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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 . 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 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' 
