The Competitiveness of Nations

in a Global Knowledge-Based Economy

Harry Hillman Chartrand

April 2002

Jean Piaget


DISCIPLINARY RESEARCH - Section II - Structures and Rules

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Table of Contents

Section Index


II - STRUCTURES AND RULES (OR NORMS)                             21

5. Concepts of structures                                                                21

6. Systems of Rules                                                                           26

7. Examples of interferences in the field of                                  28

        logical structures 

8. Systems of non-deducible norms: sociology of law,              31

      etc.; customs and habit patterns

9. Diachronic and synchronic problems in the                         33

         field of norms          



Having posed the problems in their most general forms in sections 1 to 4, let us now try to go into the details of common mechanisms by following the plan provided by the distinction between rules, values and signs.


5. Concepts of structures

One of the most general trends of avant-garde movements in all the human sciences is structuralism, which is taking the place of atomistic attitudes or ‘holistic’ explanations (emergent wholes).

The method intended to master problems of wholes - which at first seems to be the most rational and rewarding because it corresponds to the most elementary intellectual operations (those of assembling or adding together) – consists in explaining the complex by the simple, in other words in reducing phenomena to atomistic elements the sum of the properties of which is supposed to represent the whole which has to be interpreted.  Such atomistic methods of posing problems eventually lead to the laws of the structure as such being forgotten or distorted.  They have by no means disappeared from the field of human sciences and may be found for example in psychology in associationist theories of learning (school of Hull, etc.).  Generally speaking authors frequently revert to these types of additive constructions when a certain empiricism or a mistrust of theories which they consider premature impels them towards what they believe to be greater respect for directly observable facts.

The second trend which can be observed in a number of separate disciplines is one which, in the face of complex systems, consists in stressing the characteristics of ‘wholeness’ peculiar to these  stems while considering that wholeness to be directly ‘emergent’ from the assembly of elements and as imposing itself upon them, by structuring them, as a result of this constraint of the ‘whole’; above all, it consists in considering the whole to be self-explanatory by the mere fact of its description.  Two examples of such an attitude may be given, one


corresponding to certain current psychological trends and the other connected with a sociological school which is now extinct.  The first example is that of certain adherents of ‘Gestalt’ psychology which was principally the product of experimental studies on perception but was extended by W. Köhler and M. Wertheimer into the field of intelligence and by K. Lewin into that of affectivity and social psychology.  According to some of these authors we proceed in all fields from an awareness of wholes preceding any analysis of the elements, these wholes being due to effects of ‘fields’ which determine the forms by quasi-physical principles of equilibrium (minimum action, etc.); the whole being distinct from the sum of its parts,  Gestalts then obey laws of composition which are non-additive but are of qualitative predominance (Pragnauz) (the ‘best’ forms prevail by reason of their regularity, their simplicity, their symmetry, etc.)  The prevalent opinion today is that this method offers good descriptions but not explanations and that, if one advances from perceptive or motive Gestalts to forms of intelligence, these latter constitute systems which are additive but which nevertheless involve laws as being complete systems (which puts the problem in terms of algebraic structures or systems of transformations and no longer in terms of Gestalts).

In an entirely different field, Durkheim’s sociology proceeded in a similar manner by seeing in the social whole a new totality emerging on a higher scale from the assembly of individuals and reacting upon them by imposing on them a variety of ‘constraints’.  It is interesting to note that this school, whose twofold merit was to emphasize with particular vigour the specificity of sociology as distinct from psychology and to supply an impressive body of specialized work, likewise died a natural death for the lack of a relational structuralism which might have supplied some laws of composition or construction instead of referring unremittingly to a totality conceived as ready-made.

The third position, then, is that of structuralism, but interpreted as relational, that is to say as positing systems of interactions or transformations as the primary reality and hence subordinating elements from the outset to the relations surrounding them and, reciprocally, conceiving the whole as the product of the composition of these formative interactions.  It is of great interest, from our interdisciplinary point of view, to note that this trend - which is increasingly evident in the human sciences 11 - is still more general and manifests itself just as clearly in mathematics and biology.  In mathematics the Bourbaki movement has led to breaking down the frontiers between the traditional branches in order to identify certain general structures regardless of their content and to draw, by combinations or differentiations, the details of particular structures from three mother-structures.  And although this process-of-fusion has today been replaced by analysis of ‘categories’ (classes of elements with their functions), that is again a form of relational structuralism, but one which comes closer to the effective construction characteristic of the work of mathematicians.  In biology ‘organicism’ similarly represents a tertium between pseudo-mechanistic atomism and the emergent wholes of vitalism, and the most convinced theoretician of organicism has created a movement of ‘general theory of systems’ with interdisciplinary aims as regards, inter alia, the field of psychology

22  Index

(Bertalanffy has been influenced by Gestalt theory but goes considerably beyond it).

Having said this, there exists a whole range of possible ‘structures’ spread over three directions, and our first problem is to understand the relation between them (the first of these directions corresponds to what we called completed structures in section 3 and the other two to structures in process of formation or not closed):

1. Algebraic and topological structures, including logical models since logic is a particular case of general algebra (for example, the ordinary logic of propositions is based on Boolean algebra).  Thus in ethnology Levi-Strauss reduces kinship relations to group or lattice structures, etc.  In intelligence theory we have tried to describe intellectual operations the formation of which can be followed in the course of individual development by defining overall structures in the form of elementary algebraic structures or ‘groupments’ (akin to groupoids) and then, at the level of pre-adolescence and adolescence, of lattices and groups of assembled quaternities.  Structuralist linguistics likewise has recourse to algebraic structures (monoids, etc.) and the same is true of econometrics (linear and non-linear programmes).

2. Cybernetic circuits which describe systems of regulations and whose use is essential in psychophysiology and in learning mechanisms.  Ashby, the designer of the famous ‘homeostat’ which enables problems to be solved by a process of balancing, has recently supplied in his Introduction to Cybernetics a model of regulation whose feedback actions are themselves determined by an imputation table of the games theory type.  This model, which he regards as one of the most general and simplest to be made biologically, shows a possible link between psychological and praxeological or even economic regulations (see section 13).

3. Stochastic models used in econometrics, demography and often in psychology.  But whereas chance plays a constant role in human events and therefore requires to be treated on its own, it is never pure in the sense that the reaction to the fortuitous, whether favourable or unfavourable, is in varying degrees an active reaction, which brings us back to regulations.  Thus this type 3 results from a complication of 2, as type 2 is of 1 (remembering that the operation is a ‘perfect’ regulation with pre-correction of errors).

Thus structuralist research gives rise to at least three major interdisciplinary problems (without semantic correspondence with these three types of structure but in relation to them as a whole):

a. A problem of comparison of structures according to their sphere of application.  It is not by chance, for example, that structures of perception (‘good forms’, perceptual constancy regarding size, etc., systematic errors or ‘illusions’, etc.) refer to models of regulations which are more or less close, or applicable, to an assumed whole, and that structures of intelligence at various levels of equilibrium relate to algebraic models; the reason is that the latter involve a logic, whereas perceptual structures, despite their partial (but only partial, while Gestalt theory postulated direct identifications) isomorphisms with the former, contain a possibility of systematic deformation (or ‘illusions’) which from the algebraic viewpoint constitute ‘non-compensated transforma-


tions’.  The same goes for the unquestionable advantage to be found in looking among social phenomena for those which do or do not relate to a particular type of structure, which amounts in the end to delimiting what is amenable to logic and what is a matter of guesswork and readjustment.

In this connexion attempts can be made (and we have tried to do this in genetic psychology) to establish ‘partial isomorphisms’ to facilitate such comparisons between structures, in particular by specific fields.  Such a concept has no meaning from a purely formal point of view, which requires that an isomorphism must be total or not exist at all; after all, anything is partially isomorphic with anything else.  But the method acquires concrete and genetic meaning if two preliminary conditions are set for such research: 1) that one can determine the transformations which are necessary in order to pass from one structure to an adjacent one, and especially, 2) that one can show, genetically or historically, that these transformations are effectively achieved in certain situations, or are sufficiently probable (by direct affiliation or by collateral kinship, the common trunk from which the branches diverge being specified).

b. This leads us to the second of the major intradisciplinary or interdisciplinary problems raised by structuralist research.  Whereas the explanation of wholes by atomistic methods leads to a geneticism without structures and the theory of emergent wholes leads to a structuralism without genesis (which is also partially true of Gestalt theories or of any irreducible social view in sociology), the central problem of structuralism in the biological and human sciences is that of reconciling structure and genesis, since every structure involves a genesis and every genesis must be conceived as the (strictly formative) transition of an initial structure to a final structure.  In other words, the fundamental problem is that of the filiation of structures, and the triad of algebraic, cybernetic and stochastic structures immediately raises the question of the possibilities of transition from one of these categories to the others.

There is above all the problem of relations between cybernetic and algebraic structures, and in this connexion genetic psychology supplies some highly significant indications.  Between the elementary levels where cognitive conduct proceeds by trial-and-error or immediate perceptive intuitions (two forms implying regulations in the sense of cybernetic circuits) and those levels where, towards 7-8 or 12-15 years, algebraic structures recognisable by the strict co-ordination of ‘operations’ are constituted (as actions which are directed inwards, reversible and related to overall structures with their laws of composition), one finds all the intermediary stages in the form of pre-operational representations still involving simple regulations but tending towards a form of operation.  From this one may conclude that operation constitutes the limiting stage of regulation in the sense that the latter, being at first a correction of error as the result of action and later a correction of action as anticipating its possible deviations, finally becomes pre-correction of error, which is the function of operational deduction: feedback is then promoted to the rank of an inverse operation and the system by its composition alone ensures all the possible compensations.  Although it is not possible at present to say whether this process is peculiar to the field under consideration or can be more generally applied to

24  Index

others, we may conceive of similar processes in the spheres of the sociology of knowledge, sociology of law and sociology of moral facts, and possibly also in structuralist linguistics.12

c.  The third major problem which arises in comparative studies is that of the nature of the structures arrived at, i.e. whether they constitute simple ‘models’ in the service of theoreticians or whether they should be considered as inherent to the reality under study, in other words as structures of the subject or subjects themselves.  This question is fundamental, because in the eyes of authors critical of structuralism the latter is merely a language or a computing instrument which refers to the observer’s logic but not to the subject.  This problem is often raised even in psychology, where experimentation is relatively easy and where one can in certain cases be fairly sure that structure reaches down to the underlying explanatory principle of phenomena, in a sense which recalls what the philosophers call the ‘essence’, but with the addition of an undeniable deductive power.  But in disciplines where experimentation is difficult, even in the broadest sense as in econometrics, experts often stress the divergence they see between the mathematical ‘model’ and the ‘experimental design’, a model without sufficient relationship with the concrete being no more than a play of mathematical relations, whereas a model which adopts the details of the experimental design can claim the status of a ‘real’ structure.  It goes without saying that in most situations the models used in the human sciences are placed, still more than physical and even biological models, halfway between the ‘model’ and the ‘structure’, in other words between the theoretical design partially related to the observer’s decisions and the actual organization of the behaviours to be explained.

Note. - Lastly, we should say a few words about a problem allied to the preceding one which we were advised to include in the list of topics covering all the sciences of man, namely that of what some have ventured to call the ‘empirical analysis of causality’.  Two questions should be carefully distinguished here, that of causal explanation in general and that of functional dependence between observable facts which can be identified either by dissociation of factors in experimental research or by analysis of multi-variabilities in non-experimental research (in economics and sociology, of. the works of Blalock, Lazarsfeld, etc.).  The second of these questions does indeed concern all the human sciences, but from an essentially methodological point of view, without leading, properly speaking, to the discovery of new common mechanisms unless by further refining the concept of functional dependence as opposed to simple correlations.  On the other hand, the problem of causal explanation in general brings out the latent conflict which will doubtless exist for a long time yet between the partisans of a positivism wedded to observables and those authors who seek identify, beneath those observables, ‘structures’ capable of accounting for their variations.  It goes without saying that problems of causality are reduced, if such structures exist, to the lattices formation, their internal transformations and their self-adjustment; seen in this light, the search for functional dependence is only a stage towards the discovery of structural mechanisms, and the analysis of function could not be pursued to any length without arriving sooner or


later at these mechanisms.  As to which of these two fundamental lines of approach will eventually prevail, it is not for us to say.  For the moment we should merely note the rather striking convergences becoming apparent between schools of thought which may be described by the very general name of genetic structuralism in psychological research on development, in the study of ‘generative grammars’ in linguistics, and in certain analyses, outwardly very different, in economics and Marxist-inspired sociology.


6. Systems of Rules

The third problem we have raised (under c) often finds a possible solution in the following form: when following the formation of a structure one observes on its completion some modifications in the subject’s behaviour which are difficult to explain otherwise than by that completion itself, in other words by the ‘closure’ of the structure.  These are fundamental facts which are translated in the consciousness 13 of the subject by feelings of obligation or of ‘normative necessity’ and in his behaviour by obedience to ‘rules’.  Let us recall that according to the habitual, if not general, terminology of experts in the study of ‘normative facts” 14 a rule is recognized by the fact that it imposes an obligation but can be either violated or respected, contrary to a causal ‘law’ or determination which suffers no exceptions unless it be by reason of contingency variations due to a mixture of causes.

An example should explain this role of the closure of structure.  A child of 4 or 5 years is generally unable to deduce that A <C if he has noted separately that A <B and then that B < C (but without having seen A and C together).  Moreover, he is unable to construct a seriation of slightly differentiated objects A <B < C < D ... or manages to do so only by groping.  On the other hand when he later achieves a flawless construct consisting in the successive placing of the smallest of the remaining elements (hence comprehension of the fact that an element E is simultaneously greater than the preceding elements, E > D, C, etc., and smaller than the following elements, E < F, G, etc.), he resolves by so doing the problem of transitivity and will no longer judge A < C as undecidable or simply probable, but as necessary (‘it’s got to be’, etc.) if he has seen that A <B and B < C.  This feeling of logical necessity, difficult to evaluate like all states of consciousness, will be translated in behaviour by the use and recognition of transitivity.

Many other examples could be quoted in other fields of individual development such as the emergence of a sense of justice as a highly imperative norm succeeding a morality of obedience at the age where relations of reciprocity are structured outside or in opposition to relations of subordination.  In the historical development of societies it seems clear likewise that democratic ideals have gained currency as a function of changes in structures, etc.

Thus the study of rules or normative facts constitutes an important sector of the study of structures, the more so as it provides a link between structuralism and the actual behaviour of subjects.  Moreover, such rules are observed in all the


fields covered by the human sciences; even in demography it is impossible, for example, to dissociate the birth rate from a variety of moral and legal rules.  Where Durkheim saw the process of ‘constraints’ as the most general social fact, he was expressing this common characteristic of various social behaviours, namely, that they are accompanied by rules.

There arise out of this a certain number of interdisciplinary problems which are as yet far from being resolved, but in respect of which a twofold trend can be observed: they are raised in every field and they are treated by means of bilateral connexions.  We may distinguish three such problems:

a. The first question is to establish whether rules or obligations are necessarily of a social nature, that is to say whether they presuppose an interaction between at least two individuals, or whether they may be of endogenous character.  The question is merely a sub-division of the more general question whether all ‘real’ or natural structures (as opposed to exclusively theoretical ‘models’) are translated in the behaviour according to rules.

To this more general question one might be tempted to reply immediately in the negative, since there exist, for example, perceptive structures whose social component is nil or very small 15 and which are not accompanied by ‘rules’ in the normative sense.  However, they are translated by ‘predominances’ (‘good form’ wins over an irregular form, etc.), and in the opinion of certain authors there are many intermediate stages between predominance and logical necessity which would raise the question of relations between the normative and the ‘normal’, not in the sense of a simple dominant frequency but of the state of equilibrium (achieved, moreover, by self-regulation, which implies possible new connexions between the ‘regulable’ and the ‘rule’).

The question therefore is far from simple.  The dominant trends would seem to be the following: on the one hand there is increasingly general doubt as to the existence of ‘innate’ rules such as a logic or a morality transmitted through hereditary channels. 16  Natural logical operations begin to occur only very gradually (on an average hardly before 7 or 8 years in developed societies) in accordance with a constant sequential order but without that fixed regularity in age levels which would bear witness to internal or nervous maturation.  They are certainly drawn from the most general forms of co-ordination of actions, but these are collective as much as individual actions, so that they appear to be the result of a progressive balancing of a psycho-socio1ogical kind, far more than as biologically inherited (in other words the human brain contains no hereditary programming, as would be the case if logico-mathematical behaviours constituted something in the nature of instincts; instead it shows a hereditary functioning the utilization of which allows both collective life and the setting up of  general co-ordination from which these structures obtain their point of departure).  Moral obligations, as J. M. Baldwin, P. Bovet and Freud have shown, are linked in their formation with inter-individual interactions, etc.

Moreover it appears increasingly probable that if every balanced structure imposes not only regularities but also a certain predominance due to its own regulations, and if every system of regulations involves, by the very fact of its successes or failures, an obligatory distinction between the normal and the

27  Index

abnormal (concepts peculiar to living matter and devoid of meaning in physico-chemistry), there nevertheless exists a kind of limiting point which both separates and unites regulations and operations (see section 5).  This point of transition might well in many cases be that between the individual and the inter-individual.

b. A second general problem which follows on from what we have just said is that of types of obligations or rules.  Logical necessity is translated into coherent operations capable of constituting deductive structures, but there exists a large number of obligations and rules without intrinsic consistency, arising essentially from constraints of a more or less contingent or momentary kind, the extreme case being that of the rules of spelling whose arbitrary nature is sufficiently demonstrated by history.  Even independently from the questions raised under a, it is evident therefore that not every obligation extends into possible ‘operations’ in the limited sense in which we have adopted this term (section 5), but that a certain number of systems of rules do not go beyond the level of structures of regulations.

The second general problem raised by systems of rules is thus to construct, by means of interdisciplinary comparisons, a hierarchy of varieties of structures, starting with operational structures of various forms and ending with those which are based on regulations, likewise of various forms and involving a greater or lesser degree of chance.

c. The third great problem raised by systems of rules is that of interference between rules belonging to different fields.  This problem, some examples of which we shall presently discuss occurs in two forms.  First there is the question of effective intersections of structures leading to interferences between rules: for example, a legal system is a body of rules sui generis, that is to say irreducible to moral or logical rules; but objectively it involves all kinds of interferences with those other two systems by the mere fact that it must not contradict either of them (which may be easier in one case than in another). 17  But there are also intersections due to the subject’s realization of the structure, this realization perhaps being adequate but partial or distortive as a result of various subjective influences.  Thus the usual grammar of teachers is nothing other than a very incomplete and in part distortive realization of linguistic structures and generally interferes with obligations of the quasi-moral type.


7. Examples of interferences in the field of logical structures

The case of logical structures is a good example of how impossible it is today to isolate a form of research which yet is very distinct and possesses every characteristic that might have made of it a kind of absolute, secure from interdisciplinary contacts.  Formal logic is at present perhaps the most exact of disciplines in terms of the rigour of its demonstrations.  It can be placed at the starting point of mathematics, so much so that one might hesitate to include it among the sciences of man and that those responsible for the organization of the present series have not included it among the disciplines selected for study.  Above all, logic, using as it does an axiomatic or ‘formalizing’ method, ignores


the psychological ‘subject’ as a matter of principle, having become a ‘logic without subject’ so that the attributes it has mapped out for itself forbid it even to inquire whether ‘subjects without logic’ even exist.

Yet the internal evolution of logic itself as well as the external evolution of branches outside its field compel us to note the existence of numerous centrifugal trends which inevitably give rise to problems of interdisciplinary connexions.

The first of these trends arose from the discovery by K. Goedel in 1931 of the limits of formalization.  In a series of celebrated theorems Goedel showed that it is impossible for a theory of a certain richness (e.g. elementary as opposed to transfinite arithmetic) to demonstrate its own non-contradiction solely by its own means and by logical means weaker than those it implies; in this way it must of necessity arrive at certain undecidable propositions, and in order to decide these it is necessary to resort to ‘stronger’ means (e.g. transfinite arithmetic).  In other words logic is no longer an edifice resting on its base but a construct whose consistency depends on higher levels which are never completed because each in turn has need of the next.  But as soon as there is a construct we must ask: a construct of what and by whom?  And if there are limits to formalization we must ask why, to which J. Ladriere, for instance, replies by invoking the impossibility for the subject to embrace in a single field the totality of its possible operations (which in fact is an appeal to psychology to produce an epistemology of logic: see below).

Another and equally remarkable internal trend is the concern shown by certain logicians for establishing a connexion between formal logic and certain systems of norms or rules used by subjects collectively.  We have already quoted (section 4) works like those by Weinberger, etc., which apply formal logic to connexions between norms posed in the imperative.  But mention should be made especially of the important work of the Belgian logician Ch. Perelman in the field of argumentation.  Perelman sets out to study from a logical point of view the many situations where a partner seeks to act upon another not through sentiment or extrinsic arguments of authority, etc., that is to say not through those sophisms which have so wrongly been grouped under the name of ‘logic of sentiments’ (for the true logic of sentiments is morality, with which Perelman is beginning to concern himself), but through an argumentation which is logically coherent although directed and organized so as to convince.  A vast body of works has appeared on this subject 18 among which we find in particular a study by L. Apostel on the presuppositions of such a theory and more particularly on the relations between logical operations and the general co-ordination of actions (Apostel shows in this respect the kinship between Perelman’s analyses and the writer’s own research on the development of logical structures proceeding from action).  Starting from the theory of argumentation, Perelman has naturally been led to study the logic of legal structures, and a very active collaboration on this issue between jurists and logicians has been established under his direction and has already yielded a number of studies.

A third trend common to certain logicians consists in taking an interest in psychology, not of course in order to find in it the internal foundations of logic


(which would mean going from the fact to the norm, or ‘psychologism’, as little valid as the inverse movement or ‘logicism’) but with a view to its general epistemology.  If it is the nature of logic to be a construct, it becomes difficult to interpret it epistemologically as a simple language and moreover a strictly tautological one as logical positivism proposes.  That is why logicians who no longer believe this thesis or have never believed it are turning in the direction of psychological or psycho-social construction of structures.  It should be noted, however, that this is not simply a formalization of ‘natural’ thought or logic, which is of limited interest (except in situations where it develops specific techniques such as that of argumentation, which has been analysed by Perelman): first because natural logic is generally poor compared with the richness of axiomatics, but especially because it constitutes only a highly imperfect realization of the underlying structures.  What these logicians are seeking is therefore less an analysis of the consciousness of subjects than a study of structures, in their filiations and formations, which then makes it possible to show the stages whereby one arrives, starting with elementary behaviours, at the algebraic structures of logic itself (Boolean algebra and network, etc.).  This is the subject studied by the logicians working at the lnternational Centre of Genetic Epistemology in Geneva: L. Apostel, S. Papert, J. B. Grize, C. Nowinski, etc.

One of the reasons why the problem of the epistemology of logic thus forms a bridge between logic and genetic psychology, is that the latter has for years gone out to meet problems of this kind.  For it is impossible to study the development of the intelligence from the first years of childhood to adolescence or to the adult state without coming up against a certain number of findings which fall within ‘the sphere of logic.  The first of these findings is that even in the pre-language stage there exist, at the level of sensori-motor action patterns, certain structures of interlocking, order, correspondence, etc., which prefigure logic and display its links with the general co-ordination of action.  Later we find that by a process of successive balancings the common operations of classification, seriation, correspondence or intersection come to constitute (towards 7-8 years) formalizable structures halfway between ‘groups’ and ‘networks’, which we have called ‘groupings’.  We find above all that at a third stage (11-12 years) these groupings are co-ordinated simultaneously in a quaternality group and a network of interpropositional connections.  For interdisciplinary research it is of interest to note that this ‘group’ of propositional transformations, widely studied by logicians since 1950, was discovered in genetic psychology before it was analysed in its logistic formalization.

Relations between logic and economics are of two kinds, thanks to the theory of games.  On the one hand the logician may take an interest in games theory as in any other logico-mathematical procedure in order to establish its axiomatics.  On the other hand, however, induction (in other words the full range of inferences applied to a field of experience where contingency intervenes) is a ‘game’ between the experimenter and nature, and it is possible to conceive of a theory of induction based on strategies and decisions.  Since several authors regard deduction as an extreme case of induction, we thus see the connexion between logic as a whole and epistemology.  There is no need to recall that this


epistemology of logic can a fortiori be placed in relation with cybernetics by a double movement similar to that just referred to, which we may cite with T. Greniewski, an expert in connexions between logic and cybernetics.

As to exchanges between logic and linguistics, we shall come to them when discussing the latter.


8. Systems of non-deducible norms: sociology of law, etc.; customs and habit patterns

Independently of the specific questions of legal logic which have been discussed, there exists a major problem the importance of which has found expression in several contemporary trends in a variety of disciplines, namely that of the general structure of systems of norms.  From this viewpoint of overall structures, which is becoming increasingly dominant, it is by no means sufficient to know that a particular legal reasoning can be put in logical form; this does not alter the fact that a legal system in its total form in the sense employed by H. Kelsen (from the ‘fundamental norm’ and the constitution to individualized norms such as all court judgements, diplomas, etc.) is at the same time very close to a logical system and very different from it.

The analogy is that in both cases there exists a construct of normative values achieved by means of actions or operations, and that these results are valid depending on a series of transitive implications.  If such and such axioms are accepted, then such and such theorems T1 follow which lead to such and such other theorems T2, etc., according to a series of implications placed in hierarchical order.  Thus if a constitution is accepted, then parliament has the right to enact laws L which are valid by virtue of the constitutional norm; then the government has a right to take a decision D which is valid by virtue of the law L; then such and such an office has the right to settle an individual case C in a valid manner by virtue of the governmental decree D, etc.  This succession of normative constructions (each norm being at the same time the application of the previous one and the creation of the next one) is readily comparable to a series of implications, and Kelsen explicitly defines this implicative relationship under the term of ‘imputation’ (central or peripheral depending on whether it qualifies the subjects of law or the implications alone).

The great difference however is that if one knows the content of axioms, one can deduce the succeeding theorems: they were not, of course, tautologically pre-formed within the axioms, since these axioms are independent one from another, but the new combinations obtained are ‘necessary’ (they could not have been other than they are by virtue of the given operations).  In the legal system, on the other hand, one merely knows that parliament cannot violate the constitution, but within this framework it votes what it likes; in other words the constructive operations take place in a valid fashion as a function of transitive and necessary imputations, but their results remain contingent because they are not determined by the form of these operations, only their validities being so determined to the extent that they are not in contradiction with norms of a superior category.


In other words there exist normative structures whose actual form determines their content and which for this reason can be described as formal, and others whose form does not determine their content.  The former, which can give rise to ‘pure’ deductive disciplines (pure logic and mathematics) nevertheless concern all human behaviour, since economic exchanges could not proceed beyond the barter stage if everyone did not accept the fact that twice two makes four.  There is therefore some advantage in making a comparison of structures and systems of rules from the standpoint of these relations between form and content, and it will be seen at once that such comparative analyses can be carried out only by means of close interdisciplinary collaboration.

The study of moral facts offers another example of such problems and it is not pure chance that this subject has attracted the interest of sociologists, psychologists, certain logicians, jurists, 19 experts in the sociology of law and an appreciable number of economists (utilitarian explanations of moral facts are essentially the product of schools of thought built up by Anglo-Saxon economists).  The French economist J. Rueff, in a highly stimulating study on moral facts, has raised the problem of the formalization of different moralities, using the significant terms ‘Euclidian’ and ‘non-Euclidian’ moralities to bring out the differences in postulates associated with moralities observable and widespread in the social group.  By following the psychogenetic development of moral rules in the child and adolescent, the writer has been led to distinguish in that development two clearly distinct forms of structures depending on whether the source of the norms is to be found in obedience to persons who are the object of unilateral or whether it relates to a system reciprocity or mutual respect (that being, in particular, the source of concepts of justice which are acquired independently and often to the detriment of the morality of obedience).  From the point of view which concerns us here, the former of these moralities clearly belongs to those structures whose form does not determine their content, while in the latter we do observe an effect of form upon content.  The writer was accordingly able to try to formalize the second of these two systems, in which it is not difficult to find analogies with those logical operations which are involved in an inter-individual co-operation of a cognitive nature.  Thus the generality of such problems becomes evident at once.

Indeed these problems are so general that they can be found in all those aspects of social life which Durkheim described under the common term of ‘constraints’ and within which we must distinguish at least two poles: that of norms imposed by an authority or by custom, which place an obligation on the individual without his participating in their creation, and that of norms resulting from a collaboration of a kind in which the partners contribute to the formation of the norm which places an obligation upon them.  It will be seen at once that the latter case is oriented in the direction of systems whose form determines their content to varying degrees.

The problems crystallize in particular around the question (always a central one) of relations between custom or habit and obligation or rule.  When Thurnwald in a famous phrase laid down that ‘recognised constraint transforms custom into law” he was raising a much more general problem than that of the birth of

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law in tribal societies, and one which is still under study today: how does one move from a structure which is simply regular or balanced to a system of rules or norms?  In the sociology of law the formula we have quoted emphasizes with great truth that custom does not suffice so long as there has been no ‘recognition’.  Similarly in the field of moral facts neither habit nor example are sufficient, so long as a certain relation of ‘respect’ or recognition of a value connected with the person has not been established (and no longer connected merely with transpersonal functions or services, as in the legal sphere).  But in the field of intellectual operations where, as we have just seen, the very form of the norms determines their content, although logic is certainly a morality of the exchange of thought and of cognitive co-operation, a certain coefficient of internal necessity attaches to any deduction based on a balanced operational structure, as though the transition from action to reversible operation were sufficient to engender the regulated structure which governs cognitive common production as well as individual constructs.  Lastly, in the sphere of patterns of habit and perception peculiar to the individual alone, although no normative necessity is involved, there nevertheless exist phenomena of predominance due to an internal balance where there is no longer any question of norms but where we are nevertheless faced with an attenuated form of that necessity which dominates in the higher varieties of balance.

Hence the trend which we discern in this line of research would lead to the acceptance of the fact that the transition of structures into rules presupposes two conditions.  The preliminary condition is a condition of balance: the structure becomes a rule only if it closes back on itself in a sufficiently balanced form which expresses itself in predominances of different kinds if that balance is due to regulations, and by intrinsic necessity if it is operational.  The second condition appears with inter-individual relations and is once again a matter of forms of balance, but in this case forms which are relative to these collective situations: their regulations or the operations which derive from them are then expressed by those different states of consciousness which lead from trans-personal recognition or from respect for persons to various forms of obligation properly speaking.


9. Diachronic and synchronic problems in the field of norms

It is well-known that linguistics, beginning with the works of F. de Saussure, has proceeded to dissociate diachronic studies, or studies of history and evolution of language, from synchronic considerations connected with the balance of language as an existing system in a state of relative independence from its past.  We also know the extent to which economic crises can modify the state of values and so dissociate them from their previous history.  On the contrary, it is in the nature of rules or norms to introduce compulsory conservation, which is why their function is of such great importance in the life of societies and individuals.  The norm is therefore by its very nature the essential instrument of connexion between the diachronic and the synchronic.


The fact remains that structures and rules develop, that they were formed little by little, and that even in the case of progressively acquired stability new structures or norms can modify the meaning of preceding ones to a more or less deep extent, even if they do not replace them.  We are thus confronted with a new major problem of interdisciplinary comparison, that of the uniformity or variety of relations between diachronic and synchronic factors depending on different types of structures or norms.20

Taking logical norms first, these may appear to constitute the prototype of unchangeable structures since a variety of philosophers from Plato to Husserl have linked them with Ideas, a priori forms or eternal or at least timeless fundamentals.  A. Comte, one of the precursors or founders of scientific sociology, described the development of fundamental concepts in his Law of the Three States (whose value we are not called upon to discuss here), but maintained that this development concerned only the content of human reason whilst its forms, in other words the actual processes of reasoning or ‘natural logic’, remained invariable.  A trend which is fairly general today, owing to the history of sciences and techniques; to work on comparative sociology and on genetic psychology; and especially to the evolutionist viewpoints which are now dominant in ethology and zoopsychology, leads us to think on the contrary that reason was built up by stages and continues to evolve, not without reason or reasons but in such a manner that not only is the evidence transformed but even that which appears logically demonstrated or rigorous at a given stage may subsequently appear doubtful and may give rise to considerably greater degrees of rigour.

On the other hand, if reason evolves, the progressive constructs to which it give rise constitute an extremely remarkable type of development in the sense that the previous structures are not set aside or destroyed but are integrated in the subsequent ones as specific cases valid in a certain sector or at a certain scale of approximation.  The same is not true of the experimental sciences, starting with physics where a theory can be contradicted by another or retain only a limited degree of truth.  But in the field of logico-mathematical structures no structure which has been demonstrated as valid at a moment in history is subsequently abandoned, the error consisting merely in believing it to be unique and in that sense necessary, whereas later it becomes the sub-structure of a richer and broader whole.  From the point of view of relations between the diachronic and the synchronic we thus have here an exceptional situation in which the existing equilibrium appears as the product of a historical process of more or less continuous balancing (crises or momentary imbalances being no more than crises of growth or break-throughs to new problems).

If we compare this situation with that of a system of legal norms, the contrast is striking.  A well-made system of such norms does, of course, provide for its own modification in the sense that as soon as a constitution exists, and at every stage of normative construction provided and implied by it, there is a possibility of revision or modification.  In a certain sense therefore there is continuity in normative creation, and in this respect we find here the connexion between the diachronic and the synchronic which is peculiar to systems of rules as opposed

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to systems of non-normative values or signs.  Yet the situation is quite different from that which exists in the case of rational norms.  In the first place there is nothing to prevent the new norm from replacing and contradicting the one which is abolished; this does not create any break in the transitive succession of valid ‘imputations’, but it does create a discontinuity in the actual content of the norms.  Secondly, the relative continuity of which we have been speaking remains subordinate to the stability of the political régime; in the event of a revolution, the entire system is abolished for the benefit of a new one unrelated to the old.

In the field of moral norms continuity is doubtless greater, but the problem of relations between diachronic and synchronic factors nevertheless arises in very different terms from those of logical norms.  When Durkheim, who tended to subordinate the synchronic entirely to history, explained the prohibition of incest in developed societies by the exogamy of tribal organizations, he was forgetting to explain why so many other rules likewise attributed to totemism have not been perpetuated in our time.

There is no point in piling up examples to show that this is a field of interdisciplinary research of considerable general importance.  In the last analysis the question comes down to this: to what degree is contemporary man dependent on his history?  A superficial answer based on what has just been demonstrated would be to maintain that historical factors are vitally important precisely because they are timeless and are, like rational norms, a matter of invariables which history uncovers but does not create or explain; while the great historic changes which introduce continuities between certain systems of norms and the preceding ones would, by this reasoning, stress the importance of synchronic re-balancings rather than of continuous constructive processes.  In reality there is a history of events or of visible and in part contingent manifestations, and there is also the history of the underlying dynamism or of processes of elaboration and development.  We are becoming increasingly aware that organic development is far more than a history of events or a succession of phenomena, but is a matter of progressive structuration or organization whose qualitative stages are subordinate to an increasing integration.  That is why the history of civilization is becoming more and more an interdisciplinary task within which the history of science and technology, economic history, diachronic sociology, etc., have to analyse concurrently the innumerable facets of the same transformations.  But it is also why history is explicative even in what appear to be its timeless invariables, because they have become such only as a result of constructive processes and balancings which have to be reconstituted and which, by varying from one field to another, mutually illuminate one another both in their differences and in their common mechanisms.

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11. It should be noted in particular that these trends of relational structuralism show considerable similarity with those of research in epistemology and methodology in the works of a certain number of Soviet authors (V. I. Kremyanski, Y. A. Levada, G. P. Chtchedrovitski, V. N. Sadovski, V. A. Lektorski, E. G. Youdine, etc.).

12. True, one may wonder what the term ‘operation’ signifies in a social system. But if we define an operation as an action which is capable of interiorisation, reversible and related to other operations within an overall structure, it is clear that operations occur in all inter-individual actions which are not based solely on relations of force or authority and in all collective actions where norms apply, in short wherever a trace of rationality can be found in a social system (which is by no means exceptional).

13. When we say ‘translated in the consciousness’ this means that the causality involved should not be sought within the consciousness but in the underlying structures of which the subject’s consciousness knows only the results, which he translates into terms of implications (see the end of section 3).

14. A ‘normative fact’ is the establishment by the sociologist (in sociology of law, etc.) of the fact that the subject recognizes a norm as binding upon him; by establishing this fact the observer merely notes it without himself adopting any position normatively, i.e. without evaluating the norm of the subject under study.

15. The role of language in colour perception has been studied but the effect is axguable.  Bruner and Postman’s celebrated experiments on estimations of the diameter of a dollar coin or of any disc, varying with the subject’s economic level, have not been generally confirmed and are moreover open to other interpretations (centration effects) in those cases where they may possibly have been verified.

16. Exception should be made for N. Chomsky who believes that grammars have an ‘innate fixed kernel’; but one is entitled to wonder from the psychological point of view whether the rational fixed kernel does not result from the balancing of the sensori-motor mechanisms whose constitution precedes language and is only partially programmed by heredity.

17. Cf. the problem of ‘role conflicts’ (N. Gross, etc.).

18. Cf. inter alia ‘La theorie de l’argumentation. Perspectives et applications’, Logique et Analyse, nos. 21 to 24, 1963.

19. We should mention the important and still lively movement created by Petrazycki, to which we shall refer in section 12.

20. This problem coincides with one of the aspects of the question of relations between logic and history as they are formulated in Marxist literature: the relation of historical continuity in the formation of a system with structural dependence within the system under consideration (this as a reaction against the ‘unhistorical’ approach still so frequent in certain disciplines).


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