Chapter 47 The Psychogenesis of Knowledge and Its Epistemological Significance Jean Piaget

Fifty years of experience have taught us that knowledge does not result from a mere recording of observations without a structuring activity on the part of the subject. Nor do any a priori or innate cognitive structures exist in man; the functioning of intelli­gence alone is hereditary and creates structures only through an organization of succes­sive actions performed on objects.

Empiricism

The critique of empiricism is not tantamount to negating the role of experimentation, but the "empirical" study of the genesis of knowledge shows from the onset the insufficiency of an "empiricist" interpretation of experience. In fact, no knowledge is based on perceptions alone, for these are always directed and accompanied by schemes of action. Knowledge, therefore, proceeds from action, and all action that is repeated or generalized through application to new objects engenders by this very fact a "scheme," that is, a kind of practical concept. The fundamental relationship that constitutes all knowledge is not, therefore, a mere "association" between objects, for this notion neglects the active role of the subject, but rather the "assimilation" of objects to the schemes of that subject. This process, moreover, prolongs the various forms of biological "assimilations," of which cognitive association is a particular case as a functional process of integration. Conversely, when objects are assimilated to schemes of action, there is a necessary "adaptation" to the particularities of these objects (compare the phenotypic "adaptations" in biology), and this adaptation results from external data, hence from experience.

These mechanisms, which are visible from birth, are completely general and are found in the various levels of scientific thought. The role of assimilation is recognized in the fact that an "observable" or a "fact" is always interpreted from the moment of its observation, for this observation always and from the beginning requires the utilization of logico-mathematical frameworks such as the setting up of a relationship or a corre­spondence, proximities or separations, positive or negative quantifications leading to the concept of measure—in short, a whole conceptualization on the part of the subject that excludes the existence of pure "facts" as completely external to the activities of this subject, all the more as the subject must make the phenomena vary in order to assimi­late them.

As for the learning processes invoked by the behaviorist empiricists on behalf of their theses, Inhelder, Sinclair, and Bovet have shown that these processes do not explain cognitive development but are subject to its laws, for a stimulus acts as such only at a certain level of "competence" (another biological notion akin to assimilation). Briefly, the action of a stimulus presupposes the presence of a scheme, which is the true source of the response (which reverses the SR schema or makes it symmetrical [S ⅛ R]). Besides, Pribram has demonstrated a selection of inputs existing even at the neurologi­cal level.

Preformation

Is it necessary, then, to him in the direction of the preformation of knowledge? I will return later to the problem of innateness and will limit myself for the moment to the discussion of the hypothesis of determination.

However, these beautiful successive and sequential constructions (where each one is necessary to the following one) could be interpreted as the progressive actualization (related to factors such as neurological maturity) of a set of preformations, similar to the way in which genetic programming regulates organic "epigenesis" even though the latter continues to interact with the environment and its objects. The problem is therefore to choose between two hypotheses: authentic constructions with stepwise disclosures to new possibilities, or successive actualization of a set of possibilities existing from the beginning. First, let us note that the problem is similar in the history of science: are the clearly distinct periods in the history of mathematics the result of the successive creations of mathematicians, or are they only the achievement through progressive thematizations of the set of all possibilities corresponding to a universe of Platonic ideas? Now, the set of all possibilities is an antinomic notion like the set of all sets, because the set is itself only a possibility.

This brings us back to the child, since within the space of a few years he spontane­ously reconstructs operations and basic structures of a logico-mathematical nature, without which he would understand nothing of what he will be taught in school. Thus, after a lengthy preoperative period during which he still lacks these cognitive instruments, he reinvents for himself, around his seventh year, the concepts of reversi­bility, transitivity, recursion, reciprocity of relations, class inclusion, conservation of numerical sets, measurements, organization of spatial references (coordinates), morph­isms, some connectives, and so on—in other words, all the foundations of logic and mathematics. If mathematics were preformed, this would mean that a baby at birth would already possess virtually everything that Galois, Cantor, Hilbert, Bourbaki, or MacLane have since been able to realize. And since the child is himself a consequence, one would have to go back as far as protozoa and viruses to locate the seat of "the set of all possibilities."

In a word, the theories of preformation of knowledge appear, for me, as devoid of concrete truth as empiricist interpretations, for the origin of logico-mathematical struc­tures in their infinity cannot be localized either in objects or in the subject. Therefore, only constructivism is acceptable, but its weighty task is to explain both the mecha­nisms of the formation of new concepts and the characteristics these concepts acquire in the process of becoming logically necessary.

Reflective Abstraction

If logico-mathematical structures are not preformed, one must, in contrast, go far back to discover their roots, that is, the elementary functioning permitting their elaboration; and as early as the sensorimotor stages, that is to say, much before language, one finds such points of departure (though without any absolute beginning, since one must then go back as far as the organism itself; see the section on the biological roots of knowl­edge). What are the mechanisms, then, that provide the constructions from one stage to the other? The first such mechanism I will call "reflective abstraction."

It is, in fact, possible to distinguish three different kinds of abstraction. (1) Let us call "empirical abstraction" the kind that bears on physical objects external to the subject.

(2) Logico-mathematical abstraction, in contrast, will be called "reflective"* because it proceeds from the subject's actions and operations. This is even true in a double sense; thus we have two interdependent but distinct processes: that of a projection onto a higher plane of what is taken from the lower level, hence a "reflecting," and that of a "reflection" as a reorganization on the new plane—this reorganization first utilizing, only instrumentally, the operations taken from the preceding level but aiming eventual­ly (even if this remains partially unconscious) at coordinating them into a new totality.

(3) We will speak finally of "reflected abstraction" or "reflected thought" as the the- matization of that which remained operational or instrumental in (2); phase (3) thus constitutes the natural outcome of (2) but presupposes in addition a set of explicit comparisons at a level above the "reflections" at work in the instrumental utilizations and the constructions in process of (2). It is essential, therefore, to distinguish the phases of reflective abstractions, which occur in any construction at the time of the solution of new problems, from reflected abstraction, which adds a system of explicit correspon­dences among the operations thus thematized.

Reflective and reflected abstractions, then, are sources of structural novelties for the following reasons: In the first place, the "reflecting" on a higher plane of an element taken from a lower level (for example, the interiorization of an action into a conceptual­ized representation) constitutes an establishment of correspondences, which is itself already a new concept and this then opens the way to other possible correspondences, which represents a new"opening." The element transferred onto the new level is then constituted from those that were already there or those that are going to be added, which is now the work of the "reflection" and no longer of the "reflecting" (although initially elicited by the latter). New combinations thus result which can lead to the construction of new operations operating "on" the preceding ones, which is the usual course of mathematical progress (an example in the child: a set of additions creating multiplication).¹ As a rale, all reflecting on a new plane leads to and necessitates a reorganization, and it is this reconstruction, productive of new concepts, that we call "reflection"; yet well before its general thematization, reflection comes into action through a set of still instrumental assimilations and coordinations without any concep­tual awareness of structures as such (this is to be found all through the history of mathematics). Finally reflected abstraction or retrospective thematization become pos­sible, and although they are found only on preconstracted elements, they naturally constitute a new construction in that their transversal correspondences render simulta­neous that which was until now elaborated by successive longitudinal linkings (com­pare, in scientific thought, the thematization of "structures" by Bouibaki).

Constructive Generalization

Abstraction and generalization are obviously interdependent, each founded on the other. It results from this that only inductive generalization, proceeding from "some" to "all" by simple extension, will correspond to empirical abstraction, whereas construc­tive and "completive" generalizations in particular will correspond to reflective and reflected abstractions.

The first problem to be solved, then, is that of the construction of successive steps that have been established in the preceding paragraphs. Now, each one of them results from a new assimilation or operation aimed at correcting an insufficiency in the previ­ous level and actualizing a possibility that is opened by the new assimilation. A good example is the passage of action to representation due to the formation of the semiotic function. Sensorimotor assimilation consists only of assimilating objects to schemes of action, whereas representative assimilation assimilates objects to each other, hence the construction of conceptual schemes. Now, this new form of assimilation already was virtual in sensorimotor form since it bore on multiple but successive objects; it was then sufficient to complete these successive assimilations by a simultaneous act of setting into transversal correspondence before passing to the next level. But such an action implies the evocation of objects not presently perceived, and this evocation requires the formation of a specific instrument, which is the semiotic function (deferred imitations, symbolic play, mental image which is an interiorized imitation, sign language, and so on, in addition to vocal and learned language). Now, sensorimotor Signifiers already exist in the form of cues or signals, but they constitute only one aspect or a part of the signified objects; on the contrary, the semiotic function commences when signi- fiers are differentiated from what is thereby signified and when Signifiers can corre­spond to a multiplicity of things signified. It is clear, then, that between the conceptual assimilation of objects between themselves and Semiotizatioa there is a mutual depen­dence and that both proceed from a completive generalization of sensorimotor assimila­tion. This generalization embeds a reflective abstraction bearing on elements directly borrowed from sensorimotor assimilation.

Likewise, it would be easy to show that the new concepts inherent in the levels of initially concrete, then hypothetico-deductive operations proceed from completive generalizations as well. It is thus that concrete operations owe their new abilities to the acquisition of reversibility, which has already been prepared by preoperative reversibil­ity; but the reversibility, in addition, requires a systematic adjustment of affirmations and negations, that is to say, an autoregulation which, by the way, is always working within the constructive generalizations (I will return to the subject of autoregulation in the section on necessity and equilibration). As for the hypothetico-deductive opera­tions, these are made possible by the transition from the structures of "groupings" devoid of a combinatorial lattice (the elements of which are disjoint), to the structures of the "set of components" embedding a combinatorial lattice and full generalization of partitions.²

These last advances are due to a particularly important form of constructive general­izations, which consist of raising an operation to its own square or a higher power: thus, combinations are classifications of classifications, permutations are seriations of seria- tions, the sets of components are partitions of partitions, and so on.

Finally, let us call attention to a simpler but equally important form which consists of generalizations by synthesis of analogous structures, such as the coordination of two systems of references, internal and external to a spatial or cinematic process (the 11- to 12-year-old level).

The Biological Roots of Knoioledge

What we have seen so far speaks in favor of a systematic constructivism. It is nonethe­less true that its sources are to be sought at the level of the organism, since a succession of constructions could not admit of an absolute beginning. But before offering a solu­tion, we should first ask ourselves what a preformationist solution would mean biologi­cally; in other words, what a priorism would look like after having been rephrased in terms of innateness.

A famous author has demonstrated this quite clearly: it is Konrad Lorenz, who considers himself a Kantian who maintains a belief in a hereditary origin of the great structures of reason as a precondition to any acquisition drawn from experience. But as a biologist, Lorenz is well aware that, except for "general" heredity common to all living beings or major groups, specific heredity varies from one spedes to another: that of man, for instance, remains special to our own particular species. As a consequence, Lorenz, while believing as a precondition that our major categories of thought are basically inborn, cannot, for that very reason, assert their generality: hence his very enlightening formula according to which the a prioris of reason consist simply of "innate working hypotheses." In other words, Lorenz, while retaining the point of departure of the a priori (which precedes the constructions of the subject), sets aside necessity which is more important, whereas we are doing exactly the opposite, that is, insisting on necessity (see the next section), but placing it at the end of constructions, without any prerequisite hereditary programming.

Lorenz's position is therefore revealing: if reason is innate, either it is general and one must have it go back as far as the protozoa, or it is specific (spedes-spedfic or genus- spedfic, for instance) and one must explain (even if it is deprived of its essential charac­ter of necessity) through which mutations and under the influence of which natural selections it developed. Now, as research stands at present, current explanations would be reduced for this particular problem to a pure and simple verbalism; in fact, they would consist of making reason the product of a random mutation, hence of mere chance.

But what innatists surprisingly seem to forget is that there exists a mechanism which is as general as heredity and which even, in a sense, controls it: this mechanism is autoregulation, which plays a role at every level, as early as the genome, and a more and more important role as one gets closer to higher levels and to behavior. Autoregu­lation, whose roots are obviously organic, is thus common to biological and mental processes, and its actions have, in addition, the great advantage of being directly ControUable. It is therefore in this direction, and not in mere heredity, that one has to seek the biological explanation of cognitive constructions, notwithstanding the fact that by the interplay of regulations of regulations, autoregulation is eminently con­structivist (and dialectic) by its very nature.³

It is understandable, therefore, that while fuUy sympathizing with the transforma­tional aspects of Chomsky's doctrine, I cannot accept the hypothesis of his "innate fixed nucleus." There are two reasons for this. The first one is that this mutation particular to the human species would be biologicaUy inexplicable; it is already very difficult to see why the randomness of mutations renders a human being able to "leam" an articu­late language, and if in addition one had to attribute to it the innateness of a rational linguistic structure, then this structure would itself be subject to a random origin and would make of reason a collection of mere "working hypotheses," in the sense of Lorenz. My second reason is that the "innate fixed nucleus" would retain all its proper­ties of a "fixed nucleus" if it were not innate but constituted the "necessary" result of the constructions of sensorimotor intelligence, which is prior to language and results from those joint organic and behavioral autoregulations that determine this epigenesis. It is indeed this explanation of a noninnate fixed nucleus, produced by sensorimotor intelli­gence, that has been finally admitted by authors such as Brown, Lenneberg, and McNeill. This is enough to indicate that the hypothesis of innateness is not mandatory in order to secure the coherence of Chomsky's beautiful system.

Necessity and Equilibration

We still have to look for the reason why the constructions required by the formation of reason become progressively necessary when each one begins by various trials that are partly episodic and that contain, until rather late, an important component of irrational thought (non-conservations, errors of reversibility, insufficient control over negations, and so on). The hypothesis naturally will be that this increasing necessity arises from autoregulation and has a counterpart with the increasing, parallel equilibration of cogni­tive structures. Necessity then proceeds from their "interlocking."

Three forms of equilibration can be distinguished in this respect. The most simple, and therefore the most precocious, is that of assimilation and accommodation. Afready at the sensorimotor level, it is obvious that in order to apply a scheme of actions to new objects, this scheme must be differentiated according to the properties of these objects; therefore one obtains an equilibrium aimed at both preserving the scheme and taking into account the properties of the object. If however, these properties turn out to be unexpected and interesting, the formation of a subscheme or even of a new scheme has to prove feasible. Such new schemes will then necessitate an equilibration of their own. But these functional mechanisms are found at all levels. Even in science, the assimilation between linear and angular speeds involves two joint operations: common space-time relationships are assimilated while one accommodates for these nonetheless distinct solutions; similarly, the incorporation of open systems to general thermodynamic sys­tems requires differentiating accommodation as well as assimilations.

A second form of equilibrium imposes itself between the subsystems, whether it is a question of subschemes in a scheme of action, subclasses in a general class, or subsys­tems of the totality of operations that a subject has at his disposal, as for example, the equilibration between spatial numbers and measurement during calculations in which both can intervene. Now, since subsystems normally evolve at different speeds, there can be conflicts between them. Their equilibration presupposes in this case a distinction between their common parts and their different properties, and consequent­ly a compensatory adjustment between partial affirmations and negations as well as between direct or inverted operations, or even the utilization of reciprocities. One can see, then, how equilibration leads to logical necessity: the progressive coherence, sought and finally attained by the subject, first comes from a mere causal regulation of actions of which the results are revealed, after the fact, to be compatible or contradic­tory; this progressive coherence then achieves a comprehension of linkings or implica­tions that have become deductible and thereby necessary.

The third form of equilibration relies upon the previous one but distinguishes itself by the construction of a new global system: it is the form of equilibration required by the very process of differentiation of new systems, which requires then a compensatory step of integration into a new totality. Apparently, there is here a simple balance of opposing forces, the differentiation threatening the unity of the whole and the integra­tion jeopardizing the necessary distinctions. In fact, the originality of the cognitive equilibrium (and, by the way, further down in the hierarchy, also of organic systems) is to ensure, against expectations, the enrichment of the whole as a function of the importance of these differentiations and to ensure their multiplication (and not only their consistency) as a function of intrinsic (or having become such) variations of the totality of its own characteristics. Here again one clearly sees the relationship between equilibration and progressive logical necessity, that is, the necessity of the terminus ad quem resulting from the final integration or "interlocking" of the systems.

In summary, cognitive equilibration is consequently "accretive" (majorante); that is to say, the disequilibria do not lead back to the previous form of equilibrium, but to a better form, characterized by the increase of mutual dependencies or necessary implica­tions.

As for experimental knowledge, its equilibration admits, in addition to the previous laws, of a progressive transfer (passage) from the exogenous to the endogenous, in the sense that perturbations (falsifications of expectations) are first nullified or neutralized, then progressively integrated (with displacement of equilibrium), and finally incorporat­ed into the system as deducible intrinsic variations reconstructing the exogenous by way of the endogenous. The biological equivalent of this process (compare "from noise to order" in von Foerster)⁴ is to be sought in the "phenocopy," as I have endeavored to interpret and to generalize this notion in a recent paper.⁵

Psychogenesis and History of Science

As Holton said, one can recognize certain convergences between psychogenesis and the historical development of cognitive structures;⁶ this is what I will attempt to define in an upcoming work with the physicist Rolando Garda.

In some cases, before seventeenth-century science, one can even observe a stage-by- stage parallelism. For instance, in regard to the relationship between force and move­ment, one can distinguish four periods: (1) the Aristotelian theory of the two motors with, as a consequence, the model of antiperistasis; (2) an overall explanation in which force, movement, and impetus remain undifferentiated; (3) the theory of impetus (or elan), conceived by Buridan as a necessary intermediary between force and movement; and (4) a final and pre-Newtonian period in which impetus tends to conflate with acceleration. Now, one notes a succession of four very similar stages in the child. The first one is that one in which the two motors remain rather systematic as residues of animism, but with a large number of spontaneous examples of Untiperistasis (and this often occurs in very unexpected situations, and not only for the movement of projec­tiles). During a second stage, an overall notion comparable to "action" intervenes and can be symbolized by mve, in which m represents the weight, v the speed, and e the distance covered. During a third period (ages 7 to 10), the "impetus" in the sense of Buridan's middle term spontaneously appears, but with, in addition, the power of "passing through" motionless intermediaries by passing through their "interior" when a movement is transmitted through their mediation. Finally, in a fourth phase, (around the age of 11 to 12), the first inklings of the notion of acceleration appear.

For larger periods of history, obviously one does not And any stage-by-stage paral­lelism, but one can search for common mechanisms. For instance, the history of Western geometry bears witness to a process of structuration whose steps are those of a centra- Hon on an emphasis by Euclid on simply intrafigural relationships, then a construction of interfigural relationships with Cartesian coordinate systems, and then finally a pro­gressive algebrization by Klein. Now one finds, on a small scale, a similar process in children, who naturally begin with the "intrafigural," but who discover around their seventh year that in order to determinate a point on a plane, one measurement is not sufficient, but two are necessary, and they must be orthogonally arranged. After this "interfigural" stage (which is necessary also for the construction of horizontal lines) follows that which we can call the "transfigural" stage, in which the properties to be discovered cannot be read on a single diagram, but necessitate a deduction or a calcula­tion (for example, mechanical curves, relative motions, and so on).

Now, these analogies with the history of science assuredly speak in favor of my constructivism. Antiperistasis was not transmitted hereditarily from Aristotle to the little Genevans, but Aristotle began by being a child; for childhood precedes adulthood in all men, including cavemen. As for what the scientist keeps from his younger years, it is not a collection of innate ideas, since there are tentative procedures in both cases, but a constructive ability; and one of us went so far as to say that a physicist of genius is a man who has retained the creativity inherent to childhood instead of losing it in school.

Notes

1. Considering the number of these additions and not only their result.

2. Let us recall that completive generalization is a constructive process essential in mathematics: for example, the transition from passages of groupoids to semigroups, then from there to monoids, then to groups, to rings, and to bodies.

3. It is true that autoregulation is in part innate, but more in terms of functioning than in terms of structures.

4. H. von Foerster, "On Self-organizing Systems and Their Environments," in Self-organizing Systems, ed. M. Yovitz and S. E. Cameron (Elmsford, N.Y.: Pergamon Press, I960).

5. J. Piaget, Adaptation oitale et psychologic de !'intelligence: Selection organique et phenocopie (Paris: Hermana 1974).

6. G. Holtoa Thematic Origins of Scientific Thought (Cambridge, Mass.: Harvard University Press, 1973), p. 102.