Piaget's Logic

Muriel Seltman

• Publisher: Routledge
• Year: 2013
• Print ISBN: 9780415402316
• eBook ISBN: 9781135660994
• Topic: Psychology
• Subtopic: Developmental Psychology
• Index: Psychology

The literature relating to the work of Piaget is large and still growing. Some of it is Piagetian; some of it is critical. Most of this has been directed towards his experimental methodology and the conclusions drawn from it. The justification for the present contribution lies in what the authors believe to be the special embodiment in Piagetian thought of a central theme of our time. This theme is that the only possibility of truth lies in measurability and that knowledge is not recognisable unless it satisfies this criterion. This work is concentrated in the first instance on Piaget's claims that mental structures are exclusively logical mathematical in form, especially since this part of his work has received least attention. This book was first published in 1985.

1 The Central Problem of Genetic Epistemology

Some Preliminary Thoughts

If there is any overriding feature of Piaget's work it is the search for the connection between human knowledge and being through an inquiry into the genesis of knowledge. This objective is truly reflected in the name he has given to his philosophy — Genetic Epistemology.

Piaget died on 16 September 1980, in his mid-eighties which gave him a long life-span stretching back to the end of the nineteenth century — a period still associated with scientific certainty. By the time he had become to some degree aware of himself, the twentieth century was at least ten years old and that scientific certainty, which had only with difficulty preserved an outward stability in the last decade of the previous century, was already seriously undermined, in physics at least. In biology, on the other hand, the field in which Piaget was initiated into science, the latter-day molecular biological extension of neo-Darwinism, with its rigid and unalterable chain of descent, was beginning to emerge.¹ As Professor Darlington expresses it:

The whole idea that personal adaptations, the peculiarities forced upon us by lucky or unlucky circumstances, or by an ameliorative purpose in the Creator, or by the power of the will, were inherited was giving way. The new notion of hard particles ... microscopically visible and mathematically predictable, incorrigibly deterministic and resistant to the interference of any divine purpose apart from that reflected in natural selection, was taking place.²

It is no accident that by his later teens Piaget was much involved in pondering the character of biological evolution and was seeking a reconciliation of developmental theory and logic. If biology was an extremely early influence on him from one source, the other, and perhaps more rooted, influence may have come from his father whose absorption in local history seems to have been conjoined with a great stress on order and deduction.³

The mode of approach is noteworthy. The type of reconciliation sought by the young Piaget seems very much to have been along the lines of iogicising change' — of uncovering the logic of development and thus capturing its essence. In this he was adhering strictly to the nineteenth-century scientific tradition which affirmed first the establishment of fact and then the application of rigorous logical and mathematical instruments to that fact, subsuming it into the accepted framework of knowledge. The certainty of hard fact and an unshakeable belief in the empirical process involved in establishing it seems to have remained with Piaget all his life. In Insights and Illusions of Philosophy (1972, pp. 11-12) he writes:

Although speculative reflection is a fertile and even necessary heuristic introduction to all inquiry, it can only lead to the elaboration of hypotheses, as sweeping as you like, to be sure, but as long as one does not seek for verification by a group of facts established experimentally or by a deduction conforming to an exact algorithm (as in logic), the criterion of truth can only remain subjective, in the manner of an intuitive satisfaction, of'self-evidence', etc.

In his quest to 'logicise change' Piaget's ideas certainly corresponded to the major trends in twentieth-century Western thought. While the analytical schools (positivist and linguistic) in our era reject becoming by affirming the philosophical exclusiveness of the structure of thought alone — a selected aspect of being in relation to both ontology and epistemology — Phenomenology and Existentialism, despite important differences between them and between both of them and the analytical schools, also reject becoming, but do so by affirming the irrelevance of any mediation between experience and thought.⁴ In a sense these latter continental schools eliminate becoming principally by absorbing it into being.⁵

Within the most recent period, however, there have been signs in certain quarters of Western thought that the forms in which being has been asserted either by the rejection of, or by the absorption of, becoming in response to the uncertainty which has underlain twentieth-century science, ever since Quantum and Heisenberg's Principle of Indeterminacy have been accepted, are being seen increasingly as restrictive and unsatisfactory. Even within the strongest citadel of contemporary philosophy, logic itself, this is evident. The genesis of thought is once more emerging as worthy of attention after having lain somewhat fallow for 50-60 years. It is perhaps because of this fallowness that Piaget's thought, while exhibiting highly conventional characteristics, has nevertheless tended to remain solated from the main schools of twentieth-century philosophy with the possible exception of French Structuralism.⁶

Broadly speaking, this new trend takes two forms. On the one hand, there is the endeavour to cope with the question of genesis within the terms jf reference of logic and/or relate the origins of logic to some biological bedrock.⁷ Such approaches could be described as attempts to rectify the balance between being and becoming within the 'establishment'; however, there are interesting developments involving a challenge to the very foundations of Western thought as a whole. But let us look at the former varieties first.

Professor Quine, a foremost American logician, has conceded that the applicability of human logic to reality is only explicable biologically. The very notion that logic is human and does not inhere in the nature of things is a major concession to genetic themes. Similarly, the relatively recent tendency to query objectivity, per se, as a universal category in the light of what is believed to be its inappropriateness in 'the realm of quanta and the realm of the fleeting galaxies'⁸ has begun to undermine the view that logic, even many-valued logic, is a certain guarantee against error. In fact, more and more the notion of 'the object' — the universal, isolated and distinguishable Thing upon which the whole gamut of scientific method depends, together with the logical process associated with it—is coming to occupy a highly conditional position. And this is seen to be directly related to the uncertainty presented by science itself. Reichenbach writes: 'With the corporeal substance goes [the] two-valued character of our language, and even the fundamentals of logic are shown to be the product of an adaptation to the simplest environment into which human beings are born' or 'the realm of the middle dimensions', as he calls this environment elsewhere.

While on the one hand one reaction to the 'thought crisis' of the century has been to reject becoming or absorb it into a being, the opposite reaction, particularly linked to growing non-acceptance of the absoluteness of the logical process, has been to relate, or reduce, our 'objective' knowledge to a biologically determined matrix. Of course, there are those who do not accept this latter (defeatist?) position, but demand a 'bigger logic'. Thus the logician Hilary Putnam (Capek, 1970, p. 454) has put forward the view that logic, after all, may be an empirical science, and David Finkelstein (loc. cit.) has suggested that the traditional conception of logic must be 'widened' or 'generalised'. In these and other cases, it is not the limitation on logic (or objectivity) that must be accepted, but an extension and updating of it to encompass the quantum and the 'fleeting galaxies' — to absorb indeterminacy, in other words. Such a view carries forward, basically unmodified, the fundamental assumptions of the traditional outlook which is ultimately referable to Aristotle himself. Only the mechanism is to change. There seems to be no recognition of the likely outcome of doing this, that by 'widening' or 'empiricising' logic its presumptions themselves are brought into question. Especially and particularly is this so with logic, for whatever form it takes, logic always expresses an 'either—or' situation. It is essentially concerned with the discrete, the separate and identifiable, and not with the continuous and the fluid. To 'widen' logic, therefore, in order to incorporate problems of indeterminacy means either to abandon or circumscribe the logical process in so doing, or, alternatively, force these areas of inquiry into a distorting framework.⁹

The intertwining of biological considerations with the origins of knowledge, even logic itself, combined with an attempt to extend logic to include indeterminacy has, not surprisingly, produced a renewed interest in 'biological epistemology'. As M. Čapek writes, 'The central thesis of this theory (of which there are many varieties) is the claim that the structure of our reason, instead of being ready-made and immutable, is the result of the long process by which our mind [sic] gradually adjusted itself to that sector of reality which is biologically important for us' (Čapek, 1970, p. 448). Beneath the surface of this seemingly innocent and simple statement lies a mass of problems related to being and becoming and the perennial problems of philosophy in general. If genesis is thus made the key to all knowing and understanding there is a strong directive towards regarding the ultimate point of epistemological reference as transformation and not existence. One can detect a desire to move to the position where becoming rather than being is seen as 'real' which is a reversal of the situation pertaining over the past period. This is likely to be a much more difficult position to maintain than its opposite. For in making being predominant one can with relative impunity ignore the question of the origin either of existence, or how it is known, and still produce a coherent stance.¹⁰ By making becoming predominant, however, accounting for the stable or temporary 'permanence' of the forms or structures of existence cannot be excluded. The former may simply exclude the problem of novelty — how new things emerge, or, alternatively, the question of how new are new things? The latter is bedevilled with reconciliation of the 'is' with the 'is not' all the time. To attempt this and remain within a 'respectable' frame of reference, that is, the philosophical-scientific 'establishment as it currently exists, is extraordinarily difficult since it involves a constant threat to the self-evident truths any establishment must rest on. Such difficulty has already become obvious to many scientific workers and those generally familiar with the basic problems of contemporary science. In this reaction we may see the beginnings of a 'non-establishment approach in the new concern with becoming in relation to being.

Such an approach is rather older than contemporary literature of this type might suggest. To some degree it is found in the interest in non-European mysticism represented by such writers as Aldous Huxley, Clive Bell and others in the 1920s and 1930s. Alan Watts, one of the best-known writers and thinkers of this genre, produced much of his work before as well as after the Second World War, Nevertheless, it is especially since 1960 that the trend has widened and deepened to include more and more from all sections and strata of society including an increasing number of practising scientists.

The movement, if it can be called such, is characterised by a reaction against standard notions of 'objectivity', especially in the form of the 'permanent' object as such. Gaining inspiration from the oriental tradition in general, and Zen Buddhism and Taoism in particular, this thought-movement tends to abolish the concept of 'boundaries' isolating objects from each other by treating such boundaries as illusory or at least provisional

Most of Watts's writings are in the fields of theology, psychology and general philosophy, although he is also concerned with the nature of science. His influence and that of others in the West, plus the more direct influences of oriental teachings themselves, have helped to spread this type of thinking within physical science especially in the last decade or so. Names such as F. Capra (The Tao of Physics, 1975), Gary Zukav (The Dancing Wu Li Masters, 1979) and David Bohm, particularly in his latest book (Wholeness and the Implicate Order, 1980), are representative of a trend, notably in physics, which, some say, even has its parallel in the increasing use of qualitative terms in the technical heartland of sub-atomic research itself (for example, ' strange' particles and the use of the word 'charm' in relation to certain sub-atomic particles. Note also a similar feature in astrophysics: 'pulsars', 'collapsars', 'black holes', 'quarks', and so on.)

Characteristic of all these writers, scientists and non-scientists alike, is the stress on pure relationship, the rejection of 'things' in preference to processes, the predominance of the idea of totality (wholeness) and flow. All are most clearly committed to the paramountcy of becoming within which, contrary to the earlier 'establishment' philosophical tradition in the West, being must be absorbed.

Where does Piaget fit into this picture? For most of his intellectual life, until, that is, the 1960s, the objective of'logicising change' seems to have predominated. Put another way, the stability of the claimed structural character of mentality appears to have held first place, and the process of arriving at this stability was judged within its context. In the latter part of his writing life, however, Piaget appears to have swung more and more towards regarding this process as central to his theory, not the structures which are the outcome. One could perhaps describe this later emphasis as 'transformational logic' in contrast to the former phase. But in both cases Piaget reflects in his own way on the wider problems of relating being to becoming typical of this period. What we shall be considering below is Piaget's own difficulties in attempting either to impose the linearity and discreteness of logic on to Actuality or to import the continuity and flow of Actuality into the non-spatio-temporal world of logico-mathematically conceived structures. For change understood as transformation in the sense of transcendence, and not mere displacement or alteration in degree, cannot be logicised by imposing linearity upon it. In fact, the main problem, as we shall find, is to free thought from linearity in order to begin to approach an understanding of its origins. For becoming is not simply to be identified with the lapse of time, or time-governed change or evolution. Rather one should see the latter as a particular mode of the absorption of becoming into being. The historical-evolutionary concept, very much the product of the nineteenth century, is wholly linear and logico-mathematically conceived. It is more to do with predictable sequence than creativity. On the other hand, becoming-in-the-context-of-being, and vice versa (Hegel's conception of it), expresses co-existent aspects of Actuality, that is, the coincidence and co-terminousness of being-and-becoming.

Thus the (biological) evolutionary and historical aspects of Piaget's thought, whether considered individually or socially, are as much reflective of the 'logicisation of change', or alternatively 'transformational logic', that is, an imposition of logico-mathematical linearity on thought, as the structural analysis itself. It is these facts that make the study of Piagetian thought at its roots particularly useful and pertinent, which is enhanced not detracted from by the fact that he is a 'loner' with a sharply individualised approach to epistemological problems.

Piaget’s Antecedents and the Lamarckian-neo-Darwinian Controversy

There has been considerable discussion of the influences on Piaget, not least by himself in his 'Autobiography' (Boring, etal., 1969, passim) and in Insights and Illusions oj Philosophy (1972c, Eng, edn). Such influences are very numerous and sometimes it is not clear where they derive from. It is not our intention, nor is it relevant to our purposes, to investigate these in detail. Broadly speaking, one can say that they consist of two main strands, on the one hand arising from biology and biological theory, and on the other from scientific epistemology in general and logic and mathematics in particular. There is a whole galaxy of names in this last area to be tound in Piaget's writings, especially in the later books. But he himself attaches particular importance to L. Brunschvicg and, to a lesser extent, Poincare as major influences on his thought (for example Piaget, 1950, p. 112; 1971, p. 39). Perhaps Poincare's most significant impact on Piaget is to be seen in Piaget's comment in Insights and Illusions: 'as is well-known, Poincare, despite his conventionalism, made the concept of a "group" an a priori structure' (p. 73). Brunschvicg, however, appears to have had greater influence on Piaget, especially in his earliest years.

Léon Brunschvicg, a Critical Idealist philosopher, whose outlook combined Kantian constructivism with a stress on the historical approach to the study of mental activity, regarded mathematical judgement as its highest level. For him, philosophy consisted solely in the process of judgement which performs the function of uniting conceptual form and content. This is what makes philosophy, for Brun...

Table of contents

• Cover
• Title
• Copyright
• Contents
• Preface
• Acknowledgements
• 1 The Central Problem of Genetic Epistemology
• 2 Structures, Operations and Groups in Piaget's System: A Preliminary Survey
• 3 Mathematical Structures of the Concrete Operational Stage
• 4 Mathematical Structures of the Formal Operational Stage
• 5 The Equilibrium Model of Cognition
• 6 Equilibration I. The Apparatus of Cognition
• 7 Equilibration II. Cognitive Growth
• 8 Problems of Logic and Mathematics
• 9 Scientific Method and the Piagetian System
• 10 Epilogue
• Notes
• Select Bibliography
• Name index
• Subject index