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Harry Beilin
City University of New York
HISTORICAL BACKGROUND
In this chapter I elaborate on what by now should be evident, that in the years following the early 1970s Piaget and his collaboratorsâ publications moved his theory in a new direction to such a degree as to justify viewing it as a ânewâ theory. Three features of the new theory are discussed:
- the shift from an emphasis on extension (and truth testing) to intension (and meaning), and a new theoretical model I refer to as a logical hermeneutics of action,
- the shift from an emphasis on logical necessity to that of possibility, and its consequences for constructivist theory, and
- the continuing emphasis on rationality and its place in current discussions of ideology.
When Piaget (1980) declared he had previously been in error in placing almost exclusive stress on extensional, truth-table logic and that a more balanced theory of meaning was needed giving greater attention to intensional logic, it appeared as though a radical and sudden transformation had occurred in his theory. It was indeed a radical change, but it was not occasioned by a sudden shift in the direction that Piaget's theory had been taking in the 10 years prior to that time. Only recently, with the posthumous translation and publication of a series of books completed near the end of Piaget's life, has the nature and magnitude of the reformulation become apparent. The changes are sufficiently striking, as already indicated, to justify considering the late work as a new Piagetian theory. However, as with all transformations in Piaget's theory, and there were many, they were rarely wholly new; a case in point is the development of the theory of equilibration (see Chapman, this volume). The successive theories maintain a certain integrity over their entire history to such a degree as to make it evident that a core set of assumptions have sustained Piaget's research program with few modifications (Beilin, 1985). However, some of the changes have been of central importance, as with the new theory of correspondences and morphisms, but these have occurred in the context of an already formidable theoretical architecture so that their significance has escaped general notice.
First, I detail something of the major shift that occurred in the 1970s, that culminated in 1980 in the theory of meaning that was Piaget's final work, and then discuss other features of the new theory that are of importance to developmental psychology.
Early Functionalism
The 1920s and early 1930s were a time in which a series of debates were under way among a variety of theoretical systems in psychology. The field, by this time, had moved away from the confrontation between Wundt and Titchener's early structuralism and the functionalism of James, Angell, Baldwin, and Carr to a much more complex scene in which a number of schools sought to establish their right to the loyalties of the uncommitted (Beilin, 1983). There was faculty psychology, following in the tradition of Herbart, the German Gestalt psychologies, Freud's psychoanalysis, and the American pragmatism of Dewey, Thorndike, and Woodworth whose empiricism continued the tradition of functionalism. There was also Pavlov's conditioning theory, and the Continental functionalisms of Janet and Claparede.
Piaget's sympathy was with Claparede's functionalism, at the same time that he aggressively rejected the functionalism of associationism and connectionism that fueled American and Russian empiricism. Functionalism, in this way, continued to have a profound effect on both American and Continental psychology, particularly in the era leading up to the 1940s and 1950s. This functionalism took many forms, and its adherents shared some, if not necessarily all, of its fundamental assumptions. I have described the nature of these functionalisms elsewhere so do not repeat them now (Beilin, 1983; see also Kendler, 1987). Montangero (1985) commenting on Piaget's own theoretical development, divides it into four periods. The first period includes the five books published between 1923 and 1932; the second by the three books written in the 1930s. The principal difference between these two periods was the shift from social explanation to a theory of adaptation. However, both periods are characterized by the emphasis on functional analysis, and contained other aspects of the functionalist agenda, such as the emphasis on process.
Structuralist Period
A marked reformulation in Piaget's theory took place in the 1940s, that continued until the 1960s. This change entailed a shift to structural analysis. The structuralist period is represented by a series of books, on which much of Piaget's later reputation is based, books that detailed the nature of logicomathematical structures underlying cognitive development. The 1960s were a period of transition, in which structural analysis was no longer stressed, but no new models of explanation were developed (Montangero, 1985). The theory from that time, on to the last works, offers an increasing return to functionalist analysis and the products of that analysis. However, I would stress that the later functionalism is quite different from Piaget's earlier functionalism, if for no other reason that it moves in tandem with Piaget's continuing structuralism, and is profoundly affected by it. What is striking in the evolution of Piaget's theory, is that during its entire course, structuralism and functionalism play either dominant or subordinate roles, but both are always present. Reference to structure appears in the early functionalist period, and function is never lost sight of in the structuralist period. In the last period, there is an intellectual struggle apparent in Piaget, to bring these two major strains in the theory into some kind of equilibrium. This final synthesis was intended to be achieved in the last of Piaget's books, that he co-authored with Rolando Garcia (Piaget & Garcia, 1991).
THE THEORY OF MEANING
Piaget's effort to develop a theory of meaning was based first on the recognition that extensional logics, even from the logician's point of view, have inherent difficulties. More importantly, from a scientific viewpoint, many do not map onto natural thought in a wholly satisfactory way. Within logic itself, the effort to overcome the paradoxes of extensional logics began in the 1950s with the reintroduction of âintensionâ into formal logical systems. This effort resulted, in 1975, in Anderson and Belnap's elaboration of relevance or entailment logic (see Brynes, this volume, and Piaget & Garcia, 1991).
The difficulties and paradoxes of extensional logic emerge where the truth relation between propositions (or statements) is considered. For example, if either of the terms of the disjunction p.q V (or) p.q Vp.q is true, it follows that the implication p â q is true, even when there is no meaning relation between p and q, that is, p does not need to imply q in what is ordinarily understood as in a meaningful way. Following on a number of equally paradoxical consequences of the nature of extensional logic, Piaget was drawn to say that it is âindispensableâ to construct a logic of meaning whose major operator is a âmeaning implication,â which he defined as p implies q(p âq) if the meaning of q is contained in the meaning of p, and this meaning is transitive. This parallels Anderson and Belnap's conclusion that all entailments are tautologies (Anderson & Belnap, 1975). Consequently, intensional meaning embodiments, which Piaget called âinherences,â correspond to extensional nestings. That is, they conform with the forms of the truth tables, and in the sense of the new proposal, such truth tables are âpartialâ and determined by meanings. Thus, the Piaget and Garcia proposal parallels the more formal logic of entailment based on relevance and necessity of Anderson and Belnap, although it is a psychological analogue to the logical theory and not a logical theory as such (Piaget & Garcia, 1991). The proposal, presented by Garcia (in that volume), employs truth-functional connectives in an intensional implication relation, ostensibly avoiding the fallacies inherent in pure extensional logics. Garcia holds that Anderson and Belnap's formalisms are not as coherent a system as it first appeared, in that they offer their system as a collection of ad hoc rules they consider as working hypotheses for reaching certain goals. This âhighly flexibleâ approach to logic appeals to Garcia as a working model for genetic epistemology, when one is looking for the roots of ânatural logic.â
Piaget's sensitivity to developments in logic theory derive from a number of sources. In Piaget's structuralist period, the application of logicomathematical formalisms, as models to map onto developing natural thought, committed him to one form or another of logical and mathematical theory, on the assumption that the underlying structures of thought have logicomathematical form. When Piaget modified these logics to conform with demands of observed cognitive development, it led logicians to criticize Piaget's interpretation and employment of these formal logics, despite his disclaimer that what he was proposing was a psychologic and not a formal system of logic. However, sensitivity to logiciansâ criticisms undoubtedly motivated logicians in the Genevan circle to monitor continually the state of logical theory and to question and refine Genevan psychologic.
The greater impetus to change, appears to have come from the research itself. The initial source appears to have been Piaget's reconsideration, late in the 1960s, of the theory of causality (R. Garcia, personal communication June 2, 1990). The new work that followed on correspondences, functions, possibility and necessity, contradiction and consciousness, among others, was now interpreted in a new light. This research increasingly exposed the limitations of truth-table logics, to the point where Piaget felt a fundamental change in the theory was necessary. Piaget and Garcia emphasized that the direction developed in Genevan thinking toward intensional logic âconvergedâ with Anderson and Belnap's relevance-entailment logic, and is not to be seen as a formalization of Piaget's operatory logic. In fact, Garcia wondered whether logical formalizations of Piaget's operatory logic was possible.
From a âlogicalâ point of view, what Piaget's theory of meanings attempts to do, then, is integrate truth-table extensional logic with entailment-intensional logic and employ this integration as a model, if not a formalization of, operatory logical development. Historically, the effort to deal with the two aspects of logical knowledge, and of propositions specifically, goes back at least to Frege, who, in distinguishing between Sinn and Bedeutung (taken traditionally as between meaning-intension and reference or truth-extension) eventually led to Russell and Whitehead's monumental effort to purify logic by freeing it from the ambiguities of natural language. The symbolic logic they developed, which initiated a revolution in logic and philosophy, resulted in the emphasis on the truth testing of propositions to the neglect of meaning within logical form.
The attack by Wittgenstein, and others, on symbolic logic, and more generally, on the logical positivist program, has resulted in at least partial legitimization of natural language meaning in logical analysis. Piaget and Garcia, reflecting on their own efforts to develop a theory of meaning, concluded that a sharp distinction cannot be made between meaning (or intension) and truth (or extension) as was made by Frege. One might say, further, that current work in philosophy of mind and cognitive psychology is marked by the similar intent to synthesize these previously parallel but independent aspects of knowledge.
In the 1980 note declaring he had been in error in his overemphasis on extensional logic, Piaget offered the prospect that his new theory of meanings would be based on a âdecantedâ version of his earlier (truth-table) logic, as well as provide a new component that parallels the intensional logic of Anderson and Belnap. The theory of meaning book, published in France in 1983 (English translation, 1991) is entitled, Toward a Logic of Meanings, which aptly denotes the fact that the decanted version of the older theory was not developed or offered; instead, one has a programmatic statement of what such a theory should look like. Piaget's death prematurely ended the meaning project. Nevertheless, a substantial body of research was completed and a series of findings are reported on classification, seriation, collections, arithmetical operations, and more, that provide functional descriptions of how meanings precede the development of formal structures. Some striking conclusions emerge from these data and their analysis.
Considering the earlier difficulties created by Piaget's claims concerning the appearance of the 16 binary operations of propositional logic in the formal operational period, with critical reactions from logicians as well as from developmentalists, Piaget now made an even bolder claim. The data, he said, point to the very early formation of operations at the level of sensorimotor actions (well before the period of operational logic). These so-called âprotologicalâ operations, although not yet integrated into structures, are nonetheless isomorphic with one or another of the 16 binary operations of operational logic that later form the basis of groupings, and still later the INRC group. At the level of protologic, form and content are not increasingly differentiated as they are in operatory systems. The early forms of this protologic provide the first evidence of meaning (or intension) in the child's thought and provide the initial context in which the earliest elements of extensional logic are to be found.
Piaget's central thesis, now, is that at all levels, starting from the most elementary, knowledge always involves inference. Logic is first evident in the child's thought when he or she is âable to anticipate a relation between actions . . .â (Piaget & Garcia, 1991). Thus, the roots of logic appear long before language and propositional thought, in that anticipation entails inference, inference in turn, entails a logical relation, namely implication (see Perner & Astington, this volume, as a counterpoint). Consequently, a relation between actions is already a logical implication, but not in the extensional sense of requiring a determination of its truth value. Rather it is a meaning implication (i.e., an intension). Put another way, âinferences are implications between meanings (which are attributed to the properties, and to objects, and to . . . actions themselvesâ (Piaget & Garcia, 1991, p. 159). Meanings result from the subject's attribution of assimilation schemes to objectsâobjects whose properties are not simply observables, inasmuch as they always involve an interpretation of what is observed. Consistent with Piaget's concept of schemes, the meaning of an object is âwhat can be doneâ with the objectâa definition that applies at the sensorimotor level as well as at the level of preoperatory (or conceptual) thought that begins with the emergence of the semiotic function. Meanings are also what can be said of objects, that is, in their descriptions, as well as in what can be thought of them, as in classifying or relating them. For actions themselves, their meaning is in âwhat they lead toââin the transformations they produce in objects or situations.
What is most striking in Piaget's approach to these new data and the way they are interpreted, is that Piaget, in effect, is creating a new theoretical model, one that might well be called a logical hermeneutics of action. The model, as applied to the sensorimotor and preoperative periods requires a functional analysis of how subjects approach a task. An adequate model would necessarily detail the actions of the child, the objects acted on, and above all provide an interpretation of the inferences the child is making in carrying out the task. It requires an interpretation on the part of the investigator, who is attempting to characterize the meanings inherent in the situation and subsequently to identify the logical links in the system that make the meaning implications cohere. An example appears in a particular application of the method. Piaget said, in this instance,
Above all, what is involved is an inference that amounts to saying that if certain trajectories have been accomplished, others may be possible also. This leads a number of subjects to proceed from pushing to lateral or oblique movements and eventually to drawing in the object. (Piaget & Garcia, 1991, p. 15)
In other words, where the child carries out an action that entails a directed motion, that action is only one of a series of possible motions in other directions. To exploit these other possibilities requires the child to infer that motion in other directions is possible, including those that enable the object to be pulled to oneself. In this scenario, the child is not just engaged in random movement that by trial and error brings the object to oneself, but is based on an inference-generating process linked to intensional action. Here, Piaget went beyond description and even structural explanation to an interpretive model of observed action.
This example illustrates how the introduction of systematic interpretation into Piaget's method, seeking for relations of implication, at first intensional and later extensional, brings Piaget's theory and method in contact with recent hermeneutical and other interpretive traditions. It is hermeneutical in that Piaget is dealing with action just as others apply a hermeneutics to texts. However, Piaget is not, as in the Nietzschean tradition, holding that all life is text, and consequently action is text. Only, that one may seek a logic of meaning in action through the (intensional) interpretation of implications in action. Piaget's hermeneutics differs from other interpretive approaches in that his goal is to explain and characterize the logical characteristics of thought, whereas for hermeneutics generally the goal is the achievement of meaning itself, ordinarily in personal, social, and historical frameworks. Piaget differs from the hermeneutical tradition (Gadamer and Ricoeur are exceptions) too in that his hermeneutics does not lead to relativism in the way texts are said to be open to multiple interpretations, each claiming legitimacy. Rather, Piaget's interpretation of the implications in action lead to universals of intensional and extensional kinds. âDifferent strokes for different folksâ is not Piaget's motto.
Piaget and Garcia (1991), summarized their goals and achievements as follows:
1. They explain in detail how the logic of actions prepares for operatory logic, based on the new concept of action implication.
2. They sought to detail a stage of protologic at the level of actions that in respect to meaning relations is isomorphic with that of the 16 binary operations of propos...
