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Psychology
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The Psychology of
Intelligence
By
JEAN PIAGET
Dodor of Science, Professor at the University of Geneva,
Director of the International Bureau of Education
Co-Director of the Institut J. J. Rousseau, Geneva
1960
LIT TLEFIELD, ADAMS 8c
Paterson, New Jersey
CO
THE INTERNATIONAL LIBRARY OF PSYCHOLOGY,
PHILOSOPHY AND SCIENTIFIC METHOD
Edited by C. K. OGDEN
1960
PUBLISHED BY LITTLEFIELD, ADAMS & Co.
Reprinted by arrangement with Humanities Press, Inc.
For sale only in the U.S. A., its possessions, and territories.
All rights reserved. No part of this book may be reproduced in any form
without permission in writing from the publisher, except by a reviewer
who may quote brief passages and reproduce not more than three illus-
trations in a review to be printed in a magazine or newspaper. Manu-
factured in the United States of America.
La Psychologic de L' Intelligence, first published in France 1947. The
Psychology of Intelligence, translated from the French by Malcolm Piercy
and D. E. Berlyne, MA., Lecturer in Psychology in the University of
St. Andrews, first published in the English language by Routledge and
Kegan Paul, Ltd., London, in 1950 and reprinted in 1951 and 1959. Cloth
edition available from Humanities Press, Inc., New York, in the United
States of America.
PREFACE
A book on the " Psychology of Intelligence " could cover
half the realm of psychology. The following pages are con-
fined to outlining one view, that based on the formation of
" operations/' and to determining as objectively as possible
its place among others which have been put forward. The
first task is to define intelligence in relation to adaptive
processes in general (Chap. I), then to show, by examining
the " psychology of thought", that the act of intelligence
consists essentially in " grouping " operations according to
certain definite structures (Chap. II). Then, if intelligence is
thus conceived as the form of equilibrium towards which all
cognitive processes tend, there arises the problem of its
relations with perception (Chap. Ill), and with habit tChap,
IV), as well as the question of its development (Chap. V)
and of its socialization (Chap, VI).
In spite of the abundance and the value of well-known
studies, the psychological theory of intellectual mechanisms
is only in its infancy, and we are barely beginning to glimpse
the sort of precision of which it might be capable. It is this
feeling of research in progress that I have sought to express.
This little volume contains the substance of the lectures
that I had the privilege of giving at the College de France
in 1942 at an hour when university men felt the need to show
their solidarity in the face of violence and their fidelity to
permanent values. It is difficult for me, as I rewrite these
pages, to forget the welcome given by my audience, as well
as the contact which I had at that time with my friends.
T T>
PREFACE TO THE SECOND (FRENCH)
EDITION
The reception given to this little work has in general been
a favourable one, which gives us the courage to reprint it
without any alterations. Nevertheless, one criticism has
frequently been levelled at our conception of intelligence
that it makes no reference to the nervous system or to'
its maturation in the course of the individual's develop-
ment. That, we think, is a simple misunderstanding. Both
the concept of " assimilation " and the transition from
rhythms to regulations and from these to reversible opera-
tions demand a neurological as well as a psychological (and
logical) interpretation. And these two interpretations, far
from contradicting each other, can only agree. We shall
explain ourselves elsewhere on this essential point, but we
have never felt entitled to deal with it before completing the
detailed ps}^chogenetic researches which are summed up in
this little book.
NOTE
The translators desire to thank
Messrs. P. F. C. Castle and C. Gattegno
for many valuable suggestions.
VI
CONTENTS
PAGE
PREFACE V
PREFACE TO THE SECOND (FRENCH) EDITION VI
PART ONE
THE NATURE OF INTELLIGENCE
Chapter I
INTELLIGENCE AND BIOLOGICAL ADAPTATION 3
The place of intelligence in mental organization. The
adaptive nature of intelligence. Definition of intelli-
gence. Classification of possible interpretations of
intelligence.
Chapter II
"THOUGHT PSYCHOLOGY" AND THE PSYCHOLOGICAL
NATURE OF LOGICAL OPERATIONS l8
Bertrand Russell's interpretation. 'Thought Psy-
chology": Buhler and Selz. Critique of "Thought
Psychology". Logic and psychology. Operations and
their "groupings". The functional significance and
structure of "groupings". Classification of "groupings"
and of the fundamental operations of thought. Equi-
librium and development.
PART TWO
INTELLIGENCE AND SENSORI-MOTOR FUNCTIONS
Chapter III
TELLIGENCE AND PERCEPTION 53
Historical. The Gestalt theory and its interpretation of
intelligence. Critique of Gestalt psychology. Differ-
ences between perception and intelligence. Analogies
between perceptual activity and intelligence.
VII
CONTENTS
Chapter IV
HABIT AND SENSORI-MOTOR INTELLIGENCE 87
Habit and intelligence. I. Independence or direct
derivation. Habit and intelligence. II. Trial-and-error
and structuring. Sensori-motor assimilation and the
birth of intelligence in the child. The construction of
the object and of spatial relations.
PART THREE
THE DEVELOPMENT OF THOUGHT
Chapter V
THE GROWTH OF THOUGHT INTUITION AND OPERATIONS IIQ
Differences in structure between conceptual intelligence
and sensori-motor intelligence. Stages in the construc-
tion of operations. Symbolic and pre-conceptual
thought. Intuitive thought. Concrete operations.
Formal operations. The hierarchy of operations and
their progressive differentiation. The determination of
"mental age".
Chapter VI
SOCIAL FACTORS IN INTELLECTUAL DEVELOPMENT 156
The socialization of individual intelligence. Operational
"groupings" and co-operation.
CONCLUSION
RHYTHMS, REGULATIONS AND GROUPINGS 167
SHORT BIBLIOGRAPHY 174
INDEX OF SUBJECTS 177
INDEX OF NAMES l8l
VIII
PART ONE
THE NATURE OF INTELLIGENCE
CHAPTER I
INTELLIGENCE AND BIOLOGICAL ADAPTATION
EVERY psychological explanation comes sooner or later to
lean either on biology or on logic (or on sociology, but this in
turn leads to the same alternatives). For some writers mental
phenomena become intelligible only when related to the
organism. This view is of course inescapable when we study
the elementary functions (perception, motor functions, etc.)
in which intelligence originates. But we can hardly see
neurology explaining why 2 and 2 make 4, or why the laws of
deduction are forced on the mind of necessity. Thus arises
the second tendency, which consists in regarding logical and
mathematical relations as irreducible, and in making an
analysis of the higher intellectual functions depend on an
analysis of them. But it is questionable whether logic,
regarded as something eluding the attempts of experimental
psychology to explain it, can in its turn legitimately explain
anything in psychological experience. Formal logic, or
logistics, is simply the axiomatics of states of equilibrium
of thought, and the positive science corresponding to this
axiomatics is none other than the psychology of thought.
With the tasks thus allotted, the psychology of intelligence
must assuredly continue to take account of logistic dis-
coveries, but these will never go so far as to dictate to
psychology its own solutions ; they will merely raise prob-
lems for it.
So we must start from this dual nature of intelligence as
something both biological and logical. The two chapters
that follow aim to define these preliminary questions and,
in particular, will attempt to reduce to the greatest unity
possible in the present state of knowledge these two funda-
mental but at first sight irreducible aspects of human
thought.
4 THE NATURE OF INTELLIGENCE
THE PLACE OF INTELLIGENCE IN MENTAL ORGANIZATION
Every response, whether it be an act directed towards
the outside world or an act internalized as thought, takes
the form of an adaptation or, better, of a re-adaptation.
The individual acts only if he experiences a need, i.e., if the
equilibrium between the environment and the organism is
momentarily upset, and action tends to re-establish the
equilibrium, i.e., to re-adapt the organism (Clapar&de). A
response is thus a particular case of interaction between the
external world and the subject, but unlike physiological
interactions, which are of a material nature and involve an
internal change in the bodies which are present, the responses
studied by psychology are of a functional nature and are
achieved at greater and greater distances in space (percep-
tion, etc.) and in time (memory, etc.) besides following more
and more complex paths (reversals, detours, etc.). Behaviour,
thus conceived in terms of functional interaction, presupposes
two essential and closely interdependent aspects : an affec-
tive aspect and a cognitive aspect.
There has been much discussion on the relations between
affect and cognition. According to P. Janet, a distinction
must be drawn between " primary action " or the relation
between sijbjgct and object (intelligence, etc.) and " second-
ary action " or the sulSfect's reaction to his own actions ;
this reaction, which constitutes elementary feelings, consists
of regulations of primary action and ensures the release of
the energy available inside the organism. But besides these
regulations, which determine the energetics or inner economy
of behaviour, we must, it seems, take into account those
which govern its ends or values, and such values charac-
terize an energetic or economic interaction with the external
environment. According to Claparfcde, feelings appoint a
goal for behaviour, while intelligence merely provides the
means (the " technique "). But there exists an awareness
of ends as well as of means, and this continually modifies
the goals of action. In so far as feeling directs behaviour
by attributing a value to its ends, we must confine ourselves
to saying that it supplies the energy necessary for action,
while knowledge impresses a structure on it. Thus arises
INTELLIGENCE AND BIOLOGICAL ADAPTATION 5
the solution proposed by the so-called Gestalt psychology :
behaviour involves a " total field " embracing subject and
objects, and the dynamics of this field constitutes feeling
(Lewin), while its structure depends on perception, effector-
functions, and intelligence. We shall adopt an analogous
formula, with the reservation that feelings and cognitive
configurations do not depend solely on the existing " field,"
but also on the whole previous history of the acting subject.
We shall simply say then that every action involves an
energetic or affective aspect and a structural or cognitive
aspect, which, in fact, unites the different points of view
already mentioned.
Indeed, all feelings consist either of regulations of internal
energies (P. Janet's " basic feelings", Claparitde's "interest",
etc.) or of factors controlling exchanges of energy with the
external environment (" values " of all kinds, real or imagin-
ary, from the " valencies " characteristic of Lewin's " total
field " and E. S. Russell's " valencies " to interindividual or
social values). Will itself is to be thought of as a matter of
affective, and therefore energetic, operations, 1 bearing
on the higher values, and making them capable of
reversibility and conservation (moral feelings, etc.)
just as the system of logical operations does so for
concepts, r-
But if all behaviour, without exception, thus implies an
energetics or an " economy ", forming its affective aspect,
the interaction with the environment which it instigates
likewise requires a form or structure to determine the
various possible circuits between subject and object. It is
this structuring of behaviour that constitutes its cognitive
aspect. A perception, sensori-motor learning (habit, etc.), a&^
act of insight, a judgment, etc., all amount, in one way or
another, to a structuring of the relations between the environ-
ment and the organism. It is in this that they reveal^arf
certain affinity among themselves which distinguis^ /
them from affective phenomena. We shall refer to them as
1 ProL Haget wishes to make it clear that his use in this book of tj^ft
words "operation" and "operational" has no connection with t
methodological doctrine of " Operationism '*. (Translator's
6 THE NATURE OF INTELLIGENCE
cognitive functions in a wide sense (to include sensori-motor
adaptation).
Affective life and cognitive life, then, are inseparable
although distinct. They are inseparable because all inter-
action with the environment involves both a structuring and
a valuation, but they are none the less distinct, since these
two aspects of behaviour cannot be reduced to one another.
Thus we could n<5t reason, even in puremathematics, without
experiencing certain feelings, and conversely no affect can
exist without a minimum of understanding or of discrimi-
nation. v An act of intelligence involves, then, an internal
regulation of energy (interest, effort, ease, etc.) and
external regulation (the value of the solutions sought and of
the objects concerned in the search), but these two controls
are of an affective nature and remain comparable with all
other regulations of this type. N Similarly, the perceptual or
intellectual elements which we find in all manifestations of
emotion involve cognition in the same way as any other
perceptual or intelligent reactions. What common sense
caHs " feelings " and " intelligence ", regarding them as two
/opposed " faculties ", are simply behaviour relating to
persons and behaviour affecting ideas or things ; but in each
of these forms of behaviour, the same affective and cognitive
aspects of action emerge, aspects which are in fact always
associated and in no way represent independent faculties.
x^Furthermore, N intelligence itself does not consist of an
isolated and sharply differentiated class of cognitive pro-
cesses. It is not, properly speaking, one form of structuring
among others ; it is the form of equilibrium towards which
all the structures arising out of perception, habit and
elementary sensori-motor mechanisms tend. It must be
understood that if intelligence is not a faculty this denial
involves a radical functional continuity between the higher
forms of thought and the whole mass of lower types of
dognitive and motor adaptation ; so intelligence can only be
the form of equilibrium towards which these tend. This
does not mean, of course, that a judgment consists of a
co-ordination of perceptual structures, or that perceiving
means unconscious inference (although both these theories
INTELLIGENCE AND BIOLOGICAL ADAPTATION 7
have been held), for functional continuity in no way
excludes diversity or even heterogeneity among structures.
Every structure is to be thought of as a particular form of
equilibrium, more or less stable within its restricted field
and losing its stability on reaching the limits of the field.
v But these structures, forming different levels, are to be
regarded as succeeding one another according to a law of
development, such that each one brings about a more
inclusive and stable equilibrium * for the processes that
emerge from the preceding level. ^Intelligence is thus only
a generic term to indicate the superior forms or organization
or equilibrium of cognitive structurings.
This view means, right from the start, an insistence on
the central role of intelligence in mental life and in the life
of the organism itself ; intelligence, the most plastic and at
the same time the most durable structural equilibrium of
behaviour, is essentially a system of living and acting
operations. It is the most highly developed form of mental
adaptation, that is to say, the indispensable instrument for
interaction between the subject and the universe when the
scope of this interaction goes beyond immediate and
momentary contacts to achieve far-reaching and stable
relations. But, on the other hand, this use of the term
precludes our determining where intelligence starts ; it is an
ultimate goal, and its origins are indistinguishable from those
of sensori-motor adaptation in general or even from those
of biological adaptation itself.
ADAPTIVE NATURE OF INTELLIGENCE
If intelligence is adaptation, it is desirable before anything
else to define the latter. N Now, to avoid the difficulties of
teleological language, adaptation must be described as an
equilibrium between the -action of the organism on the
environment and vice versa. Taking the term in its broadest
sense, " assimilation " may be used to describe the action of
the organism on surrounding objects, in so far as this action
depends on, previous behaviour involving the same or similar
objects. In fact every relation between a living being and
its environment has this particular characteristic : the
8 THE NATURE OF INTELLIGENCE
former, instead of submitting passively to the latter, modifies
it by imposing on it a certain structure of its own. It is in
this way that, physiologically, the organism absorbs subs-
tances and changes them into something compatible with its
own substance. Now, psychologically, the same is true,
except that the modifications with which it is then con-
cerned are no longer of a physico-chemical order, but
entirely functional, and are determined by movement,
perception or the interplay of real or potential actions
(conceptual operations, etc.). Mental assimilation is thus the
incorporation of objects into patterns of behaviour, these
patterns being none other than the whole gamut of actions
capable of active repetition.
Conversely the environment acts on the organism and,
following the practice of biologists, we can describe this
converse action by the term " accommodation ", it being
understood that the individual never suffers the impact of
surrounding stimuli as such, but they simply modify the
assimilatory cycle by accommodating him to themselves.
Psychologically, we again find the same process in the
sense that the pressure of circumstances always leads, hot
to a passive submission to them, but to a simple modification
of the action affecting them. This being so, we can then
define adaptation as an equilibrium between assimilation
and accommodation, which amounts to the same as an
equilibrium of interaction between subject and object. ^
Now in the case of organic adaptation, this interaction,
being of a material nature, involves an interpenetration
between some part of the living body and some sector of the
external environment. "^Psychological life, on the other
hand, begins, as we have seen, with functional interaction,
that is to say, f roijn the point at which assimilation no longer
alters assimilated objects in a physico-chemical manner but
siniply incorporates them in its own forms of activity (and
accommodation only modifies this activity). We can
understand that, superimposed on the direct inter-
^atipai of orgaiaisiji and environment, mental life brings
h It pMfireet ^ntejaction between subject and object,
wpc| : fifces 'Effect at ever increasing spatio-temporal distances
INTELLIGENCE AND BIOLOGICAL ADAPTATION 9
and along ever mare complex paths. The whole develop-;
ment of mental activity from perception and habit to*
symbolic behaviour and memory, and to the higher oper-^
ations of reasoning and formal thought, is thus a function 1
of this gradually increasing distance of interaction, and
hence of the equilibrium between an assimilation of realities
further and further removed from the action itself and an
accommodation of the latter to the former.
It is in this sense that intelligence, whose logical operations
constitute a mobile and at the same time permanent equi-
librium between the universe and thought, is an extension
and a perfection of all adaptive processes.- Organic adapta-
tion, in fact, only ensures an immediate and consequently
limited equilibrium between the individual and the present
environment. Elementary cognitive functions, such as
perception, habit and memory, extend it in the direction of
present space (perceptual contact with distant objects) and
of short-range reconstructions and anticipations. Only
intelligence, capable of all its detours and reversals by
action and by thought, tends towards an all-embracing
equilibrium by aiming at the assimilation of the whole of
reality and the accommodation to it of action, which it
thereby frees from its dependence on the initial hie and nunc.
DEFINITION OF INTELLIGENCE
If we undertake to define intelligence, which is certainly
important for determining the field which we shall be study-
ing under this heading, it is sufficient that we be agreed on the
degree of complexity of distant interaction which we shall
call " intelligent ". But here difficulties arise, since the
lower demarcation line remains arbitrary. For some, such
as Claparfede and Stern, intelligence j? *
to nevy circumstances."* Thus ClaparMe opposes intelligence
to instinct and habit, which are hereditary or acquired adap-
tations to recurring circumstances ; but for him it begins with
the most elementary empirical trial-and-error {the origin of
the implicit trial-and-error which subsequently characterizes
the search for a hypothesis) . For K. Biihler, who also divides
mental structures into three types (instinct, training and
10 THE NATURE OF INTELLIGENCE
intelligence), this definition is too broad ; jntelligence onJv
appears with acts of inskhj (Aha-Erlebnis)> while trial-and-
error is a form of training. % Kohler likewise reserves the
term intelligence for acts of abrupt restructuring and
excludes trial-and-error. It cannot be denied that the latter
appears right from the formation of the simplest habits,
which are themselves, when they are first formed, adapta-
tions to new circumstances. x On the other hand, problem,
hypothesis, and control, whose combination is the mark of
intelligence according to Claparfede also, already exist in
embryo in the needs, the trials-and-errors and the empirical
test characteristic of the least developed sensori-motor
adaptations. \ We must therefore choose between these two
alternatives : either we must be satisfied with a functional
definition at the risk of encompassing almost the entire
range of cognitive structures, or else we must choose a
particular structure as our criterion, but the choice remains
arbitrary and runs the risk of overlooking the continuity
which exists in reality.
x However, it is still possible to define intelligence toilbe
direction towards which its development is turned^jvithout
wMchTb-gaome a
forms of equilibrium. We
can therefore regard the matter from the point of view both
of the functional situation and of the structural mechanism*
From the first of these points of view, we can say that
behaviour becomes more " intelligent " as the pathways
between the subject and the objects on which it acts cease
to be simple and become progressively more complex: Thus
perception only requires simple paths, even if the object
perceived is very remote. ""A habit might seem more
complex, but its spatio-temporal articulations are welded
ntp a unique whole with no independent or separable
:>arts, x An act of intelligence, on the other hand fe such as
inding a hidden object or recognizing the meaning of a
>ictuie, involves 'a certain number of paths (in space and
Ini^) which can be both Isolated and synthesized. Thus,
from the point of view of the structural mechanism,
elementary sensori-motor adaptations are both rigid and
INTELLIGENCE AND BIOLOGICAL ADAPTATION II
unidirectional, while intelligence tends towards reversible
mobility. That, as we shall see, is the essential property of
the operations which characterize living logic in action.
But we can see straight away that reversibility is the very
criterion of equilibrium (as physicists have taught us). ^ To
define intelligence in terms of the progressive reversibility
of the mobile structures which it forms is therefore to repeat,
in different words, thatfintelligence constitutesjthfi-SlatSJSL
equilibrium towards which teM^lLlh^-SUccessiye adap-
tations of a sensori-motor and cognitive nature^as well as
^ assiinila^^
the organism and the environment, j
CLASSIFICATION OF POSSIBLE INTERPRETATIONS OF
INTELLIGENCE
^From_ the biological point of view, intelligence thus
appears as one of the activities of thg organism, while the
a particular
_
sector of the. surrounding environment. ; jfot a s the know-
ledge that mtdljgencejbugds
is therefore natural that the psychological theories of intellk
gence should come to be placed among biological ^theories of
adaptation and theories of knowledge in general. ^tHs~6t
surprising that there should be some rektionsfifp between
psychological theories and epistemological doctrines since,
even if psychology has been freed from philosophical tutelage,
there happily remains some bond between the study of
mental functions and that of the processes of scientific
knowledge. ^But what is more interesting is that there
exists a parallelism, and a fairly close one, between the great
biological doctrines of evolutionary variation (and therefore
of adaptation) and the particular theories of intelligence
as a psychological fact ; psychologists have, in fact, often
been unaware of the currents of biological inspiration behind
their interpretations, just as biologists have sometimes
12 THE NATURE OF INTELLIGENCE
unwittingly adopted one particular psychological position
among other possible ones (cf. the role of habit in Lamarck
or of competition and strife in Darwin) ; moreover, in view
of the affinity between the problems, there may be a simple
convergence of solutions and so the latter may confirm the
former.
x From the biological point of view, the relations between
the organism and the environment admit of six possible
interpretations according to the following combinations (each
of which has led to its own solution, classical or contem-
porary^ : either (I) we reject the idea of a genuine evolution,
or else (II) we admit its existence ; then, in both cases (I and
II) we attribute adaptations (i) to factors external to the
organism, or (2) to internal factors, or (3) to an interaction
between the two. So (I) from the non-evolutionist point of
view, we may attribute adaptation (Ii) to a pre-established
harmony between the organism and the properties of the
environment, (12) to a preforaiism allowing the organism to
respond to every sjtuation by actualizing its potential struc-
tures, or else (Is) to the " emergence " of complete structures,
irreducible to elements and determined simultaneously from
within and from without. 1
As for the evolutionist points of view (II), they likewise*
explain adaptive variations, by environmental pressure
(Lamarckism III), or by endogenous mutations with subse-
quent selection (mutationism Il2} 2 , or (Us) by a progressive
interaction between internal and external factors.
1 Pre-established harmony (Ii) is the solution inherent in classical
creationism and it constitutes the only explanation of adaptation which is
in fact at the disposal of vitalism in its pure form. Preformism (12) has
sometimes been associated with vitalist solutions, but it can become
independent of them and often persists in mutationist guises among
authors who deny all constructive character to evolution and consider
every new characteristic as the actualization of potentialities which
hitherto were merely latent. Conversely, the view based on energence (13)
reveifts to explaining the innovations which arise in the hierarchy of beings
by complex structures which are irreducible to the elements of the previous
leyei s ^ From these elements there " emerges " a new totality, which is
because It unites in an indissoeiable whole both the internal
' their relations with the external environment. While
tjj^e feet of evolution,, the hypothesis of emergence thus reduces
f & series 'of syntheses, each irreducible to the others, so that it is broken
nto 1 a series of distinct creations.
\ ,,?& ^jn^^oi^^expla^tiqiis of evolution subsequent selection is due
In Darwin it was attributed to competition.
INTELLIGENCE AND BIOLOGICAL ADAPTATION 13
* Now it is striking to note how we find the same broad
currents of thought in the interpretation of knowledge
itself, regarded as a relationship between the thinking subject
and objects. Corresponding to the pre-established harmony
of creationist vitalism, there is (Ii) the realism of those
doctrines which see in reason an innate adaptation to eternal
forms or essences ; ^corresponding to preformism, there is
(la) apriorism which explains consciousness by internal
structures which precede experience ; and corresponding
to the " emergence " of new structures there is\l3) con-
temporary phenomenology, which simply analyses the
various forms of thought, refusing either to derive them
genetically from each other or to distinguish in them the
roles of subject and object. "Evolutionist interpretations, on
the other hand, reappear in those epistemological schools
which allow for the progressive development of reason;
corresponding to Lamarckism there is (Hi) empiricism, which
explains knowledge by the pressure of objects; corresponding
to mutationism there are (112) conventionalism and pragma-
tism, which attribute the fittingness of mind to reality to the
untrammelled creation of subjective ideas, subsequently
selected according to a principle of simple expediency.
Finally, interactionism (113) involves a relativism, which
would describe knowledge as the product of an indissociable
collaboration between experience and deduction.
\Without insisting on this parallelism in its most general
form, we may now note how contemporary strictly psycho-
logical theories of intelligence are inspired by the same
currents of thought, whether biological emphasis is dominant
or whether philosophical influences related to the study of
knowledge are felt.
^ There is no doubt, to begin with, that a fundamental
incompatibility divides two kinds of interpretations : those
which, while recognizing the existence of the facts of develop-
ment, cannot help considering intelligence as a primary
datum, and thus reduce mental evolution to a sort of gradual
awakening of consciousness without any real construction
of anything, and those which seek to explain intelligence -by-
its own development. Mt should be noted moreover t|t|fe|^
14 THE NATURE OF INTELLIGENCE
two schools collaborate in the discovery and analysis of
actual experimental facts. x That is why it is fitting to
classify objectively all contemporary all-embracing interpre-
tations, inasmuch as they have helped to throw light on one
particular aspect or another of the facts to be explained ; the
demarcation line between psychological theories and philo-
sophical doctrines is in fact to be found in this appeal to
experience, and not in the initial hypotheses.
Among the non-evolutionist theories, there are first of all
(Ii) those which remain constantly faithful to the idea of an
intelligence-faculty, a sort of direct knowledge of physical
entities and of logical or mathematical ideas by a pre-
established harmony between intellect and reality. We must
confess that few experimental psychologists still adhere to
this hypothesis. But the problems arising from the common
frontiers of psychology and the analysis of mathematical
thought have caused certain symbolic logicians, e.g. Bertrand
Russell, to formulate such a conception of intelligence and
even to wish to' impose it on psychology itself (cf. his
A fa Jysis of Mind) . x
^A more prevalent hypothesis (12) is that according to
which intelligence is determined by internal structures,
which are likewise not formed but gradually become explicit in
the course of development, owing to a reflection of thought
on itself. This apriorist current has in fact inspired a good
deal of the work of the German Denkpsychologie and is
consequently found at the root of numerous experimental
researches on thought, using the familiar methods of
introspection, which have been developing from 1900-1905
to the present day. Naturally this does not mean that
every use of these methods of investigation leads to this
explanation of intelligence : Binet's work testifies to the
contrary> But for K. Biihler, Selz and many others, intelli-
gence eventually became, as it were, " a mirror of logic ",
which imposes itself from within with no possible causal
explanation.
* The author desires to indicate that his discussion of Russell's views on
this and subsequent pages refers only to that writer's first period. Russell
has since* rejected this position in favour of an extreme empiricism. (Trans-
INTELLIGENCE AND BIOLOGICAL ADAPTATION 15
In the third place (13), corresponding to emergence and
phenomenology (with the actual historical influence of the
latter), there is a recent theory of intelligence which has
raised the problem anew in a very suggestive way : the
Configuration (Gestalt) theory. \The notion of a " complex
configuration ", resulting from experimental researches in
perception, involves the assertion that a whole is irreducible
to the elements which compose it, being governed by special
laws of organization or equilibrium. Now, having analysed
these laws of structuring in the realm of perception and
having come across them again in motor functions, memory,
etc., the Configuration theory has been applied to intelli-
gence itself, both in its reflective (logical thought) and
its sensori-motor form (intelligence in animals and in
children at the pre-linguistic stage). Thus Kohler, in connec-
tion with chimpanzees, and Wertheimer, in connection with
the syllogism, etc., have spoken of " immediate restruc-
turings " seeking to explain the act of insight by the
" goodness " (Prdgnanz) of well organized structures, which
are neither endogenous nor exogenous but embrace subject
and object in a total field. Furthermore, these Gestalten,
which are common to perception, movement and intelligence,
do not evolve, but represent permanent forms of equilibrium,
independent of mental development (we may in this respect
find all intermediate stages between apriorism and the
Configuration theory, although the latter is normally found
linked with a physical or physiological realism of
" structures ").
Such are the three principal non-genetic theories of
intelligence \ It may be noted that the first reduces cognitive
adaptation to pure accommodation, since it sees thought
only as the mirror of ready-made " ideas ", that the second
reduces it to pure assimilation, since it regards intellectual
structures as exclusively endogenous, and that the third
unites assimilation and accommodation in a single whole,
since, from the Gestalt point of view, there exists only the
field linking objects and the subject, with neither activity
on his part nor the isolated existence of the object. /*"
\A.s for genetic interpretations, we find once mor$ those
16 THE NATURE OF INTELLIGENCE
which explain intelligence in terms of the external environ-
ment only (associationist empiricism corresponding to
Lamarckism), the activity of the subject (the trial-and-error
theory at the level of individual adaptation, corresponding to
mutationism at the level of hereditary variations) and the
relationship between subject and object (operational theory).
\ Empiricism (Hi) is scarcely upheld any longer in its pure
associationist form, except for some authors, of predomi-
nantly physiological interests, who think they can reduce
intelligence to a system of " conditioned " responses.
But we find less rigid forms of empiricism in^ Rignano's
interpretations, which reduce reasoning to mental experience,
and especially in Spearman's interesting theory, which is both
statistical (factor analysis of intelligence) and descriptive ;
from this second point of view, Spearman reduces the opera-
tions of intelligence to the "apprehension of experience" and
to the "eduction" of relations and " correlates ", that is to
say, to a more or less complex reading of immediately given
relations. These relations, then, are not constructed but
discovered by simple accommodation to external reality.
^The notion of trial-and-error (Hz) has given rise to several
interpretations of learning and of intelligence itself. The
trial-and-error theory elaborated by Claparfede constitutes
in this respect the most far-reaching exposition : intelligent
adaptation consists of trials or hypotheses, due to the
activity of the subject, and of their . selection, effected
afterwards under the pressure of experience (successes or
failures). This empirical control, which from the outset
selects the subject's trials, is subsequently internalized in
the form of anticipations due to awareness of relations, just
as motor trial-and-error is extended into symbolic trial-and-
error or imagination of hypotheses.
\Finally, emphasizing the interaction of the organism and
tbte*envkonment leads to the operational theory of intelli-
gence (IIj), According to this point of view, intellectual
fofparatk^,, whose highest form is found in logic and mathe-
ipfa*fe^ constitute genuine actions, being at the same time
^o^ibii^ pnacfeced by the subject and a possible experiment
problem is therefore to understand how
INTELLIGENCE AND BIOLOGICAL ADAPTATION 17
operations arise out of material action, and what laws of
equilibrium govern their evolution ; operations are thus
concerned as grouping themselves of necessity into complex
systems, comparable to the " configurations " of the Gestalt
theory, but these, far from being static and given from
the start, are mobile and reversible, and round themselves
off only when the limit of the individual and social genetic
process that characterizes them is reached. 1
This sixth point of view is the one we shall develop. As for
trial-and-error theories and empiricist conceptions, we shall
discuss them with particular reference to sensori-motor
intelligence and its relations with habit (Chap. IV). The
Configuration theory necessitates a special discussion, which
we shall focus upon the important problem of the relations
between perception and intelligence (Chap. IV). As for the
doctrine of an intelligence pre-adapted to independently
subsisting logical entities and that of a thought reflecting an a
priori logic, we shall return to them at the beginning of the
next chapter. In fact these both raise what we may call the
" preliminary question " of the psychological study of
intellect : may we hope for a real explanation of intelligence,
or does intelligence constitute a primary irreducible fact,
being the mirror of a reality prior to all experience, namely
logic ?
l We should note in this respect that, although the social nature of
operations follows from their character as effective action and their gradual
grouping, we shall nevertheless, for the sake of clarity of exposition,
reserve the discussion of social factors in thought until Chapter VI.
CHAPTER II
" THOUGHT PSYCHOLOGY " AND THE
PSYCHOLOGICAL NATURE OF LOGICAL
OPERATIONS
How far a psychological explanation of intelligence is
possible depends on the way in which logical operations are
interpreted : are they the reflection of an already formed
reality or the expression of a genuine activity ? No doubt
only the notion of an axiomatic logic can enable us to escape
from this dilemma, by submitting the actual operations of
thought to a genetic interpretation, while admitting the
irreducible character of their formal connections when these
are analysed axiomatically ; the logician then proceeds as
does the geometer with the space that he constructs deduc-
tively, while the psychologist can be likened to the physicist,
who measures space in the real world. In other words, the
psychologist studies the way in which the actual equilibrium
of actions and operations is constituted, while the logician
analyses the same equilibrium in its ideal form, i.e. as it
would be if it were completely realised, and as it is imposed
on the mind as a norm.
BERTRAND RUSSELL'S INTERPRETATION
We shall start from Bertrand Russell's theory of intelli-
gence, which is marked by the maximum possible subordi-
nation of psychology to logistics. ^According to Russell,
when we perceive a white rose we conceive at the same time
the ideas of the rose and of whiteness, and this by a process
analogous to that of perception ; we apprehend directly, and
as if from without, the 'Siniversals " corresponding to
perceptible objects and " subsisting " independently of the
subject's thought. But what then of false ideas ? These are
18
" THOUGHT PSYCHOLOGY " 19
ideas as much as any others, and the qualities of false and
true are applied to concepts just as there are red roses and
white roses. As for the laws which govern universals and
which control their relations, they depend on logic alone, and
psychology can only bow/ before this previous knowledge
which is given to it ready made.
This is the hypothesis. It is no use accusing it of being
metaphysical or metapsychological just because it runs
counter to the common sense of experimentalists ; the
mathematician's common sense finds it quite acceptable and
psychology must take mathematicians into account. So
radical a thesis is even well worth pondering over. First of
all, it does away with the notion of an operation, since, if we
apprehend universals from without, we do not construct them.
In the expression i + i =2, the sign 4- signifies nothing more
than a relation between the two unities and in no way an
activity producing the number 2 ; as Couturat has clearly
indicated, the notion of an operation is essentially " anthropo-
morphic ". Russell's theory therefore dissociates a fortiori
the subjective factors of thought (belief, etc.) from the
objective factors (necessity, probability, etc.). In fact it
rejects the genetic point of view ; an English follower of
Russell once said, in order to prove the uselessness of research
on thought in children, that " the logician is interested in
true ideas, while the psychologist finds pleasure in describing
false ones/'
^But, if we have seen fit to begin this chapter with a
review of Russell's ideas, it was in order that we might note
at once that the demarcation line between the knowledge
derived from symbolic logic and psychology cannot be
crossed by the former with impunity. Even if, from the
axiomatic point of view, the operation were to appear devoid
of significance, its very " anthropomorphism " would make
at mental reality of ifX From the genetic point of view, opera-
tions are indeed genuine actions and do not consist merely
of taking note of or apprehending relations.^^When i is added
to i what happens is that the subject combines two units into
one whole, when he could keep them apart. There is no
doubt that this action, occurring in thought, acquires a
20 THE NATURE OF INTELLIGENCE
character sui generis which distinguishes it from other
actions ; it is reversible, i.e., having combined the two units,
the subject can then separate them and thus find himself
where he started. But this does not make it any the less a
genuine action, radically different from the simple reading of
a relation such as 2> i. Now to this followers of Russell will
only reply with a non-psychological argument : it is an
illusory action, since i -4-1 have made 2 from all eternity (or,
as Carnap and Wittgenstein would say, since 14-1=2 is
only a tautology, characteristic of the language of " logical
syntax ", and does not concern thought itself, whose
functioning is specifically experimental). Broadly speaking,
mathematical thought is mistaken when it believes it can
construct or invent, since it is confined to revealing the
various aspects of an already formed world (and,, according
to the Vienna circle, an entirely tautological one). ;However,
if we deny the psychology of intelligence the right to concern
itself with the nature of logico-mathematical entities, the
fact remains that individual thought cannot remain
passive in the face of ideas (or of the symbols of a logical
language) any more than it can in the presence of physical
entities, and that in order to assimilate them it has to
reconstruct them by means of psychologically real operations.
We may add that the assertions of Bertrand Russell and
the Vienna circle, regarding the independent existence of
logico-mathematical entities and the operations which seem
to engender them, are just as arbitrary from the purely
logical point of view as they are from the psychological :
in fact they will always meet the fundamental difficulty
inherent in a realism of classes, relations and numbers,
namely, that of the antinomies relating to the *' class of all
classes " and to infinity. On the other, hand, from the
operational point of view, infinite entities are only the
expression of operations capable of being repeated indefi-
nitely.
Finally, front a genetic point of view, the hypothesis of a
Direct apprehension by thought of universals, subsisting
* to^em^eiitly of it, is even more chimerical. We may
admit that the false ideas of the adult have aa existence
" THOUGHT PSYCHOLOGY " 21
comparable to that of true ideas. What then are we to think
of the concepts successively constructed by the child in the
course of the different stages of his development ? Do the
" schemata " of preverbal practical intelligence " subsist "
outside the subject ? And what of those of animal intelli-
gence ? If we reserve eternal " subsistence " solely for true
ideas, at what age does their apprehension begin ? And,
furthermore, even if stages of development simply mark
successive approximations of intelligence in its conquest of
immutable " ideas ", what proof have we that the normal
adult or the logicians of Russell's school have succeeded in
grasping them and will not be continually surpassed by
future generations ?
" THOUGHT PSYCHOLOGY " : K. BUHLER AND SELZ
The difficulties we have just encountered in Russell's
interpretation of intelligence recur ip. part in the interpre-
tation arrived at by the German Denkpsychologie, although
in this case it is the work of pure psychologists. It is true
that for the writers of this school logic is not imposed on the
mind from without but from within ; the conflict between the
exigencies of psychological explanation and those of the
logicians' deduction is certainly attenuated by it ; but, as we
shall see, it is not entrely assuaged, and the shadow of formal
logic continues as an irreducible datum to dog the explana-
tory and causal research of the psychologist as long as he
does not adopt a thoroughgoing genetic point of view. Now
the German "thought psychologists" have in fact been
inspired either by essentially apriorist trends or by pheno-
menological trends (the influence of Husserl has been
particularly clear) with all intermediate stages between the
two.
As a method, the psychology of thought came into being
simultaneously in France and in Germany. Turning away
entirely from the associationism which he defended in his
little book, La Psychologic du raisonnement, Binet recon-
sidered the question of the relations between thought
and images by an interesting method of controlled intro-
spection, and by this means he discovered the existence of
22 THE NATURE OF INTELLIGENCE
imageless thought ; in 1903, in his Etude expirimentale de
V intelligence, he maintains that relations, judgments,
attitudes, etc. go beyond imagery, and thinking cannot be
reduced to " looking at pictures/* As for knowing what
these acts of thought which resist an associationist inter-
pretation consist of, Binet reserves his opinion, confining
himself to noting the relationship between intellectual and
motor " attitudes ", and concludes that, from the point of
view of introspection alone, "thought is an unconscious
activity of the mind/' This is extremely instructive but
certainly a disappointing test of the resources of a method
which is thus shown to be more fruitful in raising problems
than in solving them.
In 1900, Marbe (Experimentette Untersuchungen uber das
Urtheil) also enquired how judgment differed from associa-
tion and likewise hoped to resolve the question by a method
of controlled introspection. Marbe meets with a most
varied range of states of consciousness : verbal represen-
tations, images, sensations of movement, attitudes (doubt
etc.), but nothing constant. Although he notes that the
necessary condition for judgment is the voluntary or
intentional character of the report, he does not consider this
condition as sufficient, and concludes with a denial which
recalls Binet's formula : there is no state of consciousness
which is invariably associated with judgment and which can
be regarded as its determinant. But he adds, and this to
us seems to have influenced directly or indirectly all German
Denkpsychologie, that judgment consequently implies the
intervention of a factor that is non-psychological because it
comes from pure logic. We see that we were not exaggerating
when we forecast the reappearance, on this new plane, of the
difficulties inherent in the logicalism of the Platonists.
Next came the work of Watt, Messer and K. Biihler,
inspired by Kulpe, for which the Wiirzburg school is famous.
Watt, using the method of controlled introspection, studies
the associations reported by the subject following instructions
(e.g. supraordinate associations, etc.) and finds that the task
may act together with images, or in an imageless state of
consciousness (Bewwsstheit), or even unconsciously. He
" THOUGHT PSYCHOLOGY " 23
therefore formulates the hypothesis that Marbe's " inten-
tion " is just the effect of the task (whether external or
internal), and thinks that he can solve the problem of
judgment by showing it to be a series of states conditioned
by a mental factor which was at one time conscious and
still exerts its influence.
Messer finds Watt's description too vague, since it is
applied to a controlled response as well as to judgment, and
he takes up the problem again with a similar technique :
he distinguishes between constrained association and judg-
ment, which is something either accepted or rejected, and
devotes the main body of his work to analysing the different
mental types of judgment.
Finally, with K. Biihler we reach the culmination of the
work of the Wiirzburg school. The poverty of the initial results
produced by the method of controlled introspection seems
to him to result from the fact that the questions used
involved processes which were too simple, and thenceforward
he undertakes to analyse with his subjects the solution of
genuine problems. The elements of thought obtained by this
procedure fall into three categories : images whose role is
accessory, and not essential as associationism would have
it ; intellectual feelings and attitudes ; and, above all,
" thoughts " themselves (Bewusstheiten). These for their
part occur in the form of " consciousness of relation "
(e.g. A<B), " consciousness of rules " (e.g. thinking of the
inverse square of the distance without knowing what objects
or what distances are involved), or of " purely formal
intentions " in the scholastic sense (e.g. thinking of the
architecture of a system). Thus conceived, the psychology
of thought arrives at a precise and often very refined
description of intellectual states, but one that is analogous to
logical analysis and in no way explains operations as such.
The work of Selz, on the other hand, goes beyond the
results of the Wiirzburg school towards an analysis of the
actual dynamics of thought and not merely of its isolated
states. Selz, like Biihler, studies the solution of actual
problems, but he attempts not so much to describe the
elements of thought as to understand how the solutions are
24 THE NATURE OF INTELLIGENCE
reached. Having studied " reproductive thought " in 1913,
he tries, in 1922, (Zitr Psychologic des produktiven Denkens
und des Irrtums] to penetrate the secret of mental construc-
tion. It is interesting to note that the more research is
directed towards the actual activity of thought, the further
it departs from logical atomism, which consists in classing
relations, judgments and isolated schemata, and the nearer it
comes to living wholes after the pattern of Gestalt
Psychology, there being a different pattern where operations
are concerned, as we shall shortly find. In fact for Selz all
thinking activity consists of completing a whole (theory of
Komplexerganz-img) : the solution of a problem cannot be
reduced to the stimulus-response schema, but consists of
filling in the gaps in " complexes " of ideas and relations.
When a problem is put, two possibilities thus present
themselves. It may be only a question of reconstruction,
no new construction being required, and the solution consists
simply in having recourse to already existing " complexes " ;
there is then " actualization of knowledge", and therefore
thought which is simply " reproductive " . Or else it may
be a genuine problem, testifying to the existence of gaps
within the complexes hitherto adopted, and so it is no longer
a matter of utilizing knowledge but of utilizing methods of
solution (applying known methods to a new case), or even
of deriving new methods from old ones ; there is, in these
last two cases, " productive " thought, and this is really
where completing wholes or already existing complexes
comes in. As for this " filling in of gaps ", it is always
orientated by " anticipatory schemata " (comparable to
Bergson's " dynamic schema "), which weave between new
data and the main body of the corresponding complex a
system of provisional global relations constituting the
pattern of the solution to be found (i.e. the directing hypo-
thesis). These relations themselves are finally made more
precise by a mechanism obeying exact laws ; these laws are
i|0me other than those of logic, of which, when all is said and
<$6i*, thought is the mirror.
i We should also note Lindworsky's work, which comes
the two studies by Selz arid anticipates his conclu-
" THOUGHT PSYCHOLOGY " ^5
sions. As for Claparfede's study of the genesis of the hypo-
thesis, this will be discussed in relation to trial-and-error
(Chapter IV).
CRITIQUE OF " THOUGHT PSYCHOLOGY "
It is clear that the researches just mentioned have
rendered considerable service to the study of intelligence.
They have freed thought from the conception of the image
as a constituent element, and have discovered, like Descartes,
that judgment is an act. They have accurately described
thte various states of thought and have thus shown, contra-
dicting Wundt, that introspection may be " controlled ",
i.e. systematized by an observer.
But first we should mention that even at the level of
simple description the relations between image and thought
have been oyer^simplified by the Wurzburg school. It
remains an acknowledged fact that the image does not
constitute an element of thought itself. It merely accom-
panies it and serves as a symbol for it, an individual symbol
completing the collective signs of language^The "Meaning"
school, inspired by Bradley's logic, has clearly shown that
all thought is a system of meanings, and it is this notion
that Delacroix and his pupils, in particular Meyerson, have
developed in connection with the relations between thought
and the image. These meanings involve in fact " signifi-
cates ", which constitute thought itself, but also " signifi-
cants ", comprising verbal signs or imaged symbols which
are formed hand in hand with thought.
On the other hand, it is obvious that the very method used
by Denkpsychologie prevents it from going beyond pure
description, and that it fails to explain the actual cons-
tructive mechanisms of intelligence, Because introspection,
even when controlled, surely deals only with the products of
thought and not with its formation. Furthermore, it is
restricted to subjects capable of reflection; whereas we
should perhaps look for the secret of intelligence in children
under the age of seven or eight 1
Lacl^j^ Ihmght
Psychology 7 ' a^aJj^es^oiily the final stages of
26 THE NATURE OF INTELLIGENCE
development. Speaking in terms of states and of completed
equilibrium, it is not surprising that it arrives at a panlogi-
cism and is obliged to give up psychological analysis when
faced with the irreducibly given nature of the laws of logic.
From Marbe, who invoked logical law directly as a non-
psychological factor which intervenes causally and fill
the gaps of mental causality, to Selz who arrived at a
sort of logico-psychological parallelism by making thought
the mirror of logic, logical fact remains for all these writers
inexplicable in psychological terms.
No doubt Selz freed himself partially from the unduly
narrow procedure of analysing states and elements in order
to try to follow the dynamics of the act of intelligence. So
he discovers the wholes which characterize systems of
thought as well as the role of anticipatory schemata in the
solution of problems. But while he frequently notes the
analogies between these processes and organic and motor
mechanisms, he does not trace their genetic formation.
So he also joins the Wiirzburg school in their panlogicism, and
even does so in a paradoxical manner, an example which
merits reflection from those who wish to free psychology
from the toils of logistic apriorism while seeking to explain
logical fact.
Indeed, in revealing the essential role played by wholes in
the functioning of thought, Selz might have drawn the
conclusion that classical logic is incapable of describing
reasoning in action, as it appears and takes form in " produc-
tive thought J> . Classical logic, even when rendered infinitely
more flexible by the subtle and precise technique of the
logistic calculus, remains atomistic ; classes, relations and
propositions are therein analysed with respect to their
elementary operations (logical addition and multiplication,
implications and contradictions, etc.). In order to interpret
the action of anticipatory schemata and of Komplexerganzung,
and thus of intellectual wholes which intervene in living
and active thought, Selz would, on the contrary, have
required a logic of wholes, and so the problem of the relations
between intelligence/as a psychological fact, and logic itself
would have been put in new terms calling for an essentially
" THOUGHT PSYCHOLOGY " 27
genetic solution. But Selz, having too much respect for
a priori logical formulations despite their discontinuous and
atomistic character, naturally meets them once more as
the residue remaining after psychological analysis has done
all it can and finds himself invoking them to explain the
details of mental elaboration.
In short, " Thought Psychology " finished by making
thought the mirror of logic, and in this lies the root of the
difficulties it has found insurmountable. The question is
then to ascertain whether it would not be better simply to
reverse the terms and make logic the mirror of thought,
which would restore to the latter its constructive indepen-
dence.
LOGIC AND PSYCHOLOGY
Logic is the mirror of thought, and not vice versa ; in
Classes, relations et nombres : essai sur les groupements de la
logistique et la rversibilit& de la penste, 1942, we were led to
this point of view by the study of the formation of operations
in the child, and that after having been persuaded from the
outset of the justice of the postulate of irreducibility which
inspires the " Thought Psychologists ". This amounts to
saying that logic is the axiomatics of reason, the psychology
of intelligence being the corresponding experimental science.
It seems to us essential to insist somewhat on this methodo-
logical point.
An axiomatics is an exclusively hypothetico-deductive
science, i.e,, it reduces to a minimum appeals to experience
(it even aims to eliminate them entirely) in order freely to
reconstruct its object by means of undemonstrable propo-
sitions (axioms), which are to be combined as rigorously as
possible and in every possible way. In this way geometry
has made great progress, seeking to liberate itself from all
intuition and constructing the most diverse spaces simply by
defining the primary elements to be admitted by hypothesis
and the operations to which they are subject. The axiomatic
method is thus the mathematical method par excellence and
it has had numerous applications, not only in pure mathe-
matics, but in various fields of applied mathematics (from
28 THE NATURE OF INTELLIGENCE
%
theoretical physics to mathematical economics). The
usefulness of an axiomatics, in fact, goes beyond that of
demonstration (although in this field it constitutes the only
rigorous method) ; in the face of complex realities, resisting
exhaustive analysis, it permits us to construct simpli-
fied models of reality and thus provides the study of
the latter with irreplaceable dissecting instruments. To
sum up, an axiomatics constitutes a " pattern " for reality,
as F. Gonseth has clearly shown, and, since all abstraction
leads to a schematization, the axiomatic method in the
long run extends the scope of intelligence itself.
But precisely because of its " schematic " character, an
axiomatics cannot claim to be the basis of, and still less to
replace, its corresponding experimental science, i.e. the
science relating to that sector of reality for which the
axiomatics forms the pattern. Thus, axiomatic geometry is
incapable of teaching us what the space of the real world
is like (and " pure economics " in no way exhausts the
complexity of concrete economic facts). No axiomatics
could replace the inductive science which corresponds to it,
for the essential reason that its own purity is merely a limit
which is never completely attained. As Gonseth also says,
there always remains an intuitive residue in the most
purified pattern (just as there is already an element of
schematization in all intuition). This reason alone is enough
to show why an axiomatics will never be the basis of an ex-
perimental science and why there is an experimental science
corresponding to every axiomatics (and, no doubt, vice
versa).
Thus the problem of the relations between formal logic
and the psychology of intelligence is to find a solution
comparable to that which has settled, after centuries of
discussion, the conflict between deductive geometry and
positive or physical geometry. As in the case of these
disciplines, logip and the psychology of thought began by
ifrefflg confused and not differentiated at all ; Aristotle
no dopbt thought he was writing a natural, history of the
qfad laawell ^ of physical reality itself) by stating the laws
'fc :$* spogism. Whan psychology was set up as an it
" THOUGHT PSYCHOLOGY " 29
pendent science, psychologists came to understand (taking
a considerable time over it) that the reflections contained in
text-books of logic on the concept, judgment and reasoning
did not exempt them from seeking to sort out the causal
mechanism of intelligence. But as a residual effect of their
original failure to draw a distinction, they still continued to
think of logic as a science of reality, placed, in spite of its
normative character, on the same plane as psychology, but
concerned exclusively with " true thought " is opposed to
thought in general, freed from all norms. Hence the deluded
outlook of Denkpsychologie, according to which thought, a
psychological fact, constitutes a reflection of logical laws.
But, on the other hand, if logic were found to be an axio-
matics, the pseudo-problem of these mutual relations would
disappear through the interchange of status.
Now it seems obvious that the more logic repudiates the
vagueness of verbal language in order to establish, under the
name of symbolic logic or logistics, an algorithm with
a rigour equalling that of mathematical language, the more
it turns into an axiomatic technique. We know, moreover,
the extent to which this technique has rapidly been linked
up with the most general fields of mathematics, till symbolic
logic has today acquired a scientific value independent of
the particular philosophies of individual logicians (Russell's
Platonism or the nominalism of the Vienna Circle). The
very fact that philosophical interpretations leave its internal
technique unchanged shows that the latter has reached the
axiomatic level ; symbolic logic thus constitutes, if for no
other reason, an ideal " model " of thought.
But this being so, the relations between logic and psy-
chology are made so much the simpler. Symbolic logic need
not have recourse to psychology, since a question of fact in no
way affects a hypothetico-deductive theory. Conversely, it
would be absurd to invoke symbolic logic to settle an
experimental question such as that of the actual mechanism
of intelligence. Nevertheless, in so far as psychology under-
takes to analyse the final states of equilibrium of thought,
there is not a parallelism but a correspondence between this
experimental knowledge and symbolic logic, just as there is
30 THE NATURE OP INTELLIGENCE
a correspondence between a pattern and the reality which
it represents. Every question raised by one of the two
disciplines corresponds to a question belonging to the other,
although neither their methods nor their solutions may
coincide.
This independence of methods may be illustrated by a very
simple example, whose discussion will moreover be useful to
us in what follows (Chapters V and VI). It is customary to say
that (real) thought " applies the principle of contradiction "
which, to take things literally, would mean the intervention
of a logical factor in the causal context of psychological facts,
and would thus contradict what we have just been asserting.
Now, on closer examination of these terms, such a statement
is found to be meaningless. The principle of contradiction is
confined, in fact, to precluding the simultaneous affirmation
and negation of a given predicate : A is incompatible with
not-A. But, for the actual thought of a real subject, the
difficulty begins when he wonders if he has the right to
assert A and B simultaneously, for logic never states directly
whether or not B implies not-A. May we, for example,
speak of a mountain which is only 100 feet high or is this a
contradiction ? Is it possible to be both a communist and a
patriot ? Can we conceive of a square with unequal angles ?
etc. To answer these questions there are only two possible
procedures. The logical procedure consists in formally
defining A and B and ascertaining whether B implies not-A.
But then the " application " of the " principle " of contra-
diction relates exclusively to definitions, i.e. to axiomatized
concepts and not to the living ideas used by thought in
reality. The procedure followed by real thought, on the
other hand, consists, not in reasoning on a basis of defini-
tions alone, which has no interest for it (definition being
from this point of view only a retrospective and often
incomplete act of awareness) but in acting and operating,
in constructing concepts according to the possible combina-
tions of these actions or operations. A concept is in fact
only a plan of action or of operation, and only carrying out
the operations producing A and B will decide whether they
are compatible or not. Far from " applying a principle ",
" THOUGHT PSYCHOLOGY " 31
actions are organized according to their inner rules of
consistency, and it is this organizational structure that
constitutes the fact of positive thought corresponding to
what is called, on the axiomatic level, the "principle of
contradiction."
It is true that in addition to the individual consistency of
actions there enter into thought interactions of a collective
order and consequently " norms " imposed by this collabor-
ation. But co-operation is only a system of actions, or of
operations, carried out in concert, and we may repeat the
preceding argument for collective symbolic behaviour, which
likewise remains at a level containing real structures, unlike
axiomatizations of a formal nature.
For psychology, therefore, there remains unaltered the
problem of understanding the mechanism with which
intelligence comes to construct coherent structures capable
of operational combination ; and it is no use invoking
" principles " which this intelligence is supposed to apply
spontaneously, since logical principles concern the theoretical
pattern formulated after thought has been constructed
and not this living process of construction itself. Brunsch-
vicg has made the profound observation that intelligence
wins battles or indulges, like poetry, in a continuous work of
creation, while logico-mathematical deduction is comparable
only to treatises on strategy and to manuals of " poetic art",
which codify the past victories of action or mind but do not
ensure their future conquests. 1
Meanwhile, and precisely because logical axioinatics
schematizes the real work of the mind after it has occurred,
every discovery in either of these two fields may give rise
to a problem in the other. There is no doubt that logical
schemata have by their exactness often helped psychological
analysis ; Denkpsychologie is a good example of this. But,
conversely, when psychologists like Selz, the " Gestaltists ",
and many others discover the role of wholes and complex
organizations in the work of thought, "there is no reason to
regard classical logic or even current symbolic logic, which
1 L. Bmnschvicg, Les Etapes de la philosophie mathdmatique, and edition,
p. 426.
32 THE NATURE OF INTELLIGENCE
has not gone beyond a discontinuous and atomistic mode of
description, as something untouchable and as the last word,
or to make of them a model of which thought is the
" mirror " ; on the contrary, we must construct a logic of
wholes if we wish it to serve as an adequate pattern for the
states of equilibrium of the mind and to analyse operations
without reducing them to isolated and psychologically
inadequate elements.
OPERATIONS AND THEIR " GROUPINGS "
The great stumbling-block in the way of any theory of
intelligence which starts from the analysis of thought in its
higher forms is the fascination that consciousness derives
from the ease of verbal thought. P. Janet has shown very
ably how language is a partial substitute for action, so
that introspection experiences the greatest difficulty in
realizing by its own methods that it is itself an item of
behaviour ; verbal behaviour is an action, doubtless scaled
down and remaining internal, a rough draft of action which
constantly runs the risk of being nothing more than *a
plan, but it is nevertheless an action, which simply replaces
things by signs and movements by their evocation, and
continues to operate in thought by means of these
spokesmen. Now, introspection, ignoring this active aspect
of verbal thought, sees in it nothing but reflection, speech
and conceptual representation, which explains the mistaken
belief of introspective psychologists that intelligence is
reducible to these privileged terminal states, and the delusion
of logicians that the most adequate logistic pattern must be
essentially a theory of " propositions ".
It is important, therefore, in order to arrive at the real
functioning of intelligence, to reverse this natural movement
of the mind and to revert to thinking in terms of action
itself ; only in this way will the role of this internal action,
the operation, appear in a clear light. And this very fact
forces us to recognize tte continuity which links operation
witjh tpte action, the source and medium of intelligence.
Xh3te i nothing more fitted to throw light on these facts
th^n a comicferation of the sort of language still a language.
" THOUGHT PSYCHOLOGY " 33
even though it is purely intellectual, transparent and free
from the deceptions of imagery which we call mathematics.
In any expression, such as (x*+y =z u)> each term refers to
a specific action : the sign ( =) expresses a possible substi-
tution, the sign ( +) a combination, the sign ( - ) a separation,
the square (* 2 ) the action of reproducing f x' % times, and
each of the values u, x, y and z the action of reproducing
unity a certain number of times. So each of these symbols
refers to an action which could be realised, but which
mathematical language contents itself with describing
abstractly in the form of internalised actions, i.e. operations
of thought. 1
Now if this is obvious in the case of mathematical thought,
it is no less true of logical thought and even of conversational
language from the dual point of view of logical analysis and
psychological analysis. It is in this way that two classes can
be added just like two numbers. In the proposition " Verte-
brates and Invertebrates constitute all the Animals ", the
word " and " (or the logical sign -f ) represents an action of
combination, which may be effected materially by classifying
a collection of objects but can also be effected mentally by
thought. Similarly, we may make classifications from
several points of view at the same time, as in a matrix, and
this operation (which symbolic logic calls logical multipli-
cation) denoted by x is so natural to the mind that the
psychologist Spearman has gone so far as to make it out
to be, under the name of the " education of correlates ", one
of the distinguishing characteristics of the act of intelligence :
" Paris is to France as London is to Great Britain/' We may
anange in series the relations A<B ; B<C, and this double
relation, which permits the conclusion that C is greater than
A, is the reproduction in thought of the action which could
have been effected materially by placing the three objects
in order of increasing size. We may in the same way
l This active character of mathematical reasoning was recognised by
Goblot in his Trait j de logique', "deduction is construction", he said.
But operational construction seemed to him simply to be controlled by the
" propositions previously admitted ", whereas the control of operatior^ is
immanent in them and is constituted by their capacity for reversible
oompositioB, in other words by their feature as " groups ":
34 THE NATURE OF INTELLIGENCE
form series based on several relations at the same time, and
come back to another form of logical multiplication or
correlation, etc.
But if we now envisage the terms themselves, i.e.,
the so-called elements of thought, class-concepts or
relational concepts, we find the same operational character
in them as in their combinations. Psychologically, a class-
concept is only the expression of the identity of the subject's
reaction to objects which he combines in one class ; logically,
this active likening appears as the qualitative equivalence
of all the members of the class. Similarly, an asymmet-
rical relation (more or less heavy or big) expresses
different intensities of action, i.e., differences as opposed
to equivalences, and in logic takes the form of serial
structures.
In short, the essential characteristic of logical thought is
that it is operational, i.e., it extends the scope of action
by internalising it. On this point we shall unite opinions
emanating from the most diverse trends, from empiricist
and pragmatist theories, which by attributing the character
of a " mental experiment " to thought are forced to accept
this basic assumption (Mach, Rignano, Chaslin), to
interpretations which are apriorist in inspiration (Delacroix).
Furthermore, this hypothesis is in agreement with the
schematisations of symbolic logic, as long as these simply
devise a technique and are not made into a philosophy
denying the existence of the very operations which they are
in actual fact constantly using.
However, this does not complete the picture, for an
operation is not simply reducible to any and every action,
and, even if operational acts are derived from actual acts,
the distance between the two is considerable, as we shall see
ift detail when we come to examine the development of
intelligence (Chapters IV and V). A rational operation can be
compared to a simple action only as long as it is viewed in
isolation, but that is precisely the fundamental error of
empiricist theories of " mental experiment ", that they
concentrate on the isolated operation ; a single operation is
not an operation at all but only a simple intuitive represen-
" THOUGHT PSYCHOLOGY " 35
tation. The specific nature of operations, as compared with
empirical actions, depends, on the other hand, on the fact
that they never exist in a discontinuous state. It is only as
an entirely illegitimate abstraction that we speak of " one "
operation ; a single operation could not be an operation,
because the peculiarity of operations is that they form
systems. Here we may well protest vigorously against
logical atomism, whose pattern has been a grievous hindrance
to the psychology of thought. In order to grasp the opera-
tional character of rational thought, we must deal with
these systems as they are, and, if ordinary logical patterns
conceal their existence, then we must construct a logic of
wholes.
To begin with the simplest example, classical psychology,
like classical logic, speaks in this way of concepts as elements
of thought. Quite apart from the fact that its definition
relies on other concepts, a " class " could not exist by itself.
As an instrument of real thought, disregarding its logical
definition, it is only a " structured ", not a " structuring ",
element, or at least it is already structured only in so far as
it structures ; it has no reality apart from all the entities to
which it is opposed or which it includes (or in which it is
included). A " class " presupposes a " classification ", and
the former grows out of the latter, because only operations
of classing can engender particular classes. Independently of
a general classification, a generic term does not signify a
class but an intuitive collection.
Similarly, a transitive, asymmetrical relation, such as
A<B, could not exist as a relation (but only as a perceptual
or intuitive relationship), were it not for the possibility of
constructing a whole succession of serial relations such as
A<B<C . . . And when we say that it does not exist as
a relation, this denial must be taken in its most concrete
sense, because we shall see in Chapter V that the child is in
fact quite incapable of thinking in terms of relations before
he can serialise. Thus " serialising " is the primary reality,
any asymmetrical relation being only an element abstracted
from it for the moment.
To take other examples : a " correlate " in Spearxrians'
36 THE NATURE OF INTELLIGENCE
sense (dog is to wolf as cat is to tiger) has meaning only as a
function of a matrix. A relation of kinship (brother, uncle,
etc.) refers to the whole constituted by a family tree, etc.
Need we remind the reader that a whole number exists,
psychologically as well as logically (in spite of Russell), only
by virtue of being an element in the sequence of numbers
(engendered by the operation 4- i), and likewise that a spatial
relation presupposes a whole space, and that a temporal
relation implies the conception of time as an exclusive
schema? And, in another field, should we insist on the fact
that a value is valid only in terms of a complete scale of
values, temporary or permanent ?
In short, in any possible domain of constituted thought
(contrasted with the states of disequilibrium which mark its
development), psychological reality consists of complex
operational systems and not of isolated operations conceived
as elements prior to these systems ; thus, only in so far as
actions or intuitive representations organise themselves in
such systems do they acquire the nature of " operations "
(and they acquire it by this very fact) . The essential problem
of the psychology of thought is then to work out the laws of
equilibrium of these systems, just as the central problem of
a logic that is to be adequate to the real work of the mind
seems to us to be the formulation of the laws governing these
wholes as such.
Now, analysis of a mathematical nature has long recognised
this interdependence of operations constituting certain well-
defined systems ; the notion of a " group ", which is applied
to the series of whole numbers, to spatial or temporal struc-
tures, to algebraic operations, etc> has thus become a central
idea in the ordering of mathematical thought. In the case of
the qualitative systems peculiar to thought that is purely
logical, such as simple classifications, matrices, series based
on relations, family trees, etc., we shall call the corresponding
complex systems "groupings". Psychologically, a
'* .grouping" consists of a certain form of equilibrium of
0f^rations ie. of actions which are internalised and
organised in complex structures, and the problem is to
<|gspibe ; tbis equilibrium both in relation to the various
" THOUGHT PSYCHOLOGY " 37
genetic levels which lead up to it and in contrast to forms of
equilibrium characteristic of functions other than intelligence
(perceptual or motor "structures", etc.) From the logico-
mathematical point of view, a " grouping " presents a well-
defined structure (related to that of a " group ", but differing
from it on several essential points), and expressing a succes-
sion of dichotomous distinctions ; its operational rules thus
constitute precisely that logic of wholes which translates
into an axiomatic or formal pattern the actual work of the
mind when it reaches the operational level of its develop-
ment, that is to say, its form of final equilibrium.
THE FUNCTIONAL MEANING AND STRUCTURE OF
" GROUPINGS "
Let us begin by connecting the foregoing considerations
with what we have learned from " Thought Psychology ".
According to Selz, the solution of a problem involves in the
first place an " anticipatory schema ", which links the goal to
be attained to a " complex " of ideas in which it creates
a gap ; then, in the second place, it means the " filling out "
of this anticipatory schema by means of concepts and
relations which serve to complete the " complex " and are
arranged according to the laws of logic. This leads to a
series of questions : what are the organisational laws of the
total " complex " ? What is the nature of the anticipatory
schema ? Can we abolish, the dualism which seems to exist
between the formation of the anticipatory schema and the
detailed processes which determine the way it is filled out ?
By way of example let us take an interesting experiment
performed by our colleague, Andre Rey ; a square with sides
a few centimetres long is drawn on a sheet of paper which is
also square (side 10-15 centimetres), and the subject is
instructed to draw with a pencil the smallest square he can
as well as the largest square which can be made on such a
sheet. Now while adults (and children over the age of 7-8)
succeed straight away in producing a square of 1-2 milli-
metres and one closely following the edges of the paper,
children under the age of 6-7 at first draw only squares
scarcely smaller and scarcely larger than the standard, and
38 THE NATURE OF INTELLIGENCE
then proceed by successive, and often unsuccessful, trial-and-
error, as though they at no time anticipated the final
solutions. We can see immediately, in this case, the part
played by a " grouping " of asymmetrical relations
(A < B < C . . . ), which is present in adults and appears to
be absent before the age of 7 ; the perceived square is
placed, in thought, in a series of potential squares, becoming
bigger and bigger or smaller and smaller in relation to the
first. We may then agree :
(i) that the anticipatory schema is simply the
pattern of the grouping itself, that is to say, the
consciousness of an ordered series of potential
operations.
(ii) that the filling out of the schema is nothing but the
putting into practice of these operations.
(iii) that the organisation of the " complex " of previous
ideas obeys the actual laws of grouping.
If this solution is of general validity, the notion of a
grouping will thus introduce a unity between the previously
existing system of ideas, the anticipatory schema and its
controlled filling-out process.
Let us now consider all those concrete problems which the
mind in action is continually setting itself : What is it ? is
it bigger or smaller, heavier or lighter, further or nearer, etc ?
where ? when ? what for ? to what purpose ? how much or
many ? etc., etc. We note that each of these questions is
necessarily dependent on a previous (t grouping " or
"group"; every individual possesses classifications, seria-
tions, systems of explanation, a personal space and time,
a scale of values, etc., as well as mathematical space and
time and numerical series. Now these groupings and groups
do not come into being when the question is put, but last
throughout the individual's life ; from infancy onwards, we
classify, compare (differences or similarities), locate in space
and time, explain, evaluate our ends and our means, count,
etc., and problems arise in relation* to these total systems
just in so far as new facts arise which have not yet been
" THOUGHT PSYCHOLOGY " 39
classified, serialised, etc. The question which governs the
anticipatory schema thus proceeds from the previously
existent grouping, and the anticipatory schema itself
is simply the direction imposed on the task by the structure
of this grouping. Every problem, whether it concerns the
anticipatory hypothesis regarding the solution or its detailed
checking, is thus no more than a particular system of oper-
ations to be put into effect within the corresponding complex
grouping. In order to find our way, we do not have to
reconstruct the whole of space, but simply to complete its
piling out in a given sector. In order to foresee an event,
repair a bicycle, make out a budget or decide on a pro-
gramme of action, there is no need to build up the whole of
causality and time, to review all accepted values, etc. ; the
solution to be found is attained simply by extending and
completing the relationships already grouped, except for
correcting the grouping when there are errors of detail, and,
above all, subdividing and differentiating it, but not by
rebuilding it in its entirety. 1 As for verification, this is
possible only in accordance with the rules of the grouping
itself, by the fitting of the new relations into the previously
existent system.
The remarkable fact in this continuous assimilation of
reality to intelligence is, in fact, the equilibrium of the
assimilatory frameworks constituted by the grouping.
Throughout its formation, thought is in disequilibrium or in
a state of unstable equilibrium; every new acquisition
modifies previous ideas or risks involving a contradiction.
From the operational level, on the other hand, the gradually
constructed frameworks, classificatory and serial and spatial,
temporal, etc., come to incorporate new elements smoothly ;
the particular section to be found, to be completed, or to
be made up from various sources, does not threaten the
coherence of the whole but harmonises with it. Thus, to
take the most characteristic example of this equilibrium of
concepts, an exact science, despite the " crises " and reforms
on Which it prides itself to prove its vitality, constitutes
a body of ideas whose detailed relationships are preserved
and even strengthened with every new addition of fact or
40 THE NATURE OF INTELLIGENCE
principle ; for new principles, however revolutionary they
may be, justify old ones as first approximations drafted to a
certain scale ; the continuous and unpredictable work of
creation to which science testifies is thus ceaselessly inte-
grated with its own past. We find the same phenomenon
again, but on a small scale, in every sane man.
Furthermore, compared with the partial equilibrium of
perceptual or motor structures, the equilibrium of groupings
is essentially a " mobile equilibrium " ; since operations are
actions, the equilibrium of operational thought is in no way a
state of rest, but a system of balancing interchanges, altera-
tions which are being continually compensated by others.
It is the equilibrium of polyphony and not that of a system
of inert masses, and it has nothing to do with the false
stability which sometimes results in old age from the slowing
down of intellectual effort.
It is a question then (and in this lies the whole problem of
grouping) of determining the conditions of this equilibrium in
order to be able subsequently to examine how it is formed
genetically. Now these conditions may be discovered both
by observation and by psychological experiment and may be
formulated with the degree of precision demanded by an
axiomatic pattern. They thus constitute, from the psycho-
logical angle, factors of a causal order explaining the
mechanism of intelligence, while their logico-mathematical
schematisation supplies rules for the logic of wholes.
These conditions are four in number in the case of
" groups " of a mathematical order, and five in the case of
" groupings " of a qualitative order.
i. Any two elements of a grouping may be combined and
thus produce a new element of the same grouping ; two
distinct classes may be combined into one comprehensive
class which embraces them both, two relations A < B and
1$ < C may be joined into one relation A < C which contains
tkw, aud so on. Psychologically then, this first condition
expresses the possibility of co-ordinating operations.
; 0* ;; ^y^y^chfijige is reversible. Thus, the two classes or
ffi0 i*> relations pst combined may be separated again and,
t, each original operation of a group
" THOUGHT PSYCHOLOGY " 4!
implies a converse operation (subtraction for addition,
division for multiplication, etc.). This reversibility is no
doubt the most clearly defined characteristic of intelligence,
for although motor functions and perception are capable of
combination, they remain irreversible. A motor habit is of
a one-way nature, and learning to effect movements in the
other direction means acquiring a new habit. A perception
is irreversible since, with each appearance of a new objective
element in the perceptual field, there is a " displacement of
equilibrium ", and since, if we restore the original situation
in the outer world, the perception is modified by the inter-
mediate states. Intelligence, on the other hand, can con-
struct hypotheses and then discard them and return to the
starting-point, can follow one path and then retrace its
steps, without affecting the ideas employed. Now thought in
the child, as we shall see in Chapter V, appears precisely more,
irreversible the younger the subject and the nearer to the
perceptuo-motor or intuitive patterns of the beginnings of
intelligence ; reversibility thus characterises not only the
final states of equilibrium but also the processes of
development themselves.
3. The combination of operations is " associative " (in
the logical sense of the term), i.e. thought always remains free
to make detours, and a result obtained in two different ways
remains the same in both cases. This characteristic seems
also to be peculiar to intelligence ; perception, like motor
functions, is capable only of following one path, since a habit
is stereotyped and since, in perception, two distinct paths
lead to different results (for example, the same temperature
perceived under different conditions of comparison does not
seem the same) . The appearance of the detour is characteris-
tic of sensori-motor intelligence, and as thought becomes
more active and mobile detours play a greater role, but
it is only in a system in permanent equilibrium that the
final term of the procedure is left constant.
4. An operation combined with its converse is annulled
e.g. -fi 1=0 or x 5 -+-5= xi). On the other haad, in
the .first forms of thought in the child, the return to the
starting-point is not accompanied by a conservation of the
42 THE NATURE OF INTELLIGENCE
latter; for example, having made a hypothesis which he
subsequently rejects, the child does not return to the
original data of the problem, because they remain somewhat
distorted by the hypothesis, even though it was discarded,
5. In the field of numbers, a unit added to itself yields a
new number, by the application of combinativity (i) ; there
is iteration. A qualitative element which is repeated is,
however, not transformed ; there is a " tautology " in this
case : A + A =A.
If we express these five conditions of grouping in a
logico-mathematical scheme, we arrive at the following
simple formulae :
(I) Combinativity : x +X 1 =y ; y +y 1 =z ; etc.
(II) Reversibility: y % =x l or yx l =x,
(III) Associativity : (x -f-* 1 ) +y l =x+(x 1 +y l ) = (2).
(IV) General operation of identity :
x x-Q; yy=O; etc.
(V) Tautology or special identities :
x +x =x ; y +y =y ; etc.
It goes without saying that a calculus of changes becomes
possible, but it necessitates, because of the presence of
tautologies, a certain number of rules whose details space
will not permit us to describe in this book (see Piaget :
Classes, relations et nombres, Paris, Vrin, 1942).
CLASSIFICATION OF " GROUPINGS/' AND OF THE FUNDA-
MENTAL OPERATIONS OF THOUGHT.
The study of the steps in the development of thought
in the child leads to the recognition not only of the
existence of groupings but also of their mutual connections,
i.e. the relations enabling us to classify them and to
list them. The psychological existence of a grouping
can in fact easily be recognised from the overt operations
of which a subject is capable. But that is not all:
without the grouping there could be no conservation of
complexes or wholes, whereas the appearance of a
grouping is attested by the appearance of a principle of
conservation. For example, the subject who is capable of
reasoning operationally in accordance with the structure of
" THOUGHT PSYCHOLOGY " 43
groupings will know in advance that a whole will be con-
served independently of the arrangement of its parts,
whereas before he would question it. In Chapter V we shall
study the formation of these principles of conservation in
order to show the role of the grouping in the development of
reason. But, for clarity of exposition, we had better first
describe the final states of equilibrium of thought, so that
we may then examine the genetic factors which would explain
how they came to be constituted. So, at the risk of pro-
ducing a rather abstract and schematic enumeration, we
shall complete the foregoing remarks by enumerating the
principal groupings, it being understood that this sketch
represents simply the final structure of intelligence and that
the whole problem of understanding their formation still
remains unsolved.
i. A first system of groupings is formed by the operations
we call logical, i.e., those which start with individual
elements which are regarded as constants, and simply
classify and serialise them, etc.
1. The simplest logical grouping is that of classification
or the formation of hierarchies of more and less
inclusive classes. It is based on a primary, funda-
mental operation : the combining of individuals in
classes, and of classes with other classes. The ideal
example is found in zoological or botanical classifi-
cations, but all qualitative classification follows the
same dichotomous pattern.
Let us suppose that a species A forms part of a
genus B, of a family C, etc. The genus B includes
other species besides A : we will call them A' (thus
A'=B A). The family C includes other genera
beside B : we will call them B 7 (thus B 7 =C B) etc.
We then have combinativity : A + A ' = B ; B +B ' = C ;
C -f C 7 =D, etc. ; reversibility : B A 7 = A, etc. ;
associativity : (A -f A 7 ) - B ' A + (A ' +B 7 ) = C, etc.,
and all the other characteristics of groupings. It
is this first grouping that gives rise to the classical
syllogism.
2. A second elementary grouping brings into play
44 THE NATURE OF INTELLIGENCE
the operation which consists not in combining indi-
viduals which are regarded as equivalent (as in i),
but in assembling the asymmetrical relations which
express their differences. The linking up of these
differences then creates an order of succession and the
grouping consequently constitutes a " qualitative
seriation " :
Let us call a the relation o < A ; b the relation
o < B ; c the relation. o < C. We may then call a'
the relation A < B ; b' the relation B < C ; and we
have the grouping : a +a' =6 ; b / +b ~c, etc. The
converse operation is the subtraction of a relation,
which is equivalent to the addition of its converse.
The grouping is parallel to the previous one except
for this difference : that the operation of addition
implies an order of sequence (and therefore is not
commutative). The transitivity peculiar to this
serialisation is the basis of the following inference :
A'<B; B<C; therefore A < C.
3. A third fundamental operation is substitution, the
basis of the equivalence which joins together the
various individuals in a class or the different simple
classes included in a composite class :
Actually, there is not the equality between two
elements Ai and A2 of the same class B that there
is between mathematical units. There is simply
qualitative equivalence, i.e. a possible substitution
but only as long as we substitute in the same way
as A'i, (i.e. the "other" elements besides Ai) the
A 7 2s (that is the "other" elements besides A2).
Hence the groupings : Ai -f A'x =A2 +A 7 2 ( -B) ;
Bi +B'i = B2 -{-B'2 ( =C) etc.
4. Now, interpreted in terms of relations, the preceding
operations give rise to the reciprocity which marks
symmetrical relations. The latter are, in fact, only
the relations uniting the elements of a given class,
tod ! therefore they are relations of equivalence (as
opposed to asymmetrical relations which denote
difference). Symmetrical relations e.g. brother, first
" THOUGHT PSYCHOLOGY " 45
cousin, etc.) are consequently grouped after the
fashion of the preceding grouping, but each operation
is identical with its converse, this being the actual
definition of symmetry : (Y =Z) = (Z = Y).
The four preceding groupings are of an additive order,
two of them (i and 3) concerning classes and the other two
relations. There exist, in addition, four groupings based on
multiplicative operations, i.e. those which deal with more
than one system of classes or relations at a time. These group-
ings correspond, one by one, with the four previous ones :
5. Two series of compound classes being given, Ai Bi
Ci . . . and A2 B2 C2 . . ., we may start by dis-
tributing the individuals according to both systems
at once : this is the procedure of matrix tables. Now,
" multiplication of classes ", which constitutes the
characteristic operation of this type of grouping, plays
an essential part in the mechanism of intelligence ;
this is what Spearman describes in psychological
terms under the name of " eduction of correlates '*.
The original operation for the two classes Bi and B2
is the product Bi xB2 =Bi.B2 ( =Ai.A2 -f Ai.A'2 +
A / i.A2 +A'i.A'2)* The converse operation is logical
division, Bi.B2-*-B2 = Bi, which corresponds to
" abstraction " (BrB2, disregarding B2, is Bi).
6. In the same way we may multiply together two series
of relations, i.e. we may find all the relations
obtaining among objects serialised according to two
sorts of relations at once. The simplest case is none
other than qualitative " one-to-one correspondence."
7 and 8. Finally, we may group individuals, not according
to the principle of matrices, as in the two previous
cases, but by making one term correspond to several,
e.g. a father to his sons. In this way, the grouping
takes the form of a family tree and is expressed either
in classes (7) or in relations (8), the latter thus being
asymmetrical in one of its two dimensions (father,
etc.) and symmetrical in the other (brother, etc.).
Thu, from the simplest combinations, we obtain eight
fundamental logical groupings, some additive (1-4), and
46 THE NATURE OF INTELLIGENCE
others multiplicative (5-8), some concerning classes and
others relations, and some arranged in combinations,
sedations or simple correspondences (i, 2 and 5, 6) and
others in reciprocities and correspondences of the " one-
many " type (3, 4 and 7, 8). Hence 2x2x2=8 possibilities
altogether.
Further, we should note that the best proof of the natural
character of the totalities constituted by these groupings of
operations is that it is only necessary to fuse together the
groupings formed by simple combination in classes (i) and
those formed by seriations (2) in order to obtain what is
no longer a qualitative grouping but the " group " consti-
tuted by the series of positive and negative whole numbers.
In fact, to combine individuals in classes means considering
them as equivalent, while serialising them according to an
asymmetrical relation expresses their differences. Now,
when we consider the qualities of objects we cannot simul-
taneously group them as both equivalent and different.-
But if we abstract qualities, by this very fact we render
them equivalent to each other and capable of being serialised
according to some form of enumeration : we thus transform
them into ordered " units ", and the additive operation
which constitutes a whole number consists in just that.
Similarly, by amalgamating multiplicative groupings of
classes (5) and relations (6), we obtain the multiplicative
group of positive numbers (whole and fractional).
II. The various foregoing systems do not exhaust all
the elementary operations of intelligence. Intelligence,
indeed, does not confine itself to operating on objects in
order to combine them in classes, to serialise or to number
them. Its action is also entailed by the construction of the
object itself and, as we shall see (Chap. IV), this work has
already been completed in the stage of sensori-motor
intelligence. Analysing and re-synthesising the object thus
constitutes the work of a second type of grouping whose
fundamental operations may consequently be called " infra-
logical ", since logical operations combine objects which are
regarded as invariant. These infra-logical operations are
just as important as logical operations, because they fashion
" THOUGHT PSYCHOLOGY " 47
our notions of space and time, whose development occupies
almost the whole of childhood. But although quite distinct
from logical operations, they are closely parallel to them.
The question of the developmental relations between these
two operational systems thus constitutes one of the most
interesting problems relating to the development of intelli-
gence :
1. Corresponding to the formation of classes is the
joining together of parts into progressively more
inclusive wholes, whose final term is the whole object
(to every possible scale, even that of the spatio-
temporal universe itself). It is this first grouping by
addition of parts that enables the mind to conceive
of atomistic composition prior to any genuinely
scientific experiment.
2. Corresponding to sedation by asymmetrical rela-
tions are the operations of locating (spatially or
temporally) and qualitative displacement (simple
change of order without measurement).
3-4 Spatio-temporal substitutions and symmetrical rela-
tions correspond to logical substitutions and sym-
metries.
5-8 Multiplicative operations simply combine the pre-
ceding operations according to several systems or
dimensions at once.
Now just as numerical operations may be regarded as
expressing a simple fusion of groupings of classes and asym-
metrical relations, operations of measurement express the
uniting into a single whole of the operations of breaking up
into parts and of displacement.
III. We may find the same divisions in the case of opera-
tions concerned with values, i.e. those expressing the relations
of means and ends which play an essential part in practical
intelligence (and whose quantification corresponds to
economic value).
IV. Finally, the whole formed by these three systems of
operations (I to III) may be interpreted in terms of simple
propositions, whence we have a logic of propositions based
on implications and contradictions between prepositional
48 THE NATURE OF INTELLIGENCE
functions ; this is what constitutes logic in the customary
sense of the term as well as the hypothetico-deductive
theories characteristic of mathematics.
EQUILIBRIUM AND DEVELOPMENT
It has been our purpose in this chapter to find an inter-
pretation of thought which does not clash with logic,
regarded as a primary and inexplicable datum, but respects
the inherent formal necessity of axiomatic logic, and this
while retaining for intelligence its psychological nature
as something essentially active and constructive.
Now, the existence of groupings and the possibility of a
rigorous axiomatisation of them satisfies the first of these
two conditions ; the theory of groupings can attain formal
precision, even though it arranges systems of logical elements
and operations into wholes comparable with the general
systems used in mathematics.
From the psychological point of view, on the other hand,
since the operations are combinative and reversible actions,
but actions nevertheless, continuity between the act of
intelligence and all other adaptive processes is still ensured.
But this is merely formulating the problem of intelligence,
while the solution still remains to be found. All that the
existence and the nature of groupings teach us is that at a
certain level thought reaches a state of equilibrium. They
tell us, no doubt, what the latter is : an equilibrium, both
mobile and permanent, such that the structure of operational
wholes is conserved while they assimilate new elements.
Further, we know that this mobile equilibrium entails
reversibility, which, incidentally, is according to physicists
the very definition of a state of equilibrium. (We must
conceive the reversibility of the mechanisms of fully
developed intelligence in terms of this actual physical
n)del, not in terms of the abstract reversibility of the
logico-inathematical pattern). Yet neither pointing out this
state of equilibrium por even stating its necessary conditions
explanation.
psychological explanation of intelligence consists in
development and showing how the latter neces-
** THOUGHT PSYCHOLOGY " 49
sarily leads to the equilibrium we have described. From
this point of view, the work of psychology is comparable to
that of embryology, i.e. a work which, in the first instance, is
descriptive and which consists in analysing the phases and
periods of morphogenesis up to the final equilibrium consti-
tuted by adult morphology, but this study becomes
" causal " once the factors which ensure the transition from
one stage to the next have been demonstrated. Our task is
therefore clear : we must now reconstruct the development
of intelligence, or the stages in its formation, until we are
able to account for the final operational level whose forms
of equilibrium we have just been describing. And since the
higher cannot be reduced to the lower-- except by distorting
the higher or prematurely enriching the lower the develop-
mental explanation can only consist in showing how, at each
new stage, the mechanism provided by the factors already in
existence makes for an equilibrium which is still incomplete,
and the balancing process itself leads to the next level.^n
this way, step by step, we may hope to give an account of
the gradual formation of operational equilibrium, without
having it ready-made from the outset, or having it emerge
ex nihilo on the way.
Briefly then, the explanation of intelligence amounts to
linking the higher operations with the whole process of
development, development being regarded as an evolution
. governed by an inherent need for equilibrium. Now this
functional continuity is quite compatible with the differen-
tiation of successive structures. As we have seen, we may
represent the hierarchy of response-patterns, right from the
early reflexes and global perceptions, as a matter of pro-
gressively extending the distances and of progressively
complicating the paths of interaction between the organism
(subject) and the environment (objects) ; thus each of these
extensions or complications represents a new structure,
while their succession is dependent on the need for an
equilibrium which must be more and more mobile as it
becomes more cpmplex. Operational equilibrium fulfils
these conditions on reaching the greatest possible distances
(since intelligence tries to embrace the universe) and the
50 THE NATURE OF INTELLIGENCE
greatest possible complexity of paths (since deduction is
capable of the greatest " detours "}. This equilibrium is
therefore to be regarded as the final limit of an evolution
whose stages are still to be traced.
Thus the organisation of operational structures goes back
far beyond the beginnings of reflective thought and even
approaches the origins of action itself. And, since all opera-
tions are grouped in well-structured wholes, they must be
compared with all "structures", perceptual and motor,
are at a lower level. The course to be followed is thus
fully sketched; we must analyse. the relations between
intelligence and perception (Chap. Ill) and motor habit
(Chap. IV), then we must study the formation of operations
in the thought of the child (Chap. V), and its socialisation
(Chap. VI). Only then will the " grouping " structure, which
characterises living logic in action, reveal its true nature,
whether it be innate or learned (and simply imposed by the
environment), or whether it be the expression of ever more
numerous and complex interactions between subject and
objects, interactions at first incomplete, unstable and
irreversible, but gradually acquiring, by the very needs
arising from the equilibrium which is forced on them, the
form of reversible combinativity characteristic of the
grouping.
PART TWO
INTELLIGENCE AND SENSORI-MOTOR
FUNCTIONS
INTELLIGENCE AND PERCEPTION
PERCEPTION is the knowledge we have of objects or of their
movements by direct and immediate contact, while jntslK*
myolvedand ....... bet^fiffi
then that
Intefi^^ the operational groupings
which characterise the final equilibrium reached in the
development of intelligence, pre-exist, wholly or in part,
from the outset in the form of organisations common to
perception and to thought. ^This particular idea is the central
^doctrine of the " Configu^i^^ ", which, although it
knows nothing of the notion of a reversible grouping, has
described laws of complex structuring which, it claims, govern
perception, response and elementary functions as well as
reasoning itself and in particular the syllogism (Wertheimer).
It is therefore essential that we should start with perceptual
structures, to enquire whether we may not derive from
them an explanation of the whole of thought, including
groupings themselves.
HISTORICAL
The hypothesis of a close relationship between perception
and intelligence has been maintained at all times by some,
and likewise rejected at all times by others. We shall
mention here writers of experimental studies only, as
opposed to the innumerable philosophers who have confined
themselves to " reflecting" on the subject.^ And we shall
set forth the point of view of experimenters who have sought
to explain perception by the intervention of intelligence as
53
54 INTELLIGENCE AND SENSORI-MOTOR FUNCTIONS
well as that of those who seek to derive the latter from the
former.
Mt was undoubtedly Helmholtz who first framed the
problem of the relations between perceptual structures and
operational structures in its modern form. \Ve know that
visual perception can show " constancy " effects which have
stimulated and still stimulate a series of studies. ^A given
size is perceived more or less correctly at a distance, in spite
of the considerable contraction of the retinal image and the
diminution due to perspective ; a shape is recognised even
at an angle ; colour is recognised in the shadow as well as
in bright illumination, etc. Now Helmholtz tried to explain
these perceptual constancies by the intervention of an
" unconscious inference " which has the effect of correcting
the immediate sensation by recourse to acquired knowledge.
When we recall Helmholtz's preoccupations with the forma-
tion of the notion of space, we can well imagine that this
hypothesis was bound to have a certain significance in his
thought, and Cassirer assumed (when he in his turn took up
the idea) that the great physiologist, physicist and geometer
tried to account for perceptual constancy by a sort of
geometrical " group ", inherent in the intelligence which
works unconsciously in perception. x Now, at this stage, it is
very interesting for comparative purposes to examine
some intellectual and perceptual mechanisms. Perceptual
" constancy " is, in fact, comparable, at the sensori-motor
level, with the various ideas of " conservation " which
characterise the first conquests of intelligence (conservation
of wholes, of substance, of weight, of volume, etc. occurring
with intuitive distortions). Now, since these ideas of conser-
vation are due to the intervention of a " grouping " or a
" group " of operations, if visual constancy were itself due
to unconscious inference in the form of a " group ", there
would then be a direct structural continuity between percep-
tion and intelligence.
^However, Hering had already replied to Helmholtz,
indicating that the fact of intellectual knowledge does not
modify a perception ; we demonstrably experience the same
optical or weight illusion etc. when the objective values of
INTELLIGENCE AND PERCEPTION 55
the perceived material are known. He therefore concluded
that reasoning is not involved at all in perception and that
" constancy " is due to purely physiological regulations.
\But Helmholtz and Hering both believed in the existence
of sensations that were prior to perception, and so they
thought of perceptual constancy as a correction of sensations,
and attributed it, in the case of Helmholtz, to intelligence
and, in the case of Hering, to neural mechanisms. The
problem was revived after von Ehrenfels in 1891 discovered
the perceptual qualities of wholes (Gestaltqualitateri), such
as that of a melody, which can be recognised despite a
transposition that changes every note (so that no elemental
sensation remains the same). ^Two schools arose as a result
of this discovery, one of them supporting Helmholtz in his
appeal to intelligence. The Graz school (Meinong, Benussi,
etc.) continue, in fact, to believe in sensations and accordingly
interpret a " whole quality " as the product of a synthesis ;
this synthesis, being transposable, is conceived as something
due to intelligence itself. Meinong has gone so far as to build
up on the basis of this interpretation a whole theory of
thought based on the idea of a whole (the " collective
objects " linking the perceptual and the conceptual). ^On the
other hand, the " Berlin school ", which marks the starting
point of Gestalt Psychology has reversed the position ; for
this school, sensations no longer exist as elements prior to
perception or independent of it (they are " structured "
instead of " structuring contents "), and the total con-
figuration, a concept applied generally to all perception, is
no longer regarded as the result of a synthesis but as a
primary fact produced unconsciously and as much physio-
logical in nature as psychological. These " configurations "
(Gestalten) are met with at every stage of the mental
hierarchy and, according to the Berlin school, we may there-
fore expect an explanation of intelligence which starts from
perceptual structures, instead of assuming that, in some
incomprehensible manner, reasoning intervenes in perception
itself.
x Among later researches, a school known as the Gestaltkreis
(of Weizsacker, Auersperg, etc,) has tried to extend the idea
5& INTELLIGENCE AND SENSORI-MOTOK FUNCTIONS
of a complex structure by regarding it as embracing percep-
tion and bodily movement from the outset, believing these to
be of necessity closely associated. Perception would then
involve the intervention of motor anticipations and reconsti-
tutions which, without implying intelligence, nevertheless
presage it. ^So we may consider this trend as a revival of
the Helmholtzian tradition, while other contemporary studies
adhere to Hering's suggestion of an interpretation of percep-
tion in purely physiological terms (Pieron, etc.).
THE GESTALT THEORY AND ITS INTERPRETATION OF
INTELLIGENCE
Special mention must be given to the Gestalt point of
view, not only because it has raised a large number of
problems anew, but especially because it has provided a
complete theory of intelligence which will remain, even for
its opponents, a model of coherent psychological interpre-
tation.
Vrhe central idea of the Gestalt theory is that mental
systems are never constituted by the synthesis or association
of elements that exist in isolation before they come together,
but always, from the outset, consist of organised wholes in a
" configuration " or complex structure. ^Thus, a perception
is not the synthesis of previous sensations ; it is governed at
each level by a " field " whose elements are interdependent
by the very fact that they are perceived as a whole. For
example, a single black dot seen on a large sheet of paper
could not be perceived as an isolated element, although it is
quite alone, since it stands out as a " figure " on a " ground "
formed by the* paper, and since this figure-ground relation
implies an organisation of the entire visual field. The truth
of this is emphasised by the fact that, strictly, one should be
able to perceive the sheet as the object (the " figure") and
the black dot as a whole, i.e. as the only visible part of the
" ground *'. Why then do we prefer the first mode of
Perception ? And if, instead of a single dot, we see three or
four fairly close together, why is it that we cannot help
forming them into potential shapes as triangles or quadri-
laterals ? It is because elements perceived in the same
INTELLIGENCE AND PERCEPTION 57
field are immediately bound together in complex structures
in accordance with precise laws, i.e., the " laws of organisa-
tion ".
^These laws of organisation governing all the relations
within a field are, according to the " Gestalt " hypothesis,
simply the laws of equilibrium governing the neural excita-
tion released both by psychological contact with external
objects and by the objects themselves, combined in a closed
circuit which embraces the organism and its immediate
environment simultaneously. ^From this point of view, a
perceptual (or motor, etc.) field is comparable to a field of
forces (electro-magnetic, etc.,) and is governed by analogous
principles of minima, or of least action, etc. Faced with
a multiplicity of elements, we impress upon them a complex
pattern, which is not just any pattern but the simplest
possible pattern which expresses the structure of the field ;
so this involves rules of simplicity, regularity, proximity,
symmetry, etc. which" will determine what configuration will
be perceived. Hence we have an essential law (called
Ptagnanz) : out of all possible configurations, the con-
figuration which predominates is always the " best ", i.e.
the best equilibrated. Moreover, a " good Gestalt " is
always capable of being " transposed ", like a melody when
all the notes are changed. But this transposition, which
demonstrates the independence of the whole with respect to
the parts, is also explained by laws of equilibrium ; the
same relations hold between the new elements, which give
rise to the same total configuration as the old elements, not
because of an act of comparison but by means of a re-
establishment of equilibrium, in the same way as canal water
keeps the same horizontal form, although at different levels,
as each sluice-gate is opened. The description of these
" good Gestalten " and the study of these " transpositions "
have given rise to a host of experimental studies of undeniable
interest, the details of which it would not help to describe
here.
v On the other hand, it must be carefully noted as essential
to the theory that the " laws of organisation " are considered
to be independent of development and consequently commQB
58 INTELLIGENCE AND SENSORI-MOTOR FUNCTIONS
to all stages. ^This statement follows automatically if we
confine it to functional organisation or " synchronous "
equilibrium of behaviour, because the necessity for the latter
operates at all stages, whence arises the functional continuity
on which we have insisted. But it is customary to make a
distinction between this constant functioning and successive
structures considered from a " diachronic " point of view,
which vary from one stage to another, ihe distinguishing
mark of the Gestalt School is that it combines function and
structure into one whole under the name of " organisation ",
and regards the laws of the latter as invariable. >Jn this way
Gestalt psychologists have striven to show, with an impres-
sive accumulation of material, that perceptual structures
are the same in the young child and the adult and, in fact,
that they are the same in vertebrates of all types,
The only point of difference between child and adult might
be the relative importance of certain common factors of
organisation e.g. proximity but the mass of factors
remains the same and the resulting structures obey the
same laws.
In particular, the famous problem of perceptual constancy
has yielded a systematic solution, concerning which the
following two points should be noticed. In the first place,
constancy such as that of size could not consist in the
correction of an initial distorting sensation\ssociated with
a diminished retinal image, because no initial isolated
sensation exists, and because the retinal image is only a link
(and not an especially privileged one) in the chain, whose
closed circuit links objects with the brain through the
medium of the neural processes involved. xThus, when an
object is seen at a distance, its real size is immediately and
directly perceived, simply by virtue of the laws of organi-
sation which make this the best of all structures. In the
iecond place, therefore, perceptual constancy is held not
to be acquired but to be completely formed at all levels, in
the animal and the infant just as in the adult. The apparent
experimental exceptions would be due to the fact that the
''perceptual field" is not always sufficiently structured,
the best constancy occurring when the object forms part of a
INTELLIGENCE AND PERCEPTION 59
complex configuration, such as a succession of objects
forming a series.
x To turn back to intelligence, it has received, from this
point of view, a remarkably simple interpretation and one
which, if it were true, would be capable of establishing an
almost complete connection between higher structures (and
especially the " operational groupings " we have described)
and the most elementary "configurations'' of a sensori-
motor or even perceptual order. x Three applications of the
Gestalt theory to the study of intelligence are especially
noteworthy : that of Kohler to sensori-motor intelligence,
that of Wertheimer to the structure of the syllogism, and that
of Duncker to the act of intelligence in general.
For Kohler, intelligence appears when perception is not
carried over directly into responses likely to ensure tfee
attainment of the objective. -A chimpanzee in a cage tries
to reach a fruit placed beyond the reach of his arm. Thus
an intermediate agent is required, whose use will constitute
the definition of the degree of complication characteristic of
intelligent behaviour. What does this consist of ? If a stick
is placed within reach of an ape but in any position, it is seen
as an indifferent object ; placed parallel with his arm, it will
promptly be perceived as a possible extension of the hand.
Thus the stick, until then neutral, will receive a meaning
from the fact of its incorporation in the complex structure.
The field will then be " restructured " and, according to
Kohler, it is these sudden restructurings that are character-
istic of the act of intelligence. The shift from a less good
structure to a better structure is the essence of insight and
is consequently a simple but mediate or indirect continuation
of perception itself.
This is the explanatory principle that occurs again in
^Wertheimer's Gestalt interpretation of the syllogism. The
major term is a "Gestalt" comparable to a perceptual
structure ; " all men " thus constitutes a whole which is
represented as located within the complex of (( mortals ".
The minor term follows the same course ; " Socrates " is an
individual located within the circle of " men ". Soothe
operation which draws the conclusion from these premises,
60 INTELLIGENCE AND SENSORI-MOTOR FUNCTIONS
" therefore Socrates is mortal ", simply amounts to .restruc-
turing the whole by abolishing the intermediate circle (men)
after first placing it, with ics content, within the large circle
(mortals). Reasoning is thus a " re-anchoring ". " Socrates "
is, so to speak, uprooted from the classof " men " in order
to be anchored in that of " mortals ". The syllogism is thus
without more ado related to the general organisation of
structures ; in this it is analogous to the restructurings
that characterise Kohler's practical intelligence, hut it now
takes place in thought, not in action.
^Finally, Duncker studied the relation of these sudden
insights (Einsicht or intelligent restructuring) to past
experience and so dealt the coup de grace to associationist
empiricism, which the concept of a Gestalt opposes from
its very origins. ^To this end, he analyses various problems
of intelligence and finds in all cases that past experience plays
only a secondary role in reasoning ;N experience never intro-
duces meaning into thought except as a function of present
organisation, vlt is the latter (i.e. the structure of the present
field) that determines- what appeals to past experience can
be made, whether it makes them useless or whether it com-
mands the summoning up and utilisation of memories.
Reasoning is thus " a contest which contrives its own
weapons ", and all this is explained by the laws of organisa-
tion, which are independent of the individual's history and,
in short, ensure the fundamental unity of the. structures of
every level, from elementary perceptual " configurations "
to those of the most exalted thought.
CRITIQUE OF GESTALT PSYCHOLOGY
We are bound to admit how well founded are the descrip-
tions given by Gestalt psychology. The essential " whole-
ness " of mental structures (perceptual as well as intelligent),
the existence of the "good Gestalt' 3 and its laws, the
reduction of variations of structure to forms of equilibrium,
etc., are justified by so many experimental studies that these
concepts have acquired the^right to be quoted throughout
cc^temporary psychology. In particular, the- method of
anatysfe that consists in always interpreting facts in terms
INTELLIGENCE AND PERCEPTION 6l
of a total field is alone justifiable, since reduction to atomistic
elements always impairs the unity of reality.
But it is as well to recognise that, if the " laws of organisa-
tion " are not derived, beyond psychology and biology, from
absolutely general " physical Gestalten " (Kohler), 1 then the
language of wholes is merely a mode of description, and the
existence of total structures requires an explanation which
is not at all included in the fact of wholeness. We have
admitted this in connection with our own groupings and we
must also admit it in connection with " configurations " or
elementary structures.
The general and even " physical " existence of " laws of
organisation " implies at the very least and Gestalt
theorists are the first to vouch for it their constancy in
the course of mental development. The essential question
for the orthodox Gestalt doctrine (we shall adhere to
this orthodoxy for the moment, but we must point out
that certain of the more cautious partisans of the
Gestalt school, such as Gelb and Goldstein, have rejected
the hypothesis of " physical Gestalten ") is thus that of
the permanence of certain essential forms of organisation
throughout mental development, e.g. that of perceptual
constancy.
^However, as far as the main point is concerned, we think
it is possible to maintain that, in the present state of know-
ledge, the facts are opposed to such an assertion. Without
going into detail, and confining ourselves to the field of child
psychology and size constancy, we must now consider the
following few points :
i. H. Frank 2 believed that he could demonstrate size
constancy in infants of n months. Now the technique of
these experiments has evoked discussion (Beyrl) and, even
if the facts are on the whole correct, .11 months already
represents a considerable development of sensori-motor
intelligence. E. Brunswik and Cruikshank have noted a
According to Kohler, "physical Gestalten" have the same role in
relation to mental structures that eternal Ideas have in relation to concepts
according to Russell, or that an a priori framework has in relation to
living logic.
a Psychol. Forschung VII, 1926, pp. 137-154-
62 INTELLIGENCE AND SENSORI-MOTOR FUNCTIONS
progressive development of this constancy during the
first six months.
2. Certain experiments, consisting of paired comparisons
of heights at a distance, which the author has carried out in
collaboration with Lambercier on children aged 5-7 years,
have enabled us to illustrate a factor which experimenters
had not taken into account : ^at every age there exists a
" systematic error of the standard " whereby the element
chosen as the standard, for the very reason that it functions
as a standard, is over-estimated in relation to the variables
that are measured by it, both when it is placed at a distance
and when it is near. This systematic error on the part of the
subject, combined with his estimations at a distance, could
give rise to an apparent and illusory constancy. Calculation
of the " error of the standard " shows our 5-7 year old sub-
jects to have moderately under-estimated under conditions
of depth perception, whilst adults tend, on the average,
towards a " superconstancy "- 1
3. Burzlaff 2 , who has also obtained variations with age in
paired comparisons, has considered it possible to maintain
the Gestalt hypothesis of the permanence of size constancy in
the case where the compared elements are enclosed in a total
" configuration " and especially when they are serialised.
With some painstaking experiments, Lambercier, at our
request, has taken up this problem of serial comparisons in
depth perception, 3 and has been able to show that a constancy
that was relatively independent of age existed only in a
single case (the very one that Burzlaff expected) : the case
where the standard equals the median of the compared
elements. \On the other hand, as soon as a standard is
chosen that is appreciably larger or smaller than the median,
systematic changes with distance are observed. Hence it is
clear that the constancy of the median depends on other
causes than constancy with distance ; it is its privileged
position as the median that ensures its invariability (it is
reduced by all higher terms and correspondingly increased
1 Arch, de PsychoL XXIX (1943), pp. 255-308.
* Zeitschr, fur PsychoL, vol. 119 (1931), pp. 177-235.
*Arch. de PsychoL XXXI (1946).
INTELLIGENCE AND PERCEPTION 63
by all lower terms : hence its stability). Again, measure-
ments of the other terms show that specific constancy with
distance does not exist in the child, while a remarkable
growth with age of the regulations conducive to this con-
stancy is observed.
4. \Ve know that when Beyrl 1 analysed size constancy in
school-children, he for his part found some increase in the
incidence of constancy up to nearly ten years of age ; ^beyond
this stage the child comes to react in the adult manner (a
parallel development was found by Brunswik with respect
to shape and colour constancy).
^The existence of a development with age of the mechan-
isms underlying perceptual constancy (and later we shall
see many other developmental changes in perception)
undoubtedly leads to a revision of the Gestalt School's
explanation. \To begin with, if there is an actual development
of perceptual structures, we can no longer dismiss either the
problem of their formation or the possible role of past
experience in the process of their coming into being. Con-
cerning this last point, Brunswik has demonstrated the
frequency of empirical Gestalten side by side with " geometri-
cal Gestalten ". ^In this way, a- figure that is intermediate
between the image of an open hand and a geometrical
pattern with five exactly symmetrical extensions, when seen
tachistoscopically, yielded in adults 50 per cent in favour of
the hand (learned shape) and 50 per cent in favour of the
geometrical " good Gestalt ".
^Concerning the genesis of Gestalten, which raises an
essential problem as soon as we reject the hypothesis of
permanent " physical Gestalten ", we may first of all point
out the illicit nature of the dilemma : either wholes or the
atomism of isolated sensations. In point of fact there are
three possible terms A A perception may be a synthesis of
elements, or else it may constitute a single whole, or it may
be a system of relations (each relation being itself a whole,
but the complete whole becoming unanalysable and not
relying at all on atomism). This being the case, there is no
reason why complex structures should not be regarded as the
1 Zeitschr. fur Psychol., vol. 100 (1926), pp. 344-371.
64 INTELLIGENCE AND SENSORI-MOTOR FUNCTIONS
product of a progressive construction which arises, not from
" syntheses ", but from adaptive differentiations and com-
bined assimilations, nor is there any reason why this construc-
tion should not be related to an intelligence capable of
genuine activity as opposed to an interplay of pre-established
structures.
"With regard to perception, the crucial point is that of
" transposition ". Should we follow Gestalt theory and
interpret transpositions (of a melody from one key to another
or of a visual form by enlargement) as the simple reap-
pearance of the same form of equilibrium between new
elements whose relations have been retained (cf. the hori-
zontal levels of systems of sluice-gates), or should we regard
them as the product of an assimilatory activity which inte-
grates comparable elements into the same schema? XThe
iact of improvement with age in ability to transpose (see the
end of this chapter) seems to us to demand this second
solution. Moreover, transposition as ordinarily understood,
which is external to the figures, should undoubtedly be
connected with the internal transpositions between elements
of the same figure, which explain the role of the factors of
regularity, equality, symmetry, etc.,, inherent in " good
Gestalten ".
^ These two possible interpretations of transposition mean
quite different things with respect to the relations between
perception and intelligence and especially the nature of the
latter.
In attempting to reduce the mechanisms of intelligence to
those characterising perceptual structures, which are in turn
reducible to " physical Gestalten 'THhe Gestalt theory re-
verts essentially to classical empiricism, although by far
more refined methods. The only difference (and considerable
though it is, it has little weight in the face of such a reduc-
tion) is that the new doctrine replaces " associations "
by structured " wholes ". But in both cases operational
activity in sensory processes fades into pure receptivity,
and abdicates in favour of the passivity of automatic
mechanisms.
canuQt insist too strongly on the fact that, although
INTELLIGENCE AND PERCEPTION 65
operational structures are bound to perceptual structures by
a continuous series of intermediate structures (and we grant
this without any difficulty), there is, nevertheless, a funda-
mental contradiction in meaning between the rigidity of a
perceived " configuration " and the reversible mobility of
operations. x Thus Wertheimer's attempted comparison
between the syllogism and the static " configurations " of
perception runs the nsk of remaining inadequate. VWhat
is essential in the mechanism of a grouping (by which
syllogisms are formed) is not the structure assumed by
premises, nor that which characterises conclusions, ^but
rather the process of combination which makes it possible to
pass from the one to the other. No doubt this process is an
extension of perceptual restructurings and recentrings (such
as those enabling us to see an " ambiguous " design alter-
nately as convex and concave). But it is even more than
this, since it is constituted by the whole system of mobile
and reversible operations of conjunction and disjunction
(A+A'-B; A-B-B'; A'B-A; B-A-A'-O, etc.)
So it is no longer static forms that are important in intelli-
gence, nor the simple uni-directional transition from one
state to another (or even oscillation between the two) ;Xthe
general mobility and reversibility of operations are what
give rise to structures. It follows that the structures
involved themselves differ in the two cases. vV perceptual
structure is characterised, as the Gestalt theory itself has
insisted, by its irreducibility to additive combination it is
thus irreversible and non-associative. ^So there is con-
siderably more in a system of reasoning than a " recentring "
(Umzentrierung) ; there is a general decentralisation, which
means a dissolution or melting down of static perceptual
forms in favour of operational mobility, and consequently
there is the possibility of constructing an infinite number of
new structures which may be perceptible or may exceed the
limits of all true perception.
As for the sensori-motor intelligence described by Kohler,
it is clear that here perceptual structures play a much bigger
part. But by the very fact that Gestalt theory is bound to
consider them as arising directly from situations as such,
66 INTELLIGENCE AND SENSQRI-MOTOR FUNCTIONS
without historical development, Kohler found himself con-
strained to exclude from the realm of intelligence, on the one
hand, the trial-and-error which precedes the discovery of
solutions and, on the other hand, the corrections and checks
which follow it. Study of the child's first two years.of life
has led us, in this context, to a different viewpoint. \There
are indeed complex structures or " configurations " in
the infant's sensori-motor intelligence, but far from being
static and non-historical, they constitute " schemata " which
grow out of one another by means of successive differentia-
tions and integrations, and which must therefore be cease-
lessly accommodated to situations by trial-and-error and
corrections at the same time as they are assimilating the
situations to themselves. The response with the stick is
thus prepared by a series of anticipatory schemata, such as
that of pulling the objective to oneself by means of its
extensions (string or struts) or that of striking one object
against another.
The following reservations must therefore be made with
respect to Duncker's thesis. Xn act of intelligence is doubt-
less determined by past experience only in so far as it
resorts to it. NBut this relationship involves assimilatory
schemata which in turn are the product of previous schemata,
from which they are derived through differentiation and
co-ordination. x Schemata thus have a history ; there is
interaction between past experience and the present act of
intelligence, not uni-directional action of past on present as 4
empiricism demands nor uni-directional appeal to the past
by the present as Duncker would have it. x lt is even possible
to formulate these relations between present and past by
saying that equilibrium is reached when all previous schemata
are embedded in present ones and intelligence can equally
well reconstruct past schemata by means of present ones and
vice versa.
^On the whole then, we see that the Gestalt theory, although
correct in its description of forms of equilibrium or well-"
structured wholes, nevertheless neglects the reality, in per-
ceptiqn as in intelligence, of genetic development and the
process of construction that characterises it.
INTELLIGENCE AND PERCEPTION 67
DIFFERENCES BETWEEN PERCEPTION AND INTELLIGENCE
The Gestalt theory ha^ revived the problem of the rela-
tions between intelligence and perception by demonstrating
the continuity which link-^ the structures characteristic of
these two fields. The fact remains that, in order to solve
the problem while respecting the complexity of genetic facts,
we must list the differences between them before considering
analogies leading to possible explanations.
\ A perceptual structure is a system of interdependent
relations. Whether geometrical forms are involved, or
weights, or colours, or sounds, the wholes can always be
interpreted in terms of relations without destroying the
unity of the whole as such. ^For the purpose of distinguish-
ing the differences as well as the similarities between percep-
tual and operational structures, it is sufficient to express
these relations in terms of " groupings ", just as physicists,
when they formulate the phenomena of thermodynamics in
reversible terms, prove that they cannot be interpreted in
such terms because they are irreversible. v The non-corres-
pondence of symbolic systems thus emphasises all the more
the differences involved. In this respect, it is sufficient to
reconsider the various well-known geometrical illusions and
to vary the factors present, or the facts relating to Weber's
law, etc., and to formulate all the relations in " grouping "
terms and their changes as a function of external modifica-
tions.
Now the results thus obtained have made themselves clear.
None of the five conditions of " grouping " is realised at the
level of perceptual structures, and where they seem to come
nearest to being realised, as in the case of " constancies ",
which herald operational conservation, the operation is
replaced by simple regulations which are not entirely
reversible (and consequently midway between spontaneous
irreversibility and operational control).
As a first example, let us take a simplified form of Delboeuf s
illusion. 1 A circle Ai, of radius 12 mm,, drawn within a
circle B of 15 mm., appears larger than an isolated circle, Aa,
1 See Piaget, Lambercier, etc., Arch, de PsychoL, XXIX (i94 2 )> PP
1-107.
68 INTELLIGENCE AND SENSORI-MOTOR FUNCTIONS
equal to Ai. We vary the external circle B by altering its
radius gradually from 15 to 13 mm., and from 15 to 40 or
80 mm.: the illusion is reduced from 15 to 13 mm.; it is also
reduced from 15 to 36 mm., reaching zero at about 36 mm.,
(i.e. when the diameter of Ai equals the width of the
zone between B and Ai) and becoming negative beyond
this point (under-estimation of the inner circle Ai). Now :
1. If we are to translate the relations occurring in these
perceptual changes into operational language, it is obvious
straight away that their combination could not be additive,
because the conservation of the elements of the system is
lacking. Furthermore, this is the essential discovery of the
Gestalt theory and, according to the theory, characterises
the idea of perceptual " wholeness ". If we call A' the inter-
vening area marking the difference between the circles Ai
and Bi, we could not write Ai +A X =B, since Ai is dis-
torted by its insertion in B, since B is distorted by the fact
of surrounding Ai, and since zone A 7 is more or less expanded
or contracted according to the relations between Ai and B.
We may prove this non-conservation of the whole in the
following manner. If, starting from a certain value of Ai,
A" and B, we enlarge (objectively) Ai, thus reducing A ' but
leaving B constant, it is possible that the whole of B will
appear smaller than before. It will thus have lost something
during the change ; or, on the other hand, it will appear
larger and something extra will have been added. The
problem then is to find a means of formulating these " uncom-
pensated changes ".
2. With this aim in view, let us interpret the changes in
terms of the combination of relations and we shall demon-
strate the irreversible nature of this combination, this irre-
versibility expressing in another form the absence of additive
combination. We will call 5 the increase in dimensional simi-
larity between Ai and B, and d the increase in dimensional
difference between the same terms. These two relations are
bound to be and to remain the converse of each other :
'-f s = d and +d = s (the sign indicating the decrease
in similarity or difference). Now, if we start with no illusion
(Ai=ia mm. aiid 6=36 mm.), we find that as objective
INTELLIGENCE AND PERCEPTION 69
similarity is increased (by compressing the circles) the
subject perceives it to be still more reinforced. Consequently,
perception has increased similarity to excess when it was
objectively increased, and inadequately maintained the
difference when it was objectively reduced. Similarly, when
the objective difference is increased (by widening the circles),
this increase is also exaggerated. There is thus a lack of
compensation in the course of the transformations. So we
may agree to set out these transformations in the following
form, which is intended to denote their non-combinative
character from a logical standpoint :
s> -d or d> -$
In fact, if in each figure considered separately the relations
of similarity are automatically always the converse of the
relations of difference, the sum of the similarities and
differences will not remain constant with transition from
one figure to another, since the wholes are not conserved (see
under i). This is the sense in which we may legitimately
regard increases in similarity as outweighing decreases in
difference or vice versa.
It is possible, in this case, to express the same idea more
concisely simply by saying that the change in the relations
is irreversible because it is associated with all " uncofnpen-
sated change " P, such that :
i S = ~d +P sd or d = -s +P sd
3. Moreover, no combination of perceptual relations is
independent of the route travelled to reach it (associativity),
but each perceived relation depends on those which im-
mediately preceded it. Thus, the perception of the same
circle A will yield palpably different results according
to whether it is compared with reference circles arranged in
ascending or in descending order. N[n this instance, the most
objective measure is a random order, that is to say, one
which employs sometimes larger and sometimes smaller
elements than A, so that they compensate each other for
the distortions due to previous comparisons.
4 and 5, It is therefore obvious that a given element
does not remain the same when compared with others
different from it and when it is compared with others of
7O INTELLIGENCE AND SENSORI-MOTOR FUNCTIONS
the same dimensions as itself. Its value \vill continually
vary as a function of the relations given, present as well
as past.
x So it is impossible to reduce a perceptual system to a
" grouping ", except by turning inequalities into equalities
by introducing " uncompensated changes " P, which measure
the extent of distortion (illusions) and bear witness to the
non-additivity and non-transitivity of perceptual relations, to
thqSr irreversibility, to their non-associativity and to their
non-identity.
This analysis (which incidentally gives us some idea of
what thinking would be like if its operations were not
" grouped " !) shows that the form of equilibrium inherent
in perceptual structures is quite different from that of
operational structures. In the latter, equilibrium is both
mobile and permanent, and changes within the system do
not modify it because they are always exactly compensated,
owing to actual or potential converse operations (reversi-
bility) A In the case of perception, on the other hand, each
modification of the value of one of the relations involved
means a change of the whole, to the extent of introducing a
new equilibrium distinct from the one characterising the
previous state. There is then " displacement of equilibrium "
(as they say in physics in connection with the study of
irreversible systems as in thermodynamics), and no longer
permanent equilibrium. This is the case, for example,
for each new value of the outer circle B, in the illusion
just described. The illusion increases or diminishes but
does not conserve its original value.
Moreover, these " displacements of equilibrium " obey
laws of maxima ; a given relation generates an illusion and
so produces an uncompensated change P, as judged by the
value of other relations, only up to a certain value. NBeyond
this value the illusion diminishes, because the distortion is
then partially compensated by the effect of the new relations
of the whole. So displacements of equilibrium give place to
regulations or partial compensations, which may be defined
as the change of sign of the quantity P (e.g. when the two
concentric circles are too close or too far apart, Delboeuf s
INTELLIGENCE AND PERCEPTION 7!
illusion is reduced). Now these regulations, the effect of
which is thus to limit or " restrict " (as they say in physics)
the displacements of equilibrium, are comparable in certain
respects to the operations of intelligence. If the system
were of an operational order, every increase in one of the
values would correspond to a decrease in another and vice
versa (there would then be reversibility, i.e. P =o) ; if, on
the other hand, there were unlimited distortion with every
external modification, the system would no longer exist as
such ; the existence of regulations thus manifests the
existence of an intermediate structure between complete
irreversibility and operational reversibility.
^But how are we to explain this relative opposition (paral-
lelled by a relative affinity) between perceptual and intelli-
gent mechanisms ? The relations which compose a total
structure such as that of a visual perception express the laws
of a subjective or perceptual space, which may be analysed
and compared with geometrical space or operational space.
Illusions (or uncompensated changes in the system of rela-
tions) may now be conceived as distortions of this space in
the direction of expansion or contraction 1 .
X According to this point of view, one essential fact governs
all relations between perception and intelligence. When
intelligence compares two terms with each other, as in
measuring one by means of the other, neither the standard
nor the compared entity (in other words, neither the measure
nor what is measured) is distorted by the comparison itself.
On the other hand, in the case of perceptual comparison, and
especially when one element acts as a fixed standard for the
evaluation of variable elements, a systematic distortion is
produced which we, in company with Lambercier, have
called the " error of the standard ". The element which is
fixated most (i.e. generally the standard itself when the
variable is at a distance from it but also sometimes the
variable when the standard is close to it and already known)
is systematically over-estimated, and this applies to com-
1 Thus, in Delboeufs illusion, the area of the inner circle Ai appears
expanded at the expense of that of the zone A' between this circle and the
outer circle B, when this zone A' is narrower than the diameter of Ai ;
when A'>Ai the effect is reversed.
72 INTELLIGENCE AND SENSQRI-MOTOR FUNCTIONS
parisons made in the frontal parallel plane as well as in
depth 1 .
Such facts as these merely constitute particular cases of a
very general process. If the standard is over-estimated (or,
in certain circumstances, the variable) it is simply because
the element which is fixated longest (or most often, or most
intensely, etc.), is by this very fact magnified, as though
the object or the region on which vision is concentrated,
occasioned an expansion of perceptual space. In this respect,
we have only to fixate two equal elements successively to see
that on each occasion the dimensions of the one fixated are
enhanced, although, taken as a whole, these successive dis-
tortions compensate each other. \Perceptual space then is
not homogeneous but is centralised from moment to moment,
and the area of centralisation corresponds to a spatial expan-
sion, while the periphery of this central zone is progressively
contracted as one proceeds outwards from the centre. This
role of centralisation and of the error of the standard is
found also in the tactile sense.
But although "centralisation" thus causes distortions,
several distinct centrings correct one another's effects.
" Decentralisation ", or co-ordination of different centrings,
is consequently a correcting factor. So we see straight away
the rudiments of a possible explanation for irreversible
distortions and for the regulation we have just been discus-
sing. Illusions of visual perception may be explained by the
mechanism of centralisation when the elements of the
figure are (relatively) too close to each other for decentralisa-
tion to occur (illusions of Delboeuf, Oppelkundt, etc.). Con-
versely, regulation occurs to the extent that there is decentral-
isation, either automatic or by active comparison.
>We see now the relationship between these processes and
those characterising intelligence. It is not only in the field
of perception that (relative) error is associated with central!-
1 The proof that it is really a question of an error bound up with the
functional status of the measure is that this error can be reduced, or even
abolished, by pretending to change the standard for each comparison
.(while actually retaining the same one throughout). The perceptual error
may even be reversed by causing the verbal judgment to be made on the
standard instead of on titie measured stimulus (if the subject says A<B we
require the judgment B>A), which reverses the functional positions.
INTELLIGENCE AND PERCEPTION 73
sation and (relative) objectivity with decentralisation, ihe
whole of the development of thought in the child, the initial
intuitive forms of which are closely related to perceptual
structures, is characterised by a transition from a general
egocentricity (which we shall reconsider in Chapter V) to
intellectual decentralisation, and thus by a process compar-
able to the one whose effects we are here ascertaining. But, for
the moment, the problem is to understand the differences be-
tween perception and complete intelligence and, in this respect,
the foregoing facts enable- us to grasp more fully the chief
of these contrasts : the contrast between what might be
called " perceptual relativity " and intellectual relativity.
Indeed, if centrings are interpreted as distortions which,
as we have seen, may be formulated by reference to (and by
contrast with) a grouping, the next problem is to measure
them as far as is possible and to interpret this quantification.
This may conveniently be done in the case where two homo-
geneous elements are compared with each other, as in the
case of two straight lines which are extensions of each other.
We may then state a law of " relative centralisation " which
is independent of the absolute value of the effects of centring,
and expresses relative distortions in the form of a single
probable value, i.e. by the relation of actual centrings to the
number of possible centrings.
We know that a line A, compared with another line A',
is underestimated if the second is larger than the first
(A<A') and overestimated in the opposite case (A>A').
The method of calculation is, in each of these two cases,
to consider the successive centralisations on A and on A'
as alternately enlarging these lines in proportion to their
lengths. The difference of these distortions, expressed
in relative sizes of A to A', thus gives the gross over-
estimation or under-estimation of A. These are then
divided by the total length of the contiguous lines A+A',
since the decentralisation is proportional to the size of
the total figure. We then obtain :
(A-AQ AVA (A'-A) A/A'
Where A>A and A+A-
where A<A'.
74 INTELLIGENCE AND SENSORI-MOTOR FUNCTIONS
Furthermore, if the measurement is made on A, these
relations must be multiplied by A 2 /(A + A') 2 , i.e. by the
square of the ratio of the part measured to the whole.
The theoretical curve obtained in this way corresponds
closely to empirical measurements of distortions and, more-
over, coincides fairly accurately with measurements of
Delbceuf 's illusion 1 (if, in the formula, A is inserted between
the two A's and this value A' is doubled).
^Expressed in qualitative language, this law of relative
centralisation simply means that every objective difference
is subjectively accentuated by perception, even in the case
where the compared elements are equally centred in vision.
In other words, all contrast is exaggerated by perception,
which immediately points to the presence of a relativity
peculiar to the latter and distinct from the relativity of
intelligence. This brings us to Weber's law, the discussion
of which in this context is particularly instructive. In its
strict sense, Weber's law states, as is well known, that the
-size of *' differential thresholds " (smallest perceptible
differences) is proportional to that of the elements compared ;
for example, if a subject distinguishes 10 mm. from n mm.
but not 10 from 10.5 mm., he will also only distinguish 10
from ii cm. and not 10 from 10.5 cm.
Let us now assume that the aforementioned lines
A and A' are of equal or nearly equal values. If they
are equal, centring on A enlarges A and decreases A 7 ,
and centring on A' enlarges A' and decreases A in the
same proportions ; hence the distortions are cancelled.
On the other hand, if they are slightly unequal but with
an inequality which is less than the distortions due to
centralisation, then centring on A yields the perception
A>A' and centring on A' the impression A'>A. In this
case, there is a contradiction between the estimations (as
opposed to the general case where an inequality, common
to both methods of viewing, simply appears greater or
smaller according to whether A or A' is fixated). This con-
tradiction is interpreted as a sort of fluctuation (compar-
able to resonance in physics) which can arrive at percep-
1 See note p. 67.
INTELLIGENCE AND PERCEPTION 75
tual equilibrium only by the equation A=A'. But this
equation remains subjective and is therefore illusory ;
it amounts to saying that two almost equal values are
confused in perception. Now this non-differentiation is
precisely what characterises the existence of " differential
thresholds " and since, by the law of relative centralisa-
tion, it is proportional to the lengths of A and A', we thus
return to Weber's law.
Weber's law applied to differential thresholds is thus
explained by the law of relative centralisation. Moreover,
since it applies with equal force to differences of any des-
cription (whether the similarities exceed the differences,
as in cases below threshold value, or whether the reverse
is the case as in the case discussed above), we may in all
cases regard it as simply expressing the factor of pro-
portionality inherent in the relations between relative
centrings (and for touch, weight, etc. just as for
vision).
'We are now in a position to state more clearly the un-
doubtedly essential opposition which separates intelligence
from perception. Weber's law is often translated by saying
that all perception is " relative ". Absolute differences are
not- discerned since i gr. may be perceived when added to
i gr. although it is not when it is added to 100 gr. On the
other hand, when the elements differ markedly the contrasts
are then accentuated, as is shown by ordinary cases of
relative centralisation, and this reinforcement is again
relative to the size of the values involved (thus a room seems
warm or cold according as one comes from a place with a
higher or lower temperature). Thus whether we are con-
cerned with illusory similarities (threshold of equality) or
illusory differences (contrasts), perceptually they are all
" relative ". But does not the same hold in the case of
intelligence also ? Is not a class relative to a classification
and a relation to a complex of relations ? In point of fact,
the word " relative " is used in quite different senses in the
two cases.
Perceptual relativity is a distorting relativity, in the sense
in which conversational language says " everything is
76 INTELLIGENCE AND SENSORI-MOTOR FUNCTIONS
relative " when denying the possibility of objectivity ; the
perceptual relation modifies the elements which it unites, and
we now understand why. \The relativity of intelligence on
the other hand is the very condition of objectivity ; thus
relativity in space and in time is a condition of their very
measurement. Everything indicates, therefore, that percep-
tion, obliged to proceed step by step by immediate but
partial contact with its object, distorts it by the very act
of centring it, although these distortions are reduced by
equally partial decentralisations, while intelligence, encom-
passing in a single whole a much larger number of facts
reached by variable and flexible paths, attains objectivity
by a much more thorough decentralisation.
XThese two relativities, the one distorting and the other
objective, are doubtless the expression both of a deep-rooted
opposition between acts of intelligence and perception, and
of a continuity which, in other respects, presupposes the
existence of common mechanisms. If perception, like
intelligence, consists in structuring and arranging relations,
why then are these relations distorting in one case and not
in another ? Might not the reason be that the first are not
only incomplete but cannot be sufficiently co-ordinated,
while the second are based on a co-ordination which can be
indefinitely generalised ? And if the " grouping *' is the
source of this co-ordination, and if its principle of reversible
combinativity carries further the work of perceptual regula-
tions and decentralisations, should we not then admit that
centrings are distorting because they are not numerous
enough, being to some extent fortuitous and so result-
ing from a sort of lottery among those which would
be necessary to ensure complete decentralisation and
objectivity ?
^We are therefore led to enquire whether the essential
difference between intelligence and perception does not
arise from the fact that the latter is a process of a statistical
nature, confined to a certain stage, while processes of an
intellectual nature determine complex relations confined to
a higher level. Perception would be to intelligence what, in
physics, irreversible functions (i.e. simple chance functions)
INTELLIGENCE AND PERCEPTION 77
and displacements of equilibrium are to mechanics
proper.
The probabilist structure of the perceptual laws of which
we have been speaking amounts precisely to the same as,
and explains, the irreversible character of the processes of
perception, as opposed to operational combinations, which
are both well defined and reversible. Why does sensation
appear as the logarithm of the excitation (which immediately
explains the proportionality expressed by Weber's law) ?
It is known that Weber's law applies not only to facts of
perception or facts of physiological excitation but also,
among other things, to the impression on a photographic
plate. In this last case it means simply that the intensity of
the impression is a function of the probability of a collision
between the photons bombarding the plate and the particles
of silver salts which compose it (hence the logarithmic form
of the law : Hhe relation between the multiplication of
probabilities and the addition of intensities). Similarly, in
the case of perception, it is easy to think of a quantity such
as the length of a line, as a mass of possible points of visual
fixation (or of segments for possible centralisation). VWhen
two unequal lines are compared, the corresponding points
will give rise to combinations or associations (in the mathe-
matical sense) of similarity, and the non-corresponding
points to associations of difference (the associations thus
increasing geometrically as the length of the lines increases
arithmetically). \i perception occurred according to every
possible combination, there would then be no distortion (the
associations would reach a constant relation and we should
have s = d). But the facts suggest that actual vision
constitutes a sort of sampling, as though only certain points
of the perceived figure were fixated while others were
neglected. It is easy, then, to interpret the foregoing laws in
terms of probabilities according to which centrings are more
likely to be placed in one direction than another. In the
case of a considerable difference between two lines, it follows
automatically that the larger of the two will catch the eye
more, hence the excess of associations of difference (the law
of relative centralisation concerning contract), while in the
78 INTELLIGENCE AND SENSORI-MOTOR FUNCTIONS
case of very small differences, associations of similarity will
outweigh others, hence Weber's threshold 1 . (We may even
calculate the various combinations and again arrive at the
formulae stated above.)
"^Finally, we may note that this probabilist character of
perceptual constructions, as opposed to the determinate
character of operational combinations, not only explains the
distorting relativity of the first and the objective relativity
of the second. Above all, it explains the essential fact which
Gestalt psychology has insisted on : ^namely, that in a
perceptual structure the whole is not reducible to the sum
of its parts. In fact, to the extent that chance is a factor in
a system, that system will be prevented from being reversible,
since this chance factor always, in one way or another,
involves the existence of a mixture and a mixture is irre-
versible.^ The result is that a system involving an element
of chance could not be liable to additive combination
(inasmuch as reality overlooks extremely unlikely combina-
tions), unlike determinate systems which are reversible and
combinative 2 .
XSo, in short, we can say that perception differs from intelli-
gence in that its structures are intransitive, irreversible, etc.
and thus not composed in accordance with laws of grouping,
the reason for this being that the distorting relativity which
is inherent in them gives them an essentially statistical
nature. This statistical composition of perceptual relations
is thus simply the same as their irreversibility and their
non-additivity, while intelligence is directed towards com-
plete and therefore reversible combinativity.
ANALOGIES BETWEEN PERCEPTUAL ACTIVITY AND INTELLI-
GENCE
How then are we to explain the undeniable affinity
between these two types of structure, both of which imply
1 See Piaget, "Essai d' interpretation probabiliste de la loi de Weber."
Arch, de PsychoL XXX (1944) PP* 95-138.
* The best example of non-additive combination of a perceptual type is
doubtless provided by a certain weight illusion wherein the part A (a piece
of cast iron) is perceived as heavier than the whole B, comprising A and A'
(an empty box of light wood exactly enclosing A). Thus B<A A' and
A>B, while objectively B =A+A'.
INTELLIGENCE AND PERCEPTION 79
constructive activity on the part of the subject and constitute
complex systems of relations, certain of which, in both fields,
arrive at " constancies " or at notions of conservation ?
Above all, how are we to account for the existence of the
innumerable intermediate structures which link elementary
centralisations and decentralisations, as well as the regu-
lations resulting from the latter, with intellectual operations ?
V. It seems that, in the perceptual field, a distinction must
be made between perception as such the totality of relations
given immediately and simultaneously with each centring
and the perceptual activity which comes into play in the
very act of centring vision or of changing the centring (as well
as in other acts.) It is clear that this distinction is still
relative, but it is remarkable that each school should be
obliged to recognise it in one form or another, un this way,
the Gestalt theory, whose whole character tends to restrict
the subject's activity in favour of whole structures, which
are prominent by virtue of both physical and physiological
laws of equilibrium, has been forced to find a place for the
subject's attitudes. The <{ analytical attitude " is invoked
to explain how wholes may be partially dissociated and,
especially, the Einstellung or mental set of the subject is
admitted as the cause of numerous distortions in perception
depending on previous states. As for von Weizsacker's
school, Auersperg and Buhrmester invoke anticipations and
perceptual reconstitutions, which involve the necessary
intrusion of the response in all perception. And so on.
Now if a perceptual structure is essentially of a statistical
nature and not composed additively, it follows automatically
that all activity which directs and co-ordinates successive
centrings will reduce the role of chance and change the
structure concerned in the direction of operational compo-
sition (needless to say, in varying degrees and without ever
completely attaining it). Side by side, therefore, with the
manifest differences between the two fields, there exist
analogies, which are no less obvious and such that it would
be difficult to say just where perceptual activity ends and
intelligence begins. This is why nowadays we cannot speak
of intelligence without defining its relations with perception.
80 INTELLIGENCE AND SENSORI-MOTOR FUNCTIONS
The crucial fact, in this connection, is the existence of a
perceptual development as a part of mental growth in
general. * Gestalt Psychology has rightly insisted on the
relative invariability of certain perceptual structures ; most
illusions occur at all ages, and in the animal just as in man ;
factors determing complex " configurations " likewise appear
to be common to all ages, etc. But these common mechan-
isms especially concern perception as such, which is in some
way receptive and immediate 1 , while perceptual activity
itself and its effects manifest far-reaching transformations,
varying with mental age. As well as size constancy, etc.,
which experiment has shown, despite the Gestalt theory,
to be built up gradually with the appearance of ever more
precise regulations, the simple measurement of illusions
shows the existence of modifications with age that would be
inexplicable without a close affinity between perception and
intellectual activity in general.
\ Here we must distinguish two cases, corresponding on/the
whole to what Binet called "innate" and "acquired"
illusions, and which we had best straight away name
" primary " and " secondary " illusions. * Primary illusions
are reducible to simple factors of centralisation and are
thus dependent on the law of relative centralisation. Now
the value of these diminishes fairly regularly with age (" error
of the standard ", illusions of Delbceuf, Oppel, Miiller-Lyer,
etc.) and this is readily explained by the increase in de-
centralisations, and in the regulations which they involve,
as the subject's activity when faced with the figures increases.
Certainly, the young child remains passive where older
children and adults compare, analyse and thus indulge in an
active decentralisation which is orientated towards opera-
tional reversibility. But, on the other hand, there are
illusions which increase in intensity with age or development,
such as the weight illusion, which is absent in the grossly
abnormal and which increases up to the end of childhood,
to decrease somewhat afterwards. But we know that what
it requires is simply a sort of anticipation of the relations of
1 T^ii& does not mean " passive ", since it already shows " laws of
orgajBsatiott J *. -
INTELLIGENCE AND PERCEPTION 8l
weight and volume, and it is clear that this anticipation
presupposes an activity which by its very nature increases
of its own accord with intellectual growth. ^Such an illusion,
produced by interaction between primary perceptual factors
and perceptual activity, may thus be called secondary and
we shall shortly be meeting others which are of the same type.
This being so, perceptual activity is distinguished in the
first place by the occurrence of decentralisation, which
corrects the effects of centralisation and thus constitutes a
regulation of perceptual distortions. ^Now, however elemen-
tary and dependent on sensori-motor functions these de-
centralisations and regulations may be, it is clear that they
all constitute an activity of comparison and co-ordination
which is allied to that of intelligence. ^ Even to look at an
object is an act and by noting whether a young child lets
his gaze dwell on the first point that presents itself or
whether he directs it so as to include the whole complex of
relations, we can almost judge his mental age A When objects
that are too distant to be included in the same centring are to
be compared, perceptual activity is extended in the form of
" transportations " in space, as though the view of one of the
objects were being superimposed on the other. These trans-
portations, which thus constitute the (potential) reconcilia-
tion of centrings, give place to genuine " comparisons " or
double transportations which, by alternating, decentralise the
distortions due to one-way transportation. Study of these
transportations has drawn our attention to a distinct reduc-
tion of distortions with age 1 , that is to say, a distinct improve-
ment in the estimation of size at a distance, and this is self-
explanatory in view of the coefficient of true activity which
occurs here.
^Now, it is easy to show that these decentralisations and
double transportations, together with the specific regula-
tions which their different varieties involve, are responsible
for the famous perceptual " constancies " of shape and size.
It is most remarkable that we scarcely ever obtain absolute
size constancy in the laboratory ; the child under-estimates
size at a distance (taking into account the error of the
1 Arch, de PsychoL, XXIX (1943) pp. 173-253.
82 INTELLIGENCE AND SENSORI-MOTOR FUNCTIONS
standard), but the adult almost always over-estimates it
slightly ! \These " superconstancies ", which writers have
in fact often observed but which they normally pass over as
though they were embarrassing exceptions, have seemed to
us to constitute the rule, and no fact could better attest the
intervention of true regulation in the construction of constan-
ciesANow when we see that infants, just at the age at which
this constancy has been noted (although its precision has been
greatly exaggerated), indulge in genuine trials, which consist
in deliberately moving to and from their eyes the objects
they are looking at 1 , we are induced to relate perceptual
activity involving transportations and comparisons to
manifestations of sensori-motor intelligence ^without
resorting to Helmholtz's " unconscious inference "). v On the
other hand, it seems obvious that the shape constancy of
objects is bound up with the actual construction of the
object. We shall return to this in the next chapter.
In brief, perceptual " constancy " seems to be the product
of genuine actions, which consist of actual or potential move-
ments of the glance or of the organs concerned ; responses
are co-ordinated in systems, whose organisation may vary
from simple directed >trial-and-error to a structure reminis-
cent of " grouping "A But true grouping is never attained
at the perceptual level, and only regulations due to these
real or potential movements take place. This is why per-
ceptual "constancy", although it recalls operational
constants or ideas of conservation depending on reversible
and grouped operations, does not arrive at the ideal precision
which alone would assure them the complete reversibility
and mobility of intelligence. Nevertheless, the perceptual
activity that characterises it is already approaching
intellectual combinativity.
^This same perceptual activity likewise presages intelligence
in the domain of temporal transportations and genuine antici-
pations. In an interesting experiment on visual analogies of
the weight illusion, Usnadze 2 gives his subjects a fraction of
a second's glimpse of two circles, 20 and 28 mm. in diameter,
i La Construction du R6el chex V Enfant, pp. i57' I 5 8 '
*Psychpl. Forsch.. XIV (1930)* P- 3 6 ^.
INTELLIGENCE AND PERCEPTION 83
and then two circles of 24 mm. The 24 mm. circle, situated
in the place previously occupied by the 28 mm. circle, is
then seen as smaller than the other (and the one replacing
the 20 mm. one is overestimated), on account of a contrast
effect due to^transportation in time (which Usnadze calls
Einstellung), Measuring this illusion in children aged 5-7
and in adults 1 , we, with Lambercier's collaboration, obtained
the following results, and it is very suggestive to consider
them as a whole with regard to the relations of perception to
intelligence. On the one hand, the Usnadze effect is appre-
ciably stronger in adults than in children (as is the weight
illusion itself), but, on the other hand, it disappears more
rapidly. After several presentations of 24+24 mm. the
adult reverts gradually to objective vision, while the child
retains a residual effect. So we cannot explain this double
difference in terms of simple memory traces without being
compelled to say that the adult's memory is superior but he
forgets more quickly ! On the contrary, it looks as if an
activity of transposition and anticipation develops with age,
towards both greater mobility and greater reversibility. This
constitutes a fresh example of perceptual development
orientated towards the operation.
A neat experiment of Auersperg and Buhrmester
consists in presenting a simple square, traced in white
lines, which is rotated on a black disk. At slow speeds
the square is seen directly, although the retinal image
now consists of a double cross enclosed by four lines at
right angles. At high speeds, only the retinal image is
seen, but at intermediate speeds a transitional figure
is seen, formed by a simple cross enclosed by the four
lines. As these writers have emphasised, a sensori-motor
anticipation undoubtedly occurs which enables the sub-
ject to reconstruct the square wholly (first phase), in
part (second phase), or which miscarries (third phase),
being upset by the excessive speed. Now, we
have found, with Lambercier and Demetriades, that
the second phase (simple cross), measured in children
aged 5-12 years, appeared later and later (i.e. at higher
and higher speeds of rotation as age increased). The
1 Arch. de Psychol., XXX (1944)* PP- I39-IQ6.
84 INTELLIGENCE AND SENSORI-MOTOR FUNCTIONS
reconstruction or anticipation of the moving square thus
improves (i.e. occurs at ever higher speeds) as the
subject develops.
But this is not all. We present the subjects with two rods
to be compared in depth perception, A at i metre and C at
4 metres. We first measure the perception of C (under-
estimation or superconstancy, etc.) then we place on this
side of C a rod B equal to A, placed 50 cm., away from it
laterally, or else we place between A and C an intermediate
series Bi, B2, 63, all equal to A (with the same lateral
interval). \ The adult, or the child older than 8-9 years,
immediately sees A =B =C(or A =Bi ==B2 =63 =C) because
he transports the perceptual equalities A=B and B=C
directly to the relation C = A, thus closing the figure! Young
children, on the other hand, see A =B, B =C and A different
from C, as though the equalities seen in the course of the
detour ABC were not transferred to the direct relation A C.
'Now before 6-7 years the child is not capable of the opera-
tional combination of the transitive relations A=B, B=C,
therefore A=C. But, curiously enough, between 7 and
8-9 years there is an intermediate phase when the subject
immediately infers by intelligence the equality A =C while
at the same time he sees C perceptually as slightly different
from A ! It is clear then from this example that trans-
position (which is a " transportation " of relations as opposed
to that of an isolated value) also arises from perceptual
activity and not from the automatic structuring common to
all ages, and that we still have to define the relations between
perceptual transposition and operational transitivity.
But transposition is not merely external to the perceived
figures ; as well as this external transposition we must
distinguish internal transpositions which enable us to recog-
nise, within the actual figures, recurring relations, symmetries
(or reversed relations), etc. Here also, there is much to be
said concerning the role of intellectual development, young
Children being by no means so apt at structuring complex
figures as some people have tried to maintain.
From all these facts, we may conclude the following.
The development of perception bears witness to the existence
INTELLIGENCE ANB PERCEPTION 85
of a perceptual activity leading to decentralisations, trans-
portations (spatial and temporal), comparisons, transposi-
tions, anticipations and, in general, an analysis becoming
more and more mobile and making for reversibility. This
activity increases with age and it is because they do not
possess it to a sufficient degree that young children perceive
in a' syncretic ' or ' global ' manner or else by accumu-
lating disconnected details.
While perception as such is characterised by irreversible
systems of a statistical nature, perceptual activity, on the
other hand, introduces into such systems, which are governed
by fortuitous or merely probable distributions of Centrings,
coherence and the power of progressive synthesis. * Does this
activity already constitute a form of intelligence ? We have
seen (Chap. I and end of Chap. II) what little meaning a
question of this type has. However, we can say that in
their origins the actions that serve to co-ordinate attention
along the lines of decentralisation, transportation^ com-
parison, anticipation and especially transposition are closely
bound up with sensori-motor intelligence, which we shall be
discussing in the next chapter. "^Transposition, in particular,
both internal and external, which embraces all other acts of a
perceptual nature, is very much like assimilation, which is a
characteristic of sensori-motor schemata, and especially like
the generalised assimilation that facilitates the transference
of these schemata.
But, if perceptual activity approaches sensori-motor intelli-
gence, its development takes it up to the threshold of opera-
tions. In proportion as the perceptual regulations due to
comparisons and transpositions tend towards reversibility,
they constitute one of the flexible supports which will be
required for the launching of the operational mechanism.
The latter, once established, will then react on them, inte-
grating them with itself by a recoil analogous to that occur-
ing in the example we have just mentioned in connection
with transpositions of equality. But, prior to this reaction,
they pave the way for the operation, introducing more and
more mobility into the sensori-motor mechanisms that con-
stitute its. substructure. In fact, it is sufficient that the
86 INTELLIGENCE AND SENSORI-MOTOR FUNCTIONS
activity underlying perception should pass beyond immedi-
ate contact with the object and act at increasing distances in
space and time, for it to transcend the perceptual field itself
and thus for it to be liberated from the limitations that
prevent it from attaining complete mobility and reversi-
bility.
\ However, perceptual activity is not the only medium of
incubation provided for the generation of operations of
intelligence ; we still have to consider the role of the motor
functions which produce habits and which are, moreover,
extremely closely linked with perception itself.
CHAPTER IV
HABIT AND SENSORI-MOTOR INTELLIGENCE
THE distinction between motor functions and perceptual
functions is legitimate only for purposes of analysis. As
von Weizsacker 1 has convincingly shown, the classical division
of phenomena into sensory stimuli and motor responses,
which is introduced by the reflex-arc schema, is just as
fallacious, and refers to laboratory products which are just
as artificial, as the idea of the reflex arc itself, conceived in
isolation. Perception is influenced by motor activity from
the outset, just as the latter is by the former. This is what we,
for our part, have asserted when speaking of sensori-motor
schemata in order to describe the simultaneously perceptual
and motor assimilation which characterises the behaviour
of the infant. 2
We are bound then to place what we have just learned
from the study of perception in its true genetic context
and to inquire how intelligence is formed prior to language.
Once he has passed beyond the level of purely hereditary
connections, i.e. reflexes, the infant acquires habits as a
result of experience. Do these habits provide the basis for
intelligence or have they nothing to do with it ? This is the
parallel problem to the one we put to ourselves with regard
to perception. The answer also is likely to be the same, and
this will enable us to advance more rapidly, and to place the
development of sensori-motor intelligence in relation to all
the elementary processes that condition it.
HABIT AND INTELLIGENCE
i. INDEPENDENCE OR DIRECT DERIVATION
Nothing is better fitted to illustrate the continuity which
1 D&Y Gestaltkreis, 1941*
1 La naissance de Vintelligence chef Venfant, 1936.
8 7
88 INTELLIGENCE AND SENSORI-MOTOR FUNCTIONS
links the problem of the birth of intelligence to that of the
formation of habits than a comparison of the various
answers to these two questions. The same hypotheses appear
in both cases, as though intelligence were an extension of those
mechanisms which in their automatic form appear as habit.
In connection with habit, we once again find the genetic
schemata of association, of trial-and-error or of assimilatory
structuring. In its treatment of the relations between habit
and intelligence, associationism goes so far as to make habit
into a primary fact which explains intelligence ; the theory
of trial-and-error reduces habit to a matter of responses
selected in the course of random behaviour and becoming
automatic, this being characteristic of intelligence itself ; the
theory of assimilation sees intelligence as a form of equi-
librium of that assimilatory activity which, in its original
form, constitutes habit. As for non-genetic interpretations,
we shall again meet the three combinations corresponding to
vitalism, apriorism and Gestalt : habit deriving from intelli-
gence, habit unrelated to intelligence and habit explained,
like intelligence and perception, by structurings whose laws
remain independent of development.
Regarding the relations between habit and intelligence
(the only question which concerns us here), we must ascertain
first whether the two functions are independent, then
whether the one derives from the other, and finally from,
which common forms of organisation they emanate at
different levels.
It is typical of the logic of the apriorist interpretation of
intellectual operations to deny that they have any relation
to habits, since they emanate from an inner structure which
is independent of experience. And it is a fact that, to an
introspection of the two types of phenomena in their final
state, their differences seem profound and their analogies
superficial. H. Delacroix has shrewdly commented on both of
them : a habitual response to repeated circumstances seems
to involve a sort of generalisation, but, in place of this
unconscious automatism, intelligence substitutes a generality
of quite a different quality, composed of deliberate choices
and insight. All this is quite correct, but the more we
HABIT AND SENSORI-MOTOR INTELLIGENCE 89
analyse the formation of a habit as opposed to the automatic
exercising of it, the more we realise the complexity of the
activities that come into play at the outset. On the other
hand, in going back to the sensori-motor origins of intelli-
gence, we come back to the setting of the learning process
in general. So, before deciding that the two types of struc-
ture are Irreducible, it is essential to inquire, while distin-
guishing vertically a series of actions of different levels, and
while taking account horizontally of how far they are novel
or automatic, whether there might not exist a certain
continuity between the limited and comparatively rigid
co-ordinations that we usually call habits, and the co-
ordinations characterising intelligence, which have greater
mobility and extreme limits which are further removed.
This was fully realised by Buytendijk, who has brilliantly
analysed the formation of elementary animal habits,
especially in invertebrates. However, the greater the
complexity this writer finds in the factors affecting habit,
the more he tends, on account of his vitalist system of
interpretation, to subordinate the co-ordination peculiar to
habits to intelligence itself, a faculty inherent in the organism
as such. The formation of a habit always involves a funda-
mental means-end relation ; an action is never a succession
of mechanically associated movements but is directed
towards a satisfaction such as contact with food or release,
e.g. Limnaea, when placed upside down, return more and
more rapidly to their normal position. But the means-end
relation characterizes inteUigent actions ; habit would then
be the expression of an intelligent organisation which, more-
over, must be co-extensive with all living structure. Just
as Helmholtz explained perception by the intervention ^ of
unconscious inference, so vitalism ends by describing
habit as the result of an unconscious organic intelligence.
But although we must fully acknowledge the justice of
Buytendijk's observations regarding the complexity of the
simplest acquisitions and the irreducibility of the relation of
need to satisfaction, which is the origin and not the effect of
associations, there is no justification for hastily explaining
everything by intelligence, considered as a primary fact.
90 INTELLIGENCE AND SENSOfct-MOTOR FUNCTIONS
Such a thesis involves a series of difficulties which are
exactly the same as those of the parallel interpretation with
respect to perception. In the first place, habit, like percep-
tion, is irreversible because it is always orientated in one
direction towards the same result, while intelligence is
reversible. Reversing a habit (e.g. writing backwards or
from right to left, etc.) means acquiring a new habit, while
a " reverse operation " of intelligence is psychologically
implied by the original operation (and logically constitutes
the same change, but in the opposite direction). In the
second place, just as intelligent insight only slightly modifies
a perception (knowledge has little influence on an illusion
as Hering pointed out in reply to Helmholtz) and,
reciprocally, elementary perception does not automatically
turn itself into an act of intelligence, so intelligence only
slightly modifies an acquired habit and, above all, the
formation of a habit is not immediately followed by the
development of intelligence. There is actually an appreciable
break in the genetic series between the appearance of the
two types of structures. Pieron's sea-anemones, which close
up at low tide and thus store the water they need, are not
evidence for a really mobile intelligence and, in particular,
they retain their habit in the aquarium for several days
before it is extinguished. Goldsmith's Gobii learn to pass
through a hole in a sheet of glass to reach food and keep to
the same route after the glass is removed : we may name this
behaviour sub-cortical intelligence, but it is still considerably
inferior to what is ordinarily called intelligence without
qualification.
Hence the hypothesis which for a long time seemed the
simplest : that habit constitutes a primary fact, explicable
in terms of passively experienced associations, and intelli-
gence grows out of it gradually, by virtue of the growing
complexity of the acquired associations. We are not going
to call associationism to trial here, since the objections to
this mode of interpretation are as well known as its resurrec-
tion in different and often disguised forms. However, it is
essential, in order to arrive at the true development of the
structures of intelligence, to remember that the most
HABIT AND SENSORI-MOTOR INTELLIGENCE 9!
elementary habits are still irreducible to the pattern of
passive association.
But the idea of the conditioned reflex, or of conditioning in
general, has afforded a recrudescence of vitality to associa-
tionism by providing it with both a precise physiological
model and a revised terminology. Hence the series of appli-
cations attempted by psychologists in the interpretation of
intellectual functions (language etc.) and occasionally of
the act of intelligence itself.
But if the existence of conditioned behaviour is a fact,
and even a very important one, its interpretation does not
imply the- reflexological associationism with which it is too
often identified. When a response is associated with a
perception there is more in this connection than a passive
association (i.e. becoming stamped in as a result of repe-
tition alone) ; meanings also enter into it, since association
occurs only in the presence of a need and its satisfaction.
Everyone knows in practice, although we too often forget
it in theory, that a conditioned reflex is stabilised only as
long as it is confirmed or reinforced ; a signal associated with
food does not give rise to an enduring reaction if real food
is not periodically presented together with the signal.
Association thus comes to be part of a complex piece of
behaviour, which starts from a need and finishes with its
satisfaction (actual, anticipated or even make-believe, etc.).
This amounts to saying that this is not a case of association
in the classical sense of the term, but rather of the constitu-
tion of a complex schema bound up with a meaning. More-
over, if a system of conditioned responses is studied with
reference to their historical sequence (and those concerning
psychology always present such a sequence, as opposed to
over-simplified physiological conditioning), the role of com-
plex structuring is seen to even better advantage. Thus
Andre Rey placed a guinea-pig in compartment A of a box
with three adjacent compartments, A, B, and C, and
administered an electric shock preceded by a signal. On
the repetition of the signal, the guinea-pig jumped into B,
then returned to A, but only a few more trials were required
for it to jump from A into B, from B into C and to return
92 INTELLIGENCE AND SENSORI-MOTOR FUNCTIONS
from C into B, and so into A. Thus, in this case, the con-
ditioned response is not the simple substitution of responses
originally due to a simple reflex, but new behaviour which
arrives at stability only by a structuring of the whole
environment. 1
Now if this is the case with the most elementary types of
habit, the same must hold a fortiori in the case of the in-
creasingly complex " associative transfers " which cany
behaviour to the threshold of intelligence. Wherever there is
an association between response and perception, the so-
called association really consists in integrating the new
element with a previous schema of activity. Whether this
previous schema is in the nature of a reflex, as in the
conditioned reflex, or belongs to much higher levels, associa-
tion is always, in point of fact, assimilation of such a kind
that the associative link is never simply the reproduction of
a relation which is given, already formed, in external reality.
This is why the study of the formatioii of habits, like that
of the structure of perceptions, concerns the problem of
intelligence in the highest degree. If early intelligence
consisted merely in exerting its action (which is a later
acquisition belonging to a higher plane) on a completed
world of associations and relations, corresponding term
for term with relations written, once and for all, in the
external environment, then this action would, in point of
fact, be illusory. On the other hand, in so far as the organis-
ing assimilatory process, which eventually arrives at the
operations peculiar to intelligence, appears from the outset
in perceptual activity and in the formation of habits, the
empiricist models of intelligence that some writers try to
build up are inadequate at all levels, since they disregard
assimilatory construction.
We know, for example, that Mach and Rignano regard
reasoning as a " mental experiment ". This description,
correct in principle, would take the form of an explanatory
i$#j$ji&D if the experiment were the copy of a cut-and-dried
\ reality. But as this is not so and as, even at
1 A. 'lley, "Les cbacluates eonclitionaes du cob^ye **' (Arch, fe
' ' " '' ' ' !
HABIT AND SENSORI-MOTOR INTELLIGENCE 93
the level of habit, adaptation to reality means an assimila-
tion of reality to the subject's schemata, the explanation of
reasoning as a mental experiment becomes circular ; t}ie
whole activity of intelligence is required to carry out an
experiment, practical or mental. In its finished state, a
mental experiment is the reproduction in thought, not of
reality, but of actions or operations which affect it, and the
problem of their formation remains untouched. Only at the
level at which thought begins in the child may we speak of
mental experiment in the sense of a simple internal imitation
of reality ; but in this case reasoning is, of course, not yet
logical.
Similarly, when Spearman reduces intelligence to three
essential activities, the " apprehension of experience ", the
" eduction of relations " and the " eduction of correlates ",
we must add that experience is not apprehended without
the intervention of constructive assimilation. The so-called
" eductions " of relations are to be thought of, then, as
genuine operations (seriation or the grouping together of
symmetrical relations). As for the eduction of correlates
" the presenting of any character together with any
relation tends to evoke immediately the knowing of the
correlative character"), 1 this is compatible with certain
definite groupings, namely those of multiplication of classes
or relations (Chap. II).
HABIT AND INTELLIGENCE
II. TRIAL-AND-ERROR AND STRUCTURING
So if neither habit nor intelligence may be explained Dy a
system of associative co-ordinations that correspond exactly
to relations previously given in external reality, but both
instead involve action on the part of the subject himself,
would not the simplest interpretation be to reduce this
activity to a series of trials occurring at random (i.e. with no
direct relation to the environment), but gradually selected by
means of the successes or failures resulting from them ?
In this way, Thorndike, studying the mechanism of learning,
places animals in a maze and measures retention by the
1 The Nature of Intelligence, 192,3, p. 9**
94 INTELLIGENCE AND SENSORI-MOTOR FUNCTIONS
decreasing number of errors. At first the animal acts
at random, i.e. it indulges in fortuitous trials, but
errors are gradually eliminated and the successful trials
retained, so determining subsequent routes. This principle
of selection by the result obtained is called the " law of
effect ". The hypothesis is tempting : action on the part
of the subject is introduced into the trials, and that of the
environment into selection, and the law of effect allows for
the role of needs and satisfactions which embrace all active
behaviour.
Moreover, it is in the nature of an explanatory scheme of
that sort to take account of the continuity which links the
most elementary habits with the most highly developed
intelligence. Claparede took up the concepts of trial-and-
error and the subsequent empirical test and made them the
basis of a theory of intelligence successively applied to animal
intelligence, to the practical intelligence of the child, and
even to the problem of " the genesis of the hypothesis " l in
the psychology of adult thought. But in the numerous
writings of this Genevese psychologist we see a significant
development from the first to the last, so that the mere
study of this development constitutes, of itself, an adequate
criticism of the concept of trial-and-erron
Claparfede begins by opposing intelligence a vicarious
function for adaptation to new conditions to (automatic)
habit and instinct, which are adaptations to repeated
circumstances. But how does the subject behave in the
.presence of new circumstances ? From Jennings' infusoria
fto man (and the scientist himself when he is confronted with
the unexpected), he acts by trial-and-error. This trial-and-
error may be merely sensori-motor or it may be internalised
in the form of " trials " in thought alone, but its function
is always the same : to contrive solutions from which experi-
ence will select afterwards.
The complete act of intelligence thus involves three
essential stages : the question which directs the quest, the
hypothesis which anticipates solutions, and the process of
testing which selects from them. However, two types
. de PsycW, XXIV (1933). PP- "55-
HABIT ANI> SENSORI-MOTOR INTELLIGENCE 95
of intelligence may be distinguished, one practical (or
" empirical "), the other deliberate (or " systematic "). In
the first the question appears in the form of a simple n$ed,
the hypothesis as a sensori-motor random trial, and the
testing process as a mere series of failures or successes. In
the second, the need is reflected in the question, trial-and-
error is internalised as a search for hypotheses and the
testing process anticipates the sanction of experience by
means of an " awareness of relations ", which is sufficient
to discard false hypotheses and to retain true ones.
Such was the outline of the theory when Claparfede
approached the problem of the genesis of the hypothesis in
the psychology of thought. Now, while emphasising the
role that trial-and-error obviously retains in the most
evolved forms of thought, Claparfede was led, through his
method of " thinking aloud ", to locate it no longer at the
actual point of departure of intelligent enquiry but, so to
speak, in the margin, or in the vanguard, and only when the
material exceeds the subject's understanding. The starting-
point seems to him, on the other hand, to be provided by an
attitude, the importance of which he had not hitherto
stressed : once the inquiry has been directed by the need or
the question (through a mechanism which in other respects
is still considered mysterious), the first thing to occur in the
presence of the data of the problem is an awareness of a
system of simple " implicative " relations. These impli-
cations may be true or false. If true they are left untouched
by experience. If false they are contradicted by experience,
and only then does trial-and-error start. Tims the
latter occurs only as a surrogate or supplement, i.e. as
behaviour derived indirectly from the initial implications.
Clapar&de concludes that trial-and-error is never pure ; it
is partly directed by the question and the implications, and
it becomes really fortuitous only when the data outstrip
these anticipatory schemata.
In what does " implication " consist ? This is where the
doctrine finds its widest scope and again links up with the
problem of habit just as much as with that of intelligence
itself. " Implication " is in essence almost the old
96 INTELLIGENCE AND SENSORI-HQTOR FUNCTIONS
" association " of the classical psychologists, but it is
accompanied by a feeling of necessity arising from within and
no longer from without. It is the manifestation of a
" primitive tendency " without which the subject could not
profit by experience at any level (p. 104). It is not due to
the " repetition of a pair of elements ", but, on the contrary,
it is the source of the repetition of like material and " comes
into being as soon as the two elements of the pair first meet ".
(p. 105). Thus experience can only refute or confirm it but
it does not create it. But when experience imposes a
coupling, the subject reinforces it with an implication. In
fact, its roots would be found in William James* " law of
coalescence " (the very law with which James explained
association I) : " The law of coalescence engenders impli-
cation at the level of action and syncretism at the level o
representation " (p. 105). Claparede thus goes so far as to
interpret the conditioned reflex in terms of implication ;
Pavlov's dog salivates at the sound of a bell, after having
heard it at the same time as he saw food, because then
the bell " implies " food.
This gradual reversal of the trial-and~error theory is
worth careful examination. To begin with an apparently
secondary point, would it not perhaps be a pseudo-problem
to ask ourselves how the question or the need directs the
search as though they existed independently of this search ?
The question and the need itself are, in fact, the expression
of previously constructed mechanisms which are simply
in a momentary state of disequilibrium. The need to suck
presupposes the complete organisation of the sucking
apparatus and, at the other extreme, questions such as
" what ? ", " where ? ", etc., are the expression of classifica-
tions, spatial structures, etc., which are already wholly or
partly constructed (see Chap. II). It follows that the schema
directs the search is the one whose previous existence is
to explain the appearance of the need or the
; these mark the awareness of the quest and, like
t, amount to a single act of assimilation of reality
to $$p schema.
This being $ is it legitimate to regard implication as a
HABIT AND SENSORI-MOTOR INTELLIGENCE 97
primary fact which is both sensori-motor and intellectual,
and the source of habit as well as of insight ? It is to be
understood, of course, that this term is not taken in its
logical sense as a necessary link between judgments, but in
the very general sense of any relation of necessity, Now do
two elements, seen together for the first time, give rise to
such a relation ? To take one of Claparfede's examples, does
a black cat, seen by an infant, involve immediately from its
first perception the relation " cat implies black ? " If the
two elements are really seen for the first time, with neither
analogy nor anticipations, they are certainly already grouped
together in a perceptual whole, in a Gestalt, which expresses
in another form James* law of coalescence or the syncre-
tism invoked by Clapar&de. It is clear enough that we are
concerned here with more than an association, in so far as
the whole results, not from the conjunction of the two
elements originally seen separately, but rather from their
immediate fusion through complex structuring. However,
this is not a necessary link ; it is the beginning of a possible
schema which, however, will only engender relations felt to
be necessary, as long as they form a genuine schema through
transposition or generalisation (i.e. an application to new
elements), in short, by introducing an assimilation. The
assimilation, then, is the source of what Claparfede calls
implication. To speak schematically, the subject will not
arrive at the relation " A implies x " on first perceiviag a&
A with the quality x, but he will be led to the relation l4 A
implies x " inasmuch as he assimilates A a to the sehOTia
(A), this schema being created precisely by the assimilation
A 2 = A: The dog that salivates at the sight of food win not
salivate in this way at the sound of a bell unless he assimilates
it, as a sign or a part of the total act, to the schema of this
action. Clapar&Je has good reason - to say that repetition
does not engender implication but that it appears only in
the course of repetition, since implication is the internal
product of the assimilation that ensures the repetition of
the external act.
Now this necessary intervention of assimilation further
supports the reservations that Ckparkfe was himself indmeed
98 INTELLIGENCE AND SENSORI-MOTOR FUNCTIONS
to make with regard to the general role of trial-and-error.
Firstly; it is obvious that when trial-and-error occurs it
cannot be explained in mechanical terms. Mechanically,
that is to say with the hypothesis of simple traces, error
should be reproduced as often as successful trials. If such is
not the case, i.e. if the " law of effect " holds, it means that
the subject anticipates his failures and successes. In other
words, each trial operates on the next, not as a channel
opening the way to new responses, but as a schema enabling
meanings to be attributed to subsequent trials. * So trial-and-
error in no way excludes assimilation.
But that is not all. The very first trials are difficult to
reduce to simple chance. 2 In maze experiments D. K.
Adams finds responses directed from the outset. W. Dennis
and also J. Dashiell lay stress on the continuation of the
sets initially adopted. Tolman and Krechevsky even speak
of " hypotheses " in describing the behaviour of rats, etc.
Hence the important interpretations reached by C. L. Hull and
E. C. Tolman. Hull insists on the contrast between psycho-
logical models involving means and ends and mechanistic
models of path-tracing : while a straight line is the only
possibility in the latter case, the former provide a number of
possible paths which will be more numerous as the act is
more complex. This amounts to saying that, from the level
of sensori-motor behaviour onwards, which is intermediate
between learning and intelligence, account must be taken of
what, in their final "groupings", becomes" the associativity "
of operations (Chap II). As for Tolman, he brings out the role
of generalisation in the formation of habits themselves.
Thus, when an animal is placed in a new maze different from
the one known to it, it perceives general analogies and
applies to the new case behaviour that met with success in
the previous case (particular routes). So there is always
complex structuring, but, for Tolman, the structures con-
cerned are not simple "configurations" in the sense of
Kohjer's theory ; they are sign-ge$taUs> i.e. schemata provided
naissance de I* intelligence chez I 'enfant, Chap. V and
' des habitudes, pp. 144-154.
i pp. 65*67.
HABIT AND SENSGRI-MOTOR INTELLIGENCE 99
with meanings, This double property of general validity
and meaning belonging to the structures considered by
Tolman is a fairly good indication that he is concerned with
what we call assimilatory schemata. Thus, from elementary
learning to intelligence, there seems to be involved an assimi-
latory activity, which is as necessary to the structuring of
the most passive forms of habits (conditioned responses and
associative transfers) as it is to the unfolding of visible
manifestations of activity (directed trial-and-error). In this
respect, the problem of the relations between habit and
intelligence is a fair parallel to that of the relations between
intelligence and perception. Just as perceptual activity is
not identical with intelligence, but links up with it as soon as
it is freecj from centring on the immediate and present
object, so the assimilatory activity that engenders habits is
not the same as intelligence but leads to the latter as soon as
irreversible and isolated sensori-motor systems are differen-
tiated and co-ordinated in mobile articulations. Besides
this, the affinity between these two kinds of activity is
obvious, since perceptions and habitual responses are
constantly united in complex schemata, and since the
" transfer " or generalisation characteristic of habit is the
exact equivalent, on the motor side, of " transposition " in
the domain of spatial figures, both involving the same
^sneralized assimilation.
SENSORI-MOTOR ASSIMILATION AND THE BIRTH OF INTELLI-
GENCE IN THE CHILD
To explain how intelligence springs from the assimilatory
activity which, at an earlier stage, engenders habits, is to
show how, from the point at which mental life is dissociated
from organic life, this sensori-motor assimilation is converted
into ever more mobile structures which have an ever wider
scope.
From hereditary structures onwards, we see, side by side
with the internal and physiological organisation of reflexes,
cumulative effects of practice and the beginnings of problem-
solving, which mark the first reactions at a distance in space
time by which we defined " behaviour " (Chap. I). A
100 INTELLIGENCE AND SENSORI-MOTOR FUNCTIONS
neonate who is spoon-fed will later have difficulty in feeding
at the breast. When he is allowed to suck from the outset,
his skill improves steadily ; when placed at the breast, he
finds the best position and will find it more and more rapidly.
Although he sucks anything, he will soon reject a finger but
retain the breast. Between feeds he will suck without food,
and so on. These commonplace observations show that even
within the closed field of hereditarily governed mechanisms
there emerge the beginnings of reproductive assimilation of
a functional order (practice), generalized or transpositive
assimilation (extension of the reflex-pattern to new objects)
and assimilation by recognition (discrimination between
situations).
It is in this already active context that the first acquisitions
due to experience come to find a place (since reflex action
does not yet lead to any genuinely new acquisition but simply
to consolidation). Whether we are concerned with an
apparently passive co-ordination such as conditioning (e.g.
a signal releasing a preparatory set for sucking), or with a
spontaneous extension of the scope of reflexes (e.g. syste-
matic thumb-sucking by co-ordination of the movements of
the arm and the hand with those of the mouth), in both
cases the elementary forms ,of the habit grow out of an
assimilation of new elements to previous schemata which are
in essence reflex-schemata. But it is important to realize
that the extension of the reflex-schemata, through the
incorporation of a new element, involves by this very fact
the formation of a schema of a higher order (a genuine habit),
which then integrates the lower schema with itself. So the
assimilation of a ne.w element to a previous schema implies
the integration of the latter, in its turn, with a higher schema.
However, it goes without saying that at the level of
these primary habits we cannot yet speak of intelligence-
Compared with reflexes, habit has a greater range in space
ipi time. But even when extended, these primary schemata
g|Eet fsffcpl ^ptrate and have no internal mobility or eo-
r^mtio^ aipqug themselves, The generalizations of which
fce|^ am p9||tlblf are still merely motor transfers eompambk
*ii \*~ ^~^ ^ aad db spite of
HABIT AND SENSORI-MOTOR INTELLIGENCE IOI
their functional continuity with later stages, there is still BO
reason to compare them in their structure with intelligence
itself.
With a third level, however, which begins with the co-
ordination of vision and prehension (between 3 and 6 months,
usually about 4^), new behaviour appears which represents a
transition between simple habit and intelligence. Let us
imagine an infant in a cradle with a raised cover from which
hang a whole series of rattles and a loose string. The cMM
grasps this and so shakes the whole arrangement without
expecting to do so or understanding any of the detailed
spatial or causal relations. Surprised by the result, lie
reaches for the string and carries out the whole sequence
several times over. J. M. Baldwin called this active repro-
duction of a result at first obtained by chance a " circular
reaction ". The circular reaction is thus a typical example
of reproductive assimilation. The first movement executed
and followed by its result constitutes a complete action,
which creates a new need once the objects to which it
relates have returned to their initial stage ; these are then
assimilated to the previous action (thereby promoted to
the status of a schema) which stimulates its reproduction,
and so on. Now this mechanism is identical with that which
is already present at the source of elementary habits except
that, in their case, the circular reaction afiects the body
itself (so we will give the name " primary circular reaction "
to that of the early level, such as the schema of thtnrf>-
sucking), whereas thenceforward, thanks to prehension, it fe
applied to external objects (we will call this befaaviotir
affecting objects the " secondary circular reaction/' altlxoiigli
we must remember that these are not yet by any meaps
conceived as substances by the cMld}*
The secondary circular reaction, then, occurs in an early
form in the structures characteristic of simple habits. As
these are independent items of behaviour, which are repeated
as wholes without any pre-established goal and affected by
chance circumstances ocewing cluring the process, they
haye m fact little in coiBmoii witib a complete act of intelli-
of projecting into the subject's
102 INTELLIGENCE AND SENSORI-MOTOR FUNCTIONS
mind distinctions that we may make on his behalf between
an original means (pulling the string) and a final goal
(shaking the cradle cover), as well as of attributing to him
conceptions of objects and space that we associate with a
situation which for him is unanalysed and global. Neverthe-
less, as soon as the response has been reproduced several
times, we see that it shows a double tendency towards
disarticulation and the internal re-articulation of its elements
and towards generalization or active transposition when
presented with new material not directly related to previous
material. Concerning the first point, it may be shown that
after the child has followed the events in the order string,
shaking, rattles the response becomes capable of rudimen-
tary analysis ; the sight of motionless rattles, and especially
the discovery of a new object which has just been suspended
from the cover, comes to stimulate reaching for the string.
Although there is still no genuine reversibility present, it is
clear that there is an increased mobility, and that there is
almost an articulation of the response-pattern into a means
(reconstructed afterwards) and an end (adopted afterwards).
On the other hand, if the child is confronted with a com-
pletely new situation, such as the sight of something moving
2-3 yards from him, or even some sound in the room, he
responds by seeking and pulling the same string, as though
he were trying to restart the interrupted spectacle by
" remote control ". Now this new action (which clearly
confirms the absence of any spatial contacts or understanding
of causality) surely constitutes an early form of true
generalization. Internal articulation, as well as this external
transposition of the circular schema, heralds the imminent
appearance of intelligence.
With a fourth stage comes greater precision. After 8-10
months the schemata constructed by secondary reaction
during the previous stage become susceptible of co-ordination
3tpif>Pg themselves, some serving as means and others setting
a goal for action. Thus* in order to grasp an objective placed
a screen which either wholly or partly conceals it, the
first remoye the screen (so utilising the schemata
or striking, etc.) and then sei^e the objective.
HABIT AND SENSORI-MOTOR INTELLIGENCE 10$
Consequently, the goal is thereafter decided on before the
means, since the subject has the intention of grasping the
objective before he has that of removing the obstacle, which
implies a mobile articulation of the elemental schemata
composing the complex schema. Moreover, the new complex
schema is susceptible of much greater generalization than
previously. This mobility, coupled with an increase in
generalization, is especially marked in the fact that the child,
when confronted with a new object, tries his most recently
acquired schemata in turn (grasping, striking, shaking,
rubbing, etc.), so that these serve as sensori-motor concepts,
so to speak, as though the subject were trying to understand
the new object through its use (in the manner of " definitions
by use " which recur much later at the verbal level).
Behaviour of this fourth level thus shows a twofold pro-
gress in the directions of mobility and of an extension of the
scope of its schemata. The routes between the subject and
the object followed by action, and also by sensori-motor recon-
stitutions and anticipations, are no longer direct and simple
pathways as at the previous stages : rectilinear as in per-
ception, or stereotyped and uni-directional as in circular
reactions. The routes begin to vary and the utilisation of
earlier schemata begins to extend further in time. This is
characteristic of the connection between means and ends,
which henceforth are differentiated, and this is why we may
begin to speak of true intelligence. But, apart from the
continuity that links it with earlier behaviour, we should
note the limitations of this early intelligence : there are no
inventions or discoveries of new means, but simply appli-
cation of known means to unforeseen circumstances.
Two acquisitions characterise the next stage, both relating
to the utilisation of past experience. The assiniilatory
schemata so far described are of course continually accornnib-
dated to external data. But this accommodation is, so to
speak, suffered rather than sought ; the subject acts accord-
ing to his needs and this action either harmonizes with
reality or encounters resistances which it tries to overcome.
Innovations which arise fortuitously are either neglected oir
else assimilated ta previous schemata and reproduced by
IO4 INTELLIGENCE AND SENSORI-MOTOR FUNCTIONS
circular reaction. However, a time comes when the inno-
vation has an interest of its own, and this certainly implies
a sufficient stock of schemata for comparisons to be possible
and for the new fact to be sufficiently like the known one
to be interesting and sufficiently different to avoid satiation.
Circular reaction, then, will consist of a reproduction of the
new phenomenon, but with variations and active experi-
mentation that are intended precisely to extract from it its
new possibilities. Thus, having discovered the trajectory
of a falling object, the child tries to drop it in different ways
or from different positions. This reproductive assimilation
with differentiated and intentional accommodation may be
called the " tertiary circular reaction ".
Thenceforward, when schemata are co-ordinated with one
another as means and ends, the child is no longer limited to
applying known means to new situations ; he differentiates
the schemata serving as means by a sort of tertiary circular
reaction and comes in consequence to discover new means.
In this way, a series of responses grows up which everybody
admits as having the character of intelligence, e.g. drawing
an objective towards oneself by means of the base on which
it rests* by means of a piece of string attached to it, or even
by means of a stick used as an independent intermediary.
But, however complex this latter behaviour may be, it is as
well to realise that it does not arise all of a sudden but is
prepared by a whole succession of relations and meanings
ctae to the activity of previous schemata the relation
of means to end, the idea that one object may set another in
motion, etc. In this respect, behaviour directed towards
the base supporting the objective is the simplest ; being
unable to reach the objective, the subject grasps at the
intervening objects (the doth on which the desired toy is
placed, etc.). The movements imparted to the objective by
grasping of the cloth are still without meaning at earlier
when in possession of the necessary relations, how-
tfee subject is aware of the possible utilisation of the
:base straight away. In such cases we see the
m tfee act of mteBigepce. As
F <p|rfc4e4 feofk fay tike scheim which assigns a
HABIT AND SENSORI-MOTOR INTELLIGENCE 105
goal to action, and by the schema selected as an initial
means, y trial-and-error is also ceaselessly directed during
successive trials by schemata capable of giving a meaning
to fortuitous events, which are thus intelligently utilised.
Trial-and-error, then, is never pure, but only constitutes
the process of active accommodation which works hand in
hand with the assimilatory co-ordinations constituting the
essence of intelligence.
Finally, a sixth stage, which occupies part of the second
year, marks the completion of sensori-motor intelligence.
Instead, of new means being exclusively discovered by
active experimentation, as at the previous level, there may
henceforth be inventions by rapid internal co-ordination of
processes now unknown to the subject. To this last category
belong the phenomena of sudden restructuring described by
Kohler in chimpanzees and Buhler's Aha-Erlebnis or
experience of sudden insight. Thus, in children who have
no occasion to experiment with sticks before the age of one
year six months, the first contact with a stick affords insight
into its possible relations with the objective to be reached,
and this without actual trial-and-error. Similarly, it seems
obvious that certain of Kohler's subjects discovered the use
of the stick, so to speak, by looking and without previous
practice.
The main problem, then, is to understand the mechanism
of these internal co-ordinations, which imply both invention
without trial-and-error and a mental anticipation closely
related to representation. We have already seen how tbe
Gestalt theory explains things by a simple perceptual
restructuring without reference to past experience. But it
is impossible not to see in the behaviour of an infant at this
sixth stage the end-result of all the development character-
izing the previous five levels. IB fact, it is dear that once he
becomes used to tertiary circular reactions and to the intelli-
gent trial-and-error that constitutes true active experimen-
tation the child sooner or later becomes capable of internal-
izing this behaviour. When the subject no longer acts when
confronted with the data of a problem, and appears to be
tWnking inste^dn (oi^e of our children, after having tried
106 INTELLIGENCE AND SENSORI-MGTOR FUNCTIONS
without success to widen Qit opening of a box of matches by
random behaviour, interrupted his activity, looked carefully
at the chink then visible, then opened and closed his own
mouth), everything seems to indicate that he continues his
attempts, but with implicit trials or internalised actions (the
imitative movements of the mouth in the foregoing example
are a very clear indication of this sort of motor thinking).
What happens then, and how do we explain the discovery
that yields the sudden solution ? Sensori-motor schemata
that have become sufficiently mobile and amenable to co-
ordination among themselves give rise to mutual assimi-
lations, spontaneous enough for there to be no further need
for actual trial-and-error and rapid enough to give an
impression of immediate restructuring. Internal co-ordi-
nation of schemata will, then, bear the same relation to the
external co-ordination of the earlier levels, as inner speech,
a simple rapid, internalised rough draft of overt language,
bears to outer speech.
But does the greater spontaneity and speed of assimilatory
co-ordination between schemata fully explain the internalisa-
tion of behaviour, or does representation begin at the present
level, thus indicating the transition from sensori-motor
intelligence to genuine thought ? Independently of the
advent of language, which the child begins to acquire at this
age (but which is absent in chimpanzees who are, neverthe-
less, capable of remarkably intelligent inventions), two types
of behaviour at this sixth stage testify to the beginnings of
representation, but beginnings which scarcely go beyond the
rather rudimentary representation of chimpanzees. On the
one hand, the child becomes capable of delayed imitation,
i.e. of producing a copy which occurs for the first time after
the perception of the model has disappeared ; now whether
delayed imitation is derived from imaginal representation
or whether it causes it, it is certainly closely linked with it
(we shall reconsider this problem in Chap. V). On the
other hand, the child simultaneously arrives at the simplest
form of symbolic play, consisting in using the body to produce
an action foreign to the present context (e.g. pretending to
sleep for fun, while he is actually wide awake). Here again
HABIT AND SENSORI-MOTOR INTELLIGENCE IO7
there appears a sort of image which is enacted, and therefore
motor, but it is already almost representative. Do not
these enacted images, characteristic of delayed imitation
and of the early make-believe symbol, act as significants in
the internalised co-ordination of schemata ? This is what
seems to be illustrated in the example we mentioned a short
while ago of the child who used his mouth to imitate the
widening of the visible gap in a box he was trying to open.
THE CONSTRUCTION OF THE OBJECT AND OF SPATIAL
RELATIONS
We have just noted the remarkable functional continuity
which links the successive structures built up by the child
from the formation of elementary habits to the spontaneous
and sudden acts of invention which characterize the highest
forms of sensori-motor intelligence. The affinity between
habit and intelligence thus becomes manifest, both arising,
although at different levels, from sensori-motor assimilation.
We must now reconsider what we said above (Chap. Ill),
concerning the affinity between intelligence and perceptual
activity, both of which depend on sensori-motor assimi-
lation at different levels ; in the one this assimilation
engenders perceptual transposition (a close relative of the
transfer of habitual movements), and the other is charac-
terized by specifically intelligent generalization.
Nothing is better fitted to illustrate the bonds between
perception, habit and intelligence, which are so simple in
their common origin and so complex in their manifold
differentiations, than an analysis of the sensori-motor
construction of the fundamental schemata formed by the
object and by space (which, incidentally, are indissociable
from causality and time). Actually, this construction is
closely correlated with the development of the pre-verbal
intelligence which we have just been considering. But it
also requires a high degree of organization of perceptual
structures and of completely integrated motor structures
built up of habits.
What in fact is the schema of the object ? In one essential
respect it is a schema belonging to intelligence. To have the
108 INTELLIGENCE AND SENSORI-MOTOR FUNCTIONS
concept of an object is to attribute the perceived figure to a
substantial basis, so that the figure and the substance that
it thus indicates continue to exist outside the perceptual
field. The permanence of the object seen from this view-
point is not only a product of intelligence, but constitutes
the very first of those fundamental ideas of conservation
which we shall see developing within the thought process
(Chap. V). But the very fact that it conserves itself and is
even reducible to this conservation means that the solid
object (the only sort to be considered in the first instance)
also conserves its dimensions and its shape ; shape and size
constancy is a schema arising at least as much from per-
ception as from intelligence. Finally, it goes without
saying that both in perceptual constancy and in the con-
servation that goes beyond the frontiers of the present
perceptual field the object is linked with a series of motor
habits which are both the source and the effects of the
construction of this schema. We thus see how much light
it is bound to throw on the true relations between intelli-
gence, perception and habit.
But how is the schema of the object constructed ? At the
reflex level there are certainly no objects, the reflex being a
response to a situation, and neither the stimulus nor the
action elicited involve anything more than the qualities
attached to perceptual displays without any necessary
substantial substrate. When the infant seeks and finds the
breast it is not necessary for him to regard it as an object,
and the conditions of sucking, together with the permanence
of the relevant postures, are sufficient to account for his
behaviour without the intervention of more complex
schemata. At the level of the earliest habits, recognition
does not imply an object either, because recognition of a
perceptual display does not imply any belief in the existence
of the perceived element apart from present perceptions and
recognitions ; similarly, calling an absent person by crying
merely requires an anticipation of his possible return as a
familiar perceived figure, and not spatial localization of this
person as a substantial object in an organized reality. On
the other hand, to follow a moving figure with the eyes and
HABIT AND SENSORI-MOTOR INTELLIGENCE 109
to continue to look for it when it disappears, or to turn the
head to look in the direction of a sound, etc., constitute the
beginnings of a practical permanence, beginnings which are,
however, closely tied to the action in progress. They are
perceptuo-motor anticipations and expectancies, determined
by immediately previous perception and response, and are not
yet by any means active searches, distinct from the response
already initiated or determined by present perception.
The fact that during the third stage (secondary circular
reactions), the child becomes capable of grasping what he
sees, allows us to verify these interpretations. According to
C. Biihler, the subject at this stage succeeds in removing a
cloth covering his face. But we have been able to show that
at this same stage the child makes no attempt to remove a,
cloth placed over a desired object, and this is the case even
when he has already initiated a movement of prehension
towards the object when it was visible. He thus behaves as
though the object were absorbed by the cloth and ceased to
exist at the very moment that it left the perceptual field ;
or else, and this amounts to the same thing, he possesses no
behaviour enabling him to search for the object which has
disappeared whether by action (lifting the screen) or by
thought (imagining). However, he is more likely at this
level than at the previous one to attribute a sort of practical
permanence or momentary continuation to the objective of
an action in progress, e.g. returning to a toy after having
been distracted (delayed circular reaction), anticipating the
position of a falling object, etc. But it is the action that
confers a momentary conservation on the object, and the
object loses this after the action in progress has ceased.
On the other hand, at the fourth stage (co-ordination of
familiar schemata) the child begins to seek for the object
behind a screen ; this constitutes the beginning of behaviour
concerning specifically the hidden object, and consequently
,the beginning of the conservation of substance. But we
often observe an interesting reaction which shows that this
early substantiality Js not yet individualized and conse-
quently remains tied to action itself : if the child is looking
for an object at A (e.g. under a cushion situated to his
110 INTELLIGENCE AND SENSORI-MOTOR FUNCTIONS
right) and the same object is moved, in his sight, to B
(another cushion to his left), he first returns to A, as though
the object which disappeared under B was to be found in its
original position ! In other words, the object is still involved
in a total situation characterized by the action that has just
led to success, and does not always entail individualization
of substance or co-ordination of successive responses.
At the fifth stage, these limitations disappear, except in
the case where representation of invisible paths is necessary
for the solution of the problem, and at the sixth stage even
this condition ceases to be a hindrance.
It is therefore evident that the conservation of the object
is prepared by the continuation of habitual responses and
is the product of a co-ordination of the schemata constitu-
ting sensori-motor intelligence. So the object, at first an
extension of the co-ordinations typical of habit, is con-
structed by intelligence itself, and constitutes the first
constant of intelligence a constant which is necessary for
the formation of space, of causality in space and, in general,
for all forms of assimilation which transcend the present
perceptual field.
But, if its connections with habit and intelligence are
obvious, the relations of the object to the perceptual con-
stancies of shape and size are no less so. At the third of the
levels that we have distinguished, a child, presented with his
feeding-bottle the wrong way round, tries to suck the glass
bottom if he does not see the rubber teat at the other end.
If he sees it, he turns the bottle round (proof that there is no
motor disability). But if, after having sucked at the wrong
end, he sees the whole of the bottle (i.e. presented to him
vertically) and then watches it being turned round, even
then he will not succeed in turning it once the teat has again
become invisible ; thus the teat seems to him to be absorbed
by the glass, except when he can see it. This behaviour,
which is typical of the non-conservation of the object,
thus involves non-conservation of the actual parts of the
bottle, that is to say non-conservation of shape. At the
next stage, however, corresponding with the construction of
the permanent object, the bottle is reversed at once, and is
HABIT AND SENSORI-MOTOR INTELLIGENCE III
thus perceived as a shape which remains constant in its
entirety, in spite of being rotated. At this same level, we
see the child slowly moving his head and taking an interest
in the changes of shape in an object due to perspective.
As for size constancy (whose absence during the early
months has recently been demonstrated by Brunswik), it
also is developed during the fourth and especially during the
fifth stage. Thus, one often sees the infant moving an
object that he is holding in his hand towards and away from
his eyes, as though he were studying changes in size with
distance. There is then a correlation between the develop-
ment of these perceptual constancies and the intelligent
conservation of the object.
Now it is easy to understand the connection between these
two kinds of reality. If constancies are actually the product
of transportations, transpositions and their regulations, it is
clear that these regulative mechanisms come from motor
functions as much as from perception. Perceptual constancy
of shape and size would thus be guaranteed by a sensori-
motor assimilation which " transports " or transposes the
relations concerned when modifications of the position or
distance of the perceived object occurjrin the same way,
the schema of the permanent object would be due to a
similar sensori-motor assimilation, which induces a search for
the object once it leaves the perceptual field, thus endowing
it with a conservation that is derived from the extension of
the subject's own actions, projected as a property of the
external world. We may thus grant that the same assimi-
latory schemata both govern the shape and size constancy
of the perceived object (by " transportations " and trans-
positions) and elicit a search for it when it is no longer
perceived ; thus, when it disappears, the object is sought
because it is perceived as constant and, when it reappears,
it is perceived as constant because it gives rise to
active seeking when it is no longer perceived. The two
aspects of perceptual activity and intelligence are in fact
much less differentiated at the sensori-motor level than is
the case with perception and reflective intelligence, since the
latter depends on symbols consisting of words or images,
112 INTELLIGENCE AND SENSORI-MOTOR FUNCTIONS
while sensori-motor intelligence depends only on perceptions
themselves and on responses,
We may thus regard perceptual activity, in general as
well as in the particular case of constancy, as an aspect of
sensori-motor intelligence an aspect which is limited to
the case of an object entering into direct and immediate
relations with the subject, whereas sensori-motor intelligence
goes beyond the perceptual field, anticipating relations which
are to be perceived subsequently and reconstructing those
which have been perceived previously. The unity of the
mechanisms affecting sensori-motor assimilation is thus
complete, which incidentally is what the Gestalt theory has
had the merit of showing, but it must be interpreted in
terms of the activity of the subject, and thus of assimi-
lation, not in terms of static configurations imposed inde-
pendently of mental development.
But there now arises a problem whose discussion leads to
the study of space. Perceptual constancy is the product of
simple regulations and we saw (Chap. Ill) that the absence at
all ages of absolute constancy and the existence of adult
" superconstancy " provide evidence for the regulative
rather than operational character of the system. There is,
therefore, all the more reason why it should be true of the
first two years. Does not the construction of space, on the
other hand, lead quite rapidly to a grouping structure and
even a group structure in accordance with Poincare's
famous hypothesis concerning the psychologically primary
influence of the " group of displacements ? "
The genesis of space in sensori-motor intelligence is com-
pletely dominated by the progressive organisation of
responses, and this in effect .leads to a " group " structure.
But, contrary to Poincare's belief in the a priori nature of
the group of displacements, this is developed gradually as the
ultimate form of equilibrium reached by this motor organi-
sation. Successive co-ordinations (combinativity), reversals
(reversibility), detours (associativity) and conservations of
position (identity) gradually give rise to the group, which
serves as a necessary equilibrium for actions.
At the first two stages (reflexes and elementary habits),
HABIT AND SENSQRI-MOTOR INTELLIGENCE 113
we could not even speak of a space common to the various
perceptual modalities, since there are as many spaces, all
mutually heterogeneous, as there are qualitatively distinct
fields (mouth, visual, tactile, etc.). It is only in the course of
the third stage that the mutual assimilation of these various
spaces becomes systematic owing to the co-ordination of
vision with prehension. Now, step by step with these co-
ordinations, we see growing up elementary spatial systems
which already presage the form of composition characteristic
of the group. Thus, in the case of interrupted circular
reaction, the subject returns to the starting-point to begin
again ; when his eyes are following a moving object that is
travelling too fast for continuous vision (falling etc.), the
subject occasionally catches up with the object by displace-
ments of his own body to correct for those of the external
moving object.
But it is as well to realise that, if we take the point of view
of the subject and not merely that of a mathematical
observer, the construction of a group structure implies at
least two conditions: the concept of an object and the
decentralisation of movements by correcting for, and even
reversing, their initial egocentricity. In fact, it is clear that
the reversibility characteristic of the group presupposes the
concept of an object, and also vice versa, since to retrieve
an object is to make it possible for oneself to return (by
displacing either the object itself or one's own body). The
object is simply the constant due to the reversible composi-
tion of the group. Furthermore, as Poincare himself has
clearly shown, the idea of displacement as such implies the
possibility of differentiating between irreversible changes of
state and those changes of position that are characterized
precisely by their reversibility (or by their possible correction
through movements of one's own body). It is obvious,
therefore, that without conservation of objects there could
not be any " group ", since then everything would appear
as a "change of state". The object and the group of displace-
ments are thus indissociable, the one constituting the static
aspect and the other the dynamic aspect of the same reality.
But this is not all : a world with no objects is a universe
114 INTELLIGENCE AND SENSORI-MOTOR FUNCTIONS
with no systematic differentiation between subjective and
external realities, a world that is consequently " adualistic "
( J. M. Baldwin) . By this very fact, such a universe would be
centred on one's own actions, the subject being all the more
dominated by this egocentric point of view because he
remains un-self-conscious. But the group implies just the
opposite attitude : a complete decentralisation, such that
one's own body is located as one element among others in a
system of displacements enabling one to distinguish between
one's own movements and those of objects.
This being so, it is clear that throughout the first two
stages, and even in the third, none of these conditions is
fulfilled ; the object is not constituted and the different
spaces, and later the single space that tends to co-ordinate
them, remain centred on the subject. From then on, even
when there seems to be (in practice) a return and a co-ordina-
tion in the form of a group, it is not difficult to distinguish
appearance from reality, the latter constantly testifying to
a privileged centralisation. In this way, an infant at the
third stage who sees an object move along the line AB to
pass behind a screen at B, does not look for it at C at the
other end of the screen, but looks back towards A ; and so on.
The moving object is therefore not yet an independent
" object " following a rectilinear trajectory that is disso-
ciated from the subject, but remains dependent on the pre-
ferred position A where it was first seen by the subject.
As far as rotation is concerned, we noted above
the example of the reversed feeding-bottle which is ^sucked
at the wrong end instead of being turned round ; this again
attests the primacy of an egocentric perspective and the
absence of the concept of an object, all of which explains the
absence of any " group ".
With the search for an object that has disappeared
behind a screen begins the attribution of objectivity to
co-ordinations and thus the construction of the sensori-
motor group. But the very fact that the subject does not
take account of successive displacements of the object and
looks for it behind the first of the screens (see above), shows
clearly enough that this nascent group is still partly " sub-
HABIT AND SENSORI-MOTOR INTELLIGENCE
jective ", i.e. centred on the subject's own action, since the
object remains dependent on the latter and only half-way
towards its independent construction.
It is not until the fifth stage, i.e., when the object is sought
in accordance with its successive displacements, that the
group is really made objective, the combinativity of dis-
placements, their reversibility and conservation of position
(" identity ") are achieved. Only the possibility of detours
(" associativity ") is still absent, for lack of sufficient antici-
pation, but it becomes more and more general during the
sixth stage. Moreover, parallel with this progress, a system
of relations between objects themselves is constructed, such
as the relations " placed upon ", " inside ", or " outside ",
" in front of " or " behind " (with the correlating of distant
planes with size constancy), etc.
We may thus conclude that the formation of the object's
perceptual constancy by means of sensori-motor regulations
goes hand in hand with the progressive construction of sys-
tems which are also sensori-motor but pass beyond the scope
of perception and lead to a group structure which, needless
to say, is still exclusively practical and not conceptual. Why
then does not perception itself also benefit from this structure
and why does it remain at the level of simple regulations? The
explanation for this is now clear ; however et decentralised "
it may be in relation to the initial centralisation of vision or
of its particular organ, a perception is still egocentric and
centred on an object in accordance with the subject's own
perspective. Furthermore, the kind of decentralisation that
characterises perception, i.e. co-ordination between successive
centrings, arrives only at a composition of a statistical order,
which is therefore incomplete (Chap. III). Thus perceptual
composition cannot rise above the level of what we have just
been describing as the "subjective" group, i.e. a system centred
with reference to the subject's own action, and capable, at
the most, of corrections and regulations. And this is still true
even at the stage at which the subject, passing beyond the
perceptual field in order to anticipate and reconstruct invis-
ible movements and objects, achieves an objectivised group
structure in the realm of immediate " practical " space.
Il6 INTELLIGENCE AND SENSORI-MOTOR FUNCTIONS
In general, we may thus conclude that there is an essential
unity between the sensori-motor processes that engender
perceptual activity, the formation of habits, and pre-verbal
or pre-representative intelligence itself. The latter does not
therefore arise as a new power, superimposed all of a sudden
on completely prepared previous mechanisms, but is only
the expression of these same mechanisms when they go
beyond present and immediate contact with the world
(perception), as well as beyond short and rapidly automatised
connections between perceptions and responses (habit), and
operate at progressively greater distances and by more
complex routes, in the direction of mobility and reversibility.
Early intelligence, therefore, is simply the form of mobile
equilibrium towards which the mechanisms adapted to per-
ception and habit tend ; but the latter attain this only by
leaving their respective fields of application. Moreover,
intelligence, from this first sensori-motor stage onwards, has
already succeeded in constructing, in the special case of
space, the equilibrated structure that we call the group of
displacements in an entirely empirical or practical form, it is
true, and of course remaining on the very restricted plane of
immediate space. But it goes without saying that this
organization, circumscribed as it is by the limitations of
action, still does not constitute a form of thought. On the
contrary, the whole development of thought, from the advent
of language to the end of childhood, is necessary in order that
the completed sensori-motor structures, which may even be
co-ordinated in the form of empirical groups, may be extended
into genuine operations, which will constitute or recon-
struct these groupings and groups at the level of symbolic
behaviour and reflective reasoning.
PART THREE
THE DEVELOPMENT OF THOUGHT
CHAPTER V
THE GROWTH OF THOUGHT INTUITION
AND OPERATIONS
WE have noted, in the first part of this work, that the
operations of thought reach their form of equilibrium when
they are formed into complex systems characterized by
reversible combinativity (groupings or groups). But if a
form of equilibrium marks the final limit of development,
this does not explain either its initial phases or its construc-
tive mechanism. In the second part, we were then able to
locate the origin of operations in sensori-motor processes ;
the schemata of sensori-motor intelligence form the practical
equivalent of concepts and relations, and their co-ordination
into spatio-temporal systems of objects and movements even
arrives, though still in a practical and empirical form, both
at the conservation of the object, and at a correlative group
structure (H. Poincare's group of experienced displacements).
But it is obvious that this sensori-motor group simply
constitutes a schema of behaviour, i.e. the equilibrated
system formed by the various possible physical movements
in near space, and that it in no way attains the rank of an
instrument of thought. 1 Certainly, sensori-motor intelli-
gence lies at the source of thought, and continues to affect it
throughout life through perceptions and practical sets. In
particular, the role of perception in the most highly developed
thought cannot be neglected, as it is by some writers when
they pass too rapidly from neurology to sociology, and this
1 If we divide behaviour into three main systems, organic hereditary
structures (instinct), sensori-motor structures (which may be learned), and
symbolic structures (which constitute thought), we may place the group of
sensori-motor displacements at the apex of the second of these systems,
while operational groups and groupings of a formal nature are at the top
of the third.
119
120 THE DEVELOPMENT OF THOUGHT
role alone bears witness to the persistent influence of early
schemata. But there is still a very long way to go from
preverbal intelligence to operational thought before reflec-
tive groupings may be established, and even if there is a
functional continuity between the two extremes, the forma-
tion of a series of intermediate structures at several hetero-
geneous levels is indispensable,
DIFFERENCES IN STRUCTURE BETWEEN CONCEPTUAL INTELLI-
GENCE AND SENSORI-MOTOR INTELLIGENCE
In order to understand the mechanism of the formation
of operations, it is first of all important to realise what it is
that has to be constructed, i.e. what must be added to
sensori-motor intelligence for it to be extended into con-
ceptual thought. Nothing indeed could be more superficial
than to suppose that the construction of intelligence is
already accomplished on the practical level, and then
simply to appeal to language and imaginal representation
to explain how this ready-made intelligence comes to be
internalized as logical thought.
In point of fact, only the functional point of view allows
us to find in sensori-motor intelligence the practical equiva-
lent of classes, relations, reasonings and even groups of dis-
placements in their empirical form as actual displacements.
From the point of view of structure, and consequently of
effect, there remain a certain number of fundamental
differences between sensori-motor co-ordinations and con-
ceptual co-ordinations, with regard both to the nature of the
co-ordinations themselves and to the distances covered by
the action, i.e. its scope of application.
In the first place, acts of sensori-motor intelligence, which
consist solely in co-ordinating successive perceptions and
(also successive) overt movements, can themselves only be
reduced to a succession of states, linked by brief anticipa-
tions and reconstructions, but never arriving at an all-
embracing representation ; the latter can only be established
if thought makes these states simultaneous, and thus
releases them from the temporal sequence characteristic of
action. In other words, sensori-motor intelligence acts like
GROWTH OF THOUGHT INTUITION AND OPERATIONS I2t
a slow-motion film, in which all the pictures are seen
in succession but without fusion, and so without the
continuous vision necessary for understanding the
whole.
In the second place, and for the same reason, an act of
sensori-motor intelligence leads only to practical satisfaction,
i.e. to the success of the action, and not to knowledge as
such. It does not aim at explanation or classification or
taking note of facts for their own sake ; it links causally and
classifies and takes note of facts only in relation to a sub-
jective goal which is foreign to the pursuit of truth. Sensori-
motor intelligence is thus an intelligence in action and in no
way reflective.
As regards its scope, sensori-motor intelligence deals only
with real entities, and each of its actions thus involves only
very short distances between subject and objects. It is
doubtless capable of detours and reversals, but it never
concerns anything but responses actually carried out and
real objects. Thought alone breaks away from these short
distances and physical pathways, so that it may seek to
embrace the whole universe including what is invisible and
sometimes even what cannot be pictured; this infinite
expansion of spatio-temporal distances between subject and
objects comprises the principal innpvation of conceptual
intelligence and the specific power that enables it to bring
about operations.
There are thus three essential conditions for the transition
from the sensori-motor level to the reflective level. Firstly,
an increase in speed allowing the knowledge of the successive
phases~oTan action to be moulded into one simultaneous
whole. Next, an awareness, not simply of the desired results
of action, but its actual mechanisms, thus enabling the
search for the solution to be combined with a consciousness
of its nature. Finally, an increase in distances, enabling
actions affecting real entities to be extended by symbolic
actions affecting symbolic representations and thus going
beyond the limits of near space and time.
We see then that thought can neither be a translation nor
even a simple continuation of sensori-motor processes in a*
122 THE DEVELOPMENT OF THOUGHT
symbolic form. It is much more than a matter of formu-
lating or following up work already started ; it is necessary
from the start to reconstruct everything on a new plane.
Perception and overt responses by themselves will continue
to function in the same way, except for being charged with
new meanings and integrated into new systems. But the
structures of intelligence have to be entirely rebuilt before
they can be completed ; knowing how to reverse an object
(cf . the bottle mentioned in Chap. IV) does not imply that
one can represent a series of rotations in thought ; physical
movement along a complex route and returning to the
starting-point does not necessarily involve understanding an
imaginary system of displacements, and even to anticipate
the conservation of an object in practice does not lead
immediately to the conception of conservations affecting a
system built up of different elements.
Moreover, in order to reconstruct these structures in
thought, the subject is going to encounter the same diffi-
culties, though transposed to this new level, that he
has already overcome in immediate action. In order to
construct a space, a time, a universe of causes and of
sensori-motor or practical objects, the child has had to
free himself from his perceptual and motor egocentricity ; by
a series of successive decentralisations he has managed to
organise an empirical group of physical displacements, by
localising his own body and his own movements amid the
whole mass of others. This construction of groupings and
operational groups of thought will necessitate a similar
change of direction, but one following infinitely more complex
paths. Thought will have to be decentralised, not only in
relation to the perceptual centralisation of the movement,
but also in relation to the whole of the subject's action.
Thought, springing from action, is indeed egocentric at first
for exactly the same reasons as sensori-motor intelligence is
at first centred on the particular perceptions or movements
from which it arises. The construction of transitive, associa-
tive and reversible operations will thus involve a conversion
of this initial egocentricity into a system of relations and
classes that are decentralised with respect to the self, and
GROWTH OF THOUGHT INTUITION AND OPERATIONS 123
his intellectual decentralisation (not to mention its social
aspect which we shall come back to in Chap. VI) will in fact
occupy the whole of early childhood.
The development of thought will thus at first be marked
by the repetition, in accordance with a vast system of
loosenings and separations, of the development which seemed
to have been completed at the sensori-motor level, before it
spreads over a field which is infinitely wider in space and more
flexible in time, to arrive finally at operational structures.
STAGES IN THE CONSTRUCTION OF OPERATIONS
In order to arrive at the mechanism of this development,
which finds its final form of equilibrium in the operational
grouping, we will distinguish (simplifying and schematizing
the matter) four principal periods, following that characterized
by the formation of sensori-motor intelligence.
After the appearance of language or, more precisely, the
symbolic function that makes its acquisition possible
(i| 2 years), there begins a period which lasts until
nearly 4 years and sees the development of a symbolic and
preconceptual thought.
From 4 to about 7 or 8 years, there is developed, as a
closely linked continuation of the previous stage, an intuitive
thought whose progressive articulations lead to the threshold
of the operation.
From 7-8 to 11-12 years " concrete operations " are
organized, i.e. operational groupings of thought concerning
objects that can be manipulated or known through the
senses.
Finally, from 11-12 years and during adolescence, formal
thought is perfected and its groupings characterize the
completion of reflective intelligence.
SYMBOLIC AND PRECONCEPTUAL THOUGHT
From the last stages of the sensori-motor period onwards,
the child is capable of imitating certain words and attribut-
ing a vague meaning to them, but the systematic acquisition
of language does not begin until about the end of the
second year.
124 THE DEVELOPMENT OF THOUGHT
Now, direct observation of the child, as well the analysis
of certain speech disturbances, shows that the use of a
system of verbal signs depends on the exercise of a more
general " symbolic function ", characterised by the re-
presentation of reality through the medium of "significants"
which are distinct from " significates ".
In fact, we should distinguish between symbols and
signs on the one hand and indices or signals on the other.
Not only all thought, but all cognitive and motor activity,
from perception and habit to conceptual and reflective
thought, consists in linking meanings, and all meaning
implies a relation between a significant and a signified
reality. But in the case of an index the significant consti-
tutes a part or an objective aspect of the significate, or else
it is linked to it by a causal relation ; for the hunter tracks in
the snow are an index of game, and for the infant the visible
end of an almost completely hidden object is an index of
its presence. Similarly, the signal, even when artificially
produced by the experimenter, constitutes for the subject
simply a partial aspect of the event that it heralds (in a
conditioned response the signal is perceived as an objective
antecedent). The symbol and the sign, on the other hand,
imply a differentiation, from the point of view of the subject
himself, between the significant and the significate ; for a
child playing at eating, a pebble representing a sweet is
consciously recognized as that which symbolizes and the
sweet as that which is symbolized ; and when the same
child, by " adherence to the sign ", regards a name as
inherent in the thing named, he nevertheless regards this
name as a significant, as though he sees it as a label attached
in substance to the designated object.
We may further specify that, according to a custom in
linguistics which may usefully be employed in psychology,
a symbol is defined as implying a bond of similarity between
the significant and the significate, while the sign is
" arbitrary " and of necessity based on convention. The
sign thus cannot exist without social life, while the symbol
may be formed by the individual in isolation (as in young
children's play). Of course symbols also may be socialized,
GROWTH OF THOUGHT INTUITION AND OPERATIONS 125
a collective symbol being generally half sign and half symbol ;
on the other hand, a pure sign is always collective. 1
In view of this, it should be noted that the acquisition of
language, i.e. the system of collective signs, in the child
coincides with the formation of the symbol, i.e. the system of
individual significants. In fact, we cannot properly speak of
symbolic play during the sensori-motor period, and K, Groos
has gone rather too far in attributing an awareness of make-
believe to animals. Primitive play is simply a form of
exercise and the true symbol appears only when an object
or a gesture represents to the subject himself something
other than perceptible data. Accordingly we note the
appearance, at the sixth of the stages of sensori-motor intelli-
gence, of " symbolic schemata/' i.e. schemata of action
removed from their context and evoking an absent
situation (e.g. pretending to sleep). But the symbol itself
appears only when we have representation dissociated from
the subject's own action : e.g. putting a doll or a teddy-bear
to bed. Now precisely at the stage at which the symbol in
the strict sense appears in play, speech brings about in
addition the understanding of signs.
As for the formation of the individual symbol, this is
elucidated by the development of imitation. During the
sensori-motor period, imitation is only an extension of the
accommodation characteristic of assimilatory schemata.
When he can execute a movement, the subject, on perceiving
an analogous movement (in other persons or in objects),
assimilates it to his own, and this assimilation, being as much
motor as perceptual, activates the appropriate schema.
Subsequently, the new instance elicits an analogous assimi-
latory response, but the schema activated is then accommo-
dated to new details ; at the sixth stage, this imitative
assimilation becomes possible even with a delay, thus
presaging representation. Truly representative imitation, on
1 This proposed terminology may conflict with existing usage in English.
For example, C. R. Morris (in Signs* Language and Behavior, New York :
Prentice Hall 1946), uses symbol to mean any sign produced by an
interpreter and acting as a substitute for another sign with which it is
synonymous. All signs which are not symbols are signals. Morris's iconic
signs and lansigns (or language-signs) appear to approximate to Piaget's
symbols and signs respectively. (Translator's note.)
126 THE DEVELOPMENT OF THOUGHT
the other hand, only begins with symbolic play because, like
the latter, it presupposes imagery. But is the image the
cause or the effect of this internalization of the imitative
mechanism ? The mental image is not a primary fact, as
associationism long believed ; like imitation itself, it is an
accommodation of sensori-motor schemata, i.e. an active
copy and not a trace or a sensory residue of perceived objects.
It is thus internal imitation and is an extension of the
accommodatory function of the schemata characteristic of
perceptual activity (as opposed to perception itself), just as
the external imitation found at previous levels is an extension
of the accommodatory function of sensori-motor schemata
(which are closely bound up with perceptual activity).
From then on, the formation of the symbol may be
explained as follows : deferred imitation, i.e. accommodation
extended in the form of imitative sketches, provides signifi-
cants, which play or intelligence applies to various significates
in accordance with the free or adapted modes of assimilation
that characterize these responses. Symbolic play thus
always involves an element of imitation functioning as a
significant, and early intelligence utilises the image in like
manner, as a symbol or significant. 1
We can understand now why speech (which is likewise
learned by imitation, but by an imitation of ready-made
signs, whereas imitation of shapes, etc., provides the signifi-
cant material of private symbolism) is acquired at the same
time as the symbol is established : it is because the use of
signs, like that of symbols, involves an ability which is
quite new with respect to sensori-motor behaviour and
consists in representing one thing by another. We may thus
apply to the infant this idea of a general "symbolic
function ", which has sometimes been used as a hypothesis
in connection with aphasia, since the formation of such a
mechanism is believed, in short, to characterize the simul-
taneous appearance of representative imitation, symbolic
play, imaginal representation and verbal thought.
To sum up, the beginnings of thought, while carrying on
the work of sensori-motor intelligence, spring from a
1 See I. Meyerson, " Les images/* in Dumas, Nouveau Traiti de Psychologic
GROWTH OF THOUGHT INTUITION AND OPERATIONS 127
capacity for distinguishing significants and significates, and
consequently rely both on the invention of symbols and on
the discovery of signs. But needless to say, for a young
child who finds the system of ready-made collective signs
inadequate, since they are partly inaccessible and are hard
to master, these verbal signs will for a long time remain
unsuitable for the expression of the particular entities on
which the subject is still concentrated. This is why, as long
as egocentric assimilation of reality to the subject's own
action prevails, the child will require symbols ; hence
symbolic play or imaginative play, the purest form of
egocentric and symbolic thought, the assimilation of reality
to the subject's own interests and the expression of reality
through the use of images fashioned by himself.
But even in the field of applied thought, i.e. the beginnings
of representative intelligence, tied more or less closely to
verbal signs, it is important to note the role of imaginal
symbols and to realize how far the subject is, during his
early childhood, from arriving at genuine concepts. We must,
in fact> distinguish a first period in the development of
thought, lasting from the appearance of language to the age
of about 4 years, which may be called the period of pre-
conceptual intelligence and which is characterized by pre-
concepts or participations and, in the first forms of reasoning,
by " transduction " or preconceptual reasoning.
Pre-concepts are the notions which the child attaches to
the first verbal signs he learns to use. The distinguishing
characteristic of these schemata is that they remain midway
between the generality of the concept and the individuality
of the elements composing it, without arriving either at the
one or at the other. The child aged 2-3 years will be just
as likely to say " slug " as " slugs " and " the mQon " as
" the moons ", without deciding whether the slugs encoun-
tered in the course of a single walk or the discs seen at
different times in the sky are one individual, a single slug or
moon, or a class of distinct individuals. On the one hand, he
cannot yet cope with general classes, being unable to distin-
guish between " all " and " some ". On the other hand,
although the idea of the permanent individual object has
128 THE DEVELOPMENT OF THOUGHT
been formed in the field of immediate action, such is by no
means the case where distant space and reappearances at
intervals are concerned ; a mountain is still deemed to
change its shape in the course of a journey (just as in the
earlier case of the rotated feeding-bottle) and " the slug " re-
appears in different places. Hence, sometimes we have true
" participations " between objects which are distinct and
distant from each other : even at the age of four years, a
shadow, thrown on a table in a closed room by means of a
screen, is explained in terms of those which are found " under
the trees in the garden "or at night-time, etc., as though
these intervened directly the moment the screen is placed on
the table (and with the subject making no attempt to go
into the " how " of the phenomenon).
It is clear that such a schema, remaining midway between
the individual and the general, is not yet a logical concept
and is still partly something of a pattern of action and of
sensori-motor assimilation. But it is nevertheless a repre-
sentative schema and one which, in particular, succeeds in
evoking a large number of objects by means of privileged
elements, regarded as samples of the pre-conceptual collec-
tion. On the other hand, since these type-individuals are
themselves made concrete by images as much as, and more
than, by words, the pre-concept improves on the symbol in
so far as it appeals to generic samples of this kind. To sum
up then, it is a schema placed midway between the sensori-
motor schema and the concept with respect to its manner of
assimilation, and partaking of the nature of the imaginal
symbol as far as its representative structure is concerned.
Now the reasoning that consists in linking such pre-
concepts shows precisely the same structures. Stern gave
the name " transduction " to these primitive reasonings,
which are effected not by deduction but by direct analogies.
But that is not quite all : pre-conceptual reasoning or
transduction is based only on incomplete dovetailings and
is thus inadequate for any reversible operational structure.
Moreover, if it succeeds in practice, it is because it merely
consists of a sequence of actions symbolized in thought, a
true " mental experiment ", ie, an internal imitation of
GROWTH OF THOUGHT INTUITION AND OPERATIONS 129
actions and their results, with all the limitations that this
kind of empiricism of the imagination involves. We thus
see in transduction both the lack of generality that is inherent
in the pre-concept and its symbolic or imaginal character
which enables actions to be transposed into thought.
INTUITIVE THOUGHT
The forms of thought we have been describing can be
analysed only through observation, since young children's
intelligence is still far too unstable for them to be interro-
gated profitably. After about 4 years, on the other hand,
short experiments with the subject, in which he has to
manipulate experimental objects, enable us to obtain regular
answers and to converse with him. This fact alone
indicates a new structuring.
In fact, from 4 to 7 years we see a gradual co-ordination of
representative relations and thus a growing conceptualiza-
tion, which leads the child from the symbolic or pre-
conceptual phase to the beginnings of the operation. But
the remarkable thing is that this intelligence, whose progress
may be observed and is often rapid, still remains pre-logical
even when it attains its maximum degree of adaptation 1 ; up
to the time when this series of successive equilibrations
culminates in the " grouping '*, it continues to supplement
incomplete operations with a semi-symbolic form of thought,
i.e. intuitive reasoning ; and it controls judgments solely by
means of intuitive " regulations ", which are analogous on
a representative level to perceptual adjustments on the
sensori-motor plane.
As an example let us consider an experiment which we
conducted some time ago with A. Szeminska. Two small
glasses, A and A 2 , of identical shape and size, are each filled
with an equal number of beads, and this equality is acknow-
ledged by the child, who has filled the glasses himself, e.g.
by placing a bead in A with one hand every time he places a
bead in A 2 with the other hand. Next, A 2 is emptied into a
differently shaped glass B, while A is left as a standard.
1 We axe disregarding here purely verbal forms of thought, such as
^nimisrn, infantile artificialism, nominal realism, etc.
130 THE DEVELOPMENT OF THOUGHT
Children of 4-5 years then conclude that the quantity of beads
has changed, even though they are sure none has been re-
moved or added. If the glass B is tall and thin they will say
that there are " more beads than before " because "it is
higher ", or that there are fewer because "it is thinner",
but they agree on the non-conservation of the whole.
First, let us note the continuity of this reaction with those
of earlier levels. The subject possesses the notion of an
individual object's conservation but does not yet credit a
collection of objects with permanence. Thus, the unified
class has not been constructed, since it is not always constant,
and this non-conservation is an extension both of the
subject's initial reactions to the object (with a greater
flexibility due to the fact that it is no longer a question of an
isolated element but of a collection) and of the absence of
an understanding of plurality which we mentioned in con-
nection with the pre-concept. Moreover, it is clear that the
reasons for the error are of a quasi-perceptual order ; the
rise in the level, or the thinness of the column, etc., deceives
the child. However, it is not a question of perceptual
illusions ; perception of relations is on the whole correct, but
it occasions an incomplete intellectual construction. It is
this pre-logical schematization, which is still closely modelled
on perceptual data though it recentres them in its own
fashion, that may be called intuitive thought. We can see
straight away how it is related to the imaginal character of
the pre-concept and to the mental experiments that charac-
terize transductive reasoning.
However, this intuitive thought is an advance on pre-
conceptual or symbolic thought. Intuition, being concerned
essentially with complex configurations and no longer with
simple half-individual, half-generic figures, leads to a rudi-
mentary logic, but in the form of representative regulations
and not yet of operations. From this point of view, there
exist intuitive " centralisations " and " decentralisations "
which are analogous to the mechanisms we mentioned in
connection with the sensori-motor schemata of perception
(Chap. III). Suppose a child estimates that there are more
beads in B than in A because the level has been raised. He
GROWTH OF THOUGHT INTUITION AND OPERATIONS
thus " centres " his thought, or his attention, 1 on the
relation between the heights of B and A, and ignores the
widths. But let us empty B into glasses C or D, etc., which
are even thinner and taller ; there must come a point at
which the child will reply, " there are fewer, because it is too
narrow ". There will thus be a correction of centring on
height by a decentring of attention on to width. On the
other hand, in the case of the subject who estimates the
quantity in B as less than that in A on account of thinness,
the lengthening of the column in C, D, etc., will induce him
to reverse his judgment in favour of height. Now this
transition from a single centring to two successive centrings
heralds the beginnings of the operation ; once he reasons
with respect to both relations at the same time, the child
will, in fact, deduce conservation. However, in the case we
are considering, there is neither deduction nor a true
operation ; an error is simply corrected, but it is corrected
late and as a reaction to its very exaggeration (as in the field
of perceptual illusions), and the two relations are seen
alternately instead of being logically multiplied. So all that
occurs is a kind of intuitive regulation and not a truly
operational mechanism.
That is not all. In studying the differences between
intuition and operation together with the transition from
the one to the other, we may consider not merely the relating
to each other of qualities forming two dimensions but their
correspondences in either a logical (i.e. qualitative) or a
mathematical form. The subject is first presented with
glasses A and B of different shapes and he is asked to place
a bead simultaneously in each glass, one with the left hand
and one with the right. With small numbers (4 or 5), the
child immediately believes in the equivalence of the two
collections, which seems to presage the operation, but when
the shapes change too much, even though the one-to-one
correspondence is continued, he ceases to recognize equality.
The latent operation is thus destroyed by the deceptive
demands of intuition.
1 Concentration of attention on one idea is precisely nothing else but
the centring of thought.
132 THE DEVELOPMENT OF THOUGHT
Let us line up six red counters on a table, supply the
subject with a collection of blue counters and ask him to
place on the table as many blue ones as there are red ones.
From about 4 to 5 years, the child does not establish any
correspondence and contents himself with a row of equal
length (with its members closer together than those of the
standard). At about 5 or 6 years, on the average, the subject
lines up six counters opposite the blue. Has the operation
now been acquired, as might appear ? Not at all ! It is only
necessary to spread the elements in one of the series further
apart, or to draw them close together, etc. for the subject to
disbelieve in the equivalance. As long as the optical corres-
pondence lasts, the equivalence is obvious ; once the first is
changed, the second disappears, which brings us back to the
non-conservation of the whole.
Now this intermediate reaction is full of interest. The
intuitive schema has become flexible enough to enable a
correct system of correspondences to be anticipated and
constructed, which to an uninformed observer presents all
the appearances of an operation. And yet, once the intuitive
schema is modified, the logical relation of equivalence, which
would be the necessary product of an operation, is shown
not to have existed. We are thus confronted with a form of
intuition which is superior to that of the previous level and
which may be called " articulated intuition " as opposed to
simple intuition. But this articulated intuition, although it
approaches the operation (and eventually joins up with it
by stages which are often imperceptible), is still rigid and
irreversible like all intuitive thought ; it is thus only the
product of successive regulations which have finally articu-
lated the original global and unanalysable relations, and it
is not yet a genuine " grouping ".
This difference between the intuitive and the operational
methods may be pinned down still further by directing the
analysis towards the formation of classes and the seriation
of asymmetrical relations, which constitute the most elemen-
tary groupings. But of course the problem must be pre-
sented on an intuitive plane, the only one accessible at this
stage, as opposed to a formal plane indissociably tied to
GROWTH OF THOUGHT INTUITION AND OPERATIONS 133
language. To study the formation of classes, we place about
twenty beads in a box, the subject acknowledging that they
are " all made of wood ", so that they constitute a whole, B.
Most of these beads are brown and constitute part A, and
some are white, forming the complementary part A'. In order
to determine whether the child is capable of understanding the
operation A -f A' =B, i.e. the uniting of parts in a whole, we
may put the following simple question : In this box (all the
beads still being visible) which are there more of wooden
beads or brown beads, i.e. is A<B ?
Now, up to about the age of 7 years, the child almost
always replies that there are more brown beads
" because there are only two or three white ones/*. We
then question further : " Are all the brown ones made
of wood ? " " Yes/' " If I take away all the wooden
beads and put them here (a second box) will there be
any beads left in the (first) box ? " ft No, because they
are all made of wood/' " If I take away the brown
ones, will there be any beads left ? " ' Yes, the white
ones/' Then the original question is repeated and the
subject continues to state that there are more brown
beads than wooden ones in the box because there are
only two white ones, etc.
The mechanism of this type of reaction is easy to unravel :
the subject finds no difficulty in concentrating his attention
on the whole B, or on the parts A and A', if they have been
isolated in thought, but the difficulty is that by centring on A
he destroys the whole, B, so that the part A can no longer
be compared with the other part A'. So there is again a
non-conservation of the whole for lack of mobility in the
successive centralisations of thought. But this is still not all.
When the child is asked to imagine what would happen if
we made a necklace either with the wooden beads or with
the brown beads, A, we again meet the foregoing difficulties
but with the following details : " If I make a necklace with
the brown ones ", a child will sometimes reply, " I could not
make another necklace with the same beads, and the neck-
lace made of wooden beads would have only white ones ! "
This type of thinking, which is in no way irrational, neverthe-
134 THE DEVELOPMENT OF THOUGHT
less shows the difference still separating intuitive thought
and operational thought. In so far as the first imitates true
actions by imagined mental experiments, it meets with a
particular obstacle, namely, that in practice one could not
construct two necklaces at the same time from the same
elements, whereas in so far as the second is carried out through
internalized actions that have become completely reversible,
there is nothing to prevent two hypotheses being made
simultaneously and then being compared with each other.
The seriation of sticks A, B, C, etc. of different lengths,
but placed side by side (to be compared in pairs), also
yields an interesting lesson. Children of 4 to 5 years
are able to construct only unco-ordinated pairs, BD,
AC, EG, etc. Then the child constructs short series and
achieves the seriation of ten elements only by groping his
way from step to step. Furthermore, when he has finished a
row he is incapable of interpolating new terms without
undoing the whole. Not until the operational level is seria-
tion achieved straight away, by such a method as, for
example, finding the smallest of all the terms and then tha
next smallest, etc. It is at this level, similarly, that the
inference (A<B) + (B<C) =(A<C) becomes possible,
whereas at intuitive levels the subject declines to derive from
the two perceptually verified inequalities A<B and B<C
the conclusion A<C.
The progressive articulations of intuition and the
differences which still separate them from the operation are
particularly clear where space and time are concerned, as
well as being very instructive owing to the possibility of com-
paring intuitive and sensori-motor reactions. We are thus
reminded of how the infant learns the action of turning a
bottle round. To reverse an object by an intelligent action
does not automatically lead to knowing how to reverse it in
thought, and the stages of this intuition of rotation constitute
largely a repetition of those of actual or sensori-motor
rotation ; in both cases we find a similar process of progressive
decentralisation from the egocentric point of view, this
decentralisation being simply perceptual and motor in the
first case, and representative in the second.
GROWTH OF THOUGHT INTUITION AND OPERATIONS 135
In this connection we may proceed in two ways, either by
moving the subject (in thought) around the object, or else
by rotating the object itself in thought. To bring about the
first situation, we may, for example, show the child card-
board mountains on a square table and ask him to choose
from several very simple drawings those which correspond
to possible points of view (the child, sitting at one side of
the table, sees a doll move round the mountain and has to
pick out the pictures that correspond to its different
positions) ; now small children still remain dominated by the
point of view that is theirs at the moment of choice, even
when they have previously walked round the table from one
side to the other. Reversals from front to behind and from
left to right are difficulties which are at first insurmountable
and only acquired gradually by intuitive regulations up to
7 or 8 years.
The rotation of the object itself,, on the other hand,
provides interesting data concerning the intuition of order.
For example, three mannikins of different colours, A, B and C,
are threaded on a single wire, or else three balls, A, B and c',
are placed into a cardboard tube (so constructed that the
balls cannot change their relative positions). The child is
required to draw the whole as an aid to memory. Then the
elements A, B and C are moved behind a screen or through
the tube and the child has to predict the order in which
they will emerge at the other end (i.e. their original order)
and the opposite order of emergence when they return. All
children foresee the original order. The opposite order, on
the other hand, is beyond them till about 4 or 5 years, the
end of the pre-conceptual period. Next, the whole apparatus
(tube or wire) is turned through 180 degrees and the subject
has to predict the order of emergence (which is thus reversed).
After the child has himself checked the result we begin again
and execute two half-circles (360 degrees in all), then three,
etc.
This demonstration enables us to follow the whole progress
of intuition step by step right up to the beginnings of the
operation. From 4 to 7 years of age the subject is unable to
foresee that half a turn will change the order ABC into
136 THE DEVELOPMENT OF THOUGHT
C BA; then, having put the matter to the test, he admits that
two half-turns will actually produce C B A. Although
undeceived by experience, he is no better able to predict the
effect of three half-turns. Moreover, children of 4 to 5 years,
after seeing sometimes A and sometimes C at the head of the
column, imagine that B also will have its turn as leader (not
knowing Hilbert's axiom, according to which, if B is
" between " A and C, it must also necessarily be " between "
C and A !) The idea of the invariability of the " between "
position is also acquired by the successive regulations that
are responsible for the articulation of intuition. Not until
about 7 is the whole system of changes understood, and often
this last phase is rather sudden on account of a general
" grouping " of the relations involved. It should be noted
straight away that the operation thus follows from intuition
not merely when the original order ( + ) can be reversed in
thought ( -) by a primary intuitive articulation but even
when two opposite orders yield the original order again
( - multiplied by - gives -f , which in this particular case
is understood at 7 -8 years !)
Temporal relations provide similar data. Intuitive time is
a time which is tied to particular objects or movements and
which has no homogeneity or uniform flow. When two
moving objects leave the same point A and arrive at
two different places, B and B', the 4-5 year-old child
acknowledges the simultaneity of the departures but usually
contests that of the arrivals, although this is easily percep-
tible. He recognises that one of the objects ceased to move
when the other stopped, but he refuses to grant that the
movements ceased " at the same time ", because there
simply is as yet no time common to different speeds. Simi-
larly, he conceives of " before " and " after " in terms of
spatial succession and not yet in terms of temporal succession.
From the point of view of duration, " faster " implies " more
time " even in the absence of verbal implication, and simply
by inspection of the data (since faster = further = more time).
When these first difficulties have been overcome by an
articulation of intuitions (due to decentralisation of thought,
which becomes accustomed to comparing two systems of
GROWTH OF THOUGHT INTUITION AND OPERATIONS 137
positions at the same time, whence a gradual regulation of
estimations), there nevertheless still exists a systematic
incapacity to combine local times into one single time.
Two equal quantities of water flowing, at the same rate
through the two branches of a tube into differently shaped
bottles, give rise, for example, to the following judgments :
the 6-7 years old child recognizes the simultaneity of starts
and stops but denies that water has been flowing into one
bottle for as long as it has flowed into the other. Ideas
concerning age give rise to similar statements ; if A was
born before B, that does not mean that he is older and, if
he is older, that does not exclude the possibility that B
might catch up with him or even overtake him !
These intuitive ideas are parallel to those encountered in
the field of practical intelligence. Andre Rey has shown how
subjects of the same age, tackling problems involving instru-
mental devices (extracting objects from a tube with hooks,
changing round plugs, rotations, etc), also show irrational
behaviour before these adaptive solutions are discovered. 1
With regard to representations without manipulation, such as
the explanation of the movement of rivers or clouds, the
floating of boats, etc., we have shown that causal links of
this type were based on bodily action ; physical movement
implies teleology, an active internal force ; the river
" leaps " over pebbles, the clouds make the wind, which
in turn pushes them, and so on. 2
This then is intuitive thought. Like symbolic thought of
a pre-conceptual nature, from which it springs directly, it is,
in a sense, an extension of sensori-motor intelligence. Just
as the latter assimilates objects to response-schemata, so
intuition is always in the first place a kind of action carried
out in thought ; pouring from one vessel to another, estab-
lishing a correspondence, joining, serialising, displacing, etc.
are still response-schemata to which representation assimi-
lates reality. But the accommodation of these schemata to
objects, instead of remaining practical, provides imitation
or imaginal significants which enable this same assimilation
1 Andr Rey, V Intelligence pratique chez I'enfant, Alcan, 1935.
8 La Causalitd physique chez I'enfant, Alcan, 1927.
138 THE DEVELOPMENT OF THOUGHT
to occur in thought. So in the second place, intuition is an
imaginal thought, more refined than that of the previous
period, since it concerns complex configurations and not
merely simple syncretic collections symbolized by type-
individuals ; but it still uses representative symbolism and
therefore constantly exhibits some of the limitations that
are inherent in this.
These limitations are obvious. Intuition, being a direct
relationship between a schema of internalized action and the
perception of objects, results only in configurations " centred "
on this relationship. Since it is unable to go beyond these
imaginal configurations, the relations that it constructs are
thus incapable of being combined. The subject does not
arrive at reversibility, because an action translated into a
simple imagined experiment is still uni-directional, and
because an assimilation centred on a perceptual configuration
is necessarily uni-directional also. Hence the absence of
transitivity, since each centring distorts or destroys the
others, and of associativity, since the relations vary with the
route followed by thought in fashioning them. Altogether
then, in the absence of transitive, reversible and associative
combinativity, there is neither a guarantee of the identity
of elements nor a conservation of the whole. Thus, we may
also say that intuition is still phenomenalist, because it
copies the outlines of reality without correcting them, and
egocentric, because it is constantly related to present action ;
in this way, it lacks an equilibrium between the assimilation
of phenomena to thought-schemata and the accommodation
of the latter to reality.
But this initial state, which recurs in each of the fields of
intuitive thought,, is progressively corrected, thanks to a
system of regulations which herald operations.. Intuition, at
first dominated by the immediate relations between the
phenomenon and the subject's viewpoint, evolves towards
decentralisation. Each distortion, when carried to an
extreme, involves the re-emergence of the relations pre-
viously ignored. Each relation established favours the possi-
bility of a reversal. Each detour leads to interactions which
supplement the various points of view. Every decentralisa-
GROWTH OF THOUGHT INTUITION AND OPERATIONS 139
tion of an intuition thus takes the form of a regulation, which
is a move towards reversibility, transitive combinativity and
associativity, and thus, in short, to conservation through the
co-ordination of different viewpoints. Hence we have
articulated intuitions, which progress towards reversible
mobility and pave the way for the operation.
CONCRETE OPERATIONS
The appearance of logico-arithmetical and spatio-temporal
operations introduces a problem of considerable interest in
connection with the mechanisms characterising the develop-
ment of thought. The point at which articulated intuitions
turn into operational systems is not to be determined by
mere convention, based on definitions decided on in advance.
To divide developmental continuity into stages recognizable
by some set of external criteria is not the most profitable of
occupations ; the crucial turning-point for the beginning of
operations shows itself in a kind of equilibration, which is
always rapid and sometimes sudden, which affects the
complex of ideas forming a single system and which needs
explaining on its own account. In this there is something
comparable to the abrupt complex restructurings described
in the Gestalt theory, except that, when it occurs, there
arises the very opposite of a crystallisation embracing all
relations in a single static network ; operations, on the
contrary, are found formed by a kind of thawing out of
intuitive structures, by the sudden mobility which animates
and co-ordinates the configurations that were hitherto more
or less rigid despite their progressive articulation. Thus, quite
distinct stages in development are marked, for example, by
the point at which temporal relations are merged in the
notion of a single time, or the point at which the elements of
a complex are conceived as constituting an unvarying whole
or the inequalities characterising a system of relations are
serialised in a single scale, and so on ; after trial-and-error
imagination there follows, sometimes abruptly, a feeling
of coherence and of necessity, the satisfaction of arriving
at a system which is both complete in itself and
indefinitely extensible.
140 THE DEVELOPMENT OF THOUGHT
Consequently, the problem is to understand what internal
process effects this transition from a phase of progressive
equilibration (intuitive thought) to a mobile equilibrium
which is reached, as it were, at the limit of the former
(operations). If the concept of " grouping " described in
Chapter II has, in fact, a psychological meaning, this is
precisely the point at which it should reveal it.
So, assuming that the intuitive relations of a given system
are at a certain moment suddenly " grouped ", the first
question is to decide by what internal or mental criterion
grouping is to be recognised. The answer is obvious : where
there is " grouping " there will be the conservation of a
whole, and this conservation itself will not merely be assumed
by the subject by virtue of a probable induction, but affirmed
by him as a certainty in his thought.
In this connection let us reconsider the first example
cited with reference to intuitive thought : the pouring of the
beads from one glass to another. After a long period during
which each pouring out is believed to change the quantities,
and after an intermediate phase (articulated intuition) when
some transfers are believed to change the whole while
others, between glasses that are just slightly different,
induce the subject to suppose that the whole is conserved,
there always comes a time (between 6 years and 7 years
8 months) when the child's attitude changes : he no longer
needs to reflect, he decides, he even looks surprised that the
question is asked, he is certain of the conservation. What has
happened then ? If we ask him his reasons, he replies that
nothing has been removed or added ; but the younger
children also are well aware of this, and yet they do not
infer identity. Thus, in spite of what E. .Meyerson says,
identification is not a primary process but the result of an
assimilation by the whole grouping (the product of the origi-
nal operation multiplied by its converse). Or else he replies
that the height makes up for the width lost by the new glass,
etc., but articulated intuition has already led to these
decentrings of a given relation without their resulting in the
simultaneous co-ordination of relations or in their necessary
conservation. Or else, and this especially, he replies that a
GROWTH OF THOUGHT INTUITION AND OPERATIONS
transfer from A to B may be corrected by a transfer from B
to A and this reversibility is certainly essential, but the
younger children have already on occasion admitted the
possibility of a return to the starting-point, without this
" empirical reversal " yet constituting a complete reversi-
bility. There is, therefore, only one legitimate answer : the
various transformations involved reversibility, combination
of compensated relations, identity, etc. in fact depend on
each other and, because they amalgamate into an organised
whole, each is really new despite its affinity with the corres-
ponding intuitive relation that was already formed at the
previous level.
Let us take another example. In the case of the elements
arranged in the order ABC and subjected to a half-rotation
(180 degrees), the child intuitively and gradually discovers
almost all the relationships : that B invariably remains
" between " A and Gand between C and A ; that one lialf-
turn changes ABC into CBA and that two half-turns lead
back to ABC, etc. But the relationships discovered one
after another are still intuitions with no link between them
.or " necessity " about them. At about 7 or 8 years, on the
other hand, we find subjects who, before any trial, foresee :
1. that ABC reversed is CBA ;
2. that two reversals result in the original order ;
3. that three reversals are equivalent to one, etc.
Here again, each of the relationships may correspond to
an intuitive discovery, but together they constitute a new
reality, since they have become deductive and no longer
consist of a succession of actual or mental experiments.
Now it is easy to see that in all such cases and they are
innumerable a mobile equilibrium is reached when the
following changes are simultaneously effected :
1. two successive actions can be combined into oa^s ;
2. the action-schema already at work in intuitive
thought becomes reversible ;
3. the same point can be reached by two different
paths without being altered ;
4. a return to the starting-point finds the starting-
point unchanged ;
142 THE DEVELOPMENT OF THOUGHT
5. when the same action is repeated, it either adds
nothing to itself or else is a new action with a
cumulative effect. In these we recognize transi-
tive combinativity, reversibility, associativity and identity,
with (in 5) either logical tautology or numerical iteration,
all of which characterize logical " groupings " or arith-
metical " groups ".
But what must be clearly understood if we are to arrive
at the true psychological nature of the grouping, as distinct
from its formulation in logical language, is that these
various closely related changes are actually the expression
of one and the same total act, namely, an act of complete
decentralisation or complete conversion of thought. The
distinguishing characteristic of the sensori-motor schema
(perception, etc.), of the preconceptual symbol and also of
the intuitive configuration, is that they are always
" centred " on a particular state of the object and a point
of view peculiar to the subject ; thus they always testify
both to jan egocentric assimilation to the subject and to a
phenomenalist accommodation to the object. On the other
hand, the distinguishing characteristic of the mobile equili-
brium peculiar to the grouping is that the decentralisation,
already provided for by the progressive regulations and
articulations of intuition, suddenly becomes systematic on
reaching its limit ; thought is then no longer tied to particu-
lar states of the object, but is obliged to follow successive
changes with all their possible detours and reversals ; and
it no longer issues from a particular viewpoint of the subject,
but co-ordinates all the different viewpoints in a system of
objective reciprocities. The grouping thus realizes for the
first time an equilibrium between the assimilation of objects
to the subject's action and the accommodation of subjective
schemata to modifications of objects. At the outset, in
fact, assimilation and accommodation act in opposite
directions ; hence the distorting character of the first and
the phenomenalist character of the second. By means of
anticipations and reconstitutions, which extend action in
both directions to ever increasing distances, from the brief
anticipations and reconstitutions characteristic of perception,
GROWTH OF THOUGHT INTUITION AND OPERATIONS 143
habit and sensori-motor intelligence to the anticipatory
schemata formed by intuitive representation, assimilation
and accommodation are gradually equilibrated-. The com-
pletion of this equilibrium explains the reversibility which
is the final term of sensori-motor and mental anticipations
and reconstitutions, and with it the reversible combinativity
which is the distinguishing mark of the grouping ; the
detailed working of operations simply expresses, in fact,
the combined conditions of a co-ordination of successive
viewpoints of the subject (with possible reversal in time and
anticipation of their sequel) and a co-ordination of percep-
tible or represent able modifications of objects (in the past,
in the present, or in the course of subsequent events).
In practice, the operational groupings, which are consti-
tuted at about 7 or 8 years of age (sometimes a little
earlier), lead to the following structures. First of all they
lead to the logical operations of fitting classes together (the
problem of the brown beads, A, being less numerous than
the wooden beads, B, is solved at about the age of 7) and of
serialising asymmetrical relations. Hence the discovery of
transitivity which permits of the deductions : A =B,
B=C, therefore A-C; or A<B, B<C therefore A<C.
Furthermore, as soon as these additive groupings are acquired,
multiplicative groupings are immediately understood in the
form of correspondences r if he knows how to serialise
objects according to the relations Ai<Bi<Ci . . . the
subject will find it no more difficult to serialise two or more
sets, such as A2<B2<C2 . . . , which correspond to each
other term for term ; when a child aged 7 has arranged
a series of mannikins in order of size, he will be able to make
a series of sticks or bags correspond to them, and he will be
able to identify which element in one series corresponds to
which in another even when they are all jumbled (since the
multiplicative character of this grouping adds no difficulty
to the additive serialising operations which have just been
discovered).
Moreover, the simultaneous construction of the groupings
of classification and of qualitative seriation means the
advent of the system of numbers. Doubtless the young
144 THE DEVELOPMENT OF THOUGHT
child does not have to wait for this operational generalisation
to construct the first numbers (according to A. Descoedres,
a new number is learnt each year from i to 5 years), but the
numbers I to 6 are still intuitive since they are bound to
perceptual configurations. Similarly, the child may be taught
to count, but experiment reveals that the verbal use of
the names of numbers has little connection with numerical
operations as such, which sometimes precede counting aloud
and sometimes follow it, with no necessary bond between
the two. All that the operations constituting number, i.e.
one-to-one correspondence (with conservation of the resulting
equivalence despite differences in shape), or simple repetition
of unity (i +i =2 ; 2 -f I =3 ; etc.) require are the additive
groupings of classification and of the serialisation of asym-
metrical relations (ordering) ; but these are blended into a
single operational whole, so that the unit i is simultaneously
an element in a class (i included in 2, 2 in 3, etc.), and in a
series (the first i preceding the second i, etc.). As long as
the subject sees the individual elements with all their
qualitative diversity, he can in fact either combine them
according to their equivalent qualities (he then constructs
classes) or arrange them according to their differences (he
then constructs asymmetrical relations), but he cannot group
them simultaneously as equivalent and different. Number,
on the other hand, is a collection of objects conceived as
both equivalent and orderable, their only difference thus
being reduced to their position in, a series. This combination
of difference and equivalence implies, in this case, the elimin-
ation of quality, and that is precisely what accounts for
the formation of the homogeneous unit i and the transition
from logic to mathematics. Now it is very interesting
to observe that this transition occurs just when logical
operations are being constructed; classes, relations and
numbers thus form a psychologically and logically
indivisible whole, in which each of the three terms
completes the other two.
But these logico-arithmetical operations constitute only
one aspect of the fundamental groupings whose construction
characterises the age, on the average, of 7-8 years. Corres-
GROWTH OF THOUGHT INTUITION AND OPERATIONS 145
ponding to these operations, which assemble objects in order
to classify, serialise or number them, are the operations that
constitute objects themselves, complex yet unique objects
such as space, time and material systems. Now, it is not
surprising that these infra-logical or spatio-temporal opera-
tions are grouped in correlation with logico-arithmetical
operations, since they are the same operations but on another
scale : the joining together of objects in classes and of
classes with one another becomes the joining of parts or pieces
in a whole ; seriation expressing differences between
objects appears as relations of order (placing operations) and
displacement, and number corresponds to measurement.
Now it so happens that while classes, relations and numbers
are being formed, we can see the construction, in a re-
markably parallel manner, of the qualitative groupings that
generate time and space. At the age of about 8, the relations
of temporal order (before and after) are co-ordinated with
duration (longer or shorter length of time), whereas the two
systems of ideas were still independent at the intuitive level ;
as soon as they become joined in a single whole they engender
the notion of a time common to various movements (internal
and external) at different velocities. Above all, there are also
constituted at the age of about 7 or 8 the qualitative opera-
tions that structure space : the spatial order of succession
and the joining together of intervals or distances ; conserva-
tion of lengths, areas, etc, ; formation of a system of co-
ordinates ; perspectives and sections, etc. In this connection,
the study of the spontaneous measurement that derives from
early estimation by perceptual " transportation " and leads,
at the age of 7 or 8, to the transitivity of operational equiva-
lences (A =B, B,=C, therefore A C) and to the formation
of the unit (by a synthesis of division and displacement),
demonstrates in the clearest possible way how the con-
tinuous development first of perceptual and then of intuitive
acquisitions leads finally to reversible operations as their
necessary form of equilibrium.
But it is important to note that these different logico-
arithmetical or spatio-temporal groupings are as yet far
from constituting a formal logic applicable to all ideas
146 THE DEVELOPMENT OF THOUGHT
to all reasoning. This is an essential point which must be
stressed, for the sake both of the theory of intelligence and of
its educational applications, if we wish to adapt teaching to
the findings of developmental psychology as opposed to the
logical bias of scholastic tradition. In fact, the same
children as reach the operations just described are usually
incapable of them when they cease to manipulate objects
and are invited to reason with simple verbal propositions.
The operations that are involved here, then, are " concrete
operations " and not yet formal ones ; being constantly tied
to action, they give it a logical structure, embracing also the
speech accompanying it, but they by no means imply the
possibility of constructing a logical discourse independently
of action. Thus, class-inclusion is understood in the concrete
problem of the beads (see above) from the age of 7-8
years, while a verbal test of identical structure is not solved
until much later (cf. one of Burt's tests : " Some of the
flowers in my bunch are yellow," says a boy to his
sisters. The first replies, " Then all your flowers are yellow, "
the second replies, "Some of them are yellow", and the
third: "None". Who is right?)
But this is not yet all. The same " concrete " inferences,
such as those leading to the conservation of the whole, to
transitivity of equality (A =B =C) or of differences
(A<B<C . . . ), may be easily handled in the case of one
particular system of ideas (such as quantity of material) and
yet be meaningless for the same subjects in the case of
another system of ideas (such as weight). In view of this
especially, it is wrong to speak of formal logic before the end
of childhood. " Groupings " are still relative to the types of
concrete ideas (i.e. internalised actions) that they have
actually structured, but the structuring of other types of
concrete ideas, which are of a more complex intuitive nature,
since they depend on quite different actions, requires a recon-
struction of the same groupings independently of time.
A particularly clear example is the notion of the conserva-
tion of the whole (which is the very hall-mark of the
grouping). Thus, the subject is given two pellets of dough
to be modelled into the same shape, size and weight, then one
GROWTH OF THOUGHT INTUITION AND OPERATIONS 147
of them is modified (made into a roll, etc.) and the subject
is asked whether the material (the quantity of dough), the
weight and the volume remain the same (volume is estimated
by the displacement of water in two glasses in which the
objects are immersed). Now after the age of 7 or 8 the
quantity of material is recognised as conserved of necessity
By virtue of the inferences already described in connection
with the conservation of complexes. But up to 9-10 years
the same subjects dispute that weight is conserved, and
this comes of relying on the intuitive inferences that they
used before 7-8 years to ascribe non-conservation to the
material. As for the inferences they have just used (often
only a few moments earlier) to prove the conservation of
substance, this is not applied to weight at all. If the roll is
thinner than the pellet the material is conserved, because
this narrowing is compensated by lengthening, but the
weight is reduced because, so it is held, narrowing acts
unconditionally ! At about 9-10 years, on the other hand,
conservation of weight is admitted by virtue of the same
inferences as have been applied to the material, but up to
ii or 12 years conservation of volume is still denied, and by
virtue of the converse intuitive reasoning ! Moreover,
seriations, combinations based on equality, etc., follow
exactly the same order of development : at 8 years two
quantities of matter that equal a third are equal to each
other, but not so two weights (which are, needless to say,
independent of perception of volume) ! The reason for
these separations is naturally to be sought in the intuitive
characters of substance, weight and volume, which facilitate
or hinder operational combinations. Thus, up to the age of
ii or 12, a particular logical form is still not independent
of its concrete content.
FORMAL OPERATIONS
The separations of which we have just seen an example
relate to operations affecting similar categories of actions or
concepts, even though they apply to distinct fields ; since
they occur during the same period, they may be called
" horizontal separations ". On the other hand, the transition
148 THE DEVELOPMENT OF THOUGHT
from sensori-motor co-ordinations to representative co-
ordinations gives rise, as we have seen, to similar reconstruc-
tions involving separations, but since these no longer relate tc
the same levels they may be called " vertical ". Now the
building up of formal operations, which begins at about
ii or 12 years, likewise necessitates a complete reconstruc-
tion, which serves to transpose " concrete " groupings to a
new level of thought, and this reconstruction is characterized
by a series of vertical separations.
Formal thought reaches its fruition during adolescence.
The adolescent, unlike the child, is an individual who thinks
beyond the present and forms theories about everything,
delighting especially in considerations of that which is not.
The child, on the other hand, concerns himself only with
action in progress and does not form theories, even though
an observer notes the periodical recurrence of analogous
reactions and may discern a spontaneous systematization
in his ideas. This reflective thought, which is characteristic
of the adolescent, exists from the age of 11-12 years, from
the time, that is, when the subject becomes capable of
reasoning in a hypothetico-deductive manner, i.e., on the
basis of simple assumptions which have no necessary relation
to reality or to the subject's beliefs, and from the time when
he relies on the necessary validity of an inference (viformae),
as opposed to agreement of the conclusions with experience.
Now, reasoning formally and with mere propositions
involves different operations from reasoning about action or
reality. Reasoning that concerns reality consists of a first-
degree grouping of operations, so to speak, i.e. internalised
actions that have become capable of combination and
reversal. Formal thought, on the other hand, consists in
reflecting (in the true sense of the word) on these operations
and therefore operating on operations or on their results and
consequently effecting a second-degree grouping of opera-
tions. No doubt the same operational content is involved ;
the problem is still a matter of classing, serialising, enumerat-
ing, measuring, placing or displacing in space or in time, etc.
But these classes, series and spatio-temporal relations them-
selves, as structurings of action and reality, are not what is
GROWTH OF THOUGHT INTUITION AND OPERATIONS 149
grouped by formal operations but the propositions that
express or " reflect *' these operations. Formal operations,
therefore, consist essentially of " implications " (in the
narrow sense of the word) and " contradictions " established
between propositions which themselves express classifica-
tions, sedations, etc.
We can now see why there is a vertical separation between
concrete operations and formal operations, even though the
second repeats to some extent the content of the first ; the
operations in question are indeed not by any means of the
same psychological difficulty. Thus, one has only to trans-
late a simple problem of seriation between three terms
presented in random order into propositions for this serial
addition to become singularly difficult, although, right from
the age of 7, it is quite easy as long as it takes the form of a
concrete seriation or even of transitive co-ordinations
considered in relation to action. The following neat example
comes from one of Hurt's tests : " Edith is fairer than Susan;
Edith is darker than Lily ; who is the darkest of the three ? "
Now this problem is rarely solved before the age of 12.
Till then we find reasoning such as the following : Edith
and Susan are fair, Edith and Lily are dark, therefore Lily is
darkest, Susan is the fairest and Edith in between. In other
words, the child of 10 reasons formally as children of 4-5
years do when serialising sticks, and it is not until the age of
12 that he can accomplish with formal problems what he
could do with concrete problems of size at the age of 7, and
the cause of this is simply that the premises are given as
pure verbal postulates and the conclusion is to be drawn
vi formae without recourse to concrete operations.
We thus see why formal logic and mathematical deduction
are still inaccessible to the child and seem to constitute a
realm on its own the realm of " pure " thought which is
independent of action. And indeed, whether we are con-
cerned with the particular language which, like every
. language, is learned of mathematical signs (signs which
are quite different from symbols in the sense defined above)
or with the other system of signs (i.e. the words expressing
simple propositions), hypothetico-deductive operations are
150 THE DEVELOPMENT OF THOUGHT
situated on a different plane from concrete reasoning, since an
action affecting signs that are detached from reality is some-
thing quite different from an action relating to reality itself
or relating to signs attached to this reality. This is why logic
dissociates this final stage from the main body of mental
development and is in fact limited to axiomatizing character-
istic operations instead of replacing them in their living
context. This always was its role, but this role certainly
gains by being played consciously. Moreover, logic was
driven to this course by the very nature of formal operations
which, since second-degree operations deal only with signs,
are committed to the schematization proper to an axiomatic.
But it is the function of the psychology of intelligence to
replace the canon of formal operations in its true perspective
and to show that it could not have any mental meaning,
were it not for the concrete operations that both pave the
way for it and provide its content. Formal logic is,
according to this view, not an adequate description for the
whole of living thought ; formal operations constitute solely
the structure of the final equilibrium to which concrete
operations tend when they are reflected in more general
systems linking together the propositions that express them.
THE HIERARCHY OF OPERATIONS AND THEIR PROGRESSIVE
DIFFERENTIATION
As we have seen, a response is a functional interaction
between subject and objects, and responses may be serialised
in an order of genetic succession, based on the increasing
distances, spatial and temporal, that characterize the
increasingly complex routes followed by these interactions.
Thus, perceptual assimilation and accommodation involve
merely a direct and rectilinear form of interaction. Habit
has routes that are more complex but shorter, stereotyped
and uni-directional. Sensori-motor intelligence introduces
reversals and detours ; it has access to objects outside the
perceptual field and habitual routes and so it goes beyond
original distances in space and time but is still limited to
the field of the subject's own action. With the beginnings
of representative thought and especially with the growth of
GROWTH OF THOUGHT INTUITION AND OPERATIONS
intuitive thought, intelligence becomes capable of evoking
absent objects, and consequently of being applied to invisible
realities in the past and partly even in the future. But it
still proceeds by way of more or less static figures half-
individual, half-generic images in the case of the pre-
concept, complex representative configurations, which are
still better articulated, in the intuitive period but they
are nevertheless figures, i.e. "stills" of moving reality,
which represent only some states or pathways out of the
mass of possible routes. Intuitive thought thus provides a
map of reality (which sensori-motor intelligence, bound up
with immediate reality, could not do), but it is still imaginal,
with many blank spaces and without sufficient co-ordinations
to pass from one point to another. When groupings of
concrete operations appear, these forms are dissolved or
blended into the all-embracing plan and decisive progress is
made towards the overcoming of distances and the differen-
tiation of routes ; thought no longer masters only fixed states
or pathways but even deals with changes, so that one can
always pass from one point to another and vice versa. Thus,
the whole of reality becomes accessible. But it is still only
a represented reality ; with formal operations there is even
more than reality involved, since the world of the possible
becomes available for construction and since thought becomes
free from the real world. Mathematical creativity is an
illustration of this new power.
Now to picture the mechanism of this process of construc-
tion and not merely its progressive extension, we must note
that each level is characterized by a new co-ordination of
the elements provided already existing in the form of
wholes, though of a lower order by the processes of the
previous level.
The sensori-motor schema, the characteristic unit of the
system of pre-symbolic intelligence, thus assimilates per-
ceptual schemata and the schemata relating to learned
action (these schemata of perception and habit being of the
same lower order, since the first concerns the present state
of the object and the second only elementary changes of
state). The symbolic schema assimilates sensori-motor
152 THE DEVELOPMENT OF THOUGHT
schemata with differentiation of function ; imitative
accommodation is extended into imaginal significants and
assimilation determines the significates. The intuitive
schema is both a co-ordination and a differentiation of
imaginal schemata. The concrete operational schema is a
grouping of intuitive schemata, which are promoted, by the
very fact of their being grouped, to the rank of reversible
operations. Finally, the formal schema is simply a system
of second-degree operations, and therefore a grouping
operating on concrete groupings.
Each of the transitions from one of these levels to the
next is therefore characterized both by a new co-ordination
and by a differentiation of the systems constituting the unit
of the preceding level. Now these successive differentiations,
in their turn, throw light on the undifferentiated nature of
the initial mechanisms, and thus we can conceive both of a
genealogy of operational groupings as progressive differentia-
tions, and of an explanation of the pre-operational levels as
a failure to differentiate the processes involved.
Thus, as we have seen (Chap. IV), sensori-motor intelligence
arrives at a kind of empirical grouping of bodily movements,
characterized psychologically by actions capable of reversals
and detours, and geometrically by what Poincar^ called the
(experimental) group of displacement. But it goes without
saying that, at this elementary level, which precedes all
thought, we cannot regard this grouping as an operational
system, since it is a system of responses actually effected ;
the fact is therefore that it is undifferentiated, the displace-
ments in question being at the same time and in every case
responses directed towards a goal serving some practical
purpose. We might therefore say that at this level spatio-
temporal, logico-arithmetical and practical (means and ends)
groupings form a global whole and that, in the absence of
differentiation, this complex system is incapable of constitut-
ing an operational mechanism.
At the end of this period and at the beginning of repre-
sentative thought, on the other hand, the appearance of the
symbol makes possible the first form of differentiation :
practical groupings (means and ends) on the one hand,
GROWTH OF THOUGHT INTUITION AND OPERATIONS 153
and representation on the other. But this latter is still
undifferentiated, logko-arithmetical operations not being
distinguished from spatio-temporal operations. In fact,
at the intuitive level there are no genuine classes or
relations because both are still spatial collections as well as
spatio-temporal relationships : hence their intuitive and pre-
operational character. At 7-8 years, however, the appearance
of operational groupings is characterized precisely by a clear
differentiation between logico-arithmetical operations that
have become independent (classes, relations and de~
spatialized numbers) and spatio-temporal or infra-logical
operations. Lastly, the level of formal operations marks a
final differentiation between operations tied to real action
and hypothetico-deductive operations concerning pure impli-
cations from propositions stated as postulates.
THE DETERMINATION OF " MENTAL AGE "
The knowledge acquired from the psychology of intelli-
gence has given rise to three kinds of applications, which do
not, as such, concern our subject, but which yield information
for checking theoretical hypotheses.
Everybody knows how Binet, with a view to determining
the degree of retardation of the abnormal, came to invent
his remarkable metrical scale of intelligence. Binet, a subtle
analyst of thought processes, was more aware than anybody
of the difficulties of arriving through his measurements at the
actual mechanism of intelligence. But precisely because of
this feeling of doubt, he had recourse to a kind of psycho-
logical probabilism and, in collaboration with Simon,
gathered together the most diverse tests and sought to
determine frequency of success as a function of age ; intelli-
gence is thus assessed by advance or retardation according
to the mean statistical age for the correct solutions.
It is indisputable that these tests of mental age have on
the whole lived up to what was expected of them : a rapid
and convenient estimation of an individual's general level.
But it is no less obvious that they simply measure a " yield "
without reaching constructive operations themselves. As
Pi^ron quite rightly pointed out, intelligence conceived in
154 THE DEVELOPMENT OF THOUGHT
these terms is essentially a value-judgment applied to
complex behaviour.
On the other hand, tests have multiplied apace and
attempts have been made to distinguish them according to
the different special aptitudes they measure. In the field
of intelligence itself, tests of reasoning, comprehension,
knowledge etc., have thus been devised. So the problem is
to work out the correlations between these statistical
results, in the hope of distinguishing and measuring the
various factors involved in the inner mechanism of thought.
Spearman and his school, in particular, have applied them-
selves to this task, using precise statistical methods 1 and
they have arrived at the hypothesis that certain constant
factors are involved. The most general of these Spearman
called " the ' g * factor " and its value is related to the
individual's intelligence. But, as this writer himself insisted,
the " g " factor is simply expressed as " general intelligence ",
i.e. the degree of efficiency common to all the subject's
aptitudes or, one might almost say, the quality of neural and
psychological organisation making a mental task easier for
one individual than for others.
Finally, there has been an attempt to react in another
way against the empiricism of simple measures of yield,
namely, by trying to ascertain the actual operations that a
given individual has at his disposal ; the term " operation ''
is here taken in a limited sense as relative to genetic con-
struction, as we have treated it in this work. In this way, B.
Inhelder has made use of the concept of a " grouping " in
testing reasoning-power. She was able to show that the
order of acquiring concepts of conservation of substance,
weight and volume recurs in its entirety in mental deficients ;
the last of these three constants (present only in slightly
backward individuals and unknown in really deficient
cases) is never found without the other two, nor the second
without the first, while conservation of substance occurs
without conservation of weight and volume and that of
substance and weight without that of volume. She was able
1 Calculation of "tetrad differences" or correlations between corre-
lations.
GROWTH OF THOUGHT INTUITION AND OPERATIONS 155
to distinguish moronism from imbecility by the presence of
concrete groupings (of which the imbecile is not capable),
and slight backwardness by an inability to reason formally,
i.e. by incompleteness of operational construction. 1 This is
one of the first applications of a method which could be
developed further for determining levels of intelligence in
general.
1 B. Inhelder, Le diagnostic du raisonnement chez les d^biles mentaux,
Delachaux et Niestte, 1944.
CHAPTER VI
SOCIAL FACTORS IN INTELLECTUAL
DEVELOPMENT
THE human being is immersed right from birth in a social
environment which affects him just as much as his physical
environment. Society, even more, in a sense, than the
physical environment, changes the very structure of the
individual, because it not only compels him to recognize
facts, but also provides him with a ready-made system of
signs, which modify his thought ; it presents him with new
values and it imposes on him an infinite series of obligations.
It is therefore quite evident that social life affects intelligence
through the three media of language (signs), the content of
interaction (intellectual values) and rules imposed on thought
(collective logical or pre-logical norms).
Certainly, it is necessary for sociology to envisage society
as a whole, even though this whole, which is quite distinct
from the sum of the individuals composing it, is only the
totality of relations or interaction between these individuals.
Every relation between individuals (from two onwards)
literally modifies them and therefore immediately consti-
tutes a whole, so that the whole formed by society is not so
much a thing, a being or a cause as a system of relations.
But these relations are extremely numerous and complex,
since, in fact, they constitute just as much a continuous plot
in history, through the action of successive generations on
each other, as a synchronous system of equilibrium at each
moment of history. It is therefore legitimate to adopt
statistical language and to speak of " society " as a coherent
whole (in the same way as a Gestalt is the resultant of a statis-
tical system of relations). But it is essential to remembe^
the statistical nature of statements in sociological language;!
since to forget this would be to attribute a mythol
156
SOCIAL FACTORS IN INTELLECTUAL DEVELOPMENT
sense to the words. In the sociology of thought it might
even be asked whether it would not be better to replace the
usual global language by an enumeration of the types of '
relation involved (types which, needless to say, are likewise
statistical).
When we are concerned with psychology, on the other
hand, i.e. when the unit of reference is the individual modified
by social relations, rather than the complex or complexes of
relations as such, it becomes quite wrong to content oneself
with statistical terms, since these are too general. The
" effect of social life " is a concept which is just as vague as
that of " the effect of the physical environment " if it is
not described in detail. From birth to adult life, the human
being is subject, as nobody denies, to social pressures, but
these pressures are of extremely varied types and are subject
to a certain order of development. Just as the physical
environment is not imposed on developing intelligence all
at once or as a single entity, but in such a way that acquisi-
tions can be followed step by step as a function of experience,
and especially as a function of the kinds of assimilation or
accommodation varying greatly according to mental
l eve l that govern these acquisitions, so the social environ-
ment gives rise to interactions between the developing
individual and his fellow, interactions that differ greatly
from one another and succeed one another according to
definite laws. These types of interaction and these laws
of succession are what the psychologist must carefully
establish, lest he simplify the task to the extent of giving
it up in favour of the problems of sociology. Now there is no
longer any reason for conflict between this science and
psychology once one recognises the extent to which the
structure of the individual is modified by these interactions ;
both of these two disciplines, therefore, stand to gain by
an investigation that goes beyond a global analysis and
undertakes to analyse relations.
THE SOCIALIZATION OF INDIVIDUAL INTELLIGENCE
The interaction with his social environment in which the
individual indulges varies widely in nature according to li|S
,58 THE DEVELOPMENT OF THOUGHT
evel of development, and consequently in its turn it modifies
the individual's mental structure in an equally varied manner.
During the sensori-motor period the infant is, of course,
already subject to manifold social influences ; people afford
him the greatest pleasures known to his limited experience
from food to the warmth of the affection which surrounds
him people gather round him, smile at him, amuse him,
calm him ; they inculcate habits and regular courses of
conduct linked to signals and words ; some behaviour is
already forbidden and he is scolded. In short, seen from
without, the infant is in the midst of a multitude of relations
which forerun the signs, values and rules of subsequent
social life. But from the point of view of the subject himself,
the social environment is still not essentially distinct from
the physical environment, at least up to the fifth of the
stages of sensori-motor intelligence that we have distin-
guished (Chap. IV). The signs that are used to affect him
are, as far as he is concerned, only indices or signals. The
rules imposed on him are not yet obligations of conscience
and he confuses them with the regularity characteristic of
habit. As for people, they are seen as pictures like all the
pictures which constitute reality, but they are particularly
active, unpredictable and the source of the most intense
feelings. The infant reacts to them in the same way as to
objects, namely with gestures that happen to cause them to
continue interesting actions, and with various cries, but
there is still as yet no interchange of thought, since at this
level the child does not know thought ; nor, consequently,
is there any profound modification of intellectual structures
by the social life surrounding him. 1
With the acquisition of language, however, i.e. with the
advent of the symbolic and intuitive periods, new social
relations appear which enrich and transform the individual's
thought. But in this context three points should be noted.
In the first place, the system of collective signs does not
create the symbolic function, but naturally develops it to
the affective point of view, it is no doubt only at the stage
at which the notion of an object is formed that there is a projection of
affectivity on to people conceived as similar centres of independent action.
SOCIAL FACTORS IN INTELLECTUAL DEVELOPMENT 159
a degree that the Individual by himself would never know.
Nevertheless, the sign as such, conventional (arbitrary) and
ready-made, is not an adequate medium of expression for the
young child's thought ; he is not satisfied with speaking, he
must needs " play out " what he thinks and symbolize his
ideas by means of gestures or objects, and represent things by
imitation, drawing and construction. In short, from the point
of view of expression itself, the child at the outset is still mid-
way between the use of the collective sign and that of the
individual symbol, both still being necessary, no doubt, but
the second being much more so in the child than in the adult.
In the second place, language conveys to the individual
an already prepared system of ideas, classifications, rela-
tions in short, an inexhaustible stock of concepts which
are reconstructed in each individual after the age-old
pattern which previously moulded earlier generations. But
it goes without saying that the child begins by borrowing
from this collection only as much as suits him, remaining
disdainfully ignorant of everything that exceeds his mental
level. And again, that which is borrowed is assimilated in
accordance with his intellectual structure ; a word intended
to carry a general concept at first engenders only a half-
individual, half-socialised pre-concept (the word " bird n
thus evokes the familiar canary, etc.).
There remain, in the third place, the actual relations that
the subject maintains with his fellow beings, i.e. " synchro-
nous " relations, as opposed to the " diachronic " processes
that influence the child's acquisition of language and the
modes of thought that are associated with it. Now these
synchronous relations are at first essential; when con-
versing with his family, the child will at every moment see
his thoughts approved or contradicted, and he will discover
a vast world of thought external to himself, which will
instruct or impress him in various ways. From the point
of view of intelligence (which is all that concerns us here), he
will therefore be led to an ever more intensive exchange of
intellectual values and will be forced to accept an ever-
increasing number of obligatory truths (ready-made ideas and
true norms of reasoning).
l6o THE DEVELOPMENT OF THOUGHT
But here again we must not exaggerate or confuse capaci-
ties for assimilation as they appear in intuitive thought with
the form they take at the operational level. In fact, as we
have seen in connection with the adaptation of thought to
the physical environment, intuitive thought, which is
dominant up to the end of early childhood (7 years), is
characterized by a disequilibrium, still unresolved, between
assimilation and accommodation. An intuitive relation
always results from a " centring " of thought depending on
one's own action, as opposed to a " grouping " of all the
relations involved ; thus the equivalence between two
series of objects is recognised only in relation to the act of
making them correspond, and is lost as soon as this action
is replaced by another. Intuitive thought, therefore,
always evinces a distorting egocentricity, since the relation
that is recognised is related to the subject's action and not
decentralised into an objective system. 1
Conversely, and precisely because intuitive thought is
from moment to moment " centred " on a given relation,
it is phenomenalistic and grasps only the perceptual appear-
ance of reality. It is therefore a prey to suggestion coming
from immediate experience, which it copies and imitates
instead of correcting. Now the reaction of intelligence at
this level to the social environment is exactly parallel to its
reaction to the physical environment, and this is self-
evident, since the two kinds of experience are indistinguish-
able in reality.
For one thing, however dependent he may be on surround-
ing intellectual influences, the young child assimilates them
in his own way. He reduces them to his point of view and
therefore distorts them without realizing it, simply because
he cannot yet distinguish his point of view from that of
others through failure to co-ordinate or " group " the points
of view. Thus, both on the social and on the physical plane,
be is egocentric through ignorance of his own subjectivity.
For example, he can show his right hand but confuses the
1 Wallon, who has criticised the concept of egocentricity, nevertheless
retains the phenomenon itself, as he neatly shows when he says that the
young child thinks in the optative and not in the indicative mood.
SOCIAL FACTORS IN INTELLECTUAL DEVELOPMENT l6l
right-left relationship in a partner facing him, since he
cannot see another point of view, either socially or geo-
metrically ; similarly, we have noted how, in problems of
perspective, he first attributes his own view of things to
others ; in questions involving time there are even cases
where a young child, while stating that his father is much
older than himself, believes him to have been born " after "
himself, since he cannot " remember " what he did before 1
In short, intuitive centralisation, as opposed to operational
decentralisation, is thus reinforced by an unconscious and
therefore all the more systematic primacy of his own point
of view. This intellectual egocentricity is in both cases
nothing more than a lack of co-ordination, a failure to
" group " relations with other individuals as well as with
other objects. There is nothing here that is not perfectly
natural ; the primacy of one's own point of view, like
intuitive centralisation in accordance with the subject's own
action, is merely the expression of an original failure to
differentiate, of an assimilation that distorts because it is
determined by the only point of view that is possible at
first. Actually, such a failure to differentiate is inevitable,
since the distinction between different points of view, as well
as their co-ordination, requires the activity of intelligence*
But, because the initial egocentricity results from a simple
lack -of differentiation between ego and alter, the subject
finds himself exposed during the very same period to all the
suggestions and constraints of his fellows, and he accommo-
dates himself without question, simply because he is not
conscious of the private nature of his viewpoint (it thus fre-
quently happens that young children do not realize that they
are imitating, and believe that they have originated the be-
haviour in question, just as they may attribute their own
private ideas to others). That is why the period of maximum
egocentricity in the course of development coincides with
the maximum pressure from the examples and opinions of
his fellows, and the combination of assimilation to the self
and accommodation to surrounding models is just as expli-
cable as that of the egocentricity and phenomenalism
characterizing the first intuition of physical relations.
l62 THE DEVELOPMENT OF THOUGHT
However, it is obvious that under these conditions (all
of which involve the absence of " grouping J> ) the coercions of
other people would not be enough to engender a logic in the
child's mind, even if the truths that they imposed were
rational in content ; repeating correct ideas, even if
one believes that they originate from oneself, is not the
same as reasoning correctly. On the contrary, in order to
teach others to reason logically it is indispensable that there
should be established between them and oneself those simul-
taneous relationships of differentiation and reciprocity which
characterize the co-ordination of viewpoints.
In short, at the pre-operational levels, extending from the
appearance of language to the age of about 7-8 years, the
structures associated with the beginnings of thought pre-
clude the formation of the co-operative social functions
which are indispensable for logic to be formed. Oscillating
between distorting egocentricity and passive acceptance of
intellectual suggestion, the child is, therefore, not yet
subject to a socialization of intelligence which could pro-
foundly modify its mechanism.
At the stage at which groupings of concrete operations and
particularly when those of formal operations are constructed,
on the other hand, the problem of the respective roles of
social interaction and individual structures in the develop-
ment of thought arises in all its acuteness. Genuine logic,
which is formed during these two periods, shows in fact
social characteristics of two kinds, and we have to decide
whether these result from the appearance of groupings or
whether they are the cause of them. On the one hand,
the more intuitions articulate themselves and end by
grouping themselves operationally, the more adept the child
becomes at co-operation, a social relationship which is quite
distinct from coercion in that it involves a reciprocity
between individuals who know how to differentiate their
viewpoints. As far as intelligence is concerned, co-operation
is thus an objectively conducted discussion (out of which
arises internalized discussion, i.e. deliberation or reflection),
collaboration in work, exchange of ideas, mutual control
(the origin of the need *f or verification and demonstration),
SOCIAL FACTORS IN INTELLECTUAL DEVELOPMENT 163
etc. It is therefore clear that co-operation is the first of a
series of forms of behaviour which are important for the
constitution and development of logic. On the other hand,
from the psychological point of view which is our point of
view here logic itself does not consist solely of a system of
free operations ; it expresses itself as a complex of states of
awareness, intellectual feelings and responses, all of which are
characterized by certain obligations whose social character is
difficult to deny, be it primary or derived. Considered from
this angle, logic requires common rules or norms ; it is a
morality of thinking imposed and sanctioned by others^
Thus, the obligation not to contradict oneself is not simply
a conditional necessity (a " hypothetical imperative ") for
anybody who accepts the exigencies of operational activity ;
it is also a moral " categorical " imperative, inasmuch as it
is indispensable for intellectual interaction and co-operation.
And, indeed, the child first seeks to avoid contradicting
himself when he is in the presence of others. In the same
way, objectively, the need for verification, the need for
words and ideas to keep their meaning constant, etc. are as
much social obligations as conditions of operational thought.
One question now arises which is inescapable : is the
" grouping " the cause or the effect of co-operation ?
Grouping is a co-ordination of operations, i.e. of actions
accessible to the individual. Co-operation is a co-ordination
of viewpoints or of actions emanating from different indi-
viduals. Their affinity is thus obvious, but does operational
development within the individual enable him to co-operate
with others, or does external co-operation, later internalized
in the individual, compel him to group his actions in opera-
tional systems ?
OPERATIONAL " GROUPINGS " AND CO-OPERATION
To such a question there must of course be two distinct
and complementary answers. One is that without inter-
change of thought and co-operation with others the indi-
vidual would never come to group his operations into a
coherent whole : in this sense, therefore, operational
grouping presupposes social life. But, on the other hand,
164 THE DEVELOPMENT OF THOUGHT
actual exchanges of thought obey a law of equilibrium which
again could only be an operational grouping, since to co-
operate is also to co-ordinate operations. The grouping is
therefore a form of equilibrium of inter-individual actions
as well as of individual actions, and it thus regains its
autonomy at the very core of social life.
It is in fact very difficult to understand how the individual
would come to group his operations in any precise manner,
and consequently to change his intuitive representations
into transitive, reversible, identical and associative opera-
tions, without interchange of thought. The grouping
consists essentially in a freeing of the individual's percep-
tions and spontaneous intuitions from the egocentric view-
point, in order to construct a system of relations such that
one can pass from one term or relation to another belonging
to any viewpoint. The grouping is therefore by its very
nature a co-ordination of viewpoints and, in effect, that
means a co-ordination between observers, and therefore a
form of co-operation between several individuals.
Let us suppose, however, with common sense, that a
superior individual, by ceaselessly shifting his viewpoints,
manages all by himself to co-ordinate them with one
another so that their grouping is assured. But how could
a single individual, even if he were endowed with sufficient
experience, manage to recall his previous viewpoints, i.e. all
the relations he has perceived at one time or another but
which he no longer perceives ? If he were capable of this,
he must have succeeded in establishing a kind of interaction
between his various successive states, i.e. he has built up,
by continual agreement with himself, a system of notation
which could consolidate his memories and translate them
into a representative language ; he would then have achieved
a " society " between his different " selves " 1 In fact, it is
precisely by a constant interchange of thought with others
that we are able to decentralise ourselves in this way, to
co-ordinate internally relations deriving from different view-
points. In particular, it is very difficult to see how concepts
could conserve their permanent meanings and their defini-
tions were it not for co-operation ; the very reversibility of
SOCIAL FACTORS IN INTELLECTUAL DEVELOPMENT 165
thought is thus bound up with a collective conservation
without which individual thought would have only an
infinitely more restricted mobility at its disposal.
But, granting all this and admitting that logical thought
is necessarily social, the fact remains that the laws of
grouping constitute general forms of equilibrium which
express both the equilibrium of inter-individual interaction
and that of the operations of which every socialized indi-
vidual is capable when he reasons internally in terms of his
most personal and original ideas. To say that an individual
arrives at logic only through co-operation thus simply
amounts to asserting that the equilibrium of his operations
is dependent on an infinite capacity for interaction with
other people and therefore on a complete reciprocity. But
this statement contains nothing that is not obvious, since
the grouping within him is already nothing more nor less
than a system of reciprocities.
Moreover, if we enquire what an interaction of thought
between individuals is, we find that it consists essentially
of systems of correspondences, and therefore of well-defined
"groupings"; to a certain relation established from A's
viewpoint there corresponds, after interaction, such and
such a relation from B's viewpoint, and a certain operation
executed by A corresponds (whether it be equivalent or
merely reciprocal) to a certain operation executed by B*
These correspondences are what, for each proposition
stated by A or B, determine the agreement (or, in the case
of non-correspondence, the disagreement) of the parties,
their obligation to conserve admitted propositions and the
lasting validity of the latter in the course of subsequent
interchanges. Intellectual interaction between individuals
is thus comparable to a vast game of chess, which is carried
on unremittingly and in such a way that each action carried
out with respect to a particular item involves a series of
equivalent or complementary actions on the part of the
opponent ; laws of grouping are nothing more or less than
the various rules ensuring the reciprocity of the players and
the consistency of their play.
More precisely, every grouping within individuals is a
l66 THE DEVELOPMENT OF THOUGHT
system of operations, and co-operation constitutes the system
of operations executed in common, i.e. co-operations, in the
true sense of the word.
It would be incorrect, however, to conclude that the laws
of grouping are superior both to co-operation and to indi-
vidual thought ; they only form, we repeat, laws of equi-
librium, and express merely the particular form of equilibrium
that is reached, on the one hand, when society no longer
exerts distorting constraints on the individual but inspires
and maintains the free play of his mental processes and,
on the other hand, when this free play of thought in each
individual no longer distorts that of other people and no
longer distorts objects, but has regard for the reciprocity
between different activities. Denned in this way, this form
of equilibrium could not be considered either as a result of
individual thought alone or as an exclusively social product ;
internal operational activity and external co-operation are
merely, taking these words in their most precise senses, two
complementary aspects of one and the same whole, since the
equilibrium of the one depends on that of the other. More-
over, since an equilibrium is never completely achieved in
practice, the ideal form which it would ultimately assume-
has to be imagined, and it is this ideal equilibrium that is
described axiomatically by logic. The logician, therefore,
works with the ideal (as opposed to the real) and is entitled
to confine himself to this, since the equilibrium with which
he deals is never fully achieved, and since it is constantly
projected still higher, as new actual constructions appear.
As for the sociologist and the psychologist, they can only
consult each other to ascertain how this equilibration is
realized in practice.
CONCLUSION
RHYTHMS, REGULATIONS AND GROUPINGS
INTELLIGENCE, viewed as , a whole, takes the form of a
structuring which impresses certain patterns on the inter-
action between the subject or subjects and near or distant
surrounding objects. Its originality resides essentially in
the nature of the patterns that it constructs to this effect.
Life itself is a " creator of patterns ", as Brachet has
remarked. 1 Certainly, these biological " patterns " are those
of the organism, of each of its organs and of the physical
interaction with the environment which they safeguard.
But in instinct, anatomico-physiological patterns are
paralleled by functional interactions, i.e. by " patterns " of
behaviour. In fact, instinct is only a functional extension
of the structure of organs ; the beak of a woodpecker finds
its extension in the pecking instinct, a digging paw in the
burrowing instinct, etc. Instinct is the logic of organs, and
that is how it arrives at responses which, if they were
realized at the level of genuine operations, would in many
cases imply a prodigious intelligence, although its " patterns"
may at first sight seem analogous (as in seeking for an object
outside the perceptual field and at various distances).
Habit and perception constitute other " patterns ", as
Gestalt theory has insisted, working out the laws of their
organization. Intuitive thought reveals still others. As
for operational intelligence, this, as we have repeatedly
seen, is characterized by mobile and reversible " patterns "
which are constituted by groups or groupings.
If we wish to bring what we have learned from an analysis
of the operations of intelligence into line with the biological
1 And, from this point of view, the assimilatory schemata which control the
development of intelligence are comparable to the "organizers'* which
intervene in embryological development.
167
l68 THE DEVELOPMENT OF THOUGHT
considerations with which we started (Chap. I), we have to
end by seeing operational structures in their relation to the
mass of possible " patterns ". Now, an operational act may,
in its content, closely resemble an intuitive act, a senSori-
motor or perceptual act and even an instinctive act ; a
geometrical figure may thus be the product of a logical
construction, a pre-operational intuition, a perception, an
automatic habit and even a building instinct. The difference
between the various levels does not, therefore, depend on the
content, i.e. on a " pattern " somehow materialized, which
results from the act, 1 but on the " pattern " of the act
itself and of its progressive organization. In the case of
reflective thought which has attained an equilibrium, this
pattern consists of a certain " grouping " of operations. In
the continuum of cases between perception and intuitive
thought, the pattern of the response is that of an adjustmen-
occurring at various speeds (sometimes almost instant
taneously), but always functioning by " regulations ". In
the case of instinctive or reflex behaviour, we are con-
fronted with a framework which is relatively complete, rigid,
and self-contained and which functions by periodic repe-
titions or " rhythms ". The order of succession of the
fundamental structures or " patterns " concerned in the
development of intelligence would thus be : rhythms,
regulations, groupings.
The organic or instinctive needs which motivate elemen-
tary behaviour are in fact periodic and therefore follow a
rhythmic structure : hunger, thirst, sexual appetite, etc.
As regards the reflex frameworks which allow of their satis-
faction and constitute the underlying structure of mental
life, we now know well enough that they form complex
systems and do not result from an additive combination of
elementary reactions ; the locomotion of a biped and, even
more so, of a quadruped (the organization of which, according
to Graham Brown, evinces an overall rhythm which domi-
nates and even precedes differentiated reflexes), the
ilt is to be noted that this external pattern is precisely what the Gestalt
theory has especially insisted on, which was bound to induce an undue
neglect of genetic construction.
RHYTHMS, REGULATIONS AND GROUPINGS 169
exceedingly complex reflexes which govern sucking in the
neonate, etc. and even the impulsive movements which
characterize the infant's behaviour, show a way of function-
ing whose rhythmical form is obvious. The instinctive
behaviour, often highly specialized, of animals also consists
of a well defined chain of responses, which take the form of a
definite rhythm, since they are repeated periodically at
constant intervals. Rhythm, therefore, characterizes the
functions that are at the junction between organic and
mental life, and this is so universally true that even in the
field of elementary perception or sensation the measurement
of sensitivity reveals the existence of primitive rhythms
which completely elude the subject's awareness ; rhythm
is likewise at the root of all effector functions including those
that constitute motor habit.
Now, rhythm shows a structure which must be borne in
mind if we are to see intelligence in its relation to the mass
of living ''patterns'', for it involves a way of linking elements
together which already heralds in an elementary form what
will appear as the reversibility characteristic of the
higher mental processes. Whether we are concerned with
particular reflex facilitations and inhibitions or, more
generally, with a succession of responses in alternating
and opposite directions, the rhythm schema always involves,
in one way or another, the alternation of two antagonistic
processes, the one functioning in the direction A-B and the
other in the opposite direction B-A. It is true that IB a
system of perceptual regulations, whether intuitive or re-
lating to responses co-ordinated according to experience,
there also exist processes which are orientated in opposite
directions ; but they follow each other irregularly and m
relation to " displacements of equilibrium " occasioned by
a new external situation. The antagonistic responses of
rhythm, on the other hand, are governed by the actual
internal (and hereditary) framework, and consequently
manifest a regularity which is much more rigid and self-
sufficient. * There is an even greater difference between
rhythm and the " converse operations " characteriziiJg
intelligent reversibility, which are intentional and
I7O THE DEVELOPMENT OF THOUGHT
ated with the infinitely mobile combinations of the
" grouping ".
Hereditary rhythm thus ensures a certain conservation
of responses which in no way precludes their being complex
or comparatively flexible (the rigidity of instincts has been
exaggerated). But, in so far as one is confined to innate
mechanisms, this conservation of periodic schemata evinces
a systematic lack of differentiation between the assimilation
of objects to the subject's activity and the accommodation
of the latter to possible changes in the external situation.
In the case of learning by experience, however, accommo-
dation is differentiated and, as this process progresses,
elementary rhythms are integrated into vaster systems
which no longer show any regular periodicity. On the
other hand, a second fundamental structure now appears
which continues the work of the original periodicity and
consists of regulations 1 ; these we have encountered from
perception right up to pre-operational intuitions. A per-
ception, for example, always constitutes a complex system
of relations and may thus be considered as the momentary
form of equilibrium reached by a multitude of elemental
sensory rhythms which combine or conflict in various ways.
This system tends to be conserved as a totality as long as
external phenomena remain unchanged, but, once they are
modified, accommodation to new phenomena involves a
" displacement of equilibrium ". But these displacements
are not uncontrolled and the equilibrium that is re-established
by assimilation to previous perceptual schemata shows a
tendency to react in the opposite direction to that of the
external change. 2 There is therefore regulation, i.e. the
occurrence of antagonistic processes comparable to those
already manifest in periodic responses, but here the pheno-
menon occurs on a larger scale, which is much more complex
and far-reaching and does not necessarily show periodicity.
The structure characterized by the existence of regulations
is not peculiar to perception. It occurs also in the " correc-
1 We refer here, of course, to structural regulations and not to the
dynamic regulations which, according to Janet, etc., characterize affective
life at these same levels.
2 E.g. see Delbceuf's illusion quoted on p. 67.
RHYTHMS, REGULATIONS AND GROUPINGS 17!
tions " belonging to motor learning. The whole of sensori-
motor development in general, up to and including the
various levels of sensori-motor intelligence, reveals analogous
systems. Only in one special case, namely that of true
displacements with reversals and detours, does the system
tend to reach reversibility and so herald the grouping, but
with the restrictions that we have seen. In most cases, on
the other hand, a regulation, while moderating and correcting
disturbing modifications and therefore working in the
opposite direction to earlier changes, does not attain com-
plete reversibility for lack of a complete adjustment between
assimilation and accommodation.
When thought begins to appear, intuitive centralisations
and the egocentricity of successively constructed relations
restrict thought to its irreversible state, as has been seen
(Chap. V) in connection with non-conservation. Intuitive
changes, therefore, are only " compensated " by a system of
regulations which, in the course of the internal trial-and-error
of representation, gradually harmonize mental assimilation
and accommodation and monopolize the control of non-
operational thought.
Now it is easy to see that these regulations themselves,
whose various types extend from elementary habits and
perceptions to the threshold of operations, grow out of the
original " rhythms " without any real discontinuity. We
should, first of all, remember that the first acquisitions to
follow the exercise of hereditary connections also present
a form of rhythm ; the " circular reactions ", which are the
first actively acquired habits, consist of repetitions with a
clearly visible periodicity. Perceptual estimations of sizes
or complex shapes (and not only those of absolute intensity)
again reveal the existence of a continuous oscillation about
a definite point of equilibrium. Similarly, it may be
assumed that components analogous to those determining
the alternating and antagonistic phases of rhythm (A-B and
B-A) also occur in a complex system subject to regulations,
but they then appear simultaneously and in momentary
equilibrium with each other, instead of each alternately
coming to the fore ; that is why, when this equilibrium is
172 THE DEVELOPMENT OF THOUGHT
changed, there is a " displacement of equilibrium " and the
appearance of a tendency to resist external modifications,
i.e. to moderate the change which is undergone (as physicists
say in connection with the well-known mechanism described
by Le Chatelier). It may therefore be understood that
when components of action constitute complex static
systems, responses orientated in opposite directions (whose
alternation formerly brought about the distinct and suc-
cessive phases of rhythm) are synchronized and represent
the elements of the system's equilibrium. In the event of
external changes, the equilibrium is upset through the
accentuation of one of the tendencies involved, but this
accentuation is sooner or later checked by the intervention
of the opposite tendency ; this reversal of direction is then
what is meant by regulation.
We now understand the nature of the reversibility
characteristic of operational intelligence, and the way in
which the converse operations of grouping derive from
regulations, and not only intuitive but even sensori-motor
and perceptual regulations. Reflex rhythms are not rever-
sible as wholes but are orientated in a definite direction ;
execution of a movement (or a complex of movements), the
termination and a return to the point of origin in order to
repeat it in the same direction such are its successive
phases, and if the return (or antagonistic) phase reverses the
original movements, this is not a case of a second action
having the same v^lue as the positive phase, but a retraction
leading to a new beginning in the same direction. Neverthe-
less, the antagonistic phase of rhythm marks the beginnings
of regulations and, beyond this, of the" converse operations "
of intelligence, and so all rhythm can be regarded as a system
of alternating regulations combined into a single unit of "suc-
cessive elements. As for regulation, which would thus consti-
tute the product of a complex rhythm whose components
ftavfc become simultaneous, this characterizes behaviour
wtucfa is still irreversible but whose reversibility is an advance
on preyious behaviour. Even at the perceptual level, the
reversal of an illusion implies that a relation (e.g. of similarity)
outweighs the opposite relation (difference) after a certain
RHYTHMS, REGULATIONS AND GROUPINGS 173
degree of exaggeration of the latter, and vice versa. In the
field of intuitive thought this is even clearer ; the relation
neglected by the centring of attention when it concentrates
on another relation dominates the latter in its turn when the
error exceeds certain limits. Decentralisation, which is the
source of regulation, leads in this case to an intuitive equiva-
lent of converse operations, especially when anticipations
and representative reconstructions increase its range and
make it almost instantaneous, which occurs more and more
when the level of " articulated intuitions " is reached
(Chap. V). Regulation has thus only to achieve complete
compensations (towards which, in fact, articulated intuitions
tend) for the operation to appear by this very fact ; operations
are, indeed, merely a system of co-ordinated changes which
have become reversible regardless of how they are built up.
So, in the most concrete and precise sense, it is possible to
regard the operational groupings of intelligence as the final
" pattern " of equilibrium towards which sensori-motor and
representative functions tend in the course of their develop-
ment, and this conception enables us to understand the
fundamental functional unity of mental growth, while at the
same time we may note the essential differences between the
structures characterizing successive levels. Once complete
reversibility has been attained which is the limit of a
continuous process, but a limit with quite different properties
from those of previous phases, since it marks the advent of
equilibrium the aggregates which were hitherto rigid have
become capable of a flexibility of composition which secures
, their stability since then, whatever operations are executed,
accommodation to experience is in permanent equilibrium
with assimilation, which is promoted by this very fact to
the rank of a necessary deduction.
Rhythm, regulations and "grouping" thus constitute
the three phases of the developmental mechanism which
connects intelligence with the morphogenetic potentialities
of life itself, and enables it to realize adaptations which are
both unlimited and mutually equilibrated, adaptations
which are impossible to realize at the org^mlc level.
SHORT BIBLIOGRAPHY
CHAPTER I
BUHLER, K. Die Krise der Psychologie, Jena (Fischer),
2nd ed., 1929.
CLAPAREDE, ED., "La Psychologic de Intelligence ",
Scientia (1917), vol. 22, pp. 253-268.
KOHLER, W., Gestalt Psychology, London, 1929.
LEWIN, K., Principles of Topological Psychology, London,
(McGraw-Hill), 1935.
MONTPELLIER, G. de, Conduites intettigentes et psychisme
chez I' animal et chez I'homme, Louvain and Paris (Vrin),
1946.
CHAPTER II
BINET, A., Etude experimental de V Intelligence, Paris
(Schleicher), 1903.
BURLOUD, A., La Pensee d'apres les recherches experimental
de Watt] de Messer et de *Buhler, Paris (Alcan), 1927
(includes references for these three writers).
DELACROIX, H., " La Psychologie de la raison" (in) Traite
de Psychologie by Dumas, 2nd ed. vol. i, pp. 198-305
Paris (Alcan), 1936.
LINDWORSKY, I., Das Schlussfolgernde Denken t Freiburg-im-
Breisgau, 1916.
PIAGET, J., classes, relations et nombres. Essai sur les
ft Groitpements " de la logistique et la reversibilite de la
pmsie, Paris (Vrin), 1942.
SELZ, 0., Zur Psychologie des produktiven Denkens und des
Irrtums, Bonn, 1924,
174
SHORT BIBLIOGRAPHY 175
CHAPTER III
DUNCKER, K., Zur Psychologic des produkiiven Denkens,
Berlin, 1935.
GUILLAUME, P., La Psychologic de la forme, Paris
(Flammarion), 1936.
KOHLER, W., The Mentality of Apes, London, 1924,
PIAGET, J., and LAMBERCIER, M., " Recherches sur le
developpement des perceptions/' / to VIII, Archives
de Psychologic, Geneva, 1943-1946.
WERTHEIMER, M,, Uber Schlussprozesse im produktiven
Denken, Berlin, 1920.
CHAPTER IV
CLAPAREDE, Ed., " La Genese de 1'hypo these ", Archives de
Psychologic (Geneva), 1934.
GUILLAUME, P., La Formation des habitudes, Paris (Alcan),
1936.
HULL, C. L., Principles of Behavior, New York, 1943.
KRECHEVSKY, L, "The Docile Nature of Hypotheses",
/. Comp. Psychol, 1933, vol. 15, pp. 4 2 5-443-
PIAGET, J., La Naissance dc V intelligence chez V enfant
Neuchatel (Delachaux et Niestle), 1936.
PIAGET, J., La Construction du reel chez V enfant, ibid., 1937.
SPEARMAN, C., The Nature of Intelligence, London, 1923.
THORNDIKE, E. L., The Fundamentals of Learning, New York
(Teacher's College), 1932.
TOLMAN, E. C., " A Behavioristic Theory of Ideas ", PsychoL
" Rev., vol. 33, pp. 352-369.
CHAPTERS V AND VI
BUHLER, C., From Birth to Maturity, London, 1935.
BUHLER, C., Mental Development of the Child, London (Kegan
Paul), 1933.
176 SHORT BIBLIOGRAPHY
INHELDER, B., Le Diagnostic du raisonnement chez Us
d&ites mentaux, Neuchatel (Delachaux et NiestI6),
1944.
JANET, P., U Intelligence avant le langage, Paris (Flammarion),
I935-
JANET, P., Les D Shuts de V intelligence, ibid. 1936.
PIAGET J., La Formation du symbole chez I* enfant, Neuchatel
(Delachaux and Niestte), 1945.
PIAGET, J., Les Notions de mouvement et de vitesse chez
I' enfant, Paris (Univ. Press), 1946.
PIAGET, J., and SZEMINSKA, A., La Gen&se du nombre chez
V enfant, Neuchatel (Delachaux et Niestle), 1941.
PIAGET, J. and INHELDER, B., Le D&ueloppement des
quantiUs chez Venfant, ibid. 1941.
REY, A., L' Intelligence pratique chez I' enfant, Paris
(Flammarion), 1942.
REY, A., L'Origine de la Pensie chez Venfant, Paris (Univ.
Press), 1945.
INDEX OF SUBJECTS
Abstraction . . -45
Accommodation 8-9, 15, 103,
105, 142-3, 150, 173
Action,
Primary and Secondary , 4
Adaptation, definition . 7-8
Adaptations, responses as . 4
Adolescence . . .148
Adualistic universe . . 114
Affect and cognition, rela-
tions . . . .4-6
Age, and perceptual develop-
ment . . . .80-1
Age, mental . . I53&
Aha-Erlebnis . . 10, 105
Anticipations . . . 79
Aphasia . . .126
Apprehension of experience . 1 6
Apriorism .13, 14, 88
Assimilation 7-8, 16, 85, 88, 92,
93* 97-9* looff., 111-13, 125,
142*3, 150, 173
Association . . .96
Associationism . . 88, 90-1
Associativity 41, 65, 69, 98, 112,
115, 138, 142
Asymmetrical relations . 144
Attention . . .131
Attitudes . . .79
Awareness of relations . 95
Axiometric method . . 27-9
Behaviour . . .119
Behaviour, aspects of . 4
Behaviour, structuring of . 5
Bewusstheit 23
Biology, intelligence and 11-12
Biology, relation to psycho-
logy .... 3
Centralization 72-3, 79, 81, 113,
130
Centralization, relative 73, 74-5,
So
Chance, and irreversibility . 78
Changes, uncompensated 68-70
Circular reaction 101, 104, 109,
113* 171
Classes . . . 33-4, 35
Classes, formation of 43, 127,
130, 132-3* H4-5
Classes, multiplication of . 45
Coalescence, law of . 96, 97
Cognition, and affect, rela-
tions .... 4
Cognitive functions . . 6
Collective objects . , 55
Combinativity 42, 43, 76, 82,
112, 119, 142
Comparisons . . .81
Conditioned responses 91, 96
Configuration theory 53, 56fL ;
see also Gestalt
Configurational psychology 5,
15 ; see also Gestalt
Conservation 42, 54, 79, 108,
.130, 140
Constancy, perceptual, 54-5-, 58,
61-3, 67, So, 81-2, io8f.
Contradiction, principle of . 30
Conventionalism . . 13
Co-operation . * 1626;
Co-ordination 40, 101, 102, 104,
109, no, 119-20
Correspondences . . 143
Decentralization 65, 72, 76^ Si,
114, 115, 122-3, 130, 173
Definitions by use . 103
Delboeuf's illusion 67-8, 70-1,
72, 74, 80, 17011.
177
INDEX OF SUBJECTS
Denkpsychologie 14, 21, 25-7, 29,
31
Differentiations . . 152
Displacements, group of 112,
113, 116, 119, 120, 152
Duration .... 145
Eduction . . .16, 45, 93
Effect, law of . . 94, 98
Egocentricity 73, 113-15, 122,
160-1
Einslcht ... .60
Einstettung . . 79, 83
Emergence . . 12-13
Empiricism . . 13, 1 6
Empiricism, associationist 60, 64
Equilibrium 4, 6-8, 39-40, 57-8,
66, 119, I4i,-i66, 170
Equilibrium, conditions of 4off.
Equilibrium, displacements
of .... 70-1
Error of the standard 62, 71-2,
80-1
Evolution . . 12-14
Experience . . 60, 63
Experiment, mental 34-5, 92-3,
128, 134
False ideas . . 19, 21
Feelings, constituents of . 5
Field, total . . .5,61
Fields, perceptual . 56-7, 60
"g" factor . . .154
Generalization 98, 100, 102, 103,
107
Geometrical illusions . 67-70
Gestalt . . .15, 16, 97
Gestalt theory 24, 55, 56-66, 67,
79-80, 88, 105, 112
Gestalten, genesis of . . 63-4
Gestalten, physical 61, 63, 64
Gestaltkreis . . - 55
Gestaltqualitdten . . 55
Groupings 36-7, 375., 53, 54, 59,
67, 82, 112, 115, 119, 120,
122, I4orf., 1635., 172-3
Groupings, classification . 425.
Habit . . 10, 87^., 150
Harmony, pre-established 12, 14
Hypothesis, genesis of the
94.95
Identification . . .140
Identity 41-2, 112, 115, 140, 142
Illusions . . 54, 67^., 90
Illusion, primary and
secondary . . . 80-1
Image and thought . . 25
Imageless thought . . 22
Imagery .... 126
Images, enacted . .107
Imitation, delayed . 1 06, 126
Imitation, development of 125-6
Implication . . 95*7
Indices .... 124
Inference, unconscious 54, 89
Instinct . . . .167
Intelligence, adaptive nature
of ... 7-9
Intelligence, definition 9-11, 53
Intelligence, dual nature . 3
Intelligence-faculty . . 14
Intelligence, Gestalt theory
and . . . 56ff., 59
Intelligence, interpretations
of, classified . . . nff.
Intelligence, nature of . 6-7
Intelligence, practical and
deliberate . . - 95
Intelligence, preconceptual 127
Intelligence, reflective . 123
Intelligence, relations with
perception 535., 675., 78ff.,
99, 107
Intelligence, reversibility 10-11
Intelligence scale . . 153
Intelligence, stages of act
of .... 94
Intelligence, sub-cortical . 90
Interaction of thought . 165
Interactionism . . . 13
Introspection . 22, 23, 25, 32
178
INDEX OF SUBJECTS
Intuition, articulated 132, 139,
140, 173
Invention. . , 105, 107
Irreversibility 68, 71, 77, 78, 85,
86, 90
Judgment . . .22-3
Knowledge . . .121
Kompkxeygansung . .26
Language 123, 125, 126, 159
Logic . . . .163
Logic, and thought . . 278.
Logic, formal . . 3, 145-6
Logic, relation to psycho-
logy .... 3
Logic, symbolic . . 29
Logical operations, nature
of ... .iSff.
Mathematics . . 20, 33
Meaning . . . .124
Meaning school . . 25
Means-end relation 89, 102, 103,
104
Miiller-Lyer's illusion. . 80
Multiplication, logical . 33-4
Mutationism . . 13
Names
Needs, organic
Numbers .
. 124
. 168
143-4
Ob j ec t , schema of the . i o jft .
Operational theory . 16, 17
Operations 19, 32ff., 54, 1238.
Operations, concrete 123, I39ff.
Operations, formal . 147*!
Operations, infra-logical . 46-7
Oppel's illusion . , 80
Oppelkundt's illusion . 7-23
Organisation, laws of 57-8, 60,
61
Participations . . 127, 128
Patterns . . . .167
Perception, and centring
activity . . .79
Perception, and motor
activity . . .87
Perception, and thought . 119
Perception, definition . 53
Perception, developmental
changes in . . 63, 80
Perception, relations with
intelligence 535., 67^,, 78!?.,
99, 107
Phenomenology 13, 15
Play, symbolic . 106, 125-7
Pragmatism . . . 13
Prdgnanz . . 15, 57
Pre-concepts . . 127, 128
Preformism . . .12
Realism . . . *3
Reasoning, formal and pro-
positional . . . 148
Recentring . . -65
Reciprocity . . -44
Recognition . . . 108
Reconstitutions, perceptual. 79
Reflection, transition to .121
Reflex-arc schema . . 87
Reflexes . . . 100, 108
Regulations 67, 71, 81, 112, 129,
138, 168, 170-3
Relations . . 67, 115
Relations, synchronous . 159
Relativism . . . 13
Relativity, of intelligence . 74-6
Relativity, perceptual . 73-6
Repetition . . -97
Representation . 1 06, 120
Responses, psychological . 4
Restructuring . 59-6o, 105
Reversibility 10-11, 40-1, 48,
65, 70, 77, 80, 85, 90, 102,
112,113, *3 8 141* 142, 172
Rhythm . . 168, 169, 170
179
INDEX OF
Sensations
Sensori-motor intelligence
59, 65-6, 85, 875., 119, i2off,,
55
Separations, horizontal and
vertical. . . 147-8
Seriation . 35, 44, 93, 134, 145
Signals . . . .124
Sign-gestalts . . .98
Significants and signifi-
cates . . . 124, 126
Signs . . i24fL, 158-9
Social life, and intelligence 1561!.
Space . . ii2ff., 145
Space, perceptual . .71-2
Speech, see Language.
Standard, Error of the, see
Error.
Statistical character of per-
ceptual structures . 78, 79
Structuring ... 5
Substance, conservation of . 109
Substitution . . -44
Superconstancies . . 82
Syllogism . 53, 59-60, 65
Symbols . . 1245., 158-9
Symmetry . . . 44-5
Tautology . . .42
Temporal order. . .145
Tests, intelligence . 153-4
Theory formation . .148
Thought, development of 119^.
Thought, formal . .123
SUBJECTS
Thought, intuitive 123, 1296*.,
151, 160
Thought, preconceptual 123$.
Thought, " pure " . -149
Thought, reflective . .148
Thought, symbolic . 123^.
" Thought psychology/' see
Denkpsyckologie.
Thresholds, differential 74-5, 78
Time .... 145
Time, intuitive . . 136
Transduction . 127, 128, 129
Transfers, associative . 92
Transitivity . 44, 84, 138, 143
Transportation . 81, 84, in
Transposition 57, 64, 84, 85, 99,
107, in
Trial and error 9, 16, 66, 88,
104-5
Umzentrierung
Universals
65
Valencies . .5
Viewpoints, co-ordination of 164
Vitalism . . .13, 88, 89
Weber's Law . 67, 74-5, 77
Whole, conservation of
the ... 146-7
Wholeness, perceptual . 68
Wholes, see Gestalt theory.
Will .... 5
180
INDEX OF NAMES
Adams, D. K. .
. 98
Gelb, A. .
. 61
Aristotle .
. 28
Goblot, E.
. 33n.
Auersperg, A. .
55, 79, 83
Goldsmith, M. .
. go
Goldstein, K. .
. 61
Baldwin, J. M. .
, 101, 114
Gonseth, F.
. 28
Benussi, V.
- 55
Groos, K.
. 125
Bergson, H,
. 24
Beyrl, F. .
61, 63
von Helmholtz, H
- 54> 55. 82, 89,
Binet, A. . 15,
21-2, 80, 153
90
Brachet, A.
. I6 7
Hering, E.
54-5, 56, 90
Bradley, F. H. .
. 25
Hilbert, D.
. 136
Brown, Graham
. 1 68
Hull, C. L.
. 98
Brunschvicg, L.
- 31
Husserl, E.
21
Brunswik, E. .
Biihler, C.
.61, 63, in
. 109
Inhelder, B.
. 154
Biihler, K. 9,
Buhrmester
Burt, C. .
Burzlaff, W. .
14, 22-4, 105
79, 83
. 146, 149
. 62
James, W.
Janet, P. .
Jennings, H. S.
96, 97
4, 5, 32, I 7 on.
94
Buytendijk, F. J.
. 89
Kohler, W. 10,
I5 59, 60, 61,
Carnap, R.
Cassirer, E.
20
. 54
Krechevsky, I.
65, 66, 98, 105
. 98
Chaslin, P.
34
Kiilpe, O. .
. 22
le Ch&telier, H. . .172
Claparede, E. 4, 5, 9, 10, 16, 25,
94> 95> 96, 97
Couturat, L. . .19
Cruikshank, R. M. . .61
Lamarck, J-B. P. A. de Monet,
chevalier de 12, 13, 1 6
Lambercier, M. .62, 71, 83
Lewin, K. ... 5
Lindworsky, I. . -24
Darwin, C.
. 12, i3n. , _
DashieU, J. F. .
9 g Mach, E. .
34, 92
Delacroix, H. .
25, 34, 88 Marbe > K -
.22, 23, 26
Demetriades, B.
g Meinong, A.
55
Dennis, W.
Descartes, R. .
9 g Messer, A.
2 - Meyerson, E.
. 22-3
. 140
Descoedres, A.
144 Meyerson, I.
. 25, I26n.
Duncker, K.
! 59 , 60, 66 Morris ' C - R '
I25n.
von Ehrenfels, C.
55 Pavlov, I. P.
. 96
Piron, H.
56, 90, 153
Frank, H. .
. 6 1 Poincar6, H.
112, 113, 119, 152
181
Rey, Andr6 . 37, 91-2, 137
Rignano, E. . .16, 34, 92
Russell, B. 14, 18-21, 29, 36, 6m.
Russell, E. S. . . 5> 61
Selz, O. . . 15, 23-7, 31, 37
Simon, T 153
Spearman, C. 16, 33, 36, 45, 93,
154
Stern, W. . . 9, 128
Szeminska, A. . . .129
INDEX OF NAMES
Thoradike, E. L.
Tolman, E. C.
Usnadze, G.
93
98-9
82, 83
Wallon, H. . . .160
Watt, H. J. . .22
von Weizsacker, V. .55, 79, 87
Wertheimer, M. 15, 53, 59, 65
Wittgenstein, L. . .20
Wundt, W. M. . . .25
182
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