. It related to
the elasticity and expansion of gases, and to this subject the superb
experimenter, its author, has devoted his whole subsequent life.
Especially interesting are his observations of the volumes of ethylene
and of carbonic acid at temperatures from 20° to 100° and at pressures
ranging from an ounce to 5000 pounds to the square inch. As soon as
Amagat had obtained these results, he remarked that the “coefficient of
expansion at constant volume,” as it is absurdly called, that is, the
rate of variation of the pressure with the temperature, was very nearly
constant for each volume. This accords with the equation of the virial,
which gives

              _dp_/_d_θ = _a_/avg(_V_) - _d_∑ avg(_Rr_)/_d_θ.

Now, the virial must be nearly independent of the temperature, and,
therefore, the last term almost disappears. The virial would not be
quite independent of the temperature, because if the temperature (i.e.,
the square of the velocity of the molecules) is lowered, and the
pressure correspondingly lowered, so as to make the volume the same, the
attractions of the molecules will have more time to produce their
effects, and consequently, the pairs of molecules the closest together
will be held together longer and closer; so that the virial will
generally be increased by a decrease of temperature. Now, Amagat’s
experiments do show an excessively minute effect of this sort, at least,
when the volumes are not too small. However, the observations are well
enough satisfied by assuming the “coefficient of expansion at constant
volume” to consist wholly of the first term, _a_/avg(_V_). Thus,
Amagat’s experiments enable us to determine the values of a and thence
to calculate the virial; and this we find varies for carbonic acid gas
nearly inversely to avg(_V_)^{0.9}. There is, thus, a rough
approximation to satisfying Van der Waals’s equation. But the most
interesting result of Amagat’s experiments, for our purpose at any rate,
is that the quantity _a_, though nearly constant for any one volume,
differs considerably with the volume, nearly doubling when the volume is
reduced fivefold. This can only indicate that the mean kinetic energy of
a given mass of the gas for a given temperature is greater the more the
gas is compressed. But the laws of mechanics appear to enjoin that the
mean kinetic energy of a moving particle shall be constant at any given
temperature. The only escape from contradiction, then, is to suppose
that the mean mass of a moving particle diminishes upon the condensation
of the gas. In other words, many of the molecules are dissociated, or
broken up into atoms or sub-molecules. The idea that dissociation should
be favored by diminishing the volume will be pronounced by physicists,
at first blush, as contrary to all our experience. But it must be
remembered that the circumstances we are speaking of, that of a gas
under fifty or more atmospheres pressure, are also unusual. That the
“coefficient of expansion under constant volume” when multiplied by the
volumes should increase with a decrement of the volume is also quite
contrary to ordinary experience; yet it undoubtedly takes place in all
gases under great pressure. Again, the doctrine of Arrhenius[70] is now
generally accepted, that the molecular conductivity of an electrolyte is
proportional to the dissociation of ions. Now the molecular conductivity
of a fused electrolyte is usually superior to that of a solution. Here
is a case, then, in which diminution of volume is accompanied by
increased dissociation.

The truth is that several different kinds of dissociation have to be
distinguished. In the first place, there is the dissociation of a
chemical molecule to form chemical molecules under the regular action of
chemical laws. This may be a double decomposition, as when iodhydric
acid is dissociated, according to the formula

                         _HI_ + _HI_ = _HH_ + _II_;

or, it may be a simple decomposition, as when pentachloride of
phosphorus is dissociated according to the formula

                      _PCl__{5} = _PCl__{3} + _ClCl_.

All these dissociations require, according to the laws of
thermo-chemistry, an elevated temperature. In the second place, there is
the dissociation of a physically polymerous molecule, that is, of
several chemical molecules joined by physical attractions. This I am
inclined to suppose is a common concomitant of the heating of solids and
liquids; for in these bodies there is no increase of compressibility
with the temperature at all comparable with the increase of the
expansibility. But, in the third place, there is the dissociation with
which we are now concerned, which must be supposed to be a throwing off
of unsaturated sub-molecules or atoms from the molecule. The molecule
may, as I have said, be roughly likened to a solar system. As such,
molecules are able to produce perturbations of one another’s internal
motions; and in this way a planet, i.e., a sub-molecule, will
occasionally get thrown off and wander about by itself, till it finds
another unsaturated sub-molecule with which it can unite. Such
dissociation by perturbation will naturally be favored by the proximity
of the molecules to one another.

Let us now pass to the consideration of that special substance, or
rather class of substances, whose properties form the chief subject of
botany and of zoölogy, as truly as those of the silicates form the chief
subject of mineralogy: I mean the life-slimes, or protoplasm. Let us
begin by cataloguing the general characters of these slimes. They one
and all exist in two states of aggregation, a solid or nearly solid
state and a liquid or nearly liquid state; but they do not pass from the
former to the latter by ordinary fusion. They are readily decomposed by
heat, especially in the liquid state; nor will they bear any
considerable degree of cold. All their vital actions take place at
temperatures very little below the point of decomposition. This extreme
instability is one of numerous facts which demonstrate the chemical
complexity of protoplasm. Every chemist will agree that they are far
more complicated than the albumens. Now, albumen is estimated to contain
in each molecule about a thousand atoms; so that it is natural to
suppose that the protoplasms contain several thousands. We know that
while they are chiefly composed of oxygen, hydrogen, carbon, and
nitrogen, a large number of other elements enter into living bodies in
small proportions; and it is likely that most of these enter into the
composition of protoplasms. Now, since the numbers of chemical varieties
increase at an enormous rate with the number of atoms per molecule, so
that there are certainly hundreds of thousands of substances whose
molecules contain twenty atoms or fewer, we may well suppose that the
number of protoplasmic substances runs into the billions or trillions.
Professor Cayley has given a mathematical theory of “trees,” with a view
of throwing a light upon such questions; and in that light the estimate
of trillions (in the English sense) seems immoderately moderate. It is
true that an opinion has been emitted, and defended among biologists,
that there is but one kind of protoplasm; but the observations of
biologists, themselves, have almost exploded that hypothesis, which from
a chemical standpoint appears utterly incredible. The anticipation of
the chemist would decidedly be that enough different chemical substances
having protoplasmic characters might be formed to account, not only for
the differences between nerve-slime and muscle-slime, between
whale-slime and lion-slime, but also for those minuter pervasive
variations which characterize different breeds and single individuals.

Protoplasm, when quiescent, is, broadly speaking, solid; but when it is
disturbed in an appropriate way, or sometimes even spontaneously without
external disturbance, it becomes, broadly speaking, liquid. A moner in
this state is seen under the microscope to have streams within its
matter; a slime-mould slowly flows by force of gravity. The liquefaction
starts from the point of disturbance and spreads through the mass. This
spreading, however, is not uniform in all directions; on the contrary,
it takes at one time one course, at another another, through the
homogeneous mass, in a manner that seems a little mysterious. The cause
of disturbance being removed, these motions gradually (with higher kinds
of protoplasm, quickly) cease, and the slime returns to its solid
condition.

The liquefaction of protoplasm is accompanied by a mechanical
phenomenon. Namely, some kinds exhibit a tendency to draw themselves up
into a globular form. This happens particularly with the contents of
muscle-cells. The prevalent opinion, founded on some of the most
exquisite experimental investigations that the history of science can
show, is undoubtedly that the contraction of muscle-cells is due to
osmotic pressure; and it must be allowed that that is a factor in
producing the effect. But it does not seem to me that it satisfactorily
accounts even for the phenomena of muscular contraction; and besides,
even naked slimes often draw up in the same way. In this case, we seem
to recognize an increase of the surface-tension. In some cases, too, the
reverse action takes place, extraordinary pseudopodia being put forth,
as if the surface-tension were diminished in spots. Indeed, such a slime
always has a sort of skin, due no doubt to surface-tension, and this
seems to give way at the point where a pseudopodium is put forth.

Long-continued or frequently repeated liquefaction of the protoplasm
results in an obstinate retention of the solid state, which we call
fatigue. On the other hand, repose in this state, if not too much
prolonged, restores the liquefiability. These are both important
functions.

The life-slimes have, further, the peculiar property of growing.
Crystals also grow; their growth, however, consists merely in attracting
matter like their own from the circumambient fluid. To suppose the
growth of protoplasm of the same nature, would be to suppose this
substance to be spontaneously generated in copious supplies wherever
food is in solution. Certainly, it must be granted that protoplasm is
but a chemical substance, and that there is no reason why it should not
be formed synthetically like any other chemical substance. Indeed,
Clifford has clearly shown that we have overwhelming evidence that it is
so formed. But to say that such formation is as regular and frequent as
the assimilation of food is quite another matter. It is more consonant
with the facts of observation to suppose that assimilated protoplasm is
formed at the instant of assimilation, under the influence of the
protoplasm already present. For each slime in its growth preserves its
distinctive characters with wonderful truth, nerve-slime growing
nerve-slime and muscle-slime muscle-slime, lion-slime growing
lion-slime, and all the varieties of breeds and even individual
characters being preserved in the growth. Now it is too much to suppose
there are billions of different kinds of protoplasm floating about
wherever there is food.

The frequent liquefaction of protoplasm increases its power of
assimilating food; so much so, indeed, that it is questionable whether
in the solid form it possesses this power.

The life-slime wastes as well as grows; and this too takes place chiefly
if not exclusively in its liquid phases.

Closely connected with growth is reproduction; and though in higher
forms this is a specialized function, it is universally true that
wherever there is protoplasm, there is, will be, or has been a power of
reproducing that same kind of protoplasm in a separated organism.
Reproduction seems to involve the union of two sexes; though it is not
demonstrable that this is always requisite.

Another physical property of protoplasm is that of taking habits. The
course which the spread of liquefaction has taken in the past is
rendered thereby more likely to be taken in the future; although there
is no absolute certainly that the same path will be followed again.

Very extraordinary, certainly, are all these properties of protoplasm;
as extraordinary as indubitable. But the one which has next to be
mentioned, while equally undeniable, is infinitely more wonderful. It is
that protoplasm feels. We have no direct evidence that this is true of
protoplasm universally, and certainly some kinds feel far more than
others. But there is a fair analogical inference that all protoplasm
feels. It not only feels but exercises all the functions of mind.

Such are the properties of protoplasm. The problem is to find a
hypothesis of the molecular constitution of this compound which will
account for these properties, one and all.

Some of them are obvious results of the excessively complicated
constitution of the protoplasm molecule. All very complicated substances
are unstable; and plainly a molecule of several thousand atoms may be
separated in many ways into two parts in each of which the polar
chemical forces are very nearly saturated. In the solid protoplasm, as
in other solids, the molecules must be supposed to be moving as it were
in orbits, or, at least, so as not to wander indefinitely. But this
solid cannot be melted, for the same reason that starch cannot be
melted; because an amount of heat insufficient to make the entire
molecules wander is sufficient to break them up completely and cause
them to form new and simpler molecules. But when one of the molecules is
disturbed, even if it be not quite thrown out of its orbit at first,
sub-molecules of perhaps several hundred atoms each are thrown off from
it. These will soon acquire the same mean kinetic energy as the others,
and, therefore, velocities several times as great. They will naturally
begin to wander, and in wandering will perturb a great many other
molecules and cause them in their turn to behave like the one originally
deranged. So many molecules will thus be broken up, that even those that
are intact will no longer be restrained within orbits, but will wander
about freely. This is the usual condition of a liquid, as modern
chemists understand it; for in all electrolytic liquids there is
considerable dissociation.

But this process necessarily chills the substance, not merely on account
of the heat of chemical combination, but still more because the number
of separate particles being greatly increased, the mean kinetic energy
must be less. The substance being a bad conductor, this heat is not at
once restored. Now the particles moving more slowly, the attractions
between them have time to take effect, and they approach the condition
of equilibrium. But their dynamic equilibrium is found in the
restoration of the solid condition, which, therefore, takes place, if
the disturbance is not kept up.

When a body is in the solid condition, most of its molecules must be
moving at the same rate, or, at least, at certain regular sets of rates;
otherwise the orbital motion would not be preserved. The distances of
neighboring molecules must always be kept between a certain maximum and
a certain minimum value. But if, without absorption of heat, the body be
thrown into a liquid condition, the distances of neighboring molecules
will be far more unequally distributed, and an effect upon the virial
will result. The chilling of protoplasm upon its liquefaction must also
be taken into account. The ordinary effect will no doubt be to increase
the cohesion and with that the surface-tension, so that the mass will
tend to draw itself up. But in special cases, the virial will be
increased so much that the surface-tension will be diminished at points
where the temperature is first restored. In that case, the outer film
will give way and the tension at other places will aid in causing the
general fluid to be poured out at those points, forming pseudopodia.

When the protoplasm is in a liquid state, and then only, a solution of
food is able to penetrate its mass by diffusion. The protoplasm is then
considerably dissociated; and so is the food, like all dissolved matter.
If then the separated and unsaturated sub-molecules of the food happen
to be of the same chemical species as sub-molecules of the protoplasm,
they may unite with other sub-molecules of the protoplasm to form new
molecules, in such a fashion that when the solid state is resumed, there
may be more molecules of protoplasm than there were at the beginning. It
is like the jackknife whose blade and handle, after having been
severally lost and replaced, were found and put together to make a new
knife.

We have seen that protoplasm is chilled by liquefaction, and that this
brings it back to the solid state, when the heat is recovered. This
series of operations must be very rapid in the case of nerve-slime and
even of muscle-slime, and may account for the unsteady or vibratory
character of their action. Of course, if assimilation takes place, the
heat of combination, which is probably trifling, is gained. On the other
hand, if work is done, whether by nerve or by muscle, loss of energy
must take place. In the case of the muscle, the mode by which the
instantaneous part of the fatigue is brought about is easily traced out.
If when the muscle contracts it be under stress, it will contract less
than it otherwise would do, and there will be a loss of heat. It is like
an engine which should work by dissolving salt in water and using the
contraction during the solution to lift a weight, the salt being
recovered afterwards by distillation. But the major part of fatigue has
nothing to do with the correlation of forces. A man must labor hard to
do in a quarter of an hour the work which draws from him enough heat to
cool his body by a single degree. Meantime, he will be getting heated,
he will be pouring out extra products of combustion, perspiration, etc.,
and he will be driving the blood at an accelerated rate through minute
tubes at great expense. Yet all this will have little to do with his
fatigue. He may sit quietly at his table writing, doing practically no
physical work at all, and yet in a few hours be terribly fagged. This
seems to be owing to the deranged sub-molecules of the nerve-slime not
having had time to settle back into their proper combinations. When such
sub-molecules are thrown out, as they must be from time to time, there
is so much waste of material.

In order that a sub-molecule of food may be thoroughly and firmly
assimilated into a broken molecule of protoplasm, it is necessary not
only that it should have precisely the right chemical composition, but
also that it should be at precisely the right spot at the right time and
should be moving in precisely the right direction with precisely the
right velocity. If all these conditions are not fulfilled, it will be
more loosely retained than the other parts of the molecule; and every
time it comes round into the situation in which it was drawn in,
relatively to the other parts of that molecule and to such others as
were near enough to be factors in the action, it will be in special
danger of being thrown out again. Thus, when a partial liquefaction of
the protoplasm takes place many times to about the same extent, it will,
each time, be pretty nearly the same molecules that were last drawn in
that are now thrown out. They will be thrown out, too, in about the same
way, as to position, direction of motion, and velocity, in which they
were drawn in; and this will be in about the same course that the ones
last before them were thrown out. Not exactly, however; for the very
cause of their being thrown off so easily is their not having fulfilled
precisely the conditions of stable retention. Thus, the law of habit is
accounted for, and with it its peculiar characteristic of not acting
with exactitude.

It seems to me that this explanation of habit, aside from the question
of its truth or falsity, has a certain value as an addition to our
little store of mechanical examples of actions analogous to habit. All
the others, so far as I know, are either statical or else involve forces
which, taking only the sensible motions into account, violate the law of
energy. It is so with the stream that wears its own bed. Here, the sand
is carried to its most stable situation and left there. The law of
energy forbids this; for when anything reaches a position of stable
equilibrium, its momentum will be at a maximum, so that it can according
to this law only be left at rest in an unstable situation. In all the
statical illustrations, too, things are brought into certain states and
left there. A garment receives folds and keeps them; that is, its limit
of elasticity is exceeded. This failure to spring back is again an
apparent violation of the law of energy; for the substance will not only
not spring back of itself (which might be due to an unstable equilibrium
being reached) but will not even do so when an impulse that way is
applied to it. Accordingly, Professor James says, “the phenomena of
habit ... are due to the plasticity of the ... materials.” Now,
plasticity of materials means the having of a low limit of elasticity.
(See the _Century Dictionary_, under _solid_.) But the hypothetical
constitution of protoplasm here proposed involves no forces but
attractions and repulsions strictly following the law of energy. The
action here, that is, the throwing of an atom out of its orbit in a
molecule, and the entering of a new atom into nearly, but not quite the
same orbit, is somewhat similar to the molecular actions which may be
supposed to take place in a solid strained beyond its limit of
elasticity. Namely, in that case certain molecules must be thrown out of
their orbits, to settle down again shortly after into new orbits. In
short, the plastic solid resembles protoplasm in being partially and
temporarily liquefied by a slight mechanical force. But the taking of a
set by a solid body has but a moderate resemblance to the taking of a
habit, inasmuch as the characteristic feature of the latter, its
inexactitude and want of complete determinacy, is not so marked in the
former, if it can be said to be present there, at all.

The truth is that though the molecular explanation of habit is pretty
vague on the mathematical side, there can be no doubt that systems of
atoms having polar forces would act substantially in that manner, and
the explanation is even too satisfactory to suit the convenience of an
advocate of tychism. For it may fairly be urged that since the phenomena
of habit may thus result from a purely mechanical arrangement, it is
unnecessary to suppose that habit-taking is a primordial principle of
the universe. But one fact remains unexplained mechanically, which
concerns not only the facts of habit, but all cases of actions
apparently violating the law of energy; it is that all these phenomena
depend upon aggregations of trillions of molecules in one and the same
condition and neighborhood; and it is by no means clear how they could
have all been brought and left in the same place and state by any
conservative forces. But let the mechanical explanation be as perfect as
it may, the state of things which it supposes presents evidence of a
primordial habit-taking tendency. For it shows us like things acting in
like ways because they are alike. Now, those who insist on the doctrine
of necessity will for the most part insist that the physical world is
entirely individual. Yet law involves an element of generality. Now to
say that generality is primordial, but generalization not, is like
saying that diversity is primordial but diversification not. It turns
logic upside down. At any rate, it is clear that nothing but a principle
of habit, itself due to the growth by habit of an infinitesimal chance
tendency toward habit-taking, is the only bridge that can span the chasm
between the chance-medley of chaos and the cosmos of order and law.

I shall not attempt a molecular explanation of the phenomena of
reproduction, because that would require a subsidiary hypothesis, and
carry me away from my main object. Such phenomena, universally diffused
though they be, appear to depend upon special conditions; and we do not
find that all protoplasm has reproductive powers.

But what is to be said of the property of feeling? If consciousness
belongs to all protoplasm, by what mechanical constitution is this to be
accounted for? The slime is nothing but a chemical compound. There is no
inherent impossibility in its being formed synthetically in the
laboratory, out of its chemical elements; and if it were so made, it
would present all the characters of natural protoplasm. No doubt, then,
it would feel. To hesitate to admit this would be puerile and
ultra-puerile. By what element of the molecular arrangement, then, would
that feeling be caused? This question cannot be evaded or pooh-poohed.
Protoplasm certainly does feel; and unless we are to accept a weak
dualism, the property must be shown to arise from some peculiarity of
the mechanical system. Yet the attempt to deduce it from the three laws
of mechanics, applied to never so ingenious a mechanical contrivance,
would obviously be futile. It can never be explained, unless we admit
that physical events are but degraded or undeveloped forms of psychical
events. But once grant that the phenomena of matter are but the result
of the sensibly complete sway of habits upon mind, and it only remains
to explain why in the protoplasm these habits are to some slight extent
broken up, so that according to the law of mind, in that special clause
of it sometimes called the principle of accommodation,[71] feeling
becomes intensified. Now the manner in which habits generally get broken
up is this. Reactions usually terminate in the removal of a stimulus;
for the excitation continues as long as the stimulus is present.
Accordingly, habits are general ways of behavior which are associated
with the removal of stimuli. But when the expected removal of the
stimulus fails to occur, the excitation continues and increases, and
non-habitual reactions take place; and these tend to weaken the habit.
If, then, we suppose that matter never does obey its ideal laws with
absolute precision, but that there are almost insensible fortuitous
departures from regularity, these will produce, in general, equally
minute effects. But protoplasm is in an excessively unstable condition;
and it is the characteristic of unstable equilibrium, that near that
point excessively minute causes may produce startlingly large effects.
Here, then, the usual departures from regularity will be followed by
others that are very great; and the large fortuitous departures from law
so produced, will tend still further to break up the laws, supposing
that these are of the nature of habits. Now, this breaking up of habit
and renewed fortuitous spontaneity will, according to the law of mind,
be accompanied by an intensification of feeling. The nerve-protoplasm
is, without doubt, in the most unstable condition of any kind of matter;
and consequently, there the resulting feeling is the most manifest.

Thus we see that the idealist has no need to dread a mechanical theory
of life. On the contrary, such a theory, fully developed, is bound to
call in a tychistic idealism as its indispensable adjunct. Wherever
chance-spontaneity is found, there, in the same proportion, feeling
exists. In fact, chance is but the outward aspect of that which within
itself is feeling. I long ago showed that real existence, or thing-ness,
consists in regularities. So, that primeval chaos in which there was no
regularity was mere nothing, from a physical aspect. Yet it was not a
blank zero; for there was an intensity of consciousness there in
comparison with which all that we ever feel is but as the struggling of
a molecule or two to throw off a little of the force of law to an
endless and innumerable diversity of chance utterly unlimited.

But after some atoms of the protoplasm have thus become partially
emancipated from law, what happens next to them? To understand this, we
have to remember that no mental tendency is so easily strengthened by
the action of habit as is the tendency to take habits. Now, in the
higher kinds of protoplasm, especially, the atoms in question have not
only long belonged to one molecule or another of the particular mass of
slime of which they are parts; but before that, they were constituents
of food of a protoplasmic constitution. During all this time, they have
been liable to lose habits and to recover them again; so that now, when
the stimulus is removed, and the foregone habits tend to reassert
themselves, they do so in the case of such atoms with great promptness.
Indeed, the return is so prompt that there is nothing but the feeling to
show conclusively that the bonds of law have ever been relaxed.

In short, diversification is the vestige of chance-spontaneity; and
wherever diversity is increasing, there chance must be operative. On the
other hand, wherever uniformity is increasing, habit must be operative.
But wherever actions take place under an established uniformity, there
so much feeling as there may be takes the mode of a sense of reaction.
That is the manner in which I am led to define the relation between the
fundamental elements of consciousness and their physical equivalents.

It remains to consider the physical relations of general ideas. It may
be well here to reflect that if matter has no existence except as a
specialization of mind, it follows that whatever affects matter
according to regular laws is itself matter. But all mind is directly or
indirectly connected with all matter, and acts in a more or less regular
way; so that all mind more or less partakes of the nature of matter.
Hence, it would be a mistake to conceive of the psychical and the
physical aspects of matter as two aspects absolutely distinct. Viewing a
thing from the outside, considering its relations of action and reaction
with other things, it appears as matter. Viewing it from the inside,
looking at its immediate character as feeling, it appears as
consciousness. These two views are combined when we remember that
mechanical laws are nothing but acquired habits, like all the
regularities of mind, including the tendency to take habits, itself; and
that this action of habit is nothing but generalization, and
generalization is nothing but the spreading of feelings. But the
question is, how do general ideas appear in the molecular theory of
protoplasm?

The consciousness of a habit involves a general idea. In each action of
that habit certain atoms get thrown out of their orbit, and replaced by
others. Upon all the different occasions it is different atoms that are
thrown off, but they are analogous from a physical point of view, and
there is an inward sense of their being analogous. Every time one of the
associated feelings recurs, there is a more or less vague sense that
there are others, that it has a general character, and of about what
this general character is. We ought not, I think, to hold that in
protoplasm habit never acts in any other than the particular way
suggested above. On the contrary, if habit be a primary property of
mind, it must be equally so of matter, as a kind of mind. We can hardly
refuse to admit that wherever chance motions have general characters,
there is a tendency for this generality to spread and to perfect itself.
In that case, a general idea is a certain modification of consciousness
which accompanies any regularity or general relation between chance
actions.

The consciousness of a general idea has a certain “unity of the ego,” in
it, which is identical when it passes from one mind to another. It is,
therefore, quite analogous to a person; and, indeed, a person is only a
particular kind of general idea. Long age, in the _Journal of
Speculative Philosophy_ (Vol. II, p. 156), I pointed out that a person
is nothing but a symbol involving a general idea; but my views were,
then, too nominalistic to enable me to see that every general idea has
the unified living feeling of a person.

All that is necessary, upon this theory, to the existence of a person is
that the feelings out of which he is constructed should be in close
enough connection to influence one another. Here we can draw a
consequence which it may be possible to submit to experimental test.
Namely, if this be the case, there should be something like personal
consciousness in bodies of men who are in intimate and intensely
sympathetic communion. It is true that when the generalization of
feeling has been carried so far as to include all within a person, a
stopping-place, in a certain sense, has been attained; and further
generalization will have a less lively character. But we must not think
it will cease. _Esprit de corps_, national sentiment, sympathy, are no
mere metaphors. None of us can fully realize what the minds of
corporations are, any more than one of my brain-cells can know what the
whole brain is thinking. But the law of mind clearly points to the
existence of such personalities, and there are many ordinary
observations which, if they were critically examined and supplemented by
special experiments, might, as first appearances promise, give evidence
of the influence of such greater persons upon individuals. It is often
remarked that on one day half a dozen people, strangers to one another,
will take it into their heads to do one and the same strange deed,
whether it be a physical experiment, a crime, or an act of virtue. When
the thirty thousand young people of the society for Christian Endeavor
were in New York, there seemed to me to be some mysterious diffusion of
sweetness and light. If such a fact is capable of being made out
anywhere, it should be in the church. The Christians have always been
ready to risk their lives for the sake of having prayers in common, of
getting together and praying simultaneously with great energy, and
especially for their common body, for “the whole state of Christ’s
church militant here in earth,” as one of the missals has it. This
practice they have been keeping up everywhere, weekly, for many
centuries. Surely, a personality ought to have developed in that church,
in that “bride of Christ,” as they call it, or else there is a strange
break in the action of mind, and I shall have to acknowledge my views
are much mistaken. Would not the societies for psychical research be
more likely to break through the clouds, in seeking evidences of such
corporate personality, than in seeking evidences of telepathy, which,
upon the same theory, should be a far weaker phenomenon?

Footnote 63:

  _The Monist_, October, 1892.

Footnote 64:

  I am rejoiced to find, since my last paper was printed, that a
  philosopher as subtle and profound as Dr. Edmund Montgomery has long
  been arguing for the same element in the universe. Other
  world-renowned thinkers, as M. Renouvier and M. Delbœuf, appear to
  share this opinion.

Footnote 65:

  By a _vera causa_, in the logic of science, is meant a state of things
  known to exist in some cases and supposed to exist in other cases,
  because it would account for observed phenomena.

Footnote 66:

  Wiedemann, _Annalen_, 1887-1889.

Footnote 67:

  See Maxwell on Spherical Harmonics, in his _Electricity and
  Magnetism_.

Footnote 68:

  The word _system_ has three peculiar meanings in mathematics. (_A._)
  It means an orderly exposition of the truths of astronomy, and hence a
  theory of the motions of the stars; as the Ptolemaic _system_, the
  Copernican _system_. This is much like the sense in which we speak of
  the Calvinistic _system_ of theology, the Kantian _system_ of
  philosophy, etc. (_B._) It means the aggregate of the planets
  considered as all moving in somewhat the same way, as the solar
  _system_; and hence any aggregate of particles moving under mutual
  forces. (_C._) It means a number of forces acting simultaneously upon
  a number of particles.

Footnote 69:

  But, in fact, an inspection of these curves is sufficient to show that
  they are of a higher degree than the third. For they have the line _V_
  = O, or some line _V_ a constant for an asymptote, while for small
  values of _P_, the values of _d_^2_p_/(_dV_)^2 are positive.

Footnote 70:

  Anticipated by Clausius as long ago as 1857; and by Williamson in
  1851.

Footnote 71:

  “Physiologically, ... accommodation means the breaking up of a
  habit.... Psychologically, it means reviving consciousness.” Baldwin,
  _Psychology_, Part III, ch. i., § 5.




                        V. EVOLUTIONARY LOVE[72]
                    AT FIRST BLUSH. COUNTER-GOSPELS


Philosophy, when just escaping from its golden pupa-skin, mythology,
proclaimed the great evolutionary agency of the universe to be Love. Or,
since this pirate-lingo, English, is poor in such-like words, let us say
Eros, the exuberance-love. Afterwards, Empedocles set up passionate-love
and hate as the two co-ordinate powers of the universe. In some
passages, kindness is the word. But certainly, in any sense in which it
has an opposite, to be senior partner of that opposite, is the highest
position that love can attain. Nevertheless, the ontological gospeller,
in whose days those views were familiar topics, made the One Supreme
Being, by whom all things have been made out of nothing, to be
cherishing-love. What, then, can he say to hate? Never mind, at this
time, what the scribe of the apocalypse, if he were John, stung at
length by persecution into a rage unable to distinguish suggestions of
evil from visions of heaven, and so become the Slanderer of God to men,
may have dreamed. The question is rather what the sane John thought, or
ought to have thought, in order to carry out his idea consistently. His
statement that God is love seems aimed at that saying of Ecclesiastes
that we cannot tell whether God bears us love or hatred. “Nay,” says
John, “we can tell, and very simply! We know and have trusted the love
which God hath in us. God is love.” There is no logic in this, unless it
means that God loves all men. In the preceding paragraph, he had said,
“God is light and in him is no darkness at all.” We are to understand,
then, that as darkness is merely the defect of light, so hatred and evil
are mere imperfect stages of ἀγἀπη and ἀγαθόν, love and loveliness. This
concords with that utterance reported in John’s Gospel: “God sent not
the Son into the world to judge the world; but that the world should
through him be saved. He that believeth on him is not judged: he that
believeth not hath been judged already.... And this is the judgment,
that the light is come into the world, and that men loved darkness
rather than the light.” That is to say, God visits no punishment on
them; they punish themselves, by their natural affinity for the
defective. Thus, the love that God is, is not a love of which hatred is
the contrary; otherwise Satan would be a co-ordinate power; but it is a
love which embraces hatred as an imperfect stage of it, an Anteros—yea,
even needs hatred and hatefulness as its object. For self-love is no
love; so if God’s self is love, that which he loves must be defect of
love; just as a luminary can light up only that which otherwise would be
dark. Henry James, the Swedenborgian, says: “It is no doubt very
tolerable finite or creaturely love to love one’s own in another, to
love another for his conformity to one’s self: but nothing can be in
more flagrant contrast with the creative Love, all whose tenderness _ex
vi termini_ must be reserved only for what intrinsically is most
bitterly hostile and negative to itself.” This is from _Substance and
Shadow_: an _Essay on the Physics of Creation_. It is a pity he had not
filled his pages with things like this, as he was able easily to do,
instead of scolding at his reader and at people generally, until the
physics of creation was well-nigh forgot. I must deduct, however, from
what I just wrote: obviously no genius could make his every sentence as
sublime as one which discloses for the problem of evil its everlasting
solution.

The movement of love is circular, at one and the same impulse projecting
creations into independency and drawing them into harmony. This seems
complicated when stated so; but it is fully summed up in the simple
formula we call the Golden Rule. This does not, of course, say, Do
everything possible to gratify the egoistic impulses of others, but it
says, Sacrifice your own perfection to the perfectionment of your
neighbor. Nor must it for a moment be confounded with the Benthamite, or
Helvetian, or Beccarian motto, Act for the greatest good of the greatest
number. Love is not directed to abstractions but to persons; not to
persons we do not know, nor to numbers of people, but to our own dear
ones, our family and neighbors. “Our neighbor,” we remember, is one whom
we live near, not locally perhaps, but in life and feeling.

Everybody can see that the statement of St. John is the formula of an
evolutionary philosophy, which teaches that growth comes only from love,
from—I will not say self-_sacrifice_, but from the ardent impulse to
fulfil another’s highest impulse. Suppose, for example, that I have an
idea that interests me. It is my creation. It is my creature; for as
shown in last July’s _Monist_, it is a little person. I love it; and I
will sink myself in perfecting it. It is not by dealing out cold justice
to the circle of my ideas that I can make them grow, but by cherishing
and tending them as I would the flowers in my garden. The philosophy we
draw from John’s gospel is that this is the way mind develops; and as
for the cosmos, only so far as it yet is mind, and so has life, is it
capable of further evolution. Love, recognizing germs of loveliness in
the hateful, gradually warms it into life, and makes it lovely. That is
the sort of evolution which every careful student of my essay _The Law
of Mind_, must see that _synechism_ calls for.

The nineteenth century is now fast sinking into the grave, and we all
begin to review its doings and to think what character it is destined to
bear as compared with other centuries in the minds of future historians.
It will be called, I guess, the Economical Century; for political
economy has more direct relations with all the branches of its activity
than has any other science. Well, political economy has its formula of
redemption, too. It is this: Intelligence in the service of greed
ensures the justest prices, the fairest contracts, the most enlightened
conduct of all the dealings between men, and leads to the _summum
bonum_, food in plenty and perfect comfort. Food for whom? Why, for the
greedy master of intelligence. I do not mean to say that this is one of
the legitimate conclusions of political economy, the scientific
character of which I fully acknowledge. But the study of doctrines,
themselves true, will often temporarily encourage generalizations
extremely false, as the study of physics has encouraged
necessitarianism. What I say, then, is that the great attention paid to
economical questions during our century has induced an exaggeration of
the beneficial effects of greed and of the unfortunate results of
sentiment, until there has resulted a philosophy which comes unwittingly
to this, that greed is the great agent in the elevation of the human
race and in the evolution of the universe.

I open a handbook of political economy,—the most typical and middling
one I have at hand,—and there find some remarks of which I will here
make a brief analysis. I omit qualifications, sops thrown to Cerberus,
phrases to placate Christian prejudice, trappings which serve to hide
from author and reader alike the ugly nakedness of the greed-god. But I
have surveyed my position. The author enumerates “three motives to human
action:

The love of self;

The love of a limited class having common interests and feelings with
one’s self;

The love of mankind at large.”

Remark, at the outset, what obsequious title is bestowed on greed,—“the
love of self.” Love! The second motive _is_ love. In place of “a limited
class” put “certain persons,” and you have a fair description. Taking
“class” in the old-fashioned sense, a weak kind of love is described. In
the sequel, there seems to be some haziness as to the delimitation of
this motive. By the love of mankind at large, the author does not mean
that deep, subconscious passion that is properly so called; but merely
public-spirit, perhaps little more than a fidget about pushing ideas.
The author proceeds to a comparative estimate of the worth of these
motives. Greed, says he, but using, of course, another word, “is not so
great an evil as is commonly supposed... Every man can promote his own
interests a great deal more effectively than he can promote any one
else’s, or than any one else can promote his.” Besides, as he remarks on
another page, the more miserly a man is, the more good he does. The
second motive “is the most dangerous one to which society is exposed.”
Love is all very pretty: “no higher or purer source of human happiness
exists.” (Ahem!) But it is a “source of enduring injury,” and, in short,
should be overruled by something wiser. What is this wiser motive? We
shall see.

As for public spirit, it is rendered nugatory by the “difficulties in
the way of its effective operation.” For example, it might suggest
putting checks upon the fecundity of the poor and the vicious; and “no
measure of repression would be too severe,” in the case of criminals.
The hint is broad. But unfortunately, you cannot induce legislatures to
take such measures, owing to the pestiferous “tender sentiments of man
towards man.” It thus appears, that public-spirit, or Benthamism, is not
strong enough to be the effective tutor of love, (I am skipping to
another page), which must, therefore, be handed over to “the motives
which animate men in the pursuit of wealth,” in which alone we can
confide, and which “are in the highest degree beneficent.”[73] Yes, in
the “highest degree” without exception are they beneficent to the being
upon whom all their blessings are poured out, namely, the Self, whose
“sole object,” says the writer in accumulating wealth is his individual
“sustenance and enjoyment.” Plainly, the author holds the notion that
some other motive might be in a higher degree beneficent even for the
man’s self to be a paradox wanting in good sense. He seeks to gloze and
modify his doctrine; but he lets the perspicacious reader see what his
animating principle is; and when, holding the opinions I have repeated,
he at the same time acknowledges that society could not exist upon a
basis of intelligent greed alone, he simply pigeon-holes himself as one
of the eclectics of inharmonious opinions. He wants his mammon flavored
with a _soupçon_ of god.

The economists accuse those to whom the enunciation of their atrocious
villainies communicates a thrill of horror of being _sentimentalists_.
It may be so: I willingly confess to having some tincture of
sentimentalism in me, God be thanked! Ever since the French Revolution
brought this leaning of thought into ill-repute,—and not altogether
undeservedly, I must admit, true, beautiful, and good as that great
movement was—it has been the tradition to picture sentimentalists as
persons incapable of logical thought and unwilling to look facts in the
eyes. This tradition may be classed with the French tradition that an
Englishman says _godam_ at every second sentence, the English tradition
that an American talks about “Britishers,” and the American tradition
that a Frenchman carries forms of etiquette to an inconvenient extreme,
in short with all those traditions which survive simply because the men
who use their eyes and ears are few and far between. Doubtless some
excuse there was for all those opinions in days gone by; and
sentimentalism, when it was the fashionable amusement to spend one’s
evenings in a flood of tears over a woeful performance on a
candle-litten stage, sometimes made itself a little ridiculous. But what
after all is sentimentalism? It is an _ism_, a doctrine, namely, the
doctrine that great respect should be paid to the natural judgments of
the sensible heart. This is what sentimentalism precisely is; and I
entreat the reader to consider whether to contemn it is not of all
blasphemies the most degrading. Yet the nineteenth century has steadily
contemned it, because it brought about the Reign of Terror. That it did
so is true. Still, the whole question is one of _how much_. The Reign of
Terror was very bad; but now the Gradgrind banner has been this century
long flaunting in the face of heaven, with an insolence to provoke the
very skies to scowl and rumble. Soon a flash and quick peal will shake
economists quite out of their complacency, too late. The twentieth
century, in its latter half, shall surely see the deluge-tempest burst
upon the social order,—to clear upon a world as deep in ruin as that
greed-philosophy has long plunged it into guilt. No post-thermidorian
high jinks then!

So a miser is a beneficent power in a community, is he? With the same
reason precisely, only in a much higher degree, you might pronounce the
Wall Street sharp to be a good angel, who takes money from heedless
persons not likely to guard it properly, who wrecks feeble enterprises
better stopped, and who administers wholesome lessons to unwary
scientific men, by passing worthless checks upon them,—as you did, the
other day, to me, my millionaire Master in glomery, when you thought you
saw your way to using my process without paying for it, and of so
bequeathing to your children something to boast of their father
about,—and who by a thousand wiles puts money at the service of
intelligent greed, in his own person. Bernard Mandeville, in his _Fable
of the Bees_, maintains that private vices of all descriptions are
public benefits, and proves it, too, quite as cogently as the economist
proves his point concerning the miser. He even argues, with no slight
force, that but for vice civilization would never have existed. In the
same spirit, it has been strongly maintained and is to-day widely
believed that all acts of charity and benevolence, private and public,
go seriously to degrade the human race.

The _Origin of Species_ of Darwin merely extends politico-economical
views of progress to the entire realm of animal and vegetable life. The
vast majority of our contemporary naturalists hold the opinion that the
true cause of those exquisite and marvellous adaptations of nature for
which, when I was a boy, men used to extol the divine wisdom is that
creatures are so crowded together that those of them that happen to have
the slightest advantage force those less pushing into situations
unfavorable to multiplication or even kill them before they reach the
age of reproduction. Among animals, the mere mechanical individualism is
vastly reënforced as a power making for good by the animal’s ruthless
greed. As Darwin puts it on his title-page, it is the struggle for
existence; and he should have added for his motto: Every individual for
himself, and the Devil take the hindmost! Jesus, in his sermon on the
Mount, expressed a different opinion.

Here, then, is the issue. The gospel of Christ says that progress comes
from every individual merging his individuality in sympathy with his
neighbors. On the other side, the conviction of the nineteenth century
is that progress takes place by virtue of every individual’s striving
for himself with all his might and trampling his neighbor under foot
whenever he gets a chance to do so. This may accurately be called the
Gospel of Greed.

Much is to be said on both sides. I have not concealed, I could not
conceal, my own passionate predilection. Such a confession will probably
shock my scientific brethren. Yet the strong feeling is in itself, I
think, an argument of some weight in favor of the agapastic theory of
evolution,—so far as it may be presumed to bespeak the normal judgment
of the Sensible Heart. Certainly, if it were possible to believe in
agapasm without believing it warmly, that fact would be an argument
against the truth of the doctrine. At any rate, since the warmth of
feeling exists, it should on every account be candidly confessed;
especially since it creates a liability to onesidedness on my part
against which it behooves my readers and me to be severally on our
guard.


                       SECOND THOUGHTS. IRENICA.


Let us try to define the logical affinities of the different theories of
evolution. Natural selection, as conceived by Darwin, is a mode of
evolution in which the only positive agent of change in the whole
passage from moner to man is fortuitous variation. To secure advance in
a definite direction chance has to be seconded by some action that shall
hinder the propagation of some varieties or stimulate that of others. In
natural selection, strictly so called, it is the crowding out of the
weak. In sexual selection, it is the attraction of beauty, mainly.

The _Origin of Species_ was published toward the end of the year 1859.
The preceding years since 1846 had been one of the most productive
seasons,—or if extended so as to cover the great book we are
considering, _the_ most productive period of equal length in the entire
history of science from its beginnings until now. The idea that chance
begets order, which is one of the corner-stones of modern physics
(although Dr. Carus considers it “the weakest point in Mr. Peirce’s
system,”) was at that time put into its clearest light. Quetelet had
opened the discussion by his _Letters on the Application of
Probabilities to the Moral and Political Sciences_, a work which deeply
impressed the best minds of that day, and to which Sir John Herschel had
drawn general attention in Great Britain. In 1857, the first volume of
Buckle’s _History of Civilisation_ had created a tremendous sensation,
owing to the use he made of this same idea. Meantime, the “statistical
method” had, under that very name, been applied with brilliant success
to molecular physics. Dr. John Herapath, an English chemist, had in 1847
outlined the kinetical theory of gases in his _Mathematical Physics_;
and the interest the theory excited had been refreshed in 1856 by
notable memoirs by Clausius and Krönig. In the very summer preceding
Darwin’s publication, Maxwell had read before the British Association
the first and most important of his researches on this subject. The
consequence was that the idea that fortuitous events may result in a
physical law, and further that this is the way in which those laws which
appear to conflict with the principle of the conservation of energy are
to be explained, had taken a strong hold upon the minds of all who were
abreast of the leaders of thought. By such minds, it was inevitable that
the _Origin of Species_, whose teaching was simply the application of
the same principle to the explanation of another “non-conservative”
action, that of organic development, should be hailed and welcomed. The
sublime discovery of the conservation of energy by Helmholtz in 1847,
and that of the mechanical theory of heat by Clausius and by Rankine,
independently, in 1850, had decidedly overawed all those who might have
been inclined to sneer at physical science. Thereafter a belated poet
still harping upon “science peddling with the names of things” would
fail of his effect. Mechanism was now known to be all, or very nearly
so. All this time, utilitarianism,—that improved substitute for the
Gospel,—was in its fullest feather; and was a natural ally of an
individualistic theory. Dean Mansell’s injudicious advocacy had led to
mutiny among the bondsmen of Sir William Hamilton, and the nominalism of
Mill had profited accordingly; and although the real science that Darwin
was leading men to was sure some day to give a death-blow to the
sham-science of Mill, yet there were several elements of the Darwinian
theory which were sure to charm the followers of Mill. Another thing:
anæsthetics had been in use for thirteen years. Already, people’s
acquaintance with suffering had dropped off very much; and as a
consequence, that unlovely hardness by which our times are so contrasted
with those that immediately preceded them, had already set in, and
inclined people to relish a ruthless theory. The reader would quite
mistake the drift of what I am saying if he were to understand me as
wishing to suggest that any of those things (except perhaps Malthus)
influenced Darwin himself. What I mean is that his hypothesis, while
without dispute one of the most ingenious and pretty ever devised, and
while argued with a wealth of knowledge, a strength of logic, a charm of
rhetoric, and above all with a certain magnetic genuineness that was
almost irresistible, did not appear, at first, at all near to being
proved; and to a sober mind its case looks less hopeful now than it did
twenty years ago; but the extraordinarily favorable reception it met
with was plainly owing, in large measure, to its ideas being those
toward which the age was favorably disposed, especially, because of the
encouragement it gave to the greed-philosophy.

Diametrically opposed to evolution by chance, are those theories which
attribute all progress to an inward necessary principle, or other form
of necessity. Many naturalists have thought that if an egg is destined
to go through a certain series of embryological transformations, from
which it is perfectly certain not to deviate, and if in geological time
almost exactly the same forms appear successively, one replacing another
in the same order, the strong presumption is that this latter succession
was as predeterminate and certain to take place as the former. So,
Nägeli, for instance, conceives that it somehow follows from the first
law of motion and the peculiar, but unknown, molecular constitution of
protoplasm, that forms must complicate themselves more and more.
Kolliker makes one form generate another after a certain maturation has
been accomplished. Weismann, too, though he calls himself a Darwinian,
holds that nothing is due to chance, but that all forms are simple
mechanical resultants of the heredity from two parents.[74] It is very
noticeable that all these different sectaries seek to import into their
science a mechanical necessity to which the facts that come under their
observation do not point. Those geologists who think that the variation
of species is due to cataclysmic alterations of climate or of the
chemical constitution of the air and water are also making mechanical
necessity chief factor of evolution.

Evolution by sporting and evolution by mechanical necessity are
conceptions warring against one another. A third method, which
supersedes their strife, lies enwrapped in the theory of Lamarck.
According to his view, all that distinguishes the highest organic forms
from the most rudimentary has been brought about by little hypertrophies
or atrophies which have affected individuals early in their lives, and
have been transmitted to their offspring. Such a transmission of
acquired characters is of the general nature of habit-taking, and this
is the representative and derivative within the physiological domain of
the law of mind. Its action is essentially dissimilar to that of a
physical force; and that is the secret of the repugnance of such
necessitarians as Weismann to admitting its existence. The Lamarckians
further suppose that although some of the modifications of form so
transmitted were originally due to mechanical causes, yet the chief
factors of their first production were the straining of endeavor and the
overgrowth superinduced by exercise, together with the opposite actions.
Now, endeavor, since it is directed toward an end, is essentially
psychical, even though it be sometimes unconscious; and the growth due
to exercise, as I argued in my last paper, follows a law of a character
quite contrary to that of mechanics.

Lamarckian evolution is thus evolution by the force of habit.—That
sentence slipped off my pen while one of those neighbors whose function
in the social cosmos seems to be that of an Interrupter, was asking me a
question. Of course, it is nonsense. Habit is mere inertia, a resting on
one’s oars, not a propulsion. Now it is energetic projaculation (lucky
there is such a word, or this untried hand might have been put to
inventing one) by which in the typical instances of Lamarckian evolution
the new elements of form are first created. Habit, however, forces them
to take practical shapes, compatible with the structures they affect,
and in the form of heredity and otherwise, gradually replaces the
spontaneous energy that sustains them. Thus, habit plays a double part;
it serves to establish the new features, and also to bring them into
harmony with the general morphology and function of the animals and
plants to which they belong. But if the reader will now kindly give
himself the trouble of turning back a page or two, he will see that this
account of Lamarckian evolution coincides with the general description
of the action of love, to which, I suppose, he yielded his assent.

Remembering that all matter is really mind, remembering, too, the
continuity of mind, let us ask what aspect Lamarckian evolution takes on
within the domain of consciousness. Direct endeavor can achieve almost
nothing. It is as easy by taking thought to add a cubit to one’s
stature, as it is to produce an idea acceptable to any of the Muses by
merely straining for it, before it is ready to come. We haunt in vain
the sacred well and throne of Mnemosyne; the deeper workings of the
spirit take place in their own slow way, without our connivance. Let but
their bugle sound, and we may then make our effort, sure of an oblation
for the altar of whatsoever divinity its savor gratifies. Besides this
inward process, there is the operation of the environment, which goes to
break up habits destined to be broken up and so to render the mind
lively. Everybody knows that the long continuance of a routine of habit
makes us lethargic, while a succession of surprises wonderfully
brightens the ideas. Where there is a motion, where history is a-making,
there is the focus of mental activity, and it has been said that the
arts and sciences reside within the temple of Janus, waking when that is
open, but slumbering when it is closed. Few psychologists have perceived
how fundamental a fact this is. A portion of mind abundantly commissured
to other portions works almost mechanically. It sinks to a condition of
a railway junction. But a portion of mind almost isolated, a spiritual
peninsula, or _cul-de-sac_, is like a railway terminus. Now mental
commissures are habits. Where they abound, originality is not needed and
is not found; but where they are in defect, spontaneity is set free.
Thus, the first step in the Lamarckian evolution of mind is the putting
of sundry thoughts into situations in which they are free to play. As to
growth by exercise, I have already shown, in discussing _Man’s Glassy
Essence_, in last October’s _Monist_, what its _modus operandi_ must be
conceived to be, at least, until a second equally definite hypothesis
shall have been offered. Namely, it consists of the flying asunder of
molecules, and the reparation of the parts by new matter. It is, thus, a
sort of reproduction. It takes place only during exercise, because the
activity of protoplasm consists in the molecular disturbance which is
its necessary condition. Growth by exercise takes place also in the
mind. Indeed, that is what it is to _learn_. But the most perfect
illustration is the development of a philosophical idea by being put
into practice. The conception which appeared, at first, as unitary,
splits up into special cases; and into each of these new thought must
enter to make a practicable idea. This new thought, however, follows
pretty closely the model of the parent conception; and thus a
homogeneous development takes place. The parallel between this and the
course of molecular occurrences is apparent. Patient attention will be
able to trace all these elements in the transaction called learning.

Three modes of evolution have thus been brought before us; evolution by
fortuitous variation, evolution by mechanical necessity, and evolution
by creative love. We may term them _tychastic_ evolution, or _tychasm_,
_anancastic_ evolution, or _anancasm_, and _agapastic_ evolution, or
_agapasm_. The doctrines which represent these as severally of principal
importance, we may term _tychasticism_, _anancasticism_, and
_agapasticism_. On the other hand the mere propositions that absolute
chance, mechanical necessity, and the law of love, are severally
operative in the cosmos, may receive the names of _tychism_, _anancism_,
and _agapism_.

All three modes of evolution are composed of the same general elements.
Agapasm exhibits them the most clearly. The good result is here brought
to pass, first, by the bestowal of spontaneous energy by the parent upon
the offspring, and, second, by the disposition of the latter to catch
the general idea of those about it and thus to subserve the general
purpose. In order to express the relation that tychasm and anancasm bear
to agapasm, let me borrow a word from geometry. An ellipse crossed by a
straight line is a sort of cubic curve; for a cubic is a curve which is
cut thrice by a straight line; now a straight line might cut the ellipse
twice and its associated straight line a third time. Still the ellipse
with the straight line across it would not have the characteristics of a
cubic. It would have, for instance, no contrary flexure, which no true
cubic wants; and it would have two nodes, which no true cubic has. The
geometers say that it is a _degenerate_ cubic. Just so, tychasm and
anancasm are degenerate forms of agapasm.

Men who seek to reconcile the Darwinian idea with Christianity will
remark that tychastic evolution, like the agapastic, depends upon a
reproductive creation, the forms preserved being those that use the
spontaneity conferred upon them in such wise as to be drawn into harmony
with their original, quite after the Christian scheme. Very good! This
only shows that just as love cannot have a contrary, but must embrace
what is most opposed to it, as a degenerate case of it, so tychasm is a
kind of agapasm. Only, in the tychastic evolution progress is solely
owing to the distribution of the napkin-hidden talent of the rejected
servant among those not rejected, just as ruined gamesters leave their
money on the table to make those not yet ruined so much the richer. It
makes the felicity of the lambs just the damnation of the goats,
transposed to the other side of the equation. In genuine agapasm, on the
other hand, advance takes place by virtue of a positive sympathy among
the created springing from continuity of mind. This is the idea which
tychasticism knows not how to manage.

The anancasticist might here interpose, claiming that the mode of
evolution for which he contends agrees with agapasm at the point at
which tychasm departs from it. For it makes development go through
certain phases, having its inevitable ebbs and flows, yet tending on the
whole to a foreordained perfection. Bare existence by this its destiny
betrays an intrinsic affinity for the good. Herein, it must be admitted,
anancasm shows itself to be in a broad acception a species of agapasm.
Some forms of it might easily be mistaken for the genuine agapasm. The
Hegelian philosophy is such an anancasticism. With its revelatory
religion, with its synechism (however imperfectly set forth), with its
“reflection,” the whole idea of the theory is superb, almost sublime.
Yet, after all, living freedom is practically omitted from its method.
The whole movement is that of a vast engine, impelled by a _vis a
tergo_, with a blind and mysterious fate of arriving at a lofty goal. I
mean that such an engine it _would_ be, if it really worked; but in
point of fact, it is a Keely motor. Grant that it really acts as it
professes to act, and there is nothing to do but accept the philosophy.
But never was there seen such an example of a long chain of
reasoning,—shall I say with a flaw in every link?—no, with every link a
handful of sand, squeezed into shape in a dream. Or say, it is a
pasteboard model of a philosophy that in reality does not exist. If we
use the one precious thing it contains, the idea of it, introducing the
tychism which the arbitrariness of its every step suggests, and make
that the support of a vital freedom which is the breath of the spirit of
love, we may be able to produce that genuine agapasticism, at which
Hegel was aiming.


                     A THIRD ASPECT. DISCRIMINATION


In the very nature of things, the line of demarcation between the three
modes of evolution is not perfectly sharp. That does not prevent its
being quite real; perhaps it is rather a mark of its reality. There is
in the nature of things no sharp line of demarcation between the three
fundamental colors, red, green, and violet. But for all that they are
really different. The main question is whether three radically different
evolutionary elements have been operative; and the second question is
what are the most striking characteristics of whatever elements have
been operative.

I propose to devote a few pages to a very slight examination of these
questions in their relation to the historical development of human
thought. I first formulate for the reader’s convenience the briefest
possible definitions of the three conceivable modes of development of
thought, distinguishing also two varieties of anancasm and three of
agapasm. The tychastic development of thought, then, will consist in
slight departures from habitual ideas in different directions
indifferently, quite purposeless and quite unconstrained whether by
outward circumstances or by force of logic, these new departures being
followed by unforeseen results which tend to fix some of them as habits
more than others. The anancastic development of thought will consist of
new ideas adopted without foreseeing whither they tend, but having a
character determined by causes either external to the mind, such as
changed circumstances of life, or internal to the mind as logical
developments of ideas already accepted, such as generalizations. The
agapastic development of thought is the adoption of certain mental
tendencies, not altogether heedlessly, as in tychasm, nor quite blindly
by the mere force of circumstances or of logic, as in anancasm, but by
an immediate attraction for the idea itself, whose nature is divined
before the mind possesses it, by the power of sympathy, that is, by
virtue of the continuity of mind; and this mental tendency may be of
three varieties, as follows: First, it may affect a whole people or
community in its collective personality, and be thence communicated to
such individuals as are in powerfully sympathetic connection with the
collective people, although they may be intellectually incapable of
attaining the idea by their private understandings or even perhaps of
consciously apprehending it. Second, it may affect a private person
directly, yet so that he is only enabled to apprehend the idea, or to
appreciate its attractiveness, by virtue of his sympathy with his
neighbors, under the influence of a striking experience or development
of thought. The conversion of St. Paul may be taken as an example of
what is meant. Third, it may affect an individual, independently of his
human affections, by virtue of an attraction it exercises upon his mind,
even before he has comprehended it. This is the phenomenon which has
been well called the _divination_ of genius; for it is due to the
continuity between the man’s mind and the Most High.

Let us next consider by means of what tests we can discriminate between
these different categories of evolution. No absolute criterion is
possible in the nature of things, since in the nature of things there is
no sharp line of demarcation between the different classes.
Nevertheless, quantitative symptoms may be found by which a sagacious
and sympathetic judge of human nature may be able to estimate the
approximate proportions in which the different kinds of influence are
commingled.

So far as the historical evolution of human thought has been tychastic,
it should have proceeded by insensible or minute steps; for such is the
nature of chances when so multiplied as to show phenomena of regularity.
For example, assume that of the native-born white adult males of the
United States in 1880, one-fourth part were below 5 feet 4 inches in
stature and one-fourth part above 5 feet 8 inches. Then by the
principles of probability, among the whole population, we should expect

                             216 under 4 feet 6 inches,
                              48   “   4   ”  5   “
                               9   ”   4   “  4   ”
                     less than 2   “   4   ”  3   “

                             216 above 6 feet 6 inches,
                              48   “   6   ”  7   “
                               9   ”   6   “  8   ”
                     less than 2   “   6   ”  9   “

I set down these figures to show how insignificantly few are the cases
in which anything very far out of the common run presents itself by
chance. Though the stature of only every second man is included within
the four inches between 5 feet 4 inches and 5 feet 8 inches, yet if this
interval be extended by thrice four inches above and below, it will
embrace all our 8 millions odd of native-born adult white males (of
1880), except only 9 taller and 9 shorter.

The test of minute variation, if _not_ satisfied, absolutely negatives
tychasm. If it is satisfied, we shall find that it negatives anancasm
but not agapasm. We want a positive test, satisfied by tychasm, only.
Now wherever we find men’s thought taking by imperceptible degrees a
turn contrary to the purposes which animate them, in spite of their
highest impulses, there, we may safely conclude, there has been a
tychastic action.

Students of the history of mind there be of an erudition to fill an
imperfect scholar like me with envy edulcorated by joyous admiration,
who maintain that ideas when just started are and can be little more
than freaks, since they cannot yet have been critically examined, and
further that everywhere and at all times progress has been so gradual
that it is difficult to make out distinctly what original step any given
man has taken. It would follow that tychasm has been the sole method of
intellectual development. I have to confess I cannot read history so; I
cannot help thinking that while tychasm has sometimes been operative, at
others great steps covering nearly the same ground and made by different
men independently, have been mistaken for a succession of small steps,
and further that students have been reluctant to admit a real entitative
“spirit” of an age or of a people, under the mistaken and unscrutinized
impression that they should thus be opening the door to wild and
unnatural hypotheses. I find, on the contrary, that, however it may be
with the education of individual minds, the historical development of
thought has seldom been of a tychastic nature, and exclusively in
backward and barbarizing movements. I desire to speak with the extreme
modesty which befits a student of logic who is required to survey so
very wide a field of human thought that he can cover it only by a
reconnaissance, to which only the greatest skill and most adroit methods
can impart any value at all; but, after all, I can only express my own
opinions and not those of anybody else; and in my humble judgment, the
largest example of tychasm is afforded by the history of Christianity,
from about its establishment by Constantine, to, say, the time of the
Irish monasteries, an era or eon of about 500 years. Undoubtedly the
external circumstance which more than all others at first inclined men
to accept Christianity in its loveliness and tenderness, was the fearful
extent to which society was broken up into units by the unmitigated
greed and hard-heartedness into which the Romans had seduced the world.
And yet it was that very same fact, more than any other external
circumstance, that fostered that bitterness against the wicked world of
which the primitive gospel of Mark contains not a single trace. At
least, I do not detect it in the remark about the blasphemy against the
Holy Ghost, where nothing is said about vengeance, nor even in that
speech where the closing lines of Isaiah are quoted, about the worm and
the fire that feed upon the “carcasses of the men that have transgressed
against me.” But little by little the bitterness increases until in the
last book of the New Testament, its poor distracted author represents
that all the time Christ was talking about having come to save the
world, the secret design was to catch the entire human race, with the
exception of a paltry 144,000, and souse them all in a brimstone lake,
and as the smoke of their torment went up forever and ever, to turn and
remark, “There is no curse any more.” Would it be an insensible smirk or
a fiendish grin that should accompany such an utterance? I wish I could
believe St. John did not write it; but it is his gospel which tells
about the “resurrection unto condemnation,”—that is of men’s being
resuscitated just for the sake of torturing them;—and, at any rate, the
Revelation is a very ancient composition. One can understand that the
early Christians were like men trying with all their might to climb a
steep declivity of smooth wet clay; the deepest and truest element of
their life, animating both heart and head, was universal love; but they
were continually, and against their wills, slipping into a party spirit,
every slip serving as a precedent, in a fashion but too familiar to
every man. This party feeling insensibily grew until by about A.D. 330
the luster of the pristine integrity that in St. Mark reflects the white
spirit of light was so far tarnished that Eusebius, (the Jared Sparks of
that day), in the preface to his History, could announce his intention
of exaggerating everything that tended to the glory of the church and of
suppressing whatever might disgrace it. His Latin contemporary
Lactantius is worse, still; and so the darkling went on increasing until
before the end of the century the great library of Alexandria was
destroyed by Theophilus,[75] until Gregory the Great, two centuries
later, burnt the great library of Rome, proclaiming that “Ignorance is
the mother of devotion,” (which is true, just as oppression and
injustice is the mother of spirituality), until a sober description of
the state of the church would be a thing our not too nice newspapers
would treat as “unfit for publication.” All this movement is shown by
the application of the test given above to have been tychastic. Another
very much like it on a small scale, only a hundred times swifter, for
the study of which there are documents by the library-full, is to be
found in the history of the French Revolution.

Anancastic evolution advances by successive strides with pauses between.
The reason is that in this process a habit of thought having been
overthrown is supplanted by the next strongest. Now this next strongest
is sure to be widely disparate from the first, and as often as not is
its direct contrary. It reminds one of our old rule of making the second
candidate vice-president. This character, therefore, clearly
distinguishes anancasm from tychasm. The character which distinguishes
it from agapasm is its purposelessness. But external and internal
anancasm have to be examined separately. Development under the pressure
of external circumstances, or cataclysmine evolution, is in most cases
unmistakable enough. It has numberless degrees of intensity, from the
brute force, the plain war, which has more than once turned the current
of the world’s thought, down to the hard fact of evidence, or what has
been taken for it, which has been known to convince men by hordes. The
only hesitation than can subsist in the presence of such a history is a
quantitative one. Never are external influences the only ones which
affect the mind, and therefore it must be a matter of judgment for which
it would scarcely be worth while to attempt to set rules, whether a
given movement is to be regarded as principally governed from without or
not. In the rise of medieval thought, I mean scholasticism and the
synchronistic art developments, undoubtedly the crusades and the
discovery of the writings of Aristotle were powerful influences. The
development of scholasticism from Roscellin to Albertus Magnus closely
follows the successive steps in the knowledge of Aristotle. Prantl
thinks that that is the whole story, and few men have thumbed more books
than Carl Prantl. He has done good solid work, notwithstanding his
slap-dash judgments. But we shall never make so much as a good beginning
of comprehending scholasticism until the whole has been systematically
explored and digested by a company of students regularly organized and
held under rule for that purpose. But as for the period we are now
specially considering, that which synchronised the Romanesque
architecture, the literature is easily mastered. It does not quite
justify Prantl’s dicta as to the slavish dependence of these authors
upon their authorities. Moreover, they kept a definite purpose steadily
before their minds, throughout all their studies. I am, therefore,
unable to offer this period of scholasticism as an example of pure
external anancasm, which seems to be the fluorine of the intellectual
elements. Perhaps the recent Japanese reception of western ideas is the
purest instance of it in history. Yet in combination with other
elements, nothing is commoner. If the development of ideas under the
influence of the study of external facts be considered as external
anancasm,—it is on the border between the external and the internal
forms,—it is, of course, the principal thing in modern learning. But
Whewell, whose masterly comprehension of the history of science critics
have been too ignorant properly to appreciate, clearly shows that it is
far from being the overwhelmingly preponderant influence, even there.

Internal anancasm, or logical groping, which advances upon a predestined
line without being able to foresee whither it is to be carried nor to
steer its course, this is the rule of development of philosophy. Hegel
first made the world understand this; and he seeks to make logic not
merely the subjective guide and monitor of thought, which was all it had
been ambitioning before, but to be the very main-spring of thinking, and
not merely of individual thinking but of discussion, of the history of
the development of thought, of all history, of all development. This
involves a positive, clearly demonstrable error. Let the logic in
question be of whatever kind it may, a logic of necessary inference or a
logic of probable inference (the theory might perhaps be shaped to fit
either), in any case it supposes that logic is sufficient of itself to
determine what conclusion follows from given premises; for unless it
will do so much, it will not suffice to explain why an individual train
of reasoning should take just the course it does take, to say nothing of
other kinds of development. It thus supposes that from given premises,
only one conclusion can logically be drawn, and that there is no scope
at all for free choice. That from given premises only one conclusion can
logically be drawn, is one of the false notions which have come from
logicians’ confining their attention to that Nantucket of thought, the
logic of non-relative terms. In the logic of relatives, it does not hold
good.

One remark occurs to me. If the evolution of history is in considerable
part of the nature of internal anancasm, it resembles the development of
individual men; and just as 33 years is a rough but natural unit of time
for individuals, being the average age at which man has issue, so there
should be an approximate period at the end of which one great historical
movement ought to be likely to be supplanted by another. Let us see if
we can make out anything of the kind. Take the governmental development
of Rome as being sufficiently long and set down the principal dates.

                B.C.  753, Foundation of Rome.
                B.C.  510, Expulsion of the Tarquins.
                B.C.   27, Octavius assumes title Augustus.
                A.D.  476, End of Western Empire.
                A.D.  962, Holy Roman Empire.
                A.D. 1453, Fall of Constantinople.

The last event was one of the most significant in history, especially
for Italy. The intervals are 243, 483, 502, 486, 491 years. All are
rather curiously near equal, except the first which is half the others.
Successive reigns of kings would not commonly be so near equal. Let us
set down a few dates in the history of thought.

    B.C.  585, Eclipse of Thales. Beginning of Greek philosophy.
    A.D.   30, The crucifixion.
    A.D.  529, Closing of Athenian schools. End of Greek philosophy.
    A.D. 1125, (Approximate) Rise of the Universities of Bologna and
       Paris.
    A.D. 1543, Publication of the “De Revolutionibus” of Copernicus.
       Beginning of Modern Science.

The intervals are 615, 499, 596, 418, years. In the history of
metaphysics, we may take the following:

                       B.C.  322, Death of Aristotle.
                       A.D. 1274, Death of Aquinas.
                       A.D. 1804, Death of Kant.

The intervals are 1595 and 530 years. The former is about thrice the
latter.

From these figures, no conclusion can fairly be drawn. At the same time,
they suggest that perhaps there may be a rough natural era of about 500
years. Should there be any independent evidence of this, the intervals
noticed may gain some significance.

The agapastic development of thought should, if it exists, be
distinguished by its purposive character, this purpose being the
development of an idea. We should have a direct agapic or sympathetic
comprehension and recognition of it, by virtue of the continuity of
thought. I here take it for granted that such continuity of thought has
been sufficiently proved by the arguments used in my paper on the “Law
of Mind” in _The Monist_ of last July. Even if those arguments are not
quite convincing in themselves, yet if they are reënforced by an
apparent agapasm in the history of thought, the two propositions will
lend one another mutual aid. The reader will, I trust, be too well
grounded in logic to mistake such mutual support for a vicious circle in
reasoning. If it could be shown directly that there is such an entity as
the “spirit of an age” or of a people, and that mere individual
intelligence will not account for all the phenomena, this would be proof
enough at once of agapasticism and of synechism. I must acknowledge that
I am unable to produce a cogent demonstration of this; but I am, I
believe, able to adduce such arguments as will serve to confirm those
which have been drawn from other facts. I believe that all the greatest
achievements of mind have been beyond the powers of unaided individuals;
and I find, apart from the support this opinion receives from
synechistic considerations, and from the purposive character of many
great movements, direct reason for so thinking in the sublimity of the
ideas and in their occurring simultaneously and independently to a
number of individuals of no extraordinary general powers. The pointed
Gothic architecture in several of its developments appears to me to be
of such a character. All attempts to imitate it by modern architects of
the greatest learning and genius appear flat and tame, and are felt by
their authors to be so. Yet at the time the style was living, there was
quite an abundance of men capable of producing works of this kind of
gigantic sublimity and power. In more than one case, extant documents
show that the cathedral chapters, in the selection of architects,
treated high artistic genius as a secondary consideration, as if there
were no lack of persons able to supply that; and the results justify
their confidence. Were individuals in general, then, in those ages
possessed of such lofty natures and high intellect? Such an opinion
would break down under the first examination.

How many times have men now in middle life seen great discoveries made
independently and almost simultaneously! The first instance I remember
was the prediction of a planet exterior to Uranus by Leverrier and
Adams. One hardly knows to whom the principle of the conservation of
energy ought to be attributed, although it may reasonably be considered
as the greatest discovery science has ever made. The mechanical theory
of heat was set forth by Rankine and by Clausius during the same month
of February, 1850; and there are eminent men who attribute this great
step to Thomson.[76] The kinetical theory of gases, after being started
by John Bernoulli and long buried in oblivion, was reinvented and
applied to the explanation not merely of the laws of Boyle, Charles, and
Avogadro, but also of diffusion and viscosity, by at least three modern
physicists separately. It is well known that the doctrine of natural
selection was presented by Wallace and by Darwin at the same meeting of
the British Association; and Darwin in his “Historical Sketch” prefixed
to the later editions of his book shows that both were anticipated by
obscure forerunners. The method of spectrum analysis was claimed for
Swan as well as for Kirchhoff, and there were others who perhaps had
still better claims. The authorship of the Periodical Law of the
Chemical Elements is disputed between a Russian, a German, and an
Englishman; although there is no room for doubt that the principal merit
belongs to the first. These are nearly all the greatest discoveries of
our times. It is the same with the inventions. It may not be surprising
that the telegraph should have been independently made by several
inventors, because it was an easy corollary from scientific facts well
made out before. But it was not so with the telephone and other
inventions. Ether, the first anæsthetic, was introduced independently by
three different New England physicians. Now ether had been a common
article for a century. It had been in one of the pharmacopœias three
centuries before. It is quite incredible that its anæsthetic property
should not have been known; it was known. It had probably passed from
mouth to ear as a secret from the days of Basil Valentine; but for long
it had been a secret of the Punchinello kind. In New England, for many
years, boys had used it for amusement. Why then had it not been put to
its serious use? No reason can be given, except that the motive to do so
was not strong enough. The motives to doing so could only have been
desire for gain and philanthropy. About 1846, the date of the
introduction, philanthropy was undoubtedly in an unusually active
condition. That sensibility, or sentimentalism, which had been
introduced in the previous century, had undergone a ripening process, in
consequence of which, though now less intense than it had previously
been, it was more likely to influence unreflecting people than it had
ever been. All three of the ether-claimants had probably been influenced
by the desire for gain; but nevertheless they were certainly not
insensible to the agapic influences.

I doubt if any of the great discoveries ought, properly, to be
considered as altogether individual achievements; and I think many will
share this doubt. Yet, if not, what an argument for the continuity of
mind, and for agapasticism is here! I do not wish to be very strenuous.
If thinkers will only be persuaded to lay aside their prejudices and
apply themselves to studying the evidences of this doctrine, I shall be
fully content to await the final decision.

Footnote 72:

  _The Monist_, January, 1893.

Footnote 73:

  How can a writer have any respect for science, as such, who is capable
  of confounding with the scientific propositions of political economy,
  which have nothing to say concerning what is “beneficent,” such
  brummagem generalisations as this?

Footnote 74:

  I am happy to find that Dr. Carus, too, ranks Weismann among the
  opponents of Darwin, notwithstanding his flying that flag.

Footnote 75:

  See _Draper’s History of Intellectual Development_, chap. x.

Footnote 76:

  Thomson, himself, in his article _Heat_ in the _Encyclopedia
  Britannica_, never once mentions the name of Clausius.




                         _Supplementary Essay_
                        THE PRAGMATISM OF PEIRCE
                                   BY
                               JOHN DEWEY


The term pragmatism was introduced into literature in the opening
sentences of Professor James’s California Union address in 1898. The
sentences run as follows: “The principle of pragmatism, as we may call
it, may be expressed in a variety of ways, all of them very simple. In
the _Popular Science Monthly_ for January, 1878, Mr. Charles S. Peirce
introduces it as follows:” etc. The readers who have turned to the
volume referred to have not, however, found the word there. From other
sources we know that the name as well as the idea was furnished by Mr.
Peirce. The latter has told us that both the word and the idea were
suggested to him by a reading of Kant, the idea by the _Critique of Pure
Reason_, the term by the “Critique of Practical Reason.”[77] The article
in the _Monist_ gives such a good statement of both the idea and the
reason for selecting the term that it may be quoted _in extenso_. Peirce
sets out by saying that with men who work in laboratories, the habit of
mind is molded by experimental work much more than they are themselves
aware. “Whatever statement you may make to him, he [the experimentalist]
will either understand as meaning that if a given prescription for an
experiment ever can be and ever is carried out in act, an experience of
a given description will result, or else he will see no sense at all in
what you say.” Having himself the experimental mind and being interested
in methods of thinking, “he framed the theory that a _conception_, that
is, the rational purport of a word or other expression, lies exclusively
in its bearing upon the conduct of life; so that, since obviously
nothing that might not result from experiment can have any direct
bearing upon conduct, if one can define accurately all the conceivable
experimental phenomena which the affirmation or denial of a concept
could imply, one will have therein a complete definition of the concept,
and _there is absolutely nothing more in it_. For this doctrine, he
invented the name _pragmatism_.”

After saying that some of his friends wished him to call the doctrine
practicism or practicalism, he says that he had learned philosophy from
Kant, and that to one “who still thought in Kantian terms most readily,
_praktisch_ and _pragmatisch_ were as far apart as the two poles, the
former belonging to a region of thought where no mind of the
experimentalist type can ever make sure of solid ground under his feet,
the latter expressing relation to some definite human purpose. Now quite
the most striking feature of the new theory was its recognition of an
inseparable connection between rational cognition and human
purpose.”[78]

From this brief statement, it will be noted that Peirce confined the
significance of the term to the determination of the meaning of terms,
or better, propositions; the theory was not, of itself, a theory of the
test, or the truth, of propositions. Hence the title of his original
article: _How to Make Ideas Clear_. In his later writing, after the term
had been used as a theory of truth,—he proposed the more limited
“pragmaticism” to designate his original specific meaning.[79] But even
with respect to the meaning of propositions, there is a marked
difference between his pragmaticism and the pragmatism of, say, James.
Some of the critics (especially continental) of the latter would have
saved themselves some futile beating of the air, if they had reacted to
James’s statements instead of to their own associations with the word
“pragmatic.” Thus James says in his California address: “The effective
meaning of any philosophic proposition can always be brought down to
some particular consequence, in our future practical experience, whether
active or passive; the point lying rather in the fact that the
experience must be _particular_, than in the fact that it must be
_active_.” (Italics mine.)

Now the curious fact is that Peirce puts more emphasis upon practise (or
conduct) and less upon the particular; in fact, he transfers the
emphasis to the general. The following passage is worth quotation
because of the definiteness with which it identifies meaning with both
the future and with the general. “The rational meaning of every
proposition lies in the future. How so? The meaning of a proposition is
itself a proposition. Indeed, it is no other than the very proposition
of which it is the meaning: it is a translation of it. But of the
myriads of forms into which a proposition may be translated, which is
that one which is to be called its very meaning? It is, according to the
pragmaticist, that form in which the proposition becomes applicable to
human conduct, not in these or those special circumstances nor when one
entertains this or that special design, but that form which is most
applicable to self-control under every situation and to every purpose.”
Hence, “it must be simply the general description of all the
experimental phenomena which the assertion of the proposition virtually
predicts.” Or, paraphrasing, pragmatism identifies meaning with
formation of a habit, or way of acting having the greatest generality
possible, or the widest range of application to particulars. Since
habits or ways of acting are just as real as particulars, it is
committed to a belief in the reality of “universals.” Hence it is not a
doctrine of phenomenalism, for while the richness of phenomena lies in
their sensuous quality, pragmatism does not intend to define these
(leaving them, as it were, to speak for themselves), but “eliminates
their sential element, and endeavors to define the rational purport, and
this it finds in the purposive bearing of the word or proposition in
question.” Moreover, not only are generals real, but they are physically
efficient. The meanings “the air is stuffy” and “stuffy air is
unwholesome” may determine, for example, the opening of the window.
Accordingly on the ethical side, “the pragmaticist does not make the
_summum bonum_ to consist in action, but makes it to consist in that
process of evolution whereby the existent comes more and more to embody
those generals...; in other words, becomes, through action an embodiment
of rational purports or habits generalized as widely as possible.”[80]

The passages quoted should be compared with what Peirce has to say in
the Baldwin Dictionary article. There he says that James’s doctrine
seems to commit us to the belief “that the end of man is action—a
stoical maxim which does not commend itself as forcibly to the present
writer at the age of sixty as it did at thirty. If it be admitted, on
the contrary, that action wants an end, and that the end must be
something of a general description, then the spirit of the maxim itself
... would direct us toward something different from practical facts,
namely, to general ideas.... The only ultimate good which the practical
facts to which the maxim directs attention can subserve is to further
the development of concrete reasonableness.... Almost everybody will now
agree that the ultimate good lies in the evolutionary process in some
way. If so, it is not in individual reactions in their segregation, but
in something general or continuous. Synechism is founded on the notion
that the coalescence, the becoming continuous, the becoming governed by
laws, the becoming instinct with general ideas, are but phases of one
and the same process of the growth of reasonableness. This is first
shown to be true with mathematical exactitude in the field of logic, and
is thence inferred to hold good metaphysically. It is not opposed to
pragmaticism ... but includes that procedure as a step.”

Here again we have the doctrine of pragmaticism as a doctrine that
meaning or rational purport resides in the setting up of habits or
generalized methods, a doctrine passing over into the metaphysics of
synechism. It will be well now to recur explicitly to Peirce’s earlier
doctrine which he seems to qualify—although, as he notes, he upheld the
doctrine of the reality of generals even at the earlier period. Peirce
sets out, in his article on the “Fixation of Belief,” with the empirical
difference of doubt and belief expressed in the facts that belief
determines a habit while doubt does not, and that belief is calm and
satisfactory while doubt is an uneasy and dissatisfied state from which
we struggle to emerge; to attain, that is, a state of belief, a struggle
which may be called inquiry. The sole object of inquiry is the fixation
of belief. The scientific method of fixation has, however, certain
rivals: one is that of “tenacity”—constant reiteration, dwelling upon
everything conducive to the belief, avoidance of everything which might
unsettle it—the will to believe. The method breaks down in practice
because of man’s social nature; we have to take account of contrary
beliefs in others, so that the real problem is to fix the belief of the
community; for otherwise our own belief is precariously exposed to
attack and doubt. Hence the resort to the method of authority. This
method breaks down in time by the fact that authority can not fix all
beliefs in all their details, and because of the conflict which arises
between organized traditions. There may then be recourse to what is
“agreeable to reason”—a method potent in formation of taste and in
esthetic productions and in the history of philosophy,—but a method
which again fails to secure permanent agreements in society, and so
leaves individual belief at the mercy of attack. Hence, finally,
recourse to science, whose fundamental hypothesis is this: “There are
real things, whose characters are entirely independent of our opinions
about them; those realities affect our senses according to regular laws,
and ... by taking advantage of the laws of perception, we can ascertain
by _reasoning_ how things really are, and any man if he have sufficient
experience and reason enough about it, will be led to the one true
conclusion.”[81]

It will be noted that the quotation employs the terms “reality” and
“truth,” while it makes them a part of the statement of the _hypothesis_
entertained in scientific procedure. Upon such a basis, what meanings
attach to the terms “reality” and “truth”? Since they are general terms,
their meanings must be determined on the basis of the effects, having
practical bearings, which the object of our conception has. Now the
effect which real things have is to cause beliefs; beliefs are then the
consequences which give the general term reality a “rational purport.”
And on the assumption of the scientific method, the _distinguishing_
character of the _real_ object must be that it tends to produce a single
universally accepted belief. “All the followers of science are fully
persuaded that the processes of investigation, if only pushed far
enough, will give one certain solution to every question to which they
can be applied.” “This activity of thought by which we are carried, not
where we wish, but to a foreordained goal, is like the operation of
destiny.... This great law is embodied in the conception of truth and
reality. The opinion which is fated to be ultimately agreed to by all
_who investigate_, is what we mean by the truth, and the object
represented in this opinion is the real.”[82] In a subsequent essay (on
the “Probability of Induction”) Peirce expressly draws the conclusion
which follows from this statement; viz., that this conception of truth
and reality makes everything depend upon the character of the methods of
inquiry and inference by which conclusions are reached. “In the case of
synthetic inferences we know only the degree of trustworthiness of our
proceeding. As all knowledge comes from synthetic inference, we must
also infer that all human certainty consists merely in our knowing that
the processes by which our knowledge has been derived are such as must
generally have led to true conclusions”[83]—true conclusions, once more,
being those which command the agreement of competent inquiries.

Summing up, we may say that Peirce’s pragmaticism is a doctrine
concerning the meaning, conception, or rational purport of objects,
namely, that these consist in the “effects, which might conceivably have
practical bearings, we conceive the object of our conception to have.
Then, our conception of these effects is the whole of our conception of
the object.”[84] “Our idea of anything is our idea of its sensible
effects,” and if we have any doubt as to whether we really believe the
effects to be sensible or no, we have only to ask ourselves whether or
no we should act any differently in their presence. In short, our own
responses to sensory stimuli are the ultimate, or testing, ingredients
in our conception of an object. In the literal sense of the word
pragmatist, therefore, Peirce is more of a pragmatist than James.

He is also less of a nominalist. That is to say, he emphasizes much less
the _particular_ sensible consequence, and much more the habit, the
generic attitude of response, set up in consequence of experiences with
a thing. In the passage in the Dictionary already quoted he speaks as if
in his later life he attached less importance to action, and more to
“concrete reasonableness” than in his earlier writing. It may well be
that the relative emphasis had shifted. But there is at most but a
difference of emphasis. For in his later doctrine, concrete rationality
means a change in existence brought about _through_ action, and through
action which embodies conceptions whose own specific existence consists
in habitual attitudes of response. In his earlier writing, the emphasis
upon habits, as something generic, is explicit. “What a thing means is
simply what habits it involves.”[85] More elaborately, “Induction infers
a rule. Now the belief of a rule is a habit. That a habit is a rule,
active in us, is evident. That every belief is of the nature of a habit,
in so far as it is of a general character, has been shown in the earlier
papers of this series.”[86]

The difference between Peirce and James which next strikes us is the
greater emphasis placed by the former upon the method of procedure. As
the quotations already made show, everything ultimately turned, for
Peirce, upon the trustworthiness of the procedures of inquiry. Hence his
high estimate of logic, as compared with James—at least James in his
later days. Hence also his definite rejection of the appeal to the Will
to Believe—under the form of what he calls the method of tenacity.
Closely associated with this is the fact that Peirce has a more explicit
dependence upon the social factor than has James. The appeal in Peirce
is essentially to the consensus of those who have investigated, using
methods which are capable of employment by all. It is the need for
social agreement, and the fact that in its absence “the method of
tenacity” will be exposed to disintegration from without, which finally
forces upon mankind the wider and wider utilization of the scientific
method.

Finally, both Peirce and James are realists. The reasonings of both
depend upon the assumption of real things which really have effects or
consequences. Of the two, Peirce makes clearer the fact that in
philosophy at least we are dealing with the _conception_ of reality,
with reality as a term having rational purport, and hence with something
whose meaning is itself to be determined in terms of consequences. That
“reality” means the object of those beliefs which have, after prolonged
and coöperative inquiry, becomes stable, and “truth” the quality of
these beliefs is a logical consequence of this position. Thus while “we
may define the real as that whose characters are independent of what
anybody may think them to be ... it would be a great mistake to suppose
that this definition makes the idea of reality perfectly clear.”[87] For
it is only the outcome of persistent and conjoint inquiry which enables
us to give intelligible meaning in the concrete to the expression
“characters independent of what anybody may think them to be.” (This is
the pragmatic way out of the egocentric predicament.) And while my
purpose is wholly expository I can not close without inquiring whether
recourse to Peirce would not have a most beneficial influence in
contemporary discussion. Do not a large part of our epistemological
difficulties arise from an attempt to define the “real” as something
given prior to reflective inquiry instead of as that which reflective
inquiry is forced to reach and to which when it is reached belief can
stably cling?

Footnote 77:

  See article on “Pragmatism,” in _Baldwin’s Dictionary_, Vol. 2., p.
  322, and the _Monist_, Vol. 15, p. 162.

Footnote 78:

  Kant discriminates the laws of morality, which are _a priori_, from
  rules of skill, having to do with technique or art, and counsels of
  prudence, having to do with welfare. The latter he calls pragmatic;
  the _a priori_ laws practical. See _Metaphysics of Morals_, Abbott’s
  trans., pp. 33 and 34.

Footnote 79:

  See the article in the _Monist_ already mentioned, and another one in
  the same volume, p. 481, “The Issues of Pragmaticism.”

Footnote 80:

  It is probably fair to see here an empirical rendering of the Kantian
  generality of moral action, while the distinction and connection of
  “rational purport” and “sensible particular” have also obvious Kantian
  associations.

Footnote 81:

  P. 26.

Footnote 82:

  P. 56-57.

Footnote 83:

  P. 105.

Footnote 84:

  P. 45.

Footnote 85:

  P. 43.

Footnote 86:

  P. 151.

Footnote 87:

  P. 53.




              BIBLIOGRAPHY OF PEIRCE’S PUBLISHED WRITINGS


I. Writings of General Interest.[88]

    _A._ Three papers in the _Journal of Speculative Philosophy_, Vol. 2
    (1868).

    1. “Questions Concerning Certain Faculties Claimed for Man,” pp.
    103-114.

    2. “Some Consequences of Four Incapacities,” pp. 140-157.

    3. “Ground of Validity of the Laws of Logic,” pp. 193-208.

These three papers, somewhat loosely connected, deal mainly with the
philosophy of discursive thought. The first deals with our power of
intuition, and holds that “every thought is a sign.” The second, one of
the most remarkable of Peirce’s writings, contains an acute criticism of
the Cartesian tradition and a noteworthy argument against the
traditional emphasis on “images” in thinking. The third contains, _inter
alia_, a refutation of Mill’s indictment of the syllogism. The same
volume of the _Journal_ contains two unsigned communications on
Nominalism and on the Meaning of Determined.

    _B._ Review of Fraser’s “Berkeley,” in the _North American Review_,
    Vol. 113 (1871), pp. 449-472.

This paper contains an important analysis on medieval realism, and of
Berkeley’s nominalism. (A Scotist realism continues to distinguish
Peirce’s work after this.)

    _C._ “Illustrations of the Logic of Science,” in _Popular Science
    Monthly_, Vols. 12-13 (1877-1878). Reprinted in Pt. I of this
    volume. The first and second papers were also published in the
    _Revue Philosophique_, Vols. 6-7 (1879).

    _D._ Ten papers in the _Monist_, Vols. 1-3 (1891-1893), and 15-16
    (1905-1906). The first five are reprinted in Pt. II of this volume.

The sixth paper, “Reply to the Necessitarians,” Vol. 3, pp. 526-570, is
an answer to the criticism of the foregoing by the editor of the
_Monist_, Vol. 2, pp. 560ff.; cf. Vol. 3, pp. 68ff. and 571ff., and
McCrie, “The Issues of Synechism,” Vol. 3, pp. 380ff.

    7. “What Pragmatism Is?” Vol. 15, pp. 161-181.

    8. “The Issues of Pragmaticism,” Vol. 15, pp. 481-499.

    9. “Mr. Peterson’s Proposed Discussion,” Vol. 16, pp. 147ff.

    10. “Prolegomena to an Apology for Pragmaticism,” Vol. 16, pp.
    492-546.

The last four papers develop Peirce’s thought by showing its agreement
and disagreement with the pragmatism of James and Schiller. The last
paper contains his Method of Existential Graphs.

    _E._ “The Reality of God,” in the _Hibbert Journal_, Vol. 7 (1908),
    pp. 96-112. (This article contains brief indications of many of
    Peirce’s leading ideas.)

    _F._ Six Papers in the _Open Court_, Vols. 6-7 (1893).

    1. “Pythagorics” (on the Pythagorean brotherhood), pp. 3375-3377.

    2. “Dmesis” (on charity towards criminals), pp. 3399-3402.

    3. “The Critic of Arguments (I.), Exact Thinking,” pp. 3391-3394.

    4. “The Critic of Arguments (II.), The Reader is Introduced to
    Relatives,” pp. 3415-3419. (The last two contain a very clear
    succinct account of the general character of Peirce’s logic.)

    5. “What is Christian Faith?” pp. 3743-3745.

    6. “The Marriage of Religion and Science,” pp. 3559-3560.

    _G._ Articles in Baldwin’s “Dictionary of Philosophy”: Individual,
    kind, matter and form, possibility, pragmatism, priority, reasoning,
    sign, scientific method, sufficient reason, synechism, and
    uniformity.

    _H._ “Pearson’s Grammar of Science,” in _Popular Science Monthly_,
    Vol. 58 (1901), pp. 296-306. (A critique of Pearson’s conceptualism
    and of his utilitarian view as to the aim of science.)

II. Writings of Predominantly Logical Interest.

    _A._ Five Papers on Logic, read before the American Academy of Arts
    and Sciences. Published in the _Proceedings of the Academy_, Vol. 7
    (1867).

    1. “On an Improvement in Boole’s Calculus of Logic,” pp. 250-261.
    (Suggests improvements in Boole’s logic, especially in the
    representation of particular propositions. The association of
    probability with the notion of relative frequency became a leading
    idea of Peirce’s thought.)

    2. “On the Natural Classification of Arguments,” pp. 261-287. (A
    suggestive distinction between the leading principle and the premise
    of an argument. Contains also an interesting note (pp. 283-284)
    denying the positivistic maxim that, “no hypothesis is admissible
    which is not capable of verification by direct observation.”)

    3. “On a New List of Categories,” pp. 287-298. The categories are:
    Being, Quality (Reference to a Ground), Relation (Reference to a
    Correlate), Representation (Reference to an Interpretant),
    Substance. “Logic has for its subject-genus all symbols and not
    merely concepts.” Symbols include terms, propositions, and
    arguments.

    4. “Upon the Logic of Mathematics,” pp. 402-412. “There are certain
    general propositions from which the truths of mathematics follow
    syllogistically.”

    5. “Upon Logical Comprehension and Extension,” pp. 416-432.
    (Interesting historical references to the use of these terms and an
    attack on the supposed rule as to their inverse proportionality.)

    _B._ “Description of a Notation for the Logic of Relations,” in
    _Memoires of the American Academy_, Vol. 9 (1870), pp. 317-378.
    (Shows the relation of inclusion between classes to be more
    fundamental than Boole’s use of equality. Extends the Booleian
    calculus to DeMorgan’s logic of relative terms.)

    _C._ “On the Algebra of Logic,” _American Journal of Mathematics_,
    Vol. 3 (1880), pp. 15-57. (Referred to by Schroeder as Peirce’s
    _Hauptwerk_ in “Vorlesungen über die Algebra der Logik,” Vol. 1., p.
    107.)

    _D._ “On the Logic of Number,” _American Journal of Mathematics_,
    Vol. 4 (1881), pp. 85-95.

    _E._ “Brief Description of the Algebra of Relatives,” Reprinted from
    ??, pp. 1-6.

    _F._ “On the Algebra of Logic: A Contribution to the Philosophy of
    Notation,” _American Journal of Mathematics_, Vol. 7 (1884), pp.
    180-202.

    _G._ “A Theory of Probable Inference” and notes “On a Limited
    Universe of Marks” and on the “Logic of Relatives” in “Studies in
    Logic by members of the Johns Hopkins University,” Boston, 1883, pp.
    126-203.

    _H._ “The Regenerated Logic,” _Monist_, Vol. 7, pp. 19-40.

    “The Logic of Relatives,” _Monist_, Vol. 7, pp. 161-217. (An
    elaborate development of his own logic of relatives, by way of
    review of Schroeder’s book.)

    _I._ Miscellaneous Notes, etc.

    1. Review of Venn’s “Logic of Chance,” _North American Review_,
    July, 1867.

    2. “On the Application of Logical Analysis to Multiple Algebra,”
    _Proceedings of the American Academy_, Vol. 10 (1875), pp. 392-394.

    3. “Note on Grassman’s ‘Calculus of Extension,’” _Proceedings of the
    American Academy_, Vol. 13 (1878), pp. 115-116.

    4. “Note on Conversion,” _Mind_, Vol. 1, p. 424.

    5. Notes and Additions to Benjamin Peirce’s “Linear Associative
    Algebra,” _American Journal of Mathematics_, Vol. 4 (1881), pp.
    92ff., especially pp. 221-229.

    6. “Logical Machines,” _American Journal of Psychology_, Vol. 1
    (1888).

    7. “Infinitesimals,” _Science_, Vol. 11 (1900), p. 430.

    8. “Some Amazing Mazes,” _Monist_, Vol. 18 (April and July, 1908),
    and Vol. 19 (Jan., 1909).

    9. “On Non-Aristotelian Logic” (Letter), _Monist_, Vol. 20.

    _J._ A Syllabus of Certain Topics of Logic. 1903. Boston. Alfred
    Mudge & Son (a four page brochure).

    _K._ Articles in Baldwin’s “Dictionary of Philosophy” on: laws of
    thought, leading principle, logic (exact and symbolic), modality,
    negation, predicate and predication, probable inference, quality,
    quantity, relatives, significant, simple, subject, syllogism,
    theory, truth and falsity universal, universe, validity,
    verification, whole and parts.

III. Researches in the Theory and Methods of Measurement.

    _A._ General and Astronomic.

    1. “On the Theory of Errors of Observation,” _Report of the
    Superintendent of the U. S. Coast Survey_ for 1870, pp. 220-224.

    2. “Note on the Theory of Economy of Research,” _Report of the U. S.
    Coast Survey_ for 1876, pp. 197-201. (This paper deals with the
    relation between the utility and the cost of diminishing the
    probable error.)

    3. “Apparatus for Recording a Mean of Observed Times,” _U. S. Coast
    Survey_, 1877. Appendix No. 15 to _Report_ of 1875.

    4. “Ferrero’s Metodo dei Minimi Quadrati,” _American Journal of
    Mathematics_, Vol. 1 (1878), pp. 55-63.

    5. “Photometric Researches,” _Annals of the Astronomical Observatory
    of Harvard College_, Vol. 9 (1878), pp. 1-181.

    6. “Methods and Results. Measurement of Gravity.” Washington. 1879.

    7. “Methods and Results. A Catalogue of Stars for Observations of
    Latitude.” Washington. 1879.

    8. “On the Ghosts in Rutherford’s ‘Diffraction Spectra,’” _American
    Journal of Mathematics_, Vol. 2 (1879), pp. 330-347.

    9. “Note on a Comparison of a Wave-Length with a Meter,” _American
    Journal of Science_, Vol. 18 (1879), p. 51.

    10. “A Quincuncial Projection of the Sphere,” _American Journal of
    Mathematics_, Vol. 2 (1879), pp. 394, 396.

    11. “Numerical Measure of Success of Predictions,” _Science_, Vol. 4
    (1884), p. 453.

    12. “Proceedings Assay Commission” Washington, 1888. (Joint Reports
    on Weighing.)

    _B._ Geodetic Researches. The Pendulum.

    1. “Measurement of Gravity at Initial Stations in America and
    Europe,” _Report of the U. S. Coast Survey_, 1876, pp. 202-237 and
    410-416.

    2. “De l’influence de la flexibilité du trépied sur l’oscillation du
    pendule a réversion,” Conférence Geodesique Internationale (1877)
    Comptes Rendus, Berlin, 1878, pp. 171-187. (This paper was
    introduced by Plantamour and was followed by the notes of Appolzer.)

    3. “On the Influence of Internal Friction upon the Correction of the
    Length of the Second’s Pendulum,” _Proceedings of the American
    Academy_, Vol. 13 (1878), pp. 396-401.

    4. “On a Method of Swinging Pendulums for the Determination of
    Gravity proposed by M. Faye,” _American Journal of Science_, Vol. 18
    (1879), pp. 112-119.

    5. “Results of Pendulum Experiments,” _American Journal of Science_,
    Vol. 20 (1880).

    6. “Flexure of Pendulum Supports,” _Report of the U. S. Coast
    Survey_, 1881, pp. 359-441.

    7. “On the Deduction of the Ellipticity of the Earth from the
    Pendulum Experiment,” _Report of the U. S. Coast Survey_, 1881, pp.
    442-456.

    8. “Determinations of Gravity at Stations in Pennsylvania,” _Report
    of U. S. Coast Survey_, 1883, Appendix 19 and pp. 473-486.

    9. “On the Use of the Noddy,” _Report of the U. S. Coast Survey_,
    1884, pp. 475-482.

    10. “Effect of the Flexure of a Pendulum upon the Period of
    Oscillation,” _Report of the U. S. Coast Survey_, 1884, pp. 483-485.

    11. “On the Influence of a Noddy, and of Unequal Temperature upon
    the Periods of a Pendulum,” _Report of the U. S. Coast and Geodetic
    Survey_ for 1885, pp. 509-512.

    _C._ Psychologic. “On Small Differences in Sensation” (in
    cooperation with J. Jastrow), _National Academy of Sciences_, Vol. 3
    (1884), pp. 1-11.

IV. Philologic.

    “Shakespearian Pronunciation” (in coöperation with J. B. Noyes),
    _North American Review_, Vol. 98 (April, 1864), pp. 342-369.

V. Contributions to the _Nation_.

    Lazelle, Capt. H. M., One Law in Nature. _Nation_, Vol. 17, No. 419.

    Newcomb, S., Popular Astronomy. Vol. 27, No. 683.

    Read, C., Theory of Logic, 1878. Vol. 28, No. 718.

    Rood, O. N., Modern Chromatics, 1879. Vol. 29, No. 746.

    Note on the _American Journal of Mathematics_. Vol. 29, No. 756.

    Jevons, W. S., Studies in Deductive Logic, 1880. Vol. 32, No. 822.

    Ribot, Th., The Psychology of Attention, 1890. Vol. 50, No. 1303.

    James, W., The Principles of Psychology, 1890. Vol. 53, Nos. 1357
    and 1358.

    Comte, A. (F. Harrison, editor), The New Calendar of Great Men,
    1892. Vol. 54, No. 1386.

    Lobatchewsky, N. (Translator: G. B. Halsted), Geometrical Researches
    on the Theory of Parallels, 1891. Vol. 54, No. 1389.

    Lombroso, C., The Man of Genius, 1891. Vol. 54, No. 1391.

    Note on William James’ abridgment of his Psychology, 1892. Vol. 54,
    No. 1394.

    McClelland, W. J., A Treatise on the Geometry of the Circle, 1891.
    Vol. 54, No. 1395.

    Buckley, Arabella B., Moral Teachings of Science, 1892. Vol. 54, No.
    1405.

    Hale, E. E., A New England Boyhood, 1893. Vol. 57, No. 1468.

    Mach, E. (Translator: T. J. McCormack), The Science of Mechanics,
    1893. Vol. 57, No. 1475.

    Ritchie, D. G., Darwin and Hegel, 1893. Vol. 57, No. 1482.

    Huxley, T. H., Method and Results, 1893. Vol. 58, No. 1489.

    Scott, Sir Walter, Familiar Letters of Sir Walter Scott. Vol. 58,
    No. 1493.

    Gilbert, W. (Translator: P. F. Mottelay), Magnetic Bodies. Vol. 58,
    No. 1494 and No. 1495.

    Forsyth, A. R., Theory of Functions of a Complex Variable, 1893; and
    Harkness, J., A Treatise on the Theory of Functions, 1893; and
    Picard, E., Traité d’analyse, 1893. Vol. 58, No. 1498.

    A Short Sketch of Helmholtz, Sept. 13, 1894. Vol. 59, No. 1524.

    Windelband, W. (Translator: J. H. Tufts), A History of Philosophy;
    and Falkenberg, R. (Translator: A. C. Armstrong), History of Modern
    Philosophy; and Bascom, J., An Historical Interpretation of
    Philosophy; and Burt, B. C., A History of Modern Philosophy. Vol.
    59, Nos. 1526 and 1527.

    Spinoza (Translators: W. H. White and Amelia H. Stirling), Ethics,
    1894. Vol. 59, No. 1532.

    Watson, J., Comte, Mill, and Spencer, 1895. Vol. 60, No. 1554.

    Jones, H., A Critical Account of the Philosophy of Lotze, 1895; and
    Eberhard, V., Die Grundbegriffe der ebenen Geometrie, 1895; and
    Klein, F. (Translator: A. Ziwet), Riemann and his Significance for
    the Development of Modern Mathematics, 1895; and Davis, N. K.,
    Elements of Inductive Logic, 1895. Vol. 61, No. 1566.

    Benjamin, P., The Intellectual Rise in Electricity, 1895. Vol. 62,
    No. 1592.

    Baldwin, J. M., The Story of the Mind, 1898. Vol. 67, No. 1737.

    Darwin, G. H., The Tides and Kindred Phenomena in the Solar System,
    1898. Vol. 67, No. 1747.

    Marshall, H. R., Instinct and Reason, 1898. Vol. 68, No. 1774.

    Britten, F. J., Old Clocks and Watches and their Makers, 1899. Vol.
    69, No. 1778.

    Renouvier, Ch., et Prat, L. La Nouvelle Monadologie, 1899. Vol. 69,
    No. 1779.

    Mackintosh, R., From Comte to Benjamin Kidd, 1899; and Moore, J. H.,
    Better-World Philosophy, 1899. Vol. 69, No. 1784.

    Ford, P. L., The Many-sided Franklin, 1899. Vol. 69, No. 1793.

    Avenel, G. d’, Le Mécanisme de la vie moderne, 1900. Vol. 70, No.
    1805.

    Reid, W., Memoirs and Correspondence of Lyon Playfair, 1899. Vol.
    70, No. 1806.

    Stevenson, F. S., Robert Grosseteste, 1899. Vol. 70, No. 1816.

    Thilly, F., Introduction to Ethics, 1900. Vol. 70, No. 1825.

    Wallace, A. R., Studies, Scientific and Social, 1900. Vol. 72, No.
    1854.

    Sime, J., William Herschel and His Work, 1900. Vol. 72, No. 1856.

    Rand, B. (Editor), The Life, Unpublished Letters, and Philosophical
    Regimen of Anthony, Earl of Shaftesbury, 1900; and Robertson, J. M.
    (Editor), Characteristics of Men, _etc._, by Shaftesbury, 1900. Vol.
    72, No. 1857.

    Bacon, Rev. J. M., By Land and Sea, 1901. Vol. 72, No. 1865.

    Jordan, W. L., Essays in Illustration of the Action of Astral
    Gravitation in Natural Phenomena, 1900. Vol. 72, No. 1876.

    Goblot, E., Le Vocabulaire Philosophique, 1901. Vol. 72, No. 1877.

    Fraser, A. C. (Editor), The Works of George Berkeley, 1901. Vol. 73,
    No. 1883.

    Frazer, P., Bibliotics, 1901. Vol. 73, No. 1883.

    Caldecott, A., The Philosophy of Religion in England and America,
    1901. Vol. 73, No. 1885.

    Review of four physical books. Vol. 73, No. 1887.

    Maher, M., Psychology: Empirical and Rational, 1901. Vol. 73, No.
    1892.

    Mezes, S. E., Ethics, 1901. Vol. 73, No. 1895.

    Report of the Meeting of the National Academy of Sciences,
    Philadelphia, 1901. Vol. 73, No. 1899.

    Crozier, J. B., History of Intellectual Developments on the Lines of
    Modern Evolution. Vol. III., 1901, Vol. 74, No. 1908.

    Richardson, E. C., Classification, Theoretical and Practical, 1901.
    Vol. 74, No. 1913.

    Vallery-Radot, R. (Translator: Mrs. R. L. Devonshire), The Life of
    Pasteur. Vol. 74, No. 1914.

    Giddings, F. H., Inductive Sociology, 1902. Vol. 74, No. 1918.

    Report on the Meeting of the National Academy of Sciences,
    Washington, D. C., 1902. Vol. 74, No. 1921.

    Emerson, E. R., The Story of the Vine, 1902. Vol. 74, No. 1926.

    Joachim, H. H., A Study of the Ethics of Spinoza, 1901. Vol. 75, No.
    1932.

    Review of four chemistry text-books, 1902. Vol. 75, No. 1934.

    Royce, J., The World and the Individual, Vol. II., 1901. Vol. 75,
    No. 1935. (For a review of Vol. I., probably by Peirce, see 1900,
    Vol. 70, No. 1814.)

    Thorpe, T. E., Essays in Historical Chemistry, 1902. Vol. 75, No.
    1938.

    Paulsen, F., Immanuel Kant: His Life and Doctrine, 1902. Vol. 75,
    No. 1941.

    Aikens, H. A., The Principles of Logic, 1902. Vol. 75, No. 1942.

    Drude, P., The Theory of Optics, 1902. Vol. 75, No. 1944.

    Valentine, E. S., Travels in Space, 1902; and Walker, F., Aerial
    Navigation, 1902. Vol. 75, No. 1947.

    Baillie, J. B., The Origin and Significance of Hegel’s Logic, 1901.
    Vol. 75, No. 1950.

    Forsyth, A. R., Theory of Differential Equations, Vol. IV., 1902.
    Vol. 75, No. 1952.

    Ellwanger, G. W., The Pleasures of the Table, 1902. Vol. 75, No.
    1955.

    Earle, Alice M., Sundials and Roses of Yesterday, 1902. Vol. 75, No.
    1956.

    Smith, Rev. T., Euclid: His Life and System, 1902. Vol. 76, No.
    1961.

    Report on the Meeting of the National Academy of Sciences,
    Washington, D. C., 1903. Vol. 76, No. 1974.

    Hibben, J. G., Hegel’s Logic, 1902. Vol. 76, No. 1977.

    Mellor, J. W., Higher Mathematics for Students of Chemistry and
    Physics, 1903. Vol. 76, No. 1977.

    Sturt, H. C. (Editor), Personal Idealism, 1902. Vol. 76, No. 1979.

    Baldwin, J. M., Dictionary of Philosophy and Psychology, Vol. II.,
    1902. Vol. 76, No. 1980.

    Note on Kant’s Prolegomene edited in English by Dr. P. Carus, 1903.
    Vol. 76, No. 1981.

    Smith, N., Studies in the Cartesian Philosophy, 1902. Vol. 77, No.
    1985.

    Hinds, J. I. D., Inorganic Chemistry, 1902. Vol. 77, No. 1986.

    Clerke, Agnes M., Problems in Astrophysics, 1903. Vol. 77, No. 1987.

    Michelson, A. A., Light Waves and their Uses, 1903; and Fleming, J.
    A., Waves and Ripples in Water, 1902. Vol. 77, No. 1989.

    Note on Sir Norman Lockyer. Vol. 77, No. 1794.

    Note on British and American Science, 1903. Vol. 77, No. 1996.

    Welby, Lady Victoria, What is Meaning? 1903; and Russell, B., The
    Principles of Mathematics, 1903. Vol. 77, No. 1998.

    Note on the Practical Application of the Theory of Functions, 1903.
    Vol. 77, No. 1999.

    Fahie, J. J., Galileo. Vol. 78, No. 2015.

    Halsey, F. A., The Metric Fallacy, and Dale, S. S., The Metric
    Failure in the Textile Industry. Vol. 78, No. 2020.

    Newcomb, S., The Reminiscences of an Astronomer, 1903. Vol. 78, No.
    2021.

    Boole, Mrs. M. E., Lectures on the Logic of Arithmetic, 1903; and
    Bowden, J., Elements of the Theory of Integers, 1903. Vol. 78, No.
    2024.

    Report on the Meeting of the National Academy of Sciences,
    Washington, D. C., 1904. Vol. 78, No. 2026.

    Lévy-Bruhl, L. (Translator: Kathleen de Beaumont-Klein), The
    Philosophy of Auguste Comte, 1903. Vol. 78, No. 2026.

    Turner, W., History of Philosophy, 1903. Vol. 79, No. 2036.

    Duff, R. A., Spinoza’s Political and Ethical Philosophy. Vol. 79,
    No. 2038.

    Allbutt, T. C., Notes on the Composition of Scientific Papers, 1904.
    Vol. 79, No. 2039.

    Sylvester, J. J., The Collected Mathematical Papers of, Vol. I. Vol.
    79, No. 2045.

    Renouvier, Ch., Les Derniers Entretiens, 1904, and Dewey, J.,
    Studies in Logical Theory, 1903. Vol. 79, No. 2046.

    Royce, J., Outlines of Psychology. Vol. 79, No. 2048.

    Straton, G. M., Experimental Psychology and its Bearing upon
    Culture. Vol. 79, No. 2055.

    Report on the Meeting of the National Academy of Sciences, New York,
    1904. Vol. 79, No. 2057.

    Boole, Mrs. M. E., The Preparation of the Child for Science, 1904.
    Vol. 80, No. 2062.

    Royce, J., Herbert Spencer, 1904. Vol. 80, No. 2065.

    Strutt, R. J., The Becquerel Rays and the Properties of Radium,
    1904. Vol. 80, No. 2066.

    Schuster, A., An Introduction to the Theory of Optics, 1904. Vol.
    80, No. 2071.

    Findlay, A., The Phase Rule and its Application, 1904. Vol. 80, No.
    2074.

    Report on the Meeting of the National Academy of Sciences,
    Washington, D. C., 1905. Vol. 80, No. 2078.

    Flint, R., Philosophy as Scientia Scientiarum, 1904; and Peirce, C.
    S., A Syllabus of Certain Topics of Logic, 1903. Vol. 80, No. 2079.

    Arnold, R. B., Scientific Fact and Metaphysical Reality, 1904, also
    a Note on Mendeleeff’s Principles of Chemistry. Vol. 80, No. 2083.

    Note on Ida Freund’s The Study of Chemical Composition. Vol. 80, No.
    2086.

    Carnegie, A., James Watt, 1905. Vol. 80, No. 2087.

    Ross, E. A., Foundations of Sociology, 1905, and Sociological
    Papers, 1905, published by the Sociological Society. Vol. 81, No.
    2089.

    Wundt, W. (Translator: E. B. Titchener), Principles of Physiological
    Psychology, 1904. Vol. 81, No. 2090.

    Roscoe, H. E., A Treatise on Chemistry, Vol. I., 1905, and de
    Fleury, M., Nos Enfants au Collège, 1905. Vol. 81, No. 2097.

    Varigny, H. de, La Nature et la Vie, 1905. Vol. 81, No. 2101.

    Note on Mr. G. W. Hill’s Moon Theory. Vol. 81, 2103.

    Report on the Meeting of the National Academy of Sciences, New
    Haven, 1905. Vol. 81, No. 2108.

    Gosse, E., Sir Thomas Browne, 1905. Vol. 81, No. 2111.

    Rutherford, E., Radio-Activity, 1905. Vol. 82, No. 2116.

    Wallace, A. R., My Life, 1905. Vol. 82, No. 2121.

    Haldane, Elizabeth S., Descartes. Vol. 82, No. 2125.

    Report on the Meeting of the National Academy of Sciences,
    Washington, D. C., 1906. Vol. 82, No. 2130.

    Rogers, H. J. (Editor), Congress of Arts and Sciences, Universal
    Exposition, St. Louis, 1904. Vol. 82, No. 2136.

    Loeb, J., The Dynamics of Living Matter; and Mann, G., Chemistry of
    the Proteids. Vol. 83, No. 2140.

    Roscoe, H. E., The Life and Experiences of Sir Henry Enfield Roscoe.
    Vol. 83, No. 2141.

    Marshall, T., Aristotle’s Theory of Conduct. Vol. 83, No. 2150.

    Joseph, H. W. B., An Introduction to Logic. Vol. 83, No. 2156.

OTHER ARTICLES AND REVIEWS

    Old Stone Mill at Newport, _Science_, 4, 1884, 512.

    Criticism on “Phantasms of the Living,” _Proc. Am. Soc. Psychical
    Research_, Vol. 1, No. 3 (1887).

    Napoleon Intime, _The Independent_, December 21 and December 28,
    1893.

    Decennial Celebration of Clark University, _Science_, 11 (1900), p.
    620.

    Century’s Great Men of Science, _Smithsonian Institute Reports_,
    1900.

    Campanus _Science_, 13 (1901), p. 809.

    French Academy of Science, N. Y. Evening _Post_, March 5, 1904.

Footnote 88:

  The following classification is arbitrary, as some of Peirce’s most
  significant reflections occur in papers under headings II. and III. It
  may, however, be useful.




 ● Transcriber’s Notes:
    ○ Text that was in italics is enclosed by underscores (_italics_).
      Text that was in bold face is enclosed by equals signs (=bold=).
    ○ Footnotes have been moved to follow the chapters in which they are
      referenced.
    ○ Numbers raised to a power are denoted by the caret sign: 2^5 is 2
      raised to the 5th power. Powers may be enclosed in curly brackets,
      so 2^{32} is 2 raised to the 32nd power.
    ○ Subscripts are denoted by an underscore followed by the subscript
      in curly brackets, so O_{2} means O followed by a subscript 2.