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                    THE OPEN COURT PUBLISHING COMPANY
                     324 DEARBORN ST., CHICAGO, ILL.
              LONDON: KEGAN PAUL, TRENCH, TRÜBNER & COMPANY




                              THE EVOLUTION
                                    OF
                              GENERAL IDEAS

                                    BY
                                TH. RIBOT
                    PROFESSOR IN THE COLLÈGE DE FRANCE

                  AUTHORISED TRANSLATION FROM THE FRENCH
                                    BY
                             FRANCES A. WELBY

                                 CHICAGO
                    THE OPEN COURT PUBLISHING COMPANY
             LONDON: KEGAN PAUL, TRENCH, TRÜBNER & CO., LTD.
                                   1899

                               COPYRIGHT BY
                      THE OPEN COURT PUBLISHING CO.
                            CHICAGO, U. S. A.
                                   1899

                          _All rights reserved._




PREFACE.


The principal aim of this work is to study the development of the mind
as it abstracts and generalises, and to show that these two operations
exhibit a perfect evolution: that is to say, they exist already in
perception, and advance by successive and easily determined stages to the
more elevated forms of pure symbolism, accessible only to the minority.

It is a commonplace to say that abstraction has its degrees, as number
its powers. Yet it is not sufficient to enunciate this truism; the
degrees must be fixed by clear, objective signs, and these must not be
arbitrary. Thus we shall obtain precise knowledge of the various stages
in this ascending evolution, and stand in less danger of confounding
abstractions highly distinct by nature. Moreover, we avoid certain
equivocal questions and discussions that are based entirely upon the very
extended sense of the terms to _abstract_ and to _generalise_.

Accordingly we have sought to establish three main periods in the
progressive development of these operations: (1) inferior abstraction,
prior to the appearance of speech, independent of words (though not of
all signs); (2) intermediate abstraction, accompanied by words, which
though at first accessory, increase in importance little by little; (3)
superior abstraction, where words alone exist in consciousness, and
correspond to a complete substitution.[1]

These three periods again include subdivisions, transitional forms which
we shall endeavor to determine.

This is a study of pure psychology, from which we have rigorously to
eliminate all that relates to logic, to the theory of knowledge, to first
principles of philosophy. We are concerned with genesis, with embryology,
with evolution only. We are thus thrown upon observation, upon the facts
wherein mental processes are enunciated, and discovered. Our material,
and principal sources of information, lie therefore: (1) for inferior
abstracts, in the acts of animals, of children, of uneducated deaf-mutes;
(2) for intermediate abstracts, in the development of languages, and the
ethnographical documents of primitive or half-civilised peoples; (3) for
superior abstracts, in the progressive constitution of scientific ideas
and theories, and of classifications.

This volume is a _résumé_ of lectures given at the Collège de France in
1895. It is the first of a forthcoming series, designed to include all
departments of psychology: the unconscious, percepts, images, volition,
movement, etc.

                                                                TH. RIBOT.

March, 1897.




TABLE OF CONTENTS.


                                                                      PAGE

                               CHAPTER I.

      THE LOWER FORMS OF ABSTRACTION.—ABSTRACTION PRIOR TO SPEECH.

    Two forms of intellectual activity: association and
    dissociation.—Abstraction belongs to the second type. Its
    positive and negative conditions. It is a case of attention:
    psychical reinforcement.—It is in embryo in concrete
    operations: in perception, and the image. Its practical
    character.—Generalisation belongs to the first type. Problem of
    the _primum cognitum_; difference or resemblance?—Hierarchy of
    general ideas: need of a notation. Three great classes.—Lower
    forms of abstraction and generalisation or pre-linguistic
    period, characterised by absence of words                            1

                                ANIMALS.

    Different observations. Numeration in animals; what does it
    consist of?—Mode of formation and characteristics of generic
    images. Reasoning in animals.—Reasoning from particular to
    particular: how this differs from simple association.—Reasoning
    by analogy.—The logic of images: its two degrees; its
    characteristics. Does not admit of substitution; always has a
    practical aim.—Discussion of certain cases                          11

                                CHILDREN.

    Does intelligence start from the general or the particular?
    A badly-stated question. Intelligence proceeds from the
    indefinite to the definite.—Characteristics of generic
    images in children; examples.—Numeration; its narrow limits.
    Difference between real numeration and perception of a
    plurality                                                           31

                               DEAF-MUTES.

    These furnish the upper limit of the logic of images.—Their
    natural language. Vocabulary. All their signs are abstractions.
    Syntax of position; disposition of terms according to order of
    importance.—Intellectual level                                      39

                          ANALYTICAL GESTURES.

    General classification of signs.—Gesture, an intellectual,
    not an emotional, instrument; its wide distribution. Syntax
    identical with that of deaf-mutes.—Comparison between phonetic
    language and language of analytical gesture.—Reason why speech
    has prevailed                                                       48

                               CHAPTER II.

                                 SPEECH.

    Language in animals.—The origin of speech; principal
    contemporaneous hypotheses; instinct, progressive evolution.
    The cry, vocalisation, articulation. Transitional forms:
    co-existence of speech and of the language of action;
    co-existence of speech and of inarticulate sounds.—The
    development of speech. Protoplasmic period without
    grammatical functions.—Roots; two theories: reality, and
    residue of analysis.—Did speech begin with words or with
    phrases?—Successive appearance of parts of speech. Adjectives
    or denominations of qualities. The substantive a contraction
    of the adjective. Verbs not a primitive phenomenon; the
    three degrees of abstraction.—Terms expressive of relations.
    Psychological nature of relation, may be reduced to change or
    movement. Function of analogy                                       54

                              CHAPTER III.

                   INTERMEDIATE FORMS OF ABSTRACTION.

    Division into two classes according to the function of the
    word.—First class. Words not indispensable, and only in a
    limited degree the instrument of substitution.—Difference
    between generic images and lower concepts. Characteristics of
    these two classes. Is there continuity between the two? Nature
    of the lower forms of intermediate abstraction, according to
    languages, numeration, etc. Concrete-abstract period.—Second
    class. Words are indispensable and become an instrument of
    substitution.—Difficulty in finding examples.—History of
    zoölogical classification: pre-scientific period: Aristotle,
    Linnæus, Cuvier, etc., contemporary writers. Progress towards
    unity                                                               86

                               CHAPTER IV.

               HIGHER FORMS OF ABSTRACTION. THEIR NATURE.

    Object of the chapter: What is there in consciousness, when we
    think by concepts?—The general idea as a psychical state may be
    reduced to varieties. Investigation of this point: the method
    pursued.—Reduction to three principal types. Concrete type the
    most widely distributed. Variation; reply by association of
    ideas. Visual typographic type: printed words seen and nothing
    further.—Auditory type; less common.—Interrogations by general
    propositions: same results. Investigation of cases in which
    words exist alone in consciousness. Is it possible to think
    with words only? Rôle of unconscious knowledge. General ideas
    are intellectual habits.—Natural antagonism between the image
    and the concept. Its causes.—Are there general ideas or merely
    general terms?                                                     111

                               CHAPTER V.

                  EVOLUTION OF THE PRINCIPAL CONCEPTS.

                   _Section I.—The Concept of Number._

    Return to lower phases: concrete and abstract.—Formation of
    idea of unity. Hypotheses as to its experimental origin: touch,
    sight, hearing, internal sensations, attention. Unity the
    result of decomposition, an abstract.—The series of numbers.
    Process of construction.—Function of signs: discussions of this
    subject                                                            137

                   _Section II.—The Concept of Space._

    Extension as a concrete fact. Variable and relative
    characteristics.—Transition to concrete-abstract period.—Space
    (abstract): the current popular conception the result of
    imagination. Idle problems.—The true concept is the result
    of dissociation.—The notion of “function.”—Imagination of an
    infinite space.—Works on ideal geometry: constructive power
    of the mind; reinforcement of distinction between space as
    perceived and conceived                                            146

                   _Section III.—The Concept of Time._

    Real (concrete) duration: the present, its reality; its
    experimental determination: maximum and minimum. Reproduction
    of duration; experiments; indifferent point.—Variable and
    relative characteristics.—Origin of concrete notion of time:
    different hypotheses: external and internal sensations:
    presumption in favor of the latter.—Abstract duration
    (time). First stage, depends on memory and imagination only:
    corresponds (1) to generic images (representation of duration
    among the higher animals), and (2) to the concrete-abstract
    period (intermediate forms of abstraction). Primitive races.
    Why has time (and not space) been personified.—Second stage
    depends upon abstraction. Function of the astronomers:
    measure of time.—Infinite time.—Current hypotheses as to the
    psychologic process which constitutes the notion of time:
    sensations and consecutive images: sensations which are
    feelings of tension, of effort. “Temporal signs.”—Full and
    empty time                                                         159

                   _Section IV.—The Concept of Cause._

    Psychical elements constituting the concept.—Experiential
    origin of the idea of cause: different solutions have all
    a common basis.—Its primitive individual character. Its
    extension.—Subjective and anthropomorphic period of generic
    images.—Period of reflexion, partial elimination of its
    subjective character, reduction to an invariable relation.—The
    notion of universal causality is acquired and remains a
    postulate.—Two ideas have hindered the development of this last
    notion: that of miracles and that of chance.—Transformation of
    the notion of cause. Rule of scientific research: its position
    is exterior. Identity of cause and effect.—Present form of the
    principle of universal causality.—Two quite distinct notions
    of cause (force, invariable relation), one of which is alone a
    concept                                                            180

                    _Section V.—The Concept of Law._

    Objective value of general ideas. Two contrary theories. Mere
    approximations to the psychologist.—Three periods in the
    development of the notion of law.—Period of generic images.
    Primitive sense of the word law.—Period of empirical laws,
    corresponding with the intermediate forms of abstraction.
    Characteristics: identity of fact and law; complexity.—Period
    of theoretical or ideal laws, corresponding to medium forms
    of abstraction. Its features: simplicity, quantitative
    determination, ideal formula                                       194

                  _Section VI.—The Concept of Species._

    Its value: contemporaneous discussion of this subject.
    Component elements of the concept of species: resemblance,
    filiation. Difficulties resulting from polymorphism, from
    alternate generation.—Races, varieties.—Temporary and
    provisional objectivity.—Genera. Theories of Linnæus and
    Agassiz.—Shifting character of the classifications above the
    species.—One common point between transformists and their
    opponents: practical value of concepts. Not realities, nor
    fictions, but approximations.—Laws and species dependent on
    conditions of existence and varying with them                      203

                               CHAPTER VI.

                               CONCLUSION.

    How was the faculty of abstracting and of generalising
    constituted? Two principal causes: utility, appearance of
    inventors.—How has it developed? Three principal directions:
    practical, speculative, scientific.—_Résumé_: necessary
    co-operation of two factors: the one conscious, the other
    unconscious                                                        216




CHAPTER I.

THE LOWER FORMS OF ABSTRACTION.


ABSTRACTION PRIOR TO SPEECH.

Save in extremely rare cases,—supposing such to occur at all, as
perhaps in the instant of surprise, and in states approximating to pure
sensation,—save in such extremely rare cases, where the mind, like a
mirror, passively reflects external impressions, intellectual activity
may always be reduced to one of the two following types: associating,
combining, unifying, or dissociating, isolating, and separating. These
cardinal operations underlie all forms of _cognition_, from the lowest to
the highest, and constitute its unity of composition.

Abstraction belongs to the second type. It is a normal and necessary
process of the mind, dependent on attention, i. e., on the limitation,
willed or spontaneous, of the field of consciousness. The act of
abstraction implies in its genesis both negative and positive conditions,
and is the result of these.

The negative conditions consist essentially in the fact that we cannot
apprehend more than one quality or one aspect, varying according to the
circumstances, in any complex whole,—because consciousness, like the
retina, is restricted to a narrow region of clear perception.

The positive condition is a state which has been appropriately termed a
“psychical reinforcement” of that which is being abstracted, and it is
naturally accompanied by a weakening of that which is abstracted from.
The true characteristic of abstraction is this partial increment of
intensity. While involving elimination, it is actually a positive mental
process. The elements or qualities of a percept, or a representation,
which we omit do not necessarily involve such suppression. We leave them
out of account simply because they do not suit our ends for the moment,
and are complementary.[2]

Abstraction being, then, in spite of negative appearances, a positive
operation, how are we to conceive it? Attention is necessary to it,
but it is more than attention. It is an augmentation of intensity,
but it is more than an augmentation of intensity. Suppose a group of
representations _a + b + c = d_. To abstract from _b_ and _c_ in favor
of _a_, would ostensibly give _a = d - (b + c)_. If this were so, _b_
and _c_ would be retained unaltered in consciousness; there would be no
abstraction. On the other hand, since it is impossible for the whole
representation _d_ to be suppressed outright, _b_ and _c_ cannot be
totally obliterated. They subsist, accordingly, in a residual state which
may be termed _x_, and the abstract representation is hence not _a_ but
_a + x_ or _A_. Thus the elements of abstract representations are the
same as those of concrete representations; only some are strengthened,
others weakened: whence arise new groupings. Abstraction, accordingly,
consists in the formation of new groups of representations which, while
strengthening certain elements of the concrete representations, weaken
other elements of the same.[3]

We see from the above that abstraction depends genetically upon the
causes which awaken and sustain attention. I have described these causes
elsewhere,[4] and cannot here return to their consideration.

It is sufficient to remark that abstraction, like attention, may be
instinctive, spontaneous, and natural; or reflective, voluntary, and
artificial. In the first category the abstraction of a quality or mode
of existence originates in some attraction, or from utility; hence it is
a common manifestation of intellectual life and is even met with, as we
shall see, among many of the lower animals. In its second form, the rarer
and more exalted, it proceeds less from the qualities of the object than
from the will of the subject; it presupposes a choice, an elimination, of
negligible elements, which is often laborious, as well as the difficult
task of maintaining the abstract element clearly in consciousness. In
fine, it is always a special application of the attention which, adapted
as circumstances require to observation, synthesis, action, etc., here
functions as an instrument of analysis.

A deeply-rooted prejudice asserts that abstraction is a mental act of
relative infrequency. This fallacy obtains in current parlance, where
“abstract” is a synonym of difficult, obscure, inaccessible. This is a
psychological error resulting from an incomplete view: all abstraction is
illegitimately reduced to its higher forms. The faculty of abstracting,
from the lowest to the highest degrees, is constantly the same: its
development is dependent on that of (general) intelligence and of
language; but it exists in embryo even in those primitive operations
which are properly concerned with the concrete, i. e., perception and
representation. Several recent authors have emphasised this point.[5]

Perception is _par excellence_ the faculty of cognising the concrete. It
strives to embrace all the qualities of its object without completely
succeeding, because it is held in check by an internal foe,—the natural
tendency of the mind to simplify and to eliminate. The same horse, at
a given moment, is not perceived in the same manner by a jockey, a
veterinary surgeon, a painter, and a tyro. To each of these, certain
qualities, which vary individually, stand in relief, and others recede
into the background. Except in cases of methodical and prolonged
investigation (where we have observation, and not perception) there
is always an unconscious selection of some principal characteristics
which, grouped together, become a substitute for totality. It must not
be forgotten that perception is pre-eminently a _practical_ operation,
that its mainspring is interest or utility, and that in consequence we
neglect—i. e., leave in the field of obscure consciousness—whatever at
the moment concerns neither our desires nor our purposes. It would be
superfluous to review all the forms of perception (visual, auditory,
tactile, etc.), and to show that they are governed by this same law of
utility; but it should be remarked that the natural mechanism by which
the strengthened elements and the weakened elements are separated, is a
rude cast of what subsequently becomes abstraction, that the same forces
are in play, and are ultimately reducible to some definite direction
given to the attention.

With the image, the intermediate stage between percept and concept,
the reduction of the object represented to a few fundamental features
is still more marked. Not merely is there among the different
representations which I may have of some man, dog, or tree, one that
for the time being necessarily excludes the others (my oak tree
perforce appears to me in summer foliage, tinted by autumn, or bereft
of leaves,—in bright light or in shade), but even this individual,
concrete representation which prevails over the others is no more than a
sketch, a reduction of reality with many details omitted. Apart from the
exceptionally gifted men in whom mental vision and mental audition are
perfect, and wholly commensurate (as it would seem) with perception, the
representations which we call exact are never so, except in their most
general features. Compare the image we have with our eyes closed of a
monument, with the perception of the monument itself; the remembrance of
a melody with its vocal or instrumental execution. In the average man,
the image, the would-be copy of reality invariably suffers a conspicuous
impoverishment, which is enormous in the less lavishly endowed; it is
here reduced to a mere schema, limited to the inferior concepts.

Doubtless it may be objected that the work of dissociation in perception
and representation is incomplete and partial. It would be strange and
illogical indeed if the abstract were to triumph in the very heart of
the concrete; we do but submit that it is here in germ, in embryonic
shape. And hence, when abstraction appears in its true form, as the
consciousness of one unique quality isolated from the rest, it is no new
manifestation but a fruition, it is a simplification of simplifications.

The state of consciousness thus attained, by the fixation of attention
on one quality exclusively, and by its ideal dissociation from the rest,
becomes, as we know, a notion which is neither individual nor general,
but abstract,—and this is the material of generalisation.

The sense of identity, the power of apprehending resemblances, is, as has
justly been said, “the keel and backbone of our thinking”; without it we
should be lost in the incessant stream of things.[6] Are there in nature
any complete resemblances, any absolutely similar events? It is extremely
doubtful. It might be supposed that a person who reads a sentence several
times in succession, who listens several times to the same air, who
tastes all the four quarters of the same fruit, would experience in each
case an identical perception. But this is not so. A little reflexion
will show that besides differences in time, in the varying moods of
the subject, and in the cumulative effect of repeated perceptions,
there is at least between the first perception and the second, that
radical difference which separates the new from the repeated. In fact,
the material given us by external and internal experience consists of
resemblances alloyed by differences which vary widely in degree,—in other
words, analogies. The perfect resemblance assumed between things vanishes
as we come to know them better. At first sight a new people exhibits
to the traveller a well-determined general type; later, the more he
observes, the more the apparent uniformity is resolved into varieties.
“I have taken the trouble,” says Agassiz, “to compare thousands of
individuals of the same species; in one case I pushed the comparison so
far as to have placed side by side 27,000 specimens of one and the same
shell (genus _Neretina_). I can assure you that in these 27,000 specimens
I did not find two that were perfectly alike.”

Is this faculty of grasping resemblances—the substrate of
generalization—primitive, in the absolute signification of the word?
Does it mark the first awakening of the mind, in point of cognition? For
several contemporary writers (Spencer, Bain, Schneider, and others) the
consciousness of difference is the primordial factor; the consciousness
of resemblance comes later. Others uphold the opposite contention.[7]
As a matter of fact this quest for the _primum cognitum_ is beyond
our grasp; like all genetical questions, it eludes our observation and
experience.

No conclusion can be formed save on purely logical arguments, and each
side advances reasons that carry a certain weight. There is, moreover, at
the bottom of the whole discussion, the grave error of identifying the
embryonic state of the mind with its adult forms, and of presupposing
a sharp initial distinction between discrimination and assimilation.
The question must remain open, incapable of positive solution by our
psychology. The incontestable truth with regard to the mind, as we know
it in its developed and organised state, is that the two processes
advance _pari passu_, and are reciprocally causative.

In sum, abstraction and generalisation considered as elementary acts of
the mind, and reduced to their simplest conditions, involve two processes:

1. The former, _abstraction_, implies a dissociative process, operating
on the raw data of experience. It has subjective causes which are
ultimately reducible to attention. It has objective causes which may be
due to the fact that a determinate quality is given us as an integral
part of widely different groups.

“Any total impression whose elements are never experienced apart must
be unanalysable. If all cold things were wet and all wet things cold,
if all liquids were transparent and no non-liquid were transparent,
we should scarcely discriminate between coldness and wetness and
scarcely ever invent separate names for liquidity and transparency....
What is associated now with one thing and now with another tends to
become dissociated from either, and to grow into an object of abstract
contemplation by the mind. One might call this the law of dissociation
by varying concomitants.”[8]

2. The latter, _generalisation_, originates in association by
resemblance, but even in its lowest degree it rises beyond this, since it
implies a synthetic act of fusion. It does not, in fact, consist in the
successive excitation of similar or analogous percepts, as in the case
where the image of St. Peter’s in Rome suggests to me that of St. Paul’s
in London, of the Pantheon in Paris, and of other churches with enormous
dimensions, of like architecture, and with gigantic domes. It is a
condensation. The mind resembles a crucible with a precipitate of common
resemblances at the bottom, while the differences have been volatilised.
In proportion as we recede from this primitive and elementary form, the
constitution of the general idea demands other psychological conditions
which cannot be hastily enumerated.

And thus we reach the principal aim of the present work, which purports,
not to reinforce the time-worn dispute as to the nature of abstraction
and generalisation, but to pursue these operations step by step in
their development, and multiform aspects. Directly we pass beyond
pure individual representation we reach an ascending scale of notions
which, apart from the general character possessed by all, are extremely
heterogeneous in their nature, and imply distinct mental habits. The
question so often discussed as to “What takes place in the mind when we
are thinking by general ideas?” is not to be disposed of in one definite
answer, but finds variable response according to the circumstances. In
order to give an adequate reply, the principal degrees of this scale must
first be determined. And for this we require an _objective notation_
which shall give them some external, though not arbitrary, mark.

The first distinguishing mark is given by the absence or presence
of words. Abstraction and generalisation, with no possible aid from
language, constitute the inferior group which some recent writers have
designated by the appropriate name of _generic images_[9]—a term which
clearly shows their intermediate nature between the pure image, and the
general notion, properly so-called.

The second class, which we have termed _intermediate abstraction_,
implies the use of words. At their lowest stage these concepts hardly
rise above the level of the generic image: they can be reduced to a vague
schema, in which the word is almost a superfluous accompaniment. At a
stage higher the parts are inverted: the representative schema becomes
more and more impoverished, and is obliterated by the word, which rises
in consciousness to the first rank.

Finally, the third class, that of the _higher concepts_, has for its
distinguishing mark that it can no longer be represented. If any image
arises in consciousness it does not sensibly assist the movement of
thought, and may even impede it. Everything, apparently at least, is
subordinated to language.

This enumeration of the stages of abstraction can for the present only
be given roughly and broadly. Every phase of its evolution should be
studied in itself, and accurately determined by its internal and external
characteristics. As to the legitimacy, the objective and practical value,
of this schematic distribution, nothing less than a detailed exploration
from one end to the other of our subject, can confirm or overthrow it.

We shall begin, then, with the lower forms, dwelling upon these at some
length, because they are usually neglected, or altogether omitted. This
is the _pre-linguistic_ period of abstraction and generalisation: words
are totally wanting; they are an unknown factor. How far is it possible
without the aid of language to transcend the level of perception, and
of consecutive images, and to attain a more elevated intellectual
standpoint? In replying empirically, we have three fairly copious sources
of information: animals, children who have not yet acquired speech, and
uneducated deaf-mutes.


ANIMALS.

It is a commonplace to say that animal psychology is full of obscurities
and difficulties. These arise mainly with regard to the question now
occupying us; for we are concerned with ascertaining, not whether
animals perceive, remember, and even, when their organisation is
sufficiently advanced, imagine (which no one denies), but if they
are capable in the intellectual order of still better and greater
achievements. The common opinion is in the negative; yet this may rest
entirely upon ambiguity of language. Without prejudging anything, we must
interrogate the facts to hand, and link them as closely as possible in
our interpretation.

As to the facts themselves we may be sparing of detail; they are to be
found in special treatises, and it is superfluous to repeat them in these
pages. It is moreover evident that a large portion of the animal kingdom
may be neglected. In its lowest regions it is so remote from us, and
has so obscure and scant a psychology, that nothing can be learned from
it. In the higher forms alone can we have any chance of finding what we
seek, i. e., (1) equivalents of concepts, (2) processes comparable with
reasoning.

In the immense realm of the invertebrates, the highest psychical
development is, by general acknowledgment, met with among the social
Hymenoptera; and the capital representatives of this group are the ants.
To these we may confine ourselves. Despite their tiny size, their brain,
particularly among the neuters, is remarkable in structure—“one of the
most marvellous atoms,” says Darwin, “in all matter, not excepting even
the human brain.” Injuries to this organ, which are frequent in their
sanguinary combats, cause disorders quite analogous to those observed in
mammals. It is useless to recall what every one knows of their habits:
their organisation of labor, varied methods of architecture, their
wars, plundering and rape, practice of slavery, methods of education,
and (in certain species) their agricultural labors, harvesting,
construction of granaries,[10] etc. We, on the contrary, must examine the
exceptional cases in which the ants depart from their general habits;
for their ability to abstract, to generalise, and to reason, can only
be established by new adaptations to unaccustomed circumstances. The
following may serve as examples:

“A nest was made near one of our tramways,” says Mr. Belt, “and to get
to the trees, the leaves of which they were harvesting, the ants had
to cross the rails, over which the cars were continually passing and
re-passing. Every time they came along a number of ants were crushed to
death. They persevered in crossing for some time, but at last set to
work and tunnelled underneath each rail. One day, when the cars were not
running, I stopped up the tunnels with stones; but although great numbers
carrying leaves were thus cut off from the nest, they would not cross the
rails, but set to work making fresh tunnels underneath them.”

Another observer, Dr. Ellendorf, who has carefully studied the ants of
Central America, recounts a similar experience. These insects cut off the
leaves of trees and carry them to their nests, where they serve various
purposes. One of their columns was returning laden with spoils.

“I placed a dry branch, nearly a foot in diameter, obliquely across their
path, which was lined on either side by an impassable barrier of high
grass, and pressed it down so tightly on the ground that they could not
creep underneath. The first comers crawled beneath the branch as far
as they could, and then tried to climb over, but failed owing to the
weight on their heads.... They then stood still as if awaiting a word of
command, and I saw with astonishment that the loads had been laid aside
by more than a foot’s length of the column, one imitating the other. And
now work began on both sides of the branch, and in about half an hour a
tunnel was made beneath it. Each ant then took up its burden again, and
the march was resumed in the most perfect order.”

They also show considerable inventiveness in the construction of bridges.
It appears from numerous observations that they know how to place straws
on the surface of water, and to keep them in equilibrium or unite their
several ends together with earth, moisten them with their saliva, restore
them when destroyed, and to construct a highway made of grains of sand,
etc. (Réaumur.) They even employ living bridges: “The ground about a
maple tree having been smeared with tar so as to check their ravages, the
first ants who attempted to cross stuck fast. But the others were not to
be thus entrapped. Turning back to the tree they carried down aphides
which they deposited on the tar one after another until they had made a
bridge over which they could cross the tarred spot without danger.”[11]

I shall cite no observations on the intelligence of wasps and bees, but
I wish to note one rudimentary case of generalisation. Huber remarked
that bees bite holes through the base of corollas when these are so long
as to prevent them from reaching the honey in the ordinary way. They
only resort to this expedient when they find they cannot reach the
nectar from above; “but having once ascertained this, they forthwith
proceed to pierce the bottoms of all the flowers of the same species.”
Doubtless association and habit may be invoked here, but before these
were produced, was there not an extension of like to like?

For the higher animals I shall also restrict myself to the upper types.
We shall of course reject all observations relating to “performing”
animals, all acquirements due to education and training by man, as also
the cases in which, as in the beaver, there is a perplexing admixture
of instinct so called (a specific property), and adaptation, varying
according to time and place.

The elephant has a reputation for intelligence which may be somewhat
exaggerated. His psychology is fairly well known. We may cite a few
characteristic traits that bear upon our subject. He will tear up bamboo
canes from the ground, break them with his feet, examine them, and repeat
the operation until he has found one that suits him; he then seizes the
branch with his trunk and uses it as a scraper to remove the leeches
which adhere to his skin at some inaccessible part of his body. “This is
a frequent occurrence, such scrapers being used by each elephant daily.”
When he is tormented by large flies he selects a branch which he strips
of its leaves, except at the top, where he leaves a fine bunch. “He will
deliberately clean it down several times, and then laying hold of its
lower end he will break it off, thus obtaining a fan or switch about five
feet long, handle included. With this he keeps the flies at bay. Say what
we may, these are both really _bona fide_ implements, each intelligently
made for a definite purpose.”

“What I particularly wish to observe,” says an experienced naturalist,
“is that there are good reasons for supposing that elephants possess
abstract ideas; for instance, I think it is impossible to doubt that they
acquire through their own experience notions of hardness and weight, and
the grounds on which I am led to think this are as follows. A captured
elephant, after he has been taught his ordinary duty, say about three
months after he is taken, is taught to pick up things from the ground
and give them to his mahout sitting on his shoulders. Now for the first
few months it is dangerous to require him to pick up anything but soft
articles, such as clothes, because the things are often handed up with
considerable force. After a time, longer with some elephants than others,
they appear to take in a knowledge of the nature of the things they are
required to lift, and the bundle of clothes will be thrown up sharply as
before, but heavy things, such as a crowbar or piece of iron chain, will
be handed up in a gentle manner; a sharp knife will be picked up by its
handle and placed on the elephant’s head, so that the mahout can also
take it by the handle. I have purposely given elephants things to lift
which they could never have seen before, and they were all handled in
such a manner as to convince me that they recognised such qualities as
hardness, sharpness, and weight.”

Lloyd Morgan, who, in his books on comparative psychology, is evidently
disposed to concede as small a measure of intelligence to animals as
possible, comments upon the above observation as follows:[12]

“Are we to suppose that these animals possess abstract ideas? I
reply—That depends upon what is meant by abstract ideas. If it is implied
that the abstract ideas are _isolates_; that is, qualities considered
quite apart from the objects of which they are characteristic, I think
not. But if it be meant that elephants, in a practical way, ‘recognise
such qualities as hardness, sharpness, and weight,’ as _predominant_
elements in the constructs they form, I am quite ready to assent to the
proposition.”

I agree fully with this conclusion, adding the one remark that between
the pure abstract notion and the “predominant” notion so called, there is
only a difference of degree. If the predominant element is not isolated,
detached, and fixed by a sign, it is certainly near being so, and
deserves on this ground to be called an abstract of the lower order.

The observation of Houzeau has been frequently quoted respecting dogs,
which, suffering from thirst in arid countries, rush forty or fifty times
into the hollows that occur along their line of march in the hope of
finding water in the dry bed. “They could not be attracted by the smell
of the water, nor by the sight of vegetation, for these are wanting. They
must thus be guided by general ideas, which are doubtless of an extremely
simple character, and, in some measure, supported by experience.”

It is on this account that the term “generic image” would in my opinion
be preferable for describing cases of this character.

“I have frequently seen not only dogs, but horses, mules, cattle, and
goats, go in search of water in places which they had never visited
before. They are guided by general principles, because they go to
these watering places at times when the latter are perfectly dry.”[13]
Undoubtedly it may be objected that association of images here plays a
preponderating part. The sight of the hollows recalls the water which,
though absent, forms part of a group of sensations which has been
perceived many times; but since the generic image is, as we shall see
later, no more than an _almost passive_ condensation of resemblances,
these facts clearly indicate its nature and its limits.

I shall merely allude without detailed comment to the numerous
observations on the aptitude of dogs and cats for finding means to
accomplish their aims, the anecdotes of their mechanical skill, and the
ruses (so well described by G. Leroy) which the fox and the hare employ
to outwit the hunter, “when they are old and schooled by experience;
since it is to their knowledge of facts that they owe their exact and
prompt inductions.” The most intelligent of all animals, the higher
orders of monkeys, have not been much studied in their wild state,
but such observations as have been made, some of which have been
contributed by celebrated naturalists, fix with sufficient distinctness
the intellectual level of the better endowed. The history of Cuvier’s
orang-outang has been quoted to satiety. The more recent books on
comparative psychology contain ample testimony to their ability to profit
by experience[14] and to construct instruments. A monkey, not having the
strength to lift up the lid of a chest, employed a stick as a lever.
“This use of a lever as a mechanical instrument is an action to which
no animal other than a monkey has ever been known to attain.” Another
monkey observed by Romanes, also “succeeded by methodical investigation,
_without assistance_, in discovering for himself the mechanical principle
of the screw; and the fact that monkeys well understand how to use stones
as hammers, is a matter of common observation.” They are also skilful in
combining their stratagems, as in the case of one who, being held captive
by a chain, and thus unable to reach a brood of ducklings, held out a
piece of bread in one hand, and on tempting a duckling within his reach,
seized it by the other, and killed it with a bite in the breast.[15]

One mental operation remains which must be examined separately, and in
its study we shall pursue the same method, wherever it occurs, throughout
this work. The process in question has the advantage of being perfectly
definite, of restricted scope, completely evolved, and accessible to
research in all the phases of its development, from the lowest to the
highest. It is that of _numeration_.

Are there animals capable of counting? G. Leroy is, I believe, the first
who answered this question in the affirmative, in a passage which is
worth transcribing, although it has been often quoted. “Among the various
ideas which necessity adds to the experience of animals, that of number
must not be overlooked. Animals count,—so much is certain; and although
up to the present time their arithmetic appears weak, it may perhaps be
possible to strengthen it. In countries where game is preserved, war is
made upon magpies because they steal the eggs of other birds.... And
in order to destroy this greedy family at a blow, game-keepers seek to
destroy the mother while sitting. To do this it is necessary to build
a well-screened watch-house at the foot of the tree where the nests
are, and in this a man is stationed to await the return of the parent
bird, but he will wait in vain if the bird has been shot at under the
same circumstances before.... To deceive this suspicious bird, the
plan was hit upon of sending two men into the watch-house, one of them
passed on while the other remained; but the magpie counted and kept her
distance. The next day three went, and again she perceived that only
two withdrew. It was eventually found necessary to send five or six men
to the watch-house in order to put her out of her calculation.... This
phenomenon, which is repeated as many times as the attempt is made, is
one of the most extraordinary instances of the sagacity of animals.”
Since then the question has been repeatedly taken up. Lubbock devotes to
it the three last pages of his book _The Senses of Animals_. According
to his observations on the nests of birds, one egg may be taken from
a nest in which there are four, but if we take away two, the bird
generally deserts its nest. The solitary wasp provisions its cell with
a fixed number of victims. Sand wasps are content with one. One species
of _Eumenes_ prepares five victims for its young, another species ten,
another fifteen, another twenty-four; but the number of the victims
is always the same for the same species. How does the insect know its
characteristic number?[16]

An experiment, methodically conducted by Romanes, proved that a
chimpanzee can count correctly as far as five, distinguishing the words
which stand for one, two, three, four, five, and at command deliver the
number of straws requested of her.[17]

Although the observations on this point are not yet sufficiently varied
and extended to enable us to speak of them as we should wish, it must
be remarked that the cases cited are not alike, and that it would be
illegitimate to reduce them all to one and the same psychological
mechanism.

1. The case of insects is the most embarrassing. It is but candid
to state a _non liquet_, since to attribute their achievements to
unconscious numeration, or to some special equivalent instinct, is
tantamount to saying nothing. Besides, we are not concerned with anything
relating to instinct.

2. The case of the monkey and his congeners stands high in the scale: it
is a form of _concrete_ numeration which we shall meet again in children,
and in the lowest representatives of humanity.

3. All the other cases resemble the alleged “arithmetic” of G. Leroy’s
magpie and similar observations. I see here not a numeration, but a
perception of plurality, which is something quite different. There are
in the brain of the animal a number of co-existing perceptions. It knows
if all are present, or if some are lacking; but a consciousness of
difference between the entire group, and the diminished defective group,
is not identical with the operation of counting. It is a preliminary
state, an introduction, nothing more, and the animal does not pass beyond
this stage, does not count in the exact sense of the word. We shall
see further on that observations with young children furnish proofs in
favor of this assertion, or at least show that it is not an unfounded
presumption, but the most probable hypothesis.

We may now without further delay (while reserving the facts which are
to be studied in the sequel to this chapter) attempt to fix the nature
of the forms of abstraction, and of reasoning, accessible to the higher
animal types.

1. The generic image results from a _spontaneous_ fusion of images,
produced by the repetition of similar, or very analogous, events.
It consists in an almost passive process of assimilation; it is not
intentional, and has for its subject only the crudest similarities. There
is an accumulation, a summation of these resemblances; they predominate
by force of numbers, for they are in the majority. Thus there is formed
a solid nucleus which predominates in consciousness, an abstract
appurtenant to all similar objects; the differences fall into oblivion.
Huxley’s comparison of the composite photographs (above cited) renders it
needless to dwell on this point. Their genesis depends on the one hand
on experience; only events that are frequently repeated can be condensed
into a generic image: on the other hand on the affective dispositions
of the subject (pleasure, pain, etc.), on interest, and on practical
utility, which render certain perceptions predominant. They require,
accordingly, no great intellectual development for their formation,
and there can be no doubt that they exist quite low down in the animal
scale. The infant of four or five months very probably possesses a
generic image of the human form and of some similar objects. It may be
remarked, further, that this lower form of abstraction can occur also
in the adult and cultivated man. If, e. g., we are suddenly transported
into a country whose flora is totally unknown to us, the repetition of
experiences suggests an unconscious condensation of similar plants; we
classify them without knowing their names, without needing to do so, and
without clearly apprehending their distinguishing characteristics, those
namely which constitute the true abstract idea of the botanist.

In sum, the generic image comes half way between individual
representation, and abstraction properly so called. It results almost
exclusively from the faculty of apprehending resemblances. The rôle of
dissociation is here extremely feeble. Everything takes place, as it
were, in an automatic, mechanical fashion, in consequence of the unequal
struggle set up in consciousness between the resemblances which are
strengthened, and the differences, each of which remains isolated.

2. It has been said that the principal utility of abstraction is as an
instrument in ratiocination. We may say the same of generic images.
By their aid animals reason. This subject has given rise to extended
discussion. Some writers resent the mere suggestion that ants, elephants,
dogs, and monkeys, should be able to reason. Yet this resentment is based
on nothing but the extremely broad and elastic signification of the
word reasoning—an operation which admits of many degrees, from simple,
empirical consecutiveness to the composite, quantitative reasoning
of higher mathematics. It is forgotten that there are here, as for
abstraction and for generalisation, _embryonic_ forms—those, i. e., which
we are now studying.

Taken in its broadest acceptation, reasoning is an operation of the mind
which consists in passing from the known to the unknown; in passing
from what is immediately given, to that which is simply suggested by
association and experience. The logician will unquestionably find this
formula too vague, but it must necessarily be so, in order to cover all
cases.

Without pretending to any rigorous enumeration, beyond all criticism, we
can, in intellectual development, distinguish the following phases in the
ascending order: perceptions and images (memories) as point of departure;
association by contiguity, association by similarity; then the advance
from known to unknown, by reasoning from particular to particular, by
analogical reasoning, and finally by the perfect forms of induction and
deduction, with their logical periods. Have all these forms of reasoning
a common substrate, a unity of composition? In other words, can they be
reduced to a single type—of induction according to some, of deduction
according to others? Although the supposition is extremely probable, it
would not be profitable to discuss the question here. We must confine
ourselves to the elementary forms which the logicians omit, or despise,
for the most part, but which, to the psychologist, are intellectual
processes as interesting as any others.

Without examining whether, as maintained by J. S. Mill, all inference
is actually from particular to particular (general propositions being
under this hypothesis only simple _reminders_, brief formulæ serving as
a base of operations) it is clear that we have in it the simplest form
of mental progress from the known to the unknown. At the same time it
is more than mere association, though transcending it only in degree.
Association by similarity is not, as we have seen, identical with
formation of generic images; this last implies fusion, mental synthesis.
So, too, reasoning from particular to particular implies something more
than simple association; it is a state of _expectation_ equivalent to
a conclusion in the empirical order; it is an anticipation. The animal
which has burned itself in swallowing some steaming food, is on its guard
in future against everything that gives off steam. Here we have more than
simple association between two anterior experiences (steam, burning);
and this state “differs from simple associative suggestion, by the fact
that the mind is less occupied with the memory of past burns than with
the expectation of a repetition of the same fact in the present instance;
that is to say, that it does not so much recall the fact of having once
been burnt as it draws the conclusion that it will be burnt.”[18]

Otherwise expressed, he is orientated less towards the past than towards
the future. Granted that this tendency to believe that what has occurred
once or twice will occur invariably, is a fruitful source of error, it
remains none the less a logical operation (judgment or ratiocination)
containing an element more than association: an inclusion of the future,
an implicit affirmation expressed in an act. Doubtless, between these
two processes,—association, inference from particular to particular—the
difference is slight enough; yet in a study of genesis and evolution, it
is just these transitional forms that are the most important.

Reasoning by analogy is of a far higher order. It is the principal
logical instrument of the child and of primitive man: the substrate of
all extension of language, of vulgar and empirical classifications,
of myths, of the earliest, quasi-scientific knowledge.[19] It is the
commencement of induction, differing from the latter, not in form, but
in its imperfectly established content. “Two things are alike in one
or several characteristics; a proposition stated is true of the one,
therefore it is true of the other. _A_ is analogous to _B_; _m_ is true
of _A_, therefore _m_ is true of _B_ also.” So runs the formula of J. S.
Mill. The animal, or child, which when ill-treated by one person extends
its hatred to all others that resemble the oppressor, reasons by analogy.
Obviously this procedure from known to unknown will vary in degree,—from
zero to the point at which it merges into complete induction.

With these general remarks, we may return to the logic of animals or
rather to the sole kind of logic possible without speech. This is,
and can only be, a _logic of images_ (Romanes employs a synonymous
expression, _logic of recepts_), which is to logic, properly so called,
what generic images are to abstraction and to generalisation proper. This
denomination is necessary; it enables us to form a separate category,
well defined by the absence of language; it permits us, in speaking of
judgment and ratiocination in animals, and in persons deprived of speech,
to know exactly what meaning is intended.

It follows that there are two principal degrees in the _logic of images_.

1. Inference from particular to particular. The bird which finds bread
upon the window, one morning, comes back next day at the same hour,
finds it again, and continues to come. It is moved by an association of
images, _plus_ the state of awaiting, of anticipation, as described above.

2. Procedure by analogy. This (at least in its higher forms in animal
intelligence) presupposes mental construction: the aim is definite, and
means to attain it are invented. To this type I should refer the cases
cited above of ants digging tunnels, forming bridges, etc. The ants are
wont to practise these operations in their normal life; their virtue lies
in the power of _dissociation_ from their habitual conditions, from their
familiar ant-heap, and of adaptation to new and unknown cases.

The logic of images has characteristics which pertain to it exclusively,
and which may be summarised as follows:

1. As material it employs concrete representations or generic images
alone, and cannot escape from this domain. It admits of fairly complex
constructions, but not of substitution. The tyro finds no great
difficulty in solving problems of elementary arithmetic (such as: 15
workmen build a wall 3 metres high in 4 days; how long will it take 4 men
to build it?), because he uses the logic of signs, replacing the concrete
facts by figures, and working out the relations of these. The logic of
images is absolutely refractory to attempts at substitution. And while it
thus acts by representation only, its progress even within this limit is
necessarily very slow, encumbered, and embarrassed by useless details,
for lack of adequate dissociation. At the same time it may, in the adult
who is practised in ratiocination, become an auxiliary in certain cases;
I am even tempted to regard it as the main auxiliary of constructive
imagination. It would be worth while to ascertain, from authentic
observations, what part it plays in the inventions of novelists, poets,
and artists. In a polemic against Max Müller, who persists in affirming
that it is radically impossible to think and reason without words, a
correspondent remarks:

“Having been all my life since school-days engaged in the practice of
architecture and civil engineering, I can assure Prof. Max Müller that
designing and invention are done entirely by mental pictures. I find
that words are only an encumbrance. In fact, words are in many cases
so cumbersome that other methods _have_ been devised for imparting
knowledge. In mechanics the graphic method, for instance.”[20]

2. Its aim is always practical. It should never be forgotten that at the
outset, the faculty of cognition is essentially utilitarian, and cannot
be otherwise, because it is employed solely for the preservation of the
individual (in finding food, distinguishing enemies from prey, and so
on). Animals exhibit only _applied_ reasoning, tested by experience;
they feel about and choose between several means,—their selection being
justified or disproved by the final issue. Correctly speaking, the
logic of images is neither true nor false; these epithets are but half
appropriate. It succeeds or fails; its gauge is success or defeat; and as
we maintained above that it is the secret spring of æsthetic invention,
let it be noticed that here again there is no question of truth or error,
but of creating a successful or abortive work.

Accordingly, it is only by an unjustifiable restriction that the higher
animals can be denied all functions beyond that of association, all
capacity for inference by similarity. W. James (after stating that, _as a
rule_, the best examples of animal sagacity “may be perfectly accounted
for by mere contiguous association, based on experience”), arrives
virtually at a conclusion no other than our own. After recalling the
well-known instance of arctic dogs harnessed to a sledge and scattering
when the ice cracked to distribute their weight, he thus explains it:
“We need only suppose that they have individually experienced wet skins
after cracking, that they have often noticed cracking to begin when
they were huddled together and that they have observed it to cease when
they scattered.” Granting this assumption, it is none the less true
that associations by contiguity are no more than the _material_ which
serves as a substratum for inference by similarity, and for the act
which follows. Again, a friend of James, accompanied by his dog, went
to his boat and found it filled with dirt and water. He remembered that
the sponge was up at the house, and not caring to tramp a third of a
mile to get it, he enacted before his terrier (as a forlorn hope) the
necessary pantomime of cleaning the boat, saying: “Sponge, sponge, go
fetch the sponge.” The dog trotted off and returned with it in his mouth,
to the great surprise of his master. Is this, properly speaking, an
act of reasoning? It would only be so, says James, if the terrier, not
finding the sponge, had brought a rag, or a cloth. By such substitution
he would have shown that, notwithstanding their different appearance,
he understood that for the purpose in view, all these objects were
identical. “This substitution, though impossible for the dog, any man
but the stupidest could not fail to do.” I am not sure of this, despite
the categorical assertion of the author; yet, discussion apart, it
must be admitted that this would be asking the dog to exhibit a man’s
reason.[21] As a matter of fact, notwithstanding contrary appearances,
James arrives at a conclusion not very different from our own. “The
characters extracted by animals are very few, and always related to
their immediate interests and emotions.” This is what we termed above,
empirical reasoning.[22]

G. Leroy said: “Animals reason, but differently from ourselves.” This
is a negative position. We advance a step farther in saying: their
reasoning consists in a heritage of concrete or generic images, adapted
to a determined end,—intermediary between the percepts and the act. It
is impossible to reduce everything to association by similarity, much
less by contiguity, alone; since such procedure results necessarily in
the formation of unchangeable habits, in limitation to a narrow routine,
whereas we have seen that certain animals are capable of breaking through
such restrictions.


ON CHILDREN.

We are here concerned with children who have not yet learned to speak,
and with such alone. In contradistinction to animals, and to deaf-mutes
when left to themselves, infancy represents a transitory state of which
no upper limit can be fixed, seeing that speech appears progressively.
The child forms his baby-vocabulary little by little, and at first
imposes it upon others, until such time as he is made to learn the
language of his country. We may provisionally neglect this period of
transition, studying only the dumb, or monosyllabic and gesture phase.

The problem proposed at the end of the seventeenth century (perhaps
before), which divided philosophers into two camps, was whether the
human individual starts with general terms, or with particulars. At a
later time, the question was proposed for the human race as a whole, in
reference to the origin of language.

Locke maintained the thesis of the particular: “The ideas that children
form of the persons with whom they converse resemble the persons
themselves, and can only be particular.”

So, too, Condillac, Adam Smith, Dugald Stewart, and the majority of those
who represent the so-called sensationalist school.

The thesis of the general was upheld by authors of no less authority,
commencing with Leibnitz:

“Children, and those who are ill-acquainted with the language they
desire to speak, or the matter whereof they discourse, make use of
general terms, such as _thing_, _animal_, _plant_, in lieu of the proper
terms which are wanting to them; and it is certain that all proper or
individual names were originally appellative or general.”[23]

The problem cannot be accepted under this form by contemporary
psychology. It is equivocal. Its capital error is in applying to the
embryonic state of intelligence and of language, formulæ that are
appropriate to adult life only—to the growing mind, categories valid for
the formed intellect alone. A reference to the physiology of the human
embryo will render this more intelligible. Has this embryo, up to three
months, a nose or mouth? Is it male or female? etc. Students of the
development of intra-uterine life in its first phases are very cautious
in propounding these and similar questions in such a manner; they do not
admit of definite answers. That which is in the state of envelopment and
of incessant becoming, can only be compared remotely with that which is
fixed and developed.

The sole permissible formula is this: Intelligence progresses from the
indefinite to the definite. If “indefinite” is taken as synonymous
with general, it may be said that the particular does not appear at
the outset; but neither does the general in any exact sense: the vague
would be more appropriate. In other words, no sooner has the intellect
progressed beyond the moment of perception and of its immediate
reproduction in memory, than the generic image makes its appearance,
i. e., a state intermediate between the particular and the general,
participating in the nature of the one and of the other—a confused
simplification.

Recent works on the psychology of infancy abound in examples of these
abstractions and inferior generalisations, which appear very early.[24] A
few examples will suffice.

Preyer’s child (aged thirty-one weeks) interested itself exclusively in
bottles, water-jugs, and other transparent vases with white contents;
it had thus seized upon a characteristic mark of one thing that was
important to it, to wit—milk. At a later period it designated these by
the syllable _môm_. Taine records an analogous case of a child to whom
_mm_ and _um_, and then _nim_ at first signified the pleasure of seeing
its pap, and subsequently everything eatable. We are assisting at the
genesis of the sign; the crude sound attached to a group of objects
becomes at a later period the sign of those objects, and later still an
instrument of substitution. Sigismund showed his son, aged less than
one year, and incapable of pronouncing a single word, a stuffed grouse,
saying “bird.” The child immediately looked across to the other side of
the room where there was a stuffed owl. Another child having listened
first with its right ear, then with its left, to the ticking of a watch,
stretched out its arms gleefully towards the clock on the chimney-piece
(auditory, not vocal, generic image).

Without multiplying examples known to every one, which give peremptory
proof of the existence of abstraction (partial dissociation), and of
generalisation, prior to speech, let us rather consider the heterogeneous
nature of these generic images, the result of their mode of formation.
They are in fact constructed arbitrarily,—as it were by accident,
depending partly on the apprehension of gross resemblances, partly,
and chiefly, on subjective causes, emotional dispositions, practical
interests. More rarely they are based upon essential qualities.

John Stuart Mill affirms that the majority of animals divide everything
into two categories: that which is, and that which is not edible.
Whatever we may think of this assertion, we should probably feel much
astonishment if we could penetrate and comprehend certain animal
generalisations. In the case of children we can do more than assume.
Preyer’s son employed the interjection _ass_ (which he had forged or
imitated) first for his wooden horse, mounted on wheels, and covered with
hair; next for everything that could be displaced or that moved (carts,
animals, his sister, etc.), and that had hair. Taine’s little girl
(twelve months), who had frequently been shown a copy of an infant Jesus,
from Luini, and had been told at the same time, “That is the baby,” would
in another room, on hearing anyone ask her, “Where is the baby?” turn
to any of the pictures or engravings, no matter what they were. _Baby_
signified to her some general thing: something which she found in common
in all these pictures, engravings of landscapes, and figures, i. e.,
if I do not mistake, some variegated object in a shining frame. Darwin
communicated the following observation on one of his grandsons to Romanes:

“The child, who was just beginning to speak, called a duck ‘quack,’ and,
by special association, it also called water ‘quack.’ By an appreciation
of the resemblance of qualities, it next extended the term ‘quack’ to
denote all birds and insects on the one hand, and all fluid substances on
the other. Lastly, by a still more delicate appreciation of resemblance,
the child eventually called all coins ‘quack,’ because on the back of a
French sou it had once seen the representation of an eagle.”[25]

In this case, to which we shall return later, there was a singular
mixture of intellectual operations: creation of a word by onomatopœia
(resemblance) and finally an unbridled extension of analogy.

Such observations might be multiplied. They would only confirm this
remark: the generic image varies in one case and another, because the
condensation of resemblances of which it is constituted depends often
upon a momentary impression, upon most unexpected conditions.

The development of _numeration_ in the child takes us to some extent out
of the pre-linguistic period; but it is advisable to consider it at this
point. In the first place we have to distinguish between what is learnt
and what is comprehended. The child may recite a series of numerical
words that have been taught to him: but so long as he fails to apply each
term of the series correctly to a number of corresponding objects, he
does not understand it. For the rest, this comprehension is only acquired
slowly and at a somewhat late period.

“The only distinction which the child makes at first is between the
simple object and plurality. At eighteen months, he distinguishes between
one, two, and several. At the age of three, or a little earlier, he
knows one, two, and four (2 × 2). It is not until later that he counts
a regular series; one, two, three, four. At this point he is arrested
for some time. Hence the Brahmans teach their pupils of the first class
to count up to four only; they leave it to the second class to count
up to twenty. In European children of average intelligence, the age of
six to seven years is required before they can count to ten, and about
ten years to count to one hundred. The child can doubtless repeat before
this age a numeration which it has been taught, but this is not what
constitutes knowledge of numbers; we are speaking of determining number
by objects.”[26] B. Pérez states that his personal observations have not
furnished any indication contradictory to the assertions of Houzeau. An
intelligent child of two and a half was able to count up to nineteen, but
had no clear idea of the duration of time represented by three days; it
had to be translated as follows: “not to-day but to-morrow, and another
to-morrow.”[27]

This brings us back to the question, discussed above, of the numeration
claimed for animals. Preyer tells us of one of his children that “it was
impossible to take away one of his ninepins without its being discovered
by the child, while at eighteen months he knew quite well whether one
of his ten animals was missing or not.” Yet this fact is no proof that
he was able to count up to nine or ten. To represent to oneself several
objects, and to be aware that one of them is absent, and not perceived—is
a different thing from the capacity of counting them numerically. If
the shelves of a library contain several works that are well known to
me, I can see that one is missing without knowing anything about the
total number of books upon the shelves. I have a juxtaposition of images
(visual or tactile), in which a gap is produced.

For the rest, much light is thrown on this question by Binet’s ingenious
experiments. Their principal result may be summarised as follows.[28]
A little girl of four does not know how to read or count; she has
simply learnt a few figures and applies them exactly to one, two, or
three objects; above this she gives chance names, say six or twelve,
indifferently to four objects. If a group of fifteen counters, and
another group of eighteen, of the same size, are thrown down on the
table, without arranging them in heaps, she is quick to recognise the
most numerous group. The two groups are then modified, adding now to
the right, now to the left, but so that the ratio fourteen to eighteen
is constant. In six attempts the reply is invariably exact. With the
ratio seventeen-eighteen, the reply is correct eight times, wrong once.
If, however, the groups are found with counters of unequal diameter,
everything is altered. Some (green) measure two and one-half centimetres,
others (white) measure four centimetres. Eighteen green counters are put
on one side, fourteen white counters on the other. The child then makes a
constant error, and takes the latter group to be the more numerous, and
the group of fourteen may even be reduced to ten without altering her
judgment. It is not until nine that the group of eighteen counters appear
the more numerous.

This fact can only be explained by supposing that the child appreciates
by _space_, and not by number, by a perception of continuous and not by
discontinuous size—a supposition which agrees with other experiments by
the same author to the effect that, in the comparison of lines, children
can appreciate differences of length. At this intellectual stage,
numeration is accordingly very weak, and restricted to the narrowest
limits. As soon as these are exceeded, the distribution between minus and
plus rests, not upon any real numeration, but upon a difference of mass,
felt in consciousness.

In children, _reasoning_ prior to speech is, as with animals, practical,
but well adapted to its ends. No child, if carefully watched, will fail
to give proof of it. At seventeen months, Preyer’s child, which could
not speak a word, finding that it was unable to reach a plaything placed
above its reach in a cupboard, looked about to the right and left, found
a small travelling trunk, took it, climbed up, and possessed itself of
the desired object. If this act be attributed to imitation (although
Preyer does not say this), it must be granted that it is imitation
of a particular kind,—in no way comparable with a servile copy, with
repetition pure and simple,—and that it contains an element of invention.

In analysing this fact and its numerous analogues, we became aware of
the fundamental identity of these simple inferences with those which
constitute speculative reasoning: they are of the same character. Take,
for instance, a scientific definition, such as that of Boole, which
seems at first sight little adapted to this connexion. “Reasoning is
the elimination of the middle term in a system that has two terms.”
Notwithstanding its theoretical aspect, this is rigorously applicable
to the cases with which we are occupied. Thus, in the mind of Preyer’s
child, there is a first term (desire for the plaything), a last term
(possession); the remainder is the method, scaffolding, a mean term to
be eliminated. The intellectual process in both instances, practical and
speculative, is identical; it is a mediate operation, which develops by
a series of acts in animals and children, by a series of concepts and
words in the adult.


DEAF-MUTES.

In studying intellectual development prior to speech, the group of
deaf-mutes is sufficiently distinct from those which we have been
considering. Animals do not communicate all their secrets, and leave
much to be conjectured. Children reveal only a transitory state, a
moment in the total evolution. Deaf-mutes (those at least with whom we
are dealing) are adults, comparable as such to other men, like them,
save in the absence of speech and of what results from it. They have
reached a stable mental state. Moreover, those who are instructed at a
late period, who learn a language of analytical signs, i. e., who speak
with their fingers, or emit the sounds which they read upon the lips of
others, are able to disclose their anterior mental state. It is possible
to compare the same man with himself, before and after the acquisition of
an instrument of analysis. Subjective and objective psychology combine to
enlighten us.

The intellectual level of such persons is very low (we shall return to
this): still their inferiority has been exaggerated, especially in the
last century, by virtue of the axiom, it is impossible to think without
words. Discussion of this antique aphorism is unnecessary; in its
rigorous form it finds hardly any advocates of note.[29] Since thought
is synonymous with comparing, abstracting, generalising, judging,
reasoning, i. e., with transcending in any way the purely sensorial and
affective life, the true question is not, Do we think without words? but,
To what extent can we think without words? Otherwise expressed, we have
to fix the upper limit of the logic of images, which evidently reaches
its apogee in adult deaf-mutes. Further, even in this last case, thought
without language does not attain its full development. The deaf-mute
who is left without special education, and who lives with men who have
the use of speech, is in a less favorable situation than if he forms a
society with his equals. Gérando, and others after him, remarked that
deaf-mutes in their native state communicate easily with one another.
He enumerates a long series of ideas, which they express in their
mimicry, and gestures, and many of these expressions are identical in all
countries.

“Children of about seven years old who have not yet been educated,
make use of an astonishing number of gestures and very rapid signs in
communicating with each other. _They understand each other naturally
with great facility_.... No one teaches them the initial signs, which
are, in great part, unaltered imitative movements.”

The study of this spontaneous, natural language is the sole process by
which we can penetrate to their psychology, and determine their mode
of thought. Like all other languages, it comprises a vocabulary and a
syntax. The vocabulary consists in gestures which designate objects,
qualities, acts; these correspond to our substantives and verbs. The
syntax consists in the successive order of these gestures and their
regular arrangement; it translates the movement of thought and the effort
towards analysis.

I. VOCABULARY—Gérando collected about a hundred and fifty signs, created
by deaf-mutes living in isolation or with their fellows.[30] A few of
these may be cited as examples:

_Child_—Infantile gesture, of taking the breast, or being carried, or
rocking in the cradle.

_Ox_—Imitation of the horns, or the heavy tread, or the jaws chewing the
cud.

_Dog_—Movement of the head in barking.

_Horse_—Movements of the ears, or two figures riding horseback on
another, etc.

_Bird_—Imitation of the beak with two fingers of the left hand, while the
other feeds it; or simulation of flight.

_Bread_—Signs of being hungry, of cutting, and of carrying to the mouth.

_Water_—Exhibition of saliva, imitation of a rower, or of a man pumping;
accompanied always by the sign of drinking.

_Letter_ (missive)—Gestures of writing and of sealing, or of unsealing
and reading.

Monkeys, cocks, various trades (carpenter, shoemaker, etc.) all
designated by imitative gestures. For sleep, sickness, health, etc., they
employ an appropriate gesture.

For interrogation: expression of two contradictory propositions, and
undecided glance towards the person addressed. This is rather a case of
syntax than of vocabulary; but a few signs may be further indicated for
some notions more abstract than the preceding.

_Large_—Raise the hand and look up.

_Small_—Contrary gestures.

_Bad_—Simulate tasting, and make grimace.

_Number_—Indicate with the help of the fingers; _high numbers_, rapid
opening of the hand several times in succession.

_Buy_—gesture of counting money, of giving with one hand, and taking with
the other.

_Lose_—Pretend to drop an object, and hunt for it in vain.

_Forget_—Pass the hand quickly across the forehead with a shrug of the
shoulders.

_Love_—Hold the hand on the heart (universal gesture).

_Hate_—Same gesture with sign of negation.

_Past_—Throw the hand over the shoulder several times in succession.

_Future_—Indicate a distant object with the hand, repeated imitation of
lying down in bed and getting up again.

It does not need much reflexion to see that all these signs are
_abstractions_ as well as imitations. Among the different characters
of an object, the deaf-mute chooses one that he imitates by a gesture,
and which represents the total object. Herein he proceeds exactly like
the man who speaks. The difference is that he fixes the abstract by
an attitude of the body instead of by a word. The primitive Aryan who
denominated the horse, the sun, the moon, etc., the rapid one, the
shining one, the measurer (of months), did not act otherwise; for him
also, a chosen characteristic represents the total object. There is a
fundamental identity in the two cases; thus justifying what was said
above: abstraction is a _necessary_ operation of the mind, at least in
man; he must abstract, because he must simplify.

The inferiority of these imitative signs consists in their being often
vague, with a tendency to the opposite sense; moreover, since they are
never detached completely from the object or the act which they figure,
and cannot attain to the independence of the word, they are but very
imperfect instruments of substitution.

II. SYNTAX—The mere fact of the existence of a syntax in the language of
the deaf-mutes proves that they possess a commencement of analysis, i.
e., that thought does not remain in the rudimentary state. This point has
been carefully studied by different authors: Scott, Tylor, Romanes,[31]
who assign to it the following characteristics:

1. It is a syntax of position. There are no “parts of speech,” i. e.,
terms having a fixed linguistic function: substantive, adjective, verb,
etc. The terms (gestures) borrow their grammatical value from the place
which they occupy in the series, and the relations between the terms are
not expressed.

2. It is a fundamental principle that the signs are disposed in the order
of their relative importance, everything superfluous being omitted.

3. The subject is placed before the attribute, the object (complement)
before the action, and, most frequently, the modified part before the
modifying.

Some examples will serve for the better comprehension of the ordinary
procedure of this syntax. To explain the proposition: After running, I
went to sleep, the order of gesture would be: to run, me, finished, to
sleep.—My father gave me an apple: apple, father, me, give.—The active
state is distinguished from the passive by its position: I struck Thomas
with a stick; me, Thomas, strike, stick. The Abbé Sicard, on asking a
deaf-mute, Who created God? obtained the answer: God created nothing.
Though he had no doubt as to the meaning of this inversion, he asked the
control question, Who makes shoes? Answer, shoes makes cobbler.

The dry, bare character of this syntax is evident: the terms are
juxtaposed without relation; it expresses the strictest necessity only;
it is the replica of a sterile, indistinct mode of thought.

Since we are endeavoring by its aid to fix an intellectual level, it
is not without interest to compare it with a syntax that is frequent
among the weak in intellect. “These do not decline or conjugate;
they employ a vague substantive, the infinitive alone, or the past
participle. They leave out articles, conjunctions, auxiliary verbs,
reject prepositions, employ nouns instead of pronouns. They call
themselves “father,” “mother,” “Charles,” and refer to other people by
indeterminate substantives, such as man, woman, sister, doctor, etc. They
invert the regular order of substantives and adjectives.”[32] Although
this is a case of mental regression, hence not rigorously comparable
with a mind that is sane but little developed, the mental resemblance
between the two syntaxes, and especially the absence of all expression of
relations deserves to be signalised, because it cannot be the result of a
fortuitous coincidence. It is the work of intellectual inferiority and of
relative discontinuity of thought.

There is little to say about _numeration_ in deaf-mutes. When untrained,
they can count up to ten with the help of their fingers, like many
primitive people. Moreover (according to Sicard and Gérando), they make
use of notches upon a piece of wood or some other visible mark.

To conclude, their mental feebleness, known since the days of antiquity
by Aristotle, by the Roman law which dispossessed them of part of their
civil rights, later on by many philosophers who refused even to concede
them memory, arises from their inaptitude to transcend the inferior
forms of abstraction and kindred operations. In regard to the events
of ordinary life, in the domain of the concrete (admitting, as is not
always done, that there are individual varieties, some being intelligent,
and others stupid), deaf-mutes are sufficiently apt to seize and to
comprehend the practical connexion between complex things.[33] But the
world of higher concepts, moral, religious, cosmological, is closed to
them. Observations to this effect are abundant, though here again—as must
be insisted on—they reveal great individual differences.

Thus, a deaf-mute whose friends had tried to inculcate in him a few
religious notions, believed before he came under instruction that the
Bible was a book that had been printed in heaven by workmen of Herculean
strength. This was the sole interpretation he gave to the gestures of his
parents, who endeavored to make him understand that the Bible contains
a revelation, coming from an all-powerful God who is in heaven.[34]
Another who was taken regularly to church on Sunday, and exhibited
exemplary piety, only recognised in this ceremony an act of obedience
to the clergy. There are many similar cases on record. Others on the
contrary, seek to inquire into, and to penetrate, the nature of things.
W. James[35] has published the autobiography of two deaf-mutes who became
professors, one at the asylum of Washington, the other in California.

The principal interest attaching to the first is the spontaneous
appearance of the moral sense. After stealing small sums of money from
the till of a merchant, he accidentally took a gold coin. Although
ignorant of its value, he was seized with scruples, feeling “that it was
not for a poor man like him, and that he had stolen _too much_.” He got
rid of it as best he could, and never began again.

The other biography—from which we make a few brief extracts—may be taken
as the type of an intelligent and curious deaf-mute. He was not placed
in an institution until he was eleven years old. During his childhood he
accompanied his father on long expeditions, and his curiosity was aroused
as to the origin of things: of animals and vegetables, of the earth, the
sun, the moon, the stars (at eight or nine years). He began to understand
(from five years) how children were descended from parents, and how
animals were propagated. This may have been the origin of the question
he put to himself: whence came the first man, first animal, first plant,
etc. He supposed at first that primæval man was born from the trunk of
a tree, then rejected this hypothesis as absurd, then sought in various
directions without finding. He respected the sun and moon, believed that
they went under the earth in the West, and traversed a long tunnel to
reappear in the East, etc. One day, on hearing violent peals of thunder,
he interrogated his brother, who pointed to the sky, and simulated the
zigzag of the lightning with his finger; whence he concluded for the
existence of a celestial giant whose voice was thunder. Puerile as they
may be, are these cosmogonic, theological conceptions inferior to those
of the aborigines of Oceanica and of the savage regions of South America,
who, nevertheless, have a vocal idiom, a rudimentary language?

To sum up. That which dominates among the better gifted, is the
creative imagination: it is the culminating point of their intellectual
development. Their primitive curiosity does not seem inferior to that
of average humanity; but since they cannot get beyond representation by
images they lack an instrument of intellectual progress.


ANALYTICAL GESTURES.

The question of signs is so closely allied to our subject—the evolution
of general ideas—that we must insist upon the language of gesture as
an instrument of analysis, before going on to speech—of which it is an
imperfect substitute.

St. George Mivart (_Lessons from Nature_) gives the following as a
complete classification of every species of sign, omitting those that are
written:

1. Sounds which are neither articulate nor rational, such as cries of
pain, or the murmur of a mother to her infant.

2. Sounds which are articulate but not rational, such as the talk of
parrots, or of certain idiots, who will repeat, without comprehending,
every phrase they hear.

3. Sounds which are rational but not articulate, such as the inarticulate
ejaculations by which we sometimes express assent to or dissent from
given propositions.

4. Sounds which are both rational and articulate, constituting true
“speech.”

5. Gestures which do not answer to rational conceptions, but are merely
the manifestations of emotions and feelings.

6. Gestures which do answer to rational conceptions, and are therefore
“external” but not “oral” manifestations of the _verbum mentale_.

This last group, the only one which concerns us for the moment, would to
my thinking be conveniently designated by the term _analytic gestures_,
as opposed to the synthetic gestures which manifest the different modes
of affective life, and constitute what is called the expression of the
emotions.

This language of gesture, intellectual and non-emotional, which
translates ideas, not sentiments, is more widely distributed than is
generally known, among primitive peoples. It has been observed in very
distinct regions of our globe; among the aborigines of North and South
America, the Bushmen, etc. It is a means of communication between tribes
who do not speak the same language; often, indeed, it is an indispensable
auxiliary to these indigent idioms. The most important work on this
subject is by an American, Col. Mallery, who with indefatigable patience
has collected and interpreted the gestures in use among the Indians of
North America.[36] This work alone reveals the variety of sign-language,
which hardly ever leaves the region of practical life: description of the
countries traversed, hints for travellers, directions to be followed,
distances, time required for halts, manner, habits, and dispositions of
tribes. We may cite a brief quotation, from another author:

    “Meeting an Indian, I wish to ask him if he saw six waggons
    drawn by horned cattle, with three Mexican and three American
    teamsters, and a man mounted on horseback. I make these signs:
    I point ‘you,’ then to his eyes, meaning ‘see’; then hold up
    all my fingers on the right hand and the forefinger on the
    left, meaning ‘six’; then I make two circles by bringing the
    ends of my thumbs and forefingers together, and, holding my
    two hands out, move my wrists in such a way as to indicate
    waggon-wheels revolving, meaning ‘waggons’; then, by making
    an upward motion with each hand from both sides of my head,
    I indicate ‘horns,’ signifying horned cattle; then by first
    holding up three fingers, and then by placing my extended right
    hand below my lower lip and moving it downward, stopping it mid
    way down the chest, I indicate ‘beard,’ meaning Mexican; and
    with three fingers again, and passing my right hand from left
    to right in front of my forehead, I indicate ‘white brow’ or
    ‘pale face.’ I then hold up my forefinger, meaning one man, and
    by placing the forefinger of my left hand between the fore and
    second finger of my right hand, representing a man astride of a
    horse, and by moving my hands up and down, give the motion of a
    horse galloping with a man on his back. I in this way ask the
    Indian, ‘You see six waggons, horned cattle, three Mexicans,
    three Americans, one man on horseback?’... The time required to
    make these signs would be about the same as if you asked the
    question verbally.”[37]

Tylor says that the language of gestures is substantially the same all
the world over, and this assertion is confirmed by all who have practised
and studied it. Its syntax resembles that of deaf-mutes, and it is
unnecessary to repeat it. The parable of the Prodigal Son was translated
by Mallery into analytic gestures; and from this language translated
afresh into the spoken tongue: “Formerly, man one, sons two,” etc., etc.
The comparison of the two texts is instructive: in the one, the thought
unfolds itself by a movement of complete analysis with relations and
shades of meaning: in the other, it resembles a line of badly quarried
blocks, put together without cement.

After what has already been said, there is nothing surprising in finding
a fundamental analogy, or even identity, between the language of
deaf-mutes and the analytic gestures of primitive peoples. It was indeed
pointed out by Akerly in an institution in New York in the beginning
of the century. Gérando gave a good many examples,[38] remarking that
the “gestures of reduction,” i. e., abridged gestures, are often enough
identical in the two cases. Mallery brought together some Utah Indians,
and a deaf-mute, who gave them a long account of a marauding expedition,
followed by a dialogue: they understood each other perfectly.

The language of analytical gesture is thus a substitute for spoken
language, and this leads us to a question which, though purely
speculative, deserves our attention for a moment.

At a time when it was almost universally admitted that man is unable
to think without words, Dugald Stewart ventured to write: “If men had
been deprived of the organs of voice or the sense of hearing, there is
no doubt that they would have invented an alphabet of visible signs
wherewith to express all their ideas and sentiments.”[39] This is no rash
assertion; we have just seen proofs of it. But is this pantomime-language
susceptible of progress?

We can hardly doubt that if humanity, with its proper cerebral
constitution, had at the same time been unable to speak, the language of
analytic gesture would, by the initiative of certain inventors, under
press of necessity, and by the influence of co-operation and of life
in common, have advanced beyond the imperfect phase at which it has
remained; and no one can say what it might have become in the accumulated
effort of centuries. Speech, too, had to traverse an embryonic period,
and oral language developed slowly and painfully. At the same time it is
an exaggeration to say that “phonetic language assumed its extraordinary
importance almost by chance, and that we cannot doubt that the language
of mimicry, had it been fashioned by social relations during secular
ages, would be hardly inferior to speech in force, facility, and
variety.”[40] In fact, man had originally two languages at his disposal;
he used the one and the other interchangeably and simultaneously. They
helped each other in the development of ideas that were as yet chaotic
and vacillating. Under these conditions, speech prevailed; the language
of gesture remained only as a survival or a substitute. There is nothing
fortuitous in this: speech has won because of its greater value.

First, for _practical_ reasons. And this is the capital factor, since
the main point is to communicate with one’s fellow-men. The language
of gesture—besides monopolising the hands, and thus keeping them from
other work—has the great disadvantage of not carrying far, and of being
impossible in the dark. To this we may add the reasons cited above: its
vague character, and (with regard to the abstract) its imitative nature,
which forbids emancipation, or complete detachment, from the concrete,
or the translation of that which cannot be represented. It is to be
remarked, however, that the invention of “reduced” signs seems to be a
transition from pure imitation to symbolism, a first step in the path of
emancipation.

Speech, on the contrary, is transmitted to a distance, and challenges
darkness. It is dependent upon the ear, an organ whose sensations are
infinite in number and kind; and in the finest expression of ideas and
of feelings, language participates in this opulence. It lends itself to
variety, delicacy, to an extreme complexity of movement in a small space,
with very little effort. We are, for the moment, citing physiological
reasons only. But these will suffice to show that the triumph of speech
has not been fortuitous, but that it is a very special case of natural
supremacy.[41]

In conclusion, there is nothing to add as to generic images, and the
logic of images. The important part which they play amongst children and
deaf-mutes testifies to their extension and importance as inferior forms
of abstraction, without in any way altering their essential nature, as
previously determined.




CHAPTER II.

SPEECH.


Before we inquire into abstraction, as fixed and expressed in
words,—whether such words are the complement of an actual or possible
representation, or exist alone in consciousness, as complete
substitutes,—it is indispensable that we should study the origin, and
still more the evolution, of this new factor. Although many linguists
resolutely abstain from considering the origin of speech (which is
certainly, like all other genetic problems, beyond the grasp of
psychology), the question is so intimately allied with that of the
evolution of articulate language, allied again in itself with the
progressive development of abstraction and of generalisation, that we
should not be justified in withholding a brief summary of the principal
hypotheses relating to this subject, while limiting ourselves to the most
recent.


I.

Launching forth then into this region of conjecture—do we, in the first
place, find among some animals, signs and means of communication which
for them are the equivalents of language? In considering this point it
matters little whether or no we accept the evolutionary thesis. It must
not be forgotten, in fact, that the problem of the origin of speech is
only a particular case of the origin of language in general: speech being
but one species among several others of the _facultas signatrix_, which
can only be manifested in the lower animals in its humblest form.

There can be no doubt that pain, joy, love, impatience, and other
emotional states are translated by proper signs, easy to determine.
Our problem, however, is different; we are concerned with signs of the
_intellectual_, not of the affective, life. In other words, can certain
animals transmit a warning, or an order, to their fellows? Can they
muster them for a co-operative act, and make themselves intelligible?
Although the interpretation is necessarily open to the suspicion of
anthropomorphism, it is difficult not to recognise a sort of language
in certain acts of animal life. Is it _a priori_ probable that animals,
which form stable and well-organised societies, should be bereft of all
means of intercommunication and comprehension?

With regard to ants, we learn from such observers as Kirby and Spence,
Huber, Franklin, that they employ a system of signs. To elucidate this
point, Lubbock undertook a series of patient experiments, certain of
which may be quoted.[42] He pinned down a dead fly so that no ant could
carry it off. The first that came made vain attempts to remove it. It
then went to the ant-hill and brought seven others to the rescue, but
hurried imprudently in front of them. “Seemingly only half awake,”
they lost the track and wandered alone for twenty minutes. The first
returned to the nest and brought back eight, who, so soon as they were
left behind by the guide, turned back again. During this time the band
of seven (or at least some of them) had discovered the fly, which they
tore in pieces and carried off to the nest. The experiment was several
times repeated, with different species, and always with the same result.
Lubbock concluded that ants were able to communicate their discoveries,
but without indicating locality. In another experiment he placed three
glasses at a distance of thirty inches from a nest of ants. One of the
glasses contained two or three larvæ, the second three hundred to six
hundred, the third none at all. He connected the nest with the glasses
by means of three parallel tapes, and placed one ant in the glass with
many larvæ and another ant in that with two or three. Each of them took a
larva and carried it to the nest, returning for another, and so on. After
each journey he put another larva into the glass with only two or three
larvæ, to replace that which had been removed, and every stranger brought
was imprisoned until the end of the experiment. Were the number of visits
to all three glasses the same? And if not, which of the two glasses
containing larvæ received the greater number of visitors? A difference
in number would seem to be conclusive as proving power of communication.
The result was that during forty-seven and a half hours two hundred
and fifty-seven friends were brought by the ants having access to the
glass containing numerous larvæ, while during an interval of fifty-three
hours there were only eighty strange visitors to the glass containing
two or three larvæ; there were no visits to the glass containing none.
Communication for bees as for ants, appears to be made by rubbing the
antennæ. If the queen is carried off in a hive, some of the bees are
sure to discover it before long. They become greatly agitated, and run
about the hive frantically, touching any companions they meet with their
crossed antennæ, and thus spreading the news through the whole community.
The bee-hunters in America discover them by choosing a clearing where
they catch a few wandering bees, which are then gorged with honey and
suffered to fly when replete. These bees return with a numerous escort.
The same process is repeated with the new comers, and by observing the
direction which they follow at their departure, the nest is discovered.

As regards the higher animals, the truth (notwithstanding the
exaggerations of G. Leroy—who asserts that when they hunt together, wait
for one another, find each other again, and give mutual aid, “these
operations would be impossible without conventions that could only be
communicated in detail by means of an articulate language [_sic_]”)
is that we know singularly little about them. It is certain that, in
addition to sounds that translate their emotions, many species have other
means of communication. According to Romanes[43] the more intelligent
dogs have the faculty of communicating with one another, by the tone of
barking, or by gesture, such simple ideas as “follow me.” This gesture is
invariably the same; being a contact of heads with a motion between a rub
and a butt, and always resulting in a definite but never complex course
of action. In a troop of reindeer the leader makes one sign for the halt,
another for the march forward, hitting the laggards one after another
with his horns. Monkeys are known to produce various sounds (the gibbon
compasses a complete octave), and several species will meet and hold a
kind of conversation. Unfortunately, notwithstanding recent researches,
we have only vague and doubtful data in regard to monkey language.

We know finally, that certain birds are able to articulate, and possess
all the material conditions of speech, the faculty being indeed by
no means uncommon. Parrots do even more; there is no doubt that they
can apply words, parts of sentences, and airs, to persons, things, or
definite events, without varying the application, which is always the
same.[44] Association by contiguity sufficiently explains this fact,
but, granting that they do not as a rule make a right intellectual use
of articulate sounds, they seem in certain instances to attach to them
the value of a _sign_. Romanes actually observed a more extraordinary
case, implying generalisation, with apposition of a sound. In the first
instance, one of his parrots imitated the barking of a terrier which
lived in the house. Later on, this barking became a denotative sound,
the proper name of the dog; for the bird barked as soon as it saw the
terrier. Finally, at a still later stage, it got into the habit of
barking when any dog, known or unknown, came into the house; but ceased
to bark at the terrier. While distinguishing individuals it therefore
perceived their resemblance. “The parrot’s name for an individual dog
became extended into a generic name for all dogs.”[45]

In short, the language of animals—so far as we know it—exhibits a very
rudimentary development, by no means proportionate to that of the logic
of images, and highly inferior to that of analytical gesture. It throws
no light, notwithstanding all that has been said, upon the problem of the
origin of speech.

In respect to this subject, which has excited human curiosity for
centuries without satiation, there appear to me (when we have eliminated
old or abandoned hypotheses) to be only two theories which have any
solidity: the one presupposes instinct; the other a slow evolution.

I. It must be remarked that if the partisans of the first theory seem at
the outset to have frankly admitted innate disposition (the fundamental
characteristic of instinct), it is more difficult to distinguish between
some of the later writers and the evolutionists.

Thus it has been said: speech is a necessary product in which neither
reflexion nor will participate, and which is derived from a secret
instinct in man (Heyse). Renan sustained a similar thesis. For Max
Müller, “man is born speaking, as he is born thinking; speech marks the
transition from (concrete) intuitions to ideas; it is a fact in the
development of the mind; it is created with no distinct consciousness
of means and end.” For Steinthal, on the contrary, “language is neither
an invention nor an innate product; man creates it himself, but it is
not begotten of the reflecting mind.” Through all these formulæ, and
others somewhat tinged with mysticism, we can discover but one point of
fact, analogous to that which states that it is in the nature of the bee
to form its comb, of the spider to weave its web. The last word of the
enigma is unconscious activity, and whether directly, or by evasions,
this school must return to innate faculties.

A somewhat recent theory,—that of L. Noiré,[46]—is distinct from the
foregoing. In these, speech is the direct (although, it is true,
unconscious) expression of intelligence; for Noiré, on the other hand,
it is the outcome of will. “Language is the result of _association_,
of community of feeling, of a sympathetic activity which, at the
outset, was accompanied by sounds...; it is the child of _will_ and not
of sensation.” Speech is derived from community of action, from the
collaboration of primitive men, from the common use of their activities.
When our muscles are in action, we feel it a relief to utter sounds. The
men who work together, the peasants who dig or thresh the grain, sailors
rowing, soldiers marching, emit more or less vibrant articulations,
sounds, exclamations, humming, songs, etc. These sounds present the
requisite characters of the constitution of articulate language; they
are common to all; they are intelligible, being associated by all with
the same acts. Action, according to Noiré, is the primitive element in
all language. Human labor is the content of primitive roots; to cut,
knock, dig, hollow, weave, row, etc. Although Max Müller adhered almost
unreservedly to this hypothesis, it has, like all others, encountered
much criticism which we need not dwell on. Is it probable, it has been
asked, that the first names should have been for acts only, not for
objects? How explain the synonyms and homonyms so frequent in primitive
language? etc.

II. The hypothesis of a progressive evolution of speech, while dating
from antiquity, has only taken a consistent form in our own days, under
the influence of transformist doctrines. The work of anthropologists and
of linguists, above all of the former, it finds support in the study of
inferior idioms and of the comparative method. Its fundamental thesis is
that articulate language is the result of a long elaboration, lasting for
centuries, in which we may with some probability reconstitute the stages.
While its authors are not in complete agreement it may be said that,
generally speaking, they admit three periods: the cry, vocalisation,
articulation.

The cry is the primordial fact, the pure animal language, a simple
vocal aspiration, without articulation. It is either reflex, expressing
needs and emotions, or, at a stage higher, intentional (to call, warn,
menace, etc.). It has been said that the speechlessness of animals is
due to the imperfection of their auditory[?] organs, and want of organic
correspondence between their acoustic images and the muscular movements
that produce sound: but the cause of this aphasia must also, and above
all, be referred to their weak cerebral development; this applies
also to primitive man. “What function could words have fulfilled when
the anthropoid of the Neanderthal or the Naulette roamed, naked and
solitary, from ditch to ditch, through the thick atmosphere, over marshy
soil, stone in hand, seeking edible plants or berries, or the trail of
females as savage as himself?”[47] It is intelligence that creates its
instruments, as well speech as all the rest.

Vocalisation (emission of vowels only) does not in itself contain the
essential elements of speech. Many animals practise it; our vowels, long
or short, even our diphthongs, can readily be recognised in the voice
of different species (dog, cat, horse, birds in large numbers, etc.).
In the child, it succeeds the period of the simple cry; and since it is
admitted that the development of the individual hints at that of the
race; that, moreover, many primitive languages or rudimentary idioms (as
such, near the time of their origin) are very rich in vowels,—it has been
concluded that there existed a longer or shorter period intermediate
between those of the cry and of articulation (this thesis has close
affinities with the theory of Darwin, Spencer, etc., which has been
rejected by other evolutionists); that speech is derived from song,
intellectual language from emotional language; in other words, that man
could sing before he could speak. Various facts are alleged in support
of this theory: (1) In monosyllabic languages, which are generally held
to be the most ancient, the accent plays a cardinal rôle; the same
syllable, according to the tone which accompanies it, takes on the most
widely different meanings. Such is the case of the Chinese. In Siamese,
_hă_ = to seek; _hâ_ = plague; _hà_ = five. (2) Other languages in which
intonation is of less importance, are nevertheless in close relation
with song, and by reason of their vocabulary and of the grammatical
construction, modulation is necessary for giving a complete sense to the
words and phrases. (3) Even in our own languages, which are completely
dissociated from song, the voice is not even in tone; it can be greatly
modified according to circumstances. Helmholtz showed that for such banal
phrases as “I have been for a walk,” “Have you been for a walk?” the
voice drops a quarter-tone for the affirmation, and rises a fifth for
the interrogation. H. Spencer called attention to several facts of the
same order, all commonplace. (4) The impassioned language of emotion
resembles song: the voice returns to its original form; “it tends,”
according to Darwin, “to assume a musical character, in virtue of the
principle of association.”

Whatever may be the force of this reasoning, conclusive for some,
doubtful for others, the conditions necessary to the existence of speech
arose with articulation only, consonants being its firmest element.
The origin of speech has been much disputed. Romanes invokes natural
selection: “The first articulation probably consisted in nothing
further than a semiotic breaking of vocal tones, in a manner resembling
that which still occurs in the so-called chattering of monkeys,—the
natural language for the expression of their mental states.”[48] It
should, however, be noted that the question, under this form, has
merely a physiological interest. The voice is as natural to man as are
the movements of his limbs; between simple voice and articulate voice
there is but the same distance as between the irregular movements of
the limbs of the newly born, and such well-co-ordinated movements as
walking. Articulation is merely one of the forms of expression: it is so
little _human_ that it is met with, as we have seen, among many of the
lower animals. The true _psychological_ problem lies elsewhere: in the
employment of articulate sounds as _objective signs_, and the attaching
of these to objects with which they are related by no natural tie.

Geiger in his _Ursprung der Sprache_ (1878) brought forward a hypothesis
which has been sustained by other authors. It may be summed up as
follows: words are an imitation of the movements of the mouth. The
predominant sense in man is that of sight; man is pre-eminently visual.
Prior to the acquisition of speech, he communicated with his fellows by
the aid of gestures, and movements of the mouth and face; he appealed
to their eyes. Their facial “grimaces,” fulfilled and elucidated by
gesture, became signs for others; they fixed their attention on them.
When articulate sounds came into being, these lent themselves to a more
or less conventional language by reason of their acquired importance. For
support of this hypothesis, we are referred to the case of non-educated
deaf-mutes. These invent articulate sounds (which of course they cannot
hear), and use them to designate certain things. While many of these
words appear to be an arbitrary creation (e. g., _ga_ = one, _ricke_ =
I will not, etc.), others result from the imitation by their mouth of
the movements perceived on the mouth of others. Such are _mumm_ = to
eat; _chip_ = to drink; _be-yr_ = barking of a dog, etc.[49] Why should
primitive man have done less than the deaf-mute, when he not only saw the
movements but heard the sounds to boot?

To conclude with a subject in which individual hypotheses abound, and
which for us is only of indirect interest, we may summarise the sketch
given recently enough (1888) by one of the principal partisans of the
evolutionary theory:

“Starting from the highly intelligent and social species of anthropoid
ape as pictured by Darwin, we can imagine that this animal was accustomed
to use its voice freely for the expression of its emotions, uttering
of danger-signals, and singing. Possibly enough also it may have been
sufficiently intelligent to use a few imitative sounds; and certainly
sooner or later the receptual life of this social animal must have
advanced far enough to have become comparable with that of an infant at
about two years of age. That is to say, this animal, although not yet
having begun to use articulate signs, must have advanced far enough in
the conventional use of natural signs (or signs with a natural origin in
tone and gesture, whether spontaneous only or intentionally imitative)
to have admitted of a tolerably free exchange of receptual ideas,
such as would be concerned in animal wants, and even, perhaps, in the
simplest forms of co-operative action. Next, I think it probable that
the advance of receptual intelligence which would have been occasioned
by this advance in sign-making, would in turn have led to a further
development of the latter,—the two thus acting and reacting on each
other until the language of tone and gesture became gradually raised
to the level of imperfect pantomime, as in children before they begin
to use words. At this stage, however, or even before it, I think very
probably vowel-sounds must have been employed in tone-language, if not
also a few of the consonants. Eventually the action and reaction of
receptual intelligence and conventional sign-making must have ended in
so far developing the former as to have admitted of the breaking up
(or articulation) of vocal sounds, as the only direction in which any
further improvement of vocal sign-making was possible. I think it not
improbable that this important stage in the development of speech was
greatly assisted by the already existing habit of articulating musical
notes, supposing our progenitors to have resembled the gibbons or the
chimpanzees in this respect. But long after this first rude beginning of
articulate speech, the language of tone and gesture would have continued
as much the most important machinery of communication. Even if we were
able to strike in again upon the history thousands of years later, we
should find that pantomime had been superseded by speech. I believe
it was an inconceivably long time before this faculty of articulate
sign-making had developed sufficiently far to begin to starve out the
more primitive and natural systems; and I believe that, even after this
starving-out process did begin, another inconceivable lapse of time must
have been required for such progress to have eventually transformed _Homo
alalus_ into _Homo sapiens_.”[50]

Among all these hypotheses we may choose or not choose; and while we have
dwelt briefly on this debated problem, whose literature is copious, we
may yet have said too much on what is mere conjecture.

One certain fact remains, that—notwithstanding the theory by which speech
is likened to an instinct breaking forth spontaneously in man—it was
at its origin so weak, so inadequate and poor, that it perforce leaned
upon the language of gesture to become intelligible. Specimens of this
mixed language are still surviving among inferior races that have nothing
in common between them, inhabiting regions of the earth with no common
resemblances.

In some cases speech coexists with the language of action (Tasmanians,
Greenlanders, savage tribes of Brazil, Grebos of Western Africa, etc.).
Gesture is here indispensable for giving precision to the vocal sounds;
it may even modify the sense. Thus, in one of these idioms, _ni ne_
signifies “I do it,” or “You do it,” according to the gesture of the
speaker. The Bushman vocabulary is so incomplete and has to be reinforced
by so many mimic signs, that it cannot be understood in the dark. In
order to converse at night, the tribe is obliged to gather round the fire.

In other cases, speech coexists with inarticulate sounds (Fuegians,
Hottentots, certain tribes of North America) which travellers have
compared, respectively, to clinking and clapping. These sounds have been
classified according to the physiological process by which they are
produced, into four (or even six) species: dental, palatal, cerebral,
lateral; it is impossible to translate them by an articulated equivalent.
“Their clappings survive,” says Sayce, “as though to show us how man,
when deprived of speech, can fix and transmit his thought by certain
sounds.” Among the Gallas, the orator haranguing the assembly marks the
punctuation of his discourse by cracking a leather thong. The blow,
according to its force, indicates a comma, semi-colon, or stop; a violent
blow makes an exclamation.[51]

It was advisable to recall these mixed states in which articulate
language had not yet left its primitive vein. They are transitional forms
between pure pantomime and the moment when speech conquered its complete
independence.


II.

In passing from the origin of speech to the study of its development,
we enter upon firmer ground. Although this development has not occurred
uniformly in every race, and the linguists—who are here our guides—do
not always agree in fixing its phases, it is nevertheless the surest
indication of the march of the human mind in its self-analysis in passing
from extreme confusion to deliberate differentiation; while the materials
are sufficiently abundant to admit of an objective study of intellectual
psychogenesis, based upon language.

This attempt has nothing in common with the “general or philosophical
grammar” of the beginning of this century. The Idealogues who founded
this had the pretension, while taking language as their basis, to analyse
the fundamental categories of intelligence: substance, quality, action,
relation. A laudable enterprise, but one which, by reason of the method
employed, could only be abortive. Knowing only the classical or modern
languages, the products of a long civilisation, they had no suspicion of
the embryonic phases; accordingly, they made a theoretical construction,
the work of logicians rather than of psychologists. Any positive genetic
investigation was inaccessible to them; they were lacking in material,
and in instruments. If by a comparison borrowed from geology, the
adult languages are assimilated to the quaternary layer; the tertiary,
secondary, and primary strata will correspond with certain idioms of less
and less complexity, which themselves contain the fossils of psychology.
These lower forms—the semi-organised or savage languages which are a
hundred times more numerous than the civilised languages—are now familiar
to us; hence there is an immense field for research and comparison. This
retrogression to the primitive leads to a point that several linguists
have designated by a term borrowed from biology: it is the protoplasmic
state “without functions of grammatical categories” (Hermann Paul).
How is it that speech issued from this undifferentiated state, and
constituted little by little its organs and functions? This question is
interesting to the linguist on certain sides, to the psychologist on
others. For us it consists in seeking how the human mind, through long
groping, conquered and perfected its instrument of analysis.

I. At the outset of this evolution, which we are to follow step by
step, we find the hypothesis of a primitive period, that of the _roots_
so called, and it is worth our while to pause over this a little.
Roots—whatever may be our opinion as to their origin—are in effect
general terms. But in what sense?

Chinese consists of 500 monosyllables which, thanks to varieties of
intonation, sufficed for the construction of the spoken language; Hebrew,
according to Renan, has about 500 roots; for Sanskrit there is no
agreement. According to a bold hypothesis of Max Müller, it is reducible
to 121, perhaps less, and “these few seeds have produced the enormous
intellectual vegetation that has covered the soil of India from the
most distant antiquity to the present day.”[52] Whatever their number
may be, the question for us reduces itself into knowing their primitive
intellectual content, their psychological value. Here we are confronted
by two very different theses. For one camp, roots are a reality; for the
other, they are the simple residuum of analysis.

“Roots are the phonetic types produced by a force inherent in the human
mind; they were created by nature,” etc., etc. Thus speaks Max Müller.
Whitney, who is rarely of the same mind, says, notwithstanding, that
all the Indo-European languages are descended from one primitive,
monosyllabic language, “that our ancestors talked with one another in
simple syllables indicative of ideas of prime importance, but wanting all
designation of their relations.”

In the other camp it is sustained that roots are the result of learned
analysis, but that there is nothing to prove that they really existed
(Sayce); that they are reconstructed by comparison and generalisation;
that, e. g., in the Aryan languages, roots bear much the same relation
to Sanskrit, Greek, and Latin words as Platonic ideas to the objects
of the real world (Bréal). It has been calculated that the number of
articulate sounds which the human voice is capable of producing amounts
to three hundred and eighty-five. These sounds, for physiological
reasons, constitute a fundamental theme in the various words created by
man. Later on, linguists in comparing the vocables used in different
languages, established the frequent recurrence of certain sounds common
to several words. These have been isolated, but we must not see in them
aught besides _extracts_. Moreover, “the first stammerings of man have
nothing in common with phonetic types so arrested in form and abstract in
signification, as _dhâ_, to place, _vid_, to see, _man_, to think, and
other analogous words.”

To sum up. In the first thesis roots come into existence, _ab initio_;
words are derived from them by reduplication, flexions, affixes,
suffixes, etc.; they are the trunk upon which a whole swarm of languages
has proliferated.

In the second thesis, words come first; then the common element
disengaged by analysis, but which never existed as such in the pure and
primitive condition.

Whether the one opinion or the other be adopted, I see no conclusion
to be drawn from it save that the first terms designated qualities or
manners of being, varying with the race. The first thesis seems the
more apt in revealing to us the primitive forms of abstraction and
generalisation. If it be selected despite its fragility, one finds in
the list of roots (even when most reduced) an extraordinary mixture of
terms applied to the most disparate things (e. g., tears, break, measure,
milk, to choose, to clean, to vomit, cold, to fear, etc.). To assert
with Max Müller (from whom I borrow the preceding terms) that “these
are the one hundred and twenty-one original concepts, the primitive
intellectual baggage of the Aryan family” is to employ an unfortunate
formula, for nothing could less resemble concepts than the contents of
this list. If the second thesis be adopted, the root then being nothing
but “the exposed kernel of a family of words,” “a phonogram,” analogous
to composite photographs, formed like these by a condensation of the
similarities between several terms, then clearly primitive abstraction
and generalisation must be sought in words, and not in roots.[53]

II. Leaving this question which, from its relation to that of the origin
of speech, shares in the same obscurity, we have further to ask if the
primitive terms (whatever nature be attributed to them) were, properly
speaking, words or phrases? Did man initially give utterance to simple
denominations, or to affirmations and negations? On this point all
linguists seem to be in agreement. “Speech must express a judgment.” In
other words it is always a phrase. “Language is based on the phrase, not
on the single word: we do not think by means of words, but by means of
phrases.”[54]

This phrase may be a single word,—or composite, formed by confusion of
words as in the so-called agglutinative, polysynthetic, holophrastic
languages,—or two words, subject and attribute; or three distinct
words, subject, attribute, and copula; but beneath all these forms the
fundamental function is unalterably to affirm or deny.

The same remark has been made of children. “We must,” says Preyer,
“reject the general notion that children first employ substantives, and
afterwards verbs. My son, at the age of twenty-three months first used
an adjective to express a judgment, the first which he enunciated in his
maternal tongue; he said _heiss_ (hot) for ‘the milk is too warm.’”
Later on, the proposition was made in two words: _heim-mimi_, ‘I want to
go home and drink some milk’ (_heim_ = home, _mimi_ = milk). Taine and
others have cited several observations of the same order.[55]

According to some authors, all language that has reached complete
development has perforce passed through the three successive periods of
monosyllabism, polysynthetism, and analysis; so that the idioms that
remain monosyllabic or agglutinative would correspond to an arrest in
development. To others, this is a hypothesis, only, to be rejected.
However this may be (and it is not a question that we need to examine),
it seems rash to assert, with Sayce, “that the division of the phrase
into two parts, subject and predicate, is a pure accident, and that
if Aristotle had been Mexican (the Aztec language was polysynthetic),
his system of logic would have assumed a totally different form.” The
appearance and evolution of analytical language is not pure accident, but
the result of mental development. It is impossible to pass from synthesis
to analysis without dividing, separating, and arraying the isolated
parts in a certain order. The logic of a Mexican Aristotle might have
differed from our own in its form; but it could not have constituted
itself without fracture of its linguistic mould, without setting up a
division, at least in theory, between the elements of the discourse. The
unconscious activity by which certain idioms made towards analysis, and
passed from the period of envelopment to that of development, imposed
upon them a successive order. Polysynthetic languages have been likened
to the performance of children who want to say everything at once, their
ideas all surge up together and form a conglomeration.[56] Evidently this
method must be given up, or we must renounce all serious progress in
analysis.

To sum up the psychological value of the phrase, independently of its
multiple forms, we may conclude by the following remarks of Max Müller:

“We imagine that language is impossible without sentences, and that
sentences are impossible without the copula. This view is both right and
wrong. If we mean by sentence an utterance consisting of several words,
and a subject, and a predicate, and a copula, it is wrong.... When the
sentence consists only of subject and predicate, we may say that a copula
is understood, but the truth is that at first it was not expressed, it
was not required to be expressed; in primitive languages it was simply
impossible to express it. To be able to say _vir est bonus_, instead of
_vir bonus_, is one of the latest achievements of human speech.”[57]


III.

The evolution of speech, starting from the protoplasmic state without
organs or functions, and acquiring them little by little, proceeding
progressively from indefinite to definite, from fluid to fixed state,
can only be sketched in free outline. In details it falls within
neither our subject nor our cognisance. But the successive points of
this differentiation, which creates grammatical forms, and parts of
discourse, are under an objective form the history of the development of
intelligence, inasmuch as it abstracts, generalises, analyses, and tends
towards an ever-growing precision. The completely developed languages—and
we are speaking only of such—bear throughout the print of the unconscious
labor that has fashioned them for centuries: they are a petrified
psychology.

We must return to the roots or primitive terms, whatever may be their
nature. Two distinct categories are generally admitted: pronominal or
demonstrative roots, verbal or predicative roots.

The first form a small group that properly indicate rather the relative
position of the speaker, than any concrete quality. They are equivalent
to here, there, this, that, etc. They are few in number, and very simple
in their phonetic relations: a vowel or vowel followed by a consonant.
Many linguists refuse to admit them as roots, and think they have dropped
from the second class by attenuation of meaning.[58] Possibly they are a
survival of gesture language.

The second (verbal or predicative) is the only class that interests us.
These have swarmed in abundance. They indicate qualities or actions; that
is the important point. The first words denominated attributes or modes
of being; they were adjectives, at least in the measure in which a fixed
and rigid terminology can be applied to states in process of forming.
Primitive man was everywhere struck with the qualities of things, _ergo_
words were all originally appellative. They expressed one of the
numerous characteristics of each object; they translated a spontaneous
and natural _abstraction_: another proof of the precocious and
indispensable nature of this operation. From its earliest developments
intelligence has tended to simplify, to substitute the part for the
whole. The unconscious choice of one attribute among many others depends
on various causes; doubtless on its predominance, but above all on the
interest it has for man. “A people,” remarks Renan, “have usually many
words for what most interests them.” Thus, in Hebrew, we find 25 synonyms
for the observance of the law; 14 for faith in God; 11 for rain, etc. In
Arabic, the lion has 500 names, the serpent 200, money more than 80; the
camel has 5,744, the sword 1,000 as befits a warrior race. The Lapp whose
language is so poor, has more than 30 words to designate the reindeer,
an animal indispensable to his life.[59] These so-called synonyms each
denominate a particular aspect of things; they witness to the abundance
of primitive abstractions.

This apparent wealth soon becomes an embarrassment and an encumbrance.
Instead of 100 distinct terms, one generic substantive, plus one or
two epithets, would suffice. But the _substantive_ was not born of the
deliberate desire to obviate this inconvenience. It is a specialisation,
a limitation of the primitive meaning. Little by little the adjective
lost its qualificative value, to become the name of one of the objects
qualified. Thus in Sanskrit _dêva_ (shining) finally signified the
god; _sourya_ (the dazzling) became the sun; _akva_ (rapid) the name
of a horse, etc. This metamorphosis of adjective into substantive by a
specialisation of the general sense occurs even in our actual languages;
as, e. g., when we say in French _un brilliant_ (diamond); _le volant_
(of a machine); _un bon_ (of bread, counting-house, bank, etc.). What
is only an accident now was originally a constant process.[60] Thus the
substantive was derived from the primitive adjective; or rather, within
the primitive organism, adjective-substantive, a division has been
produced, and two grammatical functions constituted.

Many other remarks could be made on the determination of the substantive
by inflexions, declensions, the mark of the gender (masculine, feminine,
neuter); I shall confine myself to what concerns _number_, since we are
proposing to consider numeration under all its aspects. Nothing appears
more natural and clear-cut than the distinction between one and several;
as soon as we exceed pure unity, the mother of numbers, plurality appears
to us to be homogeneous in all its degrees. It has not been so from the
beginning. This is proved by the existence of the dual in an enormous
number of languages: Aryan, Semitic, Turanian, Hottentot, Australian,
etc. One, two, were counted with precision; the rest was vague. According
to Sayce, the word “three” in Aryan language at first signified “what
goes beyond.” It has been supposed that the dual was at first applied to
the paired parts of the body: the eyes, the arms, the legs. Intellectual
progress caused it to fall into disuse.

At the close of the period of first formation which we have been
considering, the sentence was only a defaced organism reproduced by one
of the following forms: (1) that; (2) that shining; (3) that sun, that
shining.[61] The verb is still absent.

With it we enter on the period of secondary formation. It was long held
to be an indisputable dogma that the _verb_ is the word _par excellence_
(_verbum_), the necessary and exclusive instrument of an affirmation.
Yet there are many inferior idioms which dispense with it, and express
affirmation by crude, roundabout processes, with no precision,—most
frequently by a juxtaposition: snow white = the snow is white; drink me
wine = I drink (or shall drink) wine, etc. Plenty of examples can be
found in special works.

In fact, the Indo-European verb is, by origin, an adjective (or
substantive) modified by a pronoun: _Bharâmi_ = carrier-me, I carry. It
is to be regretted that we cannot follow the details of this marvellous
construction,—the result of unconscious and collective labor that has
made of the verb a supple instrument, suited for all expressions, by the
invention of moods, voices, and tenses. We may note that, as regards
tenses, the distinction between the three parts of duration (which
seems to us so simple) appears to have been established very slowly.
Doubtless it can be asserted that it existed, actually, in the mind of
primitive man, but that the imperfection of his verbal instrument failed
in translating it. However this may be, it is a moot point whether the
verb, at the outset, expressed past or present. It seems at first to have
translated a vague conception of duration, of continuity in action; it
was at first “durative,” a past which still continues, a past-present.
The adjective notion contained in the verb, indefinitely as to time,
only became precise by little and little. The distinction between the
moments of duration did not occur by the same process in all languages,
and in some, highly developed, otherwise like the Semitic languages, it
remained very imperfect.[62]

The main point was to show how the adjective-substantive, modified by
the adjunction of pronominal elements, constituted another linguistic
organ, and losing its original mark little by little, became the verb
with its multiple functions. The qualificatory character fundamental to
it makes of it an instrument proper to express all degrees of abstraction
and generalisation from the highest to the lowest, to run up the scale
of lower, medium, and higher abstractions. Ex., to drink, eat, sleep,
strike;—higher, to love, pray, instruct, etc.; higher still, to act,
exist, etc. The supreme degree of abstraction, i. e., the moment at which
the verb is most empty of all concrete sense, is found in the auxiliaries
of the modern analytical languages. These, says Max Müller, occupy the
same place among the verbs, as abstract nouns among the substantives.
They date from a later epoch, and all had originally a more material and
more expressive character. Our auxiliary verbs had to traverse a long
series of vicissitudes, before they reached the desiccated, lifeless form
that makes them so appropriate to the demands of our abstract prose.
_Habere_, which is now employed in all Roman languages to express simply
a past time, at first signified “to hold fast,” “to retain.”

The author continues, retracing the history of several other auxiliary
verbs. Among them all there is one that merits particular mention
on account of its divagations: this is the verb _être_, verb _par
excellence_, verb substantive, unique; direct or understood expression of
the existence that is everywhere present. The monopoly of affirmation,
and even the privilege of an immaterial origin have been attributed
to it.[63] In the first place, it is not met with under any form in
certain languages which supplement its absence by divers processes. In
the second, it is far from being primitive; it is derived, according
to the idioms, from multiple and sufficiently discordant elements: to
breathe, live, grow (Max Müller); to breathe, grow, remain, stand upright
(_stare_) (Whitney).

Hitherto we have examined only the stable, solid parts of speech. There
remain such as are purely transitive, translating a movement of thought,
expressive of _relation_. Before we study these under their linguistic
form, it is indispensable to take up the standpoint of pure psychology,
and to know in the first place what is the nature of a relation. This can
the less be avoided inasmuch as the question has scarcely been treated
of, save by logicians, or after their fashion, and many very complete
treatises of psychology do not bestow on it a single word.[64]

“A relation,” says Herbert Spencer, “is a state of consciousness which
unites two other states of consciousness.” Although a relation is not
always a link in the rigorous sense, this definition has the great
advantage of presenting it as a reality, as a state existing by itself,
not a zero, a naught of consciousness. It possesses intrinsic characters:
(1) It is indecomposable. There are in consciousness greater and less
states; the greater (e. g., a perception) are composite, hence accessible
to analysis; they occupy an appreciable and measurable time. The lesser
(relation) are naturally beyond analysis; rapid as lightning, they
appear to be outside time. (2) It is dependent. Remove the two terms
with which it is intercalated, and the relation vanishes; but it must be
noted that the terms themselves presuppose relations; for, according to
Spencer’s just remark, “There are neither states of consciousness without
relations, nor relations without states of consciousness.” In fact: to
feel or think a relation, is to feel or think a change.

But this psychical state may be studied otherwise than by internal
observation, and the subsequent interpretation. It lends itself to an
_objective_ study, because it is incarnated in certain words. When I
say, red _and_ green, red _or_ green, there are in either case, not
two, but _three_ states of consciousness; the sole difference is in the
intermediate state which corresponds with an inclusion or an exclusion.
So, too, all our prepositions and conjunctions (_for_, _by_, _if_, _but_,
_because_) envelop a mental state, however attenuated. The study of
languages teaches us that the expression of relations is produced in two
ways, forming, as it were, two chronological layers.

The most ancient is that of the cases or declensions: a highly complex
mechanism, varying in marked degree with the idioms, and consisting in
appositions, suffixes, or modifications of the principal theme.

But these relations have only acquired their proper linguistic organ,
specialised for this function, by means of prepositions and conjunctions.
They are wanting in many languages; gesture being then substituted for
them. The principal parts of the discourse are solitary, juxtaposed
without links after the manner of the phrases used by children. Others,
somewhat less poor, have only two conjunctions: _and_, _but_. In short,
the terms on which devolved the expression of relations are of late
formation, as it were, organs _de luxe_. In the analytical languages,
prepositions and conjunctions are nouns or pronouns diverted from
their primitive acceptation, which have acquired a value expressive
of transition, condition, subordination, co-ordination, and the rest.
The psychological notion common to the greater number, if not to all,
is that of a movement. “All relations expressed by prepositions can
be referred to repose, and to movement in space and time, i. e., to
those with which the locative, accusative (movement of approximation)
and ablative (movement of departure) correspond in declension.”[65] It
may be admitted that this consciousness of movement, of change, which
is no more, fundamentally, than the sense of different directions of
thought, belongs less to the category of clear notions than to that of
subconscious states, of tendencies, of actions, which explains why the
terms of relation are wholly wanting, or rare, and only conquered their
autonomy at a late period.

With these, the progressive work of differentiation is accomplished.
Discourse has now its materials and its cement; it is capable of complex
phrases wherein all is referred and subordinated to a principal state,
contrary to those ruder essays which could only attain to simple phrases,
denuded of connective apparatus.

We have rapidly sketched this labor of organogenesis, by which language
has passed from the amorphous state to the progressive constitution
of specialised terms and grammatical functions: an evolution wholly
comparable with that which, in living bodies, starts from the fecundated
ovule, to attain by division of labor among the higher species to a fixed
adjustment of organs and functions. “Languages are natural organisms,
which, without being independent of human volition, are born, grow,
age, and die, according to determined laws.” (Schleicher.) They are
in a state of continuous renovation, of acquisition, and of loss. In
civilised languages, this incessant metamorphosis is partially checked by
enforced instruction, by tradition, and respect for the great literary
works. In savage idioms where these coercive measures are lacking, the
transformation at times occurs with such rapidity that they become
unrecognisable at the end of a few generations.

Spoken language, as a psycho-physiological mechanism, is regulated in its
evolution by physiological and psychological laws.

Among the former (with which we are not concerned), the principal is
the law of phonetic alteration, consisting in the displacement of an
articulation in a determined direction. It is dependent on the vocal
organ; thus, after the Germanic invasion, the Latin which this people
spoke fell again under the power of physiological influences which
modified it profoundly.

Among the latter, the principal is the law of analogy, the great artisan
in the extension of languages. It is a law of economy, the basis of
which is generalisation, the faculty of seizing on real or supposed
resemblances. The word remains invariable, but the mind gives it
different applications: it is a mask covering in turn several faces. It
suffices to open a dictionary to see how ingenious and perilous is this
unconscious labor. Such a word has only a few lines; it has no brilliant
record. Such another fills pages; first we see it in its primitive sense;
then—from analogy to analogy—from accident to accident—it departs from
it more and more, and ends by having quite a contrary meaning.[66] Hence
it has been said that “the object of a true etymology is to discover
the laws that have regulated the evolution of thought.” Among primitive
people, the process that entails such deviations from the primitive
sense, is sometimes of striking absurdity; or at least appears to us
as such by reason of the strange analogies that serve the extension of
the word. Thus: certain Australian tribes gave the names of mussels
(_muyum_), to books because they open and close like shell-fish; and many
other no less singular facts could be cited. Much more might be said as
to the rôle of analogy, but we must adhere to our subject.

In conclusion: it is to be regretted that linguistic psychology attracts
so few people, and that many recent treatises on psychology, excellent
on all other points, do not devote a single line to language. Yet
this study, especially if comparative, from the lowest to the most
subtle forms, would throw at least as much light on the mechanism of
the intelligence as other highly accredited processes. _Physiological
psychology_ is much in vogue, since it is rightly concluded that if the
facts of biology, normal and morbid, are being studied by naturalists
and physicians, they are available to psychologists also, under another
aspect. So too for _languages_: comparative philology has its own aim,
psychology another, proper to it. It is incredible that any one who, with
sufficient linguistic equipment, should devote himself to the task, would
fail to find adequate return for his labors.




CHAPTER III.

INTERMEDIATE FORMS OF ABSTRACTION.


Having thus acquainted ourselves with this new factor—speech—which as an
instrument of abstraction becomes steadily more and more important, we
can take up our subject from the point at which we left it. In passing
from the absence to the presence of the word, from the lower to the
intermediate forms of abstraction, we must again insist on our principal
aim: viz., to prove that abstraction and generalisation are functions
of the completely evolved mind. They exist in embryo in perception, and
in the image, and at their extreme limit involve suppression of all
concrete representation. This conclusion will hardly be contradicted. The
difficulty is to follow the evolution step by step, stage after stage,
and to note the difference by _objective_ marks.

For intermediate abstraction, this operation is very simple. It
implies the use of words; it has passed the level of pre-linguistic
abstraction and generalisation. We may go farther, and—always _with the
aid of words_—establish two classes within the total category of mean
abstraction:

1. The lower forms, bordering on generic images, whose objective mark
is the feeble participation of the word: it can indeed be altogether
foregone, and is only in the least degree an instrument of substitution.

2. The higher forms, approximating to the class of pure concepts, and
having as their objective mark the fact that words are indispensable,
since these have now become an instrument of substitution, though still
accompanied by some sensory representation.

The legitimacy of this division can be justified only by a detailed
comparison of the two classes.


I.

Before giving examples that determine the nature and intellectual trend
of the lower forms, a theoretical question presents itself which cannot
be eluded, albeit any profound discussion of it belongs to the theory of
cognition rather than to psychology. It is as follows: Is the difference
between generic images and the lowest concepts, one of nature or of
degree? This question has sometimes been propounded in a less general and
more concrete form; Is there any radical difference, any impassable gulf
between animal intelligence[67] in its higher, and human intelligence in
its lower aspects? Some authors give an absolute negation, others admit
community of nature, and of transitional forms.

I shall first reject as inadmissible the argument that identifies
abstraction with the use of words. Taine seems at times to admit this:
“We think,” he says, “the abstract characters of things by means of the
abstract names that are our abstract ideas, and the formation of our
ideas is no more than the formation of names which are substitutes.”[68]
Clearly if abstraction is impossible without words, this operation could
only begin with speech. All that was said above (Chap. I) proves the
inanity of such an assertion.

Let us, in order to discuss the question profitably, sum up the principal
characteristics of generic images on the one hand, of inferior concepts
on the other.

Generic images are: (1) simple and of the practical order; (2) the
result of often-repeated experiences; (3) extracts from very salient
resemblances; (4) a condensation into a visual, auditory, tactile, or
olfactory representation. They are the fruit of _passive_ assimilation.

The inferior concepts most akin to them, which we are studying in the
present instance, are in character: (1) less simple; (2) less frequently
repeated in experience; (3) they assume as material, similarities mingled
with sufficiently numerous differences; (4) they are fixed by a word.
They are the fruit of _active_ assimilation.

It may be said that the two classes, when thus opposed to each other,
present but minimal differences, save for the addition of words. For the
moment, indeed, the word is only an instrument handled by a bad workman,
who ignores its efficacy and highest significance, as will be proved
below. But were it otherwise, and were the delimitation between the two
classes in no way fluctuating, the thesis of a progressive evolution
must needs be given up, unless it be admitted to begin only with the
appearance of speech.[69]

Romanes describes the passage from the generic image to the concept as
follows:

“Water-fowl adopt a somewhat different mode of alighting upon land, or
even upon ice, from that which they adopt when alighting upon water;
and those kinds which dive from a height (such as terns and gannets)
never do so upon land or ice. These facts prove that these animals have
one recept answering to a solid substance, and another answering to a
fluid. Similarly a man will not dive from a height over hard ground, or
over ice, nor will he jump into water in the same way as he jumps upon
land. In other words, like the water-fowl, he has two distinct recepts,
one of which answers to solid ground, and the other to an unresisting
fluid. But unlike the water-fowl, he is able to bestow upon each of these
recepts a name, and thus to raise them both to the level of concepts.
So far as the practical purposes of locomotion are concerned, it is,
of course, immaterial whether or not he thus raises his recepts into
concepts; but, as we have seen, for many other purposes it is of the
highest importance that he is able to do this. Now, in order to do it, he
must be able to set his recept before his own mind as an object of his
own thought: before he can bestow upon these generic ideas the names of
“solid” and “fluid,” he must have cognised them as ideas. Prior to this
act of cognition, these ideas differed in no respect from the recepts
of a water-fowl; neither for the requirements of his locomotion is it
needful that they should: therefore, in so far as these requirements are
concerned, the man makes no call upon his higher faculties of ideation.
But, in virtue of this act of cognition whereby he assigns a name to an
idea known as such, he has created for himself—and for purposes other
than locomotion—a priceless possession; he has formed a concept.”[70]

In point of fact, the transition is not so simple. Romanes omits the
intermediate stages: for with fluid and liquid we penetrate into a more
elevated order of concepts than those immediately bordering on the
generic image. What he well brings out is that the bare introduction
of words does not explain everything. It must not be forgotten that
if the higher development of the intelligence depends upon the higher
development of abstraction, which itself depends upon the development
of speech, this last is conditioned, not simply by the faculty of
articulation, which exists among many animals, but by anterior cerebral
conditions that have to be sought out.

For these, we must return to the distinction loosely established above,
between passive and active assimilation. We know that the fundamental
mechanism of cognition may be reduced to two antagonistic processes,
association and dissociation, assimilation and dissimilation; to combine,
to separate; in brief, analysis and synthesis.[71] In the formation of
the generic image, as we have seen, assimilation plays the principal
part; the mind works only upon similarities. In proportion as we recede
from this point, we have the contrary; the mind works more and more upon
differences; the primitive and essential operation is a dissociation; the
fusion of similarities only appears later. The further back we go, the
more analysis preponderates, because we are pursuing resemblances more
and more hidden by differences. Coarser minds do not rise above palpable
similarities. The peasant who hears a dialect or patois closely akin to
his own understands nothing of it; it is another language to him; whereas
even a mediocre linguist immediately perceives the identity of words that
differ only in accent.

We may represent the differences between generic images, and these
general notions that most nearly approximate to them, by the following
symbol:

     I. _A B C d e_
        _A B C e f_
        _A B C g h_, etc.

    II. _A b c d e_
        _x y z A f_
        _g A h k m_, etc.

where each line corresponds to an object, and each letter to one of the
principal characters of the object. Table I is that of the generic image.
A part, _A B C_, is constantly repeated in each experience; moreover,
it is in relief, as indicated by the capitals; the elimination of
differences is almost passive,—self-caused; they are forgotten.

Table II is that of a fairly simple general notion. Here _A_ has to
be disengaged from all the objects in which it is included. It still
has a salient character, indicated by capitals, and recurring in each
object; but as it is merged in the differences, as it represents but a
poor fraction of the total event, it is not disengaged spontaneously; it
exacts a preliminary labor of dissociation and elimination.

Thus understood, the difference between the two processes consists only
in the faculty of greater or less dissociation, and we are in no way
authorised in assuming a difference of nature.

But the question may be propounded in a different manner,—more precise
and more embarrassing. I formulate it thus: the generic image is never,
the concept is always a judgment. We know that for logicians (formerly
at any rate) the concept is the simple and primitive element; next comes
the judgment, uniting two or several concepts; then ratiocination,
combining two or several judgments. For the psychologist, on the
contrary, affirmation is the fundamental act; the concept is the _result_
of judgments (explicit or implicit), of similarities with exclusion of
differences. If in addition to this we recall what was said above: that
speech commences with phrases only, that in its simplest form it is the
word-phrase; then the debated question may be thus transformed: Is there,
between the generic image and judgment in its lower forms, a break in
continuity, or a passage by slow transformation?

For the partisans of the first theory, the appearance of judgment is
a “passage of the Rubicon” (Max Müller). It is as impossible to deny
this as to affirm it positively and indisputably. Romanes, who makes a
stand against the “passage of the Rubicon,” admits the following stages
in the development of signs, taken as indicative of the development of
intelligence itself.

1. The indicative sign; gesture or pronominal root; a dog barking for a
door to be opened, etc.

2. The denotative sign which is affixed to particular objects, qualities,
or actions; for example, the parrot which on seeing a person utters the
name of the person, or some word which it has associated with him, and
which for the animal has become the distinctive mark of the person.

3. The connotative or attributive sign, which, rightly or wrongly, is
attributed to an entire class of objects having a common quality; for
instance, the child which applies the word _star_ to everything that
shines.

4. The denominative sign; or the intentional employment of the sign as
such, with a full appreciation of its value; for example, the word _star_
in its meaning to the astronomer.

5. The predicative sign, or a proposition formed by the apposition of two
denominative signs.[72]

This hierarchical order, while in some measure open to criticism,
indicates at least schematically the progressive passage from the
concrete to the higher abstractions, and may therefore be accepted.

It is clear that the two first stages scarcely pass beyond the concrete.

To the third, Romanes attaches capital importance: judgment begins with
it. It may, however, be asked if affirmation really exists at this stage.
For my own part I am inclined to admit it as included in the generic
image in its highest degree (for here too there are degrees), under the
form _not of a proposition, but of an action_. The hunting dog assuredly
possesses generic images of man and of different kinds of game, under
the visual and more especially the olfactory form. When it starts off on
the scent of its master, of a hare, or of a partridge, this is surely
a judgment of a certain kind, an affirmation, the least doubtful of
all, seeing that it is an act. The absence of verbal expression and of
logical information in no way alters the fundamental nature of the mental
state. We have already (Chap. I.) spoken of _practical_ judgments and
ratiocinations; it is needless to reiterate.

The transition from the third to the fourth stage is even more important.
It is here that the true concept appears; this point attained, an almost
unlimited progress is possible. Now the true cause of the true concept
is reflexion. This formula appears to us the simplest, the briefest, the
most clear, and the most exact. There is the possibility of concepts
where there is the possibility in the mind of detaching a single
character (or several), extracted from among many others, of setting it
up as an independent entity, of raising it into a _known_ object, i.
e., determined in its relations with ourselves, and with other things.
Example: to form the general idea of a vertebrate. But this fundamental
act—reflexion—is not without antecedents, it does not spring forth as a
new apparition. It is the highest degree of attention, i. e., of a mental
attitude that we encounter very low down in the animal scale.

Discontinuity of evolution, in the passage from lower to higher, is thus
far from being established. Doubtless this, like all other questions
of genesis, leaves much to hypothesis, and can only be decided on
probabilities: yet these do not appear to favor a rupture in continuity,
and opposition of nature.

In sum—to confine ourselves to what is least contestable: given the
cerebral and psychological conditions for speech (not for articulate
language alone), and application of words to qualities and attributes
raised little by little into independent entities,—and the decisive step
has been taken. Such is intellectual progress, and we may remark in
passing that the process which creates the true concept, leads fatally by
the same issue to faith in idols, in the entities realised.

Without for the moment pausing at this last point, let us under a more
positive form, and strictly on the lines of experimental psychology,
examine the nature of the lower forms of intermediate abstraction,
determining it by examples. At the same time we shall fix the
intellectual level that corresponds to the moment of transition between
generic images (animal form), and the higher abstracts which have still
to be studied in detail. The best method is to take as a type such
human races as have remained in the savage or half-civilised state:
these are more instructive than childhood, because they represent fixed
and permanent conditions. We can draw on two principal sources: their
languages, and their systems of numeration. Their religious beliefs might
also be studied, with the same results, but this would take too long, and
would moreover be less definite.[73]

1. _The languages_, considered under their most general characteristics,
reveal a notable impotence for transcending the simplest resemblances,
an incurable incapacity for extended generalisations; they hardly
rise above the concrete. Words play a very indistinct part; they are
the most incomplete substitute—hardly more than a mark, a sign, like
gestures—differing from the latter only in the future they carry within
them. The study of the ascending progress of generalisation is in
effect the study of the successive phases of the emancipation of speech
up to the time when it becomes preponderant and dominating. At the
actual stage, which might be termed _concrete-abstract_, it is not yet
emancipated; it is a minor, under tutelage.

Let us take in turn substantives, adjectives, and verbs.

The indigenes of Hawaii, says Max Müller (_Lectures on the Science of
Language_, Second Series, II., p. 19), have but one word, “aloba,” to
express love, friendship, esteem, gratitude, benevolence, etc.; on the
other hand, words to express variations in the direction of the force
of the wind are very numerous, proving once more how at its origin
abstraction or dissociation is governed by practical causes. In savage
languages there are terms to express not merely each species of dog, but
their age, the color of their hair, good or bad qualities, etc. So, too,
for the horse; there are special words to designate its varieties, and
all its movements; to indicate if it is mounted, not mounted, frightened,
running away, and the like. The North American Indians have special words
for the black oak, the white oak, and the red oak, but none for the oak
in general,—still less for tree in general. The indigenes of Brazil can
point out the different parts of the body, but not the body as a whole
(Lubbock). Among several tribes of Oceania, a special word is employed
for the tail of a dog, another for the sheep’s tail, and so on, but they
have no designation for tail in general. Again, there is no common term
for the cow, but there are distinct words for red, white, or brown cows
(Sayce).

There are, however, cases of very clear progress in generalisation; the
significance of a word extends itself; from specific it becomes generic.
This metamorphosis exists _in vivo_ among the Finns and Laplanders.
The former have a name for the smallest stream, and none for river;
originally again there was a term for each finger, none for finger in
general; but latterly the term used for thumb alone has come to designate
the fingers collectively. Among the second race, certain tribes who had
a special denomination for each kind of bay, have now adopted one that
serves for all kinds (Max Müller).

The same holds good of the poverty of the adjective, the abstract term
proper. The case of the Tasmanians has often been quoted, how they could
only express qualities by concrete representations: hard = like a stone;
long = legs; round = like a ball, like the moon, etc. (Lubbock). A less
familiar case, termed by linguists “concretism,” is met with even in
certain more developed idioms, like a survival of the time when the mind
was unable to detach itself from the concrete, or to forego a complete
and detailed qualification. Instead of saying ten merchants, five hens,
the idiom is merchants ten men, hens five birds, and so on for similar
cases.

The verb is able to express all degrees of abstraction and of
generalisation as well as the adjective and substantive. At this period,
it exactly repeats the type (as described above) of the substantive with
its burdensome multiplicity,—for want of a generalisation simple enough,
according to our judgment. The North American Indians have special
words for saying: to wash one’s face, another person’s face, the linen,
utensils, etc.: in all, thirty words, but none for washing in general.
So, too, for eating bread, fruits, meat, etc., striking with the hand,
foot, axe, etc., for cutting wood, meat, or any other objects: for all
these there are special terms, but none for saying simply, to eat, to
knock, to cut (Sayce, Hovelacque.) On the other hand, we note a case of
transition, analogous to that of the Lapps and Finlanders. Certain tribes
in Brazil have a few verbs of general, simple significance: eat, drink,
dance, see, etc., even love, thank, etc. (Lubbock).

We need not multiply examples; these will suffice to throw into relief
the extreme impotence in generalising, so soon as the mind loses its hold
on the concrete. We might also recall the difficulty so often experienced
by missionaries. They find it almost impossible, even by creating new
words, or by changing the meaning of others, to translate the sacred
books into these idioms, from their paucity of concrete terms.

2. _The numeration_, taking its development as a whole, appears to
sub-divide into three principal periods: concrete numeration, as studied
above, in animals and children; concrete-abstract numeration, with which
we are now occupied; purely abstract numeration, which we shall examine
later, as translated into organised arithmetic.

We have seen that speech at its origin was so humble as to need gesture
to complete and to elucidate it. During its concrete-abstract period,
numeration is in an analogous position. At first its extension is very
limited: it progresses slowly and painfully from unity. Further, it can
operate only when sustained by the concrete; it must have a material
accompaniment. Counting is accomplished by the enunciation of words, with
the aid of enumerated objects, as perceived at the same time, or with
that of the fingers: which, let it be remarked, is the first essay in
substitution. There is simultaneously concrete or digital, and verbal
numeration.[74]

We know that many Australian and South American tribes can count verbally
to two only; some say two-one = three; two-two = four; others by the same
process arrive at six (two-three = five, three-three = six): everything
else is “much.” For the most part they count without words, with the
aid of fingers or of articulation; even when they employ words, the two
numerations—digital and verbal—are performed simultaneously.[75]

This manner of counting is in first degree concrete; the
concrete-abstract form is only there in embryo. A great advance, made
early enough in many tribes, consisted in counting by five, taking the
hand (five fingers) as a new unit, superior to the simple unit. Then:
one hand = 5; two hands or half a man = 10; two hands, one foot = 15;
two hands, two feet, or a man = 20. Such is the evident origin of the
quinary, decimal, and vigesimal numerations. Sometimes fingers, as
instruments of numeration, have been replaced by objects of a typical
number. Ex.: 1 = moon or sun; 2 = the eyes or legs, etc.

However varied these processes (of which only a few have been mentioned)
in different races and periods, they are fundamentally identical to
the psychologist. They may be reduced to this; numeration is performed
more particularly with the aids of sensible perceptions; words are
but an insignificant accompaniment, a superfluity—existing only as a
proliferation—of so little utility that they are for the most part
neglected.

Though it is less often spoken of, we may remark that the measure of
continuous quantity passed through the same concrete-abstract phase;
and here it appeared at a somewhat early stage, owing to practical and
social wants. Hence we find at the outset, the foot, the finger, the
thumb (inch = Fr. _pouce_), the palestra (four fingers’ length), span,
cubit (arm’s reach = _coudée_), fathom, etc., the stadium (distance a
good runner could cover without stopping).[76] The concrete character
of all these measures is obvious. Again, there are survivals in certain
current locutions, such as a day’s journey. More than this; they have a
_human_ character, their standard and starting-point being, at least at
the outset, certain parts of the body, or a determined sum of muscular
movements. Little by little they lost their original significance,
progressing through centuries towards our metrical system the type of a
scientific, deliberate, rationally abstract system, as far as possible
liberated from anthropomorphism.

The reader will probably obtain a more definite idea of the nature of
these lower forms by recapitulating the examples cited, than from any
long dissertation. Is their intellectual level very superior to that
of the generic image? This question is doubtful. At times the only
distinction between them is the presence of the word: at the present
stage it makes but a poor figure,—yet with all its modesty, it augurs a
new world wherein it is to be of prime importance.


II.

We now pass to a study of transition. In ascending from the lower to
the _higher_ forms of abstraction, we traverse the intermediate region
between the states directly superposed upon generic images, and the
higher concepts. In fact, we shall to some extent have to penetrate into
this extreme region, before the close of the chapter.

At the risk of repetition, we must first indicate the characteristics
by which the general notions we are at present concerned with are
distinguished from the abstractions above and below them. To recapitulate
briefly: In the concrete-abstract phase (which we are leaving) the
general notion—so-called—is constituted by concrete elements, _plus_
words, whose substitutory office is weak or null.

In the abstract phase (upon which we are entering) the concept is
constituted by an evoked or evocable image, which may exhibit every
degree from clear representation to the pure schema, _plus_ the word
that now becomes the principal element.

In the phase of higher abstractions (to be studied later), no sensory
representation arises, or should any such appear, reflexion would find
in it only a dubious support, often an obstacle: the word meantime has
acquired absolute supremacy in consciousness.

Taken as a whole, psychological development exhibits a complex
phenomenon, a binary compound, in which one element is always increasing,
the other as steadily decreasing. Words pass from nonentity to autocracy;
the concrete from supremacy to nonentity.

We must now return to the higher forms of intermediate abstraction, since
we may not content ourselves with any purely theoretical determination.
Characteristic examples must be selected; and here we find a certain
embarrassment. Does our choice fall on numeration? Yet on leaving the
concrete-abstract period, this at once finds its formative law, and
introduces us to pure abstraction. Are we to select language? This
procedure might seem to be appropriate, seeing that the general ideas
with which we are occupied constitute the substrata of our highly
civilised modern languages, when, on the other hand, the more developed
concepts (of mathematics, metaphysics, etc.) are only found rarely and
incidentally. One might even plunder the dictionary, extracting all
general terms, with elimination of those that are purely scientific, and
classification of the former according to their increasing degree of
generality. But this method, besides being very laborious and incapable
of reduction to a clear statement for the reader, would suffer the
cardinal defect of being arbitrary. How, indeed, could any common measure
be established for all these general terms, issuing from the most
diverse sources of human activity?[77]

But the best method would seem to be that of taking as our basis
the classifications of the naturalists, following their development
historically. Here we have the advantage of positive documents, since
these refer to concrete beings, and are formed according to characters
observed empirically. They create, namely, an ascending progress
from the individual to the more general notions, by a methodical
process of filiation; they operate upon living beings, or objects of
the same nature, having consequently a common standard. The history,
even in brief, of these classifications is instructive: it shows the
progressive passage of concrete-abstract ideas to more and more abstract
concepts, from a statement of gross resemblances to the quest after
subtle similarities, from the period of assimilation to that in which
dissociation predominates.

Among these different classifications, we may select those of the
zoologists, since they appear to be the most numerous, most complete,
and best elaborated. For the rest, the succeeding observations apply
equally, _mutatis mutandis_, to the classifications of the botanists.
We need scarcely add that our study is strictly psychological, that
its object is not the absolute value of classifications, but the
determination of the processes followed by the human mind, in proportion
as the zoölogical taxonomy has constituted itself.

At the outset we find a pre-scientific period as to which we know little;
for these essays in classification differ, according to times and
races. The Bible, Hindu literature, the primitive poets and historians
of Greece, do however provide sufficient indications of the manner in
which man originally classified other living beings. The repartition was
usually made in three great categories, according as the animals lived in
the water, or upon the earth, or flew in the air. The subdivisions are
remarkable. Thus, among terrestrial animals, there are some that walk,
and some that climb: in this last group there is a mixture of articulate
creatures, of molluscs, reptiles and amphibians. Among aerial animals,
we find birds, and many flying insects. These primitive classifications
are based upon perception far more than on abstraction, or at any rate
rest upon superficial resemblances. The habitual environment, air,
water, earth, determines the cardinal classes. Some easily apprehended
characteristic makes the subdivisions: e. g., flight (birds, insects),
locomotion (walking, climbing). The method employed is hardly superior
to that by which generic images are formed; and in the order of
classification, this point corresponds with the concrete-abstract period
of primitive languages, numerations, and religions, i. e., to a gross
generalisation fixed by a word.

The scientific period begins with Aristotle. It has been affirmed that he
owes numerous points to predecessors whom he fails to mention: this is
a historical matter of no interest in the present connexion. With him,
or under his name, we have the commencement of comparative anatomy which
involves a preliminary labor of analysis, unknown in the pre-scientific
period, and marking the transition from apparent and superficial to
profound and essential resemblances. His classification is of course
imperfect, often inconsistent; it bears the impress of an epoch of
transition.

His terminology is poor, unstable, floating. He distinguishes two sorts
of groups only: the genus (γένος) and the species (εἶδος). “But the term
γένος has the least constant significance: it serves as the indistinct
designation of any group of species, however great its extension, as
well what we now term classes, as other lower groups.”[78] Sometimes
however Aristotle speaks of large genera (γένη μέγαλα) and of very large
genera (γένη μέγιστα), without any precise denotation. It has been
said that penury of words was an obstacle to him: yet this is hardly a
plausible reason, seeing that he found means to create the word ἔντομα to
designate insects. The true obstacle was the insufficient determination
of character.

Again, independently of nomenclature, “while Aristotle knew a fairly
large number of animals, the notion of grouping them in definite order,
which should express their greater or less degree of similarity, does
not appear to have presented itself to his mind. Hence he did not
attempt what we call classification. He compares different animals
together, by every possible means, and endeavors to reduce the result
of his comparisons to general propositions.” In this way he arrives at
relations which are sometimes important, sometimes without importance.
For example: among animals, some have blood, some lymph, which takes its
place: this division, notwithstanding the error on which it is based,
corresponds broadly speaking with the distinction between vertebrates and
invertebrates. Animals “which have blood” are subdivided into viviparous
and oviparous. Further, animals that fly are ranged in three categories,
according as their wings are feathered (birds), or formed by a fold of
skin (bats), or dry, thin, and membranous (insects). Then there is a
division of animals into aquatic and terrestrial, social and solitary,
migratory and sedentary, diurnal and nocturnal, domestic and wild, etc.

In sum, there is co-existence of two processes: one scientific, implying
a preliminary analysis; the other of common observation, which does not
sensibly differ from concrete-abstract classifications; and the idea of a
hierarchy formed by abstraction of abstracts, by a systematic arrangement
of the animal kingdom, has not yet made its appearance. Yet Aristotle’s
work, just by reason of its composite nature, is interesting to the
psychologist who studies the evolution of the faculty of abstracting and
generalising.

We may pass over two thousand years, during which no progress was made,
till we come to Linnæus. “He was the first man who distinctly conceived
the idea of expressing, under a definite formula, what he believed to be
the system of nature.” His nomenclature is fixed. Under the names of
classes (_genus summum_), orders (_genus intermedium_), genera (_genus
proximum_), species, varieties, he proposes subdivisions of decreasing
value, embracing a greater or less number of animals which all present
in common more or less general attributes. He pursues the research after
fundamental characteristics, and _essential_ similarities, incessantly
correcting his first results. Thus it is only at the eleventh edition of
his _Systema naturæ_ that the class of “Quadrupeds” is converted into
Mammals: the Cetacea are included in this class, and no longer placed
among the fish, as also bats, which were formerly classified with birds,
etc.[79] Whatever their objective value, we have here a true system of
rational concepts.

We may instance Cuvier for the clearness with which he separates the
predominant and subordinate characteristics: “If,” he says, “we consider
the animal kingdom on the principles just laid down, regarding only
the organisation and nature of the animals, instead of their size and
utility, according to our knowledge of them, or the sum of accessory
circumstances, we find that there are four principal forms, four general
plans, if we may so express ourselves, on which all animals seem to
have been modelled,” etc. These four branches (a new word created by
him), which he held to be irreducible, were the Vertebrata, Articulata,
Mollusca, and Radiata.

Finally, since the progress of consecutive abstraction and generalisation
consists in incessantly seeking out extracts of extracts, and
simplifications of simplifications, the natural movement of the mind
tends fatally towards pure unity as its supreme end. This last phase
belongs to the nineteenth century, and still more to the contemporary
epoch. It comes from various sources, and has assumed different forms:

1. Speculative in the school of Schelling. To Oken, the highest
representative of this view, man is the prototype and measure of animal
organisation; all other animals are constructed after his pattern. “Their
body is in some sort the analysed body of a man; the human organs live,
whether in isolation, or in different combinations, in the state of
independent animals. Each such combination constitutes a class.”

2. Embryological, according to the labors of Von Baer. While Cuvier, in
classification, brought anatomy and morphology to the front, a new system
now appears, founded upon development only; the science of embryology.
To be accurate, Baer’s conception was not unitary, since it admitted
four types: peripheral (radiate), massive (molluscan), longitudinal
(articulated), bi-symmetrical (vertebrate). But little by little, the
oft-substantiated principle asserted itself and found firm footing among
his successors: the animal with the highest organisation passes, during
its individual development, through phases which, in less highly evolved
beings, are permanent states; or, more briefly, among the higher animals,
ontogenesis is a repetition of phylogenesis.

3. Transformist. The boldest partisans of this view, e. g., Haeckel,
adopt a rigorously unitary conception: all the innumerable examples of
the animal kingdom have issued from one common stock.

In all there is a fundamental trend of the mind towards the idea of
original unity. It is unimportant for the moment to examine whether
this concept of ideal unity (we might also recall the vegetable ideal
of Goethe, and the vertebrate ideal of Richard Owen) is a delusion, or
a true apprehension: we shall return to this later, in discussing the
_objective_ value of the notions of genus and species (Chap. V. § vi). At
this point, the _subjective_ psychological process alone is relevant to
our purpose.

This review has no pretensions at being even an abridged history of
zoölogical classifications. It merely aims at showing by facts, (1) how
a hierarchy of concepts is constituted, and in the travail of centuries
passes from the period of generic images to the ideal of embryological
unity, common to all beings; (2) how the work of dissociation and
analysis has always gone on, and multiplied, in quest of similarities
more and more difficult to discover—often indeed fragile or dubious—to
stop at unity only, the supreme abstraction.

We are now at the threshold of the last period of abstraction, that of
complete symbolism, and it is not without interest to note that what
passes in the theoretical order has its equivalent in another form of
human activity—the practical order—where the mechanism of exchange is
again developed by the aid of an ever-increasing substitution. Thus,
at the lowest stage, all commercial transactions are reduced to truck,
to exchange by barter. The concrete for the concrete is the method of
primitive peoples. An immense step is taken when this rudimentary process
is succeeded by the employment of precious metals. A substitutory value
is taken as the common measure of other values. At the outset, silver and
gold, in the form of powder or of small bullion, were weighed out by
the contractors for each particular transaction. Next, this inconvenient
procedure was replaced by coined money, issued under the control of an
officer, or of the social aggregate, thus conferring a general value
on the instrument of exchange. Lastly, at a much later period, bills
of exchange, bank-notes, and numerous forms of letters of credit, were
substituted for gold and silver; so that a sheet of paper worth less than
a centime may become the symbol of millions and tens of millions.

This resemblance of the two cases is by no means fortuitous. It is
based upon identity of psychological process, namely a substitution
of ascending degrees, an ever increasing simplification, whether in
the order of speculative research, or in the department of commercial
transaction: and just as paper tokens, unless financially convertible
into objects of consumption, for use or luxury, are nonentities that
can accumulate in the bank without the gain of anything more than a
simulacrum—so, if the highest symbols of abstraction cannot be reduced
to the data of experience, we may, as too often occurs, accumulate,
manipulate, build up concepts, and still be in a state of permanent
intellectual bankruptcy.




CHAPTER IV.

THE HIGHER FORMS OF ABSTRACTION. THEIR NATURE.


Before we embark on the study of the principal concepts, it is incumbent
upon us (in order to determine for each of these, separately, the
conditions of their genesis and development—as was shown for abstraction
in general) to throw as much light as possible upon the very vexed
question of the psychological nature of the concepts of pure symbolism,
where the word appears as the sole element that exists in consciousness.
Is it true that we can think effectually and usefully with words and
nothing but words, as has been sustained to satiety? Is not this
assertion founded upon the misapprehension of a factor which, although it
does not enter into consciousness, is none the less in active existence?
The investigation of this point is the prime object of the following
chapter.

It is unnecessary to enter in detail into the researches of the last
thirty years, as to the seat and the nature of images. Yet since these
have been the point of departure of the following inquiry, the results
may be briefly summarised.

It is generally admitted that the image occupies the same seat as the
percept of which it is a weak and incomplete residuum, i. e., in order
to produce itself in consciousness it demands the putting into activity
of certain definite portions of the cerebral centres. The energy of the
representative faculty does not merely vary from individual to individual
in a general manner: there are particular forms of imagination,
constituted by the very marked predominance of a certain group of
representations, visual, auditory, muscular, olfactory, gustatory.

Normal observation, and still more pathological documents, have thus
determined certain types. We may also (though this is mere hypothesis
and difficult to verify) admit a “mixed” or “indifferent” type, in which
the different species of sensations are represented by corresponding
images of equal clearness and vigor, without marked predominance of
any one group, whilst still maintaining their relative importance: e.
g., it is clear that in man the visual and olfactory images cannot be
equivalent in absolute importance. Excluding this indifferent type, we
have three principal “pure” types: visual, auditory, muscular or motor,
signifying a tendency to represent things in terms borrowed from vision,
from sound, or from movement. If we push the investigation further, we
find that these types again imply variations or sub-types. Thus there may
be a lively faculty for representation of complex visual forms (faces,
landscapes, monuments) along with a weak sense for graphic signs (printed
or written words) and so on.

The numerous works devoted to this subject, and too well known to be
insisted on here, lead us to this conclusion: that there is no general
faculty of imagination. This is a vague term which designates very
different individual variations; these last alone have any psychological
reality, and are alone important in cognising the mechanism of the
intellect.

May it not be the same for the faculty of conception? May not the word
“general idea” or “concept” be in its kind the equivalent of the word
image, namely a vague formula,—its psychological reality lying in types
or variations as yet undetermined? I am exposing for ideas, the problem
that has already been set forth for images, while recognising its much
greater obscurity. The psycho-physiological conditions of the existence
of concepts are practically unknown: this is a _terra incognita_ wherein
the new psychology has hardly adventured itself, and where it would
indeed have been chimerical to tread before the preliminary study of the
image.


I.

The question I have set myself to elucidate is very modest, very limited
and circumscribed, representing only part of the problem indicated above.
It may, however, teach us something of the ultimate nature of concepts.
It is as follows:

When we think, hear, or read a general term, what arises as sign in
consciousness, _directly and without reflexion_?

I have purposely italicised these words in order to emphasise my
principal aim, which was to discover the _instantaneous_ operations
(conscious or unconscious) that occur in such a case, in persons whose
habits of mind are widely different. I endeavored as much as possible to
eliminate reflexion and to seize the mental state. With time and effort,
minds that are least apt in abstraction will arrive at a more or less
successful translation of general terms, or at the substitution for them
of some mangled and halting definition. I set myself as far as possible
to suppress this secondary phase of the mental process, and to arrest it
at the first, in order to determine what the word evokes immediately[80]
and in what degree this differs with the individual.

In order to make the answers more exactly comparable, I interrogated only
the adults of both sexes, excluding all children. It was indispensable
to my investigation that it should comprise people of very different
degrees of culture, habits of mind, and profession. The principal classes
were mathematicians, physicists, doctors, scientists, philosophers,
painters, musicians, architects, men of the world, women, novelists,
poets, artisans. The last class made such confused replies that I must
regard their documents as worthiest. Too much is left for individual
interpretation. The total number of persons interrogated amounted to one
hundred and three.

The method was invariably the same. We said to the subject: “I am going
to pronounce certain words; will you tell me directly, without reflexion,
whether this word calls up anything or nothing in your mind? If anything,
what is suggested to you?” The reply was noted down at once; if delayed
beyond five to seven seconds, it was held to be null, or doubtful. In
the case of naïve subjects, I employed certain preliminaries: before
pronouncing abstract words, concrete terms (designating a monument, or
person) such as would evoke a simple image, were heard; then the impulse
being given, I proceeded to the enumeration of general terms.

The words which served as material for the inquiry were fourteen in
number, proceeding from the concrete to the highest abstractions. They
were enunciated in an indifferent order and were as follows: _dog_,
_animal_, _color_, _form_, _justice_, _goodness_, _virtue_, _law_,[81]
_number_, _force_, _time_, _relation_, _cause_, _infinity_.

The inquiry was invariably oral, never in writing, the greatest care
being taken to prevent the person from knowing the end in view, unless
afterwards: which led in certain cases to interesting explanations. The
very nature of my method prevented me from extending it as widely as
I could have wished. I could not, as was done in England, distribute
printed questions among the public, because it was necessary to note
the spontaneous answer immediately before it was corrected by later
reflection. Moreover, I needed unsophisticated subjects, ignorant of my
purpose, and therefore eliminated all whom I suspected of being even
indirectly acquainted with it.

The majority were interrogated on the fourteen terms cited above, others
on a few only; so that the total number of responses was over nine
hundred. It would be beside the mark to publish them here. They are
nothing more than data which have to be interpreted. Three principal
or pure types appear to stand out from them, besides the failures or
mixed cases. These may be termed the _concrete_ type, the _visual
typographic_ type, and the _auditory_ type. Each of these corresponds
with a particular mode of representing the general idea. We will examine
them separately.

1. CONCRETE TYPE. Here the abstract word nearly always evokes an image,
vague or precise; usually visual, sometimes muscular. It is not a simple
sign, it does not represent the total substitution, it is not dry, and
finally reduced. It is immediately and spontaneously transformed into a
concrete. In fact, the persons of this type think only in images. Words
are for them no more than a kind of vehicle, a social instrument of
mutual comprehension. When a sequence of general or abstract terms passes
through their minds, what really passes is a succession of concretes,
save for the very abstract words which “evoke nothing.” This is an answer
I have often received, and which, in virtue of its importance, will be
considered apart, at the end of this chapter.

The concrete type appears to be the most widely distributed; it obtains
almost to exclusion among women, artists, and all who have not the habit
of scientific abstraction. I have selected a few examples from among the
many observations belonging to this type.

A painter.—_Cause_: nothing. _Relation_: relations of terms; recital,
written report. _Law_: judges in red robes. _Number_: vague. _Color_:
contrast between green of plant, and red of drapery. _Form_: a round
block, a woman’s shoulder. _Sound_: a murmur. _Dog_: ears of a dog
running. _Animal_: vague collection, as in certain Dutch pictures.
_Force_: hits out with his fists. _Goodness_: his young mother, seen
vaguely. _Time_: Saturn with his scythe. _Infinity_: a black hole.

A woman.—_Cause_: I had been the cause of her son’s success. _Law_:
the government is bad. _Color_: sees an impressionist picture by her
son. _Form_: names a beautiful person. _Goodness and Virtue_: names
two people who each have this quality. _Force_: sees men fighting.
_Relation_: social relations between husband and wife. _Justice_: sees an
audience-hall and judges. _Dog_: sees a dog that bit one of her parents.
_Infinity_: nothing. _Time_: a metronome.

These two interrogatories are complete. I might proceed by another
method: that of taking each general term (law, cause, number, etc.) and
quoting all the answers received, among which many would be identical.
Such an enumeration would be long and superfluous: we cannot, however,
neglect a few of the particulars. For the word _cause_, several persons
(women, artists, people in society) replied “_cause célèbre_,” “_procès
célèbre_,” for the most part mentioning one only, and that some recent
trial. At first this reply annoyed me, and appeared to be useless for
my inquiry. Later, on the other hand, I felt it to be instructive,
because it characterises better than any description the type which I
have denoted as concrete, and the particular turn of this kind of mind,
in which the abstract sense does not present itself, at any rate at the
beginning.

I may also note two answers given me immediately by a celebrated
painter:—_Number_: I see many brilliant points. _Law_: I see parallel
lines. (Is this the unconscious idea of levelling by the law?)

The terms _goodness_ and _virtue_ suggested answers which are easily
summarised: they fall into two categories. (1) Nothing; this answer does
not belong to the concrete type; (2) a definite person, who was always
named and who thus becomes the incarnation, the concrete representation.

Nearly all the images evoked belong to the visual sense; the word
_force_, however, most frequently called up pure muscular images, or
the same accompanied by a vague visual representation. Example—Seeing
somebody lifting a weight; I vaguely see something pulling; a weight
suspended by a ring; a string drawing on a nail; pressure of my fist in a
fluid; the Marshal of Saxony breaking an _écu_ of six pounds, etc.

I have been describing the ordinary and principal form of the concrete
type. It consists in the immediate and spontaneous substitution of a
particular case (fact or individual) for the general term. In certain
observations a slightly different _variation_ may be detected; I have
encountered it among several historians and learned men. In the ordinary
type, the whole (general) is thought by means of the part (concrete); in
the variation, the thinking is by analogy, and the mechanism seems to be
reduced to pure association. A few examples will explain the distinction.
The replies in duplicate were given by different persons. _Number_:
the “Language of Calculation,” Pythagoras. _Cause_: Hume’s theory of
causality; Kant’s theory. _Law_: the “Tables of Malaga,” Montesquieu’s
definition. _Color_: the chemistry of the spectrum. _Justice_: Littré’s
definition. _Animal_: the πὲρι ψυχῆς of Aristotle. _Time_: a vague
metaphysical theory. _Relation_: discussion of Ampère and Tracy on
this subject. _Infinity_: books on mathematics. _Color_: treatises of
photography, etc.

It might be objected that there is a certain association in ordinary
cases as in these; but the distinction will readily be perceived. The
former proceed from that which contains, to the content—from the class
to the fact: they think the whole by means of the part; there is an
internal association. The latter form associations beside and from
without. Apparently these do not reach to the concrete, they stop half
way; for a complete generality they substitute a semi-generality. Further
than this, my data are neither sufficiently numerous, nor clear enough,
for the point to be insisted on.

2. VISUAL TYPOGRAPHIC TYPE. Nothing is easier to define. In its pure form
it consists in seeing printed words and nothing more; in three cases
words were seen _written_. Among some the vision of the printed words
was accompanied by a concrete image as in the first type, but only for
semi-concrete concepts (dog, animal, color); for the higher abstracts
(time, cause, infinity, etc.) the typographical vision alone exists.[82]
This mode of representation is widely distributed among those who have
read much; but there are many exceptions.

No doubt many of my readers will discover from self-observation that
they belong to this type. I have further noticed that all who have this
mode of representation regard it as normal, and necessary, in anyone who
knows how to read. This is a fallacy. I do not possess it myself in the
faintest degree, and have met many others who resemble me.

Thus I was little prepared to discover this type; and had even reached
my thirtieth observation without suspecting it, when I encountered such
a clear case as to put me on the track. I was interrogating a well-known
physiologist. To every word except _Law_ and _Form_, he replied “I see
them in printed characters” and was able to describe these accurately.

Even the words _dog_[83], _animal_, _color_, were unaccompanied by any
image. He volunteered further information which may be reduced to the
statement, “I see everything typographically.” The same holds good for
concrete objects. If he hears the names of his intimate friends whom
he meets every day, he sees the names printed; it is only by an effort
of thought that he sees the image. The word “water” appears to him as
if printed, and he has no vision of a liquid. If he thinks of carbonic
acid, or nitrogen, he sees indifferently either the words printed or the
symbols CO₂, N. He does not see the complex formulæ of organic chemistry,
but the words only.

Surprised (from the reasons above indicated) at this observation—of the
sincerity and precision of which there could be no doubt—I continued my
investigation, and discovered this mode of thinking in general terms to
be sufficiently common. Several cases indeed were as pure and as detailed
as the one just cited. Thenceforward I adopted the habit of invariably
asking at the close of my interrogatory “Did you see the words printed?”

Several people remarked that they had read a great deal, and corrected
many proofs, and that this would account for their belonging to the
typographical visual type. The influence of habit is certainly enormous,
but is no adequate explanation here, since there are many exceptions. I
have myself read and corrected many proofs, but no word ever appeared in
my consciousness as printed, unless after considerable effort, and then
vaguely. Hence this mode must be due in great part to natural disposition.

Among the compositors questioned I found: (1) That they saw my fourteen
words printed in some special type, which they occasionally specified;
(2) they had a concomitant image for semi-concrete terms; (3) for
abstract terms no image accompanied the typographical vision. Here we
have the superposition of two types: the one natural, and of primitive
formation (concrete type), the other acquired, and of secondary formation
(typographical visual type).

In short,—in many minds the existence of the concept is associated with a
clear vision of the printed word and nothing beyond it.

3. AUDITORY TYPE.—In its pure form this seems to be rare. It consists in
having in mind nothing but signs (auditory images) unaccompanied either
by the vision of printed words or by concrete images. Possibly it may
preponderate among orators and preachers; of this I have no documentary
evidence. Musicians do not appear to belong to this type.

One very clear and complete case of the kind I have, however,
encountered. This was a polyglot physician known as the author of several
works, who for many years had lived among books and manuscripts. He has
no trace of typographical vision, but all words “sound in his ear.” He
can neither read nor compose without articulating; as the interest of his
book or work grows upon him he speaks aloud—“He must hear himself.” In
his dreams there are few or no visual images; he hears his voice and that
of his interlocutors: “His dreams are auditory.” None of my words, even
when semi-concrete, evoked visual images.

In most cases the auditory type is not clear. For very general terms the
heard word alone exists, but in proportion as the concrete is approached,
the sound is accompanied by an image; thus returning upon our former type.

It is worth while to note that the term _flatus vocis_ “_nomina_,” first
employed in the Middle Ages and which has since become the formula of
Nominalism, seems by its nature to indicate that it was originally
invented by persons who belonged to the auditory type, and I may even
hazard an hypothesis. The typographical visual type did not exist
(printing not being invented); it is true that a substitute might have
existed in the _graphic_ visual type (reading of manuscripts). But
considering that in the Middle Ages instruction was essentially oral,
that learning came rather through listening than by reading, that the
oratorical jousts and arguments were daily and interminable, it is
undeniable that the conditions for developing the auditory type were
highly favorable here.

I need hardly say that the three types described above are rarely met
with in the pure and complete form. As a rule a mixed type prevails: a
concrete image for certain words, and typographical vision, or auditory
images, for others. To sum up: all cases seem to be capable of reduction
to the following: (1) The word heard; beyond this, _nil_ (we shall
subsequently have to examine this “nothing”); (2) typographical vision
alone; (3) the same, accompanied by a concrete image; (4) the word heard,
accompanied invariably by a concrete image.

4. Prior to the commencement of this inquiry I felt much hesitation on
one point: should one in questioning use general _words_ or general
_propositions_? I decided in favor of words because these are brief,
simple, isolated, and undisguised, and have the advantage of being
understood directly, while they in no way suggest to the subject what
line he is to follow.

I still however felt scruples in the matter. Was not the investigation
as conducted on these lines a little artificial? In point of fact,
general terms most frequently occur as members of a phrase, co-operating
with others, and connected with them by certain relations. I therefore
recommenced my inquiry, using the same method, but replacing words by
phrases. The general propositions employed are purposely trite, to avoid
contradiction, and to ascertain the immediate mental state. They were as
follows:

Cause invariably precedes effect.—Infinity has several meanings.—Is Space
infinite?—Has Time any limits?—Law is a necessary relation.—I need not
enlarge upon the results: they are _precisely the same_ as for words. In
every case, and for each person, there is one predominating word which
absorbs all the content of the phrase, and is a substitute for it. On
this the instantaneous mental operation is concentrated.

If of the concrete type, the subject sees images. In the second phrase,
e. g., everything converges on the word _infinity_. Replies: Sensation
of obscurity and depth, vague luminous circles, a sort of cupola, a
never-receding horizon, etc. If a typographic visualist, the printed
sentence is seen less clearly than the simple words: “in minute
characters; no capitals”; some persons glimpse it rapidly: others see
only “the principal word printed.”

For the pure auditory type, the answer is always very simple. “I hear the
sentence, I see absolutely nothing.”

The new method therefore simply confirms the previous observations, with
no variations. This identity of result seems to me to militate against
a distinction admitted by many authors. In the classical treatises a
distinction is made between “necessary ideas” and “necessary truths”
(I use their terms uncritically), i. e., general concepts and general
propositions. Example: cause, principle of causality. In my opinion
there is merely a difference of form between the two positions, the one
psychological, the other logical. A concept is a judgment in a state
of envelopment, or of result. The proposition is a word in the state
of development. The difference is not material, but formal; it is the
passage from synthesis to analysis.

I thought that after an interval of two years it might be interesting
to repeat the same inquiry on the same people; but the results were
not encouraging in this direction. Some, remembering the previous
investigation, declared that “they felt themselves influenced
beforehand.” Others, who had a more vague recollection (perhaps because
they did not understand the object of the inquiry) gave answers analogous
to their former replies. In short, notwithstanding the lapse of time, and
change of circumstances, each seemed to be consistent with his former
self.

I must admit that in the preceding research the psychological nature
of the concepts was studied under a particular aspect. This objection
was made at the London Psychological Congress[84] by the President,
Professor Sidgwick, whose remarks may be summarised as follows:

First, Professor Sidgwick believes that the act of suddenly calling
attention to a word, in a person not accustomed to introspective
observation, evokes a response which does not exactly correspond to
the state ordinarily aroused by such words. In his own particular case
he has found that the images evoked (usually visual) were extremely
feeble, but that when he dwelt upon them they were enlivened. Secondly,
the images vary a great deal according to the terms employed; for
example, when he is occupied with mathematical and logical trains of
thought, he sees only the printed words. If he is engaged upon the
subject of political economy, the general terms sometimes have for their
concomitants extremely fantastic images: like _value_, for instance,
which is accompanied by the indistinct and fragmentary image of a man
placing something upon the pan of a balance. Thirdly, when for such words
as _infinity_, _relation_, etc., the subject answers _nothing_, the only
conclusion justified is that the subject is incapable of describing the
confused elements which exist in his consciousness. Fourthly, Professor
Sidgwick’s own experience points to the conclusion that my types may
succeed each other in the same person.

On this last point—the co-existence of several modes of conception in
the same person—I am quite in agreement with Professor Sidgwick, and my
own data, drawn up from personal observations, would provide me with
sufficient evidence. At the same time the object of my investigation
was not to determine the manner in which each individual conceives,
but the forms under which men as a whole think of concepts. Nor did
I profess to follow the work of the mind when it resolves its general
ideas into concretes, when it makes coin out of its bank-notes, but only
to seize the subjacent labor that accompanies the current and facile
use of general terms, in speaking, listening, reading or writing. No
doubt it would be advisable to treat the subject in another manner by
studying—no longer the momentary state that corresponds with the presence
of the concept in consciousness—but the stable organised turn of mind
due to a long habit of dealing with concepts. To this end it would be
desirable more especially to question mathematicians and metaphysicians.
My data are neither numerous nor clear enough to permit of my hazarding
any dictum on this subject. Some mathematicians have told me that they
_invariably_ require a figured representation, a construction, and
that even when these are considered as purely fictitious their support
is indispensable to the train of reasoning. _Contra_ those who think
geometrically, there are others who think algebraically, eliminating all
configuration, or construction, and proceeding by simple analysis with
the aid of signs: which (with the necessary corrections and descriptions)
would bring the first under the concrete, and the second under the
audito-motor type. Among metaphysicians the typographical visual type
seems largely to predominate. One (who is well known) belongs to the pure
auditory type. All this, however, is inadequate; the investigation would
have to be followed out, by and upon others.

A young Russian doctor, M. Adam Wizel, who was interested in the subject,
put the same questions (following the method indicated above) to persons
in the hypnotic state. Admitting the unconscious mental activities
to preponderate in this state he asked whether by this procedure it
would not be possible to penetrate farther into the unknown substrate
of consciousness. His experiments were undertaken at the Salpêtrière,
in Charcot’s clinique, upon six women—hysterics of the first order.
The subjects were first put into a state of somnambulism, then after a
preliminary explanation were questioned, as above. After getting the
answers Wizel ordered the subjects to forget all that had happened, and
then woke them. He now began again in the waking state, asking the same
questions, so that he was able to compare the answers given successively
in the two cases. They are nearly always clearer and more explicit during
somnambulism than during the waking state, as may be judged by the
following example (taken from the third observation):

    QUESTIONS    SOMNAMBULISM            WAKING STATE

    Dog:         A big grey animal       Nothing
    Form:        A red cardboard head    Nothing
    Law:         A tribunal              Nothing
    Justice:     A magistrate            State of justice
    Number:      Figure 12 in white      The number of a note (?)
    Color:       Green                   Blue

Where the replies are concrete in the two cases I note a tolerable
analogy between them. M. Wizel (who eliminated all doubtful cases,
and any accompanied by crises) never encountered the typographical
visual type, nor the pure auditory type, in his experiments. His
six hysterics belong to the concrete type, with the predominance of
_visual_ images—much more rarely of motor images, provoked by the word
“force.” The answer “nothing” is very frequent; less so, however, during
somnambulism than during the waking state.


II.

We now reach the most obscure and difficult part of our subject. Among
the nine hundred and odd replies collected, the one most frequently met
with is “nothing.” There is no observation in which it does not occur
at least once: in the majority of cases it is found one, two, three,
four, or more times. If I take the word _cause_, the formula “I have no
representation,” forms fifty-three per cent. of the total of answers
collected; the rest saw the printed word or some concrete image; e. g.,
a stone falling, horses drawing, or other simulacra, of which several
have already been enumerated. It is the same with all the other highly
abstract terms (time, infinity, etc.). So that to return to the question
which was to be the _exclusive_ object of our investigation,—“Is the
general idea when thought, read, or heard, accompanied by anything in
consciousness?”—we may reply, an image, a typographical vision, or
nothing. We must now inquire, what this _nothing_ is, for it must be
something.

We are face to face with the problem which the pure Nominalists attacked,
when they took this _nil_ in its proper sense. Were there indeed any
who really pretended that we could have in mind words, and words
only—nothing besides? This is a historical problem into which it is
useless for us to enter. It is possible that some may have pushed their
reaction against the extravagances of realism even to this point, but
the thesis is totally insupportable; for at that rate there would be no
difference between a general term, and a word of any unknown language:
the latter is the pure _flatus vocis_, a sound that evokes nothing. If,
on the other hand, by word we mean sign, everything changes, since the
sign implies and envelops something. Such appears to me to be the true
interpretation.[85]

So that for the cases which alone concern us for the moment, i. e.,
those in which the reply was “Nothing,” there are two elements, the
one existing in consciousness (word heard or auditory image), the
other subconscious, but not therefore invalid and inaccurate. Hence we
must penetrate into the obscure region of the unconscious, in order to
apprehend the something which gives to the word its signification, its
life, its power of substitution.

Leibnitz wrote: “Most frequently, e. g., in any prolonged analysis, we
have no simultaneous intuition of all the characteristics or attributes
of a thing: in their place we use signs. In actually thinking, we are
accustomed to omit the explanation of these signs by reference to what
they signify—knowing or believing that we have this explanation in our
power: but we do not judge the application, or explanation, of the words
to be positively necessary.... I have termed this method of thinking,
blind or symbolic. We employ it in algebra, in arithmetic, and in fact
universally:” which is equivalent to saying that potential knowledge
is stored up beneath the general or abstract terms; nor should we be
surprised at finding this doctrine in the man who first introduced the
idea of the unconscious into philosophy.

To determine the rôle of this inevitably active, albeit silent, factor
is a difficult enterprise, and one that is necessarily inaccurate,—since
it amounts to the translation of obscure and enveloped states into the
clear and analytical language of consciousness. The simplest procedure is
to examine how we arrive at the comprehension of general terms.[86] Set
a page of a philosophical work before the eyes of a novice or of a man
wholly ignorant of the subject. He understands nothing. The only method
that will render it intelligible is to take the general or abstract
terms one after the other, and translate them into concrete events,
into facts of current experience. This labor demands an hour or two. In
proportion to the progress of the novice, the translation is effected
more quickly; it becomes superfluous for certain terms; and finally but
a few minutes are required for the comprehension of a page. Untrained
minds are often surprised, on reading a sentence consisting of abstract
terms, at understanding each word, and yet not knowing what the whole
means. This signifies that they have not beneath each word potential
knowledge sufficient to establish a connexion or relation between all
the terms, and giving meaning to them. Apart from those who are familiar
with abstraction by natural gift or by habit, it is incontestable that to
the vast majority the reading of an abstract page is a slow and painful
and very fatiguing process. This is because each word exacts an act of
attention, an effort, which corresponds to labor in the unconscious or
subconscious regions. When this labor becomes useless, and we think, or
appear to think, by signs alone all goes rapidly and easily.

In short, we learn to understand a concept as we learn to walk, dance,
fence, or play a musical instrument: it is a habit, i. e., an organised
memory. General terms cover an organised, latent knowledge which is the
hidden capital without which we should be in a state of bankruptcy,
manipulating false money or paper of no value. General ideas are habits
in the intellectual order. Suppression of effort corresponds with
perfected habit; as again with perfect comprehension.

What occurs each time we have in consciousness merely the general
term, is only a particular case of a very common psychological fact:
as follows:—The useful work is carried on below consciousness, and
above its surface only results, indications, or signs appear. The facts
enumerated above are all taken from motor activity. Their equivalents
abound in the domain of feeling. The “causeless” states of joy or sorrow,
which are frequent in the sound man, and still more in the invalid, are
only the translation into consciousness of ignored organic dispositions
operating in obscurity. What gives intensity and duration to our passions
is not the consciousness we have of them, but the depth of the roots
by which they plunge into our being, and are organised in our viscera,
and subsequently in our brain. They are no more than the expression
of our constitution, permanent, or momentary. We might run over the
whole province of psychology, with variations on the same theme. I do
not propose to do so here, but would simply recall that every state
of consciousness whatsoever (percept, image, idea, feeling, passion,
volition) has its substrate; that the concept reduced to the bare word
is but another case of the same kind, and in no wise peculiar: that
to believe that there is nothing more than the word, because it alone
exists in consciousness, is to seize only the superficial and visible
part of the event,—perhaps, all things considered, the least part. This
unconscious substratum, this organised and potential knowledge, gives
not merely value, but an actual denotation to the word,—like harmonics
superadded to the fundamental note.

To conclude: we think not with words in the strict sense (_flatus vocis_)
but with signs. Symbolic thought, which is a purely verbal operation, is
sustained, co-ordinated, vivified, by potential knowledge and unconscious
travail. To this it must be added that potential knowledge is a genus,
of which the concept is only a species. All memory can be reduced to
latent knowledge, organised, susceptible of revival, but all memory is
not material for concepts. The man who knows many languages even when
not speaking them, the naturalist capable of identifying millions of
specimens while not classifying them, have a very extended potential
knowledge, but it is all concrete. The potential knowledge which
underlies concepts consists in a sum of characters, qualities, extracts,
which are the less numerous in proportion as the concept approximates to
pure symbolism: in other terms what underlies the concept is an abstract
memory, a memory for abstracts.

In my opinion, a large measure of the obscurities and dissensions
which prevail as to the nature of concepts, arises from the fact that
the rôle of unconscious activity has for centuries been misunderstood
or forgotten,—psychology having confined itself exclusively to
consciousness: and while its action is universally admitted to-day for
all other manifestations of mental life—instincts, percepts, feelings,
volition, etc.—it is still excluded from the domain of concepts. The
whole of the foregoing discussion is an essay towards its reintegration.

Need we add that the opinion adopted as to the nature of the unconscious
matters little in the present connexion? On this point there are, we
know, two principal hypotheses. According to the one it is a purely
physiological event, and can be reduced to unconscious cerebration.
According to the other, the unconscious is still a psychical fact;
whether it be an affective rather than a representative state, or a
complex of little, scattered consciousnesses, isolated, evanescent, with
no linkage to the self, or, again, an organisation or sequence of states,
which forms another current coexistent with that of clear consciousness.
These theories, and others which I omit, have nothing to do with our
purpose. It is sufficient to recognise unconscious activity as a fact,
without any explanation, and this position would seem to be incontestable.

We have seen that abstraction, in proportion as it ascends and
strengthens, separates itself more and more from the image, until
finally, at the moment of pure symbolism, the separation becomes
antagonism. This is because there is fundamentally, and from the outset,
an opposition of nature and procedure between the two. The ideal of
the image is an ever-growing complexity, the ideal of abstraction an
ever-growing simplification, since the one is formed by addition, the
other by subtraction.

To the man who is gifted with a rich internal vision, the shape of
people, of monuments, of landscapes, surges up clearly and well defined:
under the influence of attention, and with time, details are added,—the
representation completes itself, and approaches more and more completely
to the reality. So too with internal audition: witness the musician who
hears ideally every detail of a symphony.

The contrary holds for abstraction. “There is,” says Cournot, “an
analysis which separates objects, and an analysis which distinguishes
without isolating them. The use of the refracting prism is an instance of
the analysis which separates or isolates. If, instead of isolating the
rays so as to cause them to describe different trajectories, they are
made to traverse certain media which have the property of extinguishing a
definite color, we are able to distinguish without isolating.”[87]

Abstraction belongs to this last type, with intervention of the
process described by Cournot. Attention brings a feature into relief;
inattention, and voluntary inhibition, act as extinguishers to the other
characteristics.

Let us pass from theory to practice. This antagonism is of current
observation, almost a banality, whenever men of imagination are
confronted with abstract thinkers. We must of course exclude those who
by a rare gift of nature (Goethe), or by the artifice of education, are
capable of handling the image and concept alternately.

Let us take the artists as type of the imaginative thinker: the novelist,
poet, sculptor, painter, musician, etc. Each dreams of an organic,
living work, a _complex_. Some with words, others with forms, others
with sounds; realists with the aid of minute detail, classics by means
of general sketches; all make for the same end. Music again, which from
its nature seems a thing apart, is an architecture of sounds of amazing
complexity, often exciting contradictory states of mind.

Among abstract thinkers (theorists, scientists) the tendency is always
towards unity, law, generalities—towards _simplification_: by what
is fundamental and essential, if the man be genuine; by shifting and
accidental features, if he is a charlatan. The mathematician and the pure
metaphysician have usually a distaste for facts, for multiplicity of
detail. A writer whose name has escaped me says: “Every scientist smells
of the cadaver.” This is our thesis, under the form of an image. Abstract
thought is a cadaver. It would be more just, though less picturesque,
to say a skeleton; for scientific abstraction is the bony framework of
phenomena.

The antagonism between the image and the idea is thus fundamentally
that of the whole and the part. It is impossible to be at the same
time an abstract thinker and an imaginative thinker, because one
cannot simultaneously think the whole and the part, the group and the
fraction; and these two habits of mind while not absolutely exclusive are
antagonistic.

       *       *       *       *       *

In conclusion, have we general ideas, or merely general terms? It must
first be remarked that the expressions, “general ideas or notions,”
“concepts,” are equivocal or rather multivocal. We have seen that
concepts differ widely in their psychological nature according to their
degree, having but one characteristic in common—that of being extracts.
It is therefore chimerical to attempt to include them all under a single
definition. To take the highest only, as most frequently debated, some
say, “There are no general ideas but only general terms.” To others the
general idea is only an indefinite series of particular ideas, or “a
particular idea that the mind proposes as the first stake in a forward
march.”[88] To others it is a system of tendencies accompanied or not by
the possibility of images.[89] For my own part I prefer the formula of
Höffding[90]: “General ideas exist therefore in the sense that we are
able to concentrate the attention on certain elements of the individual
idea, so that a weaker light falls on the other elements.”

This is the sole mode of existence that can be legitimately conceded to
them.

In regard to the higher concepts we have endeavored to show that they
have their distinctive psychological nature: on the one hand a clear
and conscious element which is always the word, and sometimes in
addition the fragmentary image; on the other an obscure and unconscious
factor,—without which, nevertheless, symbolic thought is only a mechanism
turning in the air, and producing naught but phantoms.




CHAPTER V.

EVOLUTION OF THE PRINCIPAL CONCEPTS.


After this general study of the nature of the most elevated forms of
abstraction, we must take the principal concepts one by one, and retrace
their evolution in outline. Let us once more note that we are concerned
with pure psychology, and are to eliminate all that depends on the
theory of knowledge and other transcendental speculations. As regards
the _first_ origin of our notions of time, space, cause, etc., each may
adopt the opinion that pleases him. Whether we admit the hypothesis of
_à priori_ forms of the mind (Kant), or that of an innate sense acquired
by repetition of experience in the species, and fixed by heredity in
the course of centuries (Herbert Spencer), or any other whatsoever—it
is clear that the appearance of these concepts, and the data of their
evolution, depend on experimental conditions, and consequently fall
within our province. Accordingly it is with their empirical genesis, and
development through experience, that we are concerned—and with that alone.


SECTION I. CONCEPT OF NUMBER.

The lower phases of this concept are already known to us. We have
traversed them in considering numeration, in brutes, children, and
aborigines. And here we return to it finally under its higher aspects.

At the outset, counting was, as we found, merely the perception of a
plurality; abstraction being practically at zero. Later on a rudiment of
numeration appeared, under a practical concrete form: we have perception
plus the word—a poor auxiliary, whose part is so insignificant as to
be mostly negligible. We noted the different stages of this concrete
abstract period, marked by the increasing importance of the word.
Finally we arrived at the point at which it is the prime and almost
the only factor. Number under its abstract form, as it results, from a
long elaboration, consists in a collection of unities that are, or are
reputed, similar. We have therefore first to examine how the idea of
unity is formed. Next by what mental operation the sequence of numbers is
constituted, lastly what is the part played by the sign.

I. To common sense nothing appears more easy than to explain how the idea
of unity is formed. I see a man, a tree, a house; I hear a sound; I touch
an object; I smell an odor, and so on: and I distinguish this single
state from a plurality of sensations. John Stuart Mill seems to admit
that number (at least in its simplest forms) is a quality of things that
we perceive, as white, black, roundness, hardness: there is a distinct
and special state of consciousness corresponding to one, two, three, etc.

Even if we admit this very doubtful thesis, we should arrive at last only
at _perceived_ numbers, with which consistent and extended numeration is
impossible. It can only be carried on with homogeneous terms, i. e., such
as are given by abstraction.

The notion of unity must however find its point of departure in
experience, at first under a concrete form; Although it may enter
consciousness by several doors, some psychologists, with no legitimate
reason, have attributed its origin to one definite mode of external, or
even internal, perception which they have chosen to the exclusion of all
others.

For some, it is the primordial sense, _the_ sense _par excellence_;
touch. The child regards as a unity the object which it can hold in its
hand (a ball, a glass), or follow uninterruptedly in all its boundaries.
Wherever his operations are interrupted, where there are breaks of
surface continuity, he perceives plurality. In other terms unity is the
continuous, plurality is the discontinuous. Numerous observations prove
that children actually have a far more exact and precocious notion of
continuous quantity (extension), than of discontinuous, discrete quantity
(number).[91]

For others, it is sight, for which all that was said above may obviously
be repeated. The retina replaces the cutaneous surface: an image
clearly perceived without discontinuity is the unity; the perception of
simultaneous images leaving intermediate lacunæ in the field of vision,
gives plurality.

The same may be said of the acoustic sensations. Preyer, in a work
on “Arithmogenesis,” claims that “hearing takes first rank in the
acquisition of the concept of number.” Number must be felt before it is
thought. Ideas of number and of addition have to be acquired, and this,
according to him, takes place in the child when it hears and compares
sounds. Subsequently, touch and sight complete this first outline. It
is known that Leibnitz assimilated music to an unconscious arithmetic.
Preyer reverses the proposition and says: _Arithmetica est exercitium
musicum occultum nescientis se sonos comparare animi._[92]

As against those who seek the origin of the idea of unity in external
events, others attribute it to internal experience.

Thus it has been maintained that consciousness of the ego as a monad
which knows itself, is the prototype of arithmetical unity. Obviously
this assertion is open to numerous objections. To wit, the late formation
of the notion of the ego, the fruit of reflexion; its instability,—still
more, this unity, like all the preceding, is concrete, complex; it is a
composite unity.

The thesis of W. James is very superior: “Number seems to signify
primarily the strokes of our attention in discriminating things. These
strokes remain in the memory in groups, large or small, and the groups
can be compared. The discrimination is, as we know, psychologically
facilitated by the mobility of the thing as a total.... A globe is one if
undivided; two, if composed of hemispheres. A sand heap is one thing, or
twenty thousand things, as we may choose to count it.”[93] This reduction
to acts of attention brings us back definitely to the essential and
fundamental conditions of abstraction.

Save this last, the hypotheses enumerated (and internal sensation
might also have been invoked; e. g., a localised pain as compared with
several scattered pains) give only percepts or images, i. e., the raw
material of abstract unity. This is itself a subjective notion. We said
above (Chapter II) that the question whether consciousness starts from
the general or the particular is a misstatement, because it applies
to the mind which is in process of formation, categories valid only
for the adult intelligence. So here. At the outset there is no clear
perception of primary unity and subsequent plurality, or _vice versa_:
neither observation nor reasoning justifies an affirmation. There is a
confused, indefinite state, whence issues the antithesis of continuous
and discontinuous, the primitive equivalents of unity and plurality.
It took centuries to arrive at the precise notion of abstract unity as
it exists in the minds of the first mathematicians, and this notion is
the result of a _decomposition_, not of any direct and immediate act
of postulation. It was necessary to decompose an object or group into
its constituent parts, which are or appear to be irreducible. Then a
new synthesis of these parts was required to reconstitute the whole, in
order that the notion of relation between unity and plurality should be
perceived clearly. It cannot be doubted that for the lesser numbers two,
three, four, the successive perception of each separate object, and then
of the objects apprehended together at a single glance, has aided the
work of the mind in the conception of this relation. We have seen that
many human races never passed beyond this phase. The abstract notion of
unity is that of the indivisible (provisory). It is this abstract quality
of the indivisible, fixed by a word, that gives us the scientific idea of
unity as opposed to the vulgar notion. Perceived unity is a concrete,
conceived unity is a quality, an abstract; and in one sense it may be
said that unity, and consequently all abstract number, is a creation of
the mind. It results like all abstraction from analysis—dissociation.
Like all abstraction, it has an ideal existence; yet this in no way
prevents it from being an instrument of marvellous utility.

II. It is owing to this that the sequence of numbers, homogeneous
in material, can be constituted; for the identity of unities is the
sole condition in virtue of which they can be counted, and the scant
numerations of the concrete-abstract period transcended. The sequence
is constituted by an invariable process of construction, which may be
reduced to addition or subtraction. “Thus the number 2, simplest of
all numbers, is a construction in virtue of which unity is added to
itself; the number 3 is a construction in virtue of which unity is
added to the number 2, and so on in order. If numbers are composed by
successively adding unity to itself, or to other numbers already formed
by the same process, they are decomposed by withdrawing unity from the
previously constructed sums; and thus, to decompose is again to compose
other numbers. For example, if 3 is 2 + 1, it is also 4 - 1. Addition
and subtraction are two inverse operations whose results are mutually
exclusive: they are the sole primitive numerical functions.”[94]

The simplicity and solidity of this process result from its being always
identical with itself, and although the series of numbers is unlimited,
some one term of the sequence is rigorously determined, because it can
always be brought back to its point of departure, unity. In this labor of
construction by continuous repetition, two psychological facts are to be
noted:

1. No sooner is unity passed, in the elaboration of numbers, than
intuition fails altogether. Directly we reach 5, 6, 7, etc, (the limit
varies with the individual), objects can no longer be perceived or
represented together: there is now no more in consciousness than the
sign, the substitute for the absent intuition: each number becomes a sum
of unities fixed by a name.

2. For our unity-type we substitute higher unities, which admit of
simplification. Thus in the predominating decimal system, ten and a
hundred are unities ten and a hundred times larger than unity, properly
so called. They may be of any given magnitude: the Hindus, whose
exuberant imagination is well known, invented the _koti_, equivalent
to four billions three hundred and twenty-eight millions of years, for
calculating the life of their gods; each _koti_ represents a single day
of the divine life.[95]

Inversely, we may consider the unity-type as a sum of identical parts,
and represent 1 = 10/10 or 100/100, etc. A tenth, a hundredth, are
unities ten times, a hundred times, smaller than unity properly so
called, but they obey the same laws in the formation of fractional
numbers.

It is well for the psychologist to note the privileged position of
what we term the unity-type, or simply 1. It originates in experience,
because unity, even when concrete, and apprehended by gross perception,
appears as a primitive element, special and irreducible. So long as the
mind confines itself to perceiving or imagining, there is in the passage
from one object to two, three, or four objects, or inversely in the
passage from four objects to three, two, or only one, an augmentation or
diminution. But below unity in the first case, and above unity in the
second, there is no longer any mental representation; unity seems to
border on nonentity and to be an absolute beginning.

From this privileged point the mind can follow two opposite directions,
by an identical movement: the one towards the infinitely great, with
constant augmentation; the other towards the infinitely small, with
constant diminution—but in one sense or the other, infinity is a never
exhausted possibility. Here we reach the much disputed question of
infinite number: psychology is not concerned with this. For some,
infinite number has an _actual_ existence. For others, it only exists
potentially, i. e., as an intellectual operation which may, as was said
above, add or subtract, without end or intermission.[96]

III. The importance of signs, as the instruments of abstraction
and generalisation, is nowhere so well shown as in their multiple
applications to discrete or continuous quantity. The history of the
mathematical sciences is in part that of the invention, and use of
symbols of increasing complexity, whose efficacy is clearly manifested
in their theoretical or practical results. In the first place, words
were substituted for the things that were held to be numerable; next,
particular signs, or figures; later still, with the invention of algebra,
letters took the place of figures, or at any rate assumed their function
and part in the problem to be solved; later still, the consideration of
geometrical figures was replaced by that of their equations; finally,
the use of new symbols corresponded with calculations for infinitesimal
quantities, negative quantities, and imaginary numbers.

These symbols are such a powerful auxiliary to the labor of the
mathematicians that those among them who affect philosophy have gladly
discoursed upon their nature and intrinsic value. They seem to be divided
into two camps.

One faction attribute reality to the symbols, or at least incline that
way. It is the introduction of the _nomina numina_ into mathematics. They
maintain that these pretended conventions are only the expression of
necessary relations which the mind is obliged, on account of their ideal
nature, to represent by arbitrary signs, but which are not invented by
caprice, or by the necessity of the individual mind—since this contents
itself with laying hold of that which is offered by the nature of the
things. Do we not see moreover that the labor accomplished by their aid
is, with necessary modifications, applicable to reality?

To the other, symbols are but means, instruments, stratagems. They mock
at those who “look upon relations once symbolised as things which have
in themselves an _à priori_ scientific content, as idols, which we
supplicate to reveal themselves” (Renouvier). Signs, whatever they may
be, are nothing more than conventions: negative quantities represent
a change in the direction of thought. Imaginary numbers “represent
important relations under a simple and abridged form.” Symbols are an
aid in surmounting difficulties, as, empirically, the lever and its
developments serve for the lifting of weights. “It is not calculation,”
said Poinsot, “that is the secret of this art which teaches us to
discover; but the attentive consideration of things, wherein the
intellect seeks above all to form an idea of them, endeavoring by
_analysis_ properly so called to decompose them into other more simple
ideas, and to review them again subsequently as if they had been formed
by the union of those simpler things of which it had full knowledge.”[97]

In sum: numbers consist in a series of acts of intellectual apprehension,
susceptible of different directions, and of almost unlimited
applications. They serve for comparison, for measurement, for putting
order into a variety of things. If we compare now the two extremes,—viz.,
the first attempt at infantine numeration and the highest numerical
inventions of the mathematician,—we must recognise the notion of
number to be a fine example of the complete evolution of the faculty
of abstraction, as applied to a particular case, the principal stages
of which we have been able to note in bringing out the ever-increasing
importance of signs.


SECTION II. THE CONCEPT OF SPACE.

The idea of space has given rise to so many theories that it is difficult
to restrain ourselves within the strict limits of psychology, and of
our particular subject. Whether or no this concept be innate, given _à
priori_ or derived from our cerebral constitution, we have here—setting
aside all question of origin—only to inquire by what ways and means we
attain full consciousness of it and determine it to be a fundamental
concept.

In order to follow its development we must necessarily set out from
experience; since space, like number or time, is perceived before it is
conceived. For the sake of clearness and precision, let us designate the
primitive concrete data, the result of perception, as _extension_, and
the concept, the result of abstraction, as _space_—properly so called.

I. At the outset what is given us by intuition is extension under a
concrete form. What first becomes known to us is not space but a limited
and determined extension—what the child can hold in its hand, reach by a
movement of its arms, later on the room which it crosses with uncertain
steps; it is a street, a square traversed, a journey made by carriage or
by train, the horizon which the eye embraces, the nebulæ vaguely seen in
the nocturnal sky, etc. All this is concrete and measurable, and can be
reduced to a measure, i. e., to a concrete extension such as the metre
and its fractions.

These different extensions, although given by the senses, and therefore
concrete, are already abstract; since they co-exist with other qualities
(resistance, color, cold, heat, etc.) from which a spontaneous analysis
separates them, in order to consider them individually. This analysis is
translated by the common terms, long, short, high, deep, near, far, to
the right, to the left, in front, behind, etc.

By a simplification which occurred much later (for it implies the
foundation of geometry) this somewhat confused and incoherent list is
replaced by a more rational analysis: height, breadth, depth, distance,
position. It marks the transition from the concrete-abstract to the
abstract period. It is in fact certain that before constituting itself
as a science founded upon reasoning, geometry traversed a semi-empirical
stage, it was born of practical needs—the necessity of measuring fields,
building houses, and the rest. Moreover certain great mathematicians
have by no means disdained to admit its relations with experience: Gauss
called it the “science of the eye,” and Sylvester declared “that most if
not all the chief ideas of modern mathematics originated in observation.”

Let us, without insisting further, recollect that extension is given us
by touch and sight. Touch is _par excellence_ the sense of extension:
thus geometry reduces the problems of equality or inequality to
superpositions, and all measure of extension is finally reducible to
tactile and muscular sensations. The terms touch and vision ought in
fact to be completely co-extensive, representing not merely a passive
impression upon the cutaneous surface, or the retina, but an active
reaction of the motor elements proper to the sensorial organs.

The term _acoustic_ space has recently come into use. Much work has been
done on the semi-circular canals, leaving no doubt as to the part they
play in the sense of bodily equilibrium;[98] some authors have even
localised a “space-sense” in them. Münsterberg relates from his personal
experience that while the vestibule and the cochlea receive excitations
whence result the purely qualitative sensations of sound (height,
intensity, etc.), the semi-circular canals receive others which depend
upon the _position_ of the source of the sound: these excitations would
produce reflexes, probably in the cerebellum, the purpose of which would
be to bring the head into the position best adapted for clear audition.
The synthesis of sounds, of the modifications perceived in the canals,
and of the aforesaid movements (or images of movement) would constitute
the elements of an acoustic space. Wundt, who opposes this theory, sees
nothing more in the semi-circular canals than internal tactile organs,
auxiliary to external touch.[99]

Leaving this hypothesis of acoustic space (which is by no means
well-established), we know from numerous observations that the different
modalities of tactile and visual extension, notably that of distance, are
only known with precision after much groping and long apprenticeship.[100]

Extension under all its aspects, whether perceived or imagined, presents
according to constitution, age, or circumstances, a character of
variability which is in complete contrast with the stability and fixity
of the concept of space. The conditions of this relativity have been
exposed at length by Herbert Spencer. “A creature without eyes cannot
have the same conception of space as one that has eyes; and it is the
same with the congenitally blind as compared with those who are in full
possession of their eyesight; and for the creature whose locomotion is
rapid and powerful as compared with the creature which moves slowly
and painfully.” Our bodily bulk and organic dimensions also affect
conceptions of space; distances which seemed great to the boy seem
moderate to the man, and buildings once thought imposing in height and
mass dwindle into insignificance. Without speaking of nervous subjects,
who illusively imagine their bodies enormously large or infinitely
small, there are also transient and momentary states of the organism
which considerably modify the consciousness of space; thus, De Quincy,
describing some of his opium dreams, says that “buildings and landscapes
were exhibited in proportions so vast as the bodily eye is not fitted to
receive. _Space swelled_, and was amplified to an extent of unutterable
infinity.”[101] “Deliberate analysis of their movements,” says Lotze,
“is so little practised by women that it can be asserted without fear of
error that such expressions as ‘to the right,’ ‘to the left,’ ‘forwards,’
‘backwards,’ etc., express in their language no mathematical relations
whatever, but merely certain particular feelings which they experience
when during work they perform movements in these directions.”[102] In
fine, the consciousness of concrete extension varies in quantity and
quality with the structure, position, age, and momentary condition of
the feeling subject.

II. Starting from these concrete data—extension as included in our
perceptions—how does the intellect arrive at the abstract notion of space?

The immense majority of men left to their own resources do not rise above
a confused notion, half-concrete, half-abstract, of the properties of
extension, and what Lotze says (_supra_) applies even better to their
total idea of space-relations. The fundamental conception in such minds
is simply the possibility of going very far in all directions, or of
placing a succession of bodies one behind the other. As to limit, this
operation remains vaguely undetermined. It is however translated into
current parlance, e. g., “bodies are in space,” and other analogues.
Space is conceived, or rather imagined, as an immense sphere which
encloses everything, as the receptacle of all extension. It contains
bodies, as a barrel holds wine. The primitive cosmologies which yet
demand a certain development of reflexion and of abstraction reveal the
nature of this conception to us when they speak of the circle of the
horizon, the vault of heaven, the firmament (a kind of _firm_ enclosure),
and other expressions which denote belief in an insurmountable limit.
This conception, which is wholly imaginative at bottom, is a fine example
of abstraction elevated into an entity, and the phantom thus created
becomes in its turn the source of idle or badly-stated problems such as
the following.

‘We have never,’ contends J. S. Mill, ‘perceived an object, or a portion
of space, without there being space beyond it, and from the moment
of our birth we have always perceived objects or parts of space. It
follows from this that the idea of an object or part of space must be
inseparably associated with the notion of a further space beyond it.
Each moment of our life tends to rivet this association, no experience
has ever interrupted it. Under the actual conditions of existence, this
association is indissoluble.... Yet we can conceive that, given other
conditions of existence, it might be possible to transport ourselves
to the limits of space, and that after there receiving impressions of
a kind totally unknown to our present state, we might instantly become
capable of conceiving the fact and of stating the truth of it. After some
experience of the new conception, the fact would seem as natural to us as
the revelations of sight to the blind man whose cure is of long standing.’

This argument is founded upon an equivocation. Mill appears to admit
as the basis of his discussion the semi-concrete, semi-abstract notion
of space, described above; namely, that of common sense. Consequently
he confounds and mixes up two perfectly distinct questions; that of
Extension, the concrete fact perceived or imagined, and Space, abstract
and conceived. In the case of the former, the problem is cosmological and
objective, and we are not concerned with it; it is, under another form,
the repetition of the discussion on infinite number,—are we, or are we
not, to admit a continuous, real magnitude? In the latter, the problem
is psychological, subjective, relative to abstraction alone, and will be
answered later on.

Up to this point, in fact, the concept of Space corresponds to the state
of evolution that we have so frequently denoted as concrete-abstract.
The true concept of space—of purely abstract space—was only constituted
when the geometricians (Greek and otherwise) disengaged from different
extensions those essential features which they termed dimensions, showing
by their science that elements thus abstracted and considered separately
can be substituted for all the rest. Stallo justly observes that the
geometrical elements are neither real, nor ideal, nor hypothetical;
they are _conceptual_, the result of abstraction. “In the processes of
discursive thought the intellect never has before it either sensible
objects or the whole complement of relations which make up their mental
images or representations, but only some single relation or class of
relations. It operates along _lines_ of abstraction, the final synthesis
of whose result never yields anything more than outlines of the objects
represented. During all its operations the intellect is fully aware
that neither any one link in the chain of abstraction nor the group
of abstract results which we call a concept (in the narrower sense
of a collection of attributes representing an object of intuition or
sensation) is a copy or an exact counterpart of the object represented.
It is always conscious that to bring about true conformity between
concepts or any of their constituent attributes with forms of objective
reality, the group of relations embodied in these concepts would have
to be supplemented with an indeterminate number of other relations
which have not been apprehended and possibly are insusceptible of
apprehension....”[103]

No one imagines that there are in Nature points, surfaces, lines,
volumes, such as geometry proposes them, nor that its concepts are
copies of these, but it is not therefore necessary to take refuge in the
_à priori_: abstraction suffices, the act, i. e., by which fundamental
qualities are abstracted, to be subsequently fixed by definition. It is
strange that Stuart Mill in his long and untoward discussion of this
subject should content himself with saying that “we have a power, when a
perception is present to our senses, or a conception to our intellect, of
attending to a part only of that perception or conception.”[104] In this
remark upon attention he is very near recognising the rôle of abstraction
(which for the rest he fails to name), but instead of insisting upon it
he returns to his thesis, that “the foundation of all sciences, even
deductive and demonstrative sciences, is induction....”

The concept of space such as the geometers have made it, namely at
its highest degree of abstraction, is thus the result of association.
It is extension emptied of all its constitutive qualities, save the
necessary conventions which determine it. This schema (apart from
all transcendental considerations) appears to us as the total of the
conditions of bodily existence in so far as they are endowed with
extension. Thus constituted, with the marks which are proper to it, and
distinguish it from all others, this concept, like that of number, is
susceptible of multiple application, while moreover it has no assignable
limits in any direction (i. e., according to the time-honored expression,
it is infinite).

Just as concrete number represents real unities or collections, while
abstract number detached from discontinuous realities admits of infinite
numeration; so concrete space (extension) corresponds to the intuition
of certain bodies, while abstract space, by an unrepresentable concept,
if not by words, implies an unlimited extension.

If, hypothetically, it were possible to count all the leaves of all the
trees in the world, this prodigious number corresponding to concrete
unities would be as nothing to the mind that can count for ever beyond
that. So for the extension determined by the movement of our arms or
legs, by days of railway travelling or sailing, by balloon ascensions,
and finally by the most powerful telescopes that can scrutinise the
infinity of the heavens,—in all these concrete, fixed, _measured_
extensions we can always imagine a beyond, because the end of one
extension is the beginning of the next. All that, however, is but the
work of the imagination manipulating abstraction. The law of construction
for infinite space is the same as for infinite number: this infinity is
only in the operation of our mind, it is a pure psychological process;
we believe we are dealing with real magnitudes, and we are only acting
upon our own judgment: we are but adding states of consciousness one
upon another. Space is only potentially infinite, and this potentiality
is in us, and in nothing but ourselves; it is a virtuality which can
neither be exhausted nor achieved. To erect it into an entity is to reify
an abstraction, to attribute an undue objective value to an entirely
subjective concept. The journey to the end of space as suggested by
Stuart Mill in the passage above cited (if by space he means the simple
possibility of containing extended bodies) would really be a journey to
the end of our minds: if he means a journey to the end of the real world,
i. e., determinable and measurable extension—which has no limits beyond
the imperfection of our instruments—then he admits implicitly that the
universe has bounds, he takes sides in a debate in which experimental
psychology (we repeat) sees nothing, and which it is even totally
incompetent to decide.

       *       *       *       *       *

During this century certain illustrious mathematicians,—Gauss, 1792, in
an unpublished work, Lobachévski in 1829, Riemann, Beltrami, Helmholtz
and many others after them, constructed a new geometry known under
various names: astral, imaginary, pangeometric, metageometric, and lastly
non-Euclidean geometry. Its fundamental principle is that our Euclidean
space is only one particular case among several possible cases, and our
Euclidean geometry one species of which pangeometry is the genus—that the
sole determining reason in its favor is that Euclidean geometry alone is
practically applicable to, and verified by, experience. These essays,
beyond their direct interest to mathematicians, have already given rise
to a considerable number of philosophical considerations. While they have
only very distant relations with psychology, they deserve notice, because
they enable us the better to understand the genesis of the concepts of
space, and are moreover a striking proof of the constructive power of the
mind, emancipated from experimental data, and subject only to the rules
of logic.

Our space being of three dimensions, the neo-geometers speculated in the
first place as to the hypothesis of a space of 4, 5, or _n_-dimensions;
later on they chose as their base of operations a space of three
dimensions, considered no longer as plane (Euclidean space) but as
spherical or pseudo-spherical, having, i. e., instead of a zero
curvature, either a positive (spherical space) or a negative curvature
(pseudo-spherical space). Their point of departure is the rejection
of Euclid’s postulate—they do not admit that it is impossible to draw
through a point more than one parallel to a given straight line. In
spherical space there is nothing analogous to the Euclidean axiom of
parallels; in pseudo-spherical space two parallels to a line can be drawn
through any point. In the first hypothesis, the sum of the three angles
of a triangle is greater than two right angles; in the second it is
smaller. Thus by deduction after deduction, the neo-geometers constructed
an edifice very different from ordinary geometry, subject to no other
conditions than that of being free from internal contradiction.

In our connexion, the sole utility of the invention of imaginary
geometries is to have reinforced, as if by a magnifying process, the
distinction between space _perceived_ and _conceived_; this assumes
various forms according to the process of abstraction employed and fixed
in definitions. “Euclidean” space has only one advantage, that it is the
simplest, the most practical, the best adapted to facts: in short, that
which involves the least disparity between the ideal and our experience,
and consequently the most useful. “Certain neo-geometers have in fact
maintained that it is uncertain whether space can, or cannot, have the
same properties throughout the whole universe ... and that it is possible
that in the rapid march of the solar system across space we might
gradually pass into regions in which space has not the same properties as
those we know”; yet this thesis, which, fundamentally, reifies an entity,
does not seem to have gained many partisans. Stallo criticises it at
length (_op. cit._, Chap. XIII).

There is no agreement as to the measure in which the new concepts
agree or disagree with the theory of space, “the _à priori_ form of
sensibility.” Some hold them to be indifferent, others to be unfavorable
to Kantism: this discussion which, for the rest, does not concern us is
still in progress.

       *       *       *       *       *

In conclusion, extension is a primary datum of perception and cannot be
further reduced: it is multiple, full, heterogeneous, continuous (at
least in appearance), variable, perhaps finite; while space (concept) is
void, unified, homogeneous, continuous, and without limits.

Many men and races never get beyond this stage of concrete
representation, which corresponds with the first moment of evolution in
the individual and in the species. The first step towards the concept of
space (concrete-abstract period) consists in representing it to oneself
as the place, the receptacle of all bodies. This is the direct result
of primitive reflexion: image rather than concept, to which the mind
attributes an illusive reality.

The true concept, resultant of abstraction, has been the elaboration of
geometricians. It is actually constituted by a synthesis of abstracts or
extracts which are, according to Riemann, size, continuity, dimension,
simplicity, distance, measure. This synthesis or association of abstracts
has nothing necessary about it; its elements may be combined in several
ways; hence the possibility of different concepts of space (Euclidean,
non-Euclidean). Space conceived as infinity reduces itself to the power
that the human mind has of forming sequences, and it forms them thanks
to abstraction, which admits of its seizing the law of their formation.

Intuition is the common basis of all concepts of space. Euclidean space
rests directly upon this, and upon definitions. Non-Euclidean space rests
directly upon it, but more particularly upon definitions.

Although inapplicable to the real world, these last—which are
constructions in which the mind is submitted to no other laws than
agreement with itself—are brilliant examples of the power of abstraction,
when it attains its highest degree of development.


SECTION III. THE CONCEPT OF TIME.

In evolving the idea of time, as in that of space, we must first examine
the concrete fact which is its starting-point, i. e., real _duration_;
next the concept which is extracted from it, time _in abstracto_—and this
must be followed in the successive stages of its development.


I.

Real, concrete duration is a quality known by itself, included among
internal and external sensations, as later on in the representations
which psychology, in what concerns it, must accept as an ultimate datum.

What is this concrete duration, furnished by experience? It might
strictly be said to be the present; yet this answer is somewhat
theoretical, for it must be admitted that what we term “the present” has
vague and fluctuating limits. Moreover, its clear and precise distinction
from what has preceded and what is to follow it—the past and the
future—is a somewhat late production. Of this we have objective witness
(see Ch. II.) in primitive languages, during the period in which the
value of the verbs was undetermined. Take again the fact, as frequently
observed, that children even at the age of three, or older, having
vague notions of past and future, make a general confusion, and do not
distinguish between “yesterday” and last week, between “to-morrow” and
next week (Sully).

Still, we must admit that the present has the privilege of appearing
in consciousness as the typical duration, the standard, the measure to
which everything must be referred. Nor can this be otherwise, seeing
that (as is too often forgotten) we live only in the present; that the
past and the future have no existence for us, are only known to us under
the condition of becoming present, of occupying _actual_ consciousness.
The present is the only psychical element, which, consciously or
unconsciously, gives a content and reality to duration.

It is essential to rid ourselves of the opinion accredited by many
authors, that the present is only an elusive moment, a transition,
a passage, a flash, a mathematical point, a zero, a nullity; on the
contrary—it alone has duration, is now long, now short. It is even
possible, to some extent, to determine its limits, and to transcend
this vague description. Here we are aided by the labors of the
psycho-physicists. We may say that this study, long restricted to
metaphysical dissertations, entered upon a positive phase with Czermak,
who (in 1857) opened out a new line, in which he has been followed by
many others. The numerous researches and experiments made upon the
“sense of time” may be omitted without prejudice to our subject, while
the discussion of them would deter us from our principal aims. We
must, however, give a rapid summary of those which relate either to the
actual perception of duration, or to the reproduction in memory of past
duration.[105]

1. This present, declared to be inapprehensible, has however been
determined as regards its _minimum_ duration. For the discrimination
period between two different sensations (taken as the type of the
briefest and simplest psychical act), Kries and Auerbach found durations
varying between 0·01 and 0·07 second with an average of 0·03 second. At
a later period, Exner, experimenting with Savart’s wheel, stated that
the interval at which two successive taps can be perceived separately
may be reduced to 0·05 second: as also for the sound produced by two
electric sparks. For the eye, the minimum perceptible interval between
two impressions falling on the yellow spot, is 0·044 second. Below this,
one of the conditions necessary to consciousness—an adequate duration—is
wanting.

Certain experiments contributed by Wundt and his pupils throw light also
upon the _maximum_ duration that can be apprehended by consciousness.
They made use, almost exclusively, of auditory sensations, which are more
closely allied than any others to the sense of time. Wundt finds that
twelve impressions equivalent to a duration varying from 3·6 to 6 seconds
can be clearly perceived to form a group. Dietze admits the continuous
perception of 40 beats of the metronome, provided the mind arranges them
spontaneously in 5 sub groups of 8, or 8 sub-groups of 5. Total duration:
12 seconds. Others vary in their conclusions from 6 to 12 seconds and
even more.[106] James is inclined to think that the actual present may
extend to a _minute_.

Of course these figures, of which we can only give a few, vary with the
subjects, quality of the impressions received, conditions of experience,
exercise, etc. Nor must we forget that these laboratory researches are
somewhat artificial, and concerned with the perception of “the present”
under studied conditions of simplicity which are not precisely those of
spontaneous consciousness. Still it is plain that “the present” is by
no means an abstraction, a nothing, and we may conclude, in the words
of James, “by saying that we are constantly conscious of a certain
duration—the specious, present—varying in length from a few seconds
to probably not more than a minute, and that this duration (with its
content perceived as having one part earlier and the other part later)
is the original intuition of time. Longer times are conceived by adding,
shorter ones by dividing, portions of this vaguely broached unit, and are
habitually thought by us symbolically.”[107]

2. Experiments relating, not to consciousness of actual duration, but
to the _reproduction_ of durations, and determination of the errors
involved, are numerous, and contradictory. I refer to them in passing
only because they are eminently suited to show the very relative and
precarious character of our concrete notions of duration.

Through all divergencies, the formula enunciated by Vierordt, the
principal initiator of these researches, remains stable; our
consciousness of time comes, not from a sensation, but from a judgment,
and in our retrospective appreciation of duration, we diminish intervals
that are long, and increase those that are short. The debates and
disagreements of the experimenters relate above all to the determination
of the “indifferent point.” Vierordt denoted by this term the interval
of time which we appreciate the most exactly, which we have no tendency
to lengthen or abridge, so that if we are required to repeat it
experimentally, the error is nil, or very rare. This duration, reproduced
according to reality, is 0·35 sec. (according to Vierordt and Mach); 0·4
sec. (Buccola); 0·72 sec. (Wundt); 0·75 sec. (Kollert); 0·71 sec.; etc.
According to another author, Glass, there is a series of points at which
we find maximum relative accuracy; 1·5 sec., 2·5 sec., 3·75 sec., 5 sec.,
6·25 sec., etc. Münsterberg again criticises the entire series of figures
and experiments, for reasons that will be given below.

Independent of these experiments, which are restricted to very simple
events, the facts of our daily life show to superabundance that our
memory of duration is almost always inexact. Thus it has often been
remarked that the years seem to be shorter with advancing age: which is
again an instance of abbreviation of the longer intervals.[108] It is
hardly necessary to say that our appreciation of duration (concrete),
like that of extension (concrete), depends upon multiple conditions, and
varies with these. Such are pre-eminently constitution and temperament:
compare a phlegmatic with a nervous individual; an Oriental for whom
time is not, with an Occidental, agitated by a feverish existence. Add
to these, age, number, and vivacity of impressions received, certain
pathological states, etc., and we find here, as for space, that the
variability of concrete knowledge is opposed to the fixity of the concept.

This consciousness of duration, fluctuating, variable, and unstable as
it may be, is nevertheless the source whence our abstract notion of time
is derived: but whence comes it, itself? Where does it originate? “Time
has been called an act of mind, of reason, of perception, of intuition,
of sense, of memory, of will, of all possible compounds and compositions
to be made up from all of them. It has been deemed a General Sense
accompanying all mental content in a manner similar to that conceived of
pain and pleasure.”[109]

Here are many answers. We may add that among these supposed origins some
authors admit only one, to the exclusion of the rest, though nothing
justifies them in such arbitrary selection.

Some prefer _external_ sensations, inasmuch as they give us the
consciousness of a sequence. Hearing has been termed the sense of time
_par excellence_. This thesis has notably been sustained by Mach:[110]
since in a melody we can separate the rhythm from the sounds which
compose it, he concludes that rhythm forms a distinct sequence, and that
there must be in the ear, as in the eye, a mechanism of accommodation
which is perhaps the organ of the “time-sense.” Others decide in favor
of the general sense, touch, capable in all animals of receiving a
succession of impressions at once distinct and forming a series. Sight,
with its fine and rapid perception of movements and changes, is an
organ admirably adapted to the formation of relations of sequence, the
constitutive elements of time. Were not, moreover, the first essays at
determining time (succession of days and nights, seasons, etc.) founded
upon visual perceptions?

The majority of contemporary psychologists are, however, inclined
with reason to seek the principal origin of the notion of duration
in _internal_ sensations; and these derive their prerogative from
the primordial and rhythmical nature which pertains to the principal
functions of life.

“A stationary creature,” says Herbert Spencer, “without eyes, receiving
distinct sensations from external objects only by contacts which happen
at long and irregular intervals, cannot have in its consciousness any
compound relations of sequence save those arising from the slow rhythm
of its functions. Even in ourselves, the respiratory intervals, joined
sometimes with the intervals between the heart’s pulses, furnish part of
the materials from which our consciousness of duration is derived; and
had we no continuous perceptions of external changes, and consequently
no ideas of them, these rhythmical organic actions would obviously yield
important data for our consciousness of Time: indeed, in the absence of
locomotive rhythms, our sole data.”[111]

“Rhythm,” to quote Horwicz, “is the measure, and the sole measure, of
time; a being incapable of regular periodic intervals could not attain to
any conception of time. All the rhythmic functions of the body subserve
this end: respiration, pulse, locomotor movements, hunger, sleep, work,
habits and needs of whatever kind.”—Guyau maintains essentially the same
thesis, under a more metaphysical aspect: “Time is embryonically in
primitive consciousness; under the form of force and effort; succession
is an abstraction of motor effort, exerted in space. The past is the
active become passive.”[112]

More recently, Münsterberg[113] has attributed a preponderant and almost
exclusive part to respiration. Although he affirms that the origin of
our notions of duration must be sought in our consciousness of muscular
effort in general, and that its primitive measure lies in the rhythm
of the bodily processes; yet the gradual rise and fall of the sense of
effort which accompanies the two phases of the respiratory function
(inspiration, expiration) seem to him the principal source of our
appreciation of duration. After a rather sharp criticism of the attempts
of his predecessors (which we have already reviewed) to determine the
“indifferent point,” he maintains that their disagreements were caused by
incomplete comprehension of the psychical events produced in the course
of experience. In the perception of the successive beats of a metronome,
or taps of Wundt’s electric hammer, only the auditory impressions are
attended to; this is a mistake. It is supposed that the sensation-limits
form the entire content of consciousness, and that the intervals between
them are empty. On the contrary, they are filled by an act of attention.
We are conscious of a process of variable tension which, from the
initial moment, goes decreasingly towards zero, and then rises again, to
adapt itself to the sonorous impression that should follow it. In other
words, there are, in the perception of three successive taps, not three,
but _five_ states of consciousness: three external and two internal
sensations. We must reckon thus if we are rigorously to determine the
_psychological_ conditions of experience. As evidence, Münsterberg brings
forward the following results, which are from his own experiments.

The “normal time” is first determined, i. e., the standard of duration
that should be reproduced by the experimenter as exactly as possible
(“time of comparison”).

In one case, different durations were given, such as 15, 7, 22, 18 secs.,
etc., without attending to the respiration (expiration or inspiration)
of the subject, who reacted independently of it. In the reproduction of
normal time, the mean error was 10·7 per cent.

In the second case, the same numbers were given again, but care was taken
that the subject began his estimation at precisely that respiratory
period which coincided with the beginning of the normal time. The mean
error did not now exceed 2·9 per cent.

In the two cases cited, there was no interruption between the
determination of the normal time and its reproduction; the two operations
succeeded each other immediately. If, on the contrary, a short pause, or
arrest, was introduced between the two, varying from 1 to 60 seconds, the
results are—proceeding at random as in the first case—a mean error of 24
per cent.; as in the second, a mean error of 5·3 per cent.

Münsterberg has been not unreasonably reproached for attributing to
respiration, among all the other internal sensations, the exclusive
privilege of measuring time. A less justifiable criticism asserts that
his thesis is devoid of value because we can appreciate the variations
in duration in the beats of a clock more readily than the changes in the
rhythm of respiration. This is confounding two distinct factors in the
genesis of the idea of duration: its period of formation and its period
of constitution; that which occurs at the commencement, and that which
takes place in the adult. Our measure is at first subjective, variable;
progress consists in the substitution of a fixed, objective measure.
Doubtless, the latter is superior in clearness and in precision; yet this
is no proof, not even presumption, that it is first in order: we shall
return to this point later on.

In short, our consciousness of duration is a complex state, more exactly,
a process—since it is less a state than a becoming. The rhythmical
visceral sensations are its core; it is an internal chronometer, fixed
in the depths of our organisation. Around this subjective element, other
objective elements are added and co-ordinated—the regular sequences which
are caused by external sensations. They form the sheath of the core, and
constitute the sensible portion of our consciousness of duration, not,
however, its totality.


II.

Until now we have considered time under its concrete form alone, whether
given as an actual event in consciousness, or revived as a past event
in memory. We have now to follow the complete development of this idea
to its extreme limit. In this study we may conveniently distinguish two
stages:

The first, which depends on memory and imagination, consists in thinking
a certain extension of duration, that may be more or less vaguely
represented: a day, a week, a year, etc.

The second, which depends on abstraction alone, gives time in general,
the pure concept, which cannot be represented, and is determined by signs
alone.

FIRST STAGE.—Certain minds never get beyond this first stage. In respect
of time, this corresponds to the lower forms of abstraction which we
have so often designated by the terms, _generic image_ and, at a higher
degree, _concrete-abstract notions_ (intermediate abstracts).

The lowest form, which is just higher than the recognition of concrete
duration, results like the generic image from the repetition of a
sequence of events that recur constantly, and are approximately uniform.
They are series of which the terms are variable, but which begin and end
always in the same manner. Such are the appearance and disappearance of
the sun, lying down to sleep and waking up again, and similar facts of
common life. The points of departure, the start and finish, are always
the same, whatever the variations in the intermediate states. These
generic images are met with among the higher brutes, children, and
primitive races.

To what extent are the higher animals capable of having a certain
representation of time, constructed from their experience of real
duration? This is an obscure problem which has been little studied. We
are not of course referring to time _in abstracto_, to the concept, but
to the recognition of certain often repeated cycles. Many animals are
known to have an approximate appreciation of sufficiently protracted
periods, supplied by the periodicity of their needs (hours at which they
get food, are taken out, etc., etc.). Prejudice apart, we know of others
which, in addition to this subjective physiological knowledge, possess a
fairly exact notion of certain regular and objectively caused periods,
determined by the progress of natural phenomena, especially by the path
of the sun.[114]

In all these instances we may assign as cause, the incontestable
preponderance (in animal life) of automatism and of routine: which is
equivalent to saying that the notion of these durations is formed by a
passive assimilation, and this—as we have seen—is the creative process of
generic images.

According to some authors, there are instances of exact appreciation
of much less simple periods. Brehm says that during a long passage
an ourang-outang visited the sailors every Wednesday and Friday at 8
o’clock, because on those days sago, sugar, and cinnamon were served
out, of which he got his share. An anecdote has often been cited after
Romanes, of “the geese who came regularly every fortnight, from afar, the
morning after the market, in a small English town, to pick up the corn
scattered on the marketplace. One year the market was postponed for a day
of national humiliation, but the geese came as usual.”[115]

These and other analogous facts seem scarcely sufficient in number, nor
strictly enough observed, to warrant any scientific conclusion.

We have previously remarked that, up to the age of three years or more,
children who already have an approximate knowledge of space relations,
(distance, proximity, within, without, upper, lower, etc.) have a very
confused notion of periods as short as three to four days, a week, etc.
It has been hypothetically suggested that the extension of the notion of
duration must for them arise in expectation rather than in memory, in an
orientation towards the future rather than the past.

The concrete-abstract period with its different degrees, limited on the
one extreme by generic images, on the other by the pure concept, is met
with among savage races, and in rising civilisations. It is a stage that
has to be traversed by every human race; many now existing have not
got beyond it. Days (solar revolution), months (lunar revolution), and
seasons, the round of the changing aspects of nature, give the primitive
and simplest notions of time in extension. No tribe is so low in the
scale as not to have reached this level. The determination of the (solar)
year, even when only approximate, marks a decisive progress.

The peculiar feature of this period, in its lowest degrees, is that
the notion of time cannot as yet be separated, or extracted, from the
sequence of events. We have already given many examples of this state of
intelligence. It is not poetical feeling that makes the savage reckon
the age of his children by the flowering of certain plants (and other
analogous locutions abound among primitive races,)—nor any innate taste
for metaphor: it is merely that he requires concrete marks to determine
duration. He cannot think the longer periods _in abstracto_; they must
be imagined, represented in virtue of a more or less arbitrary choice,
imprisoned in a concrete mould. Moreover, in the absence of any extended,
coherent, systematic numeration, the mind loses itself after the first
step. It lacks the necessary vehicle for movement in front and behind,
knowing whither it is tending. The natural phenomena which it takes as
its starting-point are poor substitutes for the absent sign, and moreover
rivet it invincibly to the concrete.

In my opinion, the culminating point of this period is arrived at in the
popular conception of time—considered as a vague entity which unrolls
itself, as it gives birth to events. This is the notion that is general
among most men of medium culture, who are ignorant of philosophical
speculation on the subject. It is the final term of common, spontaneous
reflexion, left to its own resources. Thus it is said of time that it
brings the unexpected, consoles sorrow, extinguishes passion, changes
tastes, solves difficulties, and the like; it seems to be an active
power, a thing in itself. In fact, no other abstraction has perhaps
been so often reified. We may further remark that time has often been
personified and even deified in several religions. Such an honor has
never been conceded to space. The cause of this difference is that time
has an internal, human character: above all, that it is opposed to
space as dynamic to static. It is an entity manifested in movement and
change, and thereby essentially acting and living. While, in the popular
conception, space is the _passive_ receptacle of bodies, time is the
_active_ spring by which the whole is set in motion.

SECOND STAGE.—The generic images of duration, and later, the
semi-concrete, semi-schematic representation of more prolonged lapses
of time, provide the material whence we obtain the purely abstract
concept of time. It was stated above (p. 153) that the true concept of
space was constituted on the day when the ancient geometers disengaged
from the different extensions, the essential features which they termed
dimensions. So must the first astronomers, without knowing or seeking for
what they did, have laboriously disengaged the essential characteristics
of time conceived _in abstracto_. First, they purified the notion of
duration from all anthropomorphic features, studying it objectively, in
the course of the regular phenomena of nature. Moreover, they introduced
measure. The Chaldæans of Alexander’s time, who possessed a series
of astronomical observations embracing a period of 1,900 years, who
made an error of only two minutes in their computation of the sidereal
year, who determined a cycle of 6,585 days by which they were able
to calculate eclipses;[116] who were later on the inventors of the
clepsydra, hour-glass, and other more or less imperfect instruments for
measuring the subdivisions of the day; all these counted for more than
metaphysical speculation in ridding our subject of popular conceptions—or
at least to a large extent prepared the way. Accustomed as we are in
civilised life to a convenient and exact knowledge of the flow of time,
measuring it off at any moment by clocks and watches, we forget how
widely different must be the state of mind in the man whose only guides
are approximations: such, e. g., as the varying height of the sun in
different seasons, with other natural changes apt to be misinforming.
The one life is precise, the other vague, or at least mysterious. That
our measure of time (as of aught else) is relative, matters little, and
the vexed problems of this subject do not concern us. By measure, the
notion of time acquires a _quantitative_ mark; it no longer appears as
an entity, but as a possibility of successive events, as a divisible
and subdivisible process; as an extract or abstract, set apart from the
events, dissociated from them by an intellectual operation: in short—time
is a thing no longer real or imaginary, but _conceptual_.

It is wasted labor to repeat for time what has already been said for
space, and is applicable to both concepts. Time, like space and number,
can be conceived as illimitable; but here again the infinity is only
in our mental operation. We can add century to century, million upon
million of years. This infinite time is potential only—constituted by a
two-fold process: either as a sequence of numbers, which is the ordinary,
simplest, and most abstract proceeding; or by filling it with fictitious
events, with arbitrary constructions, for the future; by evoking the
image of vanished states, when we go back to the first geological ages of
our globe, to the nebulous period, and so on. This conception of infinite
time is however quite subjective, and in itself reveals nothing as to the
nature of things: we do but add one state of consciousness to another; it
is an inexhaustible possibility of progression and retrogression; and it
is nothing more.

It is a common illusion to transform this conceived infinity into a real
infinity; we forget that the mind is only working upon the abstract, i.
e., upon a fiction, useful no doubt, but created by ourselves alone,
according to our intellectual nature.

Let us suppose that, in consequence of gradual cooling, the disappearance
of the sea, or any other cause, man and all animals capable of
appreciating duration were to disappear from the surface of the earth;
time would disappear with them. Doubtless the earth would continue to
turn round its axis, the moon round our planet, the sun to take its
course; yet nothing would exist beyond the movements. Just as—if every
eye were to disappear—there would be neither light nor color; if every
ear failed, there would be neither sounds nor noises, but only the bare
potentiality of luminous and auditory sensations if the appropriate
organs were to appear again: so, on our hypothesis, there could only be a
potentiality of time.

Consciousness is the necessary condition of any notion whatever of the
time which appears and disappears with it.

       *       *       *       *       *

It is no part of our subject to discuss the various theories that have
been advanced as to the nature of the psychological process by which the
primitive notion of time is constituted in consciousness. This question
is, on the one hand, distinct from the history of its development as an
abstract idea, which we have been endeavoring to follow, and, on the
other, from all hypotheses as to its ultimate origin (Kant’s _à priori_
form, Renouvier’s law of the mind, Spencer’s cerebral innateness) which
explains neither its appearance as a fact, nor its genesis in experience.
We may, however, complete our account by summarising the latest
psychological opinions.[117]

It is clear that a simple sequence of impressions will not suffice to
constitute the idea of time; the series must be cognised as such, felt
or thought as a sequence. How is it to be cognised? Contemporary opinion
upon this point appears to be capable of reduction into two principal
types.

1. Some admit, as adequate conditions, sensations and their consecutive
images, strong states and weak states; provided, however, that the latter
arise before the former have disappeared from consciousness.

Wundt supposes that similar beats of a clock succeed each other at
regular intervals in a vacant consciousness. When the first has
disappeared its image remains until the second succeeds it. This
reproduces the first, in virtue of the law of association by similarity,
but at the same time encounters the still persisting image. Hence
the simple repetition of the sound contains all the elements of
time-perception. The first sound (recalled by association), gives the
commencement, the second the end, and the persistent image represents
the length of the interval. At the moment of the second impression, the
entire perception of time exists simultaneously, since all the elements
are presented together: the second sound and the image directly, and the
first impression by reproduction.

“The phenomena of ‘summation of stimuli’ in the nervous system prove,”
says James, “that each stimulus leaves some latent activity behind
it which only gradually passes away. Psychological proof of the same
fact is afforded by those ‘after-images’ which we perceive when the
sensorial stimulus is gone.... With the feeling of the present thing
there must at all times mingle the fading echo of all those other
things which the previous few seconds have supplied. Or, to state it in
neural terms, _there is at every moment a cumulation of brain-processes
overlapping each other, of which the fainter ones are the dying phases
of processes which but shortly previous were active in a maximal degree.
The amount of the overlapping determines the feeling of the duration
occupied_.... Why such an intuition should result from such a combination
of brain-processes, I do not pretend to say. All I aim at is to state
the most _elemental_ form of the psycho-physical conjunction.” James
is careful to repeat in several places that he makes no attempt at
_explanation_.

2. Others admit sensations and intervals; sensations that are no longer
images, but internal sensations of tension, of effort; more properly
a subconscious element, which consciousness is able to apprehend by
observation or induction. This theory has a more active character than
that first discussed.

The cleanest and most complete form of this interpretation is that of
Münsterberg,—as set forth above.

Fouillée supports the same thesis as a particular case of his general
theory of _idées-forces_. The apparent present is a synthesis of real
presents. Our primitive perception is of change, not of stability; we are
conscious of transition. The static point of view must be completed by
the dynamic.

The complete separation of present and past is a mathematical fiction.
The sum of transition which is a factor in appetite aids in forming the
series. Time is a form of appetite; beneath the floating image there is a
tendency to movement. A non-volitional being would have no representation
of time: time is a form of appetition.[118]

“It is probable,” says Mach, “that time sensation is connected with the
organic _consumption_ necessarily associated with consciousness,—that
we feel the _work of attention_ as time.... The fatiguing of the organ
of consciousness goes on continually in waking hours, and the labor of
attention increases just as continually. These sensations connected with
greater expenditure of attention appear to us to happen later.”[119]

Others again (Waitz, Guyau, and more particularly Ward) admit _temporal
signs_ in imitation of Lotze’s “local signs.” Our successive acts of
attention leave a series of residua, variable in intensity and precision;
these “temporal signs” permit the conception of representations as
successive, and no longer as simultaneous. “What is this distance that
separates _A_ from _B_, _B_ from _C_, and so on?... It is probably that
the residuum of which I have called a temporal sign; or, in other words,
it is the movement of attention from _A_ to _B_.”[120]

These extracts will suffice to show the character of the second theory,
which seems to me the more acceptable. It is the more complete, inasmuch
as it takes into consideration, not only the clear states, existing in
consciousness, but the subconscious states also; it is not confined to
intellectual elements alone (sensations and images), but recognises the
necessary rôle of the active, motor elements.

Moreover, it seems more apt than the other to explain certain facts
of current experience. It is a matter of common observation that time
seems long to us, under two contrary conditions: (1) when it is very
long; (2) when it is very empty. Here we have an apparent psychological
contradiction. The two cases, however, are equally explained by the
quantity of the states of consciousness: the first is filled with
events, the second, with efforts. After three or four days of a journey
fertile in incident, one seems to have left home a long time, because
(in comparison with three or four days of ordinary life) the quantity
of adventures held in mind, each implying a _quantum_ of duration,
appears to us in sum as an enormous duration. On the other hand, to the
prisoner incarcerated in a cell, to the traveller at a deserted station
waiting for a train; briefly, to all who are in the state known by the
name of expectant attention, time seems to be of immeasurable extension.
This is because there is a constant expenditure of effort, a tension
incessantly renewed, incessantly frustrated; consciousness is nearly void
of representations, while it is filled with acts of attention constantly
repeated. This instance of time prolonged, while apparently empty, is
difficult to explain, if only the intellectual elements are taken into
consideration, omitting the consciousness of motor states. It should be
noticed that “full” time seems longer in the past; “empty” time, in the
present and immediate past; perhaps because the former rests principally
upon intellectual memory, which is stable; the latter, upon motor memory,
which is vague and fragile.


SECTION IV. CONCEPT OF CAUSE.

The idea of cause has for centuries been the subject of so many
speculations, that our first care must be to confine ourselves
scrupulously to our subject, i. e., to retrace its evolution simply,
marking the principal phases of its development in the individual and the
species, while as far as possible eliminating whatever lies outside this
one question.

It has been remarked that the word cause signifies sometimes an
antecedent, sometimes a process, sometimes antecedent, process, and
effect produced, taken all three together.[121] This last sense alone is
complete. For, if the primitive, popular conception tends to restrict the
cause to the antecedent, to that which acts, a little reflexion will show
us that the cause is only determined as such by its effect, that the two
terms are correlative, the one not existing without the other. Finally,
with more profound reflexion, the process itself, the transition, the
passage, the _nexus_ between antecedent and consequent, appears as the
vital point, the _proprium quid_ of causality. As psychical fact, as
state of consciousness, therefore, this notion is complex, and among the
elements which compose it, now one and now the other, according to the
epoch, has been considered the most important.

In what follows, we shall have to consider: I. the origin of the idea
of cause in experience; II. its generalisation, and passage from the
individual subjective, to the objective form; III. its transformation as
resulting from the work performed in the various sciences, its scission
into two fundamental ideas: on the one hand, that of force, energy,
active and effective power, cause in the true sense (_vera causa_), which
tends more and more to become a postulate, an x, a metaphysical residuum;
on the other, that of a constant and invariable succession, a fixed
_relation_, which becomes the scientific form of the concept of cause,
equivalent in all respects to the concept of law.

I. Every one seems agreed, fundamentally at least, upon the empirical
origin of the idea of cause. It is of internal, subjective origin;
suggested to us by our motor activity. A being who was hypothetically
perfectly passive, while seeing or feeling constant external sequences,
would have no idea of causality. It would be superfluous to show, by
multiplying our quotations, that spiritualists like Maine de Biran,
empiricists like Mill, critics like Renouvier, all the schools in short,
with varying formulæ, agree upon this point. At the same time it must
not be overlooked that some writers attribute an exclusive privilege
to the “will,” maintaining it to be the type of causality; whereas the
assertion that “our own voluntary action is the exclusive source whence
this idea is derived” is unjustifiable. If, with some authors, the word
“will” is used in a large and vague sense, as designating all mental
activity that is translated by movements, no objection can be raised.
But if it be used in the proper, restricted sense, as meaning a fully
conscious, deliberate act, resulting from motive, the statement cannot
be accepted.[122] Volition is a state that makes its appearance somewhat
tardily. It is preceded by a period of appetites, of needs, instincts,
desires, passions; and all these facts of internal activity, translated
into movements; are as apt as the “will” to engender the empirical
notion of cause, i. e., transitive action, i. e., change produced: they
have moreover the advantage of being anterior in chronological order.

Contemporary psychology has studied the rôle of movements, far more than
any of its predecessors. It attributes to them a capital importance;
it shows that motor elements are included in every intellectual state
without exception, in percepts, in images, and even in concepts. Hence
it feels no repugnance in accepting the common thesis. We must however
remember that the psychology of motion is centred in the consciousness
of muscular effort, which moreover represents the type of primitive
causality. The nature of this sense of effort has given rise to long
and animated debate. For some, it is of central origin: It is anterior
to, or at least concomitant with, the movement produced; it goes from
within outwards—it is efferent. For others, it is of peripheral origin,
posterior to the movement produced; it goes from without, inwards—is
afferent. It is an aggregate of the sensations coming from the
articulations, tendons, muscles, from the rhythm of respiration, etc.:
so that the sense of effort is no more than the consciousness of energy
that _has been_ expended, of movements that _have been_ effectuated: it
is a resultant. This second theory, without so far being decisively and
incontestably established, is daily gaining more adherents, and remains
the most probable. So that, since consciousness of effort is essentially
that of _effect_ produced, it follows that in considering the act as the
source of the idea of cause, we know much less of antecedent than of
consequent. Yet this consciousness of effort produced is not the whole,
whatever people may say, of what is in the primitive conception of a
proper, personal causality. Something more remains: this is the confused
idea, illusory or not, of a _creation_ that proceeds from us. We shall
return to this point.

To conclude: at the outset, the two terms antecedent and consequent, form
almost the exclusive elements in the notion of cause. At any rate, they
preponderate in consciousness, to the exclusion of the third, relation.
The idea of a constant invariable sequence, which was, later on, to be
the intrinsic mark of the causal process, cannot yet be distinguished.

II. The idea of cause—at first strictly individual—soon commences its
movement of extension.

1. During the first period, this extension is the work of the
imagination, rather than of generalisation properly so called. By an
instinctive tendency, well-known, though not explained, man concludes for
intentions, a will, and a causality analogous to his own, in the medium
that acts and reacts around him: his fellows, all living things, and
whatever else by their movements simulate life (clouds, rivers, etc.).
This is the period of primitive fetishism that is fixed in mythologies
and languages. It may actually be observed in children, in savage races,
in brutes (as in the dog that bites the stone by which it is hit),
even in rational man, when—becoming again for the moment a creature of
instinct—he falls into a passion at the table that has hurt him.

This period corresponds fairly well with that of generic images, because
the idea of cause thus generalised results from gross, external, partial,
accidental resemblances, which the mind perceives almost passively.
It cannot be doubted that the higher brutes have a generic image of
causality; i. e., they are capable—given an antecedent—of invariably
representing to themselves the consequence. This mental state, which has
been termed “empirical consecution,” and which is not infrequent even
among men who may never rise beyond it, resolves itself into a permanent
association of ideas, the result of repetition and of habit.[123]

All this, however, is merely an external conception of causality, of
its form, and not its nature; it is an outside view, an approximation.
The proper characteristic of this period is that it remains subjective,
anthropomorphic, representing cause as an intentional activity, which
produces movements only in view of an end.

2. The second period begins with philosophic reflection, and proceeds
by the slow constitution of the sciences. Its development may thus be
summarised: little by little it deprives the notion of cause of its
subjective, human character, without however completely attaining this
ideal end; it reduces the essentials of the concept to a fixed, constant,
and invariable _relation_ between a determined antecedent and consequent;
hence it sees in cause and effect only the two moments, or aspects of
one and the same process, which is fundamentally the affirmation of an
identity.

Here imagination recedes, to make way for abstraction and
generalisation,—for abstraction since it is less a question of terms than
of a certain relation between the terms, for generalisation because
the natural tendency of the mind is to extend causality to the whole of
experience.

It must, however, be remarked that the transition from particular
cases to generalisation, and finally to the universalisation of the
concept of cause, _in a strict sense_, has only been effected little
by little. An opinion that has gained much credit, on the authority of
the _apriorists_, is that every man has an intuitive, innate idea of
the law of causality, as universal. This thesis is equivocal. If it
means that all change suggests to every normal man who witnesses it an
invincible belief in a known or unknown agent of its production, then
the assertion is incontestable: but this, as we have seen, is only the
popular, practical, and external notion of causality. If the true concept
(that of the solidly constituted sciences), which is reducible to an
inflexible, invariable determination, is implied, then it is a fallacy
to pretend that the human mind acquired it at the outset. The belief in
a universal law of causality is no gratuitous gift of nature: it is a
conquest. The fallacy persists, because for at least three centuries this
idea has been propagated by the writings of philosophers and scientists
who have made it familiar enough. None the less, it is a late conception,
unknown to the great mass of the human species. Scientific research began
by establishing laws, (i. e., invariable relations of cause and effect)
between certain groups of phenomena, began by establishing a law of
causality that was valid for these and these only; and the transfer of
this law to all that is known and unknown has only been effected little
by little, and is even yet incomplete. In a word, the law of universal
causality is the generalisation of particular laws, and remains a
postulate.

In support of the above (without entering into historical detail) we may
note the existence in human consciousness of two ideas, which from time
to time, each after its own fashion, give check to the universality of
the principle. Although, from the development of scientific thought,
their influence has been a decreasing factor, they are still very active.
These two ideas are those of miracle and chance.

Miracle, taking this word not in the restricted, religious sense, but
in its etymological acceptance (_mirari_), is a rare and unexpected
event, produced extrinsically to, or against, the ordinary course of
events. The miracle gives no denial to cause, in the popular sense,
because it assumes an antecedent: God, an unknown power. It does deny
it, in the scientific sense, since it is an abrogation of determinism
among phenomena. Miracle is cause without law. Now, for a long period,
no belief could have appeared more natural. In the physical world, the
appearance of a comet, eclipses, and many other things were regarded as
prodigies and warnings. Many races are still imbued with weird fancies
on this subject (monsters that would swallow up the sun or moon, etc.),
and even among civilised men these phenomena produce in many minds a
certain uneasiness. In the biological world, this belief has been much
more tenacious: enlightened spirits in the seventeenth century still
admitted the _errores_ or _lusus naturæ_, held the birth of monstrosities
to be a bad augury, and so on. In the psychological world it has been
even worse. Not to speak of the widely-spread (and not yet extinct)
prejudices of antiquity as to prophetic dreams, auguries of the future;
of the mystery which so long surrounded natural or induced somnambulism,
and analogous contemporary speculations on the occult sciences; of those
who regard liberty as an absolute beginning, etc.: there is, even in
the limited circle of scientific psychology, so little well-determined
relation between cause and effect, that the partisans of contingency may
comfortably imagine anything. Useless to insist upon sociology. We need
only recall the fact that Utopians abound who, while rejecting miracle
in the religious order, admit it freely in the social; believing all
to be possible, and reconstructing human society from top to bottom
according to their dreams. If, finally, we consider that this very dry
and incomplete enumeration covers millions of cases, past and present, we
must recognise that the human mind in its spontaneous and self-governed
progress, experiences no reluctance to admit causes without law.

The idea of chance is more obscure. We might almost say that, for the
majority of people who make no attempt to clear it up, it is an event
that supposes neither cause nor law; it is sheer indetermination, a
cast of the die arriving no one knows how, by means of no one knows
what. It is very evident that chance excludes neither cause nor law,
but evident to those alone who have reflected upon its nature, and
have analysed the notion. To others, it is a mysterious, impenetrable
entity, a _Tyche_ whose acts cannot be foreseen. Hume says that “chance
is only our ignorance of true causes.” Cournot rightly observes that
this is incorrect, that chance involves something real and positive: the
conjunction, the crossing of several sequences of cause and effect, which
are independent of one another by origin, and not naturally intended to
exert any reciprocal influence. Thus one series of causes and effects
lead a traveller to take a particular train: on the other hand a totally
distinct set produces at a given place or time an accident which kills
the man.[124] There is, in short, in chance, no contravention of the laws
of universal mechanism. Why then does it seem to the vulgar mind to be an
exception, indeterminate by nature? First, because the problem set by the
unexpected is insufficiently analysed; but also in my opinion, because
the primitive idea of cause is nearly always that of a single antecedent,
whereas here the unique antecedent is not present, and cannot be
discovered. The conception of a complex causation, constituted by a sum
of concurrent conditions, of equal necessity, is the fruit of advanced
reflexion.

Accordingly, while the man who is formed by scientific discipline refuses
when confronted with these so-called prodigious or fortuitous facts,
to concede that they are exceptions to the law of universal causality,
others are quite ready to admit that the wall that surrounds phenomena
may give way at certain points, with resulting breaches.

From the point of view of pure psychology, it is impossible not to
affirm that the idea of universal causality, of uniformity in the course
of nature, of rigorous determinism (and other analogous formulæ), is
acquired—superposed. Whether this notion be applicable to the whole of
experience, although experience is not yet exhausted, or whether it is
simply a guide to research, a stratagem for introducing order into
things, is a question which psychology has no capacity for discussing,
still less power to resolve.

III. We return to the work of transformation, which, starting with the
notion of cause as it is given in experience—i. e., a force, a power,
that acts and produces—culminates finally in its last term, the law of
causality.

Just as the plurality of objects perceived in nature, forms the
material of the concept of number; as the diverse durations present
in our consciousness are the material of the concept of time; so our
consciousness of acting, of modifying our self and our environment (a
power which we attribute freely to everything that surrounds us) is the
prime material of the concept of cause. But in order that this concept
may be constituted as such—fixed and determined—a work of abstraction
is needed to isolate and bring into relief its distinctive, essential
characteristic from among all the different elements that compose the
primitive and complex notion of empirical cause (antecedent, consequent,
action or reaction, change, transformation, etc.). This distinctive
characteristic is an invariable relation of sequence (the conditions
being supposed the same); and the establishment of it has been, almost
exclusively, the result of scientific research.

A history of the secular fluctuations in the idea of cause, as affected
by the various philosophical theories and changes of method in the
sciences, would be the best review of the phases of its evolution.
Impossible here to attempt such a task. We may only note the two extreme
points: the speculations of antiquity, and the contemporaneous aspect of
the question.[125]

The ancient philosophers who (at least during the great eras) were at
once metaphysicians and scientists, constructed systems of cosmogony and
assumed “first causes,” which were conceived either as forces, principles
of action, motive elements of nature (water, air, fire, atoms), or
as rational types (numbers, ideas). On the other hand they invented
mathematics, and laid the foundations of astronomy and physics. Now, as
regards causality, these essays at the scientific investigation of nature
involved consequences which were not plainly disclosed until a much
later period. They exacted another position,—a passage from subjective
to objective: whether in relation to the fall of bodies, or to a law
of hydrostatics (such as that to which Archimedes gave his name), any
one who studies the physical world necessarily sees its changes from
without. He considers cause no longer as an internal factor revealed
by consciousness, but as a sequence given by the senses. Antecedents,
consequents, invariable succession, are for him the only useful data.
Conditions equal cause; and the important determination is that not of an
operating entity, but of a constant relation. This—the only scientific
conception of cause—it is which is covered by Stuart Mill’s definition:
“Cause is the sum of the positive and negative conditions, which, when
given, are followed by an invariable consequent.”

This external aspect, old as science itself, was big with consequences
that have only been clearly revealed in our own day, and which may
be summed up in a word as identity of cause and effect. There is no
separation between the two; the antecedent is not one thing and the
consequent another; they are two manifestations, different in time, of
a fundamental unity. It has rightly been observed that the mechanical
theory of the universe (correlation of forces, conservation and
transformation of energy, etc.) is the contemporaneous form of the
concept of natural causality. Expressed from earliest antiquity in the
form of a metaphysical anticipation (_ex nihilo nihil_), it enters in the
seventeenth century upon its scientific phase, and is completed in our
own day. The physicists who have established it upon experience and by
calculation, saw plainly the consequences it involved. To cite only one
instance, R. Mayer in his _Mechanik der Wärme_ says, “If the cause _c_
produces the effect _e_, then _c_ = _e_; if _e_ is the cause of another
effect _f_, then _e_ = _f_, and so on. Since _c_ becomes _e_, _e_ = _f_,
etc., we must consider these magnitudes as the different phenomenal
forms of one and the same object. Just as the first property of cause
is its indestructibility, so the second property is convertibility,
i. e., capacity for assuming different forms. And this capacity must
not be regarded as a metamorphosis; each cause is invariable, but
the combination of its relations is variable. There is quantitative
indestructibility and qualitative convertibility.”

It must not be forgotten that the general principles of
thermodynamics—the latest form of the concept of natural causality—are
not absolute, but are proposed as ideal. We know, _e. g._, that heat can
never give rise again to all the work from which it was produced, that
no physical event is exactly reversible, _i. e._ it cannot be reproduced
identically at the opposite end of the process, because in its first
appearance it had to overcome resistance, and thus lost part of its
energy. All this, however, is outside our scope. As much as the doctrine
of the conservation of energy is valid, so much is the actual concept of
natural causality worth. We merely undertook to follow the evolution of
this concept down to the present day, to point out its transformations,
without in any way prejudging the future, or still less attributing to it
any absolute value.[126]

What now becomes of the idea of causality taken in the other sense,
no longer as an invariable relation of antecedent to consequent,
but as a thing that acts, creates, modifies, or persists under all
transformations and clothes all masks? The scientific method, as soon
as it penetrates into any order of phenomena, tends to exclude cause, to
reduce it to the strictest limits, to make the least possible use of it.
Cause then becomes the synonym of force. But physical science defines
force only by its effects:—movement, or work done. So, too, the biologist
rejects the notion of “vital force”; non-metaphysical psychology will
have none of the “faculties,” intervention of “the soul,” and the like.
Is the notion thus discarded, totally suppressed? Nay,—for even in
mechanics and physics it cannot be entirely eliminated. It is there as a
postulate, a residuum, an unknown factor covering lacunæ. Yet, do what
we will, force or energy, in order to be more than an empty word and to
become intelligible, can only be represented and imagined under the form
of the muscular effort whence it originates, and which is its type; and
despite all the elaborations to which it is submitted in order to rid it
of its anthropomorphical character, and dehumanise it, it remains rather
a fact of internal experience than a concept. Is it destined to undergo
other transformations, by reason of more profound apprehension, or some
new aspect of the problem? Is there—along with mechanical causality and
rigorous determinism—room for any other mode of causality, proper to
psychology, to linguistics, to history, in short to the positive sciences
of the mind, as is maintained by Wundt and others? The secret remains for
the future.

The natural tendency of the mind (which is but one aspect of the instinct
of conservation) to seek and investigate in face of the unknown and
unexpected, its clear or confused need of explanation for better or
worse, at the outset concluded for an acting entity. The idea still
survives under a naïve or transcendental form; it reappears in every
unexplained contingency, whether in regard to the first origin of things,
or (for the partisans of liberty) to freedom of action. In this sense,
“causality is an altar to the Unknown God, an empty pedestal that awaits
its statue.”[127]

In its other sense, which is widely different and even contrary,
which has been slowly fixed, and more slowly extended to the whole of
experience, cause is a true concept: the resultant namely of abstraction,
summarised in the characters exclusively proper to it. Under this form it
is equivalent to the concept of law.


SECTION V. CONCEPT OF LAW.

Our general ideas, from those immediately bordering on the concrete
to those which attain pure symbolism, constitute a hierarchy of
ever-increasing simplicity. What value must be assigned to this
thinking by concepts, in proportion as it ascends higher in the scale?
We are all familiar with the debates upon this question, bearing, as
it does, fundamentally upon the _objective_ value of abstraction and
generalisation. Psychology, as the science of facts, is able to ignore
this point, since it is concerned only with the nature of the two
intellectual processes, their variations, and adaptations to multiple
cases. Still, it is reasonable enough that it should assume a position,
at any rate provisionally, and for convenience of discussion.

To recall only the two extreme opinions: On the one side we have
those who maintain that the particular alone exists—for event or
individual—that our general ideas are but a means of maintaining order,
while they teach us nothing as to the nature of things. They are
comparable to a catalogue, or to the card-index of a library which are an
easy indicator to the millions of books, leaving us totally ignorant as
to their contents and value. Hence, the higher we ascend, the farther we
penetrate into the region of the fictitious and the vacant.

On the other hand, there are those who assert that nature has general and
fixed characteristics; in discovering them, we penetrate into the essence
of things. Events and individuals have but a borrowed existence; under
their fleeting appearances, we must seek the enduring; and thus, the
greater the generalisation, the higher we rise in reality and in dignity.

The psychologist can only take up the position of relativity. To him,
general ideas are approximations: they have an objective value, but it is
provisional and momentary, dependent on the variability of phenomena and
on the state of our knowledge.

On the one hand, the similarities that are the substrata of
generalisation are not fictitious. Since, moreover, knowledge of the
laws of nature has a practical value, by enabling us to act upon things,
and since we fail, in ignorance of them,—we are fain, objections
notwithstanding, to attribute to them at least a certain measure of
objective value.

On the other, if there is evolution in nature, there must also be
evolution in our ideas, and the pretension to laws or types that are
fixed unalterably, becomes chimerical. There is no longer the sharp
distinction, as formerly admitted, between “essential” and “accidental,”
i. e., permanent and variable characters. The Primary epoch of our globe
may have obeyed laws which no longer hold for our Quaternary age: all
changes in the course of development. We shall return to this point in
the concluding section.

Without insisting further upon a debate that is of secondary interest
for the psychologist, we may remark that three principal periods can be
distinguished in the development of the Concept of Law: viz., the periods
of generic images, of concrete or empirical laws, and of theoretical or
ideal laws.

It is useless to study the first phase in detail, since it interests
us only as an embryonic form, a germ, or essay. It consists in the
mechanical conception of regularity for a very restricted number of
events. Resulting from the constant or frequent repetition of certain
cycles (the course of the sun, moon, seasons, etc.) it is organised in
the mind by a process of semi-passive assimilation, that of generic
images. Many men have had, and still have, only this shadow, this
simulacrum of law, resting upon pure association, upon practical habit,
upon the unreflecting expectation of an often-perceived recurrence.
Humble as it is, this notion was nevertheless useful in the education of
humanity, for it checked the exuberant tendency of the imagination to
people the world with capricious causes, obedient to no law. It prevented
the establishment of a rule of universal contingency; it was the first
affirmation of a faith in regular order. The progress of reflexion, and
methodical research, have done the rest.

We owe to Wundt (_Philosophische Studien_, 1886, III., p. 195 et seq.) an
observation of great interest to any one concerned in the development of
the idea of law. To-day this word is current in all the sciences; indeed
its most rigorous acceptance is in mathematics and chemical physics.
This was not always the case. In antiquity, the word was employed
almost exclusively in a social, juristic, moral sense. The concept of
natural law, regarded as a sort of order, a police-force, was only very
slowly formed and established. Copernicus and Kepler employed the word
“hypothesis.” Galileo calls the fundamental laws of nature “axioms,” and
those derived from them “theorems,” following the terminology of the
mathematicians. Descartes begins his Philosophy of Nature by laying down
certain _Regulæ sive leges naturales_. Newton says: _Axiomata sive leges
motus_. The extension of the word law is due apparently to the need of
establishing a clear distinction between the purely abstract axioms of
mathematics, and the principles to which we attribute an objective value,
an existence in nature. Montesquieu’s celebrated definition, “Laws are
the necessary relations derived from the nature of things,” exhibits
this concept in its highest degree of generalisation. We may note, in
passing, that in the enquiry referred to above (ch. IV.), nearly all the
answers indicate that images of the social juristic order were evoked,
although the scientific acceptance of the word was perfectly familiar to
a large number of the subjects: showing that the primitive signification
preponderates in the vulgar conscience.

In another article, entitled _Wer ist der Gesetzgeber der Naturgesetze?_
(_loc. cit._, pp. 493 et seq.), the same author maintains an opinion,
which, notwithstanding its paradoxical appearance, seems to me perfectly
valid. Descartes called the laws of nature “rules,” inasmuch as they
explain phenomena to us; “laws,” inasmuch as God constituted them _ab
initio_ as properties of matter. At a later period, nature takes the
place of God, which is still the survival of a pantheistic conception
of the world. Still later, the preponderating tendency is to call laws
by the names of their inventors: Mariotte, Gay-Lussac, Dulong and
Petit, Avogadro, Ohm, Weber, etc. “In the seventeenth century it was
God who established the laws of nature; in the eighteenth it was Nature
herself; in the nineteenth it is the affair of the scientists.” This
thesis agrees with what was said above, of the approximate character of
laws, of the mixture of objective and subjective elements that obtain in
their formulæ, and it is no paradox to assert that the state of mind of
a Mariotte, a Gay-Lussac, a Weber, etc., when they discover their law,
represents this approximation at a given moment.

I. Empirical laws correspond, broadly speaking, with the intermediate
forms of abstraction and of generalisation. They consist in the reduction
of a large number of facts to a single formula, but without any rational
explanation. In the course of events we discover a constant relation of
co-existence or of succession between two or several facts; we mentally
detach this regular relation from the total which includes it, and extend
it to other cases. Constancy is not even necessary for empirical laws,
frequency suffices: at least one often has to be content with it. These
laws abound in the half-sciences, and in embryo science: they are useful,
they give order and simplification.

Their first characteristic is that they are identical with fact. Laws
and facts are only two aspects of the same thing. To pass from facts to
their empirical law, is merely replacing simple and homogeneous cognition
by abstraction, multiple and heterogeneous cognition by perception.
Hence the empirical law is rightly compared to a general fact, and it
is legitimate in psychology to say the law of association or the general
fact of association. On the other hand (in virtue of the natural tendency
to anthropomorphism) vulgarisms such as “laws govern facts,” and the
like, encourage in many minds the illusion of an ideal world of law
superposed upon the world of facts, external to experience, and acting
upon it like a government.

A second characteristic, which though frequent is not universal, is
complexity. Necessarily objective, since it is a simple notation of
observed facts, the empirical law does not always succeed in embracing
the results of abstraction in one short and simple formula. Sometimes
it does so; sometimes it is confronted with a multiplicity that cannot
be reduced to a single proportion; in many cases it has to distribute
itself, and resignedly to employ a long formula. Ex.: in physiology,
Pflüger’s law (or the laws of reflexes), in linguistics, the laws
of Grimm, etc. Here there is a summary description, reduced to the
principal facts. It often has to cover a great number of details, as in
Listing’s law (of the rotation of the ocular globe). Plenty of examples
are to be found in the sciences that are in process of formation, and
ill-constituted: psychology,[128] ethics, sociology, etc. Empirical
law could only be further simplified by changing its nature, namely by
transforming it into theoretical law.

Empirical law is thus the type of law that is immanent, contained in the
facts, invoking their representation directly and indirectly by means of
intermediate abstraction, involving ascending degrees of abstraction,
that, at their highest level, bring it insensibly very near to ideal law.

II. Theoretical, or ideal, law corresponds with the higher forms of
abstraction. It exhibits increasingly approximative constructions of
the mind, in proportion as these ascend, and are farther removed from
experience. Empirical laws are the material whence they are derived, and
the transformation is accomplished at the moment, and in the degree, in
which description gives place to explanation. To minds accustomed to the
discipline of the strict sciences, this conception of law alone is valid,
and they are prone to treat with disdain or defiance the formulæ that are
a simple summing-up of the results of experience, judging them unworthy
of the name of laws. To the psychologist, the position is quite other:
empirical concept and theoretical concept are two forms, two aspects of
the same intellectual process: there is no constitutional difference
between them. Nevertheless, in its higher form, the concept of law has
its proper and special characteristics which must be noted.

1. Simplicity, as contrasted with the complexity of empirical laws; this
is the necessary corollary of the operation that gives rise to it, since
it is an abstraction of abstractions, the final result of a long series
of eliminations. Compare with the long, vague, entangled formulæ, charged
with details, of which examples were given above, the enunciation of the
higher laws, which are usually short and invariably precise. And, it may
be added, invariably lucid, at least to the scientist who is in the habit
of dealing with them, because he knows exactly what they cover. In this
connexion a saying of D’Alembert deserves to be recalled and considered,
because it discloses, better than any commentary, the psychology of
abstract minds: “The most abstract notions, such as the majority of
mankind regard as the most inaccessible, are often those which carry with
them the greatest elucidating power: our ideas seem to be blotted out by
obscurity in proportion as, in any object, we examine into its sensible
properties.”

2. Quantitative determination. The higher laws alone can assume a
numerical form, and it is a truism to say that the perfection of any
science is measured by the quantity of mathematics which it involves.
Not that mathematical formulæ imply or confer any magical virtue, but
they are the sign of reduction to clear and simple relations, and are
frequently an instrument of further progress. It is true that in the
domain of empirical law, there are many processes which attempt to
imitate quantitative determination: graphic records, curves, statistics,
percentages, etc. Yet these are often a very poor substitute for the
equation, or worse—for they offer an illusory preciseness, and are
fallacious.

3. It is well to insist upon the ideal character of these laws, because
one is apt to forget that, in virtue of their very abstraction, they can
be approximate only; and can but be applied, and reduced from theory
to practice, by means of rectifications and additions. It has been said
that “physical laws are general truths that are invariably more or less
falsified for each particular case.” All scientific men, and there are
many, who have reflected on the subject, bring out this character of
approximation.[129]

Thus—it is not absolutely true that a movement is uniform and
rectilinear. The theoretic law of the oscillation of a pendulum is
unrealisable, because there is no non-resisting medium, no totally rigid
and inextensible bar, no suspending apparatus capable of turning without
friction. A planet could only describe an exact ellipse if it alone were
turning round the sun: but as, in point of fact, there are several which
act and react upon one another, Kepler’s law remains ideal. It is known
by very accurate researches that Mariotte’s law of the relations between
the density of a gas, and the pressure which it bears, is not strictly
accurate for either; but the differences between theory and reality are
so slight that, in ordinary cases, they are negligible. The laws of
thermodynamics (conservation of energy, correlation of forces) which are
so much used in the present day because of their character of generality,
and are held by some to be the ultimate principle of phenomena, have
no absolute value. It is not, e. g., correct to say that all change
generates a change which can be re-transformed without loss or addition.
The first moment of enthusiasm passed, there was no lack of criticism and
of reservation on this point. And so in other instances, _ad infinitum_.

In brief, the concept of law, whenever it is more than a vague term in
the mind, corresponds either to a direct condensation of facts (empirical
laws), or to an ideal simplification (theoretical laws); but, imperfect
or perfect, the mental process is the same in the two cases. They differ
only in the degree of simplification attainable by analysis for any
given material or datum. If empirical law, which is in strict relation
with experience, has not been idolised, this distinction and misfortune
has frequently befallen the other categories. It has been forgotten
that, in the sciences as in the arts, the ideal is only an ideal,
although it is here attained by different means, viz., elimination,
voluntary omission for the sake of preciseness, a more or less artificial
reduction to unity. Consequently many have fallen into the strange
illusion of believing that, in manipulating experience by the labor of an
ever-growing abstraction, the absolute can be brought out.[130]


SECTION VI. CONCEPT OF SPECIES.

In departing from phenomena by successive abstractions and
generalisations, we rise to laws that are more and more extensive:
so in setting out from the individual, species, genera, orders,
branches, and the like, are formed by a succession of abstractions and
generalisations. We have already followed this labor of the intellect
in its primitive attempts to introduce order into the multiplicity and
variety of living beings (Ch. III.). We saw its start in the period
of generic images, its passage through the various degrees of the
concrete-abstract period, and its final outcome by diverse paths into
a unitary conception. We must now take up the subject from the point
at which we left it, and consider the nature of the classificatory
concepts at the final term of their development, the moment of their
highest scientific determination. If the geometers were the first who
abstracted from extension the essential data of Space; if the astronomers
accomplished an analogous operation for Time; the naturalists for
their part had by abstraction to disengage from among the numerous
characteristics of living beings, those which, as fundamental, enable
them to reduce individuals to species, species to genera, and so on.
They are the inventors of the concepts which govern this province of
experience.

The notion of the individual, which is the basis, and preliminary
material, of biological classification, is sufficiently clear so long
as we confine ourselves to the higher creatures; it becomes obscure
and equivocal in descending to the lower grades, where life multiplies
by budding, or by division. Hence it has been a great stumbling-block
to the naturalists. For our purpose, the point is negligible. We can
without inconvenience omit the debates on this subject, and presume
that individuality always has its fixed characteristics. The work of
abstraction and of generalisation alone concern us.

Among all others, the Concept of Species is certainly the one which—more
especially in our own day—has been the most studied and disputed. Many
efforts have been made to determine its essential characters, to which
some attribute, and others refuse, an objective value. In effect, and
broadly speaking—two contrary theories obtain in this connexion:

1. That of fixity of species, the oldest, and long paramount: still
perhaps finding its partisans. If we accept this, we admit at the same
time that the naturalist in determining species, reveals a mystery of
nature, and partially discovers the plan of creation.

2. The complete antithesis of the foregoing, which maintains that only
individuals exist. In its absolute and radical form, this assertion seems
rarely to have been brought forward. It has, however, been said that
“the idea of species is not given to us by nature itself.”[131] In point
of fact, the contention of the transformists is different. They do not
refuse to recognise the grouping of living beings, according to their
degrees of similarity, into varieties and species; but they grant to
species only a momentary fixedness in time and space. It does not exist,
it is not a natural type, it is transitionally a stable variation; the
individual is the reality. From our point of view, this signifies that
the specific characters isolated by abstraction are of value only as
practical means of simplification in no way helping us to penetrate into
the nature of things.

However this may be,—and without for the moment inquiring whether the
work of abstraction in this province gives objective or subjective
results, whether it limits itself to simplification in relation to man,
or discovers in relation to nature,—let us follow it in its ascending
progress. Once again, we can distinguish two principal stages: that of
species corresponding to empirical and concrete law; that of genera, and
the still higher forms, corresponding to theoretical and ideal laws.


I.

The nature of a concept is fixed by the determination of its _constituent
elements_; these are determined by abstraction. Abstraction that is not
vulgar and arbitrary, but scientific, should disclose characteristics
that are the substitutes for a group (here living beings in general),
taking its place, and enabling us to think it. These constituent elements
of the concept of species are met with in nearly all the naturalists’
definitions.[132] They are two in number; species is determined by
two essential characteristics: similarity (morphological criterion),
filiation (physiological criterion).

1. Similarity seems at first sight easy to determine—as though we had
only to open our eyes; yet by this elementary procedure we hardly pass
beyond the level of generic images, and there is risk of falling into
many errors. It is necessary to penetrate into resemblances deeper than
the superficial; and here is the first degree of complexity. Buffon
observed that “the horse and the donkey, which are distinct species,
resemble each other more than the water spaniel and the harrier, which
are of the same species.” The facts which our contemporaries denote by
the name of _polymorphism_, entirely baffle the criterion of similarity.
Not to speak of the obvious difference between the larva and the perfect
insect, the caterpillar and the butterfly, or between the males, females,
and neuters of bees, ants, and termites; there are cases in which the
disparity between the two sexes is so great that the male and the female,
taken respectively as two different creatures, have been classified in
distinct _genera_, and even _orders_: e. g., the lampyris or glow-worm,
_Lernea_, and many others. The character of the resemblance is thus too
often vague, sometimes deceptive, nearly always inadequate: it follows
that we must resort to the other, to filiation.

2. This, the physiological criterion, again appears to leave no opening
for equivocation, since it can be materially stated. Generally speaking,
one is imbued with the notion that children resemble their parents, that
the immediate product is the reproduction of the type of the progenitors.
But the alternating generations (metagenesis, geneagenesis) discovered
in the course of the present century, show that this conception is
too simple, and often fallacious. This mode of reproduction is by
no means rare; we meet with it among a great number of the lower
plants, infusoria, worms, and even insects. “The dominating fact in
the reproduction of all these creatures, is that a _sexual_ being, of
definite form, gives birth to _a-sexual_ beings which do not resemble
it, but which in their turn produce by a sort of budding, or by fission
of their bodies, the sexual creatures similar to those from which they
issued.” Vogt, accordingly, in his definition of species, is forced to
include the case of alternate generation by saying: “Species is the
reunion of all the individuals that originate from the same parents, and
are in themselves, _or in their descendants_, similar to their primordial
ancestors.”

In brief, the general notion of species depends upon two ideas, complex
notwithstanding their apparent simplicity, fluctuating in spite of their
apparent precision.

Till now, we have spoken of species as if it were directly superposed
upon individuals, as if it resulted from immediate generalisation. This
is not the naturalists’ position. Their classification descends from the
species to the individual by decreasing generalisations of the race and
the variation. Thus the human species comprises several races (white,
yellow, etc.), the white race comprises several variations (English,
Arab type, etc.). To the partisan of fixedness of species, these three
general notions have not the same value: species alone has peculiar
and irreducible characters, which are deduced from the function of
reproduction and the facts of cross-breeding.

Couple two individuals of distinct _species_: the union is generally
sterile. If otherwise, the hybrids which result from it are unfruitful.
If, as rarely happens, they propagate themselves, the offspring rapidly
return to the type of one of the ancestral species.

Couple two individuals of distinct _races_ or _variations_, the union
will be fruitful; the resulting cross-breeds are again fertile; the
progenitors are able to create and fix varieties, and even races.

Hence, it is concluded, species must be a thing that exists, that
protects itself, does not let itself be encroached upon.

Evidently the debated question is one of facts: and both the parties in
dispute adduce experimental evidence. Few in number as they may be, there
are fertile hybrids, which perpetuate themselves. They are found among
birds and mammals, e. g., the alpaca and the vicuna, the bull and the
zebu, the goat and the sheep—which have for issue the ovicaprinæ,—the
hare and the rabbit—whose offspring is the leporide, (their perpetuity
has been contested). On the other hand, if certain _species_ have thus
been formed by a durable blend, there exist _races_ that have been
refractory to all attempts at cross-breeding: i. e., the domestic and
Brazilian guinea-pig, different races of rats, of rabbits, etc.

We need not enter into the discussion, nor enumerate the observations
and experiments invoked on either side: they are to be found in special
works. Our aim was to discover the constituent elements of the notion of
species in its scientific aspect. Now, neither the morphological element
nor the physiological element has any distinguishing mark of permanence
and universality. The concept of species is possessed of no absolute
value; neither is it a simple replica in the mind of the “plan of
nature.” The result of abstraction and of generalisation, it corresponds
to something which is fixed for a certain time in certain conditions; it
has temporary and provisional objectivity.[133]


II.

Contemporary discussion is almost entirely centred upon species. Little
is said about genera, and still less of the higher divisions. We do not,
in any case, find what we require: the determination of constitutive
elements, of general acceptance, which shall be for the genus, family,
order, or class, the equivalent of the two denotative marks—morphological
and physiological—that are attributed to species.

This has not always been the case. At the time when there was general
belief in a scheme of creation, the naturalists were careful, by bringing
together species, genera, families, etc., to disengage more and more
general characters, which they regarded as essential, and determined by
the nature of the thing. We have already said that Linnæus was the first
to formulate a precise notion of genus, to which he expressly attributed
a _reality_: “You must know,” he says, in his _Philosophia botanica_,
“that it is not character that constitutes the genus, but genus the
character; that character devolves from genus, not genus from character;
that character exists not in order that genus should come about (_fiat_),
but so that the genus should be known.” In the binary nomenclature which
he adopted, the first term designates the genus, the second one of the
species included. Thus the dog and the wolf have characters by which
they resemble each other, and are distinguished from other animals (five
fingers on the anterior limbs, four only on the posterior, twenty-two
teeth in the upper and lower jaw, etc.) Linnæus classifies them as the
genus _Canis_, of which _Canis familiaris_, _Canis lupus_, _Canis
vulpes_, etc., are the species. Again, the genus _Felis_, determined
by the characters common to certain animals exclusively, comprises in
its species: the cat (_Felis catus_), the lion (_Felis leo_), the tiger
(_Felis tigris_), etc.

Agassiz, the last representative of the line of naturalists who
aspired at reproducing the order of nature in the hierarchy of their
classificatory concepts, characterises the genera and divisions superior
to them by vague formulæ. Of these we can judge from the following
passage:

“Individuals are the support, at the actual moment, of the characters
not merely of species, but of all other divisions. As representative of
_genus_, they have certain details of a definite and specific structure,
identical with those possessed by the representatives of other species.
As representative of _family_, they have a definite constitution,
expressive of a distinct and specific model, in forms resembling those
of the representatives of other genera. As representative of _order_,
they take definite rank, as compared with the representatives of other
families. As representative of _class_, they manifest the structural
plan of their ramifications by the aid of special means, and according
to specific directions. As representative of _branches_ the individuals
are all organised on a distinct plan which differs from the plan of other
branch-lines.”[134]

It was shown above (Ch. III.) that the contemporary classifications,
which are radically embryological, transformist, and generic, proceed
otherwise, and have a different aim. Their ideal is to draw up the
genealogical tree of living beings, with its multiple ramifications,
marking the principal moments of evolution.

But if, leaving aside the material of these (animal or vegetable)
classifications, we consider only the psychological labor by which they
are constituted, we find that the transformists and their adversaries
have at least one common point which is of cardinal importance. The
notion of fundamental types—conceived as fixed or provisory—is for
the one as for the other a compass, a guide in research, a normal,
by means of which deviations are appreciated. Hence, these concepts
have a practical value, and it is true that we find abstraction and
generalisation in their principal rôle, which is, not to discover, but to
simplify, above all to be useful.

In effect, the one side, yielding to the natural tendency of the mind to
reify abstractions, admit the permanence and objectivity of types: they
believe firmly that they have in certain concepts the possibility of an
ideal reconstruction of the entire world of living beings. This faith
sustains them and urges them on to more and more exact determinations.

Their opponents, the transformists of every degree, are guided by
a different ideal; they search after continuity, transition, forms
of passage. Species, genera, families, etc., are but provisory
starting-points, with intermediate lacunæ which they endeavor to bridge
over. Although the animal order, the chain of life, is itself only a
theoretical construction, a natural abstraction, many fine works could
be quoted which are inspired by this faith in continuity. Such, e. g.,
are Huxley, Cope, and others upon the genus _Equus_, establishing the
filiation of the four-fingered _Eohippus_ of the old Tertiary epoch,
with the Hipparion of the new Tertiary epoch, and with the Horse of the
Quaternary period.

The hierarchy of concepts formed by superposition of abstractions and
generalisations only facilitates the task. The sole incontestable
value that can be assigned to any notion of species, and still more
to genus, and other still more general concepts, is that of utility.
They are successful implements in the investigation of nature. All
other pretensions are open to discussion. One position more especially
is untenable: that which claims for concepts, the pure results of
abstraction, an absolute value. It is obvious that they can have none.
They are neither reality nor fiction, but approximations.

       *       *       *       *       *

Laws and species—two general notions which must be connected—were
bound to vary in the course of evolution, because they are entirely
subordinated to the conditions which govern the existence of phenomena
and of living beings. Let us—merely as an illustration to fix our
ideas—admit the hypothesis of a primitive nebula. Imagine (which is
impossible) an intelligent being, able, at that point in the world’s
history, to draw up a scheme of the existing laws. He could discover
none but those which govern matter in the gaseous state,—some of which
are still extant, others unknown to us, and unknowable—since, their
conditions of existence having ceased, they are annihilated. When at
a later time this matter, uniformly diffused and dispersed through
space, became divided from one or other cause into vast nebulous
spheres commencing their slow revolution, our hypothetical being might
have surprised the birth of the astronomical laws. Subsequently, the
constitution of the liquid state of matter, and then of the solid state
in its different degrees, would give birth to new physico-chemical laws,
others meantime disappearing. When, finally, life—whatever may have been
its origin—appeared, other laws again loomed forth, and the possibility
of classification. Yet to the hypothetical spectator, these must needs
be highly singular, highly dissimilar from our own—unless we admit the
hypothesis of a world created at one throw.

It is needless to enter into the details of this long evolution, as
it is generally admitted to have been. Enough to remember that the
matter whence abstraction deduces laws and species has varied, and may
vary again in the course of ages. If, on the other hand, we consider
the slow progress of human knowledge, and the incessant corrections
imposed by experience and reasoning from century to century, we find
ourselves confronted with two variable factors, one objective, the other
subjective. No permanence can result from their union. Long as may be
the stability of laws and species, nothing guarantees their perpetual
duration. So that after two centuries which make a brave show in the
history of the sciences, we may still advance the formula of Leibnitz:
“Our determinations of physical species are provisional and proportional
to our knowledge.”[135]

Many other concepts might be added to the preceding, among them, those of
the moral sciences. I forbear, because the history of their fluctuations
would in itself exact a volume. Till now, these have been ill-determined,
badly defined. May we even speak of any regular evolution? Have they not
rather suffered _corsi e ricorsi_, which bring them back perennially to
their point of departure? Whenever—during a development of centuries—the
work of abstraction has succeeded, we have seen it pass through
successive phases:—generic ideas, intermediate forms, higher forms—but
not by any constant process. Sometimes it has rapidly attained the period
of complete simplification, as in mathematics; sometimes it is long
arrested in its progress, as in the natural sciences: sometimes, again,
as in the less established sciences, it is incapable even to the present
day of transcending the lowest stages.




CHAPTER VI.

CONCLUSION.


We have endeavored to show how the faculty of abstracting and of
generalising has been developed empirically, and to follow it in its
spontaneous and natural evolution as shown in history,—not in the
philosophical speculations which are only its efflorescence, and which,
for the most part, ignore or despise its origins. It remains to us,
in conclusion, to seek out how, and by what causes, this intellectual
process has constituted and developed itself: further—what are the
different directions it has followed in the course of its development.

I. To contemporary psychology, the mind is a sum of processes of
dissimilar nature, whose mode of appearance and of evolution depends
upon predetermined conditions. In the total of intellectual operations,
abstraction is a process of secondary formation: it does not belong
to the primary stratum of sensations and percepts, of appetites and
tendencies, of primitive emotions. We found however that it was there in
embryo. How then, instead of remaining in this rudimentary state, has it
been so differentiated as to become a function proper to the intellect,
and with a long development that is still in progress?

The primary condition is the existence of _attention_, which brings a few
points into relief, amid the general confusion. We have shown elsewhere
that attention itself depends originally upon the instinct of individual
preservation.[136] Attention, however, can only precede and prepare
for abstraction, because it is a momentary state of application to the
variable aspects of events, and does not isolate anything.

We know how the first labor of separation, of dissociation, takes effect
in the formation of generic images, and how the extracted quality
_fixed_ itself, for better or worse, by the aid of a visual, auditory,
tactile scheme, by a movement, a gesture, which confers on it a sort of
independence.

Finally, with the word—the substitute for the abstract intuition—the
mental dissociation approximates to a real dissociation: the abstract
character, incarnated in the word, seems, as happens only too often, to
exist by itself. The process of abstraction, with its fitting instrument,
is completely constituted.

During these successive phases, and afterwards, throughout the course
of the historical development of human intelligence, the progress of
abstraction and of generalisation, depends upon two principal causes: one
general, i. e., utility; the other accidental and sporadic, the advent of
inventors.

I. In his book on _Darwinism_ (Ch. XV.) Wallace, in contesting the
theory that applies the law of conservation of variations, useful in
the struggle for existence, to the mental faculties, insists at length
upon the mathematical faculty; he maintains that it is an inexplicable
exception, a case that cannot be reduced to law. The inaptitude of
inferior races for even the simplest calculations is well known;
how—from such a rudimentary origin—could it develop into the genius of
a Newton, a Laplace, or a Gauss? What motive power accounts for this
development? The author establishes by a host of sufficiently useless
historical details, that mathematical superiority played no part in the
struggle of tribe with tribe, and later on of people with people (Greeks
against Persians), and that the victory resulted from other causes, moral
and social. For this there is abundant evidence. But since mathematical
aptitude is only a particular instance of abstraction, albeit one of the
most perfect, the question ought to be proposed under a more general
form. Had the aptitude for abstraction, _ab initio_, any practical value?
Yes, “the motive power that caused its development, that Wallace claims
without specifying it, is utility.”

To avoid possibility of equivocation, let us remark that the development
of the attitude for abstracting and generalising may be explained in
a two-fold manner: by acknowledging the influence of heredity, and by
omitting it.

In the former case, it is supposed that this aptitude appears as a
“spontaneous variation” in the individual or race, that it fixes itself,
is reciprocal, grows by slow accumulation in the course of generations.
This theory postulates the heredity of acquired characters, which is
accepted by some, rejected by others, more especially since the advent of
Weismann. I refrain from invoking it, by reason of its hypothetical and
disputed nature. The probability of any transmission would moreover be
far harder to establish here than in other psychical directions, such as
imagination, or feeling.

In the second case, with elimination of the hereditary factor, progress
must be attributed to social causes, utility and imitation. From all time
there have been minds which when face to face with practical problems
knew better than others how to extract the essential, and neglect the
accessory, in the complex of facts. The utility of abstraction is
identical with that of attention, which does not require demonstration;
it may be summed up in a single word: to simplify. As the process
succeeds, it finds imitators. There is no need to admit at the outset
any reflected and fully conscious abstraction: a happy instinct, guided
by the needs of life, is sufficient at the commencement. Races that
are poorly gifted in this respect, or little apt at imitating their
betters, have never got beyond a low level. In effect, abstraction and
generalisation are the nerve of all knowledge that transcends sensation.
Is this mode of cognition useful? There can be no possible doubt as to
the answer.

2. The rôle of inventors corresponds to the fact which, in transformist
terminology, is known as spontaneous variation. By inventors, we mean
those who are born with the talent or the genius for abstraction. It
is superfluous to prove that such have been found, in considerable
numbers. They are abstract thinkers by instinct, as others are musicians,
mechanicians, designers. The biography of the great mathematicians
abounds in examples: Pascal inventing geometry out of a few vague
indications from his father; Newton divining Euclid’s demonstrations
from the simple enunciation of the theorems; Ampère, before he could
read or understand the use of figures, making long calculations by means
of a few pebbles; Gauss, at five years old, rectifying the arithmetic
of a workman, etc. If fewer analogous facts can be quoted from the
other sciences, it is because mathematical precocity is frequent, and
is more surprising. All that is the effect of innate disposition: this
word serving only to recapitulate our ignorance of the causes which
produce such minds. In the development of knowledge by abstraction and
generalisation, the first cause—utility—may be likened to the part played
by slow actions in geology; whether in the case of practical inventions,
or of the constitution of an idiom, it is continuous, collective, and
anonymous. The rôle of the great abstract thinkers, on the contrary,
resembles the rapid and epoch-making actions.

II. If we now consider the progress of abstraction from a more general
point of view (instead of following it step by step, from its lowest
to its highest degree, as in the preceding chapters), i. e., according
to its orientation towards a given end, we find that it has followed
three principal directions during its history: practical, speculative,
scientific. These are, indeed, inseparable, inasmuch as practical
abstraction leads to science, scientific abstraction is profitable to
practice, and speculation cannot entirely forego the other two.[137]

Abstraction and practical generalisation are necessarily the first in
order, as we found in studying their first appearance in the lower
animals, in children, and in savages. They serve to distinguish the
qualities of things by some word, or sign; they subserve the simple
adaptations of daily life. Later on, at a higher stage, they note the
appearance of mixed processes, which, while more especially directed to
utility, are already the prelude to scientific knowledge. Disinterested
curiosity has awakened, and timidly makes for daylight. A minimum
acquaintance with the history of the sciences teaches us that all were at
their origin processes of _applied_ research, and that often, in their
uncertain efforts, our forbears found what they were not looking for. The
numerative systems issued from the need of counting objects, and later
on, from rude commercial exchanges. Elementary geometry was required,
in order to measure the fields, to determine a right angle, to fix
relative positions, and to furnish the indispensable parts of primitive
architecture. The invention of the lever, of the balance, of rudimentary
engines for the lifting of heavy masses, gave the first foundations of
mechanics. Astronomy arose in the desire to regulate civil life and
the religious festivals, and the wish (e. g., among the Peruvians and
Mexicans) not to irritate the gods by delaying the sacrifices due to
them. Metallurgy, and later on the search for the philosopher’s stone,
and the elixir of life, were the prelude to scientific chemistry. The
historical outset of each science would furnish a profusion of similar
facts.

The two other operations issued by an internal division of labor from
this—at first the only—tendency of the mind.

First come purely speculative, i. e., philosophical or metaphysical
abstraction and generalisation. This new trend has clean and well defined
characteristics; and it was, in antiquity, the privilege of two peoples
alone, the Greeks and the Hindus. Abstraction leads immediately to the
highest generalisations; from the crude and direct simplification of a
few facts, the mind leaps at a bound to the final causes of things;
it skips the intermediate stages: it ignores the sequence of slow
and progressive evolution. This procedure where, in point of fact,
abstraction and generalisation are only the servants of a particular form
of imagination, found its first complete expression in Plato, and the
Theory of Ideas. With Plato, the human intellect tasted for the first
time the supreme pleasures of playing with the highest abstractions,
and believing firmly that the universe can be summed up, constructed
and explained by the help of some few entities. In this direction,
notwithstanding its manifold changes of aspect, the generalising process
has remained fundamentally the same, and has done no more than repeat
itself. We are here concerned with statement, not with criticism.
Psychologists must needs admit that this tendency to construct the world
(whether or no it be illusory) is a fact inherent in the nature of the
human intellect. Stallo, in the book already quoted,[138] gives an
incisive critique of the fundamental concepts of the physical sciences,
and their unconscious trend towards metaphysics. His appreciation of the
characteristics proper to the purely speculative process of abstraction
and generalisation is so apt, that we cannot do better than transcribe it:

    “Whatever diversity may exist between metaphysical systems,
    they are all founded upon the express or implied supposition
    that there is a fixed correspondence between concepts and
    their filiations on the one hand and things and their mode
    of interdependence on the other. This fundamental error is
    in great part due to a delusory view of the function of
    language as an aid to the formation and fixation of concepts.
    Roughly stated, concepts are the meanings of words; and the
    circumstances that words primarily designate things, or at
    least objects of sensation and their sensible interactions,
    has given rise to certain fallacious assumptions which, unlike
    the ordinary infractions of the laws of logic, are in a sense
    natural outgrowths of the evolution of thought (not without
    analogy to the organic diseases incident to bodily life) and
    may be termed structural fallacies of the intellect. These
    assumptions are:

    “1. That every concept is the counterpart of a distinct
    objective reality, and that hence there are as many things, or
    natural classes of things, as there are concepts or notions.

    “2. That the more general or extensive concepts and the
    realities corresponding to them pre-exist to the less general,
    more comprehensive, concepts and their corresponding realities;
    and that the latter concepts and realities are derived from
    the former, either by a successive addition of attributes or
    properties, or by a process of evolution, the attributes or
    properties of the former being taken as implications of those
    of the latter.

    “3. That the order of the genesis of concepts is identical with
    the order of the genesis of things.

    “4. That things exist independently of and antecedently to
    their relations; that all relations are between absolute terms;
    and that therefore whatever reality belongs to the properties
    of things is distinct from that of the things themselves.”

The differences between this procedure and that proper to the third (or
scientific) direction need hardly be enumerated.

Here the advance is step by step, without for an instant losing hold of
the thread that leads back to the starting-point of experience. Even
where the mind takes giant strides, or leaps across the intermediate
generalisations, it pauses to verify its results and to take up the
thread it had loosed for the moment. This is the typical process. Since
it formed the basis of our discussion of the intermediate and higher
forms of abstraction, we need not here return to it. Yet in conclusion,
it is well to recall once more what makes it of sterling value.

To reduce the essentials of abstraction and generalisation to the
exclusive use of the word (or sign) as is customary, is an error that
can only be explained by the time-honored neglect of the function of
the _unconscious_ in psychology. The sign is no more than an instrument
of simplification, an abbreviated formula. When the mind works with the
aid of concepts, the co-operation of two factors, the one conscious,
the other unconscious or subconscious, is required, in order that its
labor may be legitimate and fruitful: on the one hand, we have words or
signs, accompanied sometimes by a vague representation; on the other
hand, a latent, potential, organised knowledge. We endeavored above (Ch.
IV.) to show how this _couple_ forms and fixes itself. The mechanism is
invariably the same, without exception. Whether we keep up a trivial
conversation by means of the abstract terms which compose our languages,
or whether we ascend to the highest generalisations, there is in the
mental state no more than a difference in degree; there is no difference
in nature. Beneath the words that are the clear factors, exists the dumb
travail, the vague invocation, of the organised experience that gives
life to them. Without this unconscious factor which may, often does,
become conscious, there is nought but illusion. When we induct, deduct,
traverse a long series of abstractions to demonstrate or to discover, the
useful work consists in new relations which establish themselves in our
organised potential knowledge; words are no more than the instruments
that commence the task, facilitate and mark its phases. When the mind
is grappling with the highest abstractions, and climbs from height to
height, what preserves it from catastrophe, and guarantees against error,
is the quantity and quality of the unconscious material stored up
beneath the words. The entomologist who at first sight, and immediately,
classifies one insect among millions of species, acts in virtue of
his long experience, impressed firmly in his memory with salient
characteristics: he proceeds from the sensory data to the name. In the
inverse operation, when he merely enunciates the name, all this acquired
knowledge is the substrate. The existence of these conscious-unconscious
couples is, so to speak, a rule in psychology: general ideas are but
a particular case, perhaps the least well-known: hence we previously
likened them (Ch. IV.) to _mental habits_.

It follows that in proportion as we ascend in generalisation we rise,
not into vacuity, as has been said, but into the simple—as also, it
must be confessed, into the approximate. The relatively empty concepts
(there are none that are absolutely void of content) are the product
of a discontinuous generalisation which prevents descent without
interruption or omission into the concrete. Of course these are chiefly
encountered in the world of pure speculation. They are names representing
a knowledge that is incomplete, partial, inadequate, or ill-organised;
they correspond not to elimination of what is useless, but to deficit of
what is necessary. Having no possible contact with reality, they float
in an unreal atmosphere, and are material for a fragile and quickly
crumbling architecture. The aim of thinking by concepts is to substitute
for complex states, simpler conditions that may be turned and re-turned
in every possible sense, in order the better to discover their relations:
whereas here, by the nature of things, the unconscious activity, the
labor that operates silently in the lower strata, is applied to a soil
that is full of faults and fissures, and can but project a false light
into consciousness.

It has frequently been stated that symbolic thought is thinking by
substitution. This formula is admissible only when we recognise that
the substitute supposes, nay expects, the _actual_ existence of that
for which it is substituted. Substitution is valid in consciousness,
but not for the total operation. To sum up in a word: the psychology of
abstraction and generalisation, is in a great measure the _psychology of
the unconscious_.

We have merely studied general ideas in so far as they have an assignable
origin in experience, and do not transcend its limits. Are there, as some
maintain, notions anterior to any sensory intuition—that can by no means
nor effort be derived from empirical data? It is not our part to discuss
this question. The thesis—whether or no it be legitimate—is a contention
in favor of innate ideas, and in whatever fashion it is conceived (_à
priori_ forms, hereditary disposition, cerebral conformation), it is the
problem of the ultimate constitution of human intelligence, which we have
rigorously eliminated from our present subject.




FOOTNOTES


[1] _La parole_ is here, and subsequently, translated by _speech_; _le
mot_ by _words_, or _language_,—_verbal_ language being throughout
understood.—_Trans._

[2] Schmidkunz, _Ueber die Abstraction_. Halle: Stricker, 1889. This
little work of forty-three pages contains a good historical and
theoretical exposition of the question.

[3] Schmidkunz, _loc. cit._ This author, who rightly insists upon the
positive character of abstraction (which is too frequently considered
as a negation) observes that no concept, not even that of infinity, is
in its psychological genesis the result of negation, for, “in order to
deduce from the idea of a finite thing the idea of infinity, it is first
necessary to abstract from that thing its quality of finality, which is
certainly a positive act; subsequently, in order to reach infinity, it
is sufficient either constantly to increase the time, magnitude, and
intensity of the finite, which is a positive process; or to deny the
limits of the finite, which is tantamount to denying the negation.”

[4] _Psychology of Attention._ Chicago: The Open Court Publishing Co.

[5] See especially Hoeffding, _Psychologie_. German translation. Second
Edition, pp. 223 et seq.

[6] W. James, _Psychology_. Vol. I., p. 459.

[7] Herbert Spencer, _Principles of Psychology_. Vol. I., Part 2, Chapter
II.—Bain (in the last chapter of _Emotions and Will_) says that nothing
more fundamental can possibly be assigned as a mark of intelligence than
the feeling of difference between consecutive or co-existing impressions.
“There are cases, however, where agreement imparts the shock requisite
for rousing the intellectual wave; but it is agreement so qualified as
to be really a mode of difference.” For a review and ample discussion
of this problem see Ladd’s _Psychology, Descriptive and Explanatory_,
Chapter XIV. The earlier psychologists, in considering the “faculty of
comparison” which acts by resemblance and difference, as primordial, had
observed the same fact, although they described it in different terms.

[8] W. James, _Psychology_. Vol. I., pp. 502 and 506.

[9] This term is borrowed from the well-known works of Galton on
composite photographs, which are scarcely more than twenty years old.
Huxley in his book on Hume (Chapter IV.) appears to be the first who
introduced it into psychology, as shown by the following passage: “This
mental operation may be rendered comprehensible by considering what
takes place in the formation of compound photographs—when the images
of the faces of six sitters, for example, are each received on the
same photographic plate, for a sixth of the time requisite to take
one portrait. The final result is that all those points in which the
six faces agree are brought out strongly, while all those in which
they differ are left vague; and thus what may be termed a _generic_
portrait of the six is produced. Thus our ideas of single complex
impressions are incomplete in one way, and those of numerous, more or
less similar, complex impressions are incomplete in another way; that
is to say, they are generic.... And hence it follows that our ideas of
the impressions in question are not, in the strict sense of the word,
copies of those impressions; while at the same time they may exist in
the mind independently of language.” Romanes employs the word “recept”
for “generic images,” as marking their intermediate place between the
“percept” which is below, and the “concept” which is above them.

[10] For details see Romanes, _Animal Intelligence_, Chapters III. and
V. As to the probability of their possessing means of communication for
assistance in their co-operative labors see below, Chapter II.

[11] Romanes. _Animal Intelligence_, Chapter III.

[12] C. Lloyd Morgan. _Animal Life and Intelligence_, Chapter IX., p. 364.

[13] Houzeau, _Etudes sur les facultés mentales des animaux_, Vol. II.,
p. 264 et seq. The same author gives an example of generalisation in bees.

[14] Darwin, _The Descent of Man_, Vol. I., Chapter III.

[15] Romanes, _loc. cit._, Chapter XVII.

[16] At the end of the passage in question there is an extraordinary
account of the arithmetical powers of a dog which Lubbock explains by
“thought reading.” I omit this instance, since we are deliberately
rejecting all rare or doubtful cases.

[17] _Mental Evolution in Man_, Chapter III., p. 58.

[18] J. Sully, _The Human Mind_, I., 460. The author gives excellent
diagrams to represent the difference in the two cases. For reasoning from
particular to particular, cf. also J. S. Mill, _Logic_, II., Chapter
III., p. 3; Bradley, _Logic_, II., Chapter II., p. 2.

[19] _In re_ analogy, consult Stern’s monograph, _Die Analogie im
volksthümlichen Denken_, Berlin, 1894.

[20] _Three Introductory Lectures on the Science of Thought, delivered
at the Royal Institution_, appendix, p. 6, letter 4; Chicago, 1888. It
should, however, be remembered that the writer who thus uses the logic of
images has a mind preformed by the logic of signs: which is not the case
with animals.

[21] _Psychology_, II., 348 et seq. James, however, recalls the case
of another dog accustomed to find and carry wedges for splitting wood.
One day he did not return. After half an hour they looked for him; he
was biting and tearing at the handle of a hatchet stuck in a block
(the wedge was not forthcoming). Had this animal clear perception of
the common character of the two instruments used for splitting? “This
interpretation is possible, but it seems to me far to transcend the
limits of ordinary canine abstraction.” (_Loc. cit._, p. 352.) James
attempts another explanation. It is singular that he does not invoke
training, and association with man: that this is an influential factor
in the intellectual development of animals cannot be doubted. It is
advisable to adduce exclusively their spontaneous inventions, with no
possible suggestion: such facts alone are clear and convincing.

[22] Lloyd Morgan, whose tendencies have already been indicated,
distinguishes three sorts of inferences: (1) unconscious inference on
immediate construction (perceptual); (2) intelligent inference (conceded
to animals), dealing with constructs and reconstructs (perceptual); and
(3) rational inference, implying analysis and isolation (conceptual).
(_Op. cit._, p. 362.)

[23] _Nouveaux Essais_, Book III., Chapter I.

[24] Cf. Taine, _L’Intelligence_, Vol. I., Book I., Chapter II., Part 2,
Note 1. Preyer, _Die Seele des Kindes_, Chapter XVI.

[25] Romanes, _Mental Evolution in Man_, p. 283.

[26] B. Pérez, _op. cit._, 210.

[27] Houzeau, _op. cit._, II., 202.

[28] Cf. _Revue Philosophique_, July, 1890.

[29] Max Müller, however, is an exception. He has not made the smallest
concession on this point in any of his works, including the last
(_Three Lectures_, etc., cited above). He even maintains that a society
of deaf-mutes would hardly rise above the intellectual level of a
chimpanzee. “A man born dumb, notwithstanding his great cerebral mass
and his inheritance of strong intellectual instincts, would be capable
of few higher intellectual manifestations than an orang or a chimpanzee,
if he were confined to the society of dumb associates” (p. 92). This
thesis was attacked by thirteen critics, including Romanes, Galton, the
Duke of Argyle, etc., but Max Müller meets them all and replies to them
without flinching. It must be confessed that the arguments invoked by his
correspondents are very unequal in merit. Some are convincing, others
not. The Duke of Argyle says happily that “words are necessary to the
progress of thought, but not at all to the _act_ of thinking.” Ebbels (p.
13, appendix) shows that Max Müller has unduly limited the question by
excluding all processes anterior to the formation of concepts; we think
in images; the transition from one form to another is imperceptible,
and the faculty of abstraction does not appear suddenly along with the
signs. On the other hand, we cannot admit as evidence the facts invoked
by other correspondents, e. g., chess-players who combine and calculate
solely by the aid of visual images; answers to letters, conceived in the
first place as a general plan before they are developed in words, etc. It
is forgotten that the persons capable of these operations have had long
practice in verbal analysis, thereby attaining a high intellectual level.
So, in the physical order, the practical gymnast, even when not executing
any particular feat, possesses a suppleness and agility of body, due to
exercise, which translates itself into all his movements.

[30] _De l’Education des sourds-muets_, 2 vol., 1827. Notwithstanding
its somewhat remote date, the book has lost none of its interest in this
particular. It must also be remembered that institutions for deaf-mutes
are far more numerous now than at the beginning of the century, and
that the children are placed in them much earlier. Formerly they were
abandoned to themselves or instructed very late; in proportion to their
age, they presented better material for the study of their development.

[31] Tylor, _Early History of Mankind_, p. 80. Romanes, _Mental Evolution
in Man_, Chapter VI.

[32] Kussmaul, _Die Störungen der Sprache_, Chapter xxx.

[33] Cf. as proof, the story related by Kussmaul (_op. cit._, VII.): A
young deaf-mute was arrested by the police of Prague as a vagabond. He
was placed in an institution and questioned by suitable methods, when
he made known that his father had a mill with a house and surroundings
which he described exactly; that his mother and sister were dead, and his
father had re-married; that his step-mother had ill-treated him, and that
he had planned an escape which had succeeded. He indicated the direction
of the mill to the east of Prague. Inquiries were made, and all these
statements were verified.

[34] Romanes, _Mental Evolution_, etc., p. 150.

[35] W. James, _Psychology_, I., 266, for the second observation;
_Philosophical Review_, I., No. 6, p. 613 et seq. for the first.

[36] _Sign-Language Among the North American Indians_, 1881. Published
in Report of the Bureau of Ethnology at Washington. Cf. also: Tylor,
_op. cit._; Romanes, _op. cit._, VI.; Lubbock, _Origin of Civilisation_,
Chapter VI.; Kleinpaul, _Zeitschrift für Völkerpsych._, VI., 353.

[37] Lubbock. _The Origin of Civilisation and the Primitive Condition of
Man_, p. 417.

[38] Gérando, _op. cit._, II., note K, p. 203. Among the gestures that
are identical under their double form may be noted stone, water, large,
tall, to see, finished, man, house, good, pretty, now, etc.

[39] _Philosophy of the Human Mind_, Ch. I., sect. 2.

[40] Kleinpaul, _loc. cit._

[41] Writing, ideography, originated in an analytical process analogous
with the language of gestures. Like the latter, it (1) isolates terms,
(2) arranges them in a certain order, (3) translates thought in a crude
and somewhat vague form. Curious examples of this may be found in Max
Müller’s _Chips from a German Workshop_, XIV. The aborigines of the
Caroline Islands sent a letter to a Spanish captain, as follows: Above, a
man with extended arms, sign of greeting. Below, to the left, the objects
he has to offer; five big shells, seven little ones, three others of
different forms. To the right and centre, drawing of the objects wanted
in exchange: three large fish hooks, four small ones, two axes, and two
pieces of iron.

[42] _Ants, Bees, and Wasps_, VII.—Romanes, _Animal Intelligence_, IV.

[43] _Animal Intelligence_, XVI., p. 445.

[44] The most interesting of the many observations on this subject
are those of Dr. Wilks, F. R. S., published in the _Journal of Mental
Science_, July, 1879.

[45] _Mental Evolution in Man_, p. 137.

[46] _Der Ursprung der Sprache_ (1877). Fr. Müller maintained a similar
view.

[47] A. Lefèvre, _Les races et les langues_ (_Bibliothèque scientifique
internationale_), pp. 5-6.

[48] _Loc. cit._, 372.

[49] Heinicke, _Beobachtungen über Stumme_, 75, 137.

[50] Romanes, _Mental Evolution in Man_, pp. 377-379.

[51] For documents, consult especially Tylor, _Primitive Culture_, V;
Sayce _Principles of Comparative Philology_, I., § 17.

[52] This list may be found in _The Science of Thought_, p. 406.

[53] How were primitive terms (roots or words) formed? A much-debated and
still unsolved question. Man had at his disposal one primary element, the
interjection. By all accounts this remained sterile, unfertile; it did
not give birth to words; it remained in articulate language as a mark
of its emotional origin. A second proceeding was that of imitation with
the aid of sound, onomatopœia. From antiquity to the present time, it
has been regarded as the parent, _par excellence_. This was accepted by
Renan, Whitney, Tylor, H. Paul, etc.; rejected by M. Müller, Bréal, P.
Regnaud, etc. No one disputes the formation of many words by onomatopœia,
but those who question its value as a universal process say that “if in
certain sounds of our idioms we seem to hear an imitation of the sounds
of nature, we must recollect that the same noises are represented by
quite different sounds in other languages, which are also held by those
who utter them to be onomatopœia. Thus it would be more just to say
that we hear the sounds of nature through the words to which our ear
has been accustomed from infancy” (Bréal). I have observed that those
who study the spontaneous formation of language in children, claim
for them but little onomatopœism. On the other hand, a word created
by undoubted onomatopœia is sometimes by means of association, or of
strange analogies, transferred successively to so many objects that all
trace of the transformations of meaning may be lost, and the imitative
origin actually denied. Such was Darwin’s case, cited above, where the
onomatopœia of the duck finally served to designate all liquids, all that
flies, all pieces of money. If the successive extensions of the term had
not been observed, who could have recovered its origin?

[54] Sayce, _loc. cit._, IV., §§ 3-5.

[55] We cannot doubt, however, that there is in the child (and so too for
primitive man) a period of pure and simple denomination, when, in the
face of perceived objects, he utters a word, as a spontaneous action,
a reflex, with no understood affirmation. But this act is rather the
prelude, and attempt at speech, an advance towards language proper.

[56] There is in Iroquois a word that signifies, “I demand money from
those who have come to buy garments from me.” Esquimaux is equally rich
in terms of this sort. Yet we must recognise that these immense composite
words, themselves formed from abbreviated and fused words, virtually
imply the beginning of decomposition.

[57] _Lectures on the Origin and Growth of Religion_, ed. 1891, p. 196.

[58] Whitney, _The Life and Growth of Language_, Chap. X. Sayce, _op.
cit._, VI., 28, rejects them absolutely.

[59] Renan, _Histoire générale des langues sémitiques_, pp. 128 and 363.

[60] We can see how little the _real_ order of evolution resembles the
theoretical order of the XVIII. century, evolved from pure reasoning:
“The complex notions of substances were the _first_ known, since they
came from the senses, and must therefore have been the first to have
names” (Condillac). “With regard to adjectives, the notion must have
developed with _exceeding difficulty_, since every adjective is an
abstract term, and abstraction is a painful, or unnatural operation” (J.
J. Rousseau).

[61] P. Regnaud, _Origine et philosophie du langage_, p. 317.

[62] On this point, consult especially Sayce, _op. cit._, II., § 9, and
P. Regnaud, _op. cit._, pp. 296-299.

[63] “The word _être_ is irreducible, indecomposable, primitive, and
wholly intellectual. I know no language in which the French word _être_
is expressed by a corresponding word representing a sensible idea. Hence
it is not true that all the roots of the language are in last resort
signs of sensory ideas.” (V. Cousin, _Histoire de la phil. au XIII
siècle_, 1841, II., p. 274.)

[64] For the psychology of relation consult Herbert Spencer,
_Psychology_, I., p. 65, II., pp., 360 et seq.; James, _Psychology_,
I., pp., 203 et seq. The latter gives the history of the subject,
which is very brief, and remarks that the idealogues form an honorable
exception to the general abstention. Thus Destutt de Tracy established a
distinction between feelings of _sensation_ and feelings of _relation_.

[65] Regnaud, _op. cit._, pp. 304 et seq.

[66] It is superfluous to give examples of such a well-known fact. See
Darmesteter, _The Life of Words_.

[67] Intelligence is taken here in its restricted sense, as the synonym
of abstracting, generalising, judging, reasoning.

[68] _De l’intelligence_, Vol. I., Bk. IV., Chap. I., p. 254, first
edition.

[69] _De l’intelligence_, I., Bk. IV., Chap. I., p. 254, first ed.

[70] _Mental Evolution in Man_, pp. 74 and 75.

[71] As Paulhan remarks, “L’abstraction et les idées abstraites”
(_Revue Philosophique_, Jan., 1889, p. 26 et seq.), these two processes
are initially linked one with the other, so that we find analytical
syntheses, and synthetical analyses.

[72] _Op. cit._, VIII., 158-165.

[73] We have touched on this subject incidentally in _La psychologie
des sentiments_ (Part II, IX, § 2, pp. 305 et seq.). Many tribes do
not get beyond polydemonism, peopling the universe with innumerable
genii; this is the reign of the concrete. A certain progress is marked
by subordinating the genius of each tree to the god of the forest, the
different genii of a river to the god of the river, etc. At a degree
higher, the intellect constitutes a single god for water, one for fire,
one for the earth, etc. Thus there come to be genii of individual,
specific, and generic origin.

[74] Tylor, _Primitive Culture_, I., gives abundant data on this
question. Chap. VII. is entirely devoted to it.

[75] In the account of his travels among the Damaras (in his _Tropical
South Africa_, p. 133) Galton says: “In practice, whatever they may
possess in their language, they certainly use no numeral greater than
three. When they wish to express four, they take to their fingers, which
are to them as formidable instruments of calculation as a sliding-rule
is to our English schoolboy. They puzzle very much after five, because
no spare hand remains to grasp and secure the fingers that are required
for ‘units,’—yet they seldom lose oxen: the way in which they discover
the loss of one, is not by the number of the herd being diminished, but
by the absence of a face they know.” [This tallies with what we said
above, Chap. I., as to so-called numeration in animals and children.]
“When bartering is going on, each sheep must be paid for separately. Thus
suppose two sticks of tobacco to be the rate of exchange for one sheep,
it would sorely puzzle a Damara to take two sheep and give him four
sticks. I have done so and seen a man first put two of the sticks apart
and take a sight over them at one of the sheep he was about to sell.
Having satisfied himself that one was honestly paid for, and finding
to his surprise that exactly two sticks remained in hand to settle the
account for the other sheep, he would be afflicted with doubts; the
transaction seemed to come out too pat to be correct, and he would refer
back to the first couple of sticks, and then his mind got hazy and
confused, and wandered from one sheep to the other, and he broke off the
transaction until two sticks were put into his hand and one sheep driven
away, and then the other two sticks given him and the second sheep driven
away.” Galton relates many other similar facts which he had himself
witnessed.

[76] And the barley-corn of English measure.—_Tr._

[77] Wundt (_Logik_, I., pp. 113 et seq.) gives what he regards as a
complete classification of concepts, but it does not correspond with our
design. It may be summarised as follows. Four classes: I. Identical or
equivalent concepts; Aristotle = Alexander’s tutor. II. Subordinate or
superordinate concepts; mammals and vertebrates, etc. III. Co-ordinated
concepts, comprising five species: i. Disjunctive concepts; sound and
noise, French and German, etc. They are subordinate to a larger concept.
ii. Correlative concepts, with reciprocal relations; men and women,
mountain and valley. iii. Contrary concepts; high and low, good and
bad. iv. Contingent concepts; such, i. e., as touch, with very minute,
perceptible differences; this highly important category comprises
numbers. v. Interferent concepts, which coincide or partially cross;
negro and slave, rectangle and parallelogram. IV. Concepts which are
interdependent; etc., space and movement, crime and punishment, demand
and supply, labor and wages. This table may suit the logician but not
the psychologist, because it presents the concepts under what may be
termed the static order, i. e., ready formed: we, on the other hand,
are considering them as dynamic, i. e., in their becoming and order of
genesis.

[78] For details, with quotations in point, consult Agassiz: _De
l’espèce_, Chap. III., and E. Perrier, _La Philosophie zoologique avant
Darwin_, Chap. II.

[79] Agassiz, _op. cit._, gives a summary of the successive improvements.
They are of interest not merely to the zoölogist, but also from our own
point of view, as showing the increasing preponderance of analysis, and
search for fundamental characteristics, to the exclusion of the external
resemblances which served as basis for the more primitive classifications.

[80] Under the heading “Observations on General Terms” the _American
Journal of Psychology_, III. i, p. 144 (Jan., 1890) gives the results of
an investigation conducted upon 113 school children aged 13 to 18. The
words _being_, _the infinite_, _literature_, _abstraction_, _number_,
_play_, _coldness_, _horror_, etc., were written down, and a few moments
were given the pupils to transcribe their impressions in each case.

The summarised answers are not devoid of interest, but the object of the
inquiry is evidently very different from our own.

[81] The word “law” was purposely chosen for its ambiguity; physical
laws, moral or social laws. The immense majority of answers were in the
juristic sense. Ex., Code, Law of the Twelve Tables, a judge, woman with
scales, etc.

[82] For the word _infinity_, those who fall under this type see the
printed word, or the mathematical sign ∞.

[83] It should be noted that he lived among these animals and
experimented with them almost daily.

[84] The results of the investigation were published, partly in the
_Revue Philosophique_, October, 1891, partly at the International
Congress of Psychology, second session, London, 1892 (_International
Congress of Experimental Psychology._ London: Williams & Norgate, pp. 20,
et seq.).

[85] Thus Taine, who is usually regarded as a Nominalist, tells us
that, “A general idea is a name, nothing more than a name, a name which
_signifies_ and _comprehends_ a sequence of similar facts, or class
of similar individuals, accompanied usually by the sensory but vague
representation of some of these facts or individuals.” (The words
italicised for emphasis are not so distinguished in the text.)

[86] We are dealing only with comprehension, and not with invention
(discovery of a law, or of general features in nature). Invention
requires quite different mental processes.

[87] Cournot, _Essai sur les fondements de nos connaissances_. I., § 109,
p. 231.

[88] Dugas. _Du Psittacisme et de la pensée symbolique_, pp. 121 et seq.

[89] Paulhan. _Revue philosophique._ July, 1889, pp. 77 et seq.

[90] Höffding. _Psychologie._ Eng. tr., p. 168.

[91] Maclellan & Dewey (_Psychology of Number and Its Application to
Methods of Teaching Arithmetic_, New York, 1895) made pedagogical
deductions from this fact. They ask, for beginners, that the examples
should be borrowed from continuous quantity, and that number be
considered as a particular species of measure.—In his book _Our Notions
of Number and Space_ (Boston, 1894) Nichols, taking a theory of James
about judgments of number as the basis of his experiments, tries to
show that the simultaneous sensation of two points applied to the skin
originates in the successive sensation of a distinct contact upon two
separate tactile circles.

[92] I do not insist on any such rash thesis. A discussion of it will be
found in the _Report of the Int. Congress of Exp. Psychol. in London_
(_cit._, pp. 35-41).

[93] _Psychology_, II., p. 653.

[94] Liard, _La science positive et la métaphysique_, p. 226. It should
be remarked that the process by subtraction is met with even among
uncivilised people, though very rarely. The plan of making numerals by
subtraction, says Tylor (_op. cit._, I., p. 264), is known in North
America, and is well shown in the Aino language of Yesso, where the words
for 8 and 9 obviously mean “two from ten,” “one from ten.”

[95] “The childish and savage practice of counting on the fingers and
toes lies at the foundation of our arithmetical science. Ten seems
the most convenient arithmetical basis offered by systems founded
on hand-counting, but twelve would have been better, and duodecimal
arithmetic is in fact a protest against the less convenient decimal
arithmetic in ordinary use. The case is the not uncommon one of high
civilisation bearing evident traces of the rudeness of its origin in
ancient barbaric life.” (Tylor, _loc. cit._, I. p. 272)

[96] For the most recent view of this discussion, with the arguments on
either side, see Couturat: _De l’Infini mathématique_ (1896). 2nd part.
Bk. III.

[97] Cournot, _op. cit._, I., p. 331 et seq. Renouvier, _Logique_, I.,
pp. 377-394. Poinsot, _Théorie nouvelle de la rotation des corps_, p. 78.

[98] For a summary of these investigations, see the chapter “Sensations
of Orientation” in Prof. E. Mach’s _Popular Scientific Lectures_, 3rd
ed., Chicago, 1898; and for original discussions of the whole subject of
space-sensations, see the same author’s _Analysis of the Sensations_,
Chicago, 1897.—_Trans._

[99] Münsterberg, _Beiträge zur experimen. Psychologie_, pp. 182 et seq.
Wundt, _Physiol. Psychologie_, 4th ed., II. pp. 95-96.

[100] This is not the place to enter into the well-known discussion
between the “nativists” and the “empiricists.” To the former all
sensation, visual or tactile, contains from its outset a _quantum_ of
extension which is the primitive element, and the foundation for our
spatial constructions. For the others there are only local signs, tactile
or visual, and movements whose synthesis suffices to constitute all the
modalities of existence. Whichever hypothesis be adopted, the extension
in point is always that given by concrete data (not that of space
conceived in the abstract)—directly cognised according to some, a genetic
construction according to others. This discussion has no direct relation
with our subject: for the full debate see Ribot’s _Psychologie allemande
contemporaine_, Ch. V. James (_Psychology_, II. Ch. XX.) has recently
taken up the nativistic theory, giving new arguments in its favor.

[101] Extracted from Spencer’s _Psychology_, Vol. I. § 90.

[102] Lotze, _Mikrokosmus_, II. p. 47.

[103] Stallo, _Concepts of Modern Physics_, Chap. XIII., p. 225, _Int.
Sc. Ser._, third ed. He also gives a very concise criticism of Mill’s
theory of induction in geology.

[104] _System of Logic_, I. Bk. II., Chap. 15, § 1.

[105] The complete history of this question, from its first beginnings to
contemporaneous work, may be studied in Nichols’s “Psychology of Time,”
_Am. J. of Psychol._, III. pp. 453-530.

[106] For these and the following experiments, cf. Wundt, _Physiologische
Psychologie_, 4th ed., I. pp. 408 et seq.

[107] _Psychol._, I. 642.

[108] M. Janet has studied this subject, under the title “Une illusion
d’optique interne” (_Rev. Phil._, 1877, III. pp. 497 et seq.) and
explains the illusion by supposing that the apparent duration of a
certain portion of time, in the life of each individual, is proportional
to the total duration of his life.

[109] Nichols, _op. cit._, p. 502.

[110] _Analysis of the Sensations_, Chicago, 1897, pp. 110 et seq.

[111] H. Spencer, _Psychology_, I., § 91, p. 215.

[112] Horwicz, _Psychologische Analysen_, III., 145. Guyau, _Genèse de
l’idée du temps_, pp. 35 et seq.

[113] _Beiträge zur experimentellen Psychologie_, II., 1889.

[114] Van Ende cites a large number of facts in point, but they are not
all equally convincing. _Histoire naturelle de la croyance_, pp. 208-212.

[115] Romanes, _Animal Intelligence_, p. 314. It should be remarked that
the author only reports the fact from another witness—that the narrator
said it had occurred “thirty years before,” and “that he did not pretend
to remember under what precise circumstances the habit of coming into the
street was acquired.”

[116] According to Delambre, the Chaldæans could only discover the
cycle which the Greek mathematicians called _saros_ by studying their
commemorative notes; i. e., from a considerable mass of observations,
they _extracted_ or _abstracted_ a constant recurrence.

[117] For details see, in addition to Nichols’s article as previously
cited, Sully, _The Human Mind_, II., Appendix E, and James, _Psychology_,
I., pp. 632 et seq.

[118] Fouillée, _Psychologie des Idées-forces_, II., 81-204.

[119] Mach, _Analysis of the Sensations_, English translation (Chicago,
1897), pp. 111-112.

[120] Ward, article “Psychology,” in the _Encyclopædia Britannica_,
Vol. XX., pp., 65 et seq.—On the metaphysics of time considered as pure
heterogeneity, see the recent work of Bergson, _Essai sur les données
immédiates de la conscience_, pp. 76 et seq.

[121] Lewes, _Problems of Life and Mind_, II. p. 375.

[122] For the discussion of this point, see Renouvier, _Logique_, II. 324.

[123] Romanes gives some examples of what he terms appreciation of
causality in animals, including that of a setter that was frightened
at thunder. “On one occasion a number of apples were being shot out of
bags upon the wooden floor of an apple room, the sound in the house as
each bag was shot closely resembled that of distant thunder. The setter
therefore became terribly alarmed; but when I took him to the apple-room
and showed him the real cause of the noise, his dread entirely forsook
him, and on again returning to the house he listened to the rumbling with
all cheerfulness.” Other analogous cases are to be found in his _Mental
Evolution in Animals_, Chap. X.

[124] For the study of Chance, see Cournot, _op. cit._, I., Chap. iii.
[Also J. Venn “The Logic of Chance,” etc.—_Tr._]

[125] Under the title _Zur Entwickelung von Kant’s Theorie der
Naturcausalität_, (_Philosophische Studien_, IX, 3 and 4), Wundt
gives us a rapid historical sketch. He holds that speculation, in
antiquity, is characterised by the method of contraries: the opposition
of being and becoming, etc. It is wholly qualitative. The ancients
progressed by definition. Elaboration of the concept of mechanical
causation was impossible, by reason of the absence of any quantitative
determination. This began with Galileo. The progress of mathematics,
and the introduction of fractional and irrational numbers made it
possible to search out, not merely measure, but also the relation between
magnitudes—i. e., _function_. This became the type, and at the same
time the goal of all intellectual elaboration, as applied to natural
phenomena. This method culminated in the seventeenth century, with the
predominance of the logical type. In consequence of the old concept of
substance, forces were taken as cause, phenomena as effect. The latter is
more frequently derived from cause by deduction, not by intuition. The
cause of a determined event might either be the total of its conditions,
or one antecedent event. This last conception prevailed, as being the
more favorable to the application of mathematics. The eighteenth century
marks the genesis of the biological sciences. The growing importance of
observation and experimental research made against the preponderance
of mathematics. The facts of experience were held more solid than the
conclusions of reason. The type of causality is placed no longer in
deduction, but in sensory intuition; it is the residuum of experience.
This tendency found its exponent in Hume. Kant endeavored to reconcile
the two theses; that which models object upon subject (seventeenth
century) and that which models subject upon object (eighteenth century).

[126] The question is sometimes raised as to whether psychical (and
consequently moral, social) facts ought to be included under the formula
of conservation of energy and correlation of forces. Since the only
evidence produced has been of the nature of theoretical affirmations, or
vague and partial experiences, without quantitative determination, the
question so far remains open. The concept of natural causality was in the
same way considered above in its positive sense, i. e., as a relation of
invariable sequence, without inquiring whether it extends to all forms of
experience,—or whether it is limited.

[127] W. James, _Psychology_, II., p. 671.

[128] Sigwart in his _Logik_, Book II. (English translation by
Helen Dendy) has made a profound study of the classification of the
psychological laws in psychology, and their relative value. He divides
them into three categories, according to the nature of the relations
which they express: 1. Psychophysical laws which formulate constant
relations between states of consciousness and the cerebral states. Ex.
the relation between the sensation directly received, and the image that
is reproduced in consciousness. 2. Psychological laws properly so-called;
these express the internal relations of the states of consciousness.
Ex. Law of conservation of impressions, law of association, law of
systematisation by volition. 3. Laws expressive of the reciprocal
action that human thoughts and volitions exert one upon the other: they
presuppose the intervention of social causes, and are to this day vague
and ill-determined; hence there are no fixed rules for the government of
humanity, or the bringing up of children.

[129] “Fundamental laws are, or should be, only the simplest, most
abridged, and most economical mode of expressing facts, within the limits
of precision possible to our observations and experiences. The laws of
nature are simple, essentially because—among all the possible modes of
expression—we choose the simplest” (see Mach, _Mechanics_, Chicago, 1893,
and _Popular Scientific Lectures_, 23d ed., Chicago, 1898, under the
headings “Economy of Thought,” “Law,” etc.). “In formulating a general,
simple, precise law, based upon relatively few experiences, which,
moreover, present certain divergencies, we only obey a necessity from
which the human mind cannot free itself.” (Poincaré.)

[130] Since our subject is the tracing out of the _concept_ of law in its
different degrees, starting from the generic image, we have no need to
study the nature of the laws proper to each science (logic, mathematics,
mechanics, physico-chemistry, biology, etc.), nor to discuss their value.
For this point, see Boutroux, _L’idée de loi naturelle dans la science et
la philosophie contemporaine_. Paris, 1895.

[131] Brown, quoted by Quatrefages (_Précurseurs de Darwin_, p. 218), who
adds, “If this were the case, one would not find many species denoted
by particular names among savages, and our own illiterate population.
The general notion of species is on the contrary one of those that are
forced upon us, directly we look round. The difficulty is to formulate
it clearly, to give it scientific precision, and this is a very real
problem.”

[132] Quatrefages (_op. cit._, pp. 219-222) gives a great number of
definitions of species. A few may be quoted: “Species should be defined
as a succession of wholly similar individuals, perpetuated by means of
generation” (De Jussieu).—“Species is a constant succession of like
individuals, which reproduce themselves” (Buffon).—“By species we mean
any collection of similar individuals, that have been produced by
individuals like unto themselves” (Lamarck).—“Species is the individual
repeated and continued in time and space” (Blainville).—“Species is the
totality of all individuals that have the same origin, and of those that
are as like them, as they are among themselves” (Brown), etc., etc.

[133] For the transformists, as is well known, variety, race, and species
are not fixed concepts. “From variety to race, from race to species,
there is a continuous insensible passage. Individual modifications, at
first slight, give rise to a variety or to a race. Continuing to augment,
and extending to a constantly increasing number of individuals, they
may come to constitute specific characters. Pursuing its evolution, the
species then finally reaches the rank of the genus, family, etc.”

[134] _De l’Espèce_, Ch. II., §§ 6 and 7.

[135] _Nouveaux Essais_, III, § 6, 23.

[136] _Psychology of Attention_, Ch. I. (Chicago: Open Court Publishing
Co.)

[137] For a study of the function and practical value of symbolism
consult Ferrero, _Les lois psychologiques du symbolisme_; Paris, F. Alcan.

[138] _The Concepts and Theories of Modern Physics_, Ch. IX., p. 137, 3rd
ed.




INDEX.


  Abstraction, a positive operation, 2;
    a process of secondary formation, 216 et seq.;
    has followed three principal directions: practical, speculative,
        scientific, 220 et seq.;
    higher forms of, 111 et seq.;
    implies a dissociative process, 8;
    intermediate forms of, 86 et seq.;
    prior to speech, 1 et seq.;
    stages of, 10 et seq.

  Abstract thought, a skeleton, 135.

  Acoustic space, 148.

  Adjective, the, 76.

  Agassiz, 7, 105, 107, 211.

  Ampère, 219.

  Analogy, 27, 84.

  Animals, causality in, 184;
    counting of, 19;
    language of, 58;
    psychology of, 11 et seq.;
    reasoning of, 30;
    time-sense of, 169.

  Antecedent and consequent, 180, 183 et seq.

  Ants, intelligence of, 12 et seq., 27, 55.

  Arabic, 76.

  Archimedes, 190.

  Architecture, 28.

  Aristotle, 45, 105 et seq.

  Arithmogenesis, 139.

  Articulation, 63.

  Artists, 134.

  Association of images, 18;
    by similarity, 24.

  Astronomers, the first, 173.

  Attention, 134, 217.

  Auditory types, 112, 121 et seq.

  Aztec language, 73.


  Baer, Von, 108.

  Bain, 7.

  Barter, 109.

  Bees, intelligence of, 14, 56.

  Belief in a universal law of causality, 185 et seq.

  Belt, Mr., 13.

  Bergson, 178.

  Binet, 37.

  Blainville, 206.

  Boole, 38.

  Boutroux, 203.

  Bradley, 25.

  Bréal, 70, 71.

  Brehm, 170.

  Brown, 205, 206.

  Buffon, 206, 207.


  Cases, grammatical, 81.

  Causality, belief in a universal law of, 185 et seq.

  Cause, empirical origin of, 181;
    history of concept of, 180 et seq.;
    universalisation of the concept of, 185 et seq.

  Chaldæans, 173.

  Chance, idea of, 187 et seq.

  Charcot, 127.

  Chess-players, 40.

  Child, numeration in the, 35;
    general ideas of, 31 et seq.;
    time-sense of, 171.

  Chinese, 62, 69.

  Class, 211.

  Classification, biological, history of, 103 et seq., 204.

  Cognition, cardinal operations of, 1.

  Communication, 55 et seq.

  Compositors, 121.

  Concepts, 11, 92, 135;
    hierarchy of, 109, 213;
    relatively empty, 225;
    the inferior, 88;
    ultimate nature of, 113.

  Concrete type, 115.

  Condillac, 31, 77.

  Consciousness, the condition of any notion of time, 175 et seq.

  Convertibility, 192.

  Cope, 212.

  Copernicus, 197.

  Counting, 35, 99, 143.

  Cournot, 134, 146, 187, 188.

  Couturat, 144.

  Cross-breeding, 208.

  Cuvier, 107, 108.

  Czermak, 160.


  D’Alembert, 201.

  Damaras, 99.

  Darmesteter, 84.

  Darwin, 12, 18, 34, 63.

  Deaf-mutes, psychology of, 39;
    language of, 41;
    syntax of, 43;
    numeration in, 45;
    religious notions of, 46.

  Decimal system, 143.

  Declensions, 81.

  Delambre, 173.

  De Jussieu, 206.

  De Quincy, 150.

  Descartes, 197.

  Determinism, 188, 193.

  Dewey, 139.

  Dietze, 161.

  Differences, 90.

  Dissociation, 27.

  Dogs, intelligence of, 17, 20, 29.

  Dual, the, 77.

  Duck, 34.

  Dugas, 136.

  Duke of Argyle, 40.

  Duration, concrete, 159 et seq.;
    perception of, 161 et seq.;
    reproduction of, 162.


  Ebbels, 40.

  Economy of thought, 202.

  Effort, sense of, 182 et seq.

  Elephant, intelligence of, 15.

  Ellendorf, Dr., 13.

  Empirical laws, 198.

  Empiricists, 149.

  Energy, conservation of, 192.

  Esquimaux, 74.

  Euclidean geometry, 156 et seq.

  Evolution in our ideas, 195.

  Exchange, 110.

  Expectation, in reasoning, state of, 25.

  Extension, concrete, feeling of, 147 et seq.;
    characterised, 158.

  Extracts, 70.


  _Facultas signatrix_, 55.

  Family, 211.

  Ferrero, 220.

  First causes, 190.

  Fouillée, 177.

  Fox, ruses of, 18.

  Franklin, 55.

  Function, notion of mathematical, 190.


  Galileo, 190.

  Galton, 10, 40, 99.

  Gauss, 148, 156, 218, 220.

  Geese, time-sense of, 170.

  Geiger, 63.

  Genera, 210 et seq.

  General ideas, thinking by, 9;
    their grades distinguished, 101;
    likened to mental habits, 131, 225;
    meaning of, 135;
    observations on, 114 et seq.

  Generalisation, 9, 185.

  Generic image, 10, 87 et seq., 93, 169, 183, 196;
    an almost passive condensation of resemblances, 18;
    a spontaneous fusion of images, 22;
    comes half way between individual representation and abstraction
        properly so called, 23.

  Genii, 95.

  Geometry, born of practical needs, 148 et seq.;
    non-Euclidean, 156 et seq.

  Gérando, 40, 41, 51.

  Gesture, language of, 48 et seq., 66.

  Glass, 163.

  Goethe, 109, 134.

  Guyau, 166, 178.


  _Habere_, 79.

  Haeckel, 108.

  Hare, ruses of, 18.

  Hebrew, 69.

  Heinicke, 64.

  Helmholtz, 62.

  Heredity of acquired characters, 218.

  Hoeffding, 4, 136.

  Horwicz, 165, 166.

  Houzeau, 17, 18, 36.

  Huber, 55.

  Hume, 187, 190.

  Huxley, 10, 22, 212.

  Hybrids, 208.

  Hysterics, 127.


  Idealogues, 68.

  _Idées-forces_, 177.

  Identity, sense of, 6.

  Ideography, 53.

  Images, logic of, 26 et seq., 40;
    also 5 et seq., 111.

  Imagination, forms of, 112.

  Indifferent point, 163.

  Individual, notion of the, 204.

  Inference, 24, 26, 30.

  Infinity, 144.

  Intelligence, 87.

  Inventors, rôle of, 219.

  Iroquois, 74.

  Isolates, 17.


  James, W., 6, 9, 29, 30, 46, 80, 140, 149, 162, 175, 176, 194.

  Janet, 163.


  Kant, 137, 158, 175, 190.

  Kepler, 197, 202.

  Kirby, 55.

  Kleinpaul, 52.

  Kussmaul, 45, 46.


  Ladd, 7.

  Lamarck, 206.

  Language, origin of, 31 et seq., 54 et seq.

  Languages, natural organisms, 83;
    savage, 95 et seq.

  Laplace, 218.

  Lapp, 76.

  Law, origin of concept of, 194 et seq.;
    theoretical or ideal, 200.

  Laws, defined, 197;
    called by the names of their inventors, 198;
    vary in the course of evolution, 213.

  Lefèvre, A., 61.

  Leibnitz, 31, 129, 140, 214.

  Leroy, G., 18, 19, 30, 57.

  Lewes, 180.

  Liard, 142.

  Linnæus, 106, 210.

  Lobachévski, 156.

  Locke, 31.

  Lotze, 150, 151, 178.

  Lubbock, 20, 50, 55, 96.


  Mach, E., 148, 163, 164, 178, 202.

  Maclellan, 139.

  Magpie, 20, 21.

  Maine de Biran, 181.

  Mallery, Colonel, 49, 50, 51.

  Mariotte, 202.

  Mathematical faculty, the, 217.

  Mathematicians, 126.

  Mathematics, originated in observation, 148.

  Mayer, R., 191.

  Measure of quantity, 100.

  Memory, 132.

  Mill, John Stuart, 24, 25, 26, 34, 138, 151, 154, 155, 181, 191.

  Mimicry, language of, 52.

  Mind, the, 9, 216.

  Miracles, 186.

  Mivart, St. George, 48.

  Monkeys, intelligence of, 19.

  Montesquieu, 197.

  Morgan, C. Lloyd, 16, 30.

  Motion, psychology of, 182.

  Motor types, 112.

  Müller, Fr., 60.

  Müller, Max, 28, 39, 40, 59, 60, 69, 71, 74, 79, 80, 92.

  Münsterberg, 148, 163, 166, 167, 177.

  Muscular types, 112.

  Mussels, 84.


  Names, individual, appellative or general?, 32.

  Nativists, 149.

  Neanderthal anthropoid, 61.

  Neo-geometers, 157.

  Neretina, 7.

  Newton, 218, 219.

  Nichols, 139, 161, 164, 175.

  Noiré, L., 60.

  Nomenclature, 105 et seq.

  Nominalists, 122, 128.

  Normal time, 167.

  Nothing, the answer, 127 et seq.

  Number, concept of, history and theories of its origin, 137 et seq.

  Numbers, sequence of, 142 et seq.;
    nature of, 146.

  Numeration, in animals, 19;
    in the child, 35;
    its development, 98.


  Observations on general terms, 114 et seq.

  Oken, 108.

  Onomatopœia, 71, 72.

  Order, 211.

  Owen, Richard, 109.


  Painter, 117.

  Parallels, axiom of, 157.

  Pascal, 219.

  Paul, Hermann, 69, 71.

  Paulhan, 90, 136.

  Perception, utility its mainspring, 4.

  Percepts, 111.

  Pérez, B., 36.

  Performing animals, 15.

  Perrier, E., 105.

  Physiologist, 119.

  Phonogram, 71.

  Photographs, composite, 10, 22.

  Plato, 222.

  Plurality, 139.

  Poincaré, 202.

  Poinsot, 146.

  Polymorphism, 207.

  Practical judgments, 93.

  Present, the, its nature, 160 et seq.

  Preyer, 33, 38, 72, 139.

  Progress, 219.


  _Quack_, 34.

  Quantity, measure of, 100.

  Quatrefages, 205, 206.


  Ratiocination, 25.

  Realism, 128.

  Reasoning, signification of, 23;
    prior to speech, 38.

  Réaumur, 14.

  Recepts, 10, 26, 89.

  Reflexion, 94.

  Regnaud, P., 71, 78, 79.

  Regularity, conception of, 196.

  Relations, 80, 81.

  Renan, 59, 69, 71, 76.

  Renouvier, 145, 146, 175, 181.

  Representation, 5.

  Representative faculty, 112.

  Reproduction, 207.

  Resemblances, 6, 90.

  Respiration, 166.

  Rhythm, 164, 165.

  Ribot, his observations on general ideas, 135.

  Riemann, 156, 158.

  Romanes, 10, 13, 14, 19, 34, 35, 40, 43, 46, 55, 57, 63, 66, 89, 93,
        170, 184.

  Roots, 69 et seq., 75.

  Rousseau, J. J., 77.

  Rubicon, passage of the, 92.


  Sanskrit, 69.

  Savage languages, 95 et seq.

  Savage races, time-sense of, 171.

  Sayce, 67, 70, 73, 75, 77, 96.

  Schelling, 108.

  Schleicher, 83.

  Schmidkunz, 2, 3.

  Schneider, 7.

  Sciences, origin of the, 221.

  Scientists, 135.

  Scott, 43.

  Semi-circular canals, 149.

  Sensation-limits, 166.

  Sequence of numbers, 142 et seq.

  Siamese, 62.

  Sicard, Abbé, 44.

  Sidgwick, Prof., 125.

  Sigismund, 33.

  Signs, logic of, 27;
    imitative, 43;
    language of, 49;
    development of, 92;
    the importance of, 144 et seq.

  Sigwart, 199.

  Similarities, 90, 195.

  Simplification, 135.

  Skeleton, abstract thought a, 135.

  Smith, Adam, 31.

  Song, speech is derived from, 62.

  Space, origin of the concept of, 146 et seq.;
    acoustic, 148;
    sense of, 148;
    abstract notion of, 151 et seq.;
    _n_-dimensional, 156;
    Euclidean, 157;
    characterised, 158.

  Species, origin and growth of the concept of, 203 et seq.;
    fixity of, 205;
    constituent elements of the concept of, 206;
    defined, 206;
    vary in the course of evolution, 213.

  Specific characters, 205 et seq.

  Speech, origin of, 54 et seq., 59 et seq.;
    development of, 67.

  Spence, 55.

  Spencer, Herbert, 7, 62, 80, 137, 150, 165, 175.

  Stallo, 153, 158, 222.

  Steinthal, 59.

  Stern, 26.

  Stewart, Dugald, 31, 51.

  Substantive, the, 76.

  Substitution, 27, 110, 226.

  Sully, J., 25, 160, 175.

  Sylvester, 148.

  Symbolic thought, 132, 226.

  Symbolism, complete, 109.

  Symbols, 145.


  Taine, 33, 34, 73, 87, 129.

  Temporal signs, 178.

  Ten, the most convenient arithmetical basis, 143.

  Thermodynamics, 192.

  Time, origin of the concept of, 159;
    consciousness of, 164 et seq.;
    sense of, 164;
    conception of infinite, 174;
    measure of, 174 et seq.;
    psychological process by which its primitive notion is constituted
        in consciousness, 175 et seq.

  Time-perception, simple repetition the elements of, 176;
    the work of attention, 178.

  Tracy, Destutt de, 80.

  Tylor, 43, 50, 67, 71, 99, 142, 143.


  Unconscious activity, 132.

  Unconscious, the, 224;
    psychology of the, 226.

  Unity, idea of, 138;
    abstract, 141.

  Unity-type, 143.

  Utility, 218, 219;
    law of, 5.


  Van Ende, 170.

  Venn, J., 188.

  _Vera causa_, 181.

  Verb, the, 78, 97.

  Vierordt, 163.

  Visual types, 112, 119 et seq.

  Vital force, 193.

  Vocalisation, 61.

  Vogt, 208.


  Waitz, 178.

  Wallace, 217.

  Ward, 178.

  Wasps, intelligence of, 14.

  Weismann, 218.

  Whitney, 69, 71, 75, 80.

  Wilks, Dr., 58.

  Will, the type of causality, 181 et seq.

  Wizel, Adam, 126.

  Words, do we think without them?, 40;
    they pass to autocracy, 102.

  Writing, 53.

  Wundt, 103, 149, 161, 162, 163, 176, 189, 196.





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