The genetic psychology of Jean Piaget

In Magnar Brekkle, Øivin Andersen, Trine Dahl, & Johan Myking (eds.), Applications and Implications of Current LSP Research. Bergen: Fagbokforlaget, 1994. Also in Linguistica e letteratura 20/21, 1995-96, 227-259.

A. ‘Classical’ versus ‘post-classical’ approaches for LSP and ‘DSP’

1. The crucial role of language for special purposes (‘LSP’) and of discourse for special purposes (‘DSP’) in the development and transmission of specialized knowledge is only slowly gaining recognition. Many specialists in science and technology have no background in the study either of language and discourse or of epistemology, and subscribe, at least implicitly, to a ‘classical realism’ that reifies knowledge into a fixed set of self-contained ‘facts’ about independent ‘objects’: the specialist need only know the ‘facts’ and the special terms for stating them ‘just as they really are’. Such a person would be suitably skilled to communicate the special knowledge to other people, witness the widespread acceptance of a college degree in a specialized field as a higher-division teaching credential without pedagogical training. Specialists uneasy about the idea of being in the business of producing not just knowledge, but discourse about knowledge.

2. So specialists with highly sophisticated knowledge of their field may hold highly naive, idealized notions of LSP and DSP, witness these statements (from a geometry textbook) (Tryon 1967: 7f):

[1] We need to make certain that every word in a scientific discussion is used according to a dictionary meaning or is defined in the text before it is put to use.

[2] A definition is an agreed use of words or symbols, each expression having a single limited meaning which remains unvaried

The provisions in [1] are either trivial because every word has a dictionary definition; or they are impractical because we lack a rigorous procedure for establishing ‘certainty’; or they are misleading for words with several dictionary definitions, only one of which is relevant to the ‘scientific discussion’. Similarly, the ‘agreed use of words’ invoked in [2] need not imply a ‘single unvaried meaning’, since uses adapt to context (Beaugrande 1984, 1988, 1991b). Both [1] and [2] signal the common failure to distinguish between language versus discourse, between what words can mean as a potential versus what they do mean as an actual occasion.

3. For many scientists and philosophers, realism is the ‘master code’ and supreme goal of knowledge, and formal logic is the model of how all knowledge should be constructed. We see this in discourse traditions reaching from 18th-century ‘empiricism’ (sample [3]) down to 20th-century ‘positivism’ and ‘unified science’ (sample [4]):

[3] the only object of the abstract sciences or of demonstration, are quantity and number [and] experimental reasoning concerning matter of fact and existence (David Hume, e.a. [= emphasis added])

[4] of these languages [of science], the physical, or that in which we speak about physical things, in everyday life or physics, is of the greatest importance [...] physical language is the basic language of all science [and] a universal language comprehending the contents of all other scientific languages (Rudolf Carnap, e.a.)

The arrogations supporting such positions call for sweeping generalizations and exclusions: ‘the only object’ [3], ‘greatest importance’, ‘basic’ or ‘universal language’, ‘all science’, ‘all others’ [4]. The peremptory tone is ominous: if the physical world is so obvious and compelling, why did Hume suggest ‘commiting to the flames’ any non-realistic book? How far is authority from authoritarianism?

4. Realist science has fostered a widespread ‘category mistake’: scientific and philosophical realism is deemed to be the prototype of human cognition and communication at large. So, the basic transaction of the mind is taken to be ‘objective observation’ and that of language to be making ‘true statements’ about ‘real objects and events’, while all other transactions are merely derivative or deviant. Ironically, the ‘category mistake’ has proliferated unrealistic models making human beings out to be inveterate realists; and illogical claims about how logically humans think.

5. We notice this in realist ‘semantics’, which, for David Wiggins (1971: 17), proposed to escape problems of ‘belief’, ‘intention’, and ‘the whole notion of use’ by arguing:

[5] for the arbitrary sentence s, to know the meaning of s is to know under what conditions the sentence would count as true [...] this may be the best theory of meaning we shall have for some time

Such an approach requires drastic restrictions on what ‘semantics’ can address:

[6] The total communicative context of an utterance, construing ‘content’ comprehensively, is too complex [...] We must rather [...] isolate what is strictly said before we can explain circumstances, conventions, and whatever else. [So] truth must be the central notion of semantics, and that the boundary between what does and what does not bear logically on the truth of what is strictly said must be the boundary between the science of semantics and the science of the further effects obtaining in a speech-exchange (1971: 20f)

Wiggins’ agenda is a slick mixture of dogma invoking ‘truth’, with expedience in excluding what seems ‘too complex’ (‘communicative context’), assumung that what can ‘account for’ (‘what is strictly said’) can be neatly ‘isolated’. Wiggins implies, with no sound evidence, that this ‘isolation’ can be achieved for all ‘sentences’ we might ‘arbitrarily’ choose — and that we thereby obtain precisely the ‘science of semantics’. No heed is given to ordinary speakers and hearers, for whom ‘truth’ is often disputatious, and ‘communicative contexts’ are evidently not ‘too complex’.

6. It is vital that studies of LSP and DSP do not repeat this naive realism. Just as the ‘new physics’ sees the physical world to be ‘not a structure built out of independently existing unanalysable objects but rather a web of relationships between elements whose meanings arise wholly from their relationships to the whole’ (Henry Stapp), we can explore discourse as another such ‘web of relationships. We can seek to develop ‘post-classical’ approaches to account for the power of discourse to construct ‘worlds’, quite apart from the presumed ‘reality’ of a group or culture. This task can go to a ‘discourse analysis’ exploring the ‘degrees of freedom’ between a ‘reality’ and its discourse representation, and between what people can know and what people can say. The task might well improve human access to knowledge through discourse (Beaugrande, in preparation.

7. We can now examine the critical potential of a ‘post-classical’ discourse analysis for looking at science as a transaction in discourse for special purposes. Our exa,ple will be the discourse of Jean Piaget, an illustrious and prescient pioneers of the ‘cognitive revolution’. In 1954, he bravely turned agains the then dominant ‘unified science’, wherein ‘the school’s logicians, linguists, and psychologists’ ‘insistently’ ‘repeat in emulation of each other that the mentalist concepts of “thought”, etc. no longer correspond to anything whatever, that all is language, and that access to logical truth is assured by no more than a healthy exercise of language’ (112) (cf. § 2f, 45).1

8. Piaget resolved to correlate ‘the invariants of intelligence and biological organization’ with ‘the invariants common to all structuring of which life is capable’ (Piaget 1952: 3). So while ‘mainstream’ psychology was ruled by orthodox and reductive behaviourism (e.g. Clark Hull, B.F. Skinner), Piaget sought to build a wide-ranging perspective on the maturational process acknowledging biological, psychological, social, and individual factors.

9. The volume The Child and Reality was published by 1976 as a — frequently inept — translation of Problèmes de psychologie génetique published in French in 1972 but compiled from earlier papers published between 1954 and 1971.2 Overall, it is a transitional ‘discourse in progress’, an ongoing meditation trying to reason rigorously from a small number of basic terms and claims to attain wide generalizations about the maturation of the human organism. Sadly, Piaget had a ‘prose style’ whose ‘obscurity’ and ‘prolixity’ will, as Margaret Boden (1979: 15) drily remarks, ensure that ‘he will win no prizes for clarity, brevity, or wit’. So his discourse has fostered a margin of uncertainty about his central terms and claims, which, I hope to show, are more closely and systematically interconnected than might be gathered from his sometimes ponderous and circuitous presentation.

10. Piaget adopted an ‘evolutionary’ approach in what he called a ‘genetic’ line of inquiry. Here, ‘the study of the development of mental functions’ is deemed the key to explaining their ‘mechanisms in the finished state’ (143). Thus, ‘genetic psychology’ hopes to ‘use child psychology to find the solution to general psychological problems’. Also, Piaget’s term ‘epigenetic’ suggested that the advanced design of the human organism in its mature state is to be accounted for as a series of internal differentiations, complications, elaborations, and so on, from its elementary stages in early life. Originally, ‘epigenetic’ is a geological term for ‘changes in the mineral character of a rock owing to outside influences’, whereas ‘ontogenetic’ would be the more usual term for the development of organisms (cf. Webster’s Collegiate Dictionary, pp. 279, 590). Piaget’s terms were influenced by Conrad Waddington’s (1957, 1975) geological metaphor of the ‘epigenetic landscape’, signals a thematic drift in the design of Piagetian discourse: namely to use as ‘control centres’ terms and concepts suggesting high degrees of determinacy and stability, and to argue ‘outwards’ from them very cautiously so as to keep these design factors under strict control (§ 2, 16f, 22). Moreover, he vows — this time fully in keeping with the academic climate of the day — to ‘restrict’ himself ‘by method to using only statements and interpretations already developed in the the field3 of scientific biology and psychology, trying to resist speculative temptations’ that might entrain him in a ‘philosophical psychology’ whose ‘existence’ he feels he must stoutly deny (164) (but cf. § 50).

25. To trace the ‘maturation’ of the child as an ‘epigenetic system’, Piaget hopes there may be fairly deterministic ‘chronological regularities not only in the sequential order of stages but also in the more or less set dates of formation’ (153f, e.a.) (but see § 27). The same vision applies to his special term ‘epigenotype’ (a superposition with ‘genotype’, hence, the genetic constitution of a group):

[7] The development of an epigenotype implies, from the biological viewpoint, the intervention of stages which show sequential character, each one being necessary to the following one in a constant order (145, e.c. [= emphasis changed])

This vision makes the discourse of Piagetian reasoning rich in expressions for determinate sequential temporality, e.g. [8-11]. Indeed, on the very first page of his book he conjectures that ‘the necessary role of time in the life cycle’ may shed light on ‘the question: does the life cycle express a basic biological rhythm, an ineluctable law?’ (1).

[8] Child development is a temporal operation par excellence. (1, opening sentence of the book)

[10] Time is necessary for duration [...] time is equally necessary for order of succession (6, 9)

[11] The order of succession is always the same [...] in order to reach a certain stage, the previous ones must be taken

In isolation, sample [10] might seem startlingly trivial: who would ever conceive of ‘duration' or ‘succession’ apart from time? Only as part of Piaget’s insistence on time as a solid anchor does the statement have a vital function.

26. If temporal connections are indeed lawlike, they make a plausible base for connections of enablement, such that earlier stages not merely precede later stages but create the sufficient and necessary conditions for them, as suggested by [7] and [11]. The sequence is ‘enriched’ (in the sense of § 18) into ‘a hierarchy of structures which are built in a certain order of integration’ (11, e.a.). This enriched control is plainly appealing to Piaget, and his account steadily strives to keep a lid on the ‘factors’ that can affect what he likes to call the ‘epigenetic mechanism’, a term which itself strongly implies a deterministic basis (cf. § 24, 30).

27. The most immediate challenge to this striving comes from temporality being more deterministic as a sequence than as a schedule: ‘the stages are precisely characterized by their set order of succession’, but they cannot be ‘given a constant chronological date’ (10, e.a.; so the phrase ‘more or less set dates’ in § 25 should be taken broadly). Maturation having a ‘soft coupling’ (in the sense of § 18) to its time-line introduces both indeterminacy and complexity into the picture:

[12] If a continuous action of the internal maturation of the organism and the nervous system alone intervened, the stages would not only be sequential but also linked to relatively constant chronological data. (146, e.a.)

Piaget constrains the instability and indeterminacy of possible ‘acceleration or retardation’ within ‘the order of succession’ by hypothesizing that ‘other factors’ beside ‘psychological’ ones ‘are added to epigenetic mechanism’ (146). Here, the term ‘psychological’ is made a ‘control centre’ by taking on a peculiar sense, namely as an ‘abbreviation’ for the whole ‘development of the intelligence’ (2). And since Piaget’s argument assumes that the lawlike aspects are best anchored in the ‘internal maturation of the organism and the nervous system’ (cf. [12]), he is prone to see this development as ‘spontaneous’ and independent of social context: ‘what the child learns by himself, what none can teach him and he must discover alone’. The ‘social aspect’ is in turn left to subsume ‘everything the child receives from without and learns in general by family, school, educative transmission’. This division too is hierarchical if we assume that ‘social development is subordinated to spontaneous and psychological development’ (3f, e.a.).

28. The stabilizing thesis that the ‘biological factors linked to the epigenetic system (interactions of the genome and of physical milieu during growth)’ ‘doubtless owe nothing to society’, supports the ‘dissociation of individual and collective development factors’ (145) — ‘psychological’ plus ‘biological’ lean toward ‘individual’, whereas ‘social’ leans toward ‘collective’ (but cf. § 29, 35). The ‘relative independence’ from ‘biological preformations’ is cautiously said to ‘hold in reserve’ some ‘possible connections with social life which, in principle, again emanate from activities peculiar to general behaviour in its psychobiological as well as its collective aspects’ (146f, e.a.) — the multiple hedges (in italics) signalling how uneasy Piaget feels about this linkage. Note here also the term ‘psychobiological’ used in a context where we might expect to see ‘individual’ as the counterpart of ‘collective’.

29. The term ‘cognitive’ becomes a ‘control centre’ when it too gets drawn toward a peculiar sense similar to the one we saw for ‘psychological’ in § 27, namely as the stabilizing side vis-à-vis the ‘social’ side, as in [13], where the ‘cognitive’ is made ‘general’ by taking on the ‘collective’ that appeared to learn toward the ‘social’ — with the odd implication that ‘education’ would not be a ‘cognitive’ issue!

[13] To treat the relation between cognitive functions and social functions, we must begin by opposing the general coordinations of collective actions to the particular cultural transmissions which crystallize in a different manner in each society. (148f )

Piaget’s choice of terms indicates that this ‘opposition’ is hardly a proper ‘control dialectic’ in my sense (§ 19): ‘the operations of socialization interfere’, and the ‘interindividual development’, notably the ‘changes’ whereby ‘individuals gather information, collaborate, discuss, oppose one another, etc.’ ‘intervenes during the whole development’ (146ff). He sounds a bit uncomfortable about intrusive ‘factors’ impinging on what would otherwise be a tidy and precisely timed ‘mechanism’ (cf. § 24, 26; [23] in § 35; [43] in § 38).

30. But he deftly regains control and stabilizes these ‘other factors’, which ‘depend on circumstances as much as on genetic potentialities’, by situating them in a process he calls ‘equilibration’, which runs by ‘self-regulation’ and stays ‘close to homeostasis’ (146f, e.a.) (cf. § 54). To ‘study equilibration’ is to address the ‘problem’ of ‘freeing the principal cognitive structures and seeking their relation with organic [cf. biological!] structures’ (167). When he frees ‘the factors of equilibration’ by stating that they ‘can be conceived of as very general and relatively independent of particular social milieu’, he seems to slam the door again on the ‘connections with social life’ he warily allowed for (§ 28).

31. The ‘stages’ he envisioned in the ‘development of an epigenotype’ are thus controlled not just by their ‘sequential character’ cited in [12] (§ 27), but by a ‘kinetic equilibrium in the sense that a deviation’ ‘is more or less compensated with a tendency to return to the normal path’ (145, e.c.) — a notion adopted from the cybernetics of his time (but cf. § 54). The concepts of ‘equilibrium’ and its corresponding process ‘equilibration’ are thereby instated as further ‘control centres’ within Piaget’s discourse. In one passage, an argument in favour of ‘progressive and autonomous equilibration factors’ is said to befit a stabilizing ‘supposition that evolution of thought structures remains the same despite linguistic variations’ (159) (compare the conception of ‘language’ in § 37-40). In another, ‘equilibrium’ is said to allow for ‘acceleration’, which limits the determinism of temporality (as we saw in § 27), but also prevents it from ‘increasing beyond certain limits’ (29).

32. The next ‘control centre’ closely follows when Piaget moves to enhance the balance and abstract elegance still further by stipulating that ‘equilibrium is defined by reversibility’ (60f):

[14] the equilibrium of a system is defined by the compensation of all its virtual transformations, that, is, precisely by reversibility. (129)

[15] [in] progressive equilibration, the equilibrium [is] the compensation by reaction of the child to outer disturbances, which leads to the operatory reversibility at the end of this development. (29)

His next move is to argue that ‘reversibility is the most apparent characteristic of the act of intelligence which is capable of detours and returns’ (61, e.a.). He sees ‘reversibility’ ‘presented in two forms’: ‘inversion or negation appearing in schoolroom logic, arithmetic, etc.’, and ‘reciprocity appearing in the operation of relations’. He is gratified to espy here a ‘privileged field of intellectual operations’ within ‘a simple and regular system of stages’, during whose course ‘reversibility increases at a regular rate’ (61).

33. His model of these ‘stages’ can be viewed in part as an ‘enrichment’ of temporality, his deepest source of determinism, as we saw (cf. § 25ff). Indeed, he makes temporal ‘constancy’ a strict requirement for the existence of stages at all:

[16] If stages are to exist, first of all the order of succession of acquisitions must be constant. [...] The structures at a given age become an integral part of the structures of the following age (50f)

[17] operations of successive equilibrium, steps toward equilibrium. The moment equilibrium is reached on a point, this structure is integrated into a new system being formed, until there is a new equilibrium ever more stable and of an ever more extensive field. (60, e.a.)

‘Equilibrium’ is maintained through ‘adaptation’ while ‘the organism constantly assimilates the milieu to its structure and accommodates the structure to its milieu’ (166). So

[18] The result of an act of intelligence [is an] equilibrium [...] between assimilation and accommodation (82)

[19] the specific result of thought would be to achieve a permanent equilibrium between assimilation of the universe to the subject and accommodation of the subject to the objects, whereas the organic and sensorimotor and chiefly perceptive forms know only constant equilibration displacements. In other words, the reversible play of anticipation and of mental reconstitution would achieve a form of equilibrium both mobile and stable in opposition to static and unstable configurations.

Here, the correlated terms assimilation and accommodation, which are among the most famous in Piaget’s work, are strategically enlisted to support the assumption that his term ‘equilibrium’ can reconcile ‘mobile’ with ‘stable’ so that possible indeterminacy remains well-constrained (cf. § 2, 16f, 22, 24, 27). Significantly, this control is allotted to ‘intelligence’ [18] and ‘thought’ [19], which thus take their places alongside ‘psychological’ and ‘cognitive’4 as ‘control centres’ in Piagetian discourse (cf. § 27, 29) but are given opposite roles to play in respect to ‘language’, as we shall see (cf. § 38).

34. As is well known, Piaget’s ‘theory of the stages of development’ (10) has four parts:

[20] first, we have a stage [of] sensorimotor intelligence [...] before about eighteen months, which precedes speech [...] Secondly, we have a stage [of] representation [...], which begins with speech and lasts for seven or eight years. [...] Between about seven and twelve [comes the third stage of] concrete operations. And finally, after twelve years, there is the stage of proportional or formal operations. (10f, e.a.)

This ‘theory’ is much what we might expect. His line of argument outlined so far distinctly calls for a scheme of development conceived as a progressive imposition of order and regularity, culminating in the most ‘formal’ stage. The sequence itself is ‘logical’ in that each stage is follows from its predecessor in a similar way as the statements in logical proof, e.g. in mathematics and geometry (see [23]).

35. In consequence, Piaget is strongly motivated to assign a foundational role to logical and mathematical operations in human activities, such as understanding and reasoning with the ‘conservation of matter’ (‘acquired at the age of eight)’, ‘of weight’ (acquired by the age of nine or ten), or ‘of volume’ (4ff, 9, 116ff). These passages are emblematic:

[21] The central problem [is] the nature of intellectual operations, especially of logico-mathematical structures (150)

[22] what characterizes cognitive aspects of behavior is their structure, [either] schemes of elementary actions, concrete operations of classification or seriation, or [else] logic of proportions (32)

[23] The relations between praxis and the fundamental mechanism of representative intelligence [are] to be conceived precisely as [...] interiorized actions coordinated in well-defined structures (logico-mathematical structures chiefly geometrical, etc.) (65)

[24] we could thus consider logic as the final form of equilibration, simultaneously individual [...] insofar as it is general or common to every individual, and likewise social insofar as it is common to every society

Notice that ‘logic’ is handed the role of reconciling ‘individual’ with ‘social’ in [24], although we recall that ‘the dissociation of individual and collective’ was at one point mentioned in connection with the ‘biological factors’ ‘doubtless owing nothing to society’ (§ 28). To be sure, the reconciliation is rather trivial in that it works by a simple syllogism or commutation of sets: what is ‘common to’ the whole set (‘society’) must be ‘common to every individual’ in the set.

36. On closer scrutiny, Piaget’s discourse hints that the whole sequence of stages, not just the final stage, is geared toward ‘logic’. The first ‘functioning elementary structures’ that are ‘used to form knowledge’ ‘on every level’ are said to already ‘outline’ and ‘prepare the logical structures’ [25]. On that basis, early ‘logico-mathematical systems’ can ‘develop spontaneously in the child’ well before they are ‘completed’ and ‘formal’ [26], e.g. at age seven [27]. So the ‘period of concrete operations’ is ‘a logic’ too, though one ‘based on objects’, at least ‘in the sense that’ ‘objects can be combined’ or ‘counted’ [28], and that ‘operations can be reversed’ and ‘coordinated’ [29]. That ‘period’ accordingly supplies ‘structures on the point of completion’ [30], which the ‘final stage’ can reapply from ‘objects’ over to ‘verbal statements’ [28] and ‘propositions’ [31-32].

[25] on every level (including perception and learning), the acquisition of knowledge [pre]supposes the beginning of the subject´s activities in forms which, at various degrees, prepare the logical structures [that] are due to the coordination of the actions themselves and hence are outlined the moment the functioning elementary structures are used to form knowledge (94, e.a.).

[26] a large number of logical, mathematical and physical operations develop [...] spontaneously in the child [and are] completed by propositional and formal operations, making the adolescent’s hypothetico-deductive deduction possible. (76, e.a.)

[27] [one] important stage of development of child intelligence [concerns] the transformations marking, at about the age of seven, the transition of preoperatory representations to the early systems of logico-mathematical operations (165)

[28] the period of concrete operations is [...] a logic which is not based on verbal statements but on the objects themselves, manipulatable objects. This will be a logic of classifications because objects can be collected all together [...]; or else it will be a logic of relations because objects can be combined [...] or else it will be a logic of numbers, because objects can be materially counted by manipulating them. [...] (20f)

[29] we are dealing with a logic in the sense that operations can be reversed — for example addition, which is the same as subtraction, but in a reversed way. It is a logic in the sense that operations are coordinated, grouped in whole systems which have their laws in terms of totalities. (21)

[30] the period of concrete operations is characterized by a series of structures on the point of completion [...]— on the logical level, [they are] classifications, successions, [..] simple or successive correspondences, multiplicative operations (58f, e.a.)

[31] [in the] period of formal operations [there arises] the logic of propositions, the capacity to study statements and no longer only objects placed on the table or immediately represented (61) (cf. § 40f).

[32] [in the] final stage, [...] a new logic of propositions, a whole set of specific operations are superposed on the preceding ones. [yielding] a unique system among the different ‘groupments’5 which until now were based on reciprocity or on inversion, on the different forms of reversibility (24f, e.a.).6

‘Propositions’ are thus made possible by the concepts of ‘reciprocity’, ‘inversion’, and ‘reversibility’, whose key role as ‘control centres’ we noticed in § 32.

37. The fact that his scheme identified the two early stages in terms of when ‘speech’ is not and then is present [20] suggests that Piaget might have an intense interest in language and discourse (that he might be even more anxious than Wiggins to ‘unpack the speech-act layer by layer’, cf. [5] in § 7). But Piaget’s stance is a bit uneasy precisely because his model is anchored in temporality and logic and requires discrete stages rather than a ‘continuity’:

[33] [if] we take the development of a child’s perception or the development of language, we observe a completely different and much greater continuity than in the field of logico-mathematical operations [..] I would be unable to give you a chart of stages similar to the one [for] intellectual operations (49, e.a.)

So Piaget’s own discourse symptomatically portrays ‘language’ having at best a ‘logic’ that is less ‘deep’ [34] and ‘clear’ [35] than ‘formal logic’ and ‘operations’, and being ‘necessary’ but not ‘sufficient’ for it [35-36], if even doing so requires him to hedge his earliest position [34]. Moreover, he surmises that language is not fully suited for ‘transmitting structures’ [37-38] such as those his logical model emphasizes. And Bruner’s ‘experiments at Harvard University’ are cited as evidence that ‘understanding’ is not richly connected to ‘concrete reasoning’ [39].

[34] forty years ago,7 I believed in the close relation between language and thought. Since then [I have learned that] there exists a logic of coordinations and actions far deeper than the logic related to language and much prior to that of propositions (109f, e.a.)

[35] the role of language in the completion of operatory structures [is] necessary although insufficient [and] can first be studied with the greatest clarity at the level of formal or hypothetico-deductive operations [that] are no longer related to the objects themselves but to statements and hypotheses verbally expressed etc. (120, e.a.)

[36] Language can constitute a necessary condition for the completion of logico-mathematical operations without being a sufficient condition for their formation. (113, e.a.)

[37] Language favors the interiorization [of] actions, [but] neither creates nor transmits ready-made these structures by exclusively linguistic means. (119)

[38] at the level of formal or propositional operations language acts less by transmission of ready-made structures than by [...] education of thought or reasoning due to the conditions of communication (121)

[39] The first facts gathered seem to show that [...] there are few connections between the two fields of verbal understanding and of concrete reasoning’; ‘interventions’ that ‘supplied verbal information were systematically negative except with children who succeeded in solving questions by hypothetical deductive means’ (122).

38. Yet a ‘close relation between language and thought’ [34] does survive in Piaget’s own discourse when his account of temporality confronts reductive behaviourism. To explain why speech appears when it does at the end of the ‘sensorimotor period’ (cf. [20] in § 34), he draws a distinction between ‘intelligence’, which works with ‘action’ rather than ‘speech’, versus ‘thought’, which works with ‘symbolic evocation’ including ‘speech’ [40-41]. This move impels him to grant to the ‘adolescent’, who has reached the final stage, something he calls the ‘logic of speech’ [42] — its predecessor and counterpart being, as we saw, the ‘logic of objects’ [28] (§ 36) — which would not be as ‘deep’ as the ‘hypothetico-deductive operations’ [34-35].

[40] Why is the acquisition of speech so late? Speech has often been reduced to a pure system of conditioning and conditioned reflexes. If such were the case, an infant would acquire speech as early as the end of the first month [...] Our reply is that speech is bound up with thought and thus [pre]supposes a system of interiorized actions [not] carried out materially but from within and symbolically [...] especially actions [...] which are reversible. (12f, e.a.)

[41] There is intelligence before speech but no thought before speech [...] Intelligence for the child is the solution of a new problem, the coordination of the means to reach a certain goal which is not accessible in an immediate manner; whereas thought is interiorized intelligence no longer based on direct action but on symbolism, the symbolic evocation by speech, by mental pictures, and by other means (11, e.a.)

[42] Adolescent logic is essentially a logic of speech [for] reasoning on propositional and verbal statements, placing ourselves in the viewpoints of others without believing the proposition.

Intriguingly, he proposes that the ‘role’ of ‘language’ depends precisely on whether it can be demonstrated to be ‘sufficiently connected’ with ‘algebra and logic’ — a demonstration, ironically, in which none of three linguists he cites are considered today to have succeeded:

[43] The question of knowing whether [...] language plays an authentically constitutive role or an indirect and auxiliary one, seems to us to be reserved for the time when linguistic structuralism ([Louis] Hjelmslev, [Knud] Togeby, [Zellig] Harris, and others) will have discovered sufficient connecting points with algebraic and logical analysis of the mechanisms of thought. (120)

39. So, apart from his earliest volume, Language and Thought of the Child (English 1926, original 1923), written when he still ‘believed in the close relation between language and thought’ [34], Piaget is much more interested in the intellectual and developmental role of language than in language itself as seen from a linguistic or communicative standpoint. His episodic invocation of ‘correspondences’ between language and logic, e.g. [44], are evidently less essential than his precepts regarding ‘operativity’ and ‘equilibration’ [45]. Also, he harnesses the ‘symbolical function resulting from a differentiation between the signifiers and the signified’ in ‘language’ (57, 73) to help account for the emergence of the stage of ‘representation’ [46]. Indeed, ‘a comparative study’ of ‘semiotic function’ might vindicate Piaget’s central quest for temporal determinism [47] (cf. § 25).

[44] The linguistic distinction of nouns and adjectives corresponds in general to the logical distinction of categories and predicates. (110)

[45] operativity leads to language structure [...] rather than the contrary [...] it would be of great interest to study the time allowed to develop operatory structures of the function of the subject´s language, [because] to suppose that evolution of thought structures remains the same despite linguistic variations [...] would argue in favour of progressive and autonomous equilibration factors (159) (cf. § 30f).

[46] The symbols and signs, once differentiated from their significations, make it possible to evoke objects in situations actually non-perceived, forming the beginning of representation between one and a half and two years (73f).

[47] A comparative study of sensory motor forms of imitation and dates of appearance of semiotic function based on deferred imitation would perhaps show certain chronological regularities, not only in the sequential order of the stages and set dates [and thereby] come closer to the possible factors of maturation which are relative to the epigenetic system (intervention of language centers, and so forth). (153f)

40. We thus do not see the detailed, coordinated analysis of language we might expect if Piaget’s final ‘stage’ hinges on manipulating ‘verbal statements’ and ‘propositions’ and relating them to each other (compare [28, 31, 32, 36]). Possibly, Piaget feared to compromise the formal and mathematical aspects he considered so essential to ‘logic’. Also, he would soon encounter the social8aspects he has downplayed on several grounds: (a) social development is ‘subordinated to psychological development’ (§ 27); (b) the ‘psychobiological’ side he emphasizes tends to be associated with the ‘individual’ (§ 28); (c) ‘socialization’ ‘interferes’ and prevents him from adducing ‘relatively constant chronological data’ for his temporal model (§ 29,); and (d) ‘social functions’ ‘differ’ from one ‘society’ to another, while ‘the factors of equilibration’ are ‘very general and relatively independent of particular social milieu’ (§ 29f). At one point in the book — when he is praising linguists like Hjelmslev who suggest ‘reducing the system of formal logic and that of language to a common principle’ (cf. § 38) — he does envision a reconciliation with both ‘language’ and ‘social actions’, namely on the grounds that they ‘continue the equilibratory operation’ he assigns to ‘actions in general’ [48]. The complexity of his own discourse in sample [48] reminds me of his densely hedged acknowledgement of ‘possible connections with social life’ cited in § 28.

[48] It is in the direction of common functioning and of common probabilist source that we can conceive the formative action of language on operations, it then being understood that this formative action outdistances the language settings themselves and on the basis of the coordination of social actions, continues the equilibratory operation already active in the field of the coordination of actions in general. (121)

Still, this proposal is restricted in ways that can lead into much the same dilemma as ‘classical semantics’ faced. Just as Wiggins would have the labour of ‘isolating what is strictly said’ from the ‘communicative context’ (§ 6f), Piaget would have the labour of isolating only such ‘formative actions of language’ as ‘outdistance the language settings’. Both labours are plainly formidable, and perhaps not even feasible — at least not if we expect a ‘logico-mathematical’ or ‘hypothetico-deductive’ system to tell us how.

41. Similar perplexities arise in regard to perception, which was also named in sample [33] as a source of ‘continuity’ for which Piaget could not ‘give a chart of stages’ (§ 37). Again like language, perception is said to depend on logic more crucially than the other way around [49], and to have less ‘reversibility’ [50] and ‘intrinsic necessity’ [51] than does logic.9 Conversely, cognitive progress is said to advance into the stage of ‘representation’ by growing less dependent on perception, upon which the stage of ‘sensorimotor intelligence is at first centered’ (Piaget 1950: 122) [52].

[49] logic would be preformed in perception, but perception would not function without the intervention of a sensorimotor scheme bound up with the whole action which itself would then be a point of departure for subsequent logical structures. In effect, perception would not account for the formation of any logico-mathematical idea [because] every idea implies the intervention of a logico-mathematical body [...] all perception, even at the most elementary level, [...] is structured by sensorimotor activities [...] for which coordinations prepare logical structures. (98) (cf. [25])

[50] The total structures intervening in the field of logical and mathematical operations are, contrary to the perceptive structures, characterized by their reversibility in the form of inversion or reciprocity and by their additive composition. (128)

[51] Any quantitative analysis leads to a mode of probabilistic composition of perceptive structures opposed to the character of intrinsic necessity peculiar to the logico-mathematical structures. (140)

[52] The symbols and signs, once differentiated from their significations, make it possible to evoke objects in situations actually non-perceived, forming the beginning of representation.

Similarly, we saw in [32] the ‘logic of propositions’ being portrayed as ‘the capacity to study statements and no longer only objects placed on the table or immediately represented’ (§ 36) (where the term ‘study’ is a quaint description of what ordinary children do). And in [25], ‘perception’ was one ‘level’ of ‘activities’ to ‘prepare the logical structures (§ 36).

42. Piaget’s uneasiness about perception reflect his findings that children tend to be misled by appearances. So unlike time, ‘space’ is subdivided into ‘appearance’ versus ‘pure systems’ [53], of which geometry is doubtless the most appealing model [54].

[53] the spatial relations simply ‘given’ in appearance between the external objects are in no way reduced in point of fact to pure systems of perceptions (77)

[54] in the period of sensorimotor praxis [...] displacements in space are gradually organized into a scheme which takes the form from what geometers call a ‘group of displacements’, and this scheme, already almost reversible, will play an important role in the organization of representative space [...] (73)

Enlisting geometry thus provides a grounding for a deeper base which links the perception of space to the more ‘logico-mathematical’ base. The idealized domain of Euclidean geometry offers a reassuring detachment from reality and realism with no loss in control (cf. Beaugrande 1991a).

43. At all events, Piaget devoted much effort to finding out when children could solve problems for which they had to predict the ‘horizontal water level in a slanted jar’, or recognize ‘conservation of lengths and distances’ — capacities he says to ‘presuppose a whole system of references bound up with Euclidian metric operations’ and impossible to ‘acquire by the merely perceptive method’ (77f).

44. For related motives, ‘gestalt theory’, to which Piaget feels much closer than to behaviourism, is criticized for attributing too much to perception and too little to logic. He finds it ‘surprising’ that ‘gestalt theory has not elaborated quantitative laws of distorted perception and of good forms’. In his view, ‘all the characteristics attributed by the theory to the perceptive good form (simplicity, regularity, symmetry, resemblance, proximity, etc.)’ ‘constitute qualities essential to the logico-mathematical structures (except proximity)’. Stated in his own terms,

[55] a gestalt is an organization obeying laws of compensation or of intrinsic and independent equilibrium of acquired experience: symmetry, regularity, simplicity. (71)

45. His much sharper criticism of behaviourism castigates both the ‘logical empiricism’ that postulates ‘knowledge furnished by experience, perception and learning independent of and prior to the logico-mathematical coordination’; and the ‘unified science’ whose supporters dispense with ‘the mentalist concepts of “thought”’ by averring that ‘all is language’ (cf. § 21, 50). His own wary position on ‘perception’ and ‘language’ may have partly been a reaction against these extreme reductions.

46. In section B, I tried to show how Piaget’s ‘discourse for special purposes’ (DSP) is more tightly woven than we might assume from the ‘obscurity’ and ‘prolixity’ some readers have diagnosed in his ‘prose style’ (§ 23). My main ‘critical’ tactic has been to explore the discourse as an economy of specialized terms and an agenda of theoretical steps (cf. Beaugrande, in prep.). This method tends to ‘reconstitute’ his mainly expository cyclical discourse into a more narrative stepwise text whose ‘story line’ or ‘plot’ could run like this: having assumed, postulated, or argued A, he had reasonably good motives to go on to B, then to C, and so on. In Piaget’s case, the ‘plot thickens’ rapidly, and the line of his argument is so relentlessly ‘textured’ by his agenda that he often has little choice about how to treat a particular issue. The discourse is thus strikingly consistent — not to say insistent — in a book whose chapters were originally single papers written and published over a span of some twenty years.

47. My discussion exemplifies critical discourse analysis, not in the sense of ‘criticizing’, i.e. finding fault, but ‘critiquing’, i.e. attempting to uncover and make explicit the controlling ideology of the discourse, i.e., the framework(s) wherein ideas are conceived and developed. An ‘ideology’ in this sense is not a term of accusation or bias but merely a heuristic term designating the necessity of having a controlling perspective, given the ‘post-classical’ acknowledgement that discourse cannot be generated directly from reality (§ 11, 13f, 17, 20). So the analysis is not intended as a refutation of a given authority like Piaget but as a bracketing whereby we inquire not whether his claims are ‘true’ in some absolute sense freed of all ideology, but how they are connected to an agenda of goals and an economy of priorities (§ 55). Such a ‘discourse analysis’ might help to reorient a ‘philosophy of science’ or ‘history of ideas’ that underestimates the role of discourse in the access to knowledge and imagines that epistemological constructs like ‘theories' or ‘paradigms’ are free-standing entities apart from the main texts that present them.

48. Putting pressure on the text in order to draw the ‘controlling ideology to the surface typically has one of two major results. Either coherence increases when we recognize the overall ‘control system’ with an operative set of central terms ‘controlling’ each other, and we see the role of claims which, if taken in isolation, might seem surprising, unmotivated, or simply vague. Or, coherence decreases when we find conflicts of interest, e.g. when an authority dismisses claims quite compatible with his own theory merely because they have been advanced by a rival.

49. These two results may well occur together, especially when the domain of investigation is as rich and diversified as human cognition and communication. ‘Internal coherence’ is enhanced at the expense of ‘external’ by carving out a tidy subdomain to explore where consistency seems easier (e.g. ‘isolating what is strictly said’ from ‘communicative context’, § 7). The inclination is correspondingly strong to construct a theory by ‘overfortifying’ its boundaries and overstating your claims about what must and must not be true. The ‘classical realism’ sketched in section A, which assumes that reality itself dictates or should dictate what we can know and say about it (§ 1f), has certainly fostered naive and idealized views of LSP and DSP that are scarcely relevant to discursive practices, and has burdened ‘classical semantics’ with a narrow and sterile agenda (§ 6f).

50. Though Piaget would have hardly expressed it in these terms, he was an astute transitional figure between ‘classical’ and ‘post-classical’ methods. He admired the appeal made by ‘unified science’ to formal logic, an area of philosophy seemingly above all suspicion of the ‘speculation’ often charged against ‘philosophical psychology’ (cf. § 24). But he also saw that the extreme ‘classicism’ of ‘unified science’ insisting on purely ‘physical’ descrption, doomed it to an obtuse reductionism in the human sciences (cf. § 4, 21, 45). So his career was above all a campaign to develop an alternative intermediary psychology no less rigorous than its competitors but much less reductive. Whereas behaviourism, (especially in the U.S.) managed to camouflage its reductiveness by studying large numbers of anonymous ‘subjects’ in sparse detail, Piaget resolved to study a small number of children, including his own, in rich detail ( like his Soviet colleagues Lev Vygotsky and Alexander Luria). He was thus strategically position to realize the unfairness of reductionism and its systematic underestimation of children’s mental capacities.

51. But he realized that his own reconciliation with ‘mentalism’ would not gain wide support unless he had some reasonably ‘classical’ groundings, and he resolved to supply them. Like the devotees of ‘unified science’, he turned to the natural sciences of mathematics and biology, but instead of merely asserting that ‘reasoning about fact and existence, quantity and number’ is the highest and most certain mode of knowledge, or that ‘physical reality’ is the universal framework (§ 4), he posed the much deeper question of how humans can acquire the capacities for reasoning and knowing in the first place. He thus stripped the ‘classical’ framework of its authoritarian, a priori status by taking some of its claims in very strict senses. If ‘unified science’ asserted that knowledge is not innate but acquired by experience, then Piaget demanded to know how human children come to have the more abstract intellectual capacities which physical experience alone could hardly generate and which orthodox behaviourism had studiously declined to explain.

52. Anticipating staunch opposition, Piaget was determined to reason on straightforward premises whose prima facie plausibility would be immediately appealing. Following our main text in section B, the framework of steps in his reason might be compressed and paraphrased as shown below (unbracketed numbering on your handout); you could easily put a ‘therefore’ or ‘ergo’ at the start of every statement from 2 onwards.

1. Human ‘functions’ in the finished state can be studied in terms of their development (§ 24).

3. A theory or model with a strong temporal orientation could indicate what ‘basic rhythm or ineluctable law’ might be at work (§ 25).

4. Such a theory or model should identify an orderly sequence of stages, wherein each stage in the sequence should prepare the conditions needed for the next one, thus ‘enriching’ temporal connections into connections of enablement (§ 25f).

5. The more regular the sequence and its timing, the more lawlike its operation should be (§ 25ff).

6. The factors that stabilize the sequence should thus be distinguished from the factors that destabilize it (§ 27f).

7. Since all humans are biologically fairly similar, stability would be supported by a rich, constraining linkage between biological and psychological factors, whence the strategic value of the composite term ‘psychobiological’ (§ 27f, 40).

8. Just such a linkage characterizes the ‘epigenetic mechanism’ and enhances its ‘chronological regularities’ (§ 26f, 30).

9. A ‘psychology’ with a biological base subsumes the factors that make people similar, whereas ‘social’ factors are the ones that make people dissimilar (§ 27ff).

10. The term ‘psychological’ and its associates, such as ‘cognitive’, therefore stand in opposition to ‘social’ and are hierarchically superior to it (§ 27ff).

11. Since psychobiological’ factors contribute stability and similarity, they are most likely to reveal ‘constant chronological data’, while ‘acceleration and retardation’ would be due to social factors (§ 27).

12. Since the ‘social’ seems obviously ‘collective’ , the ‘psychobiological’ would be associated with ‘individual’; but a model that describes what every individual shares would be ‘general’ enough to count as collective (§ 28, 35).

13. Still, stability and similarity govern all participating factors through ‘equilibration’, the tendency to seek and preserve ‘equilibrium’ (§ 30-33).

14. ‘Equilibrium’ is maintained by ‘thought’ through assimilating the universe to the subject and accommodating the subject to the objects (§ 33).

15. ‘The final form of equilibration’ is logic, which is ‘simultaneously individual and social’ (§ 35).

16. The process of maturation and the sequence of stages represents a steady gain in logical structure, the final stage being the most abstract and rigorous (§ 34ff).

17. The sequence itself is ‘logical’ in that each stage follows from its predecessor in a similar way as do the statements in logical proof, e.g. in mathematics and geometry (§ 36, 42f).

18. The sequence can be reliably charted from the emergence of skills for logical, mathematical, and geometric reasoning, such as ‘conservation of matter, weight, and volume’ (§ 35).

19. ‘Logical’ terms and concepts like ‘reversibility’, ‘inversion’, or ‘negation’ designate a ‘privileged field of intellectual operations’ within ‘a simple and regular system of stages’ (§ 32, 36)

20. Factors which are not so readily governed by logic, such as language and perception, and which have too much continuity to be captured in a tidy ‘chart of stages’, are less essential to the theory (§ 37-45).

21. Logic should be claimed ‘deeper’, ‘clearer’, ‘prior’ and more ‘necessary’ than language and perception, even though these ought to be immensely important for human development and maturation (§ 37, 41).

Stated in these reduced formulations, the tight ‘control’ from step to step helps lend the overall design of Piaget’s ‘theory of stages’ a sense of conviction if not inevitability despite the oddity of some of his theses.

53. From today’s standpoint, when solid evidence has shown that very soon after birth infants are considerably more competent that Piaget supposed (e.g. Stone et al. [eds.] 1974), the need for such a strenuous account seems less dominant. But it was extremely productive then in bringing psychology to terms with the construction of complex, abstract skills. Without research like Piaget’s, those skills might have remained in neglect while psychologists went on studying the ‘conditioning of ‘reflexes’ and ‘habits’ observed in animals (especially rats, cats, and dogs) and projecting them onto humans.

54. Moreover, today’s standpoint has been affected by recent developments in ‘complexity theory’ suggesting that a steep evolution of the type Piaget envisioned is much more probable when systems are ‘far from equilibrium’, where they ‘build themselves up and cascade to higher and higher levels of organization’ (Stuart Kauffmann) (cit. Waldrop 1992: 316). Indeed, ‘a complex adaptive system’ that does reach equilibrium isn’t just stable, it’s dead’ (John Holland) (cit. ibid. 147). The older ‘cybernetic’ model of a ‘self-regulating’ system of the kind that inspired Piaget (§ 31) is now held to be unduly ‘classical’ in making stability the pre-eminent feature of design.

55. Yet, as stressed already, my chief concern here has not been to pursue a refutation (§ 47), but only to show how much of scientific theorizing is carried by special-purpose discursive practices (§ 14). We can then better appreciate why research on discourse for special purposes is far more urgent and rewarding than has been generally acknowledged so far. Indeed, resolute and comprehensive probes of the language of science may well bear on the very possibility of science — not as a mirror of ‘reality’ or a heap of timeless ‘truths’ and ‘facts’, but as an ongoing and steadily ‘enriching’ field of human interaction.

Footnotes

1 To save space, I give only page numbers for my main sample text, namely Piaget’s The Child and Reality (cf. § 23). A reference is omitted if it is the same as for the immediately preceding quote.

2 The selection of a more popular title may suggests that the publishers were concerned about the difficulty of Piaget’s prose.

3 As we shall see, biology and psychology are strategically grasped in the singular as one ‘field’ so that the former serves to anchor the latter (§ 28).

4 It is thus fitting to read: ‘To assimilate an object is to satisfy a need and confer on the action a cognitive structure’ (66).

5 ‘Groupments’ are said to be arrays with a status ‘between groups and networks’ (58).

6 Besides‘reversibility’, Piaget also names ‘correlativity’ and ‘identity’ at this point.

7 Reckoning from 1954, when the paper was first published, he would have been merely 18 years old; probably, the passage was updated for the reissue in 1972 or 1973.

8 Given his opposition between ‘psychological’ and ‘social’ (§ 27ff), his sporadic use of the term ‘psychosocial’ may be merely a gesture.

9 ‘Perceptive forms’ were said to ‘know only constant equilibration displacements’ in [19] (§ 33), but this need not imply a negative role, since ‘displacements in space are gradually organized into a scheme which [...] already almost reversible, will play an important role in the organization of representative space’ (73).

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