The Competitiveness of Nations

in a Global Knowledge-Based Economy

Harry Hillman Chartrand

April 2002

Jean Piaget


  APA Homepage

Table of Contents

Section Index


IV - MEANINGS AND THEIR SYSTEMS                                                                             52

15. Biological signalling and semeiotic function                                                            53

16. Linguistic structures and logical structures                                                               55

17. The higher symbolisms                                                                                                    58

18. Diachronic and synchronic problems in relation to meanings                              60



Every structure or rule and every value has meanings, just as every system of signs has a structure and values.  Nevertheless, the relationship of signifiant to


signifié differs in kind from that of desirability (value) or the structural (or normative) subordination of one element to the whole to which it belongs.  And this relationship of meaning is again extremely general in scope, so that interdisciplinary problems are as important in this sphere as in the previous ones.


15. Biological signalling and semeiotic function

Reactions triggered by indices or signals are to be found at almost all levels of animal behaviour, ranging all the way from the simple sense-reaction of protoplasm in the unicellulars to the sense-reaction of the nervous system or its responses to meaningful messages.  Moreover this type of meaning, linked to signals or indices, is the only observable one in children until around 12 to 16 months (sensori-motor levels) and it remains at work in regard to perceptions and motor-conditioning throughout life.  It was therefore necessary to begin by recalling the role of this initial system of signalling. 35

Index is the name given to a signifiant which is not differentiated from its signifié (except by its signalling function), in that it constitutes a part, an aspect or a causal result of that signifié: a branch protruding over a wall is an index of the presence of a tree, and the tracks of a hare are the index of its recent passage.  A signal (like the sound of the bell which triggers the salivary reflex in Pavlov’s dog) is only an index, unless there is attached to it a conventional or social significance (telephone ringing, etc.), in which case it is a ‘sign’.

In some higher primates and in man (from the second year) there appears a set of signifiants which are differentiated from their signifiés in that they no longer simply belong to the designated object or event, but are produced by the subject (individual or collective) with a view to evoking or representing those signifies, even in the absence of any immediate perceptive stimulus on their part: such are symbols and signs, and semeiotic (or often, symbolic) function is the term given to that capacity of evocation by differentiated signifiants which then makes possible the construction of the image or thought.  But there are two levels still to be distinguished in these semeiotic instruments, although in the normal child they all appear more or less at the same time (except as a rule in drawing).

The first level is that of symbols, as the term is used by de Saussure in contradistinction to signs: these are the signifiants ‘motivated’ by a resemblance or some analogy with their signifies.  They appear in the child in completely spontaneous fashion with symbolic (or fictional) play, deferred imitation, the mental image (or interiorized imitation) and the graphic image.  The initial feature of these symbols is that the individual subject can construct them by himself, although their structuration usually coincides with language (except among the deaf and dumb who add a new term - gesture language - to the preceding series).  Their common source is imitation, which begins as early as the sensori-motor level, where it already constitutes a kind of representation, though only in actions, and then goes on to deferred or interiorized imitations, whence the preceding symbols.

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The second level characteristic of the semeiotic function (a level which, until we know more about it, would seem to be peculiar to the human species) is that of articulated language, of which the two new features as compared with the previous level are, firstly, that it implies social or educational transmission and thus depends upon the whole of society and no longer on individual reactions; and secondly that the verbal signifiants consist of ‘signs’ and no longer of symbols, the sign being conventional or ‘arbitrary’ as required by its collective nature.

The first major interdisciplinary questions which such a picture raises then are, firstly, to determine the common mechanisms and the antagonisms in and between various manifestations of the semeiotic function,- but going right back to the level of the significant indices and the currently known forms of animal language; and, secondly, to determine their connexion with the development of representation or thought in general, regardless of any possible or more particular relations between articulated language and logic.

The first of these demands collaboration between zoopsychology or ethology, genetic psychology, the psychopathology of aphasia, deaf-mutes, the blind, etc., and linguistics.  Ethology has already built up a fairly substantial body of material on the innate releasing mechanisms (IRM) which come into play at the instinctual level and on the releasing mechanisms acquired through learning.  Von Frisch’s well-known studies on the language of bees have evoked many reactions from psychologists and linguists (Benveniste), while Revesz has undertaken some systematic comparisons of the ‘languages’ of vertebrates and of man.  The general tendency is to regard animal language as being based not on systems of signs but on a ‘code of signals’ (Benveniste).  For one thing, there is neither dialogue nor the free composition of elements; for another, the signals used are essentially imitative or mimetic (though it has not yet been established whether there is already deferred imitation).  Such imitative mechanisms thus fall within the sensori-motor pattern, innate or acquired, and do not yet correspond to a conceptualization; whereas in human language not only does every word connote a concept, but the syntactical arrangement of the words itself conveys information.

It is therefore tempting to look for the source of thought itself in sign language, as indeed many psychologists and linguists believe.  But although the system of signs has undoubtedly one exceptional advantage on account of its constructive mobility and of the considerable number of meanings which it is capable of conveying, considerations of two kinds regarding the limits of its powers must be remembered.

The first is that although language is a necessary auxiliary to the fulfilment of thought insofar as the latter constitutes interiorized intelligence, it is nonetheless activated by intelligence, which precedes it in its sensori-motor form; this is a problem which we will consider again shortly in connexion with the relations between logic and language.  But it must be remembered that, however collective language may be (in its structures, findings, penalties, etc.), it is bound up in its functioning with individual intelligences outside of which its signifiants would have no signifies, and whose sensori-motor pattern itself creates a multi-



tude of meanings (space-time patterns, permanent objects, causality, etc.) which provide the sub-structure of verbal semantics.

Furthermore, the interiorization of the sensori-motor intelligence in image or thought is a matter not just of language but of the entire semeiotic function.  In this respect psycho-pathological data are of great interest and much is still awaited from co-operation between linguists, psychologists and neurologists.  Without going into the highly complex problem of aphasia, on which much work is still being done but which has so many neurological incidences that the language and thought factors cannot easily be isolated, it is interesting merely to note the case of children deaf-and-dumb, or blind, from birth, but otherwise normal.  Among the former there is, of course, some delay in the development of the intellectual operations as compared with children capable of speech, but the fundamental operations of classification, seriation, correspondence, etc., are not missing at all up to a certain level of complexity, which testifies to a pre-speech organization of those actions. 36  Among blind children, on the other hand, the delay appears to be greater because of the lack of a sensori-motor control during the formation of the action patterns, and although language makes good that lack to some extent, it is not enough to replace general co-ordinations and depend upon the latter while their build-up is necessarily retarded.


16. Linguistic structures and logical structures

The links between linguistics and logic are of unquestioned importance and are still in process of full development, particularly as they impact upon longstanding arguments between psychologists and sociologists.

This, it should first be noted, is no accident.  The convergence between the basic ideas of a linguistic doctrine like F. de Saussure’s and a sociological theory like Durkheim’s is quite remarkable: language is a collective ‘institution’ transmitted from the outside and imposing itself upon individuals; any innovations made by the latter must accord with common rules established before them, and their initiatives are subject to the approval of the linguistic group, which may reject or accept them, but in the latter case only because of needs related to the overall equilibrium of the system, etc.  Now Durkheim drew from his ideas on the social totality the conclusion that the rules of logic are imposed by the group upon the individual, in particular through language, the shaper of intelligences and the holder of structures which are imposed from childhood through education.

Current trends in social and cultural anthropology are moving in the same direction, and we all know how much the structuralism of Levi-Strauss has been influenced by Saussurian linguistics and by phonology (Troubetskoy and Jakobson), in that the system of meanings seems to him to throw light both on the economic exchanges of tribal societies and on the relations of kinship, the latter comprising a logic that is at one and the same time collective and a source of individual manipulations (hence his opposition to Lévy-Bruhl’s pre-logic which Durkheim also contested for similar reasons).

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But these trends in linguistic sociology have come up against a completely different tendency.  The vast logical positivism movement (developed by the ‘Vienna Circle’) has attempted, while reducing experimental truths to simple perceived facts, to make allowance for the logico-mathematical arrangement of knowledge, but without seeing in it a source of truth in a strict sense: it conceived of it, in the nominalist tradition, as mere language, while characterizing this linguistic status more precisely.  R. Carnap began by proposing that all logic should be reduced to a general syntax, which the natural languages would reflect with various degrees of faithfulness but the exact image of which would be supplied by the formalized language of modern symbolic logic.  Tarski, followed by Carnap, then showed the need for a general semantic system or meta-language designed to establish meanings; and finally Morris, though not with everyone’s support, proposed the constitution of a ‘pragmatic’ system, though purely in the sense of the establishment of the rules of such ‘languages’.

These concepts have been applauded by a number of linguists and in the Encyclopedia of Unified Sciences Bloomfield vigorously applauds the disappearance of the naïve idea that concepts must still be sought beneath the logical or mathematical liaisons: nothing exists except the observable, perceived fact and the system of signs, whether natural (current languages) or scientific, used to describe or connote it.

Yet this dual sociological and linguistic movement (whose unity through convergence is, however, still remarkable, despite the wide gap between the normative realism of Durkheim and the more or less conventional nominalism of the ‘logical empiricists’) is in fact being contested, and in senses that are again convergent but opposed to the previous ones, by a great deal of research now being conducted by psychologists, linguists and logicians.

On the psychological plane the author for years has been trying (and these studies are in full swing with the co-operation of linguists) to show that the sources of the logico-mathematical structures are to be sought at a deeper level than language, i.e. at the level of the general co-ordination of actions.  At the level of sensori-motor intelligence one finds indeed, in the make-up of the patterns of action and in the co-ordination of those patterns, structures of interlocking elements, of order correspondence, etc., which are already of a logical nature and which lie at the start of future thought operations.  Moreover, the operations themselves are more closely connected with the interiorization and regulating mechanisms than with the purely verbal influences.  It is not until we reach the higher levels that a logic of ‘propositions’ becomes possible in liaison with the handling of hypotheses enunciated verbally; whereas a whole period of ‘concrete’ operations, i.e. operations bearing directly upon the object, points to the lasting liaison between those operations and material action.

From the linguistic point of view it then becomes possible to carry out precise experiments on the correlations between the linguistic structure of the verbal expressions used by the child and the latter’s operational level; the results of those experiments tend to prove that the language employed is subordinate to the operational structures rather than vice-versa. 37

As regards that interminable ‘dialogue of the deaf’ between sociologists and


psychologists as to whether ‘universal’ logic, meaning applicable to all individuals, is superimposed on society or is only a product of it, the two opposing contentions are in fact out of date, in that although logic is concerned with the general co-ordination of action, that co-ordination is as much inter-individual as intra-individual: and indeed, the operations occurring in cognitive exchanges are found upon analysis to be the same as in individual constructions, so that the former are as much a source of the latter as vice versa, the two remaining inseparable by reason of their common biological roots.

On the other hand the linguists, while continuing their structuralist analyses and in particular while attempting to formalize them as precisely as possible in order to express the structural liaisons in a language based on algebraic and sometimes even on physical methods, were far from ending up with a simple logic, but discovered instead a series of structures sui generis and peculiar to sign systems as such.  This result is of two-fold interest, firstly because it shows how a system of signs differs from a system of intellectual norms of truths, and secondly because it brings up the problem of the relationship between the two.  And that relationship certainly exists, for while signs have their own laws, it is also their function, within the active range of the subjects of the language, to express meanings which are of a logical nature in varying degrees.  It was in this way that Hjelmslev, the linguist, came to propound the theory of a ‘sub-logical’ level where connexions are formed between logical and linguistic coordinations.  It would seem very likely that analysis of that sub-logic would bring us back to questions of co-ordination of action.

It must however be remembered, in particular, that linguistic structuralism, which was essentially static with F. de Saussure, has become dynamic since Z. Harris stressed the ‘creative’ aspect of language and since N. Chomsky discovered his ‘transformational grammar’, which makes it possible to derive from a ‘fixed kernel’, which he regards as innate, an indefinite number of terms in accordance with precise rules of transformation (and in conformity with a ‘monoïde’ ordinal and associative structure).  Now Chomsky attributes his ‘innate fixed kernel’ to reason itself, which is the complete reverse of the positivist position of the linguists (Bloomfield, etc.).  One can, of course, without in any way changing the purely linguistic aspects of Chomsky’s doctrine, query his innateness of reason, since the sensori-motor intelligence which precedes language is the end-product of a long structuration in which the hereditary factors (which play a part everywhere) are far from being the only ones involved; and H. Sinclair is currently trying to demonstrate that the constitution of the ‘monoide’ could be explained as the co-ordination of the sensori-motor patterns.  It is nonetheless true that, in the very sphere of linguistics, we have here a reversal of the subordination of logical structures to language, thus opening up a very broad field of experimental research to interdisciplinary collaboration (psycholinguistics, etc.) in the study of questions which have hitherto mainly been dealt with in a speculative fashion.

Furthermore, those logicians who, venturing beyond the problems of pure formalization, look into the question of the relations between logical structures and the activities of the subject, steer naturally in the direction of self-regulating

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systems capable of taking account of the self-correction proper to logical mechanisms.  Now cybernetics, which can supply such models, is a synthesis of the information or communication theories and of the guiding or regulatory theories.  It is thus on this two-fold plane that a more natural relationship than a simple and straightforward assimilation can be established between linguistics and logic.  On the one hand language is information, and various relationships are conceivable between the praxeological aspects of the codes and their logical structure.  It was along these lines that L. Apostel studied language as a system for the pre-correction of errors.  Again, logical operations constitute the extreme case of thought regulation, and there can be many intermediate stages, capable of influencing the language, between the weakest forms of such regulation and the strictest or operational forms.  It can thus be seen how interdisciplinary research, in this field also, is both necessary and promising.


17. The higher symbolisms

The general semeiology advocated by F. de Saussure provides, as we saw in section 15, for systematic comparisons between the sign systems and various symbolisms or signallings inferior in nature to articulated language.  But it also presupposes comparisons with what could be called symbolisms to the second power, or of a nature superior to language, that is to say using language but constituting ‘signifiants’ whose collective meanings are ideological and situated on a different scale from verbal semantics: such, for example, are the myths, folklore stories, etc., which are conveyed through language but each of which is itself a symbol with a religious or affective meaning conforming to very general semantic laws, as their surprising and frequently intercontinental dissemination shows.

However, the problem is not an easy one to master or even to set.  In a nominalistic conception of logic and mathematics, it could be said that any concept or particular structure is still a sign which symbolizes, together with but in addition to the words designating it, the objects to which it applies: thus the notion of a mathematical ‘group’ would merely be a higher symbol whose meaning would be reduced to the different displacements, physical states, etc., which can be described by it.  In the operative sense, on the other hand, the ‘group’ or any other logical or mathematical concept constitutes a system of actions impacting on the real, which are true actions even though interiorized and which would therefore have nothing symbolic in themselves, the symbolism coming in the arbitrary signs designating the operations but not in the operations as such.

If this latter interpretation is accepted, not all thought is necessarily symbolic, but symbolism reappears in all forms of thought whose value is linked not to its operative structure but to its affective content, conscious or unconscious: in such an interpretation there is nonetheless an immense field of human productions, with the more or less individual ‘symbolic thought’ studied by the psychoanalysts of different schools, the mythological and folklore symbols, the art


symbols and lastly perhaps certain forms of ideologies as they express momentary collective values and not rational structures (each of these manifestations, of course, being capable of ‘rationalization’ to some degree).  It can be seen that at these levels there is a substantial field of comparison open to a general semeiology and that the latter, inspired by linguistic methods, would be no less essentially interdisciplinary.

Freudian psychoanalysis, helped in this instance by Bleuler’s work on ‘autistic’ thought and followed by Jung’s dissident school, brought to light the existence of an individual ‘symbolic thought’ visible in dreams, in childrens’ play and in various pathological manifestations.  Its criterion is that whereas rational thought seeks adequation with the real, the function of symbolic thought is the direct satisfaction of desires through the subordination of representations to affectivity.  Freud began by explaining this unconscious symbolism as camouflage mechanisms due to repression, but later came round to the broader conception of Blueler who, with his ‘autism’, explained symbolism as a centring on the ego, and he pursued his research in the direction of art symbols.  Jung, on the other hand, quickly saw that this symbolism constituted a sort of affective language and, as a result of large-scale comparisons with mythologies, came to demonstrate the fairly universal nature of a great many symbols or ‘archetypes’ which he considered, without giving proof, as being hereditary, but which are very widespread - which is quite another thing.

The link thus established between the more or less subconscious symbolism which the psychoanalysts find in individuals and the mythological artistic symbolism (one recalls the typical example of the Oedipus myth and ‘complex’) is evidence that the laws of such a symbolism concern collective as much as psychological realities.  It therefore goes without saying that in the field of social and cultural anthropology the direct study of mythical representations provides a contribution of vital importance to this general semeiology at the level above language; and when Levi-Strauss, for example, conceives of it in Saussurian terms he thereby introduces into this vast and difficult field an indispensable methodology which was only too lacking in the analyses of Jung and Freud.

Nevertheless that is merely the beginning of the work, for obviously laws which are general at a certain scale of civilization must have some applications in societies which are familiar with scientific thought.  When K. Marx raised the problem of the opposition between economic and technical infrastructures and ideological superstructures, he brought up in doing so a considerable number of questions regarding the nature and functioning of the various possible types of ideological productions.  To show how necessary it is to raise these questions, it is worth recalling that one of the most determined adversaries of the Marxist doctrines, V. Pareto, brought into his sociology a distinction which was visibly based on them: for it was Pareto’s view that social behaviour patterns are governed by certain needs or affective invariants which he calls the ‘residues’; but these - and this is the only point which interests us - are in fact manifested not in naked or direct form but wrapped up in all manner of concepts, doctrines, etc., which Pareto calls ‘derivations’.  It is thus immediately apparent that these ‘derivations’ constitute an ideological superstructure, but one of an essentially

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symbolic nature since it comprises essential and constant affective meanings beneath a variable and secondary conceptual mechanism.

In this chapter, whose purpose is to seek out the common mechanisms and to stress the interdisciplinary problems from a methodological and, particularly, from a prospective point of view, mention must be made, because of its highly significant implications, of the research bearing upon the symbolic meaning of doctrines of intellectual form and affective content, since such research constitutes a striking meeting-point between the possible extensions of a general semeiology bearing upon higher-level symbolic systems and the sociological and even economic analysis of Marxian inspiration.  One remarkable example of such meeting-points has been supplied by L. Goldmann in his studies on Jansenism, and our reason for choosing this example is that it forms one of those somewhat rare cases in sociology where through theoretical research the existence of a hitherto unknown fact - in this particular case the discovery of an historical person but one overlooked by history - has been predicated.  Goldmann explained Jansenism by the social and economic difficulties of the noblesse de robe under Louis XIV: the complete withdrawal from the world preached by the doctrine was thus the symbolic manifestation of an affective and collective situation.  But pure Jansenism, as reconstituted through this analysis in terms of social symbolism, was not fully realised in any of the individuals known to history (Arnauld, etc.), and it was therefore necessary to build up the complete hypothetical Jansenist - unknown precisely because completely consistent - who had directed the movement without being seen outside.  Having thus ‘calculated’, so to speak, the existence of such a leader, Goldmann went on to find him in the person of the Abbé Barcos and proceeded to demonstrate his effective and until then unsuspected role in history.

One can thus see the number of literary, artistic and metaphysical productions which could emerge from such analyses, the syntactic and semantic aspects of which remain essential even though the most difficult to distinguish, and whose sociological and even economic aspects are obvious.


18. Diachronic and synchronic problems in relation to meanings

Comte’s sociology drew a distinction between static problems (‘order’) and dynamic ones (‘progress’), but the Saussurian linguistic system was probably the first to give a positive status to the relative opposition of synchronic and diachronic considerations in the human sciences.  The history of language and the etymology of words do not explain everything, since the meanings of words change, just as the function of biological organs may change, to meet the needs created by the balance of the language as it is at a particular point of time.

Now, systems of meanings as relations between the signifiant and the signifié occupy a special position in regard to the connexion between synchronic balance and diachronic transformations.  As we have seen (paragraph 9), the maximum dependence between these two aspects is to be found in the sphere of normative structures, because the evolution of norms - the operational


structures of the intelligence, for example - is a process of gradual equilibration: this being so, the nearer the structure under consideration is to its state of final closure (which, it should be added, in no wise excludes the possibility of its being subsequently integrated into new structures) the more closely, of course, does the synchronic balance depend upon this same self-regulating process.  We have seen an intermediate situation (section 14) in the case of values, whose dependence upon their history increases the more closely they are linked with structures (normative values) and the less nearly they correspond to the needs of a changing function.  As for the ‘signifiants’ that operate in systems of meaning, it is obvious that the more conventional or ‘arbitrary’ they are, the more subordinate to the needs of the moment and the more independent of the previous history they will be.  It is therefore in these situations that we find the minimum of relationship between present balance and diachrony.  This can be seen, for instance, in a system of artificial, technical signs such as mathematical language.  Fundamentally, the choice of signs such as A x B, AB or AB to express multiplication, or of any particular sign for other operations, depends only on the conventions of the time, and not on the history of symbols, which in any case comprises series of transformations that are explicable, but usually linked to the very overall balance of the system at each period under consideration; fidelity to the past may even be a disturbing factor rather than a useful one, if it hinders the reorganization of perspectives, which would on the contrary be facilitated by a new symbolism.

It is true that ‘signifiants’ can be divided, as F. de Saussure pointed out (and Peirce earlier, although his method of classification does not seem so logical) into motivated ‘symbols’ and arbitrary ‘signs’, and that there are transition series between the two.  The very notion of the arbitrary nature of the sign has given rise to discussion, by Jespersen in the past and by Jakobson today.  De Saussure, however, appears to have answered these objections before they were raised, by himself distinguishing between the ‘relatively arbitrary’ and the ‘radically arbitrary’.  Broadly speaking, it does seem to be true that the word used to designate a concept has not as close a relationship to it (relationship between the phonic subject and the meaning of the idea) as the concept has with its meaning and its content.  Even if the verbal signs are sometimes accompanied by symbolism (in the Saussunian sense of a relationship of resemblance or motivation between that which symbolizes and that which is symbolized) and even if, as far as the speaker is aware, there is nothing arbitrary about the word (as Benveniste has pointed out), it seems obvious that the multiplicity of languages bears witness to this conventional nature of the verbal sign.  Signs, moreover, are always social (explicit or implicit conventions originating in usage), whereas the symbol may have an individual origin, as in the symbolic games of children, or in dreams.

The problem raised by linguists of the relationship between synchronic and diachronic factors in the sphere of relations between structures and meanings is very broad in scope, and to study it may help us to understand various interdisciplinary questions, such as those of the interpretation - which may be linguistic or, on the other hand, operative and constructive - of logical and mathe-

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matical structures.  If we accept the nominalist hypothesis, according to which these structures are a mere language used to express experiential data, the relations between their syntax and their semantic should obey the general laws that govern their synchronic and diachronic relations.  And at first sight, this indeed appears to be the case: syntactical rules are continuous in time, while meanings vary.  The theorems of Euclidian geometry are true today, even though they have changed in meaning, mainly for two reasons: first, they do not seem to us today to be the expression of a unique, necessary form of space, as Kant still thought; we see them as one of several systems of measurement, and this undoubtedly alters their meaning, enriching it, moreover, with all the possible transitions between Euclidian and non-Euclidian structures; the other reason, which is still more general, is that spatial forms do not appear to us today as static figures, but as the results- of transformations, so that each form of geometry is subordinated to a basic ‘group’ of transformations, and that these groups give birth to each other in the same way as sub-groups can be differentiated within a main group.  But although these meanings depend, at every point in history, on the synchronic system of knowledge under consideration at that moment, they do not succeed each other at random, as if they were the result of accidents or exogenous factors; proceeding by reflective abstraction from previous states of construction, new inventions which alter meanings are in line with a progressive equilibration in which the synchronic balance is at once the result and the starting-point of new constructive processes.  In this respect, therefore, the situation is considerably different from that of the ‘natural’ languages, in which synchronic balance is a question of re-equilibrations that are governed by a great many external and internal factors.

This problem of the relationship between synchronic balance and diachronic evolution gives rise to another closely-allied problem - that of the nature of the innovations which change human behaviour in the course of history and necessitate re-equilibrations.  Here we may identify three possible types of innovation, which play a very different role in the relations of approximate continuity or discontinuity between present equilibrium and previous equilibration processes.  The first of these types of innovation is that of ‘discoveries’, which bring to light what was already in existence, independently of the subject, but which was not known or perceived before (for instance, the discovery of America).  Obviously, in such a case, the necessary re-equilibrations are not determined solely by the previous states of the system.  Secondly, we speak of ‘inventions’, when new combinations emerge as a result of the actions of the human subject (without going back to what some biologists have called organic ‘inventions’ in relation to highly differentiated organs that are specially adapted to a new situation).  It is the property of an invention that, however well the components that are combined may have been known (so that the innovation is only a matter of making the actual combination for the first time), yet the invention could have been a different one; to invent a new symbolism, for instance, does not imply that others could not have been invented instead.  It is obvious that in such cases also present re-equilibrations and past history are relatively independent.  There is, however, a third type of innovation in human

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behaviour, which can have considerable social significance; it is sometimes called ‘invention’ and sometimes ‘discovery’ in relation to logico-mathematical structures or the structures of intelligence in general.  Mathematical ‘invention’, however, is not a ‘discovery’ (unless one is a Platonist), since it is a new combination; the imaginary number -I, for example, is the result of a combination, made by Cardan, of the negative number and the extraction of the root.  Nor is it simply an invention, since once it is accomplished one must admit that it could not have been different, and that it therefore arose of necessity from within its own laws.  It is in this third case (many examples of which are to be found in the sphere of mental development, in the spontaneous formation of logical structures) that synchronic re-equilibration depends closely upon previous evolution, because diachronic constructions, even at that stage, were based on progressive equilibration, and because the present balance is the (provisional) termination of such a process..



35. It should even be remembered that biologists speak of the transmission of information as early as the genome level, the significant then depending on the order of the sequences in the DNA code (Watson and Crick).

36. And collectively as well as individually pre-speech, for among themselves the young deaf-mutes build up a language of gestures.

37.See H. SINCLAIR, Acquisition du language et développement de la pensie, Dunod, 1967.



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