FROM 'GENETIC TO 'EPIGENETIC EPISTEMOLOGY:
THE FORGOTTEN WORKS OF JEAN PIAGET, 1965-1974
JEREMY TREVELYAN BURMAN
A THESIS SUBMITTED TO THE FACULTY OF GRADUATE STUDIES
IN PARTIAL FULFILMENT OF THE REQUIREMENTS
FOR THE DEGREE OF
MASTER OF ARTS
GRADUATE PROGRAM IN INTERDISCIPLINARY STUDIES
YORK UNIVERSITY
TORONTO, ONTARIO
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While these forms may be included Bien que ces formulaires in the document page count, aient inclus dans la pagination, their removal does not represent il n'y aura aucun contenu manquant. any loss of content from the thesis. Canada ABSTRACT
Jean Piaget was one of the most influential psychologists of the 20th century. Yet his theory regarding "the genesis of knowledge" (genetic epistemology) has been badly misunderstood. As a result, many of the criticisms it attracted were misdirected; remedies provided to address problems that never were. To complicate matters further, the most mature of Piaget's works - those developed in the last decade of his life - have been described as promulgating a "new theory" that would revolutionize the textbook presentation of his ideas. The suggestion, there, is that this "new" Piaget should be presented as a contemporary figure; the author of an evolutionary-developmental framework that could contribute anew to those fields influenced by the "old" Piaget's decades of work. The challenge, here, is therefore double: to put the "new theory" in context by reviewing the history of its emergence, while at the same time excavating the larger theory that informed those works.
IV In memoriam
L. M. Trevelyan, 1906-2005
v ACKNOWLEDGMENTS
Given Jean Piaget's position in the upper echelon of Psychology's pantheon of heroes,1
the typical approach to such a project would have been to examine the emergence of his
"new theory" from within what would seem to have been his own discipline. (Indeed, in
this case, that was even possible: York University has an excellent program that would
have enabled such an examination—an MA in the History and Theory of Psychology.)
Yet it was not clear, at the outset, that this project was something that could have been
pursued from within anything but the texts themselves: a number of commentaries note,
for example, that Piaget's interdisciplinarity has caused problems for interpreters
approaching his work from a single perspective.2 Ensuring the overlapping of multiple
disciplinary perspectives at the level of the supervisory committee, coupled with the
Interdisciplinary Studies program's guarantee of each student's freedom to pursue their
ideas through any graduate course offered in the province, promised to help ensure that
any resulting narrative would be as unencumbered as possible by current fashion or
disciplinary allegiance. Although the path taken may not always have been optimal,
every opportunity was presented "to get things right." For making this possible, while at the same time letting me find my own way, I am grateful for the guidance and support of my supervisory committee: Matthew Clark (History), Jan Sapp (History of Biology), and
1 (Haggbloom et al., 2002) 2 This applies equally to the perspective afforded by working in a single language (as noted by, e.g., Kitchener, 1986, p. vii; Smith, 1993, p. xiv) as it does in approaching it from a single discipline (e.g., Chapman, 1988, pp. 2-3, 261; Gruber & Voneche, 1993, p. xv; Messerly, 1996, p. xiii). VI Fred Weizmann (History of Psychology). Yet despite their enormous contribution, both individually and together, they are but the most visible among the many who helped.
For encouraging me to undertake this project in the first place, I would like to thank Jordan Peterson and the members of the Peterson Lab at the University of Toronto.
(It was in Jordan's graduate-level "Maps of Meaning" course - which I was invited to audit in 2003 - that I first learned not only that so many of Piaget's works remained untranslated, but also that many of the books that do exist in English contain errors.) Jan
Sapp's encouragement a year later, in his graduate-level "Fundamentals of the History of
Biology" course (which I took as a special project after graduating with my Hon.B.Sc in
Psychology), was also of critical importance. It was there, although mostly in informal discussions after class, that Jan introduced me to the history of science as a study of more than names and dates. For giving me my first opportunity to explore some of Piaget's lesser known biological ideas, and then inviting me to join him at York, I thank Jan enthusiastically for enabling me to write what you now hold in your hands.
In developing the ideas contained herein, pursued in projects undertaken as a member of the MA program itself, a number of documents were prepared and submitted for peer-review.3 Some of the drafts for these, or for chapters that were ultimately cut from the final manuscript, were also presented at conferences and departmental colloquia.4 The project benefitted enormously from the resulting interactions: with
3 Portions of these have been used throughout, with attribution where required by University Policy (Burman, 2006, 2007b, 2008a, in press). This has been undertaken with the consent of the thesis committee, also as per University Policy. 4 (Burman, 2007c, 2007a, 2008b) vii friends (Laura Ball, Jason Goertzen, Paula Miceli); colleagues (Elizabeth Cavicchi,
Tyson Gofton, Jonathan Tsou); teachers (Chris Green, Mike Pettit, David Reid, Jan Sapp,
Thomas Teo); society members (Jan Boom, Michael Chandler, Brian Cox, Michel
Ferrari, Chris Lalonde, Cynthia Lightfoot, Constance Milbrath); editors (Roger Ariew,
Chris Nunn, Hank Stam); and eminences (Harry Beilin, Mark Bickhard, Robert
Campbell, Jeanette McCarthy-Gallagher, Leslie Smith, Phil Zelazo). Without the collaborative sharing of ideas through each of these levels, it would have been very nearly impossible to navigate the complexity of Piaget's interdisciplinarity. (Indeed, the problem itself- excavating that which underlies the transition to his "new theory" of situated meaning - arose directly from several informal discussions at the annual meetings of the Jean Piaget Society, first in Vancouver in 2005 and again a year later in
Baltimore in 2006; the core of Chapter III was then presented in Quebec in 2008.) That said, however, the project would also not have been possible without the existence and support of the Graduate Program in Interdisciplinary Studies at York University (Marlene
Kadar, Jamie Scott, Patrick Taylor, Renate Wickens, and especially Ouma Jaipaul-Gill).
Similarly, for their support during the process, I would like to thank Tony Burman,
Jennifer Dettman, Heaton Dyer, Neil and Caitlin MacGregor, and Margot Trevelyan.
The project itself was made possible through the generous financial support of my family; the Canadian Union of Public Employees, Local 3903; the Ontario Student
Opportunities Trust Fund; and the Faculty of Graduate Studies at York University. It is
viii dedicated to my grandfather, L. M. Trevelyan, who died shortly after I received the letter that accepted me to the program. TABLE OF CONTENTS
Abstract iv
Acknowledgements vi
List of Figures xiii
Introduction: The Forgotten Works of Jean Piaget, 1965-1974 1
Three Short Historical Dialogues that Define the General Problem 9
Chapter I: From Genetic to Epi-Genetic Epistemology 10
Toward the New Theory 15
Genetic Epistemologies 17
Misunderstanding Genesis 25
Beyond Genetic Epistemology 28
Evolutionary Epistemology 30
Prospective Conclusion: The Purpose and Approach of this Thesis 34
Chapter II: The Return to Biology 38
The Hard Core of the Old Theory 40
From Biology to Knowledge 41
The American Context 50
Staging the Return 53
Biologic et Connaissance 55
Reading Guide and Exegesis 56
Recapitulation 87
x Reception and Errata 87
Prospective Conclusion 90
Chapter III: An Important Secondary Narrative 92
Kurt Godel (1906-1978) 93
The Two Contexts of "Consistent" and "Complete" 96
What Piaget learned from Kurt Godel 99
Recapitulation 113
Reception and Errata 113
Prospective Conclusion 117
Chapter IV: The Development of Things to Think With 118
Functions and Structures in Biology and Knowledge 120
Memoire et Intelligence 136
Reading Guide and Exegesis 137
Recapitulation 152
Reception and Errata 153
Prospective Conclusion 156
Chapter V: The Evolution of Things to Reflect On 157
Socio-cultural Studies 160
Explanation in Sociology 161
The Biological Interpretation of the Three Forms of Epistemic Inheritance.. 172
Le Structuralisme 185
xi Reading Guide and Exegesis 186
Recapitulation 199
Reception and Errata 200
Prospective Conclusion 203
Chapter VI: Conclusion 204
Review of Core Themes 208
Misunderstanding Structures 220
Organizing the Structures of Functioning 226
From Dynamic Structures to a New Take on Dialectics 229
So What? 233
Where to From Here? 236
References 240
xn LIST OF FIGURES
Figure 1: Jean Piaget 8
Figure 2: An illustration of Piaget's stages as a staircase 13
Figure 3: A detailed examination of Piaget's articles 39
Figure 4: Piaget's conception of equilibrating interdisciplinary relations 43
Figure 5: My illustration of Piaget's take on Baldwin's circular reaction 48
Figure 6: Waddington's illustration of the "epigenetic landscape" 61
Figure 7: Waddington's illustration of an adaptive shift 81
Figure 8: Organism P is pushed to develop as P' 83
Figure 9: Rene Magritte's (1928-1929) La trahison des images 94
Figure 10: Waddington's illustration of the levels of action in selection 130
Figure 11: Piaget's illustration of the experimental setup 139
Figure 12: Piaget's illustration of the experimental setup 141
Figure 13: Piaget's illustration of the experimental setup 142
Figure 14: Piaget's illustration of the experimental setup 147
Figure 15: My illustration of Piaget's differentiation of selection pressures 159
Figure 16: My illustration of Piaget's "problem of the social" 171
Figure 17: Waddington's illustration of four of Piaget's five varieties ofLimnaea... 178
Figure 18: An illustration of the "overlapping waves" model of development 179
Figure 19: Repeat of figure 5 206
Figure 20: Repeat of figure 6 209
xiii Figure 21: Waddington's genotype-epigenotype-phenotype akin to neural net 213
Figure 22: Repeat of figure 10 215
Figure 23: Repeat of figure 16 219
Figure 24: Baldwin's circular reaction, updated 230
Figure 25: Waddington's illustration of the complex system of interactions 232
Figure 26: My modification of Waddington's illustration of the levels 235
xiv INTRODUCTION
THE FORGOTTEN WORKS OF JEAN PIAGET, 1965-1974
Jean Piaget's prodigious output helped shape decades of subsequent research in
psychology, education, cognitive science, and the philosophy of science.5 Still, there
remains an undercurrent of dissatisfaction among Piaget scholars (mostly psychologists
and educators, but also philosophers, anthropologists, and biologists)6 regarding the
treatment of the fundamentally important, though still mostly unexamined,
epistemological framework that informed his seminal ideas on child development.7
Misunderstandings of these basic issues have informed decades of work; time lost, and
resources spent, criticizing perceived flaws that were never truly there.8 Yet when
commentators - in particular Harry Beilin - began describing the most recent among
5 Piaget is consistently ranked as one of the most influential psychologists of the 20th century (Haggbloom et al., 2002). For an examination of his influence on psychology, see (Voyat, 1977; Bond & Tryphon, 2007); on education, see (Zaccaria, 1978; J. S. Hall, 2000; P. Cunningham, 2006); on cognitive science, see (Boden, 1994, 2006); on the philosophy of Thomas Kuhn, see (Tsou, 2006; Burman, 2007b). 6 The Jean Piaget Society was established in 1970. Through its committees, symposia, conferences, books, book series, and journal, it serves as the institutional framework organizing an international group of researchers interested in the evolution and development of knowledge. In 1989, a subtitle was added to reflect this more general orientation: "Society for the Study of Knowledge and Development." At the time of submission, the membership of the society's Board of Directors (22) was drawn primarily from Departments of Psychology (12), but also from Education (4), Philosophy (1), and Social Anthropology (1), as well as from several interdisciplinary institutes devoted to the study of development and learning (4). Several members also have cross-appointments to these and other faculties (e.g., Cognitive Science, Biology, and Computer Science) and many have served in senior leadership positions at other societies (esp. the American Psychological Association and the Society for Research in Child Development) and at scholarly journals (e.g., Applied Developmental Psychology, Cognitive Development, Developmental Psychology, Human Development, International Journal of Behavioral Development, International Journal of Psychology, New Ideas in Psychology) and monograph series (e.g., Monographs of the SRCD, The Developing Mind Series). Collectively, these affiliations provide a basic snapshot of the contemporary community; those with an explicit interest in Piaget's ideas, as well as others related to them. 7 This one-sidedness has recently been demonstrated empirically, using citation analysis, by (Bond & Tryphon, 2007). 8 (see e.g., Lourenco & Machado, 1996) 1 Piaget's works as constituting a "new theory,"9 it appeared as though an opportunity had emerged to address this collective frustration: the "new" Piaget could be introduced to students as a relevant contemporary figure, his mature ideas critiqued and built upon directly. But this remedy is deceptive in its simplicity: the implications of the later additions to the Piagetian corpus, and thus the divergences between "old" and "new" theories, have never been fully charted. Also, the attribution - "new" - does not follow conclusively from any one of the available primary source texts.10 And for those who wish to build on Piaget's mature theory, or to teach it, this presents a fundamental problem: Where to start? (Could Piaget be treated as two separate characters, like the early and late Wittgenstein, or should his career be taught as one long continuous historical narrative?)
To clarify what it means for the "new theory" to be new, it will be useful to outline the trajectory of Piaget's theorizing. Beilin characterized this as following four thematic periods, using dates drawn from the publication of Piaget's books. Since these books were often preceded by articles, however, Beilin's list can be revised with starting dates derived from a study of Piaget's bibliography.11 The result provides a much better
9 (Beilin, 1989a, 1992a, p. 202, 1992b, pp. 1, 6-7; see also 1980, 1989b, pp. 101-127, 1999, p. 121) 10 This is perhaps a function of number: Piaget wrote or edited 61 books and 10 shorter "brochures," collaborated on or oversaw the 37 volumes in his edited series (plus an encyclopaedia and a set of reference books), and authored or collaborated on over 520 articles. His nearly continuous publication of "results," as well as the ongoing development of the theory interpreting them, makes it difficult to point to any one volume as either "foundational" or "transitional." Of course, this is not to say that no one has tried to do so. Indeed, a large exegesis describing the empirical works from the "new" period has been published in French (Ducret, 2000). Unfortunately, however, this ignores the related advances in theory (L. Smith, 2002). 11 There are several published bibliographies of Piaget's work (e.g., Tschopp, 1975; McLaughlin, 1988). An updated listing can be found at the Piaget Foundation website: www.fondationjeanpiaget.ch 2 reflection of what was underway and when—four overlapping stages of professional development, each with a slightly different focus:
1. The child's perception of reality, as mediated by social interaction (1920-1932).12
2. A theory of sensorimotor adaptation (1927-1939).
3. The "standard theory" of child development, presented in introductory textbooks
as a theory of stages: the step-wise construction of operational structures which
enable cognitive capacities (1935-1974).
4. A "new theory" of situated meaning, synthesizing his earlier functionalist roots
with the genetic structuralism of the third period (1965-1980, with many more
posthumous publications).
The result is reminiscent of the stages of development in Piaget's own theory: each subsumes the last. However, in examining Beilin's method it is clear that his division of
Piaget's career into four parts was also based upon a series of problematic assumptions.13
The most important of these takes the form of an omission: disregarding the importance of Piaget's background and training in biology, thereby focussing the story of his intellectual life on the development of his psychology alone. (Without mentioning Beilin by name, several commentators have noted that this omission is a critical error.)14
This is the period criticized by Vygotsky, to which Piaget (1962/2000) later responded. 13 (Beilin, 1985, 1992a) lists the four periods without providing a satisfactory explanation for the omission of what Piaget did prior to undertaking them—his background and training in biology. The secondary literature typically cites (Montangero, 1985) for this, but the actual reference is to a chapter in that book authored by Beilin that he also later published separately in expanded form (Beilin, 1985). 14 (esp. Gruber & Voneche, 1993; see also Langer & Killen, 1998; Parker, Langer, & Milbrath, 2005). 3 This error can be easily remedied. By adding a formative period to Piaget's trajectory, which we will call "level zero" (to preserve the meaning of discussions of "the four Piagets" in the secondary literature in Psychology), we immediately get a fuller picture of his career:
0. Natural history and biometry (1911-1929, 1965-1976).
However, in adding this early level - and including the dates drawn from a study of both books and articles - we see immediately that taking a "stage theoretic" approach to
Piaget's development does not fit the data: there is not a clear step-wise progression. In addition, looking deeper to see the application of ideas drawn from his "formative" period at the dawn of his "new" period, Piaget's development also seems to include a
"regression."
The resulting arrangement contradicts the textbook presentation of "stages" as being like a staircase, at least in application to Piaget's own development. Yet it also highlights a key, neglected aspect of his theory which we can use to go beyond the textbook portrayals: the dialectical nature of developmental change.15 (While his early work is indeed characterized by a constructive dialectic - assimilation, accommodation, equilibration - the new theory seems also to have been inspired by a return to the questions raised by his earliest work using statistics to classify molluscs, synthesized with his psychological theory and the genetic structuralism that came after.) The addition also
15 Piaget talks about the dialectic, in general terms, from the very beginning. His intended meaning for its use in the new theory - following his discussion of Levi-Strauss' critique of related notions - is first made explicit in (Piaget, 1968/1971). This is then formalized (in Piaget, 1971/1977, 1980a) and generalized to the construction of all knowledge (in Piaget & Garcia, 1983/1989; see also Widmer & Piaget, 1977a). 4 provides a picture of Piaget's theory that is more consistent with his own conception of progress in science and child development: advances are first made within a structure, then the results of different structures are compared, and finally they are synthesized in a stronger total structure.16 That said, what is more important for our purposes is that this critical approach of Beilin's staging highlights an overlap at the transition between the periods described as belonging to Piaget's "old" and "new" theories: 1965-1974. This overlap is what will be examined here.
The articles from the first half of the transitional period between "old" and "new," spanning 1965-1969, informed (or were based on work that informed) three books.
These, in turn, collectively form the foundation of the new theory. Formerly without a place in the accepted canon of Piaget's works in psychology, and typically mentioned only as important divergences, I have come to refer to them as the "forgotten" works:
• Biology and Knowledge, 1967 (translated in 1971), in which Piaget describes the
return to his "first love" and the subject of his doctoral training - biology - as a
source of scientific explanations for psychological and epistemological problems;
• Memory and Intelligence, 1968 (translated in 1973), in which he reports the
findings of a series of empirical studies examining the implications of his return
to biology for psychological enquiry; and
• Structuralism, 1968 (translated in 1971), in which he expands the discussion
outward into social theory with the aim of laying the foundations for a
16 This is the "intra, inter, trans" dialectic introduced in (Piaget & Garcia, 1983/1989) and discussed here in Chapter VI (see also Burman, 2008b). 5 biologically- and empirically-informed theory to explain the processes involved in
developing knowledge both individually and collectively.
It is clear that these books comprise the missing link between "old" theory and "new."17
My aim in this thesis is therefore to show how they can be incorporated into the history of Piaget's theorizing, thereby revising our understanding of his later works as being discontinuous with the famous earlier studies of child development.18 In short, I suggest that it is not necessary - on the basis of the material reviewed - to separate the "new
Piaget" from the "old." In fact, one derives a better appreciation for the larger meaning of his last works by retaining the connection.
As we will see in this examination, Piaget's theory is not really about stages at all.
Rather, it is about the construction of increasingly powerful explanatory structures: internal representations of the logic of the external world, constructed by an active subject in response to anomalies encountered in experience and serving to alter that subject's exposure to future such selection pressures. Beilin's characterization of
Piaget's works as promulgating a "logical hermeneutics of action" (an internally- and externally-constrained interpretive framework for understanding acts of behaviour) is subsumed under this view, as are his earlier works on the stages of child development.
But this connection is only made clear in the three forgotten transitional books, the
17 The projects that became the first "new" books were begun just as the forgotten transitional books were published. This is made clearer in Smith's (2002) review of Ducret's (2000) overview of the new period works, in which Smith dates the empirical projects composing the "new theory" as having started in 1968 (see also Piaget & Smith, 2004/2006, p. 2). 18 This is obviously Piaget's intent, as is made clear in his final synthesis: Psychogenesis and the History of Science (Piaget & Garcia, 1983/1989). 6 collective narrative of which has never been thoroughly articulated. This thesis is therefore an attempt to deconstruct the ideas contained within those books, while putting them in context. It is, in short, an attempt to lay a firmer foundation for examining whatever in the "new theory" was considered sufficiently worthy of scholarly attention that it be labelled as such: a conceptual history of Piaget's position as it shifted toward
something new and surprising and, as Beilin suggested, potentially revolutionary.
7 Figure 1. Jean Piaget, as he appeared during the transitional period of forgotten works. 19
1 Photo by Christiane Gilleron, c.1970, published in (Gruber & Voneche, 1993, p. 2). Three Historical Dialogues that Define the General Problem
Hall: Are there any pitfalls to trap the unwary psychologist?
Piaget: The danger to psychologists lies in practical applications. Too often
psychologists make practical applications before they know what they are
applying. We must always... beware of practical applications when we do
not know the foundation of our theories.20
* * *
Evans: Are you concerned about the fact that some people who have not fully
comprehended your ideas have moved too quickly into application?
Piaget: Oh yes. That's the great danger. I have the impression that very few
01 people have understood. * * *
Bringuier: Do you feel you've been badly interpreted?
Piaget: Yes, in general.
Bringuier: As to pedagogical application, or as to understanding of your research?
Piaget: No, no. As to understanding the theory itself. Well, I think it's the
common lot. My colleagues understand it thoroughly. Besides, one keeps
thinking one will be better understood later on.
20 (in E.Hall, 1970, p. 53) 21 (in Evans, 1973, pp. 51-52) 22 Interview conducted 1969, later published (in Bringuier, 1977/1980, p. 54) CHAPTER I
FROM GENETIC TO EPI-GENETIC EPISTEMOLOGY
Jean Piaget (1896-1980) was a Swiss naturalist, philosopher, and psychologist.23
Although known primarily for his pioneering studies of child development - the influence of which place him among the most eminent psychologists of the twentieth century24 - his professional life spanned several disciplines: psychology, sociology, philosophy of science, history of science, and education.25 In addition, his early training
(and doctorate) was in what we now call "biology." These influences come together in his theory of how children grow into the world: a constructive theory regarding the genesis of knowledge, which he called "genetic epistemology."26
Genetic epistemology examines how we come to know something about anything.
It is an approach that attempts to chart the mechanisms underlying how humans think; how we each become competent to respond intelligently to the objects that surround us.
Yet this is not "just" a psychological problem, as Piaget occasionally liked to say.27
Rather, psychology brings with it a set of scientific approaches that can be used to examine a set of larger philosophical issues: namely, those surrounding the possibility of knowledge and the meaning of "truth." An extended example will make this clear.
23 (in Flavell, 1963, p. vii) 24 (Haggbloom et al., 2002; Papert, 1999, March 29) 25 Piaget had influence in other areas as well. These are simply the disciplines in which he held professorships (at the Swiss universities at Neuchatel, Geneva, and Lausanne, and the Sorbonne in Paris). 26 This phrase was ultimately incorporated into the titles of several of his works (e.g., Piaget, 1950, 1970/1971, 1970/1972, 1980b). 27 (see e.g., firinguier, 1977/1980, pp. 3-7) 10 All children grow up in a family environment. Whether this is in a house, a flat, a hut, or a cave (with one parent or two or more), the dynamics of this early environment constrain the set of behavioural possibilities that "make sense" in response to any given situation. In other words, each family dynamic has a "logic" into which the actions of the developing child must fit. Part of this logic is given by the location (house, flat, hut, or cave), and part is given by the personalities of the parents, friends, neighbours, and acquaintances who collectively define the social context. This context is in turn maintained and reinforced with a language, which is also a reflection of the logic.28
There is, in short, a "way of being" that "makes sense" in some self-consistent way—as
"norms" and "customs" (i.e., as "culture").29
If a child is to be a member of its group, rather than an outcast, it must learn the
O A logic of its context and contribute to its maintenance. It must tell the "right kind" of truths. If it fails to do this, it will not survive. (Children are simply too vulnerable: they need to be fed, kept safe, sheltered, provided for, taught, nurtured, and loved.) Worse, the family might not survive either. As a result, parents - over many generations - have thought up clever ways to address this problem; ways for the family system to stay coherent, consistent, and complete relative to the needs of its most vulnerable members.
This is the collective wisdom of the species, passed on to each new generation through myth, legend, art, culture, and science. It is taught according to a set of practices called
28 (Piaget in Piattelli-Palmarini, 1979/1980; Koechlin & Jubault, 2006) 29 (see e.g., L. Smith, 1993; L. Smith & Voneche, 2006) 30 We might generalize, using contemporary language, and call this a variety of "niche construction" (Laland, Odling-Smee, & Feldman, 2000; Odling-Smee, Laland, & Feldman, 2003). 11 apprenticeship, education, and training.31 And it is the standard according to which
"truths" are judged as a reflection of the real.32
There have been many attempts to explain how this "way of knowing and acting" works, partly as a way to extend each culture's advances into the next generation.33 In interacting with his own children, however, Piaget found that the contextual logic of the environment has a counterpart in the individual: a developing "psycho-logic" of stimulus transformation, according to which the child comes to order ("see" and "understand") the different aspects of its environment in increasingly complex ways. But rather than being received in the discipline as Piaget's contribution, the studies intended to demonstrate how this psycho-logic is constructed instead came to inform a more popular sub-theory.34
This is known now simply as "stage theory."
31 (Burman, 2008b) 32 Under this conception, an "untruth" is simply something that exists outside the logic of the social system, whether it's "really real" or not (cf. T. S. Kuhn, 1962/1993). An "untruth" is therefore not simply an irrelevance, or considered false, but it is also a threat (Peterson & Flanders, 2002). 33 Thomas Kuhn's (1962/1993) theory of scientific revolutions is the most famous contemporary example, but there are many others. (For more on the comparison between Piaget and Kuhn, see Tsou, 2006; Burman, 2007b). 34 In an analysis of the latest edition of the Handbook of Child Psychology, Bond and Tryphon (2007) found what they characterized as "selective attention" among the authors who commented on Piaget's work: "What appears relevant to child psychologists covers only a restricted period in Piaget's work, and generally does not do justice to Piaget's own explicitly epistemological perspective" (p. 1). Indeed, this treatment is in direct contradiction with what is noted explicitly in his citation from the American Psychological Association: "Starting as a biologist interested in the history of scientific thinking, he has approached heretofore exclusive philosophical questions in a resolutely empirical fashion and created epistemology as a science, separate from philosophy, but interrelated with all human sciences. Almost as a by-product of this his chief work he has amassed during half a century ingenious observations and controlled data on human thinking which represent a unique and lasting monument in the psychological literature. Having been known and honored all over the world since his early writings, he becomes the first European to receive the APA Distinguished Scientific Contribution Award. Our organization thereby recognizes the seminal influence which this Swiss scientist exerts on all scholars concerned with human knowing and its development" ("Distinguished Scientific Contribution Awards: 1969: Citation for Jean Piaget," 1970, p. 65). 12 Stage theory is a scientific construct. It tells a story about how children develop, which is commonly understood to follow a "staircase" of increasing competence.35
Structures at each stage are necessary for proper functioning at the next. There is also an invariant order of progression in the causation of competences, such that each step builds on what came before.36
Formal operational
Concrete operational Stag© Pre operational
Sensorimotor
0-2 2-7 7-12 12+ *9 e
Figure 2. An illustration of Piaget's stages as a staircase of development.
Although this construct has since been applied specifically to parse the development of individual achievement, Piaget was more interested in the development of what he called
35 See, most famously, the neo-Piagetian interpretation by (Case, 1992; critiqued by Bickhard, 1993). 36 This is one of the least well-understood aspects of the theory: the question is not "what can this child do," but "what is enabling this child to act in that way." From the results of the clinical interviewing method, Piagetian researchers make an inference regarding the causal substructure that enables the production of the observed competences. Falsification is therefore not a matter of finding an impossible behavior, but of inferring (and defending) the existence of an impossible structure. For related discussion, see (Lourenco & Machado, 1996). (Siegler, 1996, p. 85) 13 the "epistemic" subject: the ideal type of developing knower from which each individual diverges and which defines the common pattern of growth shared by every knower in all cultural contexts.
Piaget found, over many decades of experimentation, that development could be characterized as a process of "decentration." According to this interpretation, the stages are a function of the lineage of transformations that extend the mind out from the body and into the world: infants are solipsistic in their actions (treating the subjective universe as an extension of their physical being), children are self-centred (with difficulties in perspective-taking), and adults are - ideally - interested in maintaining and constructing systems to resolve ever-larger problems of self- and social-contradiction.38 This proposal has been enormously influential; within psychology, its empirical demonstration is considered Piaget's main contribution.39
Yet stage theory was a means to an end.40 As a sub-theory in genetic epistemology, the purpose of the work that informed it was to explain how knowledge is constructed; measuring, cataloguing, and describing how children develop was merely a side-effect of the attempt to achieve this larger goal.41 But this achievement would require causal mechanisms, as well as an engine to drive them. The attempts to define
38 A further implication is that any given act can be considered a reflection of the structure of thought in the mind that produced it, which can in turn be characterized relative to its adaptedness to the social context in which it developed (cf. Claparede translated in Burman, 2008b). 39 This is likely due to the influence of (Flavell, 1963) over (Hunt, 1961) in popularizing Piaget's work in the 1960s. 40 (see e.g., Vuyk, 1981, p. 192) 41 As indeed was noted by the American Psychological Association in their citation recognizing his work ("Distinguished Scientific Contribution Awards: 1969: Citation for Jean Piaget," 1970, p. 65). 14 such mechanisms would occupy the last years of Piaget's life. As we saw in the three historical dialogues that defined the general problem of Piaget scholarship, presented at the start of this section, he was often frustrated that those whom he had influenced did not understand.42
Toward the New Theory
Recently, Harry Beilin (1922-2007) - an American professor of developmental psychology who helped promote Piaget's ideas in the English-speaking world - proposed that the latest among Piaget's later works collectively reflect the emergence of a "new theory" that is dramatically different from stage theory.43 Yet the project that was to follow-up on this conjecture had to be dropped for reasons unrelated to its refutation.44
As a result, the idea has never been developed.45 That, in a nutshell, is the purpose of this
This misunderstanding has been attributed to Piaget's interdisciplinarity: "Piaget's inherently interdisciplinary orientation explains in part why his theory often has been misconstrued by psychologists from within the perspective of their own discipline. Assuming that his questions were the same as their own, they have frequently been disappointed in the answers that he gave.... This assimilation of Piaget's goals to those of mainstream psychology has [also] resulted in some serious misunderstandings. The portrayal of his theory in most psychology textbooks, the conventional wisdom shared by followers and critics alike, has been inaccurate on a number of important points" (Chapman, 1988, p. 2; see also Lourenco & Machado, 1996). Piaget's research partner, Barbel Inhelder, put it this way: "Although Piaget's publications are widely disseminated, many psychologists find his work difficult to understand. This is partly due, I believe, to the interdisciplinary character of most of Piaget's research; he sets out to solve epistemological problems experimentally by combining the developmental approach with critical studies of the history of science and by using models based on logic, mathematics, and biological cybernetics. This multidimensional approach leads to a remarkably broad perspective of the laws and mechanisms of cognitive development; yet psychology proper has for Piaget always been a by-product of his genetic epistemology" (Inhelder, 1977, p. 332). 43 For discussions of the "new theory," see (Beilin, 1989a, 1992a, p. 202, 1992b, pp. 1, 6-7; see also Korthals, 1994). For discussions of Piaget's impact, see (Voyat, 1977; Jacques J. Voneche & Vidal, 1985; Bond & Tryphon, 2007). 44 (H. Beilin, personal communication, 22 February 2006) 45 Ducret's (2000) examination of the experimental works from this period can be considered an advance on the observation that this period represents a "new theory," but it fails to examine any of the 15 thesis: to enable future researchers to stand on Beilin's shoulders. The result will be a clearer articulation of the foundations underlying the "new" ideas that he deemed worthy of further attention.
The main challenge in pursuing this goal, however, is that Beilin placed the start of the "new theory" in 1974.46 By this time, Piaget's sub-theory of developmental stages had been established within American psychology for over a decade; it was so well- known, in fact, that the collective weight of the discipline had been brought to bear in its criticism. These efforts launched a "neo" Piagetian school, composed of those attempting to remedy the flaws perceived in the original.47 But it was clear from Piaget's own efforts (at the time untranslated and therefore unknown to those in the English-speaking theory (L. Smith, 2002). That said, however, the translation of this work into English would go a long way toward helping Beilin's observation be understood. 46 Beilin puts it as follows: "The new direction in Piaget's research program began to emerge with Inhelder et al. 's (1974/) work on learning and development. In this work the Genevans began to emphasize strategies and procedures in cognitive functioning in a systematic way" (Beilin, 1989b, p. 101). 47 These competing efforts are described by Sternberg (1987), as part of his introduction to a special issue describing mid-1980s progress in neo-Piagetian theory. Yet its important to note Barbel Inhelder's response to their emergence: "Pleasing though this extension is, however, we are somewhat disturbed by the fact that the replication of our experiments does not always show a sufficient understanding of Piagetian theory on the part of the authors of these new works. We are of course the first to admit that such understanding is not easy to acquire, especially since this form of psychology is closely linked to a certain form of epistemology. Once understood, this form of epistemology appears to be that which best suits genetic psychology, as both are essentially constructivist. Constructivism implies that knowledge is not acquired merely under the impact of empirical evidence, as suggested by behaviourist theory, although of course such impact is not entirely excluded from the process. It is also opposed to innate theory, to which, it seems, recourse is frequently had today (maturation being a factor which intervenes, but not exclusively). Constructivism emphasizes the child's or the subject's activity during the course of cognitive development: in other words, everything derives from actions and is eventually translated into coherent and logical thought operations.... Piaget's explanation, which is best presented in constructivist terms, deals with the sequence of stages by a process of equilibration or autoregulation. This regulatory activity enables the subject truly to construct knowledge—something which simple maturation does not" (Inhelder, 1976, pp. 7-8). After Piaget's death, in a way considered more consistent with where the "new theory" had been headed, Inhelder worked to extend his epistemology to apply more directly to psychological problems (Brown, 2001). A third post-Piagetian approach has also since emerged in Switzerland and France (Larivee, Normandeau, & Parent, 2000; with reply to commentaries by Parent, Normandeau, & Larivee, 2000; see also Desrochers, 2008). 16 world who wished to "fix" his then-only-recently-popularized findings) that the "old" theory was not yet to be considered complete.48 Indeed, three books - and numerous articles - from the period immediately prior to 1974 had set the stage for the change
Beilin saw. And since these are mostly ignored in his discussions of the "new theory,"4 it is not clear that Beilin's separation between "old" and "new" is the most appropriate division. To examine this problem, however, we will first take a wider view: what was the state ofPiaget's theory when the neo-Piagetians broke away?
Genetic Epistemologies
There are two recognized forms of "genetic epistemology," each of which are appealed to by contemporary thoerietsts attempting to explain the genesis of knowledge. The first, proposed by James Mark Baldwin, emerged in the late-19 century and was influenced primarily by the two grandfathers of evolutionary theory: Charles Darwin and Jean-
Baptiste Lamarck. (Baldwin attempted to chart a "middle way" between the two theorists, and then used the resulting "new factor" to explain the general evolution and development of knowledge.)51 The second, encapsulated in the "old" theory proposed by
This continued even a decade later. Piaget and Inhelder put it this way: "One misunderstanding of some authors, who may agree with us or criticize us, is to present our work as a finished product, when our interpretations and even the facts on which those interpretations are based are still in a state of reelaboration, as are the analyses of the experimental results on which our theories are founded" (in the foreward to Gallagher & Reid, 1981). 49 (Beilin, 1989b, 1992b, 1992a) 50 Some of what follows in this section has been revised from a version appearing in (Burman, 2008b). 51 These biological ideas (Baldwin, 1896a, 1896b, 1902) were first developed as psychological ideas in (Baldwin, 1890, 1891, 1892, 1894) and were then expanded upon and applied in (Baldwin, 1895, 1897, 1906-1911, 1915). Piaget later remarked, in an interview with Voneche (1982), that it was these latter books which he had read (but see also Baldwin, 1909a; Baldwin, 1909b; as well as 1911). 17 Jean Piaget, emerged in the mid-201 century and was influenced primarily by Baldwin and his contemporaries.52 The two theories are therefore related, but also diverge in important ways that will be discussed throughout the remainder of this work. (In order to understand how Piaget's "new" theory emerges from the "old," however, we must also understand its use and updating of Baldwin's "even older" theory; we must therefore begin at the beginning.)
Baldwin's theory of knowledge was the result of turning the mechanisms of
Darwinian theory inward, to grow an individual child instead of a new species.53 To achieve this, he proposed the recursive "circular reaction" as a mechanism that could serve to bootstrap a mental life from differentiations of reflex and response: the imitative
52 Chief among these influences are Pierre Janet and Edouard Claparede, each of whom served as Piaget's supervisor during the earliest stages of his career in psychology. On Janet, 1919-1921, see (Piaget, 1948b, 1960; also Amann-Gainotti, 1992; Amann-Oainotti & Ducret, 2002; Burman, 2007c); on Claparede, 1921-1925, see (Piaget, 1941a, 1973c; Piaget & Grinevald, 1973). For other important psychological antecedents to the Piagetian position, see (Bayer, 1957; Phillips, 1977). 53 In the first edition of the Origin of Species, Darwin explains the problem in a way with which Piaget would have been sympathetic: "It is immaterial for us whether a multitude of doubtful forms be called species or sub-species or varieties.... But the mere existence of individual variability and of some few well-marked varieties... helps us but little in understanding how species arise in nature.... Again, it may be asked, how is it that varieties, which I have called incipient species, become ultimately converted into good and distinct species, which in most cases obviously differ from each other far more than do the varieties of the same species? How do these groups of species, which constitute what are called distinct genera, and which differ from each other more than do the species of the same genus, arise? All these results... follow inevitably from the struggle for life. Owing to this struggle for life, any variation, however slight and from whatever cause proceeding, if it be in any degree profitable to an individual of any species, in its infinitely complex relations to other organic beings and to external nature, will tend to the preservation of that individual, and will generally be inherited by its offspring. The offspring, also, will thus have a better chance of surviving, for, of the many individuals of any species which are periodically born, but a small number will survive. I have called this principle, by which each slight variation, if useful, is preserved, by the term Natural Selection" (Darwin, 1859/1964, pp. 60-61). 18 instinct manifest in assimilatory exploration, but also turned inward as accommodation in what we might today call a "feedback loop."54
The essential thing, then, in imitation... is that the stimulus starts a nervous process which tends to reproduce both the stimulus and the process again. From the physiological side, we have a circular activity, —sensor, motor; sensor, motor; and from the psychological side we have a similar circle, —reality, image, movement; reality, image, movement.55
In other words, a loop is maintained in which the subject acts repeatedly upon a perceived object with a sensed-position in reality. But, in this case, we are not talking about the sort of loop you get when you point a video camera at its own output.56 That is neither active nor "imitative." It does not reproduce a mental copy57 of the stimulus, so the result stays simple:
In reactions which are not imitative (for example, an ordinary pain-movement reaction) this circular process, whereby the result of the first movement becomes itself a stimulus to the second, etc., is not brought about.... Consciousness remains monoideistic. [Thought and behavior occur along a single track.] But in imitation the reaction performed comes in by eye or ear as a new and different stimulus; here is the state of motor polyideism [multi-tracking] necessary for the supervention of the feeling of effort.58
54 (1891, 1892, 1894; see Piaget translated in Gruber & Voneche, 1993, p. 202; cf. Dewey, 1896; with reply to Dewey by Baldwin in 1898) 55 (Baldwin, 1891, p. 117) 56 (Hofstadter, 1979,2007) 57 Baldwin uses the word "copy," in this context, which Piaget was against doing: "Knowledge is neither a copy of the object nor taking consciousness of a priori forms pre-determined in the subject; it's a perpetual construction made by exchanges between the organism and the environment, from the biological point-of-view, and between thought and its object, from the cognitive point-of-view.... The major problem in knowledge, since it isn't a copy of reality, a copy of objects, is the way it reconstructs reality. In other words, reality must be known, of course, but by recreating it through deduction [from exogenous sources] and endogenous construction" (Piaget in Bringuier, 1977/1980, pp. 110-111; see also Piaget, Henriques, Ascher, & Brown, 1990/1992). 58 (Baldwin, 1892, p. 286; cf. Claparede on need, in the appendix to Burman, 2008b) 19 In other words, the existence of multiple sensorial "idea states" in imitating a stimulus provides various different approximations of the same unitary object—with interactions along a visual loop, an auditory loop, etc. As a result of these many "tracks" being associated with a single object (and applying the universal acid of Darwinian competition in reducing inefficiency), there then emerges a tendency toward synthesis. This enables a process of self-augmentation: a single loop that imitates both visual and tactile aspects, then later a larger loop that imitates these and the object's auditory aspects, followed by an even larger loop that includes an imitation of the trajectory of its path, etc.59 (And indeed, this is what Piaget later found.) What Baldwin describes is the basis for expectancy in learning: in constructing an internal imitation of external phenomena, then acting upon them, anomalous divergences become opportunities for the genesis of knowledge (i.e., new learning).60 What he adds, however, is the recognition that the learning is constructive.
Following this self-stimulating multi-channel process, Baldwin argued that the roots of the adult mind reach down through time into the mind of the child, from which it grows:
Instead of a fixed substance, we have the conception of a growing, developing activity. Instead of beginning with the most elaborate exhibition of this growth and development, we shall find most instruction in the simplest activity that is at the same time the same activity. Development is a process of involution as well
59 (cf. Becker, 2008; with comments by Boom, 2008; Feldman, 2008) 60 This is supported by contemporary neuroscientific findings (e.g., Oliveira, McDonald, & Goodman, 2007; see also Holroyd & Coles, 2008). Of particular interest - and special relevance to the new theory - is the recent finding that semantic meaning, and not just physical action, plays a role in the production of expectancy (Ganushchak & Schiller, 2008). 20 as evolution, and the elements are hidden under the forms of complexity which they build up.61
This inward application of evolution-as-involution marks the approximate beginning of developmental psychology as a scientific discipline: treating adults and children on a continuum, with the "circular reaction" as the constructive mechanism supporting a theoretical taxonomy of mental development along it.62
Generalizing out from the individual to the social, Baldwin then suggested that each child - as it develops into an adult - contributes to the collectivity of knowledge shared by "the race" (i.e., the group).63 But, as was pointed out in the extended example
(above), any child's first learning is also a function of that shared knowledge. The result of this realization, for Baldwin, was a shift in the location of "genetic variation" (in the sense of constructive possibility)64 from the individual to the population:
Society, genetically considered, is not a composition of separate individuals; on the contrary, the individuals are differentiations of a common social protoplasm. The conclusion is drawn [in this older variety of genetic epistemology] that the individual is a "social outcome not a social unit." We are members one of another.65
Unfortunately, however, this approach ignores a fundamental problem: how is new knowledge produced if it is not already somewhere "in" the social structure? For this,
"(Baldwin, 1890, p. 351) 62 (Baldwin, 1895) 63 (Baldwin, 1895, 1897) 64 It is important to note here that the meaning of "genetic" has changed over time, adopting the modern meaning - "of that pertaining to genes" - starting only after 1905. And, as Piaget notes (1967/1971, p. 125ff), the earlier meaning remained in use outside biology long after that date. 65 (Baldwin, 1930, p. 6) 21 Baldwin appealed to "spontaneous variation." The earliest form of genetic epistemology is therefore a variation on a Darwinian67 evolutionary epistemology: new knowledge is the result of an accumulation of productive accidents, the collection of which then enables the emergence of unpredictable new qualities that later become selected-for.
Piaget's early theory of knowledge - the second kind of genetic epistemology - is similar, but without the Darwinian denial of the importance of individual action in enabling change. Instead, the argument regarding the genesis of new knowledge focuses on the role of the developing individual given the context of the environment in which it finds itself:
Genetic epistemology attempts to explain knowledge, and in particular scientific knowledge, on the basis of its history, its sociogenesis, and especially the psychological origins of the notions and operations upon which it is based.69
Rather than building directly on evolutionary theory, however, Piaget first argued against the existence of innate essences to bias future constructions of knowledge.
Piaget's most important early articulation of his "old" theory of knowledge was in arguing against Immanuel Kant's conclusion that the categories of experience are given a priori by nature.70 Instead, he suggested (and ultimately came to demonstrate through countless empirical studies) that these cognitive capacities - and the associated
66 (Baldwin, 1930, p. 7) 67 Baldwin adopted the label "Darwinian" explicitly (in Baldwin, 1909a, p. viii). 68 This is the word he used (Baldwin, 1930, p. 9), not an added frame to anticipate Piaget's later support of early systems theory (but see also Hooker, 1994). 69 (Piaget, 1970/1971, p. 1) 70 (Piaget, 1925; see commentary by Pfeiffle, 2008) 22 understanding and sophistication in the use of concepts relating to physical causality
(1927), morality (1932), quantity (1941), number (1941), groups of numbers (1942), symbols (1945), time (1946), movement and speed (1946), geometry (1948), space
(1948), chance (1951), logical contradiction (1955), logical classification (1959), perception (1961), mental images (1966), identity (1968), causality in the abstract (1971), the conservation of direction (1972), the conservation of movement (1972), the notion of force (1973), and the direction of force (1973) - are all constructed; they are grown, not given, as a result of a subject's experience with the world. In short, there is no innate kernel or seed to knowledge; no atomic individual meme; instead, there is only an onion- layering process of augmenting transformation that reaches back through history to whatever process was responsible for the beginning of life itself.
But Piaget's intent, during the transition to the new theory, was not to push the boundaries back so far as that.
In genetic epistemology, as in developmental psychology, too, there is never an absolute beginning. We can never go back to the point where we can say, "Here is the very beginning of logical structures." As soon as we start talking about the general coordination of actions, we are going to find ourselves, of course, going even further back into the area of biology [Chapter II].... And then, if we look for the roots of the nervous system... we have to go back a step further. We find more basic organic coordinations [see Chapter III].... I do not intend to go back into biology; I just want to carry this regressive analysis back to its beginnings in psychology and to emphasize again that... human thinking cannot be explained by language alone, but has its roots in the general coordination of actions [Chapters IV & V].71
71 (Piaget, 1970/1971, p. 19; see also Piaget in Piattelli-Palmarini, 1979/1980). It should be noted that recent research suggests that language itself may have its roots in the early general coordination of actions: the logic of grammar overlaid upon a logic of action (Koechlin & Jubault, 2006). This supports Piaget's general outlook, in contrast to those of his competitors who had already been declared "victors" (see e.g., Piattelli-Palmarini, 1994). 23 Piaget's intent was rather to show that how the child uses what it has (regardless of how it came to have them) is ultimately what shapes what it learns: structure anticipates content, but - in contrast to Kant's proposal - these structures are grown (not given).
This argument, formalized and updated to follow the latest in biological theory during the transitional period of the three "forgotten works," has dramatic implications for the "linguistic turn" of 20l century philosophy. For Piaget, knowing reality is not just a problem of finding the right names for the things we experience. It is also a problem of discovering the logic underlying that naming, while at the same time constructing structures that serve to approximate this logic in application:
Knowing reality means constructing systems of transformations [imitative loops] that correspond, more or less adequately, to reality. The transformational structures of which knowledge consists are not copies of the transformations in reality; they are simply possible isomorphic models among which experience can enable us to choose. Knowledge, then, is a system of transformations that become progressively adequate.73
In other words, knowing reality - understanding the set of objects available to a subject's experience - is to have fully mapped its potential behaviours as expectancies. (These are maintained in attentional loops and reflected in successful action.)74 The expectancies themselves are in turn an abstraction of the lawful invariances of the world: objects are caused to fall by gravity, otherwise they only move when they are given cause to do so
Esp. the works of Gottlob Frege and Bertrand Russell (for Piaget's response, see Chapter III; expanded in Burman & Barnhart, in prep). "(Piaget, 1970/1971, p. 15) 74 (Piaget, 1974/1978) 24 through the imposition of a force, etc. Such are the rules of the game. But these rules are learned.75 They are not simply "named."
To examine the processes involved in this "learning," Piaget - from the very beginning - linked philosophical epistemology with scientific psychology: he developed a method to discover when and how each lawful "category of knowledge" emerges through interaction. He examined the competences of thought which enable the individual to contribute to knowledge in the social sense—collective systems of transformation (shared loops), reflected in language as "explanations" but grounded in individual acts.76
Misunderstanding Genesis
There is a fundamental error driving many misunderstandings of Piaget's contribution: the works describing his results, but not the theoretical discussions of the causes of differences between groups, are taken by post-Piagetian psychologists to be wholly constitutive of "stage theory." (The accompanying theoretical discussions are considered irrelevant and overly complex, such that "contradictory findings" derived from different methods and examining different groups have come to be interpreted as "disproving" the entire system.)77 Yet the key concept that underlies every one of Piaget's studies, which
75 (e.g., Piaget, 1932/1932; Piaget, 1974/1976; also, with specific reference to some of the material that comprises the new theory, see Gallagher & Reid, 1981) 76 This was most famously demonstrated, in extended form, in his early work on moral development (Piaget, 1932/1932). 77 Many responses have been made to such claims (e.g., Beilin, 1985; R. F. Kitchener, 1986; Beilin, 1989b, 1990; Lourenco & Machado, 1996; Burman, 2008c). 25 is equally applicable to the larger problems of how we come to know the world (both individually and collectively), is actually quite simple: present forms are related by their history to past forms and, in addition, the resulting relationships can be described in formal mathematical terms.
Far from being inadequate to address the problems of knowing, as some critics maintain, this notion - "genesis" or, more recently, "construction" - has important implications for any future model of the mind. For example, as Piaget later came to explain:
By virtue of this point of view, I find myself opposed to the view of knowledge as a copy, a passive copy, of reality. In point of fact, this notion is based on a vicious cycle: in order to make a copy we have to know the model that we are copying, but according to this theory of knowledge the only way to know the model is by copying it, until we are caught in a circle, unable ever to know whether our copy of the model is like the model or not. To my way of thinking, knowing an object does not mean copying it—it means acting upon it.78
A new form in the lineage of forms (knowledge) is therefore abstracted from the object through interaction. Action is therefore the driver of change in Piaget's system.79 To tie this in with Baldwin's older theory, behaviour is the initiator of imitative loops. These are then revised with explicit reference to those internal systems describing the production of the action and anticipating its effects. The resulting "schemes" are the categories of experience as enacted, coupled with a formal instantiation of the behavioural means to experience them given a known context. (In other words, they are
(Piaget, 1970/1971, p. 15) This is discussed most recently in (Piaget, 1976/1979). 26 the structures that interact with external objects to produce subjective content-as-
experienced.)
Piaget's early contribution to psychology can therefore be understood as an
empirical proof against Kantian nativism (but not his constructivism),80 in support of
Baldwin's idea of a single evolutionary-developmental process linking children's
learning with the growth of their society's collective wisdom. Despite this, however, he
was not yet doing "his own" theoretical work; he was not explaining development, what
it means, or why it is necessary. This came later, with the most important advances made
after the neo-Piagetian split.81 Indeed, both Piaget's shift to a new theory and the neo-
Piagetian exodus reflected the same changes in priorities that characterized the larger
context of the 1960s:
...developmental psychology has been radically transformed, in numerous and complex ways, in the last two decades. While some features of the discipline - its goals, approaches, and research foci - have not changed much, its overall "look" in 1970 is vastly different from what it was in 1950 [when Piaget published his first major theoretical synthesis, "an introduction to genetic epistemology"].... Until approximately 25 years ago, developmental psychologists were primarily concerned with precise descriptions of children's capabilities at various ages and
Kant provides the following, in which both his constructivism and his nativism are made clear: "the characteristic of the human species is that Nature has planted in the species the seed of discord, and that Nature has willed that the human species, through its reason, turn discord into concord or at least creation a constant approximation of it. Concord contains its purpose in its idea, whereas discord as action contains, within the plan of Nature, the means of a supreme and for us unfathomable wisdom. This wisdom is to affect the perfection of man through cultural progress, even if this should mean some sacrifice of the pleasures of his life" (Kant, 1798/1978, p. 238). Piaget can therefore be understood as throwing out Kant's nativism (the seed of discord) while keeping his orientation to construction (turn discord to concord). The problem to be addressed, after the notion that "it is construction all the way down" has been shown to be true, is to demonstrate why it must be true. This is the task for the new theory. 81 The most well-known among his later theoretical proposals relate to what he called "the phenocopy" (Piaget, 1974/1980a, 1975/1995; see also Parker, 2005; Deacon, 2005). This is the early biological version of what was later formalized in the theory of "reflecting abstraction" (Piaget, 1977/2001), examined in Chapter VI. 27 reliable determination of age changes in psychological functions such as psychomotor performance, problem solving, and aggressive reactions [i.e., Piagetian categorical work]. .. .The major contemporary empirical and theoretical emphasis in the field of developmental psychology, however, seem to be on explanations of the psychological changes that occur, the mechanisms and processes accounting for growth and development.
Piaget's shift to a new theory can therefore be understood as being situated in the changing interests of the discipline and of the time. But it was not caused by these changes.
Beyond Genetic Epistemology
Beilin suggests that the explanatory shift toward the "new theory" resulted from advances in theories of learning, attributing the move to the influence of Piaget's collaborators.
(Beilin's history is therefore one of progress internal to Piaget's Centre in Geneva.)
When one examines Piaget's introduction in the forward from the indicated volume, however, it becomes clear that this could not have been the case: his collaborators were approaching the problem from a completely different perspective. (As Piaget put it, rather indelicately, he did not "share the epistemological point of view which oriented the authors' research.")83 I therefore propose instead that Piaget's "new theory" emerged as a result of his assimilation of developments in two disciplines external to, but close to, psychology: biology and logic. In particular, I propose that the new theory emerged from an attempted synthesis between evolutionary and developmental theories (examined in
(Mussen, 1970, p. vii). For more on the context in France specifically, see (Reuchlin, 1965). (Piaget in Inhelder et al., 1974/1974, p. ix). 28 Chapter II) and the proof of the incompleteness of formal systems (examined in Chapter
III). These influences were then generalized in application to Piaget's decades-old meta- psychological problem of how (and now why) this learning occurs during development.84
In short, I propose that the "new theory" is an extension of the "old," but also arose as a consequence of the emergence of new metaphors in nearby disciplines that could be used to explain why psychological (and epistemological) change is necessary.
This proposal makes sense in the context of an earlier programmatic statement.
Four years prior to the publication of Beilin's supposedly-transitional volume (but following the publication of the forgotten works), Piaget had already made it clear that
"learning" would inform the research conducted during his last decade:
By what means does the human mind go from a state of less sufficient knowledge to a state of higher knowledge? .. .Our problem, from the point of view of psychology and from the point of view of genetic epistemology, is to explain how the transition is made from a lower level of knowledge to a level that is judged [by logicians and other relevant experts] to be higher. The nature of these transitions is a factual question.85
In other words, starting before the publication of this statement in 1970, the processes driving increases in knowledge from one level to another were marked out for empirical investigation. But such an investigative program only makes sense if one assumes the theoretical meaning of "levels" of knowledge. (The long process by which this meaning emerged is examined in Chapter III.) The message, therefore, is clear: the foundations of
Piaget continues: "I think that B. Inhelder, H. Sinclair, and M. Bovet have discovered and proved more than they themselves are willing to admit, and I am convinced that their readers will share in my delight with their often surprising and always informative studies, which constitute a distinct advance in our knowledge of both learning and cognitive development in general" (Piaget in Inhelder et al., 1974/1974, p. xiv). 85 (Piaget, 1970/1971, pp. 12-13) Piaget's new epistemology had already been laid when his colleagues published their advances in the theory of learning. Their 1974 volume could not have been the key transitional work that ushered in the new theory, as Beilin proposed. But then how are we to understand it?
Evolutionary Epistemology
Piaget's vision of the future of genetic epistemology at the time of the transition to his
"new" theory is similar to another constructive theory of knowledge that emerged in the early 1970s - evolutionary epistemology86 - but with some important modifications.
First, it is assumed in Piaget's final works that intelligence is an extension of the biological capacity for adaptation; that the mind is like a machine built to respond to short-term change, in an auto-regulatory capacity (cf. cybernetic homeostasis), along the
on various categorical dimensions of experience. Second - since the mind and the brain are one88 - it is assumed that these mental structures follow the same formal rules as the brain, which must grow imitative approximations of these categories in order to reproduce the knowledge to be shared. This structuring (and its subsequent restructuring)
(e.g., Campbell, 1974; discussed in Freeman-Moir, 1982; see also Hooker, 1994; Kesselring, 1994) 87 (cf. Burman, 2008b; Burman & Goertzen, in prep) 88 This is an obvious statement now, but must be supported here through references to Piaget's neurological work (see e.g., Piaget, 1948a, 1949a, 1953). 30 then becomes the source of large-scale developmental "progress," with the specific details filled in during small-scale learning.89
This difference between evolutionary epistemology and genetic epistemology also generalizes to the level of the collective: in genetic epistemology, knowledge grows following the same process that drives learning and development.90 Indeed, this is
Piaget's basic assumption.
The fundamental hypothesis of genetic epistemology is that there is a parallelism between the progress made in the logical and rational organization of knowledge and the corresponding psychological processes.91
In other words, the quality of a culture's knowledge (what is known about the world) is an extension of the developing capacities of its members' growing brains in organizing, orienting to, and acting upon the various objects-of-knowledge to be found nearby.92 For this reason - since a change in individual biology results in a change in potential competence, leading to a shift in the possibilities for knowledge - the construction of social knowledge must follow the same rules as the construction of individual biology.
Furthermore, since it is known that these biological capacities change throughout development, as well as in evolution, this implies that there must also be both embryological and evolutionary explanations for knowledge. A solely evolutionary
This provides a mechanism for a similar theory: "punctuated equilibrium" (Gould, 2002/2007) was influenced by the work of Thomas Kuhn (1962/1993), whose ideas were influenced by Piaget (Burman, 2007b). 90 (T. S. Kuhn, 1962/1993; see also Tsou, 2006; Burman, 2007b) 91 (Piaget, 1970/1971, p. 13) 92 This was most recently supported - albeit indirectly - by a series of experiments showing that increases in environmental complexity, and the attendant feelings of "a loss of control," are responded to by increases in dogmatism, superstition, and ritualistic behaviour (reported by Whitson & Galinsky, 2008). 31 epistemology would therefore be incomplete. In order to develop this new position, however, Piaget needed to borrow metaphors from "new" language drawn from biology and logic.
While Piaget was busy at work conducting experiments to support his argument against Kant (thus showing that the categories of experience are constructed), biology had raced ahead: after decades of debate, Darwin's theory of natural selection had been combined with Mendel's theory of particulate inheritance in so-called "neo-Darwinism."
The result was the now familiar formula for evolutionary change: the natural selection of
"fit" genes.93 Yet this "modern synthesis" was not complete: its architects had excluded embryology, as well as the physics and chemistry of the cell. Piaget then, seeking more advanced structures to anchor his own explanatory framework, appealed to the works describing these omissions to suggest - more generally - that the implications for
"genesis" are not innate to the genes. Instead, "meaning" emerges through interaction: the interpretive mechanisms that come to embody the effects of each individual gene are subject, for example, to the contextual changes in the genetic system during development.
In short, therefore, Piaget appealed to work showing that - since "phenotype" (the adult body) is underdetermined by "genotype" (genes) - there must be a place in evolution for development.95 He then applied this to his own work, making a case for the relevance of studies of the development of intelligence to understanding the evolution of knowledge.96
93 (see e.g., Huxley, 1942) "'• (Waddington, 1969; B. K. Hall, 2005; see also Weizmann, 2001) 95 (cf. Robert, 2004,2008) 96 (Piaget & Garcia, 1983/1989) 32 In effect, the result of Piaget's "return to biology" (described in Chapter II) was to update everything in his theory that had been based on the ideas which had guided his doctoral studies: it provided a common mechanism explaining how organisms grow given the possibilities and constraints of their environment. He then replaced his earlier reliance on Baldwin with an updated theoretical framework drawn from this "post-neo-
Darwinian"97 period - "epigenetics" (a compound word meaning "beyond the study of genes") - arguing that a developing organism's interactions with its environment shape its future potential. And he used this to provide a new biological foundation to update his earlier works on child development, showing how the environment (both natural and social) serves to potentiate and shape the adult form.
As Piaget returned to biology, he had also begun to change how he used formal logic. In the "old theory," his categories formalized with models drawn from reviews of the history of logical and mathematical explanation, but only to end of the 19th century.
On the basis of this work, he had argued that his categories could be conceived as following the laws of "grouping." (This, incidentally, is what the founder of the neo-
Piagetian movement had initially criticized.)99 In the 1960s, however, it became clear that there were limits to formalism; that "groups" were fundamentally incomplete (see
Chapter III). Yet, just as this justified the position of the neo-Piagetians, it was also a salvation of sorts for Piaget's response to Kant: coupled with his update of Baldwin's
97 This is how Piaget's main source and inspiration, Conrad Waddington, characterizes his work at the time (see e.g., 1968/1975, p. 205; 1969/1975, pp. 238, 240; also 1969, 1974/1975). See Chapter II. 98 (e.g., Piaget, 1941b, 1942) 99 (Burman, 2008a) 33 circular reaction, "incompleteness" ultimately justified the construction of natural hierarchies of nested levels.100 This in turn then supported the old theory, but in a new sense: the emerging theory was new first because of the update of Baldwin (via
Waddington [Chapter II]), but new too because of the update of Grouping (via Levels
[Chapter III]).
As one would expect from Piaget's appeals to epigenetic contextualism following this update, his new use of logic implied that developmental stages are deeply embedded in their history.101 In the language of our extended example, the recognition of incompleteness also implies that development is a process of self-augmentation in which childhood is but a level in the hierarchy of human being. In a sense, therefore, children not only contribute to the logic of their group, but they also come to embody it: as they develop and move to the centre of their various groups, they become totems toward which others orient themselves—objects of knowledge, not just subjects to it.
Prospective Conclusion: The Purpose and Approach of this Thesis
The purpose of this thesis is, in short, to build a bridge spanning the distance between our current understanding of Piaget's theory and the final results of his over sixty years of research, which many contemporary researchers have had difficulty (or reluctance) in
100 This is presented in its most advanced form in (Piaget et al., 1990/1992). 101 This provides a justification for the collection of essays Piaget published in 1965. Although an extended edition was published in 1977, this collection was only recently translated as Sociological Studies (Piaget & Smith, 1928-1960, 1977/1995). For more on the connection between his biology and his sociology, see (Moessinger, 2000). For converging evidence provided by contemporary neuroscience, see (Holroyd & Coles, 2008). Sociological Studies is discussed in greater detail in Chapter V. 34 engaging. The larger proposal to be developed, in answering the largely pedagogical question of whether there are essentially two Piagets to be taught ("old" and "new"), is that this material can also be characterized as constituting Piaget's move toward an
"epigenetic" epistemology: a new theory of knowledge that, had it been completed, would have reached far beyond his or Baldwin's genetic epistemologies to touch upon issues of contemporary relevance both inside and outside Psychology.102 This builds upon advances in biological theory (Chapter II), but is also synthesized with a logico- structural reading of social theory (Chapters III & V). Yet although it is the old theory that is known by the community of "neo" researchers whose work was initially informed by the Piagetian research program (many of whom claimed after this period to have overcome its weaknesses),103 this new framework builds on the past: it would provide the means to reinterpret old findings and thereby contribute anew to the areas they influenced.104 The problem, then, is one of bridging the two positions: there is only one
Piaget, but two can clearly be seen.
The resulting narrative, here, thus revolves primarily around three inter-connected core chapters: exegesis of the books published during the transitional period of forgotten works. The first of these, Chapter II, lays the foundations for all that follows: fifty years
The prefix "epi-" can be translated as "beyond" or "over." For this reason, its use here reflects a pun on the dual meaning of terms related to Piaget's theory: it is not only "beyond" the constructive epistemological theory that led to stage theory in psychology, but it also builds upon theoretical advances in biology that go "beyond" the genome in describing the emergence of individuals from their inherited genes. It is therefore a theory of knowledge founded on the progressive differentiation of knowledge, given the individual's interactions with the world and constrained by their potential for change. 103 (e.g., Commons, Richards, & Armon, 1984; Shulman, Restaino-Baumann, & Butler, 1985; Demetriou, 1988; but see also Beilin, 1990; Lourenco & Machado, 1996) 104 For an initial attempt at this reinterpretation, which also includes two "new theory" contributions by Piaget, see (Murray, 1979). 35 after the completion of his doctorate in biology, Piaget returned to his "first love" in order to find a mechanism that could drive the stage changes he had found through his innumerable empirical studies of children's reasoning. After this, he published a collection of empirical studies examining how this mechanism would manifest in children's thinking; a sample of these studies is examined in Chapter IV. Then Piaget expanded outward into social theory, criticizing the approaches collected under the umbrella of Structuralism with a view to grounding the study of knowledge in common mechanisms found in both biology and conceptions of knowledge. This is examined in
Chapter V. That then concludes the review of the key texts. By the end of the fifth chapter, in other words, the message of Piaget's "forgotten works" will be clear: these books, and the works that informed them, provide the basis for Beilin's situated theory of meaning. Yet the effort is not purely one of historical review. Translation errors are noted throughout. And the implications of one of the most important of these errors are examined in Chapter III.
Chapter III represents a divergence from the pattern of plain historical exegesis.
In an attempt to fill a gap in the English literature, an implicit thread in Piaget's French writings is made manifest. This is accomplished with a Foucauldian archaeological survey, exposing a discontinuity in theory: in tracing Piaget's references to an argument in metamathematics - a proof of the incompleteness of formal systems - through a dozen volumes, a change in assumptions regarding the nature of structures is laid bare. This
"important secondary narrative" then informs the remainder of the thesis, having been
36 incorporated into the discussion of the two volumes examined in Chapters IV & V. Yet where its effects are implicit in Piaget's later writings, they are made explicit.
The thesis then concludes by drawing connections between the forgotten works to show how the ideas connect with the material examined by Beilin as "new," ultimately presenting a sketch of Piaget's attempt at an "epigenetic epistemology" and - since this was incomplete when he died - suggesting some future avenues for research.
37 CHAPTER II
THE RETURN TO BIOLOGY
In 1896, James Mark Baldwin (1861-1934) proposed what he called a "new factor" in evolutionary theory. His purpose was to chart a middle path between Darwin and
Lamarck; to provide for evolutionary changes driven by learned behaviours, arguing that an organism's response to environmental selection pressures could alter their effects and thereby improve the fitness of respondents in a population of non-respondents.105 In short, he suggested that learning could augment and thereby speed up evolutionary change. In 1953, following the "modern synthesis of biology" - which conceived of the process of evolutionary change in terms of Darwinian natural selection and Mendelian gene mutation and recombination106 - a name was given to this and several related proposals: "the Baldwin Effect." At the time, however, there was no proof to support the theory; no evidence to justify the claim. And because the underlying theory was tainted as Lamarckian, or apparently so, it was dismissed.108
The famed developmental geneticist Conrad Waddington (1905-1975) - who spent his career developing the neo-Baldwinian theories of "epigenesis" and "genetic
105 (Baldwin, 1896a, 1896b; see also Baldwin, 1902) 106 (Huxley, 1942; see Sapp, 2003, pp. 117-156) 107 (Simpson, 1953; see also Hinton & Nowlan, 1987; Weber & Depew, 2003; Sanchez & Loredo, 2007) 108 (Vidal, Buscaglia, & Voneche, 1983, pp. 84-85). The situation in France, and French-speaking Switzerland, was slightly different: Darwin's contributions were seen as contributing to Lamarck's theories, rather than replacing them (see e.g., Boesiger, 1980; Limoges, 1980; Faber, 1997). 38 assimilation" - suggested in 1964 that it was Piaget who had been the first to provide
the necessary proof that the Baldwin Effect was operating to augment Darwinian change:
he argued that Piaget's work on the pond snail, Limnaea stagnalis (published 1911-
1929),110 showed that developmentally-acquired changes in shell shape could come to be
inherited as a result of changes in behaviour. Indeed, it was this endorsement from
Waddington that encouraged Piaget to return to the studies that had occupied his earlier
doctoral training, intending to provide a more solid naturalistic foundation for the psychological and epistemological theories he had developed in the interval.111
Trends in Piaget's articles, 1907-1980
i^-T-iomcoh-T-iomoi^x-iomoh-T-ino) 0>O)0>O)0)G)0)0)O)0)0)0>O>O)0)0)O)0)O)
D Amateur 0 Biological • Psychological
Figure 3. A detailed examination of Piaget's articles shows a long absence from Biology, following a dramatic start in the 1910s. It also shows that he was most active in Psychology in the 1950s and 1960s, although the first psychological period - for which he received an honorary doctorate from Harvard in 1936 - clearly stands out as well. (For simplicity of display here, in black and white, his significant contributions to Philosophy and Education have been omitted.)
109 (see esp. Waddington, 1957; also Slack, 2002) 110 For an overview of Piaget's work in biology, see (Buscaglia, 1985). For details about his life at the time, see (Ducret, 1984; Vidal, 1989,1994; Barrelet & Perret-Clermont, 1996). 111 (Piaget in Bringuier, 1977/1980, p. 111) 39 The Hard Core of the Old Theory
Piaget completed his doctorate in natural history in 1918. Building on an enthusiastic adolescence collecting and cataloguing the five Swiss varieties of Limnaea pond snail, he used the Bravais-Pearson correlation coefficient to determine each specimen's species membership.112 However, he did this just as the synthesis of Darwinian natural selection with Mendelian genetic traits was making such biometrical procedures theoretically obsolete.113 And he got into trouble arguing about it - in print - with another student:
Waclaw Roszkowski, from the University of Lausanne, whose studies went beyond the measurement of his specimens' shells and instead included the dissection and examination of their internal morphology.114 This study of traits largely unaffected by development ultimately put Roszkowski on the right side of the theoretical debate. As a result, Piaget - disgraced as an anti-Mendelian at a time when Mendel was in ascendance115 - chose to leave Neuchatel for post-doctoral studies in Zurich; he left a career in biology for one focussing on philosophy, psychology, and the study of knowledge. But exactly how this came to pass is important for understanding the character of his later work: biology provides the "hard core" of his later theory.116
A history of the measure - written at around this time - is provided by (Pearson, 1920, pp. 28-32). That Pearson recanted his earlier interpretation of Bravais' importance and meaning likely did not help Piaget's prospects for using it in his second dissertation in philosophy. 113 (J. Jacques Voneche, 2003, p. 6) 114(Ducret, 1984, pp. 119-138, 165-175, 191-195; Vidal, 1994, pp. 72-91) 115 (J. Jacques Voneche, 2003, p. 5) 116 This is a reference to Imre Lakatos' synthesis of the philosophies of Karl Popper and Thomas Kuhn (see e.g., Lakatos in Worrall & Currie, 1978b, 1978a, pp. 58, 95-100,215-222). In Beilin's examination of the hard core of Piaget's assumptions, however, the "biology" was left out (noted in Chapter I). 40 From Biology to Knowledge1
Piaget's debate with Roszkowski, spanning 1912-1914, led him to ask questions about the reality of species as being more than just collections of individuals. As war sparked, and Europe burned, these questions were then paralleled by similar concerns about the reality of "society" as well: are the ties that bind people together - such as the abstract ideals of Christian virtue - real? Or are these values just words and empty rhetoric?118
The answer came to Piaget in 1914-1915, during an undergraduate class with his mentor in philosophy: Arnold Reymond (1874-1958). As Piaget recalls in his autobiography:
I understood suddenly that, at every level (of the cell, the organism, the species, concepts, logical principles, etc.), one finds the same problem of the relation between part and whole. From then on, I was convinced that I had found the solution. Finally: the union of which I had dreamed - between philosophy and biology - and, with it, the possibility of a scientific epistemology! It was thus that I started to write my system (one will wonder where I found the time, but I stole each moment whenever I could, especially during the most tedious of our lessons!). My solution was very simple: in all the domains of life (organic, mental, social) there are "totalities" which are qualitatively distinct from their parts and which impose an organization upon them. Consequently, there are no insulated "elements." Elementary reality depends necessarily on a whole which informs it.119
11 The last few paragraphs of the following section are revised from (Burman, 2008b). 118 This is one of the messages of Piaget's 68-page prose poem, La mission de I'idee (1916), which castigated Europe for allowing itself to fall apart. A translated synopsis is provided by (Gruber & Voneche, 1993, pp. 26-37). 119 My trans of the following: uje compris soudain qu'd tous les niveaux (celui de la cellule, de Vorganisme, de I'espece, des concepts, des principes logiques, etc.) on retrouve le mime probleme des relations entre lapartie et le tout; desormais j'etais convaincu d'avoir trouve la solution. Enfin emergeait Vunion etroite dontj'avais reve, entre la philosophic et la biologie, et la possibility d'une epistemologie qui meparut alors reellement scientifique ! Ainsije commenqai a ecrire mon systeme (on se demandera oiije trouvai le temps necessaire, maisje leprenais chaquefois queje lepouvais, en particulier pendant les lecons ennuyeuses !). Ma solution etait tres simple : dans tous les domaines de la vie (organique, mentale, sociale) il existe des 'totalites' qualitativement distinctes de leurs parties et qui leur imposent une organisation. Par consequent il n 'existe pas d' 'elements' isoles. La realite elementaire depend necessairement d'un tout qui I'informe" (Piaget, 1950-1976/1976, p. 6; see also Vidal, 1994, pp. 195-218). 41 In other words, the commonality between species and society is a property of their organization: the supervenience of a single whole on many parts, but within which conserving translations and transformations can be made without affecting the "total
1 90 structure." (At this point in his autobiography, Piaget remarks that - had he known about Gestalt theory at the time - he would have become an ardent supporter.)121
But he did not extend this realization to include the modification of social structures through Mendelian mutation (see also Chapter V). Instead, the key insight provided to Piaget by Reymond was the realization that logic could be used to describe all of the systems that shared in this quality of totality: cells, organisms, species, and concepts. (This was his justification for the use of "grouping" that so annoyed the early neo-Piagetians, an issue to which we will return again in Chapter III.)122
In thinking further about the parallels between life and society, Piaget realized that the common mechanism in their maintenance was "equilibration" (auto- 19^ • regulation). This preserves the balance; a change in one area is offset by a change in
The phrase used is structure totale, which - as Chapman (1988, p. 16) notes - foreshadows Piaget's later "structure of the whole" {structure d'ensemble). Chapman also quotes an alternative translation of the passage provided above, albeit in two parts (Chapman, 1988, pp. 15-16). 121 (Piaget, 1950-1976/1976, p. 7) 122 In a discussion of his doctoral coursework in his autobiography, Piaget says of what he learned in his mathematics class: "the theory of groups seemed particularly significant to me in regards to the problem of totality and its parts" (my trans of Piaget, 1950-1976/1976, p. 7). 123 Piaget was influenced in this primarily by his early reading of (Bergson, 1907/1911). Bergson's proposals regarding the existence of a vital organizing principle {elan vitale) justified for Piaget a connection between biology and knowledge, but the rigorous scientific bridge to span this gap had been missing until Reymond provided it (Chapman, 1988, pp. 14-15). This notion is later stripped of its vitalism and formalized - during the new period - in (Piaget, 1975/1985). To put this final version in the context of the larger story presented here, the project that became the book cited was discussed in a talk given by Piaget at the first meeting of the Jean Piaget Society in May 1971 (published as Piaget, 1972). The language used is distinctive of a work originating after his return to biology (see esp., pp. 5, 12; also the comment by Furth, 1972a). 42 another. Although this later became operationalized in the psycho-logical notions
"reversibility" and "non-contradiction," it was first a social imperative: the evils of war are to be balanced by the activism of innocence and youth. The progression of history is thus a cycle caused by constantly re-equilibrating forces: from harmony to chaos and back again.125 This occurs in the sciences too, where developments in one discipline push out its boundaries and cause it to impinge on its neighbours, which then react and cause further perturbations throughout the system as whole while it re-equilibrates.126
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Figure 4. Piaget's conception of equilibrating interdisciplinary relations: the Circle of Sciences.127 This early illustration explains why Piaget turned to biology and logic to update his psychology.
124 Summarized in (Gruber & Voneche, 1993, pp. 47-50; cf. Piaget, 1924/1928, pp. 171-172) 125 (Gruber & Voneche, 1993, p. 46). For the Christian context in developmental psychology, as well as Piaget's situation relative to it, see (Vandenberg, 1993). For Piaget's later comments on the apparent parallel to Marx, see (Piaget in Widmer & Piaget, 1977a). 126 The parallel between learning and development and scientific change in Piaget's new theory is examined briefly in (Burman, 2008b). This is developed further in application to the problem of integration/unification in (Burman, in press). The arguments in these two papers will then by synthesized with the material covered in (Burman, 2007b) as part of the forthcoming (Burman & Goertzen, in prep). 127 (Piaget, 1918, p. 59; qtd. in Ducret, 1984, p. 406; illustrated in Gruber & Voneche, 1993, p. 45). For more on the Circle of Sciences, see volume 3 of (Piaget, 1950, pp. 273-278) and (Piaget, 1967d, pp. 1172-1224). 43 Individual scientists can thus also be considered sub-parts of disciplinary wholes, with the rationality of their world defined from a perspective imposed top-down.128 (In this way, scientists are a bit like children: explorers constrained within systems of logic.)
The problem for Piaget with such a proposal, however, is that it could only be taken on faith. His turn to psychology, following the completion of his doctorate in natural history, was therefore out of a need for a critical method.130 How can the emergence of individual knowing be used to understand progress in knowledge more generally?
In 1918, Piaget travelled to Zurich to study experimental psychology with Gottlob
Friedrich Lipps (1865-1931) and Arthur Wreschner (1866-1932). This, however, was disappointing. Their approach "seemed to have little relationship with fundamental problems,"131 so he stayed with them for only one semester. Of more importance was
Piaget's time in the psychiatric clinic run by Eugen Bleuler (1857-1939), the eminent host of conferences attended by Oskar Pfister (1873-1956) and Carl Jung (1875-1961). It was in this tight psychoanalytic circle that Piaget found his method: clinical interviewing.132
After two semesters in Zurich, and a summer spent back in the mountains near
Neuchatel, Piaget was hired in 1919 to work in the Parisian laboratory school founded by
Alfred Binet (1857-1911). His task would be to standardize Burt's intelligence tests for
128 The parallel here between Piaget and Thomas Kuhn is discussed by (Tsou, 2006; Burman, 2007b). 129 (cf. D. Kuhn, 1992; Gopnik, 1996; Breuer, Chinn, & Samarapungavan, 1998; but see also Burman, 2008b, p. 174) 130 (Piaget, 1950-1976/1976, p. 7) 131 My trans of (Piaget, 1950-1976/1976, p. 8) 132 (Opper, 1977; Mayer, 2005) 44 use with French children. But his main interest was not in intelligence testing. This was just a job. (Although he had clearly expressed an interest in psychology, it was his advanced training in statistics that qualified him for the position.) Piaget's psychological turn was actually intended to push his larger epistemological agenda: after he completed his first doctorate, he had intended to pursue a second—in philosophy.
When Piaget arrived in Paris in the Fall of 1919, he registered at the Sorbonne for classes in philosophy and psychology. (He also secured an apprenticeship at the
Salpetriere.)133 Soon after, on 4 December 1919, his proposed dissertation - titled, Essai sur lejugement de valeur et la methode biologique dans les sciences de Vesprit [Essay on the judgment of value and the biological method in the sciences of the mind] - was approved by the Faculty of Arts at the University of Neuchatel.134 It was also around this time that he had begun to use the statistical methods of his first doctorate to classify the kinds of errors his students made on Burt's tests.
Applying his additional training in the Zurich style of clinical interviewing
(mostly to relieve the boredom of his task standardizing test questions), he asked the children why they answered as they did.135 What he found was surprising: the children's justification for their errors could be grouped according to age (biometrically), as if different cohorts could be considered as belonging to different species of mind. But by the time he would have been able to submit the resulting thesis, in 1925, he had succeeded to the Chair held by Reymond—his supervisor at Neuchatel. Since he would
133 (Piaget, 1950-1976/1976, pp. 9-10) 134 (Bessire & Beguelin, 1996, p. 88) 135 (Piaget, 1950-1976/1976, p. 9) 45 have had to oversee his own defence, he never received the degree. Yet this minor inconvenience was of far less significance, both personally and professionally, than the ideas he had developed in Paris. These he tested back in Neuchatel, following the birth of the first of his three children. (Jacqueline was born in 1925; his second daughter,
Lucienne, was born in 1927. Laurent, his son and present-day literary executor, was born in 1931.)
On the basis of experiments first conducted on his girls (really, just playing games), Piaget began to refine his Parisian ideas.136 For example: he found that his youngest daughter lost interest if he hid his old gold watch under a pillow, while the elder would go looking for it. But, as she got older, she would continue to look in the same place if he changed the pillow under which the watch was hidden. Then, later, it was as if she just figured it out: the effect of a switch, if seen, would be obvious. And this pattern was played out in the same way with his son: a progression from attention to visible objects only, to ritualized searching, and finally to an emergence of understanding, followed ultimately by the generalization of the lesson to new situations.138 Clearly, something was driving how these children came to understand their father's games. But they were not learning its contents, because the contents were
These early studies were reported in (Piaget, 1923/1926, 1924/1928). Piaget's first psychological period can therefore be understood as collecting the works derived from the research begun in Paris (Beilin, 1992a, pp. 192-195). 137 Edouard Claparede, for whom Piaget worked prior to succeeding to the Chair held by Reymond, called this moment of realization "the grasp of consciousness" (Claparede, 1917, 1918; see also Piaget, 1974/1976; footnote 18 and appendix in Burman, 2008b, pp. 171, 180-183). 138 These studies were reported in (Piaget, 1936/1952, 1937/1954, 1945/1962). Piaget's second psychological period can therefore be understood as being based on research conducted with his own children (Beilin, 1992a, pp. 195-197). Yet the issues examined remained fresh as the theory developed: one of Piaget's last books is a summary of new research on generalization (Piaget & Henriques, 1978). 46 meaningless: they did not use the watch to tell time, or as a fashion accessory, etc.
Rather, they were learning what to expect from the game's rules—its implicit logic.139
(Structures were being reconstructed internally to produce a mental representation of the game's possibilities, which in turn defined the children's rational expectations of what could happen.)
As Piaget's methods developed, so too did his theory. For example: writing about his eldest daughter's experiences in the first year of her life, Piaget proposed - explicitly borrowing from Baldwin - what would today be considered the equivalent of an evolutionary explanation for the construction of knowledge:
.. .an excellent description of [exploratory] behaviour has been given by numerous authors. It begins with what Baldwin called the circular reaction, the first step toward all other accommodations. The child does something at random, and when he gets an interesting result, he repeats the action indefinitely. In this way, he learns to suck his thumb, to seize objects, to make noises by knocking hard things together, and so on. The circular reaction is therefore the utilization of chance.140
Piaget then reiterates, taking another perspective to make the point:
The first causal experience the baby has is certainly what Baldwin called a circular reaction, which we have already touch upon from another point of view: the child does something by chance, takes pleasure in the result, and does it over and over again as if he wants to reproduce the same result (it matters little if this desire for reproduction is the cause or the result of the act reproduced).141
In other words - building upon basic acts provided by reflex (i.e., inherited as a result of evolutionary selection pressures) and refined through memories of success (Chapter IV) - continued interaction draws out the implications of actions and lays the foundations for
These notions were tested in studies reported, most famously, in (Piaget, 1932/1932). 0 (Piaget, 1927/1977, p. 202) 1 (Piaget, 1927/1977, p. 206) 47 further exploration. More advanced behavioural "schemes" are then constructed through additional circular repetitions, following the application of the same basic process 142
Brain (Equilibrating)
Assimilation Accommodation of the object by of the scheme to the scheme the object
Reality (Nature) Reality (Culture)
Figure 5. My illustration of Piaget's take on Baldwin's circular reaction.
In this system, ongoing behaviour leads to encounters with novel stimuli, which are assimilated to rudimentary knowledge structures and then corrected to accommodate new information. The result is a system that can be said to be "equilibrated" relative to its environment.
A few years later, in The Origins of Intelligence in Children - the first book based on the study of his children, although only published in 1936 - Piaget developed these ideas further.143 Instead of focusing solely on the result of actions, he also suggested that the "locus of attention" shifts ever-outward: the knower decentres the subjective meaning of its experiences, shifting away from solipsism and coming increasingly to distance
; This basic perspective is continued into the period of the new theory (Piaget in Evans, 1973, p. 22) (1936/1952) 48 itself from the objects in its reality. (To paraphrase: "this experience was not because of me, but because of it") Thus, in the beginning, actions are reflexive and experiences random: the infant flails about, without purposeful intent or even an awareness of action.
Then, at the second level of this decentring, the "primary" - adapting - circular reaction begins to connect actions and experiences: the child looks in order to see and listens in order to hear, but all without a goal separate from the activity itself. As activities-and- experiences are further differentiated, the "secondary" - coordinating - circular reactions that appear in level three then begin to enable the child to distinguish between cause and effect: actions are repeated in order to experience an effect (e.g., sucking). Later, this becomes intentional. Instead of simply repeating effects, actions in level four are undertaken in order to produce them (e.g., an object is brought to the mouth so that it can be sucked). In level five, "tertiary" - exploratory - circular reactions begin to enable new experiences to be sought (e.g., different objects are desirable for sucking). In level six, this groping becomes insightful, with ends sought instead of stumbled into (e.g., pulling a blanket to bring a desired object closer so that it can be sucked). This is the explanatory basis for stage theory: stages are the genetic wholes - structures constructed as part of the same lineage - inside of which functions are constructed as phenotypic adaptations.144
The first functions are sensorimotor: touching and feeling. These are then replaced with operations: doing. And this is then replaced with meta-operations: thinking, then later formal planning.
144 This interpretation justifies Piaget's argument that each stage is associated with the invention of a more complex logic-of-action (see e.g., Inhelder & Piaget, 1955/1958). 49 The American Context145
This theory is well known in psychology today. But what is not well known is that Piaget emerged as a significant figure in American psychology twice. And this double appearance is of great significance to our story.
Piaget first made an impact in the US in the 1920s-1930s through his writings on the socially-mediated nature of children's early learning and the different meanings derived by children-in-interaction (i.e., his first period).146 These efforts earned him an honorary doctorate from Harvard in 1936 - which he received alongside Jung - for having articulated a promising sociology of mental development. But his early works were received in the discipline primarily for the novelty of their methods: as Jerome
Bruner would later note, Piaget - as read by Americans in the 1940s - was "fascinating, but not as a theorist."14* Rather, it was during the drive to reform the American school
145 This section is revised from (Burman, 2008a). 146 Elton Mayo describes Piaget's approach at this time: "I do not know what diverted his attention to the human organism, but we should remember that his original distinction was achieved as an authority on mollusks. To some extent, therefore, he still retains the point of view he thus acquired: the human infant is still to some extent a mollusk who develops amazing powers of comprehension, control, and adaptation to other mollusks. .. .For him the mollusk is active or passive during the twenty-four hours, and the activities or passivities of the organism at any age must be studied as functions that serve that organism. Such functions are not identical in the human at four and at forty; however apparently similar, they must therefore be studied in relation to the organism's developed powers and the stage of its development" (Mayo, 1930, p. 141). Compare Piaget's roughly contemporary use of similar ideas: "To say that intelligence is a particular instance of biological adaptation is thus to suppose that it is essentially an organization and that its function is to structure the universe just as the organism structures its immediate environment" (Piaget, 1936/1952, pp. 3-4). 147 (Hsueh, 2004) 148 (Bruner, 1983, p. 133) 50 curriculum in the 1960s, and with the rise of the Head Start movement, that his early theoretical work was first raised into prominence.149
Upon his initial "rediscovery,"150 Piaget was once again read by the Americans as a methodological innovator: a producer of consistent and interesting results. Yet he claimed to be going a step further; that he was actually not doing "psychology."
Eschewing paper-and-pencil tests (and the potentially illusory statistical analyses that accompany them) in favour of the intimacy of clinical interviewing, Piaget - and his army of collaborators and assistants at the International Centre for Genetic Epistemology
(founded in 1955) - attempted to peak behind the curtain of children's thinking. Theirs was a search for the causes of knowing, not correlations in knowing; the underlying question was not What do you think?, but How do you know?. Psychology, for Piaget, was a method; a set of interventional techniques to be used in examining larger epistemological questions.151 His answer to these, in their myriad instantiations, was to posit a process for constructing "logico-mathematical structures."
A structure, for Piaget, is an endogenous (internal) behavioural approximation that serves to address an exogenously-produced (external) stimulus. It is an axiomatic transformation that meets a need; an accommodation that returns the organism to a state of equilibrium relative to its assimilated environment. For example: the characteristic
149 Frank Murray explained it thus: "because Piaget and his collaborators in Geneva were virtually the only psychologists before the 1960s to write about how children understand concepts that are actually parts of school curricula, educators and others quickly turned to them whenever education and schooling were thought to be in crisis" (Murray, 1992, p. 287; see also Bliss, 1995). 150 Hsueh (2005) attributes this label to Eleanor Duckworth, who served as one of Piaget's key American translators. 151 (Piaget in Flavell, 1963, pp. viii-ix) 51 movements of the rooting reflex, in which newborn infants turn toward and move to suckle the source of a slight stimulation of their cheek, is for Piaget a function of the basic inherited structures that help ensure successful breastfeeding. Similarly, heuristics of "bigness" operate in children too young to conserve "number" in counting. But, crucially, these early structures are updated and replaced with more powerful structures that later enable "counting."
Indeed, for Piaget, all development can be traced to the construction and extension of "structures." During his rediscovery in America, however, such structures were all but invisible. Bruner, who became one of the most influential of Piaget's early
American interpreters, simply never saw their purpose. Piaget explained as follows:
.. .in his view, these are constructs ridden with "logicism" [the fallacy of reducing all acts of behaviour to productions of logical formalism] which do not render the psychological facts in and of themselves. He does not credit the subject with cognitive acts and "strategies".... Bruner tries to account for the intellectual growth of the child in terms of the way in which he meets conflict among the various modes of representation at his disposal—speech, images, action-schemes themselves. But if each of these models furnishes him with an incomplete and sometimes even distorting perception of reality, how can he resolve such conflicts unless he appeals either to some "copy" of reality or to "structures" as described by us, as coordinations of all instruments of representation?152
It seems clear that Bruner also inherited Baldwin's loops (if only implicitly) but without recognizing the meaning of "imitation through integration and augmentation" (Chapter I).
As a result, in America during the 1960s, Piaget was a structuralist without structures.
Stages happened, as a recapitulation of the species of mind attained during the evolution
(Piaget, 1968/1971, p. 72) 52 of the human species; they were not caused}53. Their emergence followed laws, to be sure, but these - "assimilation," "accommodation," "equilibration" - went largely undefined for English-speaking audiences; their epistemological consequences unexamined.154
Staging the Return
According to Piaget, Waddington endorsed his early work in biology at a conference held at the Centre International de I'Epistemologie Genetique in Geneva in 1964.155 A year later, in 1965, Piaget then delivered his own talk on the subject (titled "intelligence and biological adaptation")156 and followed this with an essay published in 1966 on "biology and knowledge."157 This seems to approximate the initial chronology for his "return to biology." That said, however, Piaget later also claimed that he had never really left it.158
In the preface to Biologie et Connaissance, the book published in 1967 that formalizes the results of his return, Piaget notes that he had continued to publish both in zoology159 and botany.160 Yet, in examining the dates of these publications, a gap of over
153 (Vidaletal., 1983) 154 This is Piaget's complaint about the textbook adopted by Bruner at Harvard: "his [the author's] approach is perhaps too exclusively psychological and insufficiently epistemological" (Piaget in Flavell, 1963, p. viii). He continues, demonstrating the importance of what follows: "The picture of our work which Professor Flavell provides extends only up to about 1960 and thus it cannot be considered the final word" (Piaget in Flavell, 1963, p. ix). 155 (Piaget, 1967/1971, p. 14; see also Waddington, 1973/1975) 156 (my translation of Piaget, 1967c) 157 (my translation of Piaget, 1966a) 158 (Bringuier, 1977/1980, p. 110) 159 (in 1929a; 1929b; and 1965) 160 (in 1966b) 53 thirty years remains unexplained. Piaget's claim is also in conflict with how he characterizes the period in his autobiography:
Increasingly excited by this return [retour] to my first loves as a biologist, I came from there [the ideas introduced in Biology and Knowledge] to a basic hypothesis that was close to Lamarckism but interpreted very differently, and according to which the principal engine of macro-evolution would be none other than behaviour.161
To make his two statements commensurable, however, it should also be noted that this book serves to update and revise the evolutionary notions discussed in The Origins of
Intelligence in Children162 and at least two chapters from the third of his three-volume
Introduction a I'epistemologie genetique (on "the structure of biological knowledge" and
"the epistemological significance of the theories of adaptation and evolution").163 Taken together, these texts demonstrate a consistency in the presentation of his biological thinking, while at the same time enabling a "return" in terms of active research.
That said, Piaget's other writings from this period suggest that he was doing more than just returning to biology. Although he was indeed able to take rhetorical advantage of advances not available to him during his dispute with Roszkowski, the same secondary narrative still remains: the relationship between whole and parts, formalized in logic.
This time, however, the larger discussion is not about the development of a shell and its implications for the reality of "society" and the possibilities for social change; this time, evolutionary-developmental alterations are of "structures" in general. (The newly- emerging framework supporting this position is examined in Chapter III, then continued
161 (my translation of Piaget, 1950-1976/1976, p. 40) 162 (1936/1952) 163 My translations (1950) 54 from a more specifically psychological perspective in Chapter IV and a more social perspective in Chapter V.) This larger discussion provides the justification for claiming that Piaget's return to biology also represents a return to the issue proposed for his second
dissertation: the use of the biological method in understanding the judgment of values.
Indeed, from this perspective, the foundations of the "new theory" are to be found in an
examination of explanation as a way to produce and share knowledge and values: explanation to oneself is psychological, while explanation to others is social.
Biologie et Connaissance
Piaget summarized the early fruits of his "return" as Biologie et Connaissance (translated as Biology and Knowledge) in 1967. In returning to biology, and specifically in writing this book, he intended to pursue one goal: "to show the relationship and functional continuity that connect the process of the formation and development of knowledge to the biological mechanisms of auto-regulation peculiar to the organism."164 In other words, his purpose was to revisit the issue of equilibria in whole-part relationships while taking advantage of theoretical advances made following his turn away from biology in 1918.
The effect of this effort would be to re-ground his descriptive theory of categorical knowledge, building a new explanatory narrative upon foundations provided by contemporary work.
(Piaget, 1975/1995, p. 803) 55 Reading Guide and Exegesis
Biology and Knowledge is divided into seven parts. Although each has several sub sections, they all summarize historical arguments related to an overarching theme and then present Piaget's synthetic conclusion. The result is a complex, but fairly complete, introduction to each of the major themes behind the emergence of the "new theory."
• The justification of appeals to post-neo Darwinian theory;
• The use of multiple methods, drawn from multiple disciplines;
• The application of biological explanations to psychological problems;
• The comparison of similarities in structure and function between organisms and
the hunters and gatherers of knowledge;
• Organization within and across levels;
• The forms possible in explaining the inheritance of knowledge.
Taken as the first of the three forgotten books, however, only the first three sections stand alone; the subjects of the remaining sections are introduced in Biology and Knowledge, but then are also developed further later in the transition. It is therefore on the first three sections that we will focus the bulk of our attention in Chapter II, with the fourth and the sixth sections each examined on their own to introduce the larger narratives presented in
Chapter IV and Chapter V. (The fifth section, which focuses on the different levels of intelligence, expands in detail on ideas made clear here in Chapters III-IV and so is mentioned only in passing; the seventh is a recapitulation of the whole, excluding those
56 aspects further developed after the book's publication in 1967, and is therefore unnecessary to review as part of our larger examination.)
Part 1 of 3: Posing the Problem while Justifying the Answer. In the first part of Biology and Knowledge, Piaget attempts to articulate the problem that motivated his "return." He begins with a brief review of the various types of organic interaction that had been discussed to that point in the history of psychology (conditioned reflexes, action patterns, stimulus-response patterns, feedback, etc.), and then concludes by abstracting an assumption common to all of these explanations: "life is essentially autoregulation."165
In other words, life is the circular reaction - equilibration - writ large. He suggests, too, that this regulatory process can be thought of in two ways: statically or dynamically.
From this new perspective, Piaget's earlier findings on child development can be interpreted either as illustrating the fulfillment of a progressive sequence of stages predetermined by the evolution of the species (recapitulation), or as indicating an underlying constructive process of transformation. In other words, the infantile stage of sensorimotor action either leads to (old theory) or enables (new theory) a childhood stage of pre-operational semiotic-linguistic representation, which in turn is either followed by
(old) or makes possible (new) the early teenage stage of propositional implications.166
And while this could be a purely maturational process, the developmental delays manifest
165 (Piaget, 1967/1971, p. 26) 166 More recently, a systems-theoretic variation on this "new" constructive perspective has been proposed: "generative entrenchment" (see e.g., Wimsatt, 1985; Schank & Wimsatt, 1986; Wimsatt, 1999, 2001; Wimsatt & Griesemer, 2007). The parallels between these two positions - Piaget's and Wimsatt's - ought to be examined further in future research. 57 among those lacking normal experiential abilities (e.g., blind people) suggests a different interpretation. Indeed, Piaget's years of research on the construction of the various different categories of experience - which had each afforded a slightly different set of empirically-derived developmental stages - collectively suggested a single sequential process: a common set of transformations shared by all children, with advances and delays attributable to differences in exposure. In returning to biology to explain this finding, the theory he offers as a "tool for thought" is Waddington's updating of the embryological theory of "epigenesis."168
The key parallel Piaget makes, in attempting to update the biology behind his psychology, is to propose that mental development is like an embryogenesis of mind:
"The problem of stages in developmental psychology is analogous to that of stages in embryogenesis."169 If this follows, then epigenesis - the most advanced explanation for
167 (Piaget, 1967/1971, p. 18) and deaf-mute children (Piaget, 1968/1971, p. 93) 168 Karl Ernst von Baer espoused an earlier version of epigenesis, borrowed and developed by Baldwin. The scientific value of Waddington's explanation, over this earlier one, is that it is situated in a post-neo- Darwinian theoretical context. 169 This is the full quote, from another document written during the transitional period: "The problem of stages is developmental psychology is analogous to that of stages in embryogenesis. The question that arises in this field is also that of making allowance for both genetic preformation and an eventual 'epigenesis' in the sense of construction by interactions between the genome and the environment. It is for this reason that Waddington introduces the concept of 'epigenetic system' and also a distinction between the genotype and the 'epigenotype.' The main characteristics of such an epigenetic development are not only the well-known and obvious ones of succession in sequential order and of progressive integration (segmentation followed by determination controlled by specific 'competence' and finally 'reintegration') but also some less obvious ones pointed out by Waddington. These are the existence of 'creodes,' or necessary developmental sequences [pathways], each with its own 'time tally,' or schedule, and the intervention of a sort of evolutionary regulation, or 'homeorhesis.' ...Each of the preceding characteristics can be observed in cognitive development if we carefully differentiate the construction of the structures themselves and the acquisition of specific procedures through learning (e.g., learning to read at one age rather than another)" (Piaget, 1968/1970, p. 710). In an interview given a year later, Piaget repeats this now-familiar refrain: "The embryological stages are sequential, in the sense that each is necessary to the appearance of the following one. And presupposes the preceding one. In other words, no stage can be skipped. Well, now, I believe that the same thing 58 the developmental change of an embryo - ought to be the process by which constructions occur in both domains. We are led thus to a new take on his old hypothesis: the quality and character of the mind is not preformed, but instead emerges as a result of the organization of its early interactions. In this new formulation, the set of all interactions that grows an adult organism from the potential given by its inheritance (genes, as well as the blastula's internal cellular environment, the zygote's internal maternal environment, the infant's parenting, the child's education, etc.) can be understood as being constrained by a series of historical pathways. One's momentary position relative to the set of all possible positions is thus a reflection of the pathways leading up to that point, such that all past constructions both enable and constrain future behaviour.
The expression Waddington used to describe this equilibration is based on the notion of "homeostasis." However, in recognizing that the balancing could not be based on a static set-point (like the ideal temperature set on a thermostat), he proposed a new term to signal his intended meaning: "homeorhesis," from a combination of Greek roots implying a dynamic process responsible for the maintenance of "similar" (homeo)
"flows" (rhea). Crucially, this does not suggest the action of a homeostatic "controller,"
appears in the stages of development of the cognitive functions of intelligence" (Piaget in Bringuier, 1977/1980, p. 37; see also Piaget, 1950/1995, pp. 35-36). 170 Waddington calls these "chreods," but his language is unnecessarily complicated for our purposes. Where possible, such technical terms will be rephrased or - if necessary to the argument - explained. 171 This led Waddington to suggest - at the 1964 symposium in Geneva - that even logico- mathematical abstractions, such as geometrical theorems, develop in the same way: "each is rendered indispensable by the sum of those preceding it, though none is directly derived from the axioms underlying the original one" (described by Piaget, 1967/1971, p. 14). This observation, which Piaget considered "profound," provides a simple biological argument on behalf of genetic epistemology: history matters, as a constraint on the future. In future research, the transcript of Waddington's comments will have to be added to the larger narrative. 59 but rather implies the same kind of bounded necessity as a pathway with walls.172
Waddington illustrated this by equating the pathways with "channels" in a landscape: as a marble rolls down a surface, its motion is constrained by the surface's features. In his illustration of the metaphor, maturation is therefore given by one "dimension" (temporal distance from the top), while change is given by another (motion side to side).173 A third dimension, the height of the hills and depth of the valleys, is a reflection of the energy required to leave one pathway for another. In this way, although they must be interpreted relative to the position (i.e., the "perception") of the marble, the walls can be seen as the source of perturbations (or, at longer timescales, selection pressures) pushing it into new conformations.174
172 This key point has been missed by some commentators (see e.g., Haroutunian, 1980; with comments by Doll Jr., 1981). 173 Piaget uses the word "dimension" in a similar context, in a discussion of the organism's relationship with its environment and the subject's relationship with its objects (Piaget, 1967/1971, p. 99). 174 This is the metaphor used by (Burman, 2006) to parse the findings associated with the "enactivist" approach to psychological research, as a philosophical response to "cognitivism" (which views intelligence as the rule-bound manipulation of symbols [viz. Searle, 1980/1981]). 60 Figure 6. Waddington's illustration of the "epigenetic landscape."
Of course, thought experiments have their limits, as Waddington recognizes:
Although the epigenetic landscape only provides a rough and ready picture of the developing embryo, and cannot be interpreted rigorously, it has certain merits for those who, like myself, find it comforting to have some mental picture, however vague, for what they are trying to think about.
This was presented originally in a chapter on "the cybernetics of development" (Waddington, 1957, p. 29; reprinted in Waddington, 1974/1975, p. 259) but later became part of a larger systems-theoretic proposal regarding the multidimensionality of development and evolution. 176 (Waddington, 1957, p. 30). Twenty years later, however, this metaphor was updated to follow the same kind of systems theoretical terms that Piaget endorsed in his discussions of cybernetics: "Embryos, like ecosystems, are multifactorial. They have many characteristics and they are affected by many factors, for instance, a multitude of genes and many environmental conditions. Changes in embryos therefore have to be symbolized by trajectories in multidimensional phase space.... Any orderliness we can discover in an embryonic system can be described in terms of constraints on the courses of these trajectories. These constraints can be visualized as attractor surfaces. If the system starts from any condition, which will be represented by a point in the multidimensional phase space, the trajectory from that point will first of all move to the nearest attractor surface, and then move along that surface.... An attractor surface modeled in such a manner is called an epigenetic landscape.... To avoid having to use the only metaphorical name of a 'valley,' for what is really a characteristic of an attractor surface in a multidimensional space, I have coined the word 'chreod.' The cross-sectional shape of the chreod describes the reaction of the system to fluctuations affecting it. In a chreod with a canyon-like shape, it will be very difficult to divert the developing system from the very bottom of the valley. If this is done by a strong enough influence, the system will immediately find its way back to the bottom as soon as the influence ceases. Such a system is very stable.... On the other hand, if the chreod 61 But this is how Piaget seems to use the idea: a "post-neo" metaphor to reinvigorate and update his "pre-neo" theory. Although for Waddington the focus is initially on the chemistry of the cell and the developing embryo, Piaget's interpretation generalizes the explanation to a much larger problem: the imposition of selection pressures, and their resolution, during development (i.e., updating the Baldwin Effect).178
For Piaget, the epigenetic landscape represents the necessary set of possible paths along which development can occur; homeorhetic equilibrium is maintained relative to the pressures exerted by the "walls" of the "channels." (Psychologically, and later epistemologically, these can be thought of as provided first by parenting and then by teaching.)179 All organisms therefore begin life with simple reflexes, provided by their species' evolutionary history, and then come to follow different developmental pathways as they mature and interact with their environment. These pathways both reflect and enable different constructed "competences"1 ° in responding, which then shape future reactions according to their logic.
By the end of part one of Biology and Knowledge, therefore, Piaget has indicated his theoretical orientation. He has described what he considers a set of shared isomorphisms between explanations of cognitive function and the organization of life
has the shape of a broad river floodplain, it will be very easy to divert the system from the very lowest point and it will return there only after a meandering at random for quite some distance. This is a system with little stability" (Waddington, 1976a, pp. 244-245). 177 For an overview of Piaget's evolutionary theory, see (Messerly, 1996) 178 Waddington (1974/1975) later generalized, proposing a larger systems-theoretic role for development in evolution (see also Waddington, 1977). 179 (Piaget, 1967/1971, p. 21; see also Burman, 2008b) 180 (Piaget, 1967/1971, p. 22) 62 (the process of embryological development), while presenting the means by which he
intends to unify them: the post-neo-Darwinian theory of epigenesis, which will enable
him to update his Baldwin-inspired theory of the genesis of knowledge. In part two, he
anchors what he describes as his "euphoria"181 over the new metaphor with an historico-
critical review of the set of possible methods that could be used to examine it with rigour.
Part 2 of 3: Methods of Approach and Control. Part two, an examination of the kinds of
explanations one can give while using biological metaphors to explain psychological
phenomena, begins with a series of rejections. For example, Piaget rejects Cuenot's
"combinatorial intelligence" for attributing something like adult intentionality to things
that cannot have it (e.g., cells), and therefore espousing a kind of vitalism that cannot be
addressed scientifically. What we presently call "greedy reductionism" - reduction to
explain away, rather than to elucidate182 - is also rejected, as psychology cannot be fully
181 (Piaget, 1967/1971, p. 38) 182 This is Daniel Dennett's turn of phrase. He defines it in a discussion about what reduction means for science: "we must distinguish reductionism, which is in general a good thing, from greedy reductionism, which is not.... The most common fear about Darwin's idea [evolution by natural selection] is that it will not just explain but explain away the Minds and Purposes and Meanings that we all hold dear. People fear that once this universal acid has passed through the monuments we cherish, they will cease to exist, dissolved in an unrecognizable and unlovable puddle of scientistic destruction. This cannot be a sound fear; a proper reductionistic explanation of these phenomena will leave them still standing but just demystified, unified, placed on more secure foundations. We might learn some surprising or even shocking things about these treasures, but unless our valuing these things was based all along on confusion or mistaken identity, how could increased understanding of them diminish their value in our eyes?" (Dennett, 1995, pp. 81-82). Despite Piaget's dismissal of reduction here, however, he is clearly not against reduction to the relevant whole: although his "circle of sciences" assumes a knock-on influence from physics to chemistry to biology to social science to logic and math then back to physics, these are discrete disciplines (Piaget, 1918, p. 45). For Piaget, these fields cannot be reduced one to the other because of how each epistemic structure is constructed in relation to the whole of science: the dialectical relations between each of the parts pushes the boundaries of all, as relevant elements peripheral to each discipline are cross- pollinated out from a hard axiomatic core that remains relatively stable (cf. Lakatos in Worrall & Currie, 63 explained by appeals to physiology alone; nor can higher cognition be merely the result
of a set of "associations and elementary conditionings," as a "copy of some outer
reality." Language is also rejected as an inappropriate basis for explaining cognitive
function because, although it certainly does become important for higher learning, no
purely linguistic theory can explain the prior organic conditions that enabled its original
construction.184 Then finally, and controversially (given the dominance of Behaviourism
to that point in his psychological career), Piaget concludes that - irrespective of the
method followed - the correct approach will be one that explains not only the nuance of
biological action, but also the bootstrapping of conscious experience.185
1978b, 1978a, pp. 58, 95-100,215-222). Indeed, this is the basic driving force behind his interdisciplinarity. (Language on "axioms" is developed in Chapter III.) 183 (Piaget, 1967/1971, p. 46). A few years later, Piaget expanded this criticism. He described his disagreement with behaviorist empiricism, using language that is consistent with the material covered in the chapter errata below: "Empiricism implies that reality can be reduced to observable features and that knowledge must limit itself to those features. Biologists have shown that the organism constantly interacts with its environment; the view that it submits passively to the environment has become untenable. How then can man be simply a recorder of outside events? When he transforms his environment by acting upon it he gains a deeper knowledge of the world than any copy of reality ever could provide.... In biology, the exact counterpart of behaviorist empiricism is the Lamarckian theory of variation and evolution—a long- abondoned doctrine. When we look at the famous stimulus-response schema we find that the behaviorist psychologists have retained a strictly Lamarckian outlook. The contemporary biological revolution has passed them by. If we are to get to a tenable stimulus-response theory we must completely modify its classical meaning. Before a stimulus can set off a response the organism must be capable of providing it. We talked earlier about the idea of competence in embryology. If this concept applies in learning - and my research indicates that it does - then learning will be different at different developmental levels. It would depend upon the evolution of competences. The classical concept of learning suddenly becomes inadequate.... Each man is the product of interaction between heredity and environment. It is virtually impossible to draw a clear line between innate and acquired behavior patterns" (in E. Hall, 1970, p. 53; see also Piaget & Inhelder, 1969). 184 (Piaget, 1967/1971, pp. 46-47). This position is developed further in a debate with Chomsky (in Piattelli-Palmarini, 1979/1980). 185 Although the reference here is to (Piaget, 1967/1971, pp. 48-49), this position is consistent with other related arguments from the time. For example, after a similar dismissal of Behaviourism, the neurologist Roger Sperry offers: "In my own hypothetical brain model, conscious awareness [is] ... a very real causal agent and rates an important place in the causal sequence and chain of control in brain events, in which it appears as an active, operational force. Any model or description that leaves out conscious forces, according to this view, is bound to be sadly incomplete and unsatisfactory. The conscious mind in this 64 In seeking the most appropriate approach of this problem, Piaget discards the
"local"186 concerns involved in the analysis of sensorimotor learning (which leads to questions regarding nerve function), intelligence (cerebral cortex), and instinct
(neurological and genetic history). Instead, just as he did at the beginning of his career, he chooses to focus on the "problem of the relations between subject and object."187 As a result, his introductory comments regarding auto-regulation (equilibration) being the driver of life become especially meaningful: the subject is the whole organism, objects are the constituent parts of any organism's environment, and the subject's knowledge of adjacent objects can be described as a function of the character and quality of its ongoing and constantly equilibrating relationships with them—the relationship between parts and
scheme, far from being put aside as a by-product, epiphenomenon, or inner aspect, is located front and center, directly in the midst of the causal interplay of cerebral mechanisms. Mind and consciousness are put in the driver's seat, as it were: They give the orders, and they push and haul around the physiology and the physical and chemical processes as much as or more than the latter processes direct them. This scheme is one that puts mind back over matter, in a sense, not under or outside or beside it. It is a scheme that idealizes ideas and ideals over physical and chemical interactions, nerve impulse traffic, and DNA. It is a brain model in which conscious mental psychic forces are recognized to be the crowning achievement of some five hundred million years or more of evolution" (Sperry, 1965, p. 78). He continues, anticipating Piaget's position (as described in Chapter IV), "The argument is simple and goes as follows: First, it contends that mind and consciousness are dynamic, emergent (pattern or configurationai) properties of the living brain in action.... Second, the argument goes a critical step farther and insists that these emergent properties in the brain have causal potency" (Sperry, 1965, p. 78). Then he concludes, again anticipating Piaget's position (as described in Chapter V), "In the brain model proposed here, the causal potency of an idea, or an ideal, becomes just as real as that of a molecule, a cell, or a nerve impulse. Ideas cause ideas and help evolve new ideas. They interact with each other and with other mental forces in the same brain, in neighboring brains, and, thanks to global communication, in far distance, foreign brains. And they also interact with the external surroundings to produce in toto a burstwise advance in evolution that is far beyond anything to hit the evolutionary scene yet, including the emergence of the living cell" (Sperry, 1965, pp. 82-83). Piaget's unique contribution is therefore not the idea itself, but how he gets there. This is the focus of the remainder of Chapter II. What it seems he intends to do with it is discussed in the Conclusion. 186 (Piaget, 1967/1971, pp. 50-51) 187 (Piaget, 1967/1971, p. 51) 65 whole. He then parses this into three sub-problems, which he believes are shared by
explanatory approaches in both biology and knowledge:
1. The role played by historical necessity (e.g., instincts endowed by evolution);
2. The individual's ability to adapt to change (i.e., plasticity);
3. The maintenance of the historical self, in relation to changing environmental
demands (i.e., equilibration as homeorhesis).188
This division then lends itself to six methodological approaches,189 each of which is used to varying degrees throughout the remainder of the transition to the new theory.
The first approach is to examine functional connections.190 For example, if one were to equate biological functioning with abstract mathematical formulae (i.e., purely epistemological constructions), such as>> -f(x), it is clear that both share distinct senses of change and determining activity: the character of previous steps (e.g., finding food and eating it) leads to the quality of the next step (e.g., digestion).191 In this way, we can see that both biology and knowledge support the "assimilation" of external objects to the
subject: the nutrients in a foodstuff are incorporated into the physical body, just as the solution to a formula includes both its inputs and their transformation. In making this connection between biology and knowledge, Piaget therefore proposes that objects can be thought of as sources of "information" to be transformed by an actively hunting and gathering "consumer." In other words, the subject manipulates inputs according to the
188 (Piaget, 1967/1971, pp. 52-53) 189 Piaget doesn't use this division as a means to parse the problem, so he instead refers to "seven" approaches. In other words, the version presented here is slightly simplified. 190 (Piaget, 1967/1971, pp. 54-57). This is enacted in (Piaget, Grize, Szeminska, & Bang, 1968/1977). 191 (cf. Piaget in Bringuier, 1977/1980, p. 42) 66 functions of its structures and thereby produces a set of appropriate responses.192 (This is still Behavioristic, since it follows the S->R formula, but Piaget's focus in method 1 is on what happens between stimulus and response: to start unpacking "the black box" of cognition.)
The second approach Piaget outlines is to examine structural isomorphisms.194 In defining the process of this comparison, he delimits two requirements for meaningfully equating two structures:
1. Two structures are at least partially isomorphic when it is possible, by a series of
hypothetical transformations, to translate one into the other (i.e., they are
topologically homologous);
2. Such an observation achieves significance when a known process can be shown to
be capable of performing the required transformation.
He then appeals - using his standard rhetorical ploy of borrowing useful explanations from related disciplines - to Woodger's attempt to describe cognitive structures and organic mechanisms according to logical axioms, which Piaget suggests would enable the clear comparison between stages in a transformative sequence.195 (These first two
192 Piaget doesn't extend the metaphor provided by the equation, but its implication is clear: the formula itself doesn't change as it assimilates external data and transforms them into outputted "solutions." Its manipulation of the data is therefore a function of its structure. If it had a different structure, such as y = f(-x), it would output something different. (In this case, if the functions were plotted on a graph, the two lines would mirror each other across the x-axis. Obviously, much more complex behaviour is possible given more complex functions.) If the subject was to discover an object that didn't fit the equation, and this became a problem, an accommodation would be necessary. (For more on this, see Burman, 2008b) 193 See also (Piaget, 1973a) 194 (Piaget, 1967/1971, pp. 57-60) 195 (Piaget, 1967/1971, pp. 59-60, 16On) 67 methodological approaches are examined in further detail in part 4, which concludes this
chapter; the limitations of axiomatization are examined in greater detail in Chapter III.)
Piaget's third approach is to use abstract models of functioning. This is offered
with the recognition that Woodger's formalization of structures, while rigorous, has not
led to the production of new knowledge.196 He then suggests that cybernetic modeling -
through its formal articulation, and simulation, of the functions of structures197 - would
provide the means to combine the various findings of the second approach
(isomorphisms) with a test of their collective functional significance.
The fourth approach seeks to delimit the grey areas that the use of such models
can produce: to differentiate between groupings with similar characteristics, thereby
This is Piaget's usual complaint about philosophy: formalization is a process of organization in search of wisdom, such that found implications can be integrated with existing knowledge, abstracted, modeled, and understood. However, it is not the means to achieving "new" knowledge, which first requires exploration (see e.g., Piaget, 1965/1971). In the language of circular reactions developed above, philosophy is the second step in producing knowledge (coordination), while science provides the third (purposeful exploration). The first step is simply action: behaviour (cf. Piaget, 1976/1979). 197 (Piaget, 1967/1971, pp. 60-61, 1968/1971, p. 69; see also Von Glasersfeld, 1999) 198 This is developed in the untranslated 22nd volume of Piaget's edited series, Etudes d'epistemologie genetique (Cellerier, Papert, & Voyat, 1968). Yet it is significant for the reception of this aspect of Piaget's "new theory" in the U.S. that one of his colleagues in Geneva, Seymour Papert, went on to co-direct the MIT Artificial Intelligence Laboratory with Marvin Minsky. Although Piaget cites Papert and Minsky's competitors - McCulloch and Rosenblatt - approvingly in a number of works, MIT's symbolic processing approach to artificial intelligence would not be overtaken by McCulloch and Rosenblatt's neural network approach until the late-1980s (Boden, 2006, pp. 911-923). By that time, however, Piaget's influence would be on the wane. From the perspective of continuing the work begun during this transitional period, the delay to AI caused by this incomplete communication of Genevan discourses has been measurable. For example, Waddington's (1974/1975, p. 255) sketch of the mediating effect of the epigenetic space on the translation of information from genotype space to phenotype space is remarkably similar to that of the "perceptron" neural network critiqued by Papert (see Cellerier et al., 1968, p. 98). And although work continued in other related areas (e.g., by Hinton & Nowlan, 1987, to formalize the Baldwin Effect), this particular parallel has only recently been rediscovered (Dopazo, Gordon, Perazzo, & Risau-Gusman, 2001). And it's clear from the re-discoverers' exposition - especially the description of the anomalies encountered - that this effort is far from finished. (For example, for an unsurprising and totally consistent explanation of their "halting effect," see Laland, Odling-Smee, & Feldman, 1999, p. 10246.) 68 constructing a useful hierarchy where there was once just a blurry continuum. This,
Piaget notes, is the domain of epistemology. Yet - because it assumes the formal
articulation of structures and functions - it can also lead to the infinite regress of a search
for first causes. (What is it about nerve function that enables sensorimotor learning? or the cerebral cortex that enables intelligence? etc.) This is why the methodological focus must be on comparison: first causes become irrelevant, making progress possible.199
The fifth methodological approach is related to the fourth, but is also more philosophical. Rather than comparing between levels to ask about the differences between what is known, this method examines the qualities of objects to ask what can be known.200 In this way, since "the object of an act of knowing is never completely
independent of the activities of the subject,"201 the competences of the subject can be assessed indirectly. Yet, because objects themselves cannot be directly known by the
subject (since they only exist in relation to the subject), three conditions must be met in
seeking objective representations:
It is in this context that Piaget then explains the perspective that motivated the bulk of his own research with children: "If we take epistemology to mean, not the causal or psycho-physiological study of the factors enabling a piece of knowledge to function (for example, the nervous conditions and the material terms which go to express the variations of an act of perception), but the analysis of conditions of truth (adequation [satisficing] or adaptation) of the things known, the relaying of information between subject and object, it will be seen that the epistemological problem [how an organism comes to 'know'] is to be confronted at every level. Just as a study can be made of the epistemological questions of space, time, causality, and the conservation of the object in the mind of the human young, from 1-3 months to 12-18 months, so also a great many analogous questions... can and should be asked about the entire range of animal evolution" (Piaget, 1967/1971, pp. 62-63). This is the basic summary statement of Piaget's decades of work extending Baldwin's "genetic epistemology," which the return to biology now seeks to reground with its search for a set of general principles. It is also why he described himself as an epistemologist while doing psychological research: "the study of behaviour is the field in which comparative epistemology is likely to make the most decisive advances" (Piaget, 1967/1971, p. 63; see also Piaget, 1966/1971). 200 (cf. Piaget, 1981/1987, 1983/1987) 201 (Piaget, 1967/1971, p. 64) 69 1. It must be recognized that "objectivity" is derived through a process of
approximation, following the circular reaction, and therefore attempts at
objectivity require repetition;
2. "Objectivity" is not produced by the collective weight of observation, since there
is a requirement for the subject to "decentre" its subjective position and thereby
rid itself of its prejudgements (which are simply assumed to be accurate);
3. "Objectivity" is the result of fitting the observed behaviour of an object into a
rigorous epistemic framework, external to the subject but accessible given its
usual activities (and constrained by the limitations of circular construction).202
Indeed, this is the basis for Piaget's use of the clinical method in examining children's knowledge: interviewing to collect instances of justification for acts, then fitting these instances to a larger framework that describes the logic of their production. In addition, it reflects the action of that which drives progress in his application of epigenetic explanations: if the subject's usual activities bring it into contact with lots of objects with complex interrelations, then its epistemic framework must become increasingly rigorous and expansive to accurately approximate their behaviour.203 (As we shall see, this also forms the basis of his explanation for the growth of knowledge.)
202 This perspective of "objectivity" situates Piaget in the larger lineage examined by (Daston & Galison, 2007) 203 This is the basic Godelian undercurrent in Piaget's new theory (see Chapter III). Indeed, it is this appeal to Godel that distinguishes Piaget from Herbert Spencer's progressive evolutionism: selection pressures result in the construction of structures - including institutions - that alter the effects of disequilibrating perturbations through a series of levels in a hierarchy. (For more on Spencer, see Sapp, 2003, pp. 44-45; Bowler, 1993). Crucially, for Piaget, construction is only of the next higher level. Individuals must therefore be exposed to the "correct" amount of complexity {cf. \Burman, 2008 #368}. 70 The sixth (and final) methodological approach is also philosophical, as it involves the application of explanations drawn from biology.204 This has two benefits: the first is to provide a heuristic guide to the pursuit of scientific research in psychology, while the second is to remind biologists that intelligence is the cognitive form of adaptation.205
Part 3 of 3: Evolutionary Patterns in Biological Explanation, Applied to Psychology.
Part three of Biology and Knowledge builds directly upon these six methods. In parsing the problem of a subject's relationship with the objects in its environment, Piaget follows
Saussure (using method 4) in distinguishing two temporal dimensions: the "diachronic"
(viz. evolution and development) and the "synchronic" (viz. homeostasis and inheritance).206 Although these two dimensions interact to some extent, they can (for the moment and following the standard neo-Darwinian narrative) be treated as separate domains—as if operating along the two axes in the metaphorical epigenetic landscape, united by their history but separated by their momentary integration of its shaping effects.
In application to the problem of knowledge, then, as the explanatory marble rolls through the landscape of its epistemic environment, the interactive effects of selection pressures are balanced at both levels. Thus, although they are first considered separately, Piaget ultimately argues that there is an interaction between the diachronic and the synchronic.
204 (Piaget, 1967/1971, pp. 66-68) 205 (see also Piaget, 1974/1980a) 206 Surprisingly, this division is made without any attribution to Saussure (in Bally & Sechehaye, 1916/1959). The reference is actually only made explicit later, in Structuralism (Piaget, 1968/1971; see also Chapter V). 71 Part 3 then concludes with a discussion regarding how their interaction becomes a causal factor in construction: Piaget's argument updating the Baldwin Effect.
Piaget begins with an historical review of conceptions of the "diachronic"
(method 6), each having a different interpretation of genesis:
• Aristotle's hierarchy of forms, with souls "suspended from each other in an order
of perfection."207
• Creationism's pre-established plan, an "eternal order conceived of in stages"208
corresponding to the Biblical days of Creation.
• Essentialist classification, according to a natural "principle of logical
interconnections,"209 with the Lamarckian variation attributing to the resulting
series an order in time.
• Neo-Darwinian combinatorial genomics, in which all future possibilities are
subject to necessities given by the functions of the pre-existing structures that
collectively compose DNA, "the carrier of genetic information."210
• Darlington's constructive theory of evolution, which argued on behalf of the
historical emergence of a common "genetic system" to manage the "meaning" of
genetic "information."
Piaget then draws attention to the similar genealogy of theories about reasoning, equating modern psychological conceptions of intelligence-faculties (e.g., Spearman's g) with
207 (Piaget, 1967/1971, p. 75) 208 (Piaget, 1967/1971, p. 75) 209 (Piaget, 1967/1971, p. 76) 210 (Piaget, 1967/1971, p. 77) 72 Creationism and Essentialism. He also lists a series of influential theorists inspired by similar "anti-evolutionary"211 perspectives of adaptation: Descartes (innate ideas),
Leibnitz (pre-established harmony of monads), Kant (a priorism), and Cuenot
• •917
(vitalism). He then suggests, by way of providing a way forward, four sources of pro- evolutionary approaches that could provide useful interdisciplinary explanations of the phenomena he wishes to explain: the history of ideas (in the form of the "historico- critical method in epistemology"),213 comparative psychology and ethology, developmental psychology, and the study of genes associated with the functions of intelligence (especially "the phylo- and ontogenetic processes of cerebralization").214 In addition, he cites Kurt Godel's theorems (following method 3) as providing an important theoretical argument for construction.215
The connection Piaget makes from Godel to developmental theory is cryptic; the indicated leap to Waddington's epigenetic landscape is unclear. (If the subject matter is explanation, then how are all of these different disciplines to be united in one argument?)
Yet the significance of his intended project is laid plain in tracing the reference to Godel: in the face of even the slightest continuing selection pressure, the subject is encouraged to
211 (Piaget, 1967/1971, p. 78) 212 Later, he would also add Chomsky's linguistics to this list. This is discussed in Chapter V. 213 The translation misspells this as "historic-critical" (Piaget, 1967/1971, p. 79). The translation given here matches the original text (Piaget, 1967a, p. 118). 214 The translation misspells this as "philo-" (Piaget, 1967/1971, p. 80). The translation given here matches the original text (Piaget, 1967a, p. 119). 215 Piaget supports this rhetorical "throw-away" with an internal reference to a later comment, which the translator renders as "section 30, sub-section 4" (Piaget, 1967/1971, p. 80). Unfortunately, this passage doesn't exist; the book ends at section 23. In the original, however, the reference is to "section 20, sub section 4" (Piaget, 1967a, p. 119). My interpretation here is therefore read through this intended background definition. See the Errata, below, for more. 73 make its approximated models of the world - including even the axioms of its constructed "psychologic" - more consistent and more complete, leading to the construction of ever more complex approximations of those objects to which the subject has had problems adapting (see Chapter III).
Indeed, when speaking specifically about the development of organisms, the only such "model" that all young organisms can modify (by way of response to the problems posed by nearby objects) is in the function and the structure of their growing bodies.216
The result, if we include Piaget's implicit reference to Darlington's "genetic system"
(method 6), is a conception of change in context:
...the information supplied by the genotype [the organismic blueprint] is not only transmitted [inherited] but also transformed in the course of all this development [the construction of the organism from its blueprint], so that the essential system is no longer the genotype in isolation but a total "epigenetic system" in Waddington's sense of the term.... Moreover, selection is no longer thought of as having a direct bearing on the genes [because the epigenetic level is more plastic than that of the genome].... Selection does, however, have some influence on phenotypes [the set of adaptive possibilities enacted in adult bodies] insofar as it causes the genome as a whole to make "functional responses" to the stimuli and tensions of the environment. As a result, at every level of its development, the phenotype becomes an essential instrument of variation.... 17
In other words, contrary to what Roszkowski had argued in his dispute with Piaget in
1912-1914, the shape of- for example - a mollusc's shell is indeed relevant to questions regarding the origin of species: alterations in phenotype reflect the effects of perturbations on development, which if unresolved will be reflected in future evolutionary change as selection pressures. In Piaget's new theory, the Baldwin Effect
Behavioural response is also possible, as in the Baldwin Effect, but it is too complex to assume for the youngest and most basic of organisms. 217 (Piaget, 1967/1971, p. 81) 74 therefore becomes a shield against natural selection; the result, constant change leading to periods of stability. In short, Piaget argues that evolutionary-developmental change is a process of equilibration leading to a series of dynamically-equilibrated stages:
Thus, the stages of development have the appearance of graduated steps in a progressive equilibration with its dual aspects: the diachronic (homeorhesis...) and the synchronic (final homeostasis.. .)218
Hence, in returning to biology and mining it for more advanced explanations, Piaget offers a new understanding of child development: it is an active system of continuous transformation, but with a stepwise appearance.
But Piaget's intent was not to reinvent stage theory. Instead of declaring victory at this point, and laying down a new theoretical foundation for the findings that made him famous in psychology, he reviews - and rejects - related historical ideas that could explain the same progression in general: for example, von Baer's early version of epigenesis and its application by Baldwin to explain adult reactions by studying children.
He also notes that it was Rousseau, in Emile, who first thought to argue that the child is not simply the adult in miniature. Rousseau simply did not have access to the "right kind of theory" to explain why that must be.219 Piaget provides a corrective:
Today it is known that this organization consists of a construction of operational structures beginning with the general coordination of actions.... Moreover, we are fairly certain that these processes are directed by a form of autoregulation or progressive equilibration, and that they naturally presuppose a continuous
218 (Piaget, 1967/1971, p. 82) 219 Such a statement now seems horribly Whiggish, as history, but that's how Piaget presents the argument. It must be recognized, however, that Piaget does not present these episodes as "history." (We already know, from comments presented above, that he was inclined to celebrate the new metaphor.) His purpose is rather to chart the development of thinking; the evolution of explanation. The result is that moments of high functioning are celebrated as exemplary of new possibilities for thought. 75 interaction between the subject and its objects, which means that there is a dual movement of assimilation to the structures and accommodation to the external world?20
This "dual movement" is a function of the familiar mechanism for constructive change: the circular reaction. This made clear, the discussion then shifts to questions regarding how the subject organizes the results of this construction - its experiences - internally. In other words, Piaget shifts from the diachronic mode of explanation to the synchronic.
In the histories of biology and psychology, conceptions of the synchronic have typically related to a structure's equilibrated stability. In attempting to chart this path, while at the same time explaining the concept, Piaget once again returns to the larger subject of his debate with Roszkowski and examines history of the changing meaning of what it means to be an organized totality—a species:
• Before evolutionary theory, Linnaeus' taxonomy was a lexicon of organized but
unrelated totalities.221 In other words, it was reflective of an implicit logic of
grouping.222 Organized instead according to a hierarchy inspired by Creationist
ideals, Linnaeus proposed that individual varieties (i.e., each "specie" or "kind")
reflected the Creator's original intentions; each was defined according to its
reciprocal elementary uses by others higher up.
• Later, as evolutionism began to emerge, Lamarck argued that each individual
organism was "fashioned" by the demands of its environment, but "without any
220 (Piaget, 1967/1971, pp. 84-85 [my emphasis]) 221 (Piaget, 1967/1971, p. 85) 222 According to Linnaean binomial nomenclature, each organism can be grouped according to genus (e.g., Homo) and further distinguished by its specific variety (e.g., sapiens). 223 (Piaget, 1967/1971, pp. 86-87; see also Sapp, 2003, pp. 23, 61, 120) 76 endogenous constructions or any resistance from internal structures." As a
result, the species grouping became an arbitrary abstraction; a lineage, but with
constant variation. The line dividing one species from another was blurred, in this
conception, with individuals in the hierarchy having "relationships" rather than
belonging to discrete "classes." (Piaget puts Darwin in this group.)
• More recently, following the synthesis of Darwin with Mendelian genetics (and
the associated anti-embryological "mutationism of... [Thomas Hunt]
Morgan"),225 the notion of relational totalities emerged. Species thus became
equilibrated, self-regulating wholes.
Yet even as this "modern" idea of species-as-related-wholes has gained support, Piaget points out that the early atomistic ideas have remained.
In contemporary discussions, distinctions between types in a related whole are often described as "impure" (phenotypic) reflections of a single "pure" (genotypic) lineage.226 Thus, for the contemporary synchronic science of "genetics" [genomics], development is secondary: divergences are from an ideal type (i.e., a eugenic "kind"). At the same time, however, it is recognized that future change is also constrained by the group's potential for change (i.e., the variation inherent to a population's "genetic pool").
The contemporary conception of biological change therefore includes the changes that can occur within a relational totality, but only at the level of the population: a group's
224 (Piaget, 1967/1971, p. 87) 225 (Piaget, 1967/1971, p. 87; see also Sapp, 2003, pp. 112,113-114, 134, 136-137, 140, 181) 226 (Piaget, 1967/1971, pp. 88-89; see also Sapp, 2003, pp. 134-135) 77 individual phenotypes are collectively a reflection of their genotype, aspects of which are then "selected" according to the demands of their environment. As a result, novelty is a function of an alteration in the whole—the genotype. Piaget argues that contemporary neo-Darwinian genetics is therefore a science of stability without change: synchronic equilibration without diachronic evolution, except through the random mutation that starts a new lineage.227 Yet the historical trend he charts in the changing structure of biological explanation suggests that more modern conceptions of "species" will follow a more complex way of thinking.
This pattern in the evolution of "species" as a "tool for thought" is replayed in the evolution of explanations regarding the meeting point between genesis and development.
Piaget points to the differences between Aristotle's union between male "form" and female "matter," Mendel's conception of particulate genes and the discontinuous effects of their redistribution over generations, and - ultimately - Darlington's internal relational totality in the appearance of a "genetic system."228 Thus, it seems to Piaget, there has been an increase over time in explanatory power and complexity: a move from
"transcausal totality to atomism and from that to relational totality, relying on autoregulatory mechanisms."229 In other words, although the causes of biological change have remained the same, it appears that there has been an historical transformation in our
This is what Piaget means by "mutationism," a concept that returns in Chapter V as part of his critique of structuralist theories. 228 (Piaget, 1967/1971, pp. 90-91) 229 (Piaget, 1967/1971, p. 90) 78 understanding of change: whereas change was once supernatural, it is now becoming both diachronic and synchronic (with auto-regulatory re-equilibrations at each level).
In the history of describing thought, too, Piaget suggests that we can observe an
(approximately) isomorphic series of transformations: from the unconsciousness of organic forms invigorated with a life force230 to the felt-consciousness of individual ego- driven action,231 and from that to the emergent consciousness of relational neural networks.232 In our attempts to understand the problems of "intelligence," it was therefore inevitable - he says - that the line between animals and humans became blurred: "the ape shows itself to be superior to the human child, because it [the ape] has a similar schematism of action (assimilation schemata and coordinations) and interindividual exchanges which takes it [the ape] almost as far as formulating symbols."233 But, Piaget explains, it is not clear - in our explanations - if this has occurred as a result of shared evolutionary history or similar developmental pathways: are the common structures in both species innate, or are they the result of a homologous kind of interaction? This question reflects the core of his "old" research program and his response to Kant: is human potential to be properly considered innate or is it constructed?2^ How is this updated following his return to biology?
230 (Piaget, 1967/1971, pp. 93-94) 231 (Piaget, 1967/1971, p. 94) 232 (Piaget, 1967/1971, pp. 94-95) 233 (Piaget, 1967/1971, pp. 96-97) 234 Innumerable animal studies have since shown the apparently "evolutionary" effects of positive developmental interaction: apes can be taught to sign, parrots to count, dogs to fetch, etc. Some of these are discussed in (Piaget, 1950/1995, p. 31), which is mentioned in Chapter V. 79 If individual development can be characterized as a kind of evolution (since both evolution and involution involve processes of diachronic change), then it is clear that intelligence - whether in the child or the ape - "is never modified without 'reason.'"235
By this, Piaget means that the qualities of intelligence can be understood as being a part of an adaptive response to selection pressures, subject to the laws of auto-regulation.236
Furthermore, in application to the problem of understanding knowledge at the social level, we can see that groups of individuals are organized as relational totalities. Each of these individuals is changing diachronically relative to the stable synchronically- equilibrated wholes to which they belong (which we call "development"), while at the same time the whole population is changing diachronically relative to the synchronic stability of individuals ("evolution"). In other words, each is changing in relation to the other, but following the same rules of organization.237
Ultimately, we are left with a conception of the changing social environment as an epigenetic system. The landscape metaphor easily applies: as long as there is auto- regulation (movement in response to the necessities of selection pressures that lead to the exploration of new possibilities), the result will be a dynamic balancing of stability and change—the organism in its environment; the subject with its objects. Yet, in this conception, how does "progress" come about?
235 (Piaget, 1967/1971, p. 97; cf. Claparede on need and intelligence, translated in Burman, 2008b) 236 (Piaget, 1967/1971, p. 97) 237 (Piaget, 1967/1971, p. 98) 80 environment plane
Figure 7. Waddington's illustration of an adaptive shift, E->E*, in an epigenetic landscape. The energy required to cross the threshold causes discontinuities in change.238 In Piaget's terms, this discontinuity is called a "decalage."239 It is a delay in progress.
In responding to the myriad historical variations on this question, Piaget suggests that there have been three basic approaches to questions regarding the driver of "progress."240
1. The environment is in complete control of the organism, influencing and
moulding even its hereditary structures (i.e., nurture over nature);
2. The organismic population - as a collection of replicators - imposes certain traits
on the environment, which then filters the "unfit" (i.e., nature over nurture);
3. There is a co-constructive balance between organism and environment, such that
neither has greater importance (i.e., nature and nurture together in interaction).
In each of these approaches, the resulting conception of "progress" is different. Yet the lineage from one to another is not straight-forward. And tracing these influences from biology to similar theories in psychology is complex, especially since some "older"
; (Waddington, 1974/1975, p. 262) 239 (see e.g., Piaget, 1932/1932, p. 56ff, 1962/2000, p. 252; Piaget et al., 1968/1977, pp. 58, 82, 108, 118, 185; Piaget & Garcia, 1987/1991, p. 27) 240 (Piaget, 1967/1971, p. 99) concepts remain to this day. The "preevolutionist doctrine" of an established harmony between organism and environment, for example, is paralleled in conceptions of an unchanging intelligence-faculty. Similarly, Piaget argues that vitalism and finalism ("the power to foresee external demands") have been fallaciously united in arguments regarding, for example, the eye's having been "made for" sight.241 Such speculations always ignore the most important question: How? It is the answer to this more fundamental question that has, for the most part, followed the trajectory of increases in explanatory power and complexity.
Lamarck's late-18th century solution to the problem of "caused progress" was provided through "the inheritance of acquired characteristics." (This is a conception of progress driven by exercise, the results of which are inherited by the next generation.)
Yet this approach ignored the role of plasticity in responding to selection pressures.
According to Piaget, natural change is indeed driven by the active engagement of an organism with the external environment, but constrained by the flexibility of its internal structures:
If Lamarck was right, the organism ought to be infinitely malleable and constantly varying, whereas, as a general rule, the modifications it undergoes take place only within the "reaction norm." ...To put it another way, the organism is less passive than Lamarck supposed: it makes a positive reaction when it assimilates the environment to its structures instead of letting them give way in all directions through indeterminate accommodations. It is true, of course, that the organism is capable of learning: but every time it registers some piece of information from the outside, this process is linked up with assimilatory structures.242
(Piaget, 1967/1971, p. 103; cf. Darwin, 1859/1964, pp. 186-194) (Piaget, 1967/1971, pp. 106-107) 82 In other words, perturbations are not really of the organism as a whole. Instead, this new conception suggests that selection pressures operate on structures that constrain certain kinds of change and enable others. This is because the eventual change is of a sub
structure, not of the organism (i.e., not of the "total structure").
The argument goes as follows: following a radical environmental disequilibration,
assuming the whole population does not die immediately, some individuals will be pushed to the limits of their plasticity (reaction norm) in responding. These few will then
survive to have offspring having similar norms, the "highest" of which will in turn
survive. Over time, the mean in the distribution of norms will then begin to shift, such that "high plasticity" respondents come to have a greater distribution even in
environments similar to that prior to the disequilibration.
i3 ft.
Figure 8. Organism P is pushed to develop as P' (a). Over time, via natural selection, the new norm for P' shifts to Q (b). This then becomes heritable: under reverse stress, Q' does not revert to P.243
This, in short, is Waddington's solution to Lamarck's problem:
The acquired character... has, one might loosely say, become inherited, because it no longer disappears completely when we remove the particular environmental
243 (Waddington, 1959/1975, p. 50) 83 stress which initially brought it into being. We have indeed brought about exactly the same end-result as would be produced by a Lamarckian inheritance of acquired characters. But it is important to remember that this result does not occur because the characters are themselves inherited, as Lamarck suggested. There is no direct transmission... from an animal which acquired it... to its offspring. The apparently Lamarckian end result has been produced through a long course of natural selection operating on the population.24
Waddington's position, although still forbidden under the neo-Darwinian paradigm as quasi-Lamarckist, has become increasingly well-supported as cybernetic systems theory has continued to make gains in influence and power.245
Indeed, cybernetics (method 3) proposes an interactive response to the
"preformist mutationism"246 of neo-Darwinian theory; a tertium quid to address its weaknesses, just as the Baldwin Effect bridges the gap between (pre-neo) Darwinian theory and Lamarckism. For example: Ivan Schmalhausen - one of the founders of the modern synthesis who, like Waddington, also worked to update the Baldwin Effect - came to apply the cybernetic notion of phenotypic interaction to problems of information flow in evolution and development, which he also saw as "automatic" and "self-
244 (Waddington, 1962, p. 94; cf. West-Eberhard, 2003). After citing Waddington, Piaget then again defends his unorthodox position: "But it must be repeated that to accept the second basic fact of the Lamarckian position [the inheritance of acquired characteristics] does not involve acceptance of the Lamarckian explanation of it" (Piaget, 1967/1971, p. 108). The importance of such statements will be made clear in examining the errata, below. 245 Waddington (1974/1975) ultimately formalized his position in "a catastrophe theory of evolution." This was then integrated with a final statement about modelling and systems in general (Waddington, 1977). This post-neo Darwinian-turned-cybernetic approach continues in post-Piagetian psychology, with labels applied according to fashion: "catastrophe theory" (van der Maas & Molenaar, 1992), "regulatory systems theory" (Hooker, 1994), and - more recently - "dynamical systems theory" (Stevens, 2000; van Geert, 2000; Boom, 2004; see also L. B. Smith & Thelen, 2003). New methods inspired by cybernetics, such as the use of "artificial life" simulations (Parisi & Schlesinger, 2002; with commentary by Muller & Grobman, 2003), have also emerged in application to Piagetian problems. 246 (Piaget, 1967/1971, p. 120) regulating."247 The problem with this formulation for Piaget, however, was that it treated active responses by organisms as "random noise" in the behaviour of a larger population.
Despite their similarities,248 Piaget's endorsement of Waddington over Schmalhausen therefore came as a result of the former's synthesis of cybernetics249 (method 3) with four evolutionary subsystems (method 6):
1. "the genetic system" (cf. Darlington),
2. "the epigenetic system" (i.e., embryological development),
3. "the utilization of environment" (cf. Lamarck), and
4. "the actions of natural selection" (cf. Darwin).250
Feedback loops between these subsystems are then accepted to be what drives evolutionary-developmental "progress."
That said, however, the term "progress" implies a notion of directedness (i.e., progression toward) that is undesirable in diachronic explanations. Piaget instead uses
"vection," implying change along a lineage given a particular context.252 He then
247 (Piaget, 1967/1971, pp. 120-121; see also Levit, Hossfeld, & Olsson, 2006, pp. 98-100) 248 (Levit et al„ 2006, pp. 100-102) 249 Waddington endorses cybernetics explicitly (Waddington, 1976b, pp. 14-15) 250 (Piaget, 1967/1971, p. 121) 251 This is why Piaget later comes to argue that behaviour is the motor of evolution: without a cause of disequilibration, there can be no change (Piaget, 1976/1979). 252 Two commentators, Richards and von Glasersfeld, explain the difference between progress and vection: "Any claim of progress requires an end, a goal. In this case it is an ultimate claim, and it requires a final truth toward which we progress. Vection, or direction, indicates discernibly consecutive change. This we may see, for instance, in the child's increasing ability to work with and understand number concepts. Thus we may speak of direction or change within a particular context, and from within that context it makes perfectly good sense to speak of progress. But that is quite distinct from progress in any ultimate sense or outside of any particular learning context" (Richards & Von Glasersfeld, 1980, p. 30). Elsewhere, 1 have referred to this as "progress from" (Burman, 2007b, 2008b), but Richards and von Glasersfeld amplify the point: "Progress is normative; vection indicates consecutive change. This distinction is essential to Piaget's theory. An organism does not evolve to solve future problems. Changes 85 discusses several candidate theories describing what this means, but concludes by endorsing the position espoused by Bernhard Rensch (another one of the architects of the modern synthesis)—that "progress," in contrast to specialization, means increasing the opportunities for exposure to selection pressures (i.e., an "opening up" of
"possibility").253
This then leads to the conclusion Piaget seeks. Rensch's perspective of progress in biological evolution leads directly to epistemological evolution:
...from this standpoint analyses in biological progress naturally end up, without any recourse to value judgments, by regarding knowledge a necessary final achievement, in that it multiplies the field of these possibilities.254
The emergence of a search for knowledge is therefore the inevitable product of biological progress: "cognitive mechanisms... constitute the actual organs of regulation during exchanges with the environment."255 Increases in knowledge, both individual and collective, can thus be described using the same explanations as are used to describe biological change.256 (This proposal becomes a cornerstone of the new theory; it will be examined in further detail in Chapter VI.)
occur accidentally, and they may or may not bestow selective advantage. Evolution is change, but the success is for the moment" (Richards & Von Glasersfeld, 1980, p. 32). 253 Although somewhat counterintuitive, the move - following Rensch — toward "generalization" (instead of specialization) makes sense as an adaptive strategy. When thought of using an economic metaphor, which Piaget uses in material discussed in Chapter V, becoming exposed to multiple sources of selection pressures can be considered as a diversification of risk: if one source of food collapses, a generalized organism can shift to another source while the specialist would die. In high-risk, low-stability contexts, the selective pressure would therefore be toward generalization; reliance upon lots of things for a little, instead of on a few things for a lot. This was later examined, in the context of children's learning, by Piaget and Henriques (1978). 254 (Piaget, 1967/1971, p. 123) 255 (Piaget, 1967/1971, p. 127) 256 (Piaget, 1967/1971, pp. 126-137) 86 Recapitulation
Mental development is like embryogenesis, but of the mind (function) and its embodied and situated brain (total structure). As a result, because embryology was left out of the
"modern synthesis" of evolutionary biology, psychologists cannot appeal to neo-
Darwinian evolutionary ideas in grounding their developmental theories. Instead, they must go beyond neo-Darwinian explanations to include metaphors drawn from more recent research.257
In Piaget's own attempt to update the biology that informed his earlier work, he appealed to the post-neo Darwinian notion of the "epigenetic landscape" - the set of all perturbations that impinge upon the developing organism as it travels through life - and connects this to notions of "plasticity" in change. As a result, although he updated the foundations for his famous stage theory, he also laid the groundwork for the argument that "knowledge" (seen as a functional structure) is a result of- and the means to - altering selection pressures. What this means, and how he argued it is achieved, is examined in subsequent chapters.
Reception and Errata
The translation of Biology and Knowledge was deemed "well-done" and the book itself
"highly recommended for the serious student of genetic epistemology." Yet a number of mistakes were made that collectively alter the sense of the text. (Several examples
257 (cf. Robert, 2008) 258 (Furth, 1972b) 87 were footnoted in the discussion of Part 3, with others footnoted in Chapter IV.) Two of these are so important as to affect the meaning of everything that follows. By unpacking the first, the second will become obvious.
Piaget's justification for arguments regarding the necessity of constructivism in approaching problems of development is anchored by an internal reference to a later comment about the implications of Kurt Godel's results on the incompleteness of formal systems. The translator renders this as being found in "section 30, sub-section 4."259
Unfortunately, this passage doesn't exist in the English edition; the book ends at section
23. In the original French edition, however, the reference is to "section 20, sub-section
4."260 Interpretations of his argument in the return should therefore be read through this intended background, expanded upon in greater detail in Chapter III.
Godel demonstrated... that a system which is otherwise sufficient for its own purposes... cannot, by its own or by weaker means, succeed in verifying its own noncontradiction. In order to establish noncontradiction, one has to go beyond the limits of the system and integrate it with a "stronger one".... In other words, the development of a structure cannot be made entirely on its own level, by mere extension of given operations and combination of known elements; the progress made consists of the construction of a wider structure, embracing the former but Oft)
introducing new elements.
With this lost, however, so too was the constraint on meaning preventing a further error.
In the second major translation error, a single word was dropped. This alters the meaning of a crucial passage regarding the "necessity" afforded by past constructions -
9(Piaget, 1967/1971, p. 80) 0 My trans of (Piaget, 1967a, p. 119) '(Piaget, 1967/1971, p. 319) 88 in the form of "conserved organization" (inherited axioms) - with results formalized
according to a kind of grown "organic" logic:
.. .the transmission of hereditary characteristics from the genome upward presupposes, as a preliminary condition, that this genome is organized and this organization is conserved and extended without interruption, not only during the transition from one generation to the next, but also during the guiding of embryonic development from the moment the genes become active. In this sense, the organization qua functioning is not transmitted by heredity as are characteristics such as shape, color, etc.; it continues and succeeds itself... as a condition necessary to every transmission and [not] as a transmitted content.
The effect of this omission - and others like it - was a shift in interpretation away from
structures in an updating of Baldwin and toward a rehashing of Lamarck. This is perhaps
understandable in light of what has been perceived as the French resistance to neo-
Darwinian thinking.263 Yet it is due to this misunderstanding - writ large, in the form of
continuing claims regarding Piaget's implicit Lamarckism264 - that two sequels,265 and a
262 The original gives the following: "La transmission des caracteres hereditaires a partir du genome suppose comme condition prealable l'organisation de celui-ci et cette organisation se conserve et se prolonge sans interruption, tant durant le passage de la generation precedente a la suivante que durant le guidage du developpement embryonnaire a partir de l'activite des genes. En ce sens ('organisation en tant que fonctionnement n'est pas transmise hereditairement a la maniere d'un caractere quelconque de forme ou de couleur, etc.: elle se continue et se poursuit, en tant done que fonctionnement, a titre de condition necessaire de toute transmission et nonpas a titre de contenu transmis'" (Piaget, 1967a, p. 210). The translated passage, corrected in the text above, is provided by (Piaget, 1967/1971, p. 148; error noted by Chapman, 1988, p. 270; for a discussion of some of the implications of this omission, see Burman, 2007b). 263 (see e.g., Boesiger, 1980; Limoges, 1980; Faber, 1997) 264 (e.g., Thomas, 1977; Deacon, 2005; but see also Messerly, 1996) 265 These are more focused variations on the general theme outlined here, retelling the same story while highlighting the contributions of different characters in the overall meta-narrative. Adaptation and Intelligence (Piaget, 1974/1980a) focuses on "the phenocopy" subplot, Piaget's poorly-understood application of the Godelian hierarchy to evolutionary and developmental change. Behaviour and Evolution (Piaget, 1976/1979) - originally entitled Behaviour, Motor of Evolution (my translation) - then retells the story of updating Baldwin with Waddington (and others). These themes are taken up in the following chapters, albeit from different perspectives. 89 large public debate, would become inevitable. Regrettably, these did little to resolve the misunderstanding, as Piaget would later note in an interview:
If you explain it as a direct action of the environment [on] the genome.... Of course it's Lamarckism, that's the long and short of it. But if you explain it as Waddington does... it's a reconstruction by selection, but a selection imposed, as I see it, by the internal environment.267
With the return to biology misunderstood, so too was the rest of the transition to the "new theory."
Prospective Conclusion
The return to biology did not occur in a vacuum. The likely reason for Piaget's excitement, as he returned to his "first love," can be found in an important secondary narrative: what he learned from Kurt Godel (Chapter III). This afforded a new perspective of the whole-part relationship that had originally provided Piaget with a means to unify the mechanisms of biology and knowledge, while at the same time addressing some of the criticisms that led to the emergence of a "neo-Piagetian" school.
All of his original questions then also returned, which prompted psychological and historico-critical studies to attempt to address the same issues he had intended to pursue
This is the influential meeting between Piaget and Chomsky, along with their followers and contemporaries (in Piattelli-Palmarini, 1979/1980). It was presented implicitly as a debate between neo- Darwinians and neo-Lamarckians, although this is clearly misleading. Unfortunately, Piaget also died before a resolution could be agreed upon. The result was that both parties concluded that they had won the debate, but without convincing the other, producing a state of confusion that was worse even than what had existed before. This has since led to conclusive endorsements by previously impartial observers (e.g., Piattelli-Palmarini, 1994), and a blind adherence to dogma in the face of contradictory evidence. For example: that the cortical representation of language really does seem to emerge from the coordination of sensorimotor actions schemes (Koechlin & Jubault, 2006). 267 (Piaget in Bringuier, 1977/1980, pp. 112-113; cf. Waddington, 1976b, pp. 14-15) 90 in his second doctorate (see Chapters IV & V). In the later material of the new theory, however, this is all made implicit. Rather than continuing to cite Godel, Piaget cites subsequent scholars who built on his work. In other words, Piaget's use of Godel culminates in the three transitional works discussed here: Biology and Knowledge,
Memory and Intelligence, and Structuralism. And to fully understand these, we must first understand that.
e.g., the work of Gerhard Gentzen, followed by that of Alan Anderson and Nuel Belnap (in Piaget & Garcia, 1987/1991, pp. 146-147). 91 CHAPTER III
AN IMPORTANT SECONDARY NARRATIVE
Behind, and under, Piaget's return to biology is an important supporting narrative: a series of appeals to a meta-mathematical argument regarding the "incompleteness" of formal systems. Although the proof of this itself has been maligned and misused by scholars in innumerable fields since it was first demonstrated by Kurt Godel in 1931,269
Piaget's continuing endorsements - spanning almost three decades, starting in 1949 - provide a series of entry points into his perspective as it evolved. Seen in the light of his return to biology, tracing these appeals to Godel provides a deeper appreciation of how his ideas were developing prior to the emergence of what is now known as the "new" theory.
Piaget described Godel's theorems, in Biology and Knowledge, as providing
"impressive arguments in favor of constructivism."270 Briefly put, Godel demonstrated that no formal system can be both internally consistent and totally complete relative to all possible external demands; that there will always be true propositions that cannot be proven using the structures of the system used to describe them. Hence, if the mind is a system of equilibrated structures constructed through the assimilation of external stimuli
269 The standard reference here is to Penrose (1989, 1994), who used an interpretation of Godelian incompleteness to argue that "true" artificial intelligence is an impossibility. An extensive accounting of the idea's other uses and abuses is given by (Franzen, 2005). Yet that work is very complex technically and should not be used as an introduction to the topic. Indeed, its coverage goes well beyond the scope of this thesis; it is noted, however, as an important contribution to Godel scholarship. 270 (Piaget, 1967/1971, p. 80) 92 (as Piaget proposed), then it is also subject to the limits of Godelian incompleteness in their accommodation: the mind - an internally-consistent system of endogenous reconstructions - will interpret the meaning of external stimuli according to the functions of its structures, failing occasionally to capture their full implications and resulting inevitably in the emergence of new contradictions to be resolved.271 In short, the deeper meaning imparted to Piaget's program by Godel's formalism - along with the post-neo
Darwinian elements provided by Waddington - gave him the means to build toward a newer, stronger articulation of his earlier "genetic" theory of knowledge.
This chapter examines Piaget's use of Godel's ideas. Before going into detail, however, they are first put in context. And from this it becomes clear why there is an
"old theory" and a "new." An error of translation is then corrected, laying the foundations for the further discussion of Piaget's developing understanding of individual intelligence (Chapter IV) and his later attempt to find a compatible theory of culture
(Chapter V).
Kurt Godel (1906-1978)
Godel was born to German-speaking parents in 1906, in what is now the Czech city of
Brno.272 He took classes at university in physics, but ultimately specialized in logic and mathematics. After Godel completed his doctoral dissertation in 1929, which included a
271 Examined empirically in (Piaget, 1974/1980b, 1975/1985) 272 The most recent, and most popular, non-specialist introduction to Godel's life and work is Goldstein's Incompleteness: The Proof and Paradox of Kurt Godel. Yet this has been so thoroughly criticized as to be worth noting only as a paradigmatic example of how not to write a biographic history (see e.g., Feferman, 2006). The standard scholarly biography is (Dawson Jr., 1997). 93 proof of the "completeness" of arithmetic (i.e., the non-contradiction of its methods), he began work on the paper that made him famous: a two-part proof of the "incompleteness" of the general systems that are sufficiently complex to allow arithmetical statements.
The key assumption of Godel's 1931 discovery is that statements about mathematics, if properly constructed, can themselves be treated as mathematical propositions. As a result, they can in turn be proven: either the meta-level statement is demonstrably true, or it is demonstrably false. But by building on the Liar Paradox - typically presented as, "this statement is false" - Godel was able to set up a self- referential contradiction: a mathematical proposition about the truth of its own truthfulness. ("If this statement is true, then it is false.")
Ceci n eM fixu one fu>fi&.
Figure 9. Rene Magritte's (1928-1929) La trahison des images [The Treachery of Images] reflects the same self-referential spirit as Godel's (1931) formal proof of incompleteness. The caption says, "This here is not a pipe."
94 The details of how, exactly, this was accomplished is beyond the scope of this thesis.
However, by constructing the mathematical equivalent of a Liar Paradox - roughly, "this statement is not provable in the formal system A" - Godel proved that A was incomplete.
This undermined a key assumption of Bertrand Russell and Alfred North Whitehead's
Principia Mathematica, which had been assumed to provide a solid justification for the relationship between logic and the external world: if formal systems were complete, then the world could be fully reduced and described using logico-mathematical terms. But
Godel undermined this program: he showed there can be no such thing as a "universal truth machine."273
The initial reception of this result, relative to its present popularity, was chilly.274
In fact, aside from a handful of professionals, virtually no one noticed; the first expository article simplifying "incompleteness" for a popular audience was published in
1956—twenty-five years after the fact.275 In the intervening years, Godel produced a number of other important proofs and worked to extend his earlier results. He also fled the Nazi occupation of Austria for the United States, in 1940, and turned philosophical.
This shift, from pure math to philosophy, led to the emergence of two different contexts for his key discovery.
This was the challenge of David Hilbert's 1928 address to the International Congress of Mathematicians, to which Godel's proof of incompleteness ultimately responded (Feferman, 2008). Hilbert consequentially plays an important role in the emergence of Godel's theorems, but - except insofar as he argued for the formalization of mathematics in axiomatic form ("Hilbert's program"), which Piaget attempted to follow within psychology - he did not have the same impact on the emergence of Piaget's new theory. Although Hilbert is mentioned in many of the same volumes as is Godel, his ideas are not developed to the same extent. As a result, he will not be discussed here further. 274 (Dawson Jr., 1997, pp. 53-79; Casti & DePauli, 2000, p. 50) 275 This article (Nagel & Newman, 1956) was later turned into a bestselling book (Nagel & Newman, 1958). For a discussion of the resulting dispute, see (Feferman, 2007). 95 The Two Contexts of "Consistent and Complete"
The value of logical systems is that they enable the valid inference of "truth" or "falsity"
about a conclusion drawn from a set of propositions known to be either "true" or "false."
Godel's 1931 paper showed, however, that in all such systems there are true propositions that cannot be shown to be truthful; no amount of logical calculus - operational transformations of known axioms - would afford a determination "true." (This was
accomplished by equating "truth" with "provability.") If a table were constructed of all the possible transformations of a given system,276 which everyone agreed was non-
contradictory (i.e., consistent), then there would be known "answers" - truths of reality - which would still not be contained within it as provable statements. This system,
although consistent, is incomplete: it cannot be used to predict all the truths of reality.
Yet this was simply a result, intended to contribute to logic and pure mathematics.
In 1933, building on his mathematical result, Godel delivered a lecture at
Cambridge in which he argued for the importance of finding a means to ground mathematics on firm foundations; that a proof of non-contradiction would have to be
Beilin describes these "truth tables" (e.g., Piaget, 1952a) as the cornerstone of Piaget's old structuralist theory (Beilin, 1992a, p. 202). In the new theory, however, the reliance on "truth table logics" is replaced. Piaget explains: "Our work on the development of a logic of meanings is in many ways a continuation of that on the logic of operations. As conceived at the time, this logic of operations was too closely linked to the traditional model of extensional logic and truth tables. A better way, I now believe, of capturing the natural growth of logical thinking in the child is to pursue a kind of logic of meanings" (Piaget, 1980b, p. 5). He continues, in the Godelian sense unpacked in the Errata below: "At all levels of development there are implications between actions or meanings; then there are dialectical relations that lead the subject to go beyond what he has already acquired. These spiralling [sic] constructions of a dialectical nature constitute what I have long considered to be the essence of the growth of knowledge. Development does not simply consist of ever new equilibrations, but of 'augmentative' equilibrations, i.e. which lead to new equilibria that do not simply revert to a former state of equilibrium but which involve enrichment" (Piaget, 1980b, pp. 6-7; cf. Burman, 2008c). 96 found by "constructive" means. (In mathematics, a formal system is "constructive" if it produces the object it intends to prove: the proof is in the production, not the inference.)
Eight years later, in 1941,G6del delivered a similar lecture at Yale in which he described how "intuitionistic" logics - the view that mathematics and logic can be treated as internally-consistent tools for thought, rather than as revelations of the natural order - could be considered "constructive" in this way.277 A much longer (and more formal) version of this talk was eventually published, in German, in December 1958. And it had such an impact - popularizing his theory and igniting a firestorm of commentary - that it became known as the "Dialectica interpretation," after the journal in which it was published.278
Godel wrote the Dialectica interpretation as interest in his ideas was on the rise.
His purpose, however, was not to engage the various misunderstandings that had emerged in their popularization. (This was his first paper in German since emigrating almost twenty years before!) Rather, he approached the problem of the genesis of new proofs: where the insights mathematicians rely on in constructing truths of reality come from.
The character of his solution is - once again - too complex to go into here, but he introduces the effort simply:
277 All this is not to say, of course, that there is no real order to nature; or that the order we observe is socially constructed. Indeed, Godel explicitly denies this in the second part of his 1951 Gibbs lecture. The full nature of that order simply needs to be discovered and communicated (see esp. Godel, 1995e, pp. 314- 323; cf. Chapter IV). The development of this position is described by (Feferman, 1993, pp. 23-32). The lectures cited are included in the Collected Work as (Godel, 1995d) and (Godel, 1995a), respectively. 278 This is also known as GodePs "functional interpretation," although it is unclear how much overlap exists between GodePs functionalism and Piaget's structural-functionalism. A first attempt to lay the foundations for such an examination is presented here, but further research will need to be conducted for a proper assessment to be made. 97 .. .in the proofs we make use of insights... that spring not from the combinatorial (spatiotemporal) properties of the sign combinations representing the proofs [i.e., not from the manipulations of logical calculus], but only from their meaning}19
In other words, proofs do not emerge from the arrangements of the letters and numbers
that comprise them. Rather, the production of a proof is a function of the theorist's
competence in manipulating the meaning of the symbols (transforming their relations
using accepted operations directed toward an ideal goal), but it is not a function of the
symbols themselves. In other words, success in the genesis of mathematical knowledge
is a function of the mathematician's understanding.
Godel's larger purpose was to make the meaning of "meaning" more accessible.
To do this, he relied on the notion of "recursion" - a formal implementation of the
circular reaction (see Chapter II)280 - to distinguish between levels of complexity in
mathematical explanation: a proof requiring one operation is simpler than one requiring a transformation of that operation. (A statement that relies on recursive self-reference is more complicated than one that doesn't.) "Meaning" is therefore that abstract quality
which is reflected down through the levels of this complexity, from the deep and nuanced
279 Italics as in the original (Godel, 1958/1990, p. 241) 280 The relevant references here are to Godel's appeals to Alan Turing's (1937) proposals regarding the use of abstract computational devices. Of particular importance to us here, Godel provides the following correction of a popular misconception: "Turing in his 1937, page 250..., gives an argument which is supposed to show that mental procedures cannot go beyond mechanical procedures. However, this argument is inconclusive. What Turing disregards completely is the fact that mind, in its use, is not static, but constantly developing, i.e., that we understand abstract terms more and more precisely as we go on using them, and that more and more abstract terms enter the sphere of our understanding. There may exist systematic methods of actualizing this development, which could form part of the procedure. Therefore, although at each stage the number and precision of the abstract terms at our disposal may be finite, both (and, therefore, also Turing's number ofdistinguishable states of mind) may converge toward infinity in the course of the application of the procedure. Note that something like this indeed seems to happen in the process of forming stronger and stronger axioms of infinity in set theory" (italics as in the original Godel, 1972/1990, p. 306; see also Burman, 2008c). 98 understanding of the constructing mathematician to constrain the elegance-in- formalization of their final proof: their result is so, then, because it must be according to the implications of its meaning. In contrast to previous - purely mechanical - conceptions of the activities involved in proof-making, Godel's Dialectica interpretation implies that the necessity of results is constrained both "bottom-up" (by the signification of the given symbols) and "top-down" (by the understanding of the mathematician and their competence in formalization). Meaning is projected downward, while implication is projected up (see Chapter VI).
What Piaget learned from Kurt Godel
Were Piaget's ideas affected by the Dialectica interpretation? There is good evidence to suggest that Piaget could read German: first, it was on his high school curriculum in
1912-1915; second, while undertaking postdoctoral studies in Zurich in 1918-1919, he attended lectures in German; and third, his Traite de Logique contains many references to texts originally published in German, rather than to their French translations.282 There is also evidence that he was intimately familiar with the journal Dialectica, which was founded by his friend Ferdinand Gonseth. (Not only did he publish several articles there,
281 A corollary: New "meaning" can also be produced iteratively, in the augmentative translation across levels, by using old proofs to construct a new one of greater complexity. As Piaget (1948/1972) put it, "to understand is to invent" (see also Piaget, 1974/1978; Burman, 2008b). 2821 am indebted to Les Smith and Richard Kohler for these observations (personal correspondence, 25 June 2008). See, for references to claims between each semicolon, (Schaller-Jeanneret, 1996); (Piaget, 1950-1976/1976, pp. 8-9); and (Piaget, 1949b). Horst Pfeiffle also notes, however, that the more elderly Piaget of our period of interest was not comfortable conversing in German: "During my stays in Switzerland I occasionally tried to talk to Piaget in German, but he always managed somehow to turn the conversation back into French. And as far as I am aware and can remember, he also spoke French with Barbel Inhelder" (personal correspondence, 26 June 2008). 99 but he also cited some of the material that followed the publication of Godel's paper.)
He does not, however, cite the work of 1958 directly. Rather, he cites the original from
1931 and a French commentary published in I960.284
What is significant, in terms of Piaget's emerging new theory, is that Godel effectively undercut the foundations upon which Piaget's old theory had been based. For example: Piaget's early essay on logical groupings and the reversibility of the structures contained within them, published in 1942, had supported a recapitulationist theory of stages with a review of the history of logical explanation extending only up to Russell and Whitehead's Principia.2S5 (The resulting conception of development was of a kind of progression through various different species of mind [see Chapters II, V]). Then, although Godel's later proof of the incompleteness of this system ultimately provided
Piaget with the means to implement the kind of system he had proposed in 1925 (in his critique of Kant [see Chapter I]), the character of his later constructivism only began to become clear after the publication of the Dialectica interpretation in 1958. There was, in other words, a delay in the updating of that which grounded his theory. And since
Piaget's first references to Godel preceded this later date, there are two distinct Godelian phases - characterized by two different explicit uses of his proof- apparent in Piaget's
283 (e.g., Piaget, 1968/1971, p. 35) 284 The article that seems to have caught Piaget's attention, leading to his use of Godelian incompleteness in its Dialectica interpretation, was published by (Ladriere, 1960). Piaget's preference for a French source, rather than the German one, supports Pfeiffle's observation over Smith's (Op. cit.) for this later period. 285 (Piaget, 1942; see also Piaget, 1941b) 100 writing.286 The first uses are merely historical, with Godel's name included as an incidental in larger discussions of explanation in logic and math; in the later uses, however, this history is generalized in application to what becomes the basis for Piaget's new theory. Our examination will therefore be presented in three parts: Piaget's first
Godelian phase, the commentary Piaget uses instead of the Dialectica interpretation, and
Piaget's second Godelian phase.
Part 1 of 3: The First Godelian Phase. The first reference to Godel in Piaget's writing came in 1949, when Piaget published a follow-up to his earlier essay on the logic of thinking: Traite de Logique, which had apparently been destined to replace the textbook
9547 used at the Sorbonne. Here, Piaget mentioned Godel twice: both references were to his doctoral dissertation, completed in 1929, showing the "non-contradiction" (i.e., the
286 The first such phase was described by (L. Smith, 1999a, 1999b, 1999c) as Fregean, rather than Godelian. A follow-up to this proposal, developed from the perspective of the division described in this chapter, is currently in preparation (Burman & Barnhart, in prep). It will address criticisms by (Beilin, 1999) that some of Smith's conclusions were ultimately refuted by Piaget's later work: while it seems clear that Frege's influence continued into the second phase (L. Smith, 1999c, p. 136), it is also clear that its anti- Kantian elements were eliminated (Beilin, 1999, p. 121). This can be reconciled by attributing Piaget's later (continuing) Kantianism to the influence of Godel over Frege; the influence of one replacing the other, in tune with Piaget's own ideas, would eliminate any internal conflict. Evidence supporting this claim - of Godel's endorsements of, and sympathies toward, Kant - can be found in his Collected Works: in his published papers (e.g., Godel, 1947/rev ed. 1964/1990, p. 268, 1949/1990, p. 202ff), in his unpublished papers (e.g., Godel, 1995b, p. 338, 1995c, pp. 384-387, 1995f), and in his private correspondence (with Bernays, Grandjean, and Giinther in Feferman, Dawson Jr., Goldfarb, Parsons, & Sieg, 2003, pp. 147, 187- 189,203,207, 221, 225-229,447,450, 503). Additional detail is provided in the accompanying notes (e.g., Dawson Jr., 1986, p. 37). However, there is no mention of Piaget in any of the five volumes: although Godel certainly had an impact on Piaget, Piaget does not seem to have had any impact on Godel (cf. Piaget on Frege, in L. Smith, 1999c, pp. 134-135). 287 (Beth, 1950, p. 258; Piaget & Grize, 1972, p. xi) 101 internal consistency) of systems of arithmetic.288 But Piaget's treatment of the subject, generally, earned the ire of professional logicians. Evert Beth, for example, lampooned him: the book was deemed "mediocre" and "negligent," redolent of "failures hidden by pretences of technicality capable of impressing only a reader naive in logic."289 This unsympathetic response led to the second edition being re-titled, following the original subtitle, as "An Essay on Operational Logic."290 (This edition was also substantially revised by a proper logician, Jean-Blaise Grize, who became an important collaborator during the later phase of Piaget's Godehan research.) The name change made it clear that the book was not about logic per se, but Piaget's operational "psycho-logic"—how the mind's growing organization can be described using logical terms.292 (By the time
288 While the citation provided in Piaget's references in the first edition of Traite is to the 1931 paper, the text itself cites Godel's 1929 dissertation (Piaget, 1949b, pp. 20,223). In the second edition, however, the first in-text citation is updated to match the references (Piaget & Grize, 1972, p. 18) and the second removed. From the context, which remained unchanged in the update, it is clear this update was in error: a presentist "correction" of an earlier citation to match the later Godelian position extant at the Centre. In addition, replacing the second citation, a new reference to the 1931 paper was added later in the text (Piaget & Grize, 1972, p. 387). 289 My trans of (Beth, 1950, p. 258) 290 My trans of the title for (Piaget & Grize, 1972) 291 J.-B. Grize (1922-) worked with Piaget at the Centre from 1958 until 1968, when he launched the Semiological Research Centre at the University of Neuchatel. He then became president of the University of Neuchatel in 1975, serving in this role until 1979. During this time, however, he continued to collaborate with Piaget and the members of his Centre. 292 Piaget notes afterward in Logic and Psychology (1952b, p. 25), translated from three lectures based on the Traite, that this term was proposed by another reviewer in a discussion of where his proposals seemed to lead. As one reviewer notes, it is intended as a new science, located between logic and psychology: "This intermediate science [psycho-logic] would be concerned with the psychological foundation both of the deductive (pre-mathematical) calculus and of mathematics, and would thus bring out the elements common to the two. But it would equally be concerned with the psychological foundations of every other type of inferential reasoning, or rules and procedures of intelligence, and their relations to mathematics and pure non-mathematical deduction as well as to one another. Nor could the complex psychology and logic of the universal instrument of all thought, viz. language, be left out of account" (Isaacs, 1951, p. 188). This reviewer's comments are cited in Piaget's response to Beth as a source of ideas more sympathetic to his aims (Piaget, 1951, p. 244ff). The problem is taken up again in (Piaget, 1970/1971, pp. 11-12). 102 this second edition was published, however, Piaget was no longer groping for answers; he had found them, as a direct result of Beth's criticisms.)
Piaget's next appeal to Godel came a year later, in 1950, and followed the same pattern that had offended Beth in the Traite: mere mentions in a larger history. Once again, however, the references were only to the 1929 dissertation. Although this second review served to update Piaget's previous history of logic, from 1942, there was no immediate impact on his theory. This change would occur over the following decade.
Piaget's response to Beth's criticisms was to invite him to collaborate on a project aligning their perspectives.293 This led Beth to attend a series of symposia at the Centre
International de I'Epistemologie Genetique, held in 1956, 1959, and 1960. It also resulted in a series of writing projects, which then informed a book: Epistemologie
Mathematique et Psychologie, published in 1961 as volume 14 of Piaget's series and translated in 1966 as Mathematical Epistemology and Psychology. Here, Piaget's appeals to Godel follow Beth's. (Beth wrote his section of the book before Piaget wrote his own in response.)295
Beth discusses incompleteness - the result of Godel' s 1931 paper - in great detail: he introduces the proof historically, albeit using more complex and rigorous terms than in the section above, and develops it following Godel's use of self-referential meta-
(Piaget, 1951, p. 244) (Beth & Piaget, 1961/1966, p. 5) (Beth & Piaget, 1961/1966, p. xxi) 103 mathematical statements. He then generalizes the result to all formal systems, showing that even the system brought in to replace an earlier one, proven to be incomplete, is itself incomplete in a different way.297 Beth also cites Godel's first extended philosophical statement, published in 1944, which expanded upon his earlier critique of Russell and introduced in print the notions of "construction" that would be formalized in the
Dialectica interpretation.298 Crucially, he then points to work showing that unprovable truths can become provable - with the system itself "rendered more adequate"299 - simply through the addition of new axioms. (In other words, the source of a contradiction can be accommodated either through the addition of new assimilatory schemes or the generalization of old ones.)300
Around the same time this first section was delivered to Piaget, the Dialectica interpretation was published. (Beth does not cite it.) Whether Piaget read it or not at this time is largely irrelevant, to our purposes, as its effects - and those of Godel's increasing popularity - certainly reached him. There is considerable evidence that one commentary in particular caught his eye.
Part 2 of 3: The Commentary. Jean Ladriere published his response to the then-extant questions regarding the meaning of "incompleteness" in 1960, two years after the
296 (Beth & Piaget, 1961/1966, pp. 54-55, 70, 120-122). For more on this procedure, now known as "Godel numbering," see e.g., (Hofstadter, 1979, pp. 18-19,261-272,438-451; Dawson Jr., 1997, pp. 63-68; Casti & DePauli, 2000, pp. 43-52; Hofstadter, 2007, pp. 131-143). 297 (Beth & Piaget, 1961/1966, p. 69) 298 (Beth & Piaget, 1961/1966, p. 112; citing Godel, 1944/1990) 299 My trans of (Beth & Piaget, 1961/1966, p. 122) 300 (see e.g., Piaget, 1977/2001; Piaget & Henriques, 1978) 104 appearance of Godel's Dialectica interpretation (and in the same journal). In it, he
examines the limits of formalism from the perspective of their philosophical significance.
He starts by explaining Godel's result:
The significance of Godel's theorem is that its proof includes the construction of an undecidable proposition.... This proposition has a rather paradoxical character because... it affirms of itself that it is non-derivable. Its meaning thus corresponds to the following statement: "I am not derivable in the system to which I belong." .. .Godel's theorem therefore implies the following: In all the systems obeying the conditions of the theorem [i.e., they are sufficiently powerful to enable basic arithmetic], there are proposals which... are true and are however not derivable.301
But it is the specific wording of Ladriere's explanation of what this means that is most
important in terms of understanding Piaget's reception of his interpretation.
When one constructs a formal system, one is generally interested in the representational possibilities offered by that system; with the correspondence that can exist between the system and a domain in which one can formulate true or false statements, and for which one has a criterion allowing one to distinguish the true statements from the false statements.... Ideally, for correspondences of this kind to be considered satisfactory, it is necessary that its theorems correspond to true statements and, equivalently, that every stated truth be represented by a theorem of the system.... However, Godel's theorem teaches us that such correspondences are not fully realizable; that there are proposals associated with true statements... which are not theorems, i.e. which are not derivable in the considered system, but which are also not refutable and thus remain undecided.
301 My trans of the following: "La signification du theoreme de Godel tient a ce que sa demonstration comporte la construction effective d'uneproposition indecidable.... Cettepropositionpossede d'ailleurs un caractere assezparadoxalparce que, consider ee selon son sens intuitif elle affirme d'elle-meme qu'elle est non derivable. Elle correspond done a I 'enonce suivant: 'Je ne suis pas derivable dans le systeme auquelj'appartiens.' ...Le theoreme de Godel nous place done devant la situation suivante : Dans tous les systemes obeissant aux conditions du theoreme, ily a des propositions qui, selon leur sens (intuitive), sont des propositions vraies et qui cependant ne sont pas derivables^ (Ladriere, 1960, p. 283). 302 My trans of the following: "Quandon construit un systeme formel, on s 'inter esse en general aux possibilites de representation offertespar ce systeme, en d'autres termes a la correspondance quipeut exister entre le systeme et un certain domaine apropos duquel onpeutformuler des enonces vrais oufaux, et pour lequel on dispose d'un critere permettant de distinguer les enonces vrais des enonces faux.... Idealement, pour qu 'une correspondance de ce genre puisse etrejugee satisfaisante, ilfaudrait que tout 105 Here, we see an early hint of what likely excited Piaget about Waddington's epigenetics:
it provides an evolutionarily-sound means by which "true statements" (adaptive groping)
can be distinguished from the unfit and irrational, as well as a means according to which
"theorems" (behavioral responses) can be described as originating in a formal system.
(Piaget's later research, such as that on correspondence, then serves as an empirical check
on the resulting theory.)303 But it is where Ladriere takes the discussion next that seems
most likely to have caused the shift in Piaget's use of Godel's work: Ladriere alludes to
"recent research" supporting the construction of a "hierarchy" composed of increasingly
complex levels. This was almost certainly an appeal to the Dialectica interpretation.304
There are two ways to avoid the Godelian trap, explains Ladriere, following the
Dialectica interpretation; two ways to function despite incompleteness. The first is to
disabuse oneself of the notion that one fully understands the implications of the
operations used in constructing any single proof. The second, more useful escape is to
posit an open system with indefinite extension:
If this second way is taken, one is brought to envision an infinite, and even transfinite, hierarchy of systems.... On the first level, one can formalize a given domain; then, while grounding oneself on this first level, one can then formalize a larger domain, and so on. One can thus also go as far as one wants, but without
theoreme du system corresponde a un enonce vrai et, reciproquement, que tout enonce vrai soit represents par un theoreme du systeme.... Or ce que le theoreme de Godel nous apprend, c 'est qu'une telle correspondance, en general, n 'est pas realisable, c 'est qu 'il existe des propositions associees a des enonces vrais... qui ne sontpas des theor ernes, c'est-a-dire qui ne sontpas derivables dans le systeme considere, et qui n 'y sont d'ailleurs pas nonplus refutables, qui res tent done non-decidees" (Ladriere, 1960, pp. 283-284). 303 For example, on correspondence (Piaget, 1980c) 304 Although (Ladriere, 1960, p. 287) doesn't reference Godel's Dialectica interpretation, it seems likely - since his own article was also published in Dialectica - that this is the "recent research" to which he referred. 106 ever arriving at an end.
The solution to the reality of incompleteness is therefore the possibility of construction without end. This is what Piaget takes from Ladriere's reading of Godel.
Part 3 of 3: The Second Gbdelian Phase. Piaget first cited the Ladriere commentary explicitly in an article that appeared in 1964, the same year that Waddington gave his influential talk in Geneva (Chapter II). Indeed, while arguing for the use of the limits of formalism as a means to bridge the gap between logic and psychology - to "reintroduce an operatory constructivism which refers implicitly or explicitly... to the subject's activities" (i.e., psycho-logic) - Piaget described it as "great work."307 He expanded on what this meant in an encyclopaedia he edited in response to the impact of the "Godelian crisis"^0 on those fields touched by logic or mathematics. There, he highlighted
Ladriere's suggestion that "formal systems are the abstract products [objectivation] of mental activity"310 and that these exist in a hierarchy of levels. n Piaget also mentioned
305 My trans of the following: "Si V on prendl'autre voie, on est amene a envisager une hierarchie infinie, et meme transfinie, desystemes.... A un premier niveau, on pent formaliser tel domaine; puis, en s 'appuyant sur ce premier niveau, on pent formaliser un domaine plus vaste, et ainsi de suite. On peut aller ainsi aussi loin qu 'on veut, mais sans arriver jamais a un terme" (Ladriere, 1960, p. 299). 306 This has its effects throughout the remainder of Piaget's life. For example, in an interview published in the Journal de Geneve, Piaget says the following: "I think that the intelligence is constructed by a self-regulatory mechanism, hence by equilibration. This process is augmentative: that is to say that there is no return to the former level in cases of perturbation. Rather, a broader and stronger overall level of equilibration is constructed. And I think that this [ultimate] equilibrium is never reached" (my trans of Piaget in Widmer & Piaget, 1977b). 307 Both quotes from (Piaget, 1964/1971, p. 135). A similar point is made, with reference to both Godel and Ladriere, in (Piaget, 1970a, p. 487; in a chapter later reprinted as Piaget, 1970/1973, p. 29). 308 My trans of (Piaget, 1967f, p. 8) 309 Not only was Ladriere invited to contribute a chapter expanding upon his earlier work (Ladriere, 1967), but Piaget also mentions him in three chapters of his own. 310 My trans of (Ladriere, 1960, p. 321; cited by Piaget, 1967b, p. 378). Ladriere in Le Structuralisme, the third of our forgotten works (Chapter V). This quote is provided - retranslated, corrected, and in the proper context - as a capstone statement in the chapter Errata (below). Yet perhaps most telling, in terms of our larger discussion of
Piaget's use of Godel, is that Piaget's response to Beth follows Ladriere's take on the
Dialectica interpretation.
Piaget's attributes the realization of the necessity of hierarchies to Beth,312 but his ultimate use of the idea- in his section of Mathematical Epistemo logy and Psychology - clearly goes beyond Beth's usage. In fact, the difference in their use is quite striking:
Suppose that we have two formal systems 7" and T" and that T" allows us to establish the non-contradiction of 7"; then we can conclude that the resources of T" are greater than those of T\ or that T" is "more powerful" than T'.... Thus Godel's results allow us to "evaluate" the relative strength of the different "grand logics rm
The reason for the difference in use is in their intent. Beth intends to comment on the nature of formal systems, speculating only in conclusion about the possibility of
"thinking machines."314 Piaget is more ambitious. He intends the application of
Godelian hierarchies to understand the development of living minds—collective knowledge and individual thought as the result of "progress," rather than "specific creation" (see Chapter II). In short, for Piaget, Godel provides a formal justification for developmental change that goes beyond the recapitulation of a species' evolutionary history:
311 (Piaget, 1967b, p. 383) 312 (Piaget in Beth & Piaget, 1961/1966, p. 273) 313 (Beth in Beth & Piaget, 1961/1966, p. 59) 314 (Beth & Piaget, 1961/1966, pp. 114-126; see also Grize, 1961/1966) 108 In the perspective of genetic constructivism,.. .the irreducibility of the higher to the lower [T" to T'] not only fits easily into the framework of "reflective abstraction" [see Chapter VI], but also leads directly to the underlying reasons for the construction. The chief difficulty of [the] genetic interpretation consists, in fact, of explaining why the constructions progressively succeed one another and in particular, why they achieve new forms.... Godel's results suggest a first reply...: the construction continues indefinitely because no system is self- sufficient, not as regards any other, but because it lacks sufficient internal coherence to assure its own non-contradiction. Every system must therefore proceed in the direction in which its own consistency can be reinforced. This would be the psychological lesson to be derived from the irreducibility of the higher to the lower, and we hope to show that the new operations which enter into reflective abstraction... tend not only to enlarge the initial structure or to generalize it, but do so in the very direction which will reinforce non contradiction.315
In other words, in Piaget's interpretation, it follows from Godel's result that development is the means by which organisms respond to perturbations that prove the incompleteness of their genomic axioms. To ensure survival in the next generation, the inheritance of past adaptive solutions is necessary but not sufficient; survival requires the construction of levels intermediate between the genome and the adult body.
The most obvious moment of separation from Beth's take on traditional logic, and toward the new theory, is found in a footnote to Piaget's section of Mathematical
Epistemology and Psychology. Here, Piaget suggests that the hierarchical levels can themselves be considered the equivalents of axiomatic systems, with the abstraction from one to another corresponding to a valid (albeit upward) deduction:
Without needing to discuss the mathematical concept of construction, which we are not competent to do, we confine ourselves to maintaining that even a classical deduction corresponding to a literal interpretation of the axioms (and thus foreign
315 (Piaget in Beth & Piaget, 1961/1966, pp. 274-275; see also Piaget, 1974/1980b; Piaget & Henriques, 1978) 109 to construction in the limiting mathematical sense) can be interpreted epistemologically.... In the constructivist interpretation (in the genetic sense), the axioms themselves are constructed, in so far as they are the result of a reflective abstraction starting from operational co-ordinations, and the whole deduction is thus constructive, whether it preserves its classical aspect or is subordinated to the idea of construction in the narrow [mathematical] sense of the term.316
In this, Piaget differs dramatically from Beth: he reverses the direction of logical
"necessity." Instead of deducing downward, from valid premises to a conclusion that follows from them necessarily (as in syllogistic reasoning), Piaget uses abstraction from incomplete axioms to reflect upward to the next more complete level in the formal hierarchy (see also Chapter VI). Despite this divergence, however, Beth's influence continues into Piaget's later writings: in his discussion of Godel in Sagesse et illusions de philosophie, for example, Piaget adopts a variation on Beth's (and Grize's) speculations regarding the possibility of "thinking" machines:
A machine sufficiently complex to simulate an intellectual task, and rigorously determined as far as its mechanism and its interactions with the external world, cannot compute at a time t what its state will be at a time t + 1; it can only do this to the extent to which its determination, incomplete in itself, is subordinated to a machine of a higher order, but which is then no longer completely self- 117
determined; and so on.
But, rather than undermining the newly emerging theory, this realization simply makes the point that one's location on the spiral of life can only be understood retrospectively: there is no "progress toward," only "progress from" (see Chapter II: "vection").
The impossibility of "progress toward" is made more explicit in Piaget's next appeal to Godel, in 1967; in Biology and Knowledge, he builds on the inability of one to
(Piaget in Beth & Piaget, 1961/1966, p. 295ff) (Piaget, 1965/1971, p. 41) 110 "know" t + 1, but from an evolutionary perspective. Here, perturbation through the imposition of selection pressures (i.e., the natural disproof of inherited axioms) is presented in the language of epigenetics. Evolutionary change is not caused not by mutation, on this account, but by the "transmission" of "information" - the proof incompleteness - through each level of plasticity: feedback, from one level to another, until the disequilibration is resolved.318 (Mutation, on this view, is the means by which disequilibration is addressed at the level of the genome; but it is not the cause of that change.) For example: behavioral changes in response to a found-challenge leads to the colonization of new environments in which the next generation develops, resulting in the abstraction of a new interbreeding group from the original; this then also abstracts a new set of axioms, which are themselves complete relative to the contexts in which they have been tested (for more, see Chapters II & IV). Natural selection does the rest.
In his final appeals to Godel, Piaget turns the "thinking machine" analogy back on psychology, and then generalizes (what he at this point considers) the Godelian- constructivist insight to explain regressive tendencies in scientific explanation:
In all fields of knowledge the situation arises periodically where the concepts in use divide into two levels, of which one is more complex, hence 'higher', and there is then a tendency to reduce the higher to the lower or a contrary tendency as a reaction against the excesses of the former.... In the biological field [for example] there have been attempts to reduce living processes to known physico- chemical phenomena, attempts that failed to note the possibility of change in a discipline which is continually being modified; and the reaction was an anti- reductionist vitalism, whose sole merit was the entirely negative one of denouncing the illusions engendered by such premature reductions. In
(Piaget, 1967/1971, pp. 295ff-296ff) (Piaget, 1970b, p. 280ff) 111 psychology [similarly] there has been the attempt to 'reduce' everything to the stimulus-response scheme, to associations, etc....320
He continues, foreshadowing his new take on dialectics that emerges in the new theory period (see Chapter VI):
In cases where it has been possible to resolve the problem, the end result has been a situation surprisingly in agreement with constructivist hypotheses: between two structures of different levels there can be no one-way reduction, but rather there is reciprocal assimilation such that the higher can be derived from the lower by means of transformations, while the higher enriches the lower by integrating it.... Clearly, then, these reciprocal assimilations proceed in the manner of reflective abstractions, which, ensuring as they do the passage between two hierarchical levels, produce new reorganizations through this very fact. In short, the construction of new structures seems to characterize a general process which is constitutive in character and not reducible to a method for achieving a predetermined end.321
And indeed, this perspective is manifest in the characteristic presentation of his histories
(see Chapter II). In the later material of the new theory, however, it is all made implicit.
Rather than continuing to cite Godel after 1970, Piaget cites subsequent scholars who built on his work.322 An exception is made in 1978, in Piaget's summary of the results presented in Recherches sur la Generalisation, when Godel is reintroduced to ground a deeper discussion of operational levels: "operations on operations," where axiomatic systems can be seen as being nested one within another.323 Yet here, again, Piaget's
320 (Piaget, 1970/1972, p. 92) 321 (Piaget, 1970/1972, p. 93) 322 e.g., the work of Gerhard Gentzen, followed by that of Alan Anderson and Nuel Belnap (in Piaget & Garcia, 1987/1991, pp. 146-147). 323 (Piaget & Henriques, 1978, p. 238) also mentions Gentzen. 112 language follows that introduced by Ladriere in his commentary on the Dialectica
324 interpretation.
Recapitulation
There is a clear discontinuity in the style of Piaget's appeals to Godel. After the popularization of the Dialectica interpretation, Piaget shifts from mentioning his work as a footnote in the history of mathematics and logic to incorporating its arguments into his theory. In other words, after Dialectica, stage theory becomes a sequence of nested levels in a hierarchy that extends beyond the individual and into the social realm. It also provides a justification for Piaget's "euphoria" in returning to biology: incompleteness is proved through the disequilibrium caused by selection pressures (Chapter II).
Reception and Errata
The importance of Piaget's appeals of Godel has been missed by virtually every English- language interpreter of his work. The effect of this omission has been to cause a basic misunderstanding of part of the framework behind the new theory as it emerged, before receding into the background. And this, in turn, has had a pernicious effect on the
324 (see esp. Ladriere, 1960, pp. 294-295) 325 A near exception is the two-volume examination of the period of Piaget's new theory by Rita Vuyk. She notes Piaget's use of Godel but - despite mentioning its two different applications (Vuyk, 1981, pp. 34-35,47) - misses the effects of Piaget's reading of Ladriere's commentary on the Dialectica interpretation. Ducret's (2000) summary of the empirical works from the new period suffers from the same problem, although compounded in that case by his choice not to examine the underlying theory. On the other hand, by failing to "do the history" (as we have attempted here), Seltman and Seltman's critique of Piaget's logic entirely missed the significance of his appeals to Godel (see esp. Seltman & Seltman, 1985, pp. 273,281; cf. R. Kitchener, 1991). 113 resulting English editions of his books. For example: in the translation of Piaget's Le
Structuralisme (examined in more detail in Chapter V), the English text replaces the
French word for "stage" (etage) with the English "story."326 Taken as part of an apparently larger discussion of cultural structures, and making explicit the translator's almost-too-clever pun on "story" as meaning both "level" and "narrative," this interpretation seems to make sense. Indeed, the development of shared narratives could certainly be understood as belonging to an historical lineage, in which roles recur and contemporary actors find themselves in positions previously occupied by their ancestors. But in the stricter sense of construction meant by Godel, Piaget's original text has a much stronger meaning not served by the English translation; he is not redoing
Levi-Strauss (see Chapters V & VI). He reaches further, following the Dialectica interpretation, as we see in this extended re-translation of the relevant passage:
The first point of interest of such observations is that they introduce, into structures, the notion of greater or lesser strength and weakness (relative to the domains in which they are comparable). The hierarchy thus introduced therefore suggests the idea of construction, just as in biology the hierarchy of characters suggested evolution: indeed, it seems reasonable that a weak structure uses basic elements and that more powerful forces correspond to instruments whose development is more complex.328
He continues, updating his earlier conception of the structure of knowledge:
326 (Piaget, 1968/1971, p. 34) 327 Indeed, this is how the translation is used by (Moger, 1983, p. 26). Yet this is in this sense of "finding the same thing at another level" provided by (Hofstadter, 1979), not Piaget. 328 My trans of the following: "Le premier interet de telles constatations est qu'elles introduisent la notion de la plus out moins grande force oufaiblesse des structures, en un domaine delimite ou elles sont comparables. La hierarchie ainsi introduite suggere alors aussitot une idee de construction, de meme qu 'en biologie la hierarchie des caracteres a suggere I 'evolution : il semble, en effet, raisonnable qu 'une structure faible utilise des moyens plus elementaires et qu 'a la force croissante correspondent des instruments dont I'elaboration est plus complexe" (Piaget, 1968a, p. 30). 114 The second fundamental lesson of Godel's discoveries is... that to complete a theory in the direction of demonstrating its non-contradiction, it is no longer sufficient to analyze its presuppositions. It has also become necessary to construct its replacement. One could therefore consider a lineage of theories as forming a beautiful pyramid resting upon a foundation of self-sufficiency; the lowest stage, formed of the simplest instruments, would be the most solid. But if this simplicity were recognized as a sign of weakness, and reinforcing a stage required the construction of its replacement, then the overall consistency of the pyramid as a whole is in reality suspended from its peak. And, with this height itself unfinished (and having to be unendingly high), the image of the pyramid must then be reversed and - more precisely - replaced by that of an upwardly broadening spiral.329
Piaget then finishes, abridging (and ultimately citing) Ladriere:
The idea of the structure as system-of-transformations thus becomes interdependent with a constructivism of continuous formation. However, despite its general significance, the reason for this is simple: one can draw from Godel's results important considerations regarding the limits of formalization. For example, one could show the existence of levels - in addition to the formal levels - that are distinct from semi-formal and semi-intuitive knowledge, or which could be approached to differing degrees according to their patience (so to speak) in awaiting the arrival of their turn at formalization. The frontiers are thus mobile, or "vicariant," and are not closed once and for all like a wall marking the limits of an empire. J. Ladriere proposed the clever interpretation: "we cannot survey, at
329 My trans of the following: "ie second enseignement fondamental des decouvertes de Goedel est... pour achever urte theorie dans le sens de la demonstration de sa non-contradiction, il ne suffitplus d'analyser ses presuppositions mais il devient necessaire de construire la suivante ! On pouvait jusque-ld considerer les theories comme formant une belle pyramide reposant sur une base se suffisant a elle-meme, I'etage inferieur etant leplus solide [p. 31] puisque forme pas les instruments les plus simples. Mais si la simplicite devient signe defaiblesse et que pour consolider un etage il faille construire le suivant, la consistance de lapyramide est en realite suspendue a son sommet et a un sommetpar lui-meme inacheve et devant etre eleve sans cesse: I'image de lapyramide demande alors a etre renversee et plus precisement remplaceepar celle d'une spirale a tours deplus en plus larges enfonction de la montee" (Piaget, 1968a, pp. 30-31; this is anticipated in Beth & Piaget, 1961/1966, p. 273; and Piaget, 1967e, p. 117, 1967d, p. 1167; see also Piaget, 1970b, p. 270, 1970/1972, p. 67). This reconnects with Piaget's "circle of sciences" concept, introduced in his early philosophical novel (Piaget, 1918) and later formalized in (Piaget, 1950, 1967d). In this version, however, epistemic change occurs in a spiral: proofs of incompleteness in one area leads to reorganization, with implications for neighboring ideas that relied on the earlier idea. The notion is developed in greater detail in Main Trends in Interdisciplinary Research, which can - as he explains (Piaget, 1970/1973, p. 7) - be understood as an extension of'Structuralism (see Chapter V). 115 one glance, all the possible operations of thought...."
Although the original translation includes hints of what is made clear here, it loses the
parallels to biological theory (e.g., by switching vicariantes for "vicarious" rather than
"vicariant"—the technical term for that which divides a group of organisms and, through
the isolation of a subpopulation, thereby leads to the emergence of a new species)331 and
at the same time pushes the reader toward an overly narrow anthropological
interpretation. By returning Godel to Piaget's developing theory, however, we return
specificity to his otherwise apparently vague biological addition to the old theory rhetoric
and can clearly see it as a new take on his old debate with Roszkowski: a logico-
mathematical group is like a species that exists in an abstract world defined by a level of
reality (i.e., it is a consistent whole inside of which productive operations may take
place), while the full hierarchy of levels is like a nested ecology of innumerable
interacting groups. Species at one level serve to ensure the life possibilities of those at
another, while interactions across the levels serve to complete the system as a whole.332
My trans of the following: "En fait, I'idee de la structure comme systeme de transformations devient ainsi solidaire d'un constructivisme de la formation continue. Or, la raison de cet etat de choses apparait en definitive assez simple et deportee assez generate. On a tire des resultats de Goedel des considerations importantes sur les limites de laformalisation etl'on apu montrer I 'existence, en plus des pollers formels, depaliers distincts de connaissances semi-formelles et semi-intuitives ou approchees a des degres divers qui attendent, pour ainsi dire, la venue de leur tour de formalisation. Les frontieres de la formalisation sont done mobiles ou vicariantes, et non pas fermees unefoispour toutes comme une muraille mar quant les limites d'un empire. J. Ladriere a propose I'interpretation ingenieuse selon laquelle 'nous nepouvons pas survoler d'un sel coup toutes les operations possibles de lapensee... "'(Pmget, 1968a, p. 31; citing Ladriere, 1960, p. 321). 331 This is the term used in (Piaget, 1970/1972, p. 67). 332 In future research, Piaget's use of Godel and Waddington should be compared with Bronfenbrenner's (1979, 1942-2001/2005) conception of development as a system embedded within a multi-level "human ecology." 116 The goal of development, then, becomes to travel through the worlds defined by these levels and emerge as a well-adjusted adult able to address challenges similarly arising.
Prospective Conclusion
In returning Godel to Piaget's emerging new theory, we can now profitably examine those other advances made following Piaget's return to biology: just like a species can be considered a logico-mathematical group, so can a "species of mind." (Indeed, as was shown the year of Piaget's death, intellectual operations can be regarded as the implementation of formal axioms. )333 By the same token, societies of mind can be understood to complete the gaps in cognition or rationality experienced by any one member. These will be examined in the next two chapters. Yet, to put these in the context developed here, Piaget offered an explanation in the language of our newly retranslated capstone statement:
.. .how can we explain the vicariant boundaries of formalization? The suspected analogy with genetic construction suggests a solution: that the concepts of form and content are essentially relative and that a form or a formal structure is unable to achieve a complete autonomy. This is clear in the developmental field: the sensori-motor structures are forms in relation to the simple movements they co ordinate, but content in relation to the interiorized and conceptualized actions of the subsequent level; 'concrete' operations are forms in relation to these latter actions, but content with respect to the already formal operations of eleven to fifteen years; and these again are only content in relation to the operations applying to them at later levels.334
In other words, how you think and what you think are two sides of the same coin.
(Balzer, 1980) (Piaget, 1970/1972, pp. 67-68). 117 CHAPTER IV
THE DEVELOPMENT OF THINGS TO THINK WITH335
When Piaget received the "distinguished scientist award" from the American
Psychological Association in 1969 - after he had published the forgotten works but before they had been translated into English - he was described as "an epistemologist who made a science of philosophy."336 But this is not quite right, as we now see from his return to biology (Chapter II) and his appeals to Kurt Godel (Chapter III).337 Instead, he might be more appropriately understood as a "meta-epistemologist" or an empirically- informed "philosopher of knowledge,"338 where "knowledge" is defined generally as an extension of the natural adaptive processes of organisms and "empirically-informed philosophy" is defined at least in part by the attempt to interpret and synthesize sets of experimentally derived "facts" (functions) into coherent discipline-spanning narratives
(structures). In short: Piaget's emerging theoretical approach - a constructive take on the genesis of knowledge, with mechanisms operating at both the individual and the collective levels - is a biologically-informed framework for describing how individuals come to act (a function of their developing explanations of why things are the way they are), given the constraints provided by the contexts in which they find themselves (viz. an epistemic landscape).
335 This introduction is based on material in (Burman, 2007b) 336 ("Distinguished Scientific Contribution Awards: 1969: Citation for Jean Piaget," 1970) 337 Also (Beilin, 1999, pp. 119-120) 338 First quote from (R. F. Kitchener, 1986, p. 143), second from (Youniss, 1980, p. xii). 339 (Piaget, 1965/1971, 1970/1973) 118 While this description does not diverge dramatically from what one might find in an introductory textbook, it does lead to a simple gloss of Piaget's core assumptions that would:
1. Every thought is constructed from material (physical) foundations: they are
abstractions from the effects of perturbations imposed by objects in the
environment;
2. These constructions are founded upon earlier inherited positions (e.g., reflexes),
each of which are modified through experiences garnered during encounters with
the world (in a process called "assimilation") and organized into coherent wholes
(in a process called "accommodation") that then become new positions;
a. such constructions (which, in Piaget's formulation, are called "knowledge
structures") are not true reflections of the world, but rather represent the
best possible functional approximation at that moment given the history
involved in reaching that position (which Piaget calls an "equilibrated"
state);
b. the constructed logic organizing such structures is different from their
content, such that the meaning of content may change dramatically when
the logic itself is made more coherent during the accommodation of new
experiences to the whole (in a process Piaget calls "re-equilibration"); and
3. Such structures are modified following experiences of discord (which Piaget
called "disequilibration" and "contradiction," but which we have called -
119 following Baldwin and Waddington - the felt-effects of "perturbations" or
"selection pressures").340
What this highlights is that, when knowledge has been constructed and is therefore believed to be true, divergences from this "truth" will be felt as errors. (This is the anomalous "feeling of what it is like" to prove of the incompleteness of a previously adequate explanation.) The question - to be examined here - is how this occurs in a developing mind, where an "explanation" is isomorphic with the biological structure that describes it. This leads to a series of experiments, exemplary of Piaget's empirical approach, reported in the second of the forgotten works: Memory and Intelligence. It is to that which we will turn in this Chapter, after showing how Piaget sets up the transition in Biology and Knowledge.
Functions and Structures in Biology and Knowledge
Part Four of Biology and Knowledge is critical to enabling the transition to the "new theory." It solidifies the shift away from Piaget's 30-year-long "structural period"341 toward a blended structural-functionalism. And it starts by defining terms (with a view to applying methods 1 and 2 from Chapter II). This introduction, here part 1 of 3, is
followed by examinations of "the organization function" (part 2 of 3) and its use in understanding cognition (part 3).
340 An earlier version of this three-point gloss was sent to the Jean Piaget Society listserv in early April 2006, where it was generally well-received. Another was published in Theory & Psychology (Burman, 2007b; cf. Beilin, 1985, pp. 12-13). 341 (Beilin, 1992a; Burman, 2008b) 120 Part 1 of 3: Functional and structural isomorphisms between Organism and Knower. A structure, according to Piaget, is an organized whole: parts and relations; elements and connections. These can be considered independently—synchronically as "parts" and
"wholes" or diachronically as "lineages" and "systems." They can also be thought of categorically in terms of logical "groupings," such that two similar structures can be considered "homologous." Then, in cases where there is an exact correspondence (e.g., the bones of hands and paws and fins), homologues can be more strongly labelled
"isomorphic." In this way, they can be understood as reflections of a higher level abstraction, or ideal type, and treated as "wholes" unto themselves (i.e., the set of all carpals, tarsals, etc.).343 The challenge, as Piaget noted in outlining method 2 (in Chapter
II), comes in distinguishing "partial isomorphisms" from similar wholes with "divergent substructures."
To be isomorphic, and thus a reflection of the same ideal abstraction, two homologues must be relatable through both translation and lineage (i.e., they must be relatable both synchronically and diachronically). Divergences may result from alterations at lower levels of abstraction, but these can be analyzed by subdividing
342 Piaget defines "structure" (Piaget, 1967/1971, p. 139), but not "element." Yet for the earlier form of genetic epistemology - for Baldwin - this refers to the most basic structures of experience: "Any content of consciousness in which introspection fails to detect internal complexity" (Baldwin & Stout in Baldwin, 1901, p. 313). For Piaget, who uses a "clinical" method to assess introspective claims and can be understood to build on Baldwin's work, this comes also to incorporate a formal aspect: "the simplest idea which enters into a conception or system of conceptions is called an element of that conception or system" (Stetson in Baldwin, 1901, p. 313). This formal version then gains its greatest significance in "new theory" discussions of the role of exploratory behavior in constructive growth and, just prior to this, of the implications of Kurt GodePs incompleteness theorems for psychology and the philosophy of science (see Chapter III). 343 The connection from here to "stage theory" can be made with reference to Piaget's focus on the "epistemic subject" (the average knower in general) rather than individual differences. 121 "wholes" into their constituent "parts" at the relevant level. For example: while the
stomach is commonly understood to be a structure unto itself, it can also be conceived as a "substructure" when considered relative to the primitive digestive tract. In taking this perspective (i.e., omitting the oesophagus and gut), one is only partially isomorphic with the other.344 (The result is that any generalizations made from findings about the digestive tract in general cannot necessarily be translated to apply to the stomach in particular.) Thus, although translating up from part to whole can be revealing, translations down from whole to part are often misleading.
More generally, the activities of isomorphic structures are their "function."
(Similarly, the meaningful elements of a function are what its structures are doing.)
Divergences - changes in a part relative to the whole - can therefore be disequilibrating.
As a result, in addition to the upward part-whole relationship, there is also a downward whole-part relationship: an auto-regulatory "organization function," such that meaningful interactions among elements in the system tend to preserve the functional quality of the total structure to which they belong. But so long as the production of this "meaning"
(function) continues, there is no pressure to preserve specific involvement from particular sub-structures: if substructure A2 replaces A] following a disequilibration - without at the same time affecting the quality of the total function - then we can speak of another kind of relationship: "correspondence."
(Piaget, 1967/1971, pp. 140-141) 122 At higher levels, the labelling of functions becomes much more abstract: to speak
of "memory" in one setting is to imply a simple conservation, while in another it may
suggest a cause for a change in behaviour.345 It is in this connection that Piaget then provides a programmatic statement for his "new theory" works:
The lines along which our research will proceed are thus clearly laid out. Where function is concerned, it will be a question, in each sector, or [sic] deciding which functions are common to both organic and cognitive mechanisms, and what the specific functions and specializations are that belong to the latter. After which, and keeping within such a functional framework as alone [sic] is likely to bring out the significance of the structures under comparison, we shall have to undertake the study of structural correspondence....346
In other words, Piaget makes it clear that he is returning to his earlier functionalism while
at the same time adopting a structuralist framework. Indeed, the first studies using this approach examined the "organization function" provided by memory (reviewed below).
Part 2 of 3: Organization Functions. In discussing the "organization function," Piaget notes that we run the risk of reducing the bottom-up emergence of a top-down auto- regulatory maintenance principle ("meaning") into the same "vital essence" once thought to invigorate "life."347 To prevent this, he suggests - while at the same time appealing to the methods outlined in Chapter II348 - that biological and epistemological "order" can be described in six ways:
(Piaget, 1967/1971, pp. 143,145; see also Chapter IV) 346' ,(Piaget , 1967/1971, pp. 206/145-146) 347 (Piaget, 1967/1971, p. 148) 3481 PiagePiaget trefer referss onlonlyy t oto th thee firsfirst t twotwo, ,whic whi h he calls methods 2 and 3 (Piaget, 1967/1971, p. 138). In simplifying their presentation, as noted in Chapter II, the total number of methods was reduced by one. 123 1. As continuity and conservation of function, despite changes in the interaction of
many structural parts. The structural parts themselves can also change, Ai ->A2,
so long as their functions are reconstructed in the outcome. In other words,
memory in this conception becomes in part a conservation of form rather than of
content: f(Aj) =f(A2). And indeed the same could be said of consciousness: only
through the constructed categories of experience are the effects of external stimuli
reflected meaningfully in the mind. In other words, the meaning of concepts is
retained fully only within the same logic as that which orders the categories of
experience: "there is no cognitive impression without the intervention of some
organizing functioning, conserved from previous situations, which can be traced
back to innate reactions."349
2. As a reflection of the forms of organization taken on by these conservations. But
of course (recalling Piaget's appeals to Godel) we recognize that such
reconstructions are "incomplete" relative to all possible worlds; that there will be
truths (causes of perturbations) that cannot be proved from within the system
(assimilated [cf. prop. 1]). As a result, the effects of external stimuli are only ever
approximated in the responses given by the functions of internal structures. This
then leads to questions regarding the degree of "fit" between internal form and
external content.
(Piaget, 1967/1971, p. 150) (Piaget, 1967/1971, p. 152) 124 3. As a reflection of the relationships existing between parts, where the existence of
the circular reaction enables the regulation of similar flows (homeorhesis). Citing
cybernetic interpretations with approval, Piaget connects this idea with
Bertalanffy's notion of "open systems" (cf. prop. 2). In this sense, therefore, all
self-maintaining hierarchical systems (i.e., systems having groupings of
substructures at various levels of organization, which collectively contribute to
the overall functioning of the total structure) include implicit within their
definition a context of inputs and outputs.
4. As a reflection of the hierarchical levels themselves. Again relying on the notion
of species classification, Piaget describes the construction of hierarchical levels in
a way that is consistent with his earlier approach to the construction of categories.
In this way, categories are artificially-derived explanatory groupings: a group of
similar organisms (A], A2, A3) can be classified as a single species (A), while two
similar groupings (A and not-A) can belong to the same "genus" (B), various
collections of which can then be grouped again as a "family" (C), etc.352 The
resulting familial resemblances then diverge down the line only insofar as there
has been a progressive differentiation of characteristics through the lineage and
across levels.353 In other words, inheritance is understood to be "pure" only to the
degree that characteristics have been regulated given the extant contexts (cf. prop.
351 (Piaget, 1967/1971, pp. 155-156) 352 "Groupements" (e.g., Piaget, 1942, pp. 37ff, 39-42,278-293) and "emboitements" (e.g., Piaget, 1942, pp. 47-52) 353 (Piaget, 1967/1971, p. 160) 125 3). The conservation of function despite change (prop. 1) then implies a degree of
responsiveness to this context, which can also in turn be characterized by
levels.354 In other words, the reality of an individual (Aj) can be understood to
exist at a different level than that of the species (A) to which it belongs, although
its possibilities are also constrained by that relation. (Similarly, the "reality" of
the component parts of A] can also be understood to follow levels.)
5. As a reflection of the real organizing structures. In the case of classificatory
systematics, as in the above example, the act of creating hierarchical levels by
grouping individuals into explicit categories (species, genus, family, etc.) goes
beyond their physical existence as material objects. The act - really, a thought
enacted (later to become an explanation institutionalized) - produces a structure
that can in turn be used as an epistemic regulator (cf. prop. 1). This then results in
the conservation of the label, rather than the objects it describes.355 On the
physical side, "behavioural barriers" to species propagation have similar effects.
(For example: two biologically compatible species become separated following
the emergence of incompatible mating practices.) Piaget refers to this later as
"vicariance.'
6. As a reflection of the shared traits underlying these organizing structures. In
distinguishing this from proposition 4, Piaget relies on the notion of
354 (Piaget, 1967/1971, pp. 162-163) 355 This was recently demonstrated by Sapp (2005) in his discussion of the classification of single- celled organisms as either prokaryotes or eukaryotes: the act of organization regulated the thought of an entire generation, such that "prokaryotes" and "eukaryotes" became reified as objects for consideration. A similar argument has been made about the reification of "race" (Weizmann, 2004). 126 correspondence in comparing structured classes: categories can be imposed top-
down, as an approximative label (cf. prop. 5), or they can be constructed bottom-
up. In the former, there is nothing necessary about the result (the whole is less
than the sum of its parts). Yet in the latter, the result emerges from the
interactions between the parts as a necessary consequence of their interaction. To
illustrate his point, he then combines the species definition (prop. 4) with the
realization of the necessity of development (implied by Godel) in an epigenetic
landscape (Waddington) to point out that species are in fact "multiplicative"
structures: each group of organisms, considered diachronically as a population of
changing individual wholes, has a reality that exists at many levels. This reality is
both reflective of, and at the same time separate from, their labelling. Contrary to
proposition 5, therefore, there is no species "type." Rather, Piaget points out that
there is a structure (DNA) that is translated (via RNA) into a variety of other
structures (epigenotype), which are then subject to still further interactions as the
many levels of the total structure (organism) develops.
In summarizing these six propositions, Piaget implies that it is the sixth that is most powerful: its transformations follow a pattern that can be examined using the five previous propositions and apply equally well to knowledge as to biology,357 except that their application in construction enables the attribution of "necessity" to the resulting
356 (Piaget, 1967/1971, p. 168) 357 (Piaget, 1967/1971, pp. 165-166). This observation returns in Structuralism, when Piaget accuses Foucault of failing to account for the evolution of structures (see Chapter V; also Burman, 2007b, for commentary). 127 categories. As a result, the quality of variations in substructure is not contingent relative to overall context; so long as function is maintained at each structural level (i.e., so long as each level is complete relative to the extant selection pressures), the necessities implied by the history of their construction are transmitted upward to the level of the whole being.359
Piaget's leap from this sixth proposition to "adaptation," and by extension from there to "intelligence," has only recently been supported empirically: when the variation in structures is constrained through different functional levels, even random changes in their constituent elements are likely to lead to productive variation (rather than death, as thought under the neo-Darwinian paradigm).360 But, because organisms are open to inputs from the environment, Piaget also notes that we must distinguish between
"adaptation" as a state (adapted) and as a process (adapting).361
In unpacking the notion of adaptation, Piaget equates it - via auto-regulation - with his old notion of equilibration and returns to his well-known constructive processes: assimilation and accommodation, borrowed from Baldwin's "circular reaction." Whereas
358 (Piaget, 1967/1971, p. 169) 359 Piaget's later "phenocopy" model of change through epigenetic interaction is basically this in reverse: if a disequilibrating stimulus can be addressed at a high level, then it will have little to no effect on lower levels (for details, see Piaget, 1974/1980a, 1975/1995). 360 This is the confirmed lesson of contemporary evolutionary-developmental biology, known colloquially as "evo-devo" (Robert, 2004; discussed most popularly in Carroll, 2005). It has begun to be applied to psychology, as a competitor to "pure" evolutionary psychology (see e.g., Burman, 2006; Robert, 2008). A similar proposal has also recently emerged in developmental psychology: "the levels of consciousness model" (Zelazo, 2004; see footnotes in Burman, 2008b, for commentary). Following Piaget's indicated direction, discussed in Chapter V, this has also since been expanded into the social realm (W. A. Cunningham, Zelazo, Packer, & Van Bavel, 2007). Yet this discussion remains psychological; although some efforts have been made toward the "new theory" (e.g., Zelazo & Lourenco, 2003; see footnotes in Burman, 2008b, for commentary), a great deal remains to be accomplished in future research. 361 (Piaget, 1967/1971, p. 171) 128 the common informal definition relies on metaphors (e.g., the digestion of cabbage by a rabbit),362 here he presents a more formal definition building on the notion of functional structures. Given the interactions, A ', by rabbit A leads to the normal life activities of that rabbit, such as the eating of cabbage B that leads to the absorbtion of vitamins C etc.:
(A * A') -» (B * B') -* (C * C) -> ... ^ (Z * Z') ^ (A * A')
These are the nested axioms of the rabbit's life: the quality of one assumes the functioning of the others. These become obvious as levels when a temporary change in interaction A' to A " - as a result of the farmer's switching cabbage for lettuce - leads to a change in activity B to B2, but extends no further through the organism's system of transformations and has no lasting implications for its structure as a whole:
{A * A ") -» (B2 * B') -» (C * C) -> ... -> (Z * Z') -> (A * ^')
This is an assimilation (of lettuce), followed by structural accommodations (change in the availability of vitamins used in the synthesis of proteins leading to life activities), but resulting in no overall functional change. The overall total structure of the rabbit can thus be said to be adapted to the context - it is equilibrated - but only as a result of the
36 The problem is parsed here using Piaget's favourite example, which is not in the volume discussed here but was instead articulated in an interview in 1969: "A rabbit that eats a cabbage doesn't become a cabbage; it's the cabbage that becomes rabbit—that's assimilation. It's the same thing at the psychological level. Whatever the stimulus is, it is integrated with internal structures.... There is no assimilation without accommodation because the scheme of assimilation is general, and as soon as it's applied to a particular situation, it must be modified according to the particular circumstances of the situation. This is true at every level.... [T]here can be no assimilation without accommodation, because the assimilatory scheme is general and must always be accommodated to the particular situation" (published in Bringuier, 1977/1980, pp. 42-43). 129 adapting of its lower level axiomatic systems to accommodate the change in diet. 363
Adaptation, then, is the process of dynamic change resulting from the pairing of assimilation and accommodation. This pairing, in turn, is a consequence of the interaction between structure and function across levels of organization.
genotypes of generation « THE EXPLOITIVE SYSTEM
THE BPIGENETIC SYSTEM
\ THE GENETIC SYSTEM
genotypes of generation »+ I
Figure 10. Waddington's illustration of the levels of action in selection, 364
363 In the same interview, given in 1969, Piaget says of this: "An equilibrated system is a system in which all the errors have been corrected, the excesses compensated for" (published in Bringuier, 1977/1980, p. 44). 364 (Waddington, 1959/1975, p. 57; reprinted in Waddington, 1961/1975, p. 274) 130 Piaget's mature mechanism for naturalistic change (the phenocopy) is not named here, or anywhere else in Biology and Knowledge, but it is clear that the following discussion forms the basis for that later proposal: that behaviour (choice) - by actively engaging the environment and assimilating its structures, disequilibrating levels as a result, introduces variations to be selected-for naturally - can be seen as the motor of evolutionary change.365 Importantly, however, Piaget's later argument (regarding "the phenocopy") seems to assume the reader's familiarity with this earlier notion of levels in functional structures.
In a system of nested levels, such as the sort illustrated by Waddington (above), high-level phenotypic changes can be understood as a "response" to the interaction between organism and environment. This "response" can then come to be inherited by its altering of selection pressures, resulting in low-level genotypic alterations. In this conception, the cause of change is shifted from random processes (neo-Darwinian
365 (Piaget, 1974/1980a, 1975/1995, 1976/1979) 366 It seems clear that the loss of this multi-level conceptualization, which Piaget attributes to the influence of Jerome Bruner's dismissal of structures (Piaget, 1968/1971, p. 72), led to several of the misunderstandings we now see in the literature. For example, Howard Gardner's theory of "multiple intelligences" misinterprets Piaget's "logico-mathematical structure" as "logical and mathematical content." This shift in interpretation, from functional organizing structure to content within a domain, then leads to his positing of multiple domains for intelligent action: linguistic, musical, logical-mathematical, spatial, bodily-kinaesthetic, and personal intelligences (Gardner, 1983/1993; building on Gardner, 1972). In this interpretation, the fundamental nature of domain-contents limits a subject's constructive possibilities: learning only occurs within domains that exist externally, rather than being constructed internally by an active subject. This reverses the necessity of development: for Gardner, the quality of development is a function of external structure constrained by innate possibility. For Piaget, in contrast, development is a function of change in internal structures building up from the possibilities afforded by innate necessities (e.g., instruments and reflexes). 131 mutation) to active exploration-producing-disequilibration (updated Baldwin Effect).367
But crucially, given the errata noted at the end of Chapter II, Piaget adds the following:
This is by no means the equivalent... of postulating the heredity of acquired characteristics in the Lamarckian sense of the term. It is simply a matter of affirming the fact that no exogenous variation is possible in a general conservation of structure that varies on this point—in other words, without some assimilation of the elements involved, or of the effects produced by them, into the structure undergoing the variation.
This is important for where he takes the discussion next: a justification for behavioural epigenetics and the beginnings of his move toward an epigenetic epistemology.369
In making a shift from an epigenetics of physicochemical change to one of altering behavioural "schemes,"370 and thereby going beyond what Waddington had intended, Piaget is suggesting that the form of their explanations is isomorphic. He notes, for example, that both follow the same circular pattern. He also notes that the explanatory metaphors of ingestion and digestion (assimilation and accommodation) apply to both: just as a snail needs calcium to make its shell, so does a sparrow need straw to build its nest.371 He clarifies: "in both cases there is an assimilation of the environment into a form constructed by the organism."372 And indeed, it is this form that is accommodated when alterations are made in assimilation.
367 (Piaget, 1967/1971, pp. 175-176) 368 (Piaget, 1967/1971, p. 173) 369 This is also important for understanding the sequel that expands on this section (Piaget, 1974/1980a). 370 This is erroneously translated as "schemata" in the English version (Piaget, 1967/1971, p. 177), while the original has "schemes" (Piaget, 1967a, p. 250). This is a common mistake. 371 (Piaget, 1967/1971, p. 178). Piaget notes, in addition, that hermit crabs are transitional between these two: the borrowed shell, "although organic, is only an external object assimilated as part of a behavior pattern" (Piaget, 1967/1971, p. 179ff). 372 (Piaget, 1967/1971, p. 179) 132 The basic argument is that "forms" direct interactions along certain pathways.
This is a generalization of Waddington's "chreods" proposal, which Piaget differentiates across the levelled hierarchy of functions into instincts, reflexes, conditioning, and sensorimotor habits. (These are each examined in part five of Biology and
Knowledge,374 but in a way that is irrelevant to our purposes here.) Most important, for our purposes, is that the same pattern exists at the level of cognitive functioning.
Part 3 of 3: Cognition as Functional Level. The challenge in using this argument to generate hypotheses that could be used to understand cognition is that thought is tied so closely to language. "But," Piaget says, making an important distinction, "language is not thought, nor is it the source of the sufficient condition of thought."375 The origins of cognition, like other structural forms, are rather to be found in behaviour: action by the subject, in interaction with the objects of its environment.376 Cognition can therefore be understood tentatively as a further set of levels that builds on the prior physicochemical levels ([A * A'] -> [B * B'], etc.) and following the pattern of development found in
373 (Piaget, 1967/1971, p. 180) 374 (Piaget, 1967/1971, pp. 215-265) 375 (Piaget, 1967/1971, p. 181) 376 This prediction was recently borne out in a study of the regions of the brain used to process language, using fMRI to scan the brains of prelinguistic children (Koechlin & Jubault, 2006). The finding has wide-ranging implications, one of which may be to shift support away from Noam Chomsky toward a more constructivist position, as argued by Piaget during his debate with Chomsky in 1975 (Piattelli- Palmarini, 1979/1980). 133 Piaget's earlier works on children's learning. Yet the isomorphism is not perfect.
There is a fundamental distinction to be made between these kinds of change:
The essential difference between intellectual adaptation [258] and organic adaptation is that the 'forms' of thought, as they come to be applied across increasing distances in space and time (and following further progressive differentiations of scale), abut the constitution of a "milieu" that is infinitely more extended; thus, more stable. At the same time, operational instruments - enacted via semiotic auxiliaries, namely language and writing - retain their own history. In the mind, as thought, they also acquire continuity and reversibility. As a result, these forms develop a dynamic stability inaccessible to biological organization. It then follows from this, first, that conceptual or operational assimilation is much more "preserving" than is assimilation in the realm of organic forms.... Second, if the re-equilibration of forms incorporates an unforeseen irreducible element that continues to manifest in disequilibrium, acts of intellectual accommodation present with no fewer than two additional characteristics than what occurs in the realm of organic accommodation. [259] We can call the first of these "permanent" accommodations.... The second, "anticipative."378
These are listed in Chapter I. The problem of abstracting new levels is examined as part of the new theory (in Piaget, 1977/2001). 378 (my abridged translation of Piaget, 1967a, pp. 257-259). This new version fixes several errors in the standard English text, which resulted in part from stylistic quirks in the original: the omission of necessary punctuation; two peculiar grammatical constructs; a presentation which, in English, converts into run-on sentences even if taken even sense-for-sense; and allusions to other aspects of Piaget's theory that aren't explained in this context. The original translator also switched "milieu" in the original for "environment" in the translation, mistakenly directing readers away from the narrative arc provided by the "forgotten works" and toward a more specifically Lamarckian interpretation. (In addition, in my version, the original "conservcmte" is replaced with "preserving" instead of "conserving" to avoid implying a connection to the unrelated notion of Conservation; the sentence starting "Second" was rewritten for clarity, with the final two phrases shortened to match.) Interestingly, in this new version of the quote, we can see hints of what Kuhn (1962/1993) had called "incommensurability." The parallel is further reinforced when one notices that the original unabridged version of the passage also includes mention of Euclid, from whom Kuhn originally borrowed this idea (Burman, in press; see also Burman, 2007b). For comparison purposes, the original translation of the above is provided here: "The essential difference between intellectual and organic adaptation is that thought forms, when applied to increasing distances in space and time (with progressive differentiation of the scales) leads to the setting up of an 'environment' which is infinitely more extensive and therefore more stable, whereas operational instruments, for their part, being dependent on semiotic auxiliaries (language and writing), retain their own past and acquire some continuity and stability, which is unattainable by the biological organization. One result of this is that conceptual or operational assimilation is much more 'conserving' than is assimilation in the realm of organic forms.... On the other hand, while accommodation to new experiences has a certain irreducible quality of the unforeseen which is constantly threatening the new adaptations all over again, yet such accommodation made by intellectual assimilation schemata to the unforeseeable data of environment 134 The first of these is revisited in detail in Chapter V. Briefly, however, the exemplar of a
"permanent" accommodation is a logical or mathematical theorem: once proven it cannot
be falsified. (This, incidentally, is why Piaget uses explanations in logic and mathematics
in attempting to anchor his new theory: if the developing mind is constructing "logico-
mathematical structures" in a way akin to how logicians and mathematicians construct theorems, then this imparts Godelian directionality to the lineage of transformations.)
Although such structures also provide a degree of anticipation, in the sense of scaffolding
a constrained set of possible responses, the exemplar Piaget provides to illustrate this
second characteristic of intellectual adaptation is "memory." The rest of this chapter is
devoted to its examination.
In his initial examination of memory, Piaget distinguishes between its function in the "acquisition of information" and its role in the "preservation of information." The
former includes a capacity for recognition; the latter, the symbolic "evocation" of objects outside perception.379 Both require assimilation schemes: the recognition of an object V requires assimilating an experience that "solves for" the logico-mathematical structure that describes 'x,' while evocation (recall) requires "projecting" a solution V through that structure in the absence of the object described. Yet rather than examining Piaget's theoretical discussion of these issues, which revolves around logical and mathematical
does have two remarkable characteristics that confer on it a greater degree of compatibility with assimilation than in the case of organic accommodations. The first of these characteristics is the existence of certain accommodation forms which are, so to speak, permanent.... The second striking characteristic of intellectual accommodation is its capacity for anticipation" (Piaget, 1967/1971, pp. 183-184). 379 (Piaget, 1967/1971, p. 186) 135 transformations that go beyond the scope of this thesis,380 we will turn instead to his empirical study of the phenomenon itself.
Memoire et Intelligence
The bridge from Piaget's theoretical discussion of memory to its empirical study in
Memoire et Intelligence (translated as Memory and Intelligence) can be traced to a
11)1 T Q'l reference to his post-doctoral supervisor, Pierre Janet, in all three forgotten works.
This serves as a convenient conceptual anchor for our transition away from Biologie et
Connaissance, but at the same time also anticipates Piaget's later examination of permanent accommodations in the form of cultural narratives inLe Structuralisme (examined in Chapter v).
...we must establish to what extent the memory involves a reconstruction, which is what P. Janet meant when he said that the memory was bound up with 'narrative conduct', and to what extent it lingers on, between the imprinting of the data and their recall, thanks to the [preservation] of unconscious pictures (such as Penfield was able to resurrect by electrical stimulation of the temporal lobes).383
In the language of our earlier discussion, a cultural narrative is the performance of a structure that "solves for" the relevant problems of a people. "Narrative conduct" - which Janet also refers to more simply as "narrative memory" - is the enactment of the same structure by an individual. Thus the problem examined by Piaget is whether memory is an "unconscious picture" (as is often assumed) or if it is an enacted
380 (Piaget, 1967/1971, pp. 188-213). The ideas presented are developed in the "new theory" works. 381 (Burman, 2007c; see also Amann-Gainotti, 1992; Amann-Gainotti & Ducret, 2002) 382 (Piaget, 1967/1971, p. 187; Piaget & Inhelder, 1968/1973, p. 7; Piaget, 1968/1971, p. 70) 383 (Piaget & Inhelder, 1968/1973, p. 7). Replaced "conservation" with "preservation," as in the above. 136 "reconstruction of observed data." The resolution of this problem has deep implications not only for our conception of development, but also of the mind (and Psychology) more generally.
Reading Guide and Exegesis
At the outset, it is worth noting that a number of earlier studies by Piaget's group had already suggested that the problem of memory is more complex than typically thought.384
In addition, the existence of phenomena like self-regulation and equilibration in development (i.e., auto-regulation) requires that memory be more than a result of
IOC association and conditioning. The most important of the experiments to be conducted were therefore those that assessed the effects of this regulation over time, beyond what would be possible assuming only Behavioristic principles. We will review the results of three such studies, chosen from among the dozens published during the period of interest.
Study 1 of 3: Numerical and Spatial Correspondences. The first study updates some of
Piaget's earlier work on Conservation in application to the problem of memory.386 The question examined is whether the inability of the average child under 8 years of age to
384 Piaget also cites the then-unpublished volume to which Beilin attributes the emergence of the new theory (Inhelder et al., 1974/1974). It is clear from its treatment here, however, that Piaget considers that work as part of a lineage and not the beginning of something new. 385 (Piaget & Inhelder, 1968/1973, p. 8) 386 Another update of this earlier work, published the same year but not included in a book-form compilation, was published in Science (Piaget, 1968c). Although memory is not discussed, the themes from the transitional period are evident, as is another taken up explicitly during the "new theory" period: a critique of Chomsky's nativism (see also Piattelli-Palmarini, 1979/1980). 137 "conserve" in an experimental interaction would affect their recollection (mental preservation) of that interaction. Before getting to that, however, we must first define what Piaget means by "conserve." (This is especially important in the context of these translations, since the translators did not seem to be aware of how loaded the term was in choosing it over an equivalent - e.g., "preserve" - in discussions of memory.)
Conservation is a prototypical Piagetian problem. The type of examination it inspires typically varies on a basic theme offered in most introductory psychology textbooks: When does judged volume (for example) become more than a dichotomy between height and width and instead become a reflection of both height and width?
(Non-conserving children judge a volume of water to have changed if it is moved from a tall-thin glass to a short-fat glass: "there's less because it's shorter," they explain.)387 The key question of conservation experiments, in other words, is to ask: When do children begin to make judgments, and craft explanations, using more than one heuristic dimension? Thus, similarly, when does the perception of length begin to incorporate a measure of a line's "wiggliness," rather than just being a reflection of the horizontal distance it travels?388
When the conservation problem is presented using multiple segments of equal length, it becomes a problem of "numerical and spatial correspondence." This, as we
387 See, for example, the discussion in (Bringuier, 1977/1980, pp. 32-35). Similarly, a ball of clay rolled into a cigar can be both "bigger" and "smaller" than the original, according to how it is manipulated by the experimenter (Bringuier, 1977/1980, pp. 29-32). 388 It is curious that a young Benoit Mandelbrot, who later discovered "wiggly" mathematics (fractals), collaborated with Piaget during the early phases of his Center's development (Piaget, Apostel, & Mandelbrot, 1957; Piaget, Jonckheere, & Mandelbrot, 1958). This connection ought to be examined in future research. 138 showed above, is a kind of isomorphism: a learned link between number and distance.
To assess the effects of this type of cognitive demand on memory, Piaget and his collaborators presented 78 children (one group of five-year-olds and a second of eight- year-olds) with four matchsticks arranged in two different patterns: a straight line and a
'W shape.389
C*"..V.S
Figure 11. Piaget's illustration of the experimental setup.390
It is clear from the picture than the horizontal distance travelled by the straight line is greater than the distance travelled by the ' W shape. It is also clear that the "wiggliness" of the ' W shape is greater than that of the straight line. Because they are composed of the same number of match sticks, and therefore span the same absolute distance, the ' W shape is necessarily both shorter and wider than the straight line. This adult understanding of the two lines is the "unconscious picture" to which the children's recollections will be compared in the resulting conservation experiments; if there are consistent divergences from this form shared by a group of children (thus describable as sharing the same stage of development), then that will be indicative ex hypothesi of an intervening cognitive structure of lesser explanatory power. And, indeed, this is what
Piaget and his colleagues found.
389 Of course, it was not described to the children in this way. Even to describe the line as ' W shaped would have been to apply a structure! 390 (Piaget & Inhelder, 1968/1973, p. 75) In interviewing the children about what they remembered, and examining their drawings, Piaget found four types of error. The first kind of error, made by a few of the 5-year-olds, was to organize all of the matchsticks into a single line: , 111, or / / /.
An hour after the first presentation, these children had forgotten the distinction between the two objects (or had forgotten that there were two to start with) and just drew one.
The second kind of error reflected a focus either on equality of number or on inequality of length, matching the horizontal span by extending the 'W out as a series of zigzags or exaggerating the size of its individual segments. The third kind of error reflected a conflict between equality of number and inequality of length, extending the ends of the
'W to match the span of the line. And the final kind of error matched for length, but used an arbitrary number of segments. The fifth group then produced an accurate reconstruction, with some slight variations.392 Comparing the ages at which each of these errors is made shows a clear progression with age and across types of error, as one would expect from Piaget's earlier experiments showing that children of different ages reason as if they belong to different "species of mind." What is surprising is that this earlier finding applies to memory as well as to reasoning: if children cannot conserve, then they also cannot preserve. (How you think affects how you remember; improvements in the structuring of thought leads to improvements in the structuring of memory, which follows a sequence of increasing constructive complexity.)
391 Attention to error has a long history in Piagetian research, going back to his post-doctoral days at the Binet-Simon Lab in Paris (1919-1921). 392 (Piaget & Inhelder, 1968/1973, pp. 77-78) 140 Study 2 of 3: Horizontal Levels. The second study also builds on the Conservation task.
In this version, instead of being asked to transfer a volume of liquid from one container to another, the children were asked only to remember "what it looks like" before any manipulation. The challenge here is that the idea of "horizontality" - a universal description for the surface of a liquid in a container under normal conditions - is a function of operational procedures that do not develop until 9 or 10 years of age; younger children can perceive "the horizontal," of course, but do not see it as a necessary relation between the properties of external objects. (Rather, as earlier studies had showed, the young child's perception operates as a function of their own line of sight and body position.)
Piaget initially showed 66 subjects three objects: a bottle on its side, half-filled with red liquid; a toy car, right-side-up and half painted red; and an inverted bottle, also half-filled with red liquid.
r=\ W
Figure 12. Piaget's illustration of the experimental setup.394
393 Two books (Piaget, Bruner, Bresson, & Morf, 1959; Piaget, 1961/1969) collected, summarized, and updated the perception-related studies conducted by Piaget and his colleagues starting in the early 1940s. A handful of additional articles were published after the appearance of the second book, as did a volume in his series (Bovet, Greco, Papert, & Voyat, 1967), but these don't concern us here. 394 (Piaget & Inhelder, 1968/1973, p. 296) 141 He then asked the children to draw what they had seen. An hour later, following a similar pattern as in the first study, several of the five-year-olds conflated the two bottles: they drew a single bottle with the liquid pressed against its side. But, as predicted from the first study, the reconstructed memory - their explanation - had also become the reality experienced:
Mic (5;3) drew two upright bottles with the liquid pressed vertically against one wall. He was then shown a motor car with a horizontal band, but continued to maintain that the band in the bottle was vertical. Next, he was shown a drawing of a recumbent bottle with the liquid parallel to the base: Wo, that's not what you showed me.'
Older children - those 6- to 7-years-old - made similar mistakes, but would typically recall that they had seen two bottles.
To reduce the complexity of the problem, and ensure the accuracy of the results, a modification then was presented to the children: a single inclined bottle, half-filled with red liquid.
C
Figure 13. Piaget's illustration of the revised experimental setup.
(Piaget & Inhelder, 1968/1973, pp. 297-298) (Piaget & Inhelder, 1968/1973, p. 300) 142 Again, although some children of each age correctly reproduced the image an hour later, a pattern of errors was observed. The first type of error (most prevalent among the youngest children) was to draw the bottle in an upright or inclined position, liquid aligned vertically with the bottle wall; the second type inclined the bottle, but aligned the liquid horizontally with the bottle base; the third and fourth types inclined both the bottle and the liquid, but at compensatory angles either over or under the correct amount; and the fifth type of error was to reproduce the bottle as various angles but full. (Roughly a third of 8-year-olds get it right; 9-year-olds do better, but only slightly.) This is the same pattern - a correlation between type and frequency of error and age of subject397 - that was observed in the first study. Where things get interesting is in tracking the changes in response from one hour out to one week and beyond—to six months after.
In conducting the longitudinal trend analysis, Piaget combined the first two types of error into one group and the final three types into another. Adding to this the "adult" reproductions achieved by the older children affords three stages of performance: recalling the liquid as being level relative to the (explicit) bottle, inclined but at an arbitrary angle, and level relative to the (implicit) ground. Piaget suggests that this reflects a progression in "notional" development; the cause of a child's consistency in responding at certain stages. And it highlights the important role played by cognition in memory; the importance of structure in explanation.
(Piaget & Inhelder, 1968/1973, pp. 300-302) 143 Six months after the initial interaction, all of the children (i.e., the 55 the experimenters were able to bring back to the lab) remembered the bottle as being half- filled with liquid. But the distribution of error type among the youngest children narrowed and shifted down, suggesting a regression in performance to the lowest stage of notional development: "These responses underline the fact that the excellent initial memories of these subjects do not go hand in hand with operational understanding."398
Rather than memory serving as a function of their original "perception," their responses at six months were a function of "deductive anticipation."399 Their memory reflected the logic of what ought to have been, given their understanding of how the world works. (In other words, it reflected the not only the structures of their functioning, but also the weak explanatory power of the structures they had constructed.) This interpretation was reinforced by the progress made by the older children.
Among the older children, the distribution of error type also narrowed after six months. But, in contrast to what happened with the younger children, it shifted up. The older children had gotten better at remembering. Why? In some cases, as Piaget discovered through questioning each child's justification for their reasoning,400 the older children simply took additional information into account in reconstructing their experience (i.e., increased complexity). In others, however, the children had advanced to a higher stage of "notional" development: they knew why their description had to be so
398 (Piaget & Inhelder, 1968/1973, p. 303) 399 (Piaget & Inhelder, 1968/1973, p. 302) 400 This is an example of his "clinical method" (for more, see Opper, 1977; Mayer, 2005). 144 (i.e., why their explanation was necessary). As a result, their "memories" produced a closer approximation of what an adult would expect; the "right" answer.402
In a later study of this "reconstructive" aspect of memory, the results were even more dramatic: both normal and dyslexic students performed at levels significantly better
- six, twelve, and even sixteen months later - than one would have expected on the basis of their recall after an hour.403 Indeed, children above a certain age seem to "learn" without exposure; their "memory" gets better over time. We are thus left with a new hypothesis. When "recall" is reconceptualised to include an active process (rather than passive reception and reproduction), the larger role of operational structures becomes clear: the developing "lens" (structure) through which a problem is perceived is also that
This theme is re-examined in detail in (Piaget, 1983/1987; see also L. Smith, 1993). 402 Although Piaget doesn't deny the existence of a "real" world external to the subject (and thus also the existence of a "really true" right answer) - as constructivists are often accused - it is important to note that there is a problem of verisimilitude in approximating solutions to puzzles of knowledge: fit not only between external object (V) and internal knowledge structure (describing and explaining V), but also with common understanding (accepted descriptions of and explanation for V). Piaget doesn't explicitly use this word (verisimilitude), but his continuing reference to Godel in support of his constructivism suggests that he assumes incompleteness in constructing structures, requiring continuing interaction between objects of knowledge and the notions used to reflect on them (Burman, 2008c). This, in short, is what produces the quality of things thought about; it provides the content-rich foreground of the development of the things thought with. But the complexity of the knowledge structure itself is a function of the complexity manifested by the object, as well as of the ways of looking at it. On this account, the emergence of a new tool to reflect on a puzzle would lead to the subsequent emergence of new things thought about: new ways of interacting with the external object. As a result, in response to the exploration wrought by innovation, a previously adequate solution could become inadequate. Hence, a "right" answer can only ever be asserted to be approximately true relative to the standards applied in the problem's assessment and the context in which the claim to knowledge is made. (This is examined in further detail in Chapter V.) That's not to say, of course, that - anticipating a standard objection to constructivist argumentation - there is some scepticism about, for example, the ability of airplanes to fly. They do: a solution to the puzzle of flight has been constructed, its explanation abstracted as "lift and drag." Rather, it is to suggest that we can only claim to safely assume airplanes will fly given circumstances similar to those in which they have flown previously. A new context provides new rules: the space shuttle must fly differently from a jet fighter merely as a result of its different required range of function. (That's a complicated way of saying something simple: It works, but it needs a different structure to allow it to survive in different situations than the other structures in its lineage.) 403 (Piaget & Inhelder, 1968/1973, p. 356) 145 through which it is reconstructed (as function and as explanation). If this lens changes during development, then so too will the reconstruction.
Study 3 of3: The Evolution of Memory. In our third study (the last of those reported in
Memory and Intelligence), Piaget delves deeper into the reconstructive aspect of memory and its apparent improvement with age over time.405 The challenge in distinguishing this from "raw" memory, however, is that most assessments blur the line between pure reproduction and performative reconstruction.406 (As a result, psychometrics can be inadvertently biased in favour of those children whose thinking more closely resembles the members of the group upon which the measures were validated, be they separated by
This seems now to be the general opinion of memory researchers. However, the idea is today reframed using a more contemporary metaphor: the mind as a computer, with its memory as an active simulation. Indeed, recent experiments have explicitly tied together the themes examined in Piaget's transitional studies on memory with his slightly earlier studies of mental imagery (Piaget & Inhelder, 1966/1971). (Kent and Lamberts, 2008, put it this way: "re-enactment of encoding processes is functional for retrieval" [p. 97].) As a result, even though these two volumes originate in approximately the same transitional period, it only seems necessary to describe the results of the one that fits explicitly into our narrative arc. That said, there are of course several other related works that could be used to flesh out the story in more detail as part of a larger examination of the period (e.g., Piaget, 1968b; as a bridge to Piaget, Sinclair, & Bang, 1968, which remains untranslated). 405 Recall that "improvement with age" is a common misconception of Piaget's argument. The focus is rather on the transformations of operational schemes due to experience, abstraction, and generalization (Lourenco & Machado, 1996). Improvements with age are therefore only "apparent." 406 Here, Piaget implicitly references early work on memory by Hermann Ebbinghaus (1885/1913), but doesn't mention him by name: "to evaluate the remembrance of nonsense syllables, we must ask the subject to repeat them, which amounts to a reconstruction" (Piaget & Inhelder, 1968/1973, p. 361; the reference is made explicit in Inhelder, 1969/1976, p. 100). This is typical of Piaget's writing: he often assumes the reader knows what he's talking about. The result is usually just a challenging read. But this can become "a problem" when the translator doesn't recognize the reference and then mistakenly alters a passage's implication. Indeed, it seems likely that this is the cause of the apparent Lamarckism of the English versions of Piaget's biologically-inspired works: the translators weren't fully aware of the history driving the implicit meaning of words they were rendering in a new scientific context, which then blinded them to their own explicit errors (e.g., dropping the "not" noted in the errata of Chapter II). The problem of translation here is therefore one of historical implication - of theoretical lexicology - rather than of simply choosing terms from the target language while operating under constraints imposed by the strict lexicographical meaning of words used in the source text. (This also seems to follow from the forgotten works themselves; see Chapter VI.) The logic of meaning is, at least in part, a function of context. 146 age or culture.)407 Yet a still greater challenge is the problem posed by what such measures fail to capture:
.. .no matter what material we present to our subjects, we are invariably inviting them to engage in mental co-ordinations based on a regard for order, resemblances and contrasts, spatial structures, etc.... These complex relations, which intervene continuously in all presentations, are in fact meanings, for we are not entitled to reserve this term for purely abstract and highly conceptualized notions. In fact, perception itself is a system of meanings that are partly isomorphous with conceptual and even with operational meanings—the same criteria apply to both perceptive and conceptual 'good forms.'
Here, Piaget foreshadows his later turn toward the articulation of a logic of meanings.409
But in this early approach, he is more concerned with the effects of the structures themselves.
In this last study, rather than presenting the children with a simple object (or sets of simple objects), Piaget provides a complex set having both regular and contingent features. It has organization, but this is of so many dimensions that it is of more benefit to the experimenter than to the subjects. ££><^
Figure 14. Piaget's illustration of the experimental setup.'
407 (Dasen, 1984; Shayer, 2008) 408 (Piaget & Inhelder, 1968/1973, p. 361) 409 (Piaget & Garcia, 1987/1991; see also Lourenco, 1995) 410' ,(Piage t & Inhelder, 1968/1973, p. 360) 147 Still, he reminds the reader about the role of intelligence - and interpreted meaning - in shaping both the memory and the evoked explanation:
It is... essential to bear in mind that, no matter what material we present, the subject's intelligence necessarily intervenes during the three essential phases of mnemonic activity: during fixation, by determining the general structuring of the data to be retained; during retention, by presiding over the organization of the 'memory traces'; and during recall and reconstruction, by determining the re- elaboration of what has been retained.
His purpose in providing this caveat is to set up an appreciation for the nuances of this type of study, while at the same time alluding to its purpose: to examine the structures of intelligence which intervene in memory, while at the same time minimizing the effects of meaning (either provided or interpreted) in shaping it.
To enable a comparison between mnemonic methods (i.e., different organization functions), the participants - 68 five- to thirteen-year-olds - were split into two groups.
The first group of thirty [Method I] were asked to classify the objects in the complex set by arranging a second jumbled set of cardboard cut-outs representing individual figures
(pink circles, squares, and triangles) and bars (all black) into all the various groups they could invent, trying as many times as they needed to exhaust the perceived possibilities.
Then they were asked to use these figures to make a copy of the original: they manipulated their set of cut-outs to match the complex set. At each meeting in the longitudinal follow-up (after one hour, after a week, and after six to ten months), the children were asked to produce reconstructions of this copy: to re-present their actions.
4,1 (Piaget & Inhelder, 1968/1973, p. 361) 148 In contrast, the second group of thirty-eight children [Method II] were shown the set - the elements of which the experimenter named and acted out (e.g., by miming the bars
"running" across the table) - and were asked only to return for their longitudinal reconstructions (i.e., they did not make a copy and were only asked to "remember").
Then, when an initial inter-group comparison showed few differences in performance for either the five- to six-year-olds or the twelve- to thirteen-year-olds, twenty additional seven- to eight-year-olds were brought in.412 (The total number of participants was therefore 88.) These new subjects were then split into sub-groups to further differentiate the effects of organizing the materials and copying the set: the first ten [Method I A] were asked to group the cut-outs but not copy the set, while the second ten [Method IIA] were asked to copy the set without first organizing the cut-outs. The reconstructions were performed by all participants using the same jumbled set of figures and bars, plus some additional pieces. (In the end, of the 33 subjects who returned for the final reconstruction, 17 had been tested by Method I and 16 by Method II.)413
The results for all 88 children showed a similar pattern of errors as reported in the previous two studies. In this case, however, the children's competence in reconstructing the complex set could be characterized following a single hierarchical series: any success at all on criterion D, for example, was predictive of the child achieving all aspects of A,
(Piaget & Inhelder, 1968/1973, p. 362) (Piaget & Inhelder, 1968/1973, p. 364) 149 B, and C, but none of E, F, or G. (Correctly remembering the number of figures [D] seemed necessary to if the child was to correctly identify the number of different positions the bars could occupy relative to those figures [G], but not their basic orientations [C and A] which could be remembered independently of the number of participating figures.) A breakdown of this hierarchy then revealed a set of stages in
"schematization." The first stage, involving sizes and orientations [A-C], was presented as reflecting a primitive form of organization based on resemblance.415 The second stage, involving variations on number and form [D-F], was based on a more exact bottom-up ordering of content relative to the system in which it has meaning. And the third stage, characterized by position and succession [G-I], seemed to involve the imposition of a global top-down reorganization of these earlier forms.416
Piaget argued that the stages would manifest in memory over time either as a successful depiction of the observed objects, being an "adequate" reconstruction (and thus a good match between the complexity of the exogenous phenomenon and its endogenous approximation), or else would lead to "failure and distorting simplification."417 Given the existence of a predictive hierarchy, however, the errors
Piaget cites "Guttmann" as the methodological influence in constructing this hierarchy (Piaget & Inhelder, 1968/1973, p. 424/364), but this is almost certainly a spelling mistake. See errata for commentary. 415 (Piaget & Inhelder, 1968/1973, pp. 364, 368) 416 (Piaget & Inhelder, 1968/1973, pp. 365, 368-369) 417 (Piaget & Inhelder, 1968/1973, p. 369). This again betrays the influence of Godel in Piaget's thinking: he is constructing a hierarchy that is also a formal system, with the same problems of completeness as any other: "Remembrance of the fortuitous or contingent elements cannot... be divorced from the schematizations: it is largely as a function of the [schemes] he employs that the child treats the arbitrary elements as so many obstacles to be eliminated or, on the contrary, as so many elements to be 150 themselves are crucial to understanding how each child reasons. In short, the complexity of a child's recall reflects the complexity of their schematizations; "stages" are a merely descriptive conceit, sitting atop a functional (causal) substructure.419 But, before we get to that (in Chapter VI), what do we learn from the seven- to eight-year-olds who showed differences in performance?
In reviewing the effects of the two methods, and their variants, Piaget found a clear benefit to the use of Method I: asking the child to classify the object-to-be- remembered, then having the children copy the overall organization of the set, increases
retained because of the contrasts or special classifications they introduce" (Piaget & Inhelder, 1968/1973, p. 371). 418 This is another foreshadowing of Piaget's new theory, although the explicit study of "reason" as an object of scientific enquiry would be his last. He died before completing it, although his notes have since been published (Piaget & Smith, 2004/2006). This interest can be traced, in the lineage, to earlier works that followed directly from those reported here: on "success and understanding" (Piaget, 1974/1978) and "the grasp of consciousness" (Piaget, 1974/1976), which describes the feeling of what happens when the observer realizes their observations are due to the behaviour of a single super-structure. 419 (cf. Niaz, 1998). This provides a new perspective of the then-emerging neo-Piagetian arguments. For example, Juan Pascual-Leone's M-Power theory of constructive intelligence can now be seen through the lens provided by Piaget's use of Guttman (see errata discussion below) in supporting his multi-level organization structure: "It is well known that [the] heuristically powerful notion of general stages offers the possibility of constructing a natural ordinal scale of intellectual development. The dimension on which this scale is located appears to the present writer to be the informational complexity of the task considered from the subject's point of view.... An important corollary of this view is that any general stage of cognitive development could in principle have one numerical characteristic: the number of separate schemes (i.e. separate chunks of information) on which the subject can operate simultaneously using his mental structures" (Pascual-Leone, 1970, p. 302). From here, however, their interpretations begin to diverge. For Pascual-Leone's neo-Piagetian approach, stage change up the hierarchy is driven by increases in M: the size of the central computing space, as a function of the maturation of innate faculties. For the emerging new theory, by contrast, it seems Piaget's argument was that - as the child constructs structures of increasing complexity - more of the world can be assimilated in one "chunk" (i.e., that increases in M are illusory, or at best co-constitutive). In other words, the basic disagreement seems to revolve around two different interpretations of the meaning of "information." Although Piaget developed his perspective in increasing detail throughout the "new" period, this final study in Memory and Intelligence lays the foundations: information is the product of how an organism acts on an object, assimilating its features to internal structures and accommodating them to incorporate found-resistances (selection pressures) and better approximate/simulate/model its behaviour in future. For Pascual-Leone, by contrast, it seems the information is already in - or, perhaps more charitably, it is "afforded" by (cf. Gibson, 1979/1986) - the object; lower level subjects simply can't read it. 151 the accuracy of their recall. Yet that the twelve- to thirteen-year-olds showed no differences in performance across methods suggests that the effects of this "external" structure are ultimately internalized during development.420 The effect of this internalization, then, is that higher levels in the hierarchy become progressively easier to attain.
To sum up: at all levels there is convergence between the classificatory levels and the levels of the mnemonic schematization, and this regardless of whether or not the subjects and had been asked to supply prior classifications.... It follows that the reconstructive memory is a natural entity obeying the laws of general development and of mnemonic structuring.... As regards mnemonic structuring, we hope that we have shown to the reader's satisfaction that reconstructions presuppose schematizations, the levels of which can be determined by means of... hierarchical order... and also by an examination of the stages of the child's development.421
Recapitulation
Memory and Intelligence presents a series of studies examining the structures of mind that shape the quality of our thought. The key finding is that memory does not just improve with age, but also with schematization.422 External structures can serve as scaffolding for performance, as predicted by Vygotsky,423 yet their benefits are mitigated by what is provided endogenously. In addition, in the context of our discussion of
This interpretation was also suggested by the results of an earlier study (reported in Piaget & Inhelder, 1968/1973, pp. 331-359). 421 (Piaget & Inhelder, 1968/1973, pp. 376-377) 422 Elkhonon Goldberg (2005) has recently called this the "wisdom paradox." 423 Vygotsky is now famous for what has become known as his "scaffolding theory" of socio-cultural learning (but see Stone, 1998). For those who are frustrated with Piaget, this has been raised to the level of panacea (see e.g., Berk & Winsler, 1995). However, he died young and was born the same year as Piaget. As a result, his work - and especially his criticisms of Piaget - were later addressed and eclipsed by the Genevan School (Piaget, 1962/2000; see also Beilin, 1996). Yet, despite this, many scholars believe their ideas should be synthesized as a new foundation for developmental theory (e.g., Shayer, 2003; Pass, 2004, 2007). 152 Piaget's return to biology, we can conclude that the function of memory is to provide a
framework through which useful information can be reconstructed accurately on the basis
of the minimum amount of data; that it reflects the imposition of a top-down
"organization function" preserving accommodations to the effects of selection pressures that are distant from the organism in space or time.424 This is an effect of interpreted meaning: explanation in action and recollection.
Reception and Errata
Upon first publication, the book received only a cursory note in the English literature.425
After its translation, however, it was treated to a more serious examination. Yet this presentation follows the logic of Piaget's old stage theory: memory changes with development. The most surprising finding - that memory can improve over time, as a result of further development in the underlying schematizations - is noted but goes undeveloped.
In the series of studies reported in this book, "memory" and "intelligence" are shown to be two sides of the same problem: the developing structure of explanation. This was noted by another reviewer in response to a related set of studies:
Their experiments encourage [Piaget and Inhelder] to conclude that the memory is not an immutable given; that it changes and that its contents are shaped by the structures of an evolving mind. For Piaget there would be no conservation of memory outside of the overall system of intelligence. Memory, in a strict sense,
(cf. Janet, 1920/forthcoming) (Elkind, 1970) (Liben, 1975) 153 is a particular case of knowledge (that of the past) and it is in this guise that it is integrated with intelligence.
But, in its popular reception, the important aspects of this idea were developed no further.
As a result of failing to appreciate the underlying theoretical argument (regarding the importance of a causal substructure in shaping the developing quality of thought), many of the usual litany of criticisms - described by one reviewer as "the all too popular
American sport, Piagetsnipmg" - are also misdirected.
In terms of textual errors, the most important incidence of meaning loss is in
Piaget's citation of "Guttmann" as the methodological influence in constructing his predictive hierarchy. This is almost certainly a spelling mistake, as it occurs in both the original and in the translation. It seems more likely that the reference is to Guttman
(1944) and his method of characterizing qualitative data in quantitative terms. In the third study reported above, what Guttman calls a "coefficient of reproducibility" (an assessment of fit similar to a correlation between data and descriptive model) is not reported, but Piaget does describe the data as being "fitted almost perfectly" to such a hierarchy.430 This language seems to confirm that the reference is indeed to this source.
The use of a Guttman Scale is significant for what it implies of Piaget's emerging new theory. It confirms the suspicions unearthed during the excavation of his Godelian influences (Chapter III) and provides converging evidence that Piaget's new theory has a formal component that goes beyond simple characterizations of "stages" in learning and
427 (My translation of Tzortzis, 1971, p. 241; cf. Charlesworth, 1971) 428 (Liben, 1975) 429 (Piaget & Inhelder, 1968/1973, p. 424/364) 430 (see also Piaget & Inhelder, 1968/1973, pp. 366-367) 154 development. The structures characterized by the Guttman scale can be transformed, but
- as in a Godelian hierarchy - their sequence is both invariant and predictive: there are necessary low-level elements in the perception/construction of high-level phenomena.
What is growing, during development, is an endogenous formal system for internally approximating the external world via its selection pressures. But - crucially, for the new theory - any resulting meanings "have sense" because of how we make them, not because they are themselves "out there." In other words, such meanings are manifest as part of the epigenetic landscape; the product of interactions between internal and external structures, with effects transmitted up and down the hierarchy.
But it does not end there. In tracing the reference, we find that Guttman (1944) hints at the possibility for complex mathematical manipulations that would enable the analyst to derive further meaning from the scale and its characteristics. While the details of his argument go well beyond the scope of this thesis, and the limits of space, it is sufficient for our purposes to point out that Piaget's "structures" have formal logico- mathematical underpinnings that make them more than mere containers for content. The results of Piaget's eventual attempt to fulfill Guttman's prediction were presented in his last book, Toward a Logic of Meanings, but he died before he was able to finish it. This final work, although published and translated, remains incomplete to this day.431
431 Indeed, the most important change distinguishing Piaget's "new theory" from the "old theory" is the argument that the genesis of knowledge can be more rigorously described using the new logic of entailment (Piaget & Garcia, 1987/1991; citing Anderson & Belnap, 1975). The completion of this project would not only make all textbook presentations of Piagetian theory obsolete (Beilin, 1992b, 1992a), but it would also revolutionize the fields in which this theory has been applied (e.g., education [Burman, 2008b]). 155 Prospective Conclusion
From the studies reported in Memory and Intelligence, we know that the correspondence between external structure (object) and internal structure (cognition) will be reflected in the accuracy of the explanation given (i.e., the memory reported).432 But since the individual only really "knows" things when taken relative to a social context, this otherwise purely psychological problem also has a sociological element: a truth not only exists "in here," but it must also exist "out there." How that can be characterized in the framework developed thus far is the problem examined in Chapter V. Yet, from our earlier examination of Piaget's appeals to Godel, we already see that institutions at the
(higher) level of the social serve to "complete" the implications of axioms constructed at the (lower) level of the individual (top-down). At the same time, the social is itself a level that emerges from the collectivity of individuals (bottom-up). The integration of this perspective with the remaining elements of the "old" theory then lay the foundations for the "new."
(cf. Piaget, 1980c) 156 CHAPTER V
THE EVOLUTION OF THINGS TO REFLECT ON
There has been some confusion regarding what it was, after 1965, that Piaget had
intended to achieve with his constructive theory of knowledge.433 This is almost certainly
the result of a conflation of his genetic epistemology with Baldwin's:
No knowledge confined to one private head, repeated in other private heads an infinity of times, could ever become an organic system of common knowledge. It must already, in its constitution, reflect its social origin and fitness. The single item of knowledge, the private self-contained thought of a single thinker, is the result of refined processes of cognitive differentiation. The private thought is not a cognitive unit; it is a cognitive outcome. The thought that claims the isolation and absolute lack of common control of an individual unit, is read off as eccentric and unreal, and its damnation is no less sure. Knowledge is common property not . 434
a private possession.
We might rephrase this to make the following claim: truth is a property of the collective,
which individuals come to learn following a developmental process that follows a similar
pathway as its original evolution as a social reality. And indeed, it was such an
interpretation that Steven Jay Gould claimed in 1977 - correctly, it seems435 - would
constitute a form of Haeckelian recapitulation: that individual development
("ontogeny...") retraces the steps produced through the various historical stages of a
433 Indeed, clarifying this was the purpose of Vuyk's (1981) important 2-volume study. 434 (Baldwin, 1930, pp. 15-16) 435 Baldwin actually cites both Haeckel and von Baer. The differences between these two, and Baldwin's reading of their positions, will need to be unpacked in future research. 157 group's evolution (".. .recapitulates phylogeny"). However, Gould misattributed the claim, suggesting that it was Piaget's argument, not Baldwin's.
Hypotheses regarding Piaget's recapitulationism are contradicted by the basic presupposition behind his empirically-informed theory of child development, of which his epistemology is an extension:
I believe... that the child is more primitive than any adult, including prehistoric man, and that the source of knowledge lies in ontogenesis [development]. Any adult you choose, whether cave man or Aristotle, began as a child and for the rest of his life used the instruments he created in his earliest years. Consequently, in the field of knowledge... ontogenesis is basic. .. .it's more primitive than phylogenesis [evolution].437
In other words - as we have seen in our discussion of the return to biology - Piaget's argument at the time of Gould's commentary was that change occurs first in development; that adaptation (and thus evolution) proceeds from disequilibrations unmet by changes made at higher levels of plasticity. And although "knowledge" may exist as a social phenomenon, it has its effects at the level of the individual who learns it.
If we expand our earlier illustration of the "circular reaction" (Chapter II), the result of this conception of individually-directed development is a cycle of epistemological construction: the brain and its embodied inherited instruments (e.g., reflexes) are at the centre, but selection pressures from both nature and culture cause disequilibrations that in turn - by proving the incompleteness of the constructed structures (Chapter III) - lead to change. In this process, the invariances of reality are
(Gould, 1977, pp. 144-147). Interview from 1975-1976, published in (Bringuier, 1977/1980, p. 92). 158 approximated by the adapting individual and new knowledge structures are abstracted that reflect both the quality of the instrument and the form of the disproof of the previous approximation. These explanations are then acted upon as if real, and shared, becoming coordinated social structures. And, in turn, they are then approximated by others, scaffolding individual learning and bootstrapping performance. Ultimately, they become the basis for exploration; shared learning and memories, rather than inherited reflexes, become the foundation for new possibilities.
Reality (Culture)
Assimilation Accommodation
Reality (Nature)
Figure 15. My illustration of Piaget's differentiation of the selection pressures driving the "circular reaction" to reflect two sources of "the real."
The result of this new take on the old argument - Piaget's update of Baldwin's genetic epistemology in his emerging sketch of an epigenetic epistemology - is a tertium quid 159 between two competing theories of truth: empirical discoveries "correspond" with reality,
but the interpretations of their meaning (and how this is explained) are mediated by a
logical demand for "coherence" within the pre-existing cultural narratives.438 And yet,
given that it is the actually developing structures which can affect how an individual
interprets this meaning (Chapter IV), this middle way still does not explain how the
narrative itself evolves. In short: How are the interpretive frameworks driving the
implications drawn from our "logics of meaning" constructed? Piaget's answer to these
questions forms the foundation for his new theory.
Socio-cultural Studies
In 1966, Piaget published a short collection of essays: Etudes Sociologiques.439 These
four "sociological studies" - originally published 1941-1950 - were repackaged as a new
whole just as "the return" was getting underway. The first is an essay on the emergence
of values in interactions between individuals. The second focuses on the isomorphism of
structures underlying morality and the law. The third extends the problematic notion of groupements (which we have previously discussed) to the emergence of a logic operating
at the level of individuals to organize them collectively. And the fourth summarizes the results of all three, while at the same time providing a general overview of the varieties of
This is a more formal version of the argument presented in Insights and Illusions of Philosophy (Piaget, 1965/1971). In that book, Piaget uses the word "wisdom" (sagesse) instead of "coherence." 439 The expanded second edition of this volume was translated in 1995 as Sociological Studies (Piaget in L. Smith, 1928-1960/1995). 160 sociological explanation to that point in history. Since it is clearly this last essay that was intended to do the most work in Piaget's return to his early concerns regarding the reality of society (it serves as the first chapter of the repackaged book), it is that to which will now turn our attention.
Explanation in Sociology
Piaget's capstone, and later introductory, essay on "explanation in sociology" was originally published in 1950 in the three-volume Introduction a I'epistemologie genetique441 There, just as here, it comprised the third part of a three-part examination of biological, psychological, and sociological approaches to knowledge (cf. Chapters II,
IV, and V). And it in turn has seven parts, each of which will be reviewed below.
Collectively, these parts lay the foundations for the later examinations of the social in
Biology and Knowledge, to which we will briefly return, and Le Structuralisme
(examined below).
Part 1 of 7: Sociological, Psychological, and Biological Explanations. Piaget begins his essay with a justification: the social study of knowledge is essential because the production of knowledge - be it scientific or not - is by definition a collective activity.442
He then lists a number of discoveries related to the production of knowledge in the animal world that, while biological, are also properly social: the dancing-language of
440(Piaget, 1941/1995,1944/1995, 1945/1995, 1950/1995) 441 (Piaget, 1950) 442 (Piaget, 1950/1995, p. 30) 161 bees, the imitative learning of birdsong, etc. Indeed, without their dance (or their song), bees (and birds) would be completely different creatures; their way of life is, at least in part, a function of their sociality. As a result, Piaget suggests the following:
These truly social facts, constituted by external transmission and interaction, modifying individual behaviour, call for a new method of analysis at the level of the group (seen as a system of constructive interdependencies) which should supplement biological explanations of organic or instinctual structures.443
This need to understand social facts extends especially to explanations of human action.
The notion of race, Piaget notes by way of example, has "become a simple affective symbol rather than an objective notion."444 Understanding the meaning of such notions necessitates going beyond the biological.
While the latter [biological explanation] is concerned with internal transmission (heredity) and the characters thereby determined, sociological explanation is concerned with external transmission, or the external interactions among individuals and constructs a set of notions designed to account for this distinctive type of transmission. It is in this way that sociological explanation will show why the mentality of a people depends much less on its race than on its economic history, the historical development of its technology and of its collective representations, where this 'history' amounts to an inherited patrimony, indeed a cultural patrimony, i.e. a set of behaviour patterns which are transmitted externally through the generations, but with modifications due to the totality which is the social group. It is in this way, moreover, that the biological aspects of demographic phenomena (birth-rate, death-rate, longevity, mortality related to type of illness, etc.) are strictly subordinate to systems of (especially economic) values and rules, which are the outcome of the external interactions of individuals.445
In other words, the social - including its abstraction in education - operates at a different level from the biological, which it augments: "For example, language acquisition
(Piaget, 1950/1995, p. 31) (Piaget, 1950/1995, p. 31; see also Weizmann, 2004) (Piaget, 1950/1995, p. 31) 162 presupposes... a pre-existing biological state... the capacity to learn an articulated
language."446 But the social also has its impact on biology only over time: there is an
interaction, between the individual and the social structure as a source of selection
pressures, such that its effects on thought change throughout development.
Just as the child decentres during development to become less self-centric, so
does she become more socio-centric. Only later will she decentre once again, to
transcend the pseudo-necessities imposed by her own belief in social explanation and
begin to focus instead on "the real."447 But, despite this decentring, the meaning of what
she finds in reality will always be framed by what came before in the history of her own
development, which does indeed reflect aspects of the history of her culture's evolution
(but only insofar as these have been encapsulated in her education).448
Part 2 of 7: Social Totalities. The meaning of "the whole" in the social, in relation to its parts, has changed many times over the past several hundred years. Piaget notes the shift
from a theological to a naturalistic focus as an example, starting with Rousseau's noble
savage: born free according to nature yet held everywhere by chains of social bondage.449
But this shift also introduced the problematic notion of an innate (and competent)
446 (Piaget, 1950/1995, p. 32) 447 This perspective actually originates in later work (Piaget, 1981/1987, 1983/1987). At the time this essay was originally written, Piaget had not yet realized adolescent thinking is different from operational thinking. This is reported in (Inhelder & Piaget, 1955/1958). 448 (Piaget, 1950/1995, p. 37; see also Burman, 2008b) 449 (Piaget, 1950/1995, p. 39) 163 "human nature" that exists prior to interaction, with social institutions imposing artificial
(and unjust) constraints on the natural rights of those they come to shape.
By way of an historical simplification, Piaget then offers the following progression of forms: from nativist atomism (exemplified in this case by Rousseau) to
Gestaltist emergentism (Comte and Durkheim), and then to dialectical interactivism
(Marx and Baldwin).450 In terms of searching for a sociological approach compatible with the biological and psychological explanations previously reviewed, the third seems to Piaget to be the only extant choice upon which to build. From there, social norms become learned as individual values (social structure reflected in operational structure), with signs and symbols serving as link between the two.451
Part 3 of 7: Synchronic and Diachronic Explanations, Norms, especially when formalized as rules, exist both in the moment (synchronically) and over time
(diachronically). They are reflected structurally in signs, but their meaning is a function of their history. As a result, there must therefore be - Piaget reasons - two distinct kinds of sociological explanation: one synchronic and another diachronic. (Comte, he notes, contrasted a static theory of "order" with a dynamic theory of "progress." Marx,
similarly, proposed a theory of "equilibrium" and another of "evolution.")452 The challenge for theorists, Piaget concludes, is therefore in unifying the two.
450 (Piaget, 1950/1995, pp. 40-41) 451 (Piaget, 1950/1995, pp. 42-47) 452 (Piaget, 1950/1995, p. 48) 453 (Piaget, 1950/1995, p. 51) Piaget's eventual solution to this challenge was to appeal to the hierarchy of levels made possible by Godel's Dialectica interpretation (Chapter III), coupled with the naturalistic mechanism for disproving their "completeness" provided by Waddington's epigenesis (Chapter II). Here, though, he equates the synchronic with implicative explanations ('#' implies 'y following a logical transformation) and the diachronic with causal explanations (V can be shown historically to have caused 'v').454 Hence, norms and their signs are caused to have implications both through the history that provides their context (social) and through how these meanings have been learned (individual).
Part 4 of 7: Rhythms, Regulations, and Groupings. Another point of connection between the sociological, the psychological, and the biological is rhythm. (Rhythm, Piaget notes later in Le Structuralisme, is both structured and structuring—"by virtue of symmetries and repetitions.")455 At each level, the tempo of "production" and "exchange" is driven by a natural beat; change this, and the associated structures re-equilibrate.
The importance of a rhythm of this kind derives from, among others, the following considerations: it is certain that, if such a rhythm were sufficiently modified, in the sense that the generations succeeded each other much more rapidly or much more slowly, the whole society would be profoundly transformed; thus it is enough to imagine a society in which almost all individuals were contemporaries, having experienced little of the family and school constraints which affected the preceding generation and exercising hardly any on the next generation, to see the nature of such possible transformations, especially
454 (Piaget, 1950/1995, pp. 51-56) 455 This comes at the end of the introductory chapter. The full quote is worth reprinting, as Piaget's comments have been made current again by the present interest in the oscillations of brainwave patterns: "Rhythm too is self-regulating, by virtue of symmetries and repetitions. Though the self-regulation that is here involved is of a much more elementary sort, it would not do to exclude rhythmic systems from the domain of structure" (Piaget, 1968/1971, p. 16). 165 in respect of the diminishing influence of 'sacred' traditions, etc.456
Rhythm can therefore serve as an important modifier to the regulation provided by sources of selection pressure. Expectations regarding the reasonable repayment of a debt, for example, allow for the free-flow of capital to meet perceived needs in production.
Small oscillations then result from "errors of prediction" as the structure as a whole corrects itself through the collective actions of many imperfectly-rational individuals.457
(This is the famous "random walk" of Wall Street.)458 Large oscillations, by contrast, reflect a failure of external regulatory structures in sustaining the levels upon which this stable equilibrium is built; at the same time, however, they reflect the emergence of new transitory equilibria as other compensatory structures come into play.459 These structures, Piaget argued in 1950, can then be characterized according to the logic of grouping; as if different species of mind are operating at cross purposes, with the result that the system as a whole becomes disequilibrated relative to its previous stability.460
(The new theory would then later suggest that the foundation had been disproved.)
Part 5 of 7: Real Explanation and Axiomatic Reconstruction. Piaget distinguishes between two methods that are useful in differentiating the causes of these various sources of disequilibration:
456 (Piaget, 1950/1995, p. 57) 457 (Piaget, 1950/1995, p. 59) 458 (see e.g., Malkiel, 1973/2007) 459 (Piaget, 1950/1995, pp. 57-59; cf. Malkiel, 1973/2007, pp. 34-51) 460 (Piaget, 1950/1995, pp. 59-64) 166 One of these methods is real explanation, which puts the operatory aspects of thought or of collective morality in relation to concrete work, the techniques and modes of collaboration occurring in causal actions; while the other aspects of the collective unconscious then appear as being tied to the symbolic interpretation which society offers of its own conflicts. The other method is the formal or even axiomatic reconstruction of the implications involved in operatory mechanisms. Although at first sight this method appears to have little relevance to sociological explanation (any more than the relations between logic and psychological explanation are immediately apparent), in fact it does have a useful role to play, in that it, also, leads to a rigorous dissociation between the ideological and the operatory in 'groupings' of rules.461
The difference here is equivalent to what, in Biology and Knowledge, Piaget would later describe as the examination of functional connections (Chapter II, method 1) and abstract modelling (method 3). He then continues his examination of the history of economic theory following this division.462 In updating this perspective to take advantage of his later work from the transition, however, we can see that the advantage of formalization over "doing a history" is that it enables a test of inferred causes: if the phenomenon to be understood can be imitated in approximation using a formal model, then the factors driving the maintenance of its equilibrium can be differentiated and examined in turn.463
Part 6 of 7: Sociocentric Thought. Between the purely functional thought of tool-use-to- achieve-results (e.g., modelling the behaviour of a stock market to make profits) and the operational thought of scientific calculation, deduction and explanation (e.g., understanding the factors driving this model well enough to predict and explain market
461 (Piaget, 1950/1995, p. 64) 462 (Piaget, 1950/1995, pp. 65-70) 463 In other words, formalization enables the theorist to decentre their examination from the larger social context, thereby increasing the likelihood of producing objective knowledge (cf. Chapter II, method 5). This is the basis for the core criticism upon which (Burman, in press) is based. 167 failures), Piaget argues that there is a third form of thought which occasionally gets in the way:
...the set of collective forms of thought which are neither practical nor operatory, but proceed from simple speculation; these are ideologies of all kinds, cosmogonic or theological, political or metaphysical, which are placed between the most primitive collective representations and the most refined contemporary systems of thought.... While technology and science constitute two kinds of objective relationship between man in society and the universe, ideology in all its forms is a representation of things which centres the universe on the aspirations and conflicts of human society. Just as the advent of operational thought in the individual requires decentration with respect to egocentric thought and to the self... so scientific thought has always required social decentration from ideologies and from society itself, a decentration which is necessary to permit scientific thought to continue the work of technology....464
In other words, the myths and rituals of "the social" intervene between action on the real and one's understanding of it.465 And, just as individual cognition develops in its competence to accurately recall events (Chapter IV), so too do the forms of collective representation evolve in their ability to accurately represent objects of knowledge.
Thus, by an extremely revealing paradox, the process of objective knowledge requires a similar decentration in both society and in the individual; just as individuals become liberated from intellectual egocentrism by becoming conscious of their own point of view and situating it among others, so collective thought becomes liberated from sociocentrism in discovering the ties which bind it to society, and situated itself in the set of relations which link it with nature
(Piaget, 1950/1995, p. 71) (cf. Whitson & Galinsky, 2008) (Piaget, 1950/1995, p. 80) 168 Any adequate sociology of knowledge must therefore take this double-decentration into
account, lest it fall prey to the fallacy of equating the forms of scientific explanation with
those of mysticism.467
Part 7 of 7: Formal Operations and Cooperation. Piaget concludes his essay on
sociological explanation by coming full-circle in his response to Baldwin: How is truth possible if it is not already 'in' the collective understanding? His answer is, once again,
to point to structures: if those individuals party to a collective understanding share the
same logic of order (i.e., they share the same structures of explanation), then new
implications can be brought forward as "discoveries."468 Contradictions between the
implications of contents, produced as a reflection of their organization, then enable
change at the structural level. These too are "discoveries," but of a different kind; these
prove the incompleteness of a structure, then offer a new formulation for consideration.
(Theory '_y' provides a better explanation for V given V than does Theory 'JC' given '&'
for the following 'z' reasons—discuss.) 69 The difference between these two "modes of
discovery" is similar to the distinction Piaget makes between science and philosophy:
science is directed toward discovering "facts" about "reality," while philosophy is
467 (Piaget, 1950/1995, pp. 72-80) 468 (Piaget, 1950/1995, p. 81) 469 The difference between these two "modes of discovery" is similar to the distinction Piaget (1965/1971) makes between science and philosophy. Science is directed toward discovering "facts" about "reality," while philosophy is directed toward producing "wisdom" by organizing these discoveries. The logical framework describing propositions with histories ("relevance" or "relevant logic") is developed in application to the problems described here in (Piaget & Garcia, 1987/1991). directed toward producing "wisdom" by organizing these discoveries into complete and consistent explanations.470
But how do we get there from here? Piaget suggests that the construction of "a logic of order" does not require that the individual members of an ordered collective be capable of "logic" in the formal operational (scientific) sense; it requires only that their interactions be subject to natural rhythms and regulations, which - through the circular reaction, applied to the process of discovery - eventually come to augment the background against which individuals operate.
In explaining the emergence of formal operational logic without it already being
'in' the social structure, Piaget reverts to the language of his response to Kant: formalism emerges as an organizational structure only after it has been constructed in individual action, just like the grasping of space and time as things-in-themselves.
Logic asserts itself, it is true, after a certain level of development, and with the consciousness of necessity, but this is the necessity of a final equilibrium toward which practical and mental coordinations necessarily tend, and not an a priori necessity. Logic becomes a priori, as it were, but only from the time of its achievement, and without having been present from the beginning! Without doubt, the coordinations between actions and movements, from which logic proceeds, themselves rest in part on hereditary coordinations..., but these do not in anyway contain logic in advance: they contain certain functional relations which, once abstracted from their context, are reconstructed in new forms during later stages (without this abstraction from previous coordinations of actions, nor this reconstruction, representing any a priori structure).471
To differentiate the cycle of causes further is impossible, due to the circularity of their construction. That said, however, the logic of formal operations is a "propositional"
"(Piaget, 1965/1971) '(Piaget, 1950/1995,p.82) logic.472 And this, says Piaget (citing the Vienna Circle), makes it a matter of cooperation and subject to acts of communication.473 Thus, since during development self-centric (operational) logic is proved incomplete by the subsequent emergence of socio-centric (propositional) logic, we can conclude that the social "completes" (cf.
Chapter III) the individual in some significant way that then enables it to more fully engage "the real."474
Reality (Culture)
Assimilation Accommodation
Reality (Nature)
Figure 16. My illustration of Piaget's "problem of the social." As the individual decentres her worldview, the world seems to get bigger. But assimilations of this larger world are still conducted through the structures provided by earlier accommodations (i.e., using those aspects of reality that have been inherited to the current perception).
472 (Inhelder & Piaget, 1955/1958) 473 (Piaget, 1950/1995, p. 89) 474 (cf. McGann & Torrance, 2005, p. 184; qtd. in Burman, 2006, p. 117) 171 The Biological Interpretation of the Three Forms of Epistemic Inheritance
In the preface to his repackaged Etudes Sociologiques, Piaget explains that - had he written the essays it collected at the time of their reprinting - his arguments would have been updated to take advantage of more recent work.475 This then becomes the task for
Biologie et Connaissance (1967) and Le Structuralisme (1968). We return first to
Piaget's arguments in the former; then we will continue our discussion by turning to the latter.
The problem with the social, for Piaget, is that it emerges from the coordination of individual actions; it does not "exist" in the same "real" way as nature. (It is a level contingent on the behaviour of those lower level elements which compose it.) As a result
- even though its constituent interactions come to operate as an "organization function," especially as they are institutionalized - cultures reflect shared articulations of individual knowledge, which are in turn built upon foundations inherited from previous generations.
In part six of Biology and Knowledge, to which we now return as the anchor in our continuing discussion, Piaget distinguishes between the three forms such an inheritance could take. Presented more formally, in his language, these are:
1. Innate knowledge and its hereditary instruments, such as that which enables the
seeing of colour;476
2. Constructed logico-mathematical structures, a more formal presentation of the
schematizations discussed in Chapters III-IV; and
475 These comments are dated "April 1965" (Piaget in L. Smith, 1928-1960/1995, pp. 23,27). 476 (example given by Piaget, 1967/1971, p. 266) 172 3. Knowledge acquired through the results of experimental learning.477
We will examine each of these in turn, then we will move to examine how Piaget plans to construct an answer to the question of "how we know" (rather than "how one knows").478
Part 1 of 3: Innate knowledge and hereditary instruments. Piaget is generally reluctant to accept any argument regarding innate capacity: "There are no innate ideas, in the
Cartesian sense."479 (In other words, there is no knowledge without experience.) The reason for this dismissal is the collective weight of his work demonstrating the genesis of the supposedly a priori Kantian categories (see Chapter I). However, he does accept that certain inherited mechanisms - "the brain, the eyes, the hands, and so on" - present a common means by which individuals come to know and adapt to their circumstances.481
(In other words, for Piaget, there are heritable structures, but not heritable contents.) It is in this connection that he describes the perception of three-dimensions in vision and, more generally, the basis for the shared contents of our consciousness: they are enabled and shaped by inherited structures, "our means of action."
477 For a discussion of learning that is consistent with what is presented here, see (Burman, 2008b). 478 The latter problem is the one addressed by his psychological study of the "epistemic subject" (see e.g., R. Kitchener, 1993). Criticisms of the applicability of this model to the study of individuals led to several attempted modifications (e.g., Niaz, 1992). Recently, however, Niaz (1999) has argued that - when the number of impediments is reduced - individual performance does indeed approximate that of the ideal "epistemic subject." This reflects the elimination of the impact of daily hassles on cognition (cf. Janet, 1920/forthcoming; for details on how this shaped Piaget's theory, see Burman, 2007c). 479 (Piaget, 1967/1971, p. 269) 480 (Piaget, 1967/1971, p. 269) 481 The confusion regarding Piaget's position on nativism is made clear in his debate with Chomsky (in Piattelli-Palmarini, 1979/1980). 482 (Piaget, 1967/1971, p. 271) 173 In returning to his historico-critical method, Piaget suggests that the traditional
biological response to this sort of argument is that proposed by the neo-Lamarckians.
Yet he also recognizes that to speak of the "inheritance of acquired characteristics" is
forbidden under the neo-Darwinian explanatory paradigm, as is the "transmission" of
"information" from the environment to the genome.483 Only chance mutations are
allowed, since content and structure are considered to be one and the same. But he is
sceptical about this too:
This theory... leaves out of account the fact that selection itself is not just a matter of sifting through a sieve, through which the mutated organization must either pass or fail to pass. .. .mutationism is led to attribute the organization to chances which are already partly organized and to selections which are themselves controlled, so that there is a perpetual vicious circle. As a result, when those who oppose this doctrine ask how a living being can emerge from a series of lotteries or random groupings based on unorganized matter, or how an organ or instinct can be adapted by chance mutations that usually succeed only in disrupting the living creature rather than enriching it, the mutationist claims to see chance and selection only as positive factors, because he is, without realizing it, setting them 484
in an organization context.
In other words, the mutationist implicitly sees mutations on a background provided by
complete and consistent structures.485 Divergences are therefore from a functional whole; they are not, according to Piaget, truly "random."
In understanding such complex productions as "instinct," the mutationist
approach argues that behaviours arise by chance; that selection occurs after the fact.
(That, for example, birds laid their eggs haphazardly until "a nest" emerged by
483 (Piaget, 1967/1971, pp. 271-273) 484 (Piaget, 1967/1971, pp. 275-276) 485 This also seems to be the lesson provided by the discovery of "homeobox" genes (see e.g., Carroll, 2005). 174 accident.)486 It is clear to Piaget, however, that this is all just a misleading digression from the key point: previous organizations are preserved and selections are of divergences from a foundation provided by a functional level (cf. Chapter III). The set of all possible random events is therefore constrained by a history of workable solutions.487
On this basis, Piaget argues that the advent of population genetics - which, by incorporating the same statistical perspective of species that informed the original arguments in his doctoral dissertation (Chapter II), treats instincts as "transindividual"488
- is a step in the right direction.
Population genetics assumes a level distinct from that of the individual organism.
Under this perspective, evolutionary change occurs at the level of the population, which is in turn composed of individuals who share in "a common 'genetic pool.'"489 This shared resource is the source both of possibility and of necessity: mutations add minor fluctuations, but the system as a whole is auto-regulating through recombination. (The
"pool" is continually repopulated by the next generation, who "filter" it through their
"reaction norms.") The result is stability - of the whole - despite environmental change.
As a result, new possibilities for selection emerge: combinations of otherwise recessive genes have different equilibria than their dominant types.490 This allows sub-species to move into different environments, in turn creating sub-populations with different relative
486 (example given by Piaget, 1967/1971, p. 276) 487 (cf. Schank & Wimsatt, 1986; Wimsatt, 1999; Wimsatt & Griesemer, 2007 ) 488 (Piaget, 1967/1971, pp. 277-278) 489 (Piaget, 1967/1971, p. 278) 490 (Piaget, 1967/1971, pp. 279-280) 175 genetic distributions. Thus, although the environment "selects" the next generation, each new generation could also be said to "select" their environment.
Selection is, in mechanism, a modification of the characteristic proportions of the genetic pool.... Looked at in this way, selection may be "dynamic" or it may again be an equilibration factor, but this time in direct interaction with the environment.... But the main point is to recognize that there are two ways in which to look at selection: from the point of view of the present, concerning survival and genetic homeostasia, and from the point of view of the future of the pool, concerning its plasticity and the range of all possible responses.... Selection, insofar as it modifies or maintains proportions, must therefore be seen from an essentially probabilistic angle. .. .and thus it constitutes an equilibrium mechanism that is both dynamic and synchronic, since here, once again, the essential consideration is the population, not individuals as such. '
In other words, although individuals experience selection pressures throughout their development, speciation occurs across generations and at the level of the population.
And this can be explained in the same way as any other social phenomenon: historically, or through simulations.
From the perspective of how to explain instinct, this shift in thinking toward the probabilistic is critical for Piaget. As a result, useful evolutionary changes become - in a sense - irreversible: once an adaptive mutation spreads throughout the population pool, it is unlikely to disappear completely. Changes leading to "advances" in instincts therefore spread and build upon one another: the formal Godelian system defined by the species' genetic potential is internally consistent (the group can inter-breed), while at the same time it is externally complete relative to the historical demands of its environment.
(Piaget, 1967/1971, pp. 280-281) 176 In extending the implications of this new perspective to the level of the individual, it is clear that there is an interaction between individuals and group. Although the constitution of each individual is "determined" by the group, the future of the group also results from the collective action of individuals. The individuals at one time, ti, are therefore the "cause" of the group at another, t2.492 (In other words, behaviour at ti affects each individual's encapsulation of the overall genetic potential for a future lineage at t2.)
And thus, selection pressures experienced during development have effects on future groups: epigenetic change, and selection at the edge of individual reaction norms, alters the relative distribution of possibility in future generations. Those who can adjust their exposure survive to produce offspring, while those who cannot do not.493 The newly- filtered genetic pool, one generation later, then reflects this selection.494
The earliest example of this process - described in Piaget's early biological work and endorsed by Waddington in 1964 (see Chapter II) - is given by the epigenetic development of the Limnaea pond snail. This comes in five varieties of shell shape, three of which Piaget found to be hereditarily fixed.
492 (Piaget, 1967/1971, pp. 282-283) 493 (Piaget, 1967/1971, pp. 284-287) 494' iPiage t extends this examination into a "speculative" discussion regarding the application of the idea of individual-as-population and the alteration of the expression of various genes, citing both Waddington and Baldwin in footnotes (Piaget, 1967/1971, pp. 285-300). This is irrelevant to our purposes, however, so the details will be omitted. The gist is encapsulated in the narrative above. 177 Figure 17. Waddington's illustration of four of Piaget's five varieties of Limnaea. Piaget's biometrical analyses were based on a ratio comparing the length of the shell with the width of its opening ("relative elongation"). Elongated forms live in still water; shorter forms, in rough.
Yet each of these varieties is also distinguished by the strength of its "columellar muscle."496 Piaget's experiments showed that it is the exercise of this muscle which causes the initial difference in shell shape: rougher waters force juveniles to attach more securely to the pebbles in their environment, increasing muscular tension and resulting in a shortened shell. (The pressure of being pushed up against a pebble then also increases the size of the aperture further.) But it is a subsequent migration that leads to the hereditary fixation of the shortening.497 As a result, the various sub-populations live in slightly different environments, overlapping in the larger lakes.498
Making the connection back from snails to children, a recent monograph proposed a post-Piagetian view of development that looks very much like the distribution of
Limnaea through the Swiss alpine lakes.
(Waddington, 1973/1975, p. 93) (Piaget, 1967/1971, pp. 301-304) Additional details in (Piaget, 1974/1980a) (Piaget, 1967/1971, p. 301) 178 Younger Older Age
Figure 18. An illustration of the "overlapping waves" model of development.499
Here, instead of "age" of children and "percent use" of strategies, we see the different varieties of Limnaea coping with different depths and turbulences of water. (Different
"species of mind" distributed according to where they fit, relative to how they have been affected by historical selection pressures.) Where two "strategies" coexist at one age in this more recent model of child development, we can also see that two varieties could coexist at the same depth in Piaget's older model of snail adaptation. And this parallel can be made because, for Piaget, the explanations of the changes are for both groups isomorphic.500 Both have mechanisms that are auto-regulating: each group equilibrates to fit the demands of the environment.
(Siegler, 1996, p. 89) This is later formalized as the theory of "the phenocopy" (Piaget, 1974/1980a, 1975/1995). 179 Part 2 of 3: Logico-mathematical structures and their significance. In Piaget's
explanation of the biological roots of cultural knowledge, logico-mathematical structures
sit midway between instincts and experimental learning. But they are not intuitively-
friendly as a concept.501 (Indeed, Jerome Bruner's scepticism resulted in their being left
out of the American popularizations of Piaget's theories; see Chapter II.)502 Upon first
encountering "number," for example, the assumption is that it is a property of the objects
described. This, however, is deceptive. An example provided to Piaget by one of his
friends, who became a mathematician on the basis of this realization, makes the point:
When he was a small child, he was counting pebbles one day; he lined them up in a row, counted them from left to right, and got ten. Then, just for fun, he counted them from right to left to see what number he would get, and was astonished that he got ten again. He put the pebbles in a circle and counted them, and once again there were ten. He went around the circle the other way and got ten again. And no matter how he put the pebbles down, when he counted them, the number came to ten.... But how did he discover this? .. .Is it true that the pebbles, as it were, let him arrange them in various ways; he could not have done the same thing with drops of water. So in this sense there was a physical aspect to his knowledge. But the order was not in the pebbles; it was he, the subject, who put the pebbles in a line and then in a circle. Moreover, the sum was not in the pebbles themselves. The knowledge that this future mathematician discovered that day was drawn, then, not from the physical properties of the pebbles, but from the actions that he
Several eminent commentators have been confused by them. This includes Howard Gardner, who constructed an entire educational metaphysics on the basis of what appears to be a misunderstanding. 502 Piaget explains: "...we should mention the fact that, especially in America, our kind of structuralism is not unanimously endorsed. J. Bruner, for example, does not believe in 'structures' or in 'operations'; in his view, these are constructs ridden with 'logicism' which do not render the psychological facts in and of themselves. He does not credit the subject with cognitive acts and 'strategies'.... Bruner tries to account for the intellectual growth of the child in terms of the way in which he meets conflict among the various modes of representation at his disposal—speech, images, action-schemes themselves. But if each of these models furnishes him with an incomplete and sometimes even distorting perception of reality, how can he resolve such conflicts unless he appeals either to some 'copy' of reality or to 'structures' as described by us, as coordinations of all instruments of representation?" (Piaget, 1968/1971, p. 72). 180 carried out on the pebbles.
The realization of "number," in this example, is reflective of the proto-mathematician's
abstraction of a logico-mathematical structure which supervenes upon all countable sets.
It is a constraint that the elements of any such set must obey, no matter the
transformation. And it is this quality of "necessity" that gives the structure its properties.
On this account, "logico-mathematical structures" are not content; they are rather
content-holders. (We saw this in our discussion of the role of schematizations in
memory, in Chapter IV.)504
In addition, logico-mathematical structures can also be understood as a response to impositions by the social group: a downward "organization function" that brings order to interactions as well as to thought (cf. hierarchical levels in Chapter III). But they
might be more appropriately understood, following Piaget's earlier unpacking of the
organism's position within their own population, as a capacity of group-oriented
individuals.505 In short, building on the above example: nature presents a countable set of pebbles, which is then organized and given a label-of-practice ("ten") that will apply
irrespective of who counts them or how—so long as they follow the same practice. The
From a lecture delivered at Columbia University in 1968, published (Piaget, 1970/1971, pp. 16-17) 504 Indeed, logico-mathematical structures are the main feature examined in Conservation Tasks: Volume is constrained by height, width, and depth, so an amount of water moved between two containers of different size is necessarily the same. If a child recognizes this, then they are deemed able "to conserve." 505 (Piaget, 1967/1971, p. 307). The contemporary version of this proposal is known as the "social brain hypothesis" (see e.g., Dunbar & Shultz, 2007). This posits that the cause behind large brains is the increasing demand placed on the mind by ever-larger social circles. However, as we saw in the essay on sociological explanation, this is potentially distracting: the social completes the individual, making more complex forms thought possible. (There is therefore a balancing of complexity across levels.) The difference between these two positions will have to be examined in greater detail in future research. 181 label reflects the structure-in-action: a sign. Yet its full meaning also presupposes the
completion of a developmental trajectory: learning how to reason with numbers (as
opposed to performing "counting"), which involves the same processes as learning to think and to remember (see Chapter IV).
Infants are not constrained by such "relations of necessity" in their thinking, but
adolescents are.506 (For an adolescent, something is necessarily so as a consequence of
its being in relation to other things; for infants, by contrast, there is only "the feeling.")
Adolescents' orientation toward "meaning through implication" is therefore grown into.
At the same time, however, learning the use of number-as-a-cognitive-tool goes beyond
"ordinary learning mechanisms."507 The experience of number is not of the objects'
content (exogenous), but of the operations that can be performed upon them
(endogenous) and what those operations then imply.508 During development, the location
of this necessity is shifted from the self-experienced qualities of external objects to
internally-reconstructed relations (following "decentration").509 Until this internal
structure is abstracted, however, quantity is experienced as a function of the objects'
grouping in terms of size and spread: more because bigger, not more numerous. (Until new containers are constructed, objects are interpreted through instinct; bigness heuristics, not "number.")
506 This theme is revisited in detail, as it relates to the problem of what constitutes "the real," in (Piaget, 1983/1987). 507(Piaget, 1967/1971, p. 309) 508 (Piaget, 1967/1971, pp. 310-311) 509 Piaget later uses this term explicitly: "experimental action is oriented... in the direction of logico- mathematical decentering, whereas the error or subjective illusion corrected by such experiment is brought about by centering upon immediate appearance" (Piaget, 1967/1971, p. 337). 182 Logico-mathematical learning also differs from instincts and experimental learning in that its structures are neither inherited nor discovered. They are not found in the subject or in the world; they are "invented" as an abstraction of previous interactions, but not by way of reduction.510 Citing Godel with approval once again, Piaget argues that the solution to a problem with no answer (i.e., no endogenous response-function) cannot be derived from existing structures. It must be invented:
In order to establish non-contradiction, one has to go beyond the limits of the system and integrate it into a "stronger" one.... In other words, the development of a structure cannot be made entirely on its own level, by mere extension of given operations and combination of known elements; the progress made consists of the construction of a wider structure, embracing the former but introducing new elements.511
In other words, in application to the development of cognitive structures, each stage
"subsumes" the previous one while progressively widening the subject's exposure to external selection pressures.512 Past constructions thereby lay the foundations of present
510 Piaget purposefully uses "invented," rather than "created" (Piaget, 1967/1971, p. 440/318). A related idea was proposed by Jerome Bruner - concept attainment through induction (Bruner, Goodnow, & Austin, 1956) - but this proposal is much more reductionist: an a posteriori search for exemplary attributes (cf. T. S. Kuhn, 1970). Piaget's more prospective version, introduced here as "reflective abstraction" (Piaget, 1967/1971, p. 320), was formalized as part of his new theory (Piaget, 1977/2001). However, he later unravelled some aspects of his explanation (Piaget et al., 1990/1992), which remain unresolved and thus this aspect of the new theory remains open to future researchers. 511 (Piaget, 1967/1971, p. 319) 512 This language is explicit, both before and after the transition (e.g., Piaget, 1950/1995, pp. 35, 48; Piaget & Garcia, 1983/1989, pp. 10, 225; see also commentary by Smith in Piaget & Smith, 2004/2006, p. 11). He adds, in Structuralism: "progress in [science] never takes the form of simply 'adding on' new information—new discoveries M, N always lead to a complete recasting of preceding knowledge^, B, C while leaving room for some future discovery of Q, R, S; ...even in physics attempts to reduce the complex to the simple... lead to syntheses in which the more basic theory becomes enriched by the derived theory, and the resulting reciprocal assimilation reveals the existence of structures as distinct from additive complexes" (Piaget, 1968/1971, p. 45). 183 necessity, while at the same time enabling possibilities in future constructions.513 In this way, such structures are - in short514 - the cognitive instruments of auto-regulation.
Part 3 of 3: Acquired Knowledge and Physical Experimentation. In learning through experimentation, knowledge is acquired of the object from responses made by the object; the information derived is not solely a function of the subject's act, but of the qualities of the object and its reactions to that act. Such learning is externally-focused, even as it is internally-driven and -organized.515 Also, while the initial cause of this learning can be either instinctual or reflexive, any resulting "content" is ultimately contained within a logico-mathematical framework. As a result, perceptual qualities are never just "read off' of- or, as Baldwin had it, "copied from" - an object. But objects are necessary, even if only to serve as a core to the abstraction of number and mathematics.516 (Indeed, no cultural structure can exist meaningfully outside each individual's conception of it; meaning must be constructed, practiced, and communicated.)
The philosophical results of scientific experimentation - formal logical or mathematical models - are therefore consistent with the world as a result of their nature as abstractions.517 To the degree that such descriptions are a complete reflection of the world, they predict what can be observed. To the degree that they are incomplete, further
513 These are examined in (Piaget, 1981/1987, 1983/1987). 514 (Piaget, 1967/1971, pp. 322-333). The speculative language in this section is formalized in the experimental studies performed during the "new theory" period. 515 (Piaget, 1967/1971, p. 334; cf. Gibson, 1979/1986) 516 (Piaget, 1967/1971, pp. 334-338). 517 (cf. Piaget, 1968/1971, p. 5) 184 experimentation helps to refine them. This explanation of the genesis of knowledge is not Lamarckian, nor is it Darwinian; learning is not a copying of the environment, nor
SIR does it involve random change. It is, Piaget argues in offering this new sort of explanation, an internal reconstruction by an actively-engaging subject. But how is this
shared as a cultural norm? How does such learning shield the next generation from disequilibrating selection pressures? Simple: Humans, like pond snails, build structures that protect them from the pressures of their "milieu."519
Le Structuralisme
Piaget's choice of title for the third of his forgotten transitional books — Le Structuralisme
(translated simply as "Structuralism") - is deceptive, as its intent was not to extend his theory into social anthropology. Rather, following the same historico-critical method that characterized his return to biology, Piaget presents and synthesizes the various then- contemporary approaches to explaining "cultural meaning" as a way to narrow in on a definition of the problems to be addressed by his own future research.
Fundamental to this volume is Piaget's differentiation of the three forms of knowledge presented in Biology and Knowledge: innate knowledge and hereditary instruments, logico-mathematical structures, and experimental learning (reviewed above).
But, as is immediately clear from the title, "structures" play the key role. Following the
(Piaget, 1967/1971, pp. 341-342) The use of "milieu" here reflects the corrected usage discussed in Chapter IV. 185 lessons he drew from the experiments reported in Memory and Intelligence (reviewed in
Chapter IV), his basic approach is simple:
I think that all structures are constructed; the basic fact about them is the process of their construction, and at the beginning nothing more is "given" than some few points that support the rest. But structures are not given in advance, neither in the human mind nor in the external world as we perceive and organize it. They are constructed by the interaction between the individual's activities and the object's 520
reactions.
The logical starting point for his discussion is therefore to define what he means by
"structure" in a cultural context. Prior to this, his meaning has been focused on their use by individual subjects: a structure is an auto-regulatory construct, produced during interactions as an endogenous abstraction that addresses the demands of external selection pressures while at the same time organizing future interactions and serving as a lens to interpret their results. Here, in application, Piaget widens the meaning as it takes shape as an inherited (not instinctual nor innate, but still reflexive) organizational form.
Reading Guide and Exegesis
Structuralism opens with an attempt at synthesis: all the varieties of "structuralism" - mathematical, linguistic, psychological, and philosophical - have aspired to "an ideal of intelligibility," Piaget says.
.. .once we focus on the positive content of the idea of structure, we come upon at least two aspects that are common to all varieties of structuralism: first, an ideal (perhaps a hope) of intrinsic intelligibility supported by the postulate that structures are self-sufficient and that, to grasp them, we do not have to make
From an interview conducted in May-June 1969, published in (Bringuier, 1977/1980, p. 37; cf. McGann & Torrance, 2005, p. 184; qtd. in Burman, 2006, p. 117). 186 reference to all sorts of extraneous elements; second,.. .to the extent that one has succeeded in actually making out certain structures, their theoretical employment has shown that structures in general have, despite their diversity, certain common and perhaps necessary properties.521
In other words, to use some of the language developed in previous chapters, a structure is an axiomatic522 system of lawful transformations. As a result, like algebra, its productions will always be internally-consistent. Structures are therefore to be distinguished from "aggregates," which are not subordinated to a single set of laws (i.e., aggregates are not part of a single relational whole).524
The auto-regulatory nature of wholes implies a constant structuring, as a dynamic process, rather than just "the state of being structured."525 We saw in Chapters III & IV that this structuring could span across several levels. Here, Piaget begins to formalize what this means in greater detail. But it will not be necessary to review every example;
521 (Piaget, 1968/1971, pp. 4-5) 522 Piaget uses this word later in the text, just prior to returning to his discussion of Godel: "More explicitly, the basis of such an axiomatic system consists of (1) certain primitive or undefined conceptions, which serve to define the rest; (2) certain axioms or undemonstrated propositions, which serve to demonstrate the rest. The undefined conceptions are primitive or indefinaWe and the undemonstrated propositions axiomatic or indemonstraWe within the particular system under consideration, but they may well turn up derived in some other system" (Piaget, 1968/1971, p. 29). 523 Indeed, the use of such Godelian language is warranted by Piaget's continued citation of his work: "Godel's conception of a structure's relative 'power' or 'weakness' introduces a genealogical relation among structures which provides a method less open to epistemological objections. But once we take this tack the central problem, not as yet of the history or psychogenesis of structures but of their construction, and of the relation between structuralism and constructivism, is no longer avoidable. This will, then, be one among our several themes" (Piaget, 1968/1971, p. 13). He continues in this vein: "the transformations inherent in a structure never lead beyond the system but always engender elements that belong to it and preserve its laws.... It is in this sense that a structure is 'closed,' a notion perfectly compatible with the structure's being considered a substructure of a larger one; but in being treated as a substructure, a structure does not lose its own boundaries [cf. Chapter IV]; the larger structure does not 'annex' the substructure; if anything, we have a confederation, so that the laws of the substructure are not altered by conserved and the intervening change is an enrichment rather than an impoverishment" (Piaget, 1968/1971, p. 14). 524 (Piaget, 1968/1971, pp. 7-9) 525 (Piaget, 1968/1971, pp. 10-16) 187 our earlier reference to his story about the abstraction of "number" from a group of
similar elements, differently arranged, will be sufficient to make the point.526 (Arranging a single set of pebbles into many different smaller piles - following the variety of their shapes or colours or textures - allows for the construction of "sub-groups" organized under the "parent structure" of number, each of which in turn exists separately from the operations used to alter their "membership" or "order" relations.) The abstraction of the structure-of-the-whole is made possible by counting's fundamental incompleteness as a performance; it is internally-consistent, but also incomplete relative to the abstraction of the set of real numbers. This incompleteness is proved by the selection pressures imposed by the necessity of re-performing a counting every time a count is required (such as after an exchange), rather than abstracting a number from an operation.
(Understanding that "20 goats less 2 goats leaves 18 goats" is much simpler than having to recount the herd after every transaction, especially as the counts get higher.)
When changes occur within a structure - according to Piaget, in this new formulation - it is not a matter of shifting description, but of altering cause. (Either there are more pebbles, or fewer goats, or not.) Measurements are therefore of the real, even if conducted through an external theory of measurement.527 Knowledge, as a result of the
526 The discussion of how the theory of mathematical groups underlies algebra, and in particular the history of the Bourbaki Collective (Piaget, 1968/1971, pp. 17-28), is beyond the scope of this thesis. However, it is clear that Piaget's transitional studies of "identity" could be incorporated here comfortably, as he used the results of his historico-critical review of structuralism to inform that research (see Piaget et al., 1968). This later work is property part of the new theory, however, and it is clear from the present text that it is directly related to the ideas that would eventually be discussed in (Piaget et al., 1990/1992; cf. Piaget, 1968/1971, pp. 27-28). 527 (Piaget, 1968/1971, pp. 37-38) 188 implications of its structures on real contents, is therefore an open but still-logical system:
it is consistent and complete, but only relative to how its results have been "tested."
(Eventually, a "count" will have to performed as a check on "number"—an "audit.")
Yet, in this sense, such explanations are still more than merely descriptive.
Causal explanation requires that the operations that "fit" the real "belong" to it, that reality itself be constituted of operations. Then and only then does it make sense to speak of "causal structures," for what this means is the objective system of operators in their effective interaction.... Languages are not in the habit of forecasting the events they describe; rather, it is a correspondence of human operations with those of object-operators, a harmony, then, between this particular operator - the human being as body and mind - and the innumerable operators in nature—physical objects at their several levels.528
To phrase this differently, following our earlier example, the ways in which "number" is constructed tracks the ways in which causes can be attributed in providing explanations: the elements of the organized group of pebbles, and the methods used to arrange them,
"causes" - in the sense that it constrains, but does not determine529 - the abstraction of their "number." As Piaget puts it, in more formal terms, "its general coordinations involve certain elementary structures sufficient to serve as a point of departure for reflective abstraction and, eventually, more complex constructions."530
There is no Bergsonian "vital essence" driving change, here; in social exchange, there are only individuals and the institutions that organize them.531 Similarly, at the level of individuals, there are only structures and the transformations that enact them.
"Emergence" is therefore a problem, not a solution (as initially suggested by Baldwin's
My italics on "the real" are used only to simplify reading (Piaget, 1968/1971, pp. 40-41) 9 (cf. Neta, 2008) 0 (Piaget, 1968/1971, p. 44) '(Piaget, 1968/1971, p. 117) 189 application of the circular reaction). But auto-regulation, in the form of both homeostasis and homeorhesis, operates across all levels of the total structure: through its openness to inputs, an organism (or a culture) can be self-maintaining. And the ways of this self-maintenance - its transformative operations - are its ways of making meaning.533
To make his point, Piaget returns to psychology, where the most easily recognized structures are "the Gestalten" and their "fields." (A Gestalt is a perceptual whole, such that the experienced quality of its field of effect is preserved even after a change; popular melodies, for example, are felt to have the same overall effect even after a key-change.)
Yet, as Piaget explains, the approach to such structures by Gestaltists betrays a kind of essentialism:
...the psychological Gestalt represents a type of structure that appeals to those who, whether the acknowledge it or not, are really looking for structures that may be thought "pure," unpolluted by history or genesis, functionless and detached from the subject.534
Meaning is taken to be "in" the Gestalt, rather than being a consequence of the relationships between its elementary parts and how they are enacted operationally as a group-in-experience.535 Piaget suggests instead that the meaning of a Gestalt is in how its forms are transformed by the active perceiver; that its "correctness" is a function of auto- regulation by the subject, not the imposition of an innate essential "field."53
532 (Piaget, 1968/1971, pp. 46-47) 533 (Piaget, 1968/1971, p. 48) 534 (Piaget, 1968/1971, p. 55) 535 (Piaget, 1968/1971, pp. 56-57) 536 (Piaget, 1968/1971, pp. 57-60; cf. Piaget, 1961/1969) 190 In application to Piaget's own approach to developmental and child psychology, this proposal reverses the direction of necessity. Because reflective abstraction is a fundamentally creative process - and because auto-regulation works to preserve only those structures with functional significance - necessary relations become an outcome of learning, rather than their precondition.537 Inherited reflexes and memories still ground the whole affair, of course, but the results of attempts at meaning-making are constrained only by what has been learned before.538 The abstraction of new "levels," such as learning the use of language in orienting to the world, enables the "projection" of earlier- learned elements to form new functional structures.539 These then enable still-newer forms of organization, but not in the sense understood of "goal-directed" learning;
Piaget's is therefore a view of learning as "vection," or "progress from" (cf. Chapter
II).540 What is socially acceptable as an outcome - given that it is the individual who is active in learning - then serves as a source of selection pressures, disequilibrating
"illogical" and "unfit" structures that are nonetheless produced-in-abstraction.541
This top-down imposition from group to individual (by individuals) is made clearest in the examination of language. Indeed, even its rules are composed of structures with a history: each element in the linguistic group is related to an earlier form, which existed in its own context and which in turn was related to a still-earlier form in another.
' This is examined in more detail in (Piaget, 1981/1987,1983/1987) 538 (Piaget, 1968/1971, pp. 62-63) 539 (Piaget, 1968/1971, p. 64) 540 See also my commentary in (Burman, 2007b, 2008b) 541 (Piaget, 1968/1971, p. 66; see also Piaget, 1932/1932) 191 Language, in other words, is a long lineage of interrelations; arbitrary signs learned by
each generation and imposed on the next as an "indispensable instrument of thought."5 2
Piaget suggests that the most influential description of this organization was provided by Saussure, who - as was mentioned in Chapter II - distinguished between
synchronic and diachronic dimensions of linguistic change. Although Saussure's usage
of these concepts was narrower than Piaget's, since his conception of language did not
include an explanation of its genesis, his theory still implies an equilibrated whole—its productions are internally consistent.
Chomsky's "transformational-generative" theory added a diachronic component to Saussure's basic approach, while at the same time preserving its auto-regulatory aspects.543 But this, Piaget says, is deceptive: Chomsky's structures are still innate to the individual, as evolved functions of reason.544 Acts of social creativity are therefore only departures from a pre-existing linguistic Gestalt; novelty through error and irrationality.545 Despite its erroneous nativism, however, Piaget argues that the use of
Chomsky's methods to examine the grammatical structures constructed by children - which clearly show how different they are in their thinking from adults - highlights the need for the preservation of Saussure's separation between langue (social language) and
542 (Piaget, 1968/1971, p. 75) 543 (Piaget, 1968/1971,p. 81) 544 Chomsky (1979/1980) accepts this label. 545 (Piaget, 1968/1971, pp. 82-83) 192 parole (individual speech). The basic developmental problem thus remains, to which
Piaget responds simply: "epigenesis."547
As we have discussed previously, Piaget's interpretation of epigenetic theory involves an interaction between selection pressures and functional levels of various plasticities. (Pressures are accommodated at a higher level before the remainder is
"transmitted" to a lower one.) In specific application to his perspective of the structuring of individual intelligence, it is clear also that language plays a key role as a source of high-level pressure.548 Linguistic formalism - langue - structures thought, while competence at language in its performative aspect -parole - is itself the result of a structuring of thought: what a child says, to herself or to others, is a function of how she thinks. And this, as we saw in Chapter IV, is in turn predictive of performance in memory tasks: how she thinks shapes what she will remember. But how can the source of this structuring best be characterized at a socio-cultural level? How can language be understood to shape memory and intelligence? To answer these questions, Piaget turns to the structuralisms of social science.
Piaget distinguishes between two structural approaches in the social sciences:
"analytic" (e.g., Levi-Strauss) and "global" (e.g., Durkheim).549 In the latter, structures
"emerge" in the manifestation of phenomena; while in the former, they "underlie" to cause them. At the same time, however (and irrespective of the approach), all structures
546 (Piaget, 1968/1971, p. 85). The translator, strangely, rendered these in English without keeping the original terms. 547 (Piaget, 1968/1971, p. 89) 548 (Piaget, 1968/1971, p. 94) 549 (Piaget, 1968/1971, pp. 97-98) 193 are logico-mathematical abstractions. They are therefore not "facts" to be discovered, like the physical existence of Piaget's mathematician friend's pebbles; they are
"organizations," like the forms into which the pebbles were ordered.
The social structure, like causality in physics, is a theoretic construct, not an empirical given. It is related to the observable social relations as, in physics, causality is related to physical laws, or as, in psychology, psychological structures do not belong to consciousness but to behaviour.55
Only when these organizations are formalized at a new causal level, as institutions, do they become "fact-like." But, even before this, their cultural reality exerts selection pressures on the ideas of developing individuals; a new epistemic pathway laid down that operates on the individual, projected down from the level of the collective.551
In searching for an example to make his point, Piaget locates such a proposal at the intersection of psychology and sociology: Talcott Parsons' structural-functionalism.
Parsons' way of linking functions to values should be taken very seriously. In the social context, structures, no matter how "unconscious," express themselves sooner or later in the form of norms or rules to which individuals are, to a greater or lesser extent, subject. Now, however, convinced one may be of the permanence of structures themselves... the rules generated by them can nevertheless change their function, as is shown by changes of value; values do not, of themselves, have "structure," except precisely to the extent that certain forms of value, such as moral value, are based on norms. Value seems, then, to point up a distinct dimension, the dimension of function; thus, the duality and re-
550 (Piaget, 1968/1971, pp. 98-99) 551 Here, Piaget adds some thoughts - expanded upon by the translator - about Kurt Lewin's topological psychology and the application of Gestalt field theory to social relations (Piaget, 1968/1971, pp. 99-101). He doesn't endorse it, though: "Unfortunately, the psychological topology is not really mathematical, that is, there is not one known topological theorem that can be given a direct psychodynamic interpretation; nevertheless, the basic topological conception of a purely qualitative analysis of spatial relations does find application. Lewin offers his topological analysis as determining possible 'movements' or 'paths.' To account for the subject's actual behavior the concept offeree, hence of 'vectors,' must be introduced. This utilization of physical concepts has the great advantage of making field diagrams applicable to dynamic psychology and of suggesting network structures" (Piaget, 1968/1971, p. 100). 194 established interdependence of value and norm seem to testify to the necessity of distinguishing and connecting structure and function.
Similar, too, is the structuralism of economic theory: Piaget notes the early emphasis on equilibrium, followed by a shift to a focus on business cycles between "displaced" equilibria. But the value in markets is driven by feedback (individual action), not self- regulation (structural form). For this, there is only the Law and the norms it imposes on those who choose to participate. Economics therefore only presents a piece of the puzzle. It is rather in Anthropology that these social structures can be examined in their most elementary forms. Here, Piaget unpacks his earlier distinction between Levi-
Strauss' "analytic" and Durkheim's "global" approach.
Levi-Strauss' structures are different from Piaget's in that they are "neither functional, nor genetic [constructed], nor historical."554 But they are similar in that they both insist on the primacy of the individual over the social: "Behind the 'concrete' social relations there is always 'conceptual structure.'"555 Both Levi-Strauss and Piaget also reverse the causal direction of meaning-making found in Durkheim's theory: theirs are constructed bottom-up from the experiences and interests of the individuals in a social group, rather than emerging top-down as a consequence of the essence of the group itself.
Despite the similarities, however, Piaget does not see a way to coordinate Levi-Strauss' social-anthropological structuralism with his own biological and psychological constructivism: the problem with adopting an apparently synchronic presentism in one's
552 (Piaget, 1968/1971, pp. 102-103) 553 (Piaget, 1968/1971, pp. 104-105) 554 (Piaget, 1968/1971, p. 106) 555 (Piaget, 1968/1971, p. 107) 195 method, he says, is the setting up of an inherent conflict with the diachronic. Yet if structures are permanent and invariant, as Piaget suggests is the case in Levi-Strauss' analyses,556 then that methodological problem largely disappears: since nothing ever changes, diachronic mechanisms are unnecessary. It is rather Levi-Strauss' lack of functionalism that Piaget finds most troubling: "one thing is clear, in biology and psychology structural analysis must... be supplemented by functional considerations."557
In moving beyond Levi-Strauss (although we will return to him later), Piaget recalls the conclusions of his recent studies and makes a key observation about his basic mechanism - auto-regulation, in the form of equilibration - across functional levels.
...once it is recalled that every form of equilibrium is definable in terms of a "group" of "virtual" transformations and that a state of equilibrium must always be distinguished from the process of equilibration, the processes whereby equilibrium becomes established in these increasingly complex systems account not only for the regulations characteristic of each level but even for the form which these regulations take at the final stage [of cognitive development in adolescence], when they become "reversible operations." The equilibration of the "cognitive" and the "practical" functions contain all that is necessary for an explanation of the rational schemata: a system of lawful transformations and an opening to the possible.... From this perspective, there is no longer any need to choose between the primacy of the social or that of the intellect; the collective intellect is the social equilibrium resulting from the interplay of the operations ceo
that enter into all cooperation.
This is Piaget's solution, in outline, to the problem of cognition: intelligence "is the equilibrated form of all cognitive functions,"559 including emotion.560 And although life is generally not "intelligent," per se, its "vital processes" are equilibrated in the same way (Piaget, 1968/1971, p. 108) (Piaget, 1968/1971, p. 109) (Piaget, 1968/1971, pp. 113-114) (Piaget, 1968/1971, p. 114; see also Piaget, 1975/1985) (Piaget, 1973a, 1954/1981) 196 as the intelligence comes to be structured.561 In short, Piaget's reply to Baldwin is to posit equilibration within levels and between them, both up and down the great chain of being. Even the symbolic function of language, Piaget suggests (following Saussure), has not always been as it is today: the causally-connected "index" became the motivated
"symbol," which then became the arbitrary "sign."562 As such structures are institutionalized and stabilized (e.g., in the kinship systems examined by Levi-Strauss), they begin to take on a reality separate from the individuals who enact them: they become part of the environment into which children grow, as a source of constraint - inherited necessity and obligation - in structuring thought.563
Where Piaget sees potential, as he lays the foundations for his future research, is in Foucault. Les mots et les choses (translated as The Order of Things) is described as
"dazzling" and "brilliant."564 But it is also lacking in three important areas:
What we would want of Foucault is... that he prepare the way for a second Kant to reawaken us, along with himself, from dogmatic slumber. In particular, we would expect the author of a work with such revolutionary intentions to offer a constructive critique of the human sciences, an intelligible account of the new fangled notion of episteme [a more general version of Kuhn's "paradigm"], and an argument that would justify his restrictive conception of structuralism.565
Piaget's disappointment with the treatment of "episteme," in particular, is almost poignant:
His concept of episteme looks promising at first; it seems to call for some sort of epistemological structuralism, which would be very welcome. Foucault's
561 (Piaget, 1968/1971, p. 114; see also Piaget, 1974/1980a) 562 (Piaget, 1968/1971, p. 115ff; see also Piaget in Piattelli-Palmarini, 1979/1980) 563 (Piaget, 1968/1971, p. 117) 564 (Piaget, 1968/1971, p. 128) on (Foucault, 1966/2002) 565 (Piaget, 1968/1971, pp. 129-130) 197 epistemes do not form a Kantian system of a priori categories, for, unlike Levi- Strauss' human reason, they are neither necessary nor permanent; they simply follow one another in the course of history. They are not systems of observable relations resulting from intellectual habits, nor are they constraints upon thought in general which somehow become manifest at a given moment in the history of science. They are "historical apriorities," [which] like Kant's transcendental forms "conditions for knowledge" but, unlike these, [provide] conditions which apply for only a limited period and which, when their vein has been exhausted, yield to others.566
In short, Foucault's weakness - for Piaget - is his lack of a comprehensible method.
There's no logic underlying the structure of its revolutions.567
His epistemes follow upon, but not from, one another, whether formally or dialectically. One episteme is not affiliated with another, either genetically or historically. The message of this "archaeology" of reason is, in short, that reason's self-transformations have no reason and that its structures appear and disappear by fortuitous mutations and as a result of momentary upsurges. The history of reason is, in other words, much like the history of species as biologists conceived of it before cybernetic structuralism.... To call Foucault's structuralism a structuralism without structures is, accordingly, no exaggeration.
Despite this, however, Foucault does eventually receive Piaget's endorsement—
"Foucault's corrosive intelligence has performed a work of inestimable value: that of demonstrating that there cannot be a coherent structuralism apart from constructivism."569
As this concludes the volume, one is left with the sense that Piaget's future research will
566 This difficult passage (Piaget, 1968/1971, pp. 111-112/131-132) is made more complex by the translator's loose rendering of the source, coupled with an apparent reluctance to re-punctuate as necessary. 567 Piaget compares Foucault's epistemes to Thomas Kuhn's paradigms (Piaget, 1968/1971, p. 132), but concludes Foucault's would be the more useful conception if only there were a method behind them. For more on Piaget and Kuhn, see (Tsou, 2006; Burman, 2007b). 568 (Piaget, 1968/1971, p. 134) 569 (Piaget, 1968/1971, p. 135) 198 incorporate aspects of Foucault's episteme into a constructive theory of knowledge that operates simultaneously at several levels.570
Recapitulation
Piaget's message in Structuralism is simple: structures constrain possibilities by positing as axiomatic certain necessities.571 Yet how this has been used and understood across the various disciplines touching on the problem of social knowledge is anything but simple.
His anthropological reply to Levi-Strauss and Durkheim, in this regard, is the most cogent:
Structures are not simply convenient theoretical constructs; they exist apart from the anthropologist, for they are the source of the relations he observes; a structure would lose all truth value if it did not have this direct connection with the facts. But neither are they transcendent essences.... The recurrent formula [for Levi- Strauss] is that structures "emanate from the intellect," from the human mind as ever the same; this is why they are prior to, rather than, as Durkheim would have it, derivative from the social order; prior to the "mental" as well... and, a fortiori, to the "organic".... But what manner of existence is left, then, for the mind, if it is neither social, nor mental in the subjective sense, nor organic?572
To this question, Piaget ultimately provides the answer we deconstructed in Chapter IV: the mind exists at one of the many levels of undergoing constant adaptive change. It is both constrained and it is constraining. During development, low-level structures are entrained to those demands of the higher. In addition, higher levels exist because past
570 Two such levels - child development and progress in science - are examined in (Piaget & Garcia, 1983/1989) 571 This is taken up again during the new theory (Piaget, 1981/1987, 1983/1987) 572 (Piaget, 1968/1971, p. 112) 199 constructions have enabled them, yet at the same time they also enable. The mind is therefore much more than an epiphenomenon of the larger system in which it participates: it is a causal force, but only insofar as it can abstract meaning from the extant selection pressures. In this, the mind is unique; no other level has such intentionality. None but the individual level affords choice. (This is discussed in greater detail in Chapter VI.)
Reception and Errata
Of the three transitional "forgotten works," Structuralism is the most popular by far. (In the process of researching this chapter, I found no fewer than eight book reviews published in scholarly journals.) Although included in a series composed primarily of short general introductions to the titular topic, two reviewers noted explicitly that such a description is misleading in this case.574 They argue that presenting Piaget's work as an historical review of the varieties of structuralism is too simplistic: "an adequate understanding of many of Piaget's arguments requires a good deal of familiarity with original sources."575 Indeed, many reviewers missed its nuances. But not all of them; its lessons were also eloquently described.
Piaget showed that (1) the elementary cannot be equated with the fundamental; (2) fundamental structures need to be constructed, by a transformation of elementary structures; (3) this transformation lies outside the internal power of
573 There is an educational imperative implied here, which is taken up in several of Piaget's writings (Piaget, 1930-1976/1998). My own perspective, developed in the process of researching and writing this thesis, is outlined in (Burman, 2008b). 574 (Berringer, 1971, p. 1124; Bloch, 1972, p. 331) 575 (Berringer, 1971, p. 1124) 200 elementary structures [cf. Godel], and therefore can only occur through a synthesis between them in a process which is both dialectical and diachronic [i.e., abstracted through reflecting abstraction]; (4) two types of transformations must be distinguished, those within a structure [learning], and those from one structure to another [development].576
What this summary misses, however, is the levels model articulated in Chapter IV: elementary structures exist below the level of fundamental structures, which in turn exist below synthesized structures. (The process of abstracting from one level to the next is formalized during the new theory, which we will examine briefly in Chapter VI.) The translation error that likely led reviewers astray, on this point, is discussed in the Errata of
Chapter III: replacing "stage" with "story" - thereby suggesting something closer to a narrative (rather than logico-mathematical and, in the larger context, evolutionary- developmental) cause for the existence of Levi-Strauss' kinship relations - dramatically weakened the strength of the formal argument Piaget sought to endorse.
Another reviewer focuses on aspects of the work which, in hindsight, can be seen to foreshadow some of the newest elements of the new theory:
The essence or nature of structures is discovered or formed from the notion of categories. Categories are classes which comprise 'functions' and therefore 'morphisms' (forms), among their elements.... Our understanding of anything is dependent on our being aware of the different categories, being able to make distinctions and recognize relations; this lies at the root of all knowledge.577
This reflects the return to that which originally inspired Piaget's psychological research: not only his biology, and its first failed application in philosophy (Chapter II), but also his critique of Kant (Chapter I). However, this "new" position also relies on our
(Harvey, 1968, p. 460) (Berenson, 1973, p. 106; see also Piaget et al., 1990/1992) 201 important secondary narrative: Godel's demonstration of the necessity behind
constructing and maintaining categories (Chapter III).
While there were no other clear instances of meaning loss in the translation, there were many divergences with implications that go beyond the aesthetic. For instance,
difficult passages that derived their meaning from earlier in the lineage of Piaget's work were occasionally made more obscure in an attempt to make their language simpler;
failures to re-punctuate where necessary also make the text more challenging that it ought to be. That said, the text's only serious error - with no close parallel in the original -
leaps from the page:
He [Foucault] has no canon for the selection of an episteme's characteristics; important ones are omitted, and the choice between alternative ones is arbitrary. Furthermore, heterogeneous attributes which happen to be found together in the same historical period, though they really belong to different levels of thought, are treated as of one kidney [sic].578
A more internally-consistent rendering of the same passage in the original source provides the following:
Two dangers were then inevitable [as a result of Foucault's lack of method]: first, the characters attributed to an episteme acquired an arbitrariness, with some qualities being selected over other possibilities and still others omitted in spite of their importance; and, in the second place, historically-contemporary properties pertaining to different levels of thought became "merely heterogeneous."579
My emphasis of the translated passage in (Piaget, 1968/1971, p. 133) 79 The original gives the following: "Deux dangers etaient alors inevitables : en premier lieu I'arbitraire dans les caracteres attribues a une episteme, les uns etant choisis a la place d'autres possibles et certains omis malgre leur importance; et, en second lieu, I'heterogeneite desproprietes supposees solidaires, mais appartenant a des niveaux differents depensee quoique historiquement contemporaines" (Piaget, 1968a, p. 113). 202 In the original, the task for Piaget's subsequent "new theory" is made clear: to provide a method for the selection of mutually supporting epistemic possibilities, while preserving the developmental necessities that ground each individual as they grow into the larger context. Yet, perhaps because the volume was read as a stand-alone text, this task goes unnoticed by the myriad reviewers who took on its challenges.
Prospective Conclusion
With the conclusion of this chapter, the arguments of the three "forgotten works" of the transitional period have been fully reviewed. All that remains is for them to be synthesized and integrated with the history of how Piaget developed his new theory.
That is accomplished in the following chapter, which concludes this project.
203 CHAPTER VI
CONCLUSION
This thesis began with an extended example. By way of a first approximation of the larger explanation developed through its five chapters, this example offered a common narrative: as each child navigates the challenges of their childhood, sometimes with joy and occasionally with frustration, they grow up and became "adult." The meanings brought to each moment of this journey - the highs and lows - are provided by family:
...each family dynamic has a "logic" into which the actions of the developing child must fit. Part of this logic is given by the location (house, flat, hut, or cave), and part is given by the personalities of the parents, friends, neighbours, and acquaintances who collectively define the social context. This context is in turn maintained and reinforced with a language. This is also a reflection of the logic. There is, in short, a "way of being" that "makes sense" in some self-consistent way—as "norms" and "customs" (i.e., as "culture").580
The frustrations of childhood are therefore a result of chaos (the child) running headlong into order (the logics of reality and culture), but not knowing why it is so. These logics must be learned; they must be approximated through the construction of an internal logic.
The claim throughout this thesis has been that children not only develop in context, but also that it is this context which shapes how they come to know: that learning is a kind of development, which can alter the effect of evolutionary selection pressures.
Piaget's most famous contribution was simply to show that this occurs. He
See supra Chapter I 204 demonstrated, through innumerable studies, that children are different from adults and that these differences follow patterns common to all cultures.
Piaget found that the contextual logic of the environment has a counterpart in the individual: a developing "psycho-logic" of transformation, according to which the child comes to order ("see" and "understand") the different aspects of its environment in increasingly complex ways.581
This was the basis for his stage theory of development, but also much more. It was upon this foundation that Piaget built his evolutionary-developmental theory of the genesis of knowledge: an embryology of mind, building on ideas that emerged following the modern synthesis of evolutionary biology (which conceived of change as resulting solely from the natural selection of randomly-mutating genes) and extended out to become a kind of embryology of knowledge.
This theory has two distinct incarnations: the "old" and the "new." The former was itself informed by an earlier theory - James Mark Baldwin's "genetic epistemology"
- and shares many of its features, including its name and a reliance on what Baldwin called "the circular reaction."
See supra Chapter I 205 Brain (Equilibrating)
Assimilation Accommodation of the object by of the scheme to the scheme the object
Reality (Nature) Rea lity (Culture)
Figure 19. My illustration of Piaget's take on Baldwin's circular reaction, from Chapter II.
The latter theory, by contrast, was left incomplete when Piaget died. Here, it has been called "epigenetic epistemology."
The label I have adopted for the new theory takes advantage of a pun on the prefix epi-, which means "beyond" or "over," while at the same time referencing the framework
Piaget uses to replace Baldwin's explanation for the genesis of knowledge: epigenetics.
The new theory therefore not only goes "beyond" the constructive theory that led to stage theory in psychology, but it also builds upon theoretical advances in biology that go
"beyond" the genome in describing the emergence of individual adults from their inherited genes. (Piaget was able to do this by following a trend in how theories are constructed, arguing that scientific descriptions for child development should have the same structure as descriptions of the development of embryonic organisms.)
But while the attribution "new" is relatively uncontroversial, because the theory certainly is different, the proper dating of the transition from "old" theory to "new" is 206 critical. The scholar who suggested that the theory promulgated in Piaget's last works be thought of as "new," Harry Beilin (who died after only a few brief consultations), suggested that the point-of-inflection occurred in 1974. Unpacking this proposal led to a check against Piaget's own comments, followed by an examination of the assumptions upon which the suggestion was based. The result was the delimiting of a "transitional period" between the "old" theory and the "new," which contained the three "forgotten works" that became the core of this thesis.
In examining the articles and books that informed these "forgotten works," it became clear that the transitional period was the result of a process that began in the
1960s. It was at this time that Kurt Godel's important proofs of the incompleteness of formal systems were given a new interpretation and that Conrad Waddington endorsed
Piaget's early results in biology. In addition, American educational reforms created a surge of interest in Piaget's work among English audiences. These three events together led to the divergence in theory that Beilin saw as resulting in the emergence of something new.
The dramatic increase in interest in educational policy ensured that the Piaget whose work got popularized was "the old" Piaget (the one whose work had already been translated). As this importation was underway, however, the lessons inferred from these early works were being re-examined by their author: Godel's new interpretation provided
Piaget the means to update his oft-criticized conception of "groups" (groupements), while
Waddington's endorsement gave him the opportunity to revisit his earliest ideas about the
207 reality of species and of society. The resulting ideas then became the basis for new psychological studies, as well as for a renewed look at the importance of context in learning and development. As a result, the famous stage theory of development was given a new reading.
Piaget's earlier findings regarding cognitive development can be interpreted either as illustrating the fulfillment of a progressive sequence of predetermined stages (recapitulation), or as indicating an underlying constructive process of transformation: the infantile stage of sensorimotor action either leads to or enables a childhood stage of pre-operational semiotic-linguistic representation, which in turn is either followed by or makes possible the early teenage stage of propositional implications. And while this could be a purely maturational process, the developmental delays manifest among those lacking normal experiential abilities (e.g., blind people) suggests a different interpretation.582
How the theory evolves from here into the "new theory" is largely a matter of details.
These will be reviewed below, starting with a summary of the preceding four chapters.
Review of Core Themes
Part 1 of 4: The Return to Biology. Waddington's endorsement of Piaget's early work led to a "return," not only to those ideas of his doctorate in biology but also to the interests that originally led him to consider pursuing a second doctorate in philosophy.
The results of this return were first presented systematically in 1967, in a book titled
Biologie et Connaissance (translated as Biology and Knowledge).
Biology and Knowledge begins by re-presenting Piaget's early constructive mechanism (Baldwin's circular reaction) as fundamental to all processes of change:
See supra Chapter II, Part 1 of 4 208 "autoregulation," which he also refers to elsewhere - more simply - as "equilibration."
This is the core assumption behind Piaget's theory: all life, and all of the phenomena associated with life, is characterized by the seeking of stability-through-equilibrium.
Piaget argued that this mechanism is just as central to explanations of child development as it is to those of embryogenesis and the evolution of species: external perturbations are accommodated in such a way as to return the system to a dynamic form of stability.
Waddington illustrated this as a landscape, with a marble that rolls through the valleys of development and responds to perturbations (selection pressures) by changing its path.
Figure 20. Waddington's illustration of the "epigenetic landscape," from Chapter II.
Piaget described the feeling he had in hearing and reading Waddington as one of
"euphoria."585 The reason, as I have shown, is that Waddington's work enabled Piaget to
583 {see esp. \Piaget, 1972 #712; Piaget, 1985 #83} 584 See supra Chapter II, Part 1 of 4, cites (Waddington, 1974/1975, p. 259). 585 See supra Chapter II, Part 1 of 4. 209 return to the issues that had led him to psychology in the first place: the search for a science of knowledge. Yet he tempered this excitement with a review of the various methods that could be used to ground any resulting investigations in scientific rigour.
To achieve his goal, Piaget reviewed the history of the use of biological metaphor in psychological explanation, rejected a number of failed approaches, and concluded that the most fruitful for his purposes would be to examine the relationship between the organism-as-subject and the objects to be found in its environment. He then suggested that this relationship could be examined using six methods:
1. Examining functional connections, by tracing information flows as external
stimuli are transformed by actively-engaging subjects.
2. Examining structural isomorphisms, in the sense of comparing related structures.
3. Examining the results produced by abstract models, such as in cybernetics (and, in
Chapter V, economic forecasting). This would allow changes in structure
(method 2) to be examined for changes in function (method 1).
4. Examining the groupings (later, levels) of results produced by models, but
through comparison rather than a potentially endless search for first causes.
5. Examining the structures of the groups (levels) to ask what can be known, given
what the model seeks to reproduce.
6. Examining the implications of theories drawn from outside psychology, and
particularly from biology, for psychological phenomena.
210 Collectively, these provide the methodological foundation for all work conducted by
Piaget and his collaborators into the 1970s and beyond.586
Following these methods (but particularly method 6), and with a view to explaining the development of knowledge, Piaget then examined the history of explanations regarding "genesis." This led to a similar examination of conceptions regarding the origins of thought. The two were then synthesized via Godel, whose work is examined in Chapter III (and summarized below in Part 2 of 4), to provide a conception of change through levels: a new formulation for stage theory. Piaget followed this with another history of the ideas that could explain such a progression, concluding with an endorsement of post-neo Darwinian evolutionary-developmental theory: augmentative change is subject to the pressures provided by context.
From here, the link back to Piaget's work on child development - and our extended example - is obvious: the family environment provides the selection pressures that lead to the construction of structures to anticipate their effects, which then (if successful) later become part of the culture of families as a whole. But how does
"progress" in this development occur? To find an answer, Piaget once again reviewed the history of related ideas; he mined past explanations, searching for a parallel to use in his own theory. He then concluded not only by endorsing Waddington, but also suggesting that Waddington's style of post-neo Darwinian solution is the only kind that really makes sense. Thus, for Piaget, progress is movement through a lineage given a
586 A short list of some of the works written by Piaget's collaborators has been provided by the Piaget Foundation: http://www.fondationjeanpiaget.ch/tjp/site/bibliographie/index_livres articles_ls.php 211 history-in-context ("vection") while at the same time the opportunities to experience selection pressures are increased. "Higher" stages are therefore those that are "more open" to challenge than "lower" stages, while still remaining stable (equilibrated). What this means is made clear is Piaget's arguments regarding the "function" of "structures."
Part 2 of 4: An Important Secondary Narrative. In the old theory, a structure was a
"group"—an organized totality, like a species, in which parts could be translated without affecting the whole. During the transition to the new theory, however, the "group" was replaced with "levels." This was accomplished through a series of appeals to Kurt
Godel's proof of the incompleteness of formal systems.
There are two phases in Piaget's appeals to Godel's proof, with a discontinuity corresponding to the publication in 1958 of a paper known commonly as "the Dialectica interpretation." But Piaget never seems to cite this directly. Rather, he cited a French- language commentary published in 1960. And it is there that we see what it was in
Waddington's work that likely excited Piaget:
...it provides an evolutionarily-sound means by which "true statements" (adaptive groping) can be distinguished from the unfit and irrational, as well as a means according to which "theorems" (behavioural responses) can be described as COT
originating in a formal system.
In other words: if a proposition is not dis-equilibrating of anticipation (i.e., it is expected), then it is explainable within the existing structures (i.e., it is a theorem of the system's axioms). If it is dis-equilbrating, however, then the system is proved incomplete; 587 See supra Chapter III, Part 2 of 3. 212 attempts are then made to abstract a new level at which completeness can be demonstrated.
In short, for Piaget, Godel provides a formal justification for developmental change that goes beyond the recapitulation of evolutionary history.... [I]n Piaget's interpretation, it follows from Godel's result that development is the means by which organisms respond to perturbations that prove the incompleteness of their genomic axioms. To ensure survival in the next generation, the inheritance of past adaptive solutions is necessary but not sufficient; survival requires the construction of levels intermediate between the genome and the adult body.588
This affords a result that can be easily synthesized with the interactive, cybernetic perspective that Piaget came to favour.
epigenetic environment phenotype space P space I?
Figure 21. Waddington's illustration of the construction of phenotype from genotype is reminiscent of the neural networks examined by Piaget's group in Geneva, in which selection pressures have different weights in responding across levels.589
It also leads Piaget to suggest an interesting reversal in the direction of "deduction."
Instead of deducing downward, from valid premises to a conclusion that follows from them necessarily (as in syllogistic reasoning), Piaget uses abstraction from incomplete axioms to reflect upward to the next more complete level in the formal hierarchy....590
! See supra Chapter III, Part 3 of 3. ' (Waddington, 1974/1975, p. 255; cf. Cellerier et al., 1968, p. 98) ' See supra Chapter III, Part 3 of 3. 213 This reversal then also provides the basis for his eventual formalization of "reflecting
abstraction" (discussed below).
Part 3 of 4: The Development of Things to Think With. Piaget suggested that this
"upward deduction" could be characterized in six different ways:
1. As a reflection of the continuity and conservation of function across levels.
2. As a reflection of the forms of organization taken on by these conservations.
3. As a reflection of the relationships between the parts, relative to the whole.
4. As a reflection of the hierarchy of levels deduced.
5. As a reflection of the real structures involved in the organization of levels.
6. As a reflection of the traits shared by these structures.
These share obvious similarities with the six methods previously delimited. But what is most interesting is what they imply for his equilibration model: change occurs through levels, with disequilibration "transmitted" both down through the levels until the next generation (when it is projected back up).
214 genotypes of generation n THE EXPLOITIVE SYSTEM
\ THE GENETIC SYSTEM reproduction
genotypes of generation » +1
Figure 22. Waddington's illustration of the levels of action in selection, from Chapter IV.591
As an organism explores the world, if a perturbation is not resolved at the behavioural level then it is "transmitted" down a level and comes to perturb the physiological systems upon which this behaviour relies. If this perturbation continues to remain unresolved following developmental change, then it is once again "transmitted" down a level and comes to affect the genes inherited by the next generation as a populational whole
591 See supra Chapter IV, Organization Functions, which cites (Waddington, 1959/1975, p. 57; reprinted in Waddington, 1961/1975, p. 274) 215 (following Darwin's formulation for natural selection). In that next generation, changes in distribution at these lower levels are then projected back up through the hierarchy to affect possibilities as a new group of individuals begins to explore its environment.592
This Godel-inspired reading of epigenesis is reflected in the style of Piaget's histories. In the material covered in Chapter II, for example, his focus was on the evolving structure of biological explanation, not on "the facts" as discovered. He follows the same pattern in reviewing the social theories discussed in Chapter V: the focus is on
"explanation" and how to construct a good one given the extant context. In Chapter IV, however, this is turned into a testable hypothesis: if memory is like a "retroactive explanation," then changes should be observed in testing a child's recollection over time.
The null hypothesis examined is simple: If memory is not driven by the development of the same structures as intelligence, and it is just a copying of objects external to the subject (i.e., if memory is an "unconscious picture"), then there will be no improvement in memory with development. This, surprisingly, was easily rejected.
Contrary to popular opinion, Piaget and his colleagues found that the developing structures of intelligence do indeed play a key role in memory. Memory can therefore be thought of, in a sense, as a "reconstruction of the observed data" (as if the child's recollection of the world were being projected through the developing structures of their mind).
Indeed, this is the basis for Piaget's later "phenocopy" proposal (see e.g., Piaget, 1974/1980a; 1975/1995; cf. Gottlieb, 2000). 216 Indeed, children above a certain age seem to "learn" without direct exposure; their "memory" gets better over time. In short, when "recall" is reconceptualised to include an active process (rather than passive reception and reproduction), the larger role of operational schemas becomes clear: the developing "lens" (structure) through which a problem is perceived is also that through which it is reconstructed (as function). If this lens changes during development, then so too will the reconstruction.593
More important than this to the larger goal, however, was the finding that these results on the development of memory could be characterized in the same hierarchy of complexity as could "explanations" in the history of biology. Not only did this replicate
Piaget's earliest findings - age-correlated groupings conceived as different species of mind - but it also supported the new Godel-inspired levels-framework.
The new framework justifies Piaget's move away from "stages" as a metaphor toward a more dynamic, constructive conception of development. As I put it in Chapter
IV:
...the complexity of a child's recall reflects the complexity of their schematizations; "stages" are a merely descriptive conceit, sitting atop a functional (causal) substructure.594
But this set of experiments increased the rigour of his investigation by only so much;
Piaget's "euphoria" had to this point only been partially controlled. For his framework to be completely acceptable given the methods outlined at the outset, external sources of selection pressure would have to be describable in terms similar to those used to explain the internal construction of functional structures—social evolution would have to be
See supra Chapter IV, Study 2 of 3. See supra Chapter IV, Study 3 of 3. 217 describable in terms similar to that of learning and development. Then the whole thing
would need to be formalized in a model; its predictive functions tested against reality.
Part 4 of 4: The Evolution of Things to Reflect On. Piaget began this next phase of his
research by arguing for the importance of the social in studying the genesis and
acquisition of knowledge.
Just as the child decentres during development to become less self-centric, so does she become more socio-centric. Only later will she decentre once again, to transcend the pseudo-necessities imposed by her own belief and begin to focus instead on "the real."595 But, despite this decentring, the meaning of what she finds in reality will always be framed by what came before in the history of her own development, which does indeed reflect aspects of the history of her culture's evolution (but only insofar as these have been encapsulated in her education).596
In other words, the process of learning "true knowledge" requires first that the child become social, and then requires that she become independent. Building on the emerging
levels model, this "double decentration" is necessary because the social affords better
approximations of reality than would be possible to acquire alone starting from a position
of ignorance. But then, once armed with a first approximation of truth, further individual
exploration enables the refutation of socially-imposed conjecture. And this, argued
Piaget, is the common driver of all change: exploratory behaviour.597 Simply put:
Without actively engaging and exploring the world, one's approximations of its "truths"
595 This actually comes from later work (Piaget, 1981/1987,1983/1987). At the time this chapter was originally written, Piaget had not yet realized adolescent thinking is different from operational thinking. This is reported in (Inhelder & Piaget, 1955/1958). 596 See supra Chapter V, Part 1 of 7 597 (Piaget, 1976/1979; see also Burman, 2007a) 218 cannot be relied upon to exclude the pernicious effects of prejudgement, speculation, or ideology.
Reality (Culture)
Assimilation Accommodation
Reality (Nature)
Figure 23. My illustration of Piaget's explanation of the development of knowledge, including the effects of the social, from Chapter V: social conjectures are tested against reality.
With the psychological aspects of the social explained to his satisfaction, Piaget then turned to conceptions of its evolution as a structure-in-itself (a "total structure" or
"structure of the whole").
A social structure is, at base, a shared psychological structure. This can result from shared instruments (e.g., ears, eyes, and hands), from shared abstractions (e.g., signs, language, and institutions), or from shared experiences (leading to inferences like "glowing red means hot!"). In formalizing the relationships that occur between subjects and the shared objects of knowledge, with a view to making them more intelligible, a variety of "structuralisms" have emerged. In Piaget's examination, the variety proposed by Levi-Strauss bears the brunt of the criticism.
Despite the similarities... Piaget does not see a way to coordinate Levi-Strauss' social-anthropological structuralism with his own biological and psychological constructivism: the problem with adopting an apparently synchronic presentism in one's method is the setting up of an inherent conflict with the diachronic.599
The conception Piaget seeks is one that includes both function and structure, across synchronic and diachronic dimensions, while at the same time offering a single mechanism that operates at all levels. Although this is constructed following the publication of the forgotten transitional works, as part of the new theory itself, the process will be examined briefly below.
Misunderstanding Structures
In 1972, Piaget received the Erasmus Prize for his "exceptionally important contributions to European culture." The following year, Levi-Strauss received the same honour. This provided one historian, Jacques Grinevald, with an irresistible opportunity:
This is perhaps an occasion for bringing up once again the controversy which you began, perhaps indirectly, with your little book, Structuralism, in which you criticized Levi-Strauss for working with too static a view of the human mind—for not having emphasized its self-constructive nature, the self-construction of cognitive functions.600
See supra Chapter V, The Biological Interpretation of the Three Forms of Epistemic Inheritance See supra Chapter V, Le Structuralisme: Reading Guide (Grinevald in Piaget & Grinevald, 1973/1983, p. 73) 220 Piaget's response to this question will be examined below in Part 1, with Levi-Strauss' reply reviewed in Part 2. Through the synthesis of their positions, after addressing the fundamental misunderstandings, we will then be led to the core of Piaget's new theory.
Part 1 of 2: Piaget on Levi-Strauss. Grinevald's interview was conducted in Geneva in
December 1973, after the translation of Structuralism but before the appearance of the first of Piaget's "new theory" works. During their conversation, Piaget suggests that his purpose was not to criticize Levi-Strauss, but rather to draw him out of "his splendid isolation." The problem, however, is that the response Piaget received did not address the issues he had hoped to have answered:
...to my great surprise, he [Levi-Strauss] replied very favourably. But The Naked Man [volume four ofIntroduction to a Science of Mythology] is not really an answer. It is more a misunderstanding.601
Piaget's purpose was rather to draw Levi-Strauss' attention to the problems posed to conceptions of the social by his studies of development.
When one first finds a culture, new to the investigator but having its own history, the initial problem is to find the sources and structures of meaning in daily interaction.
For this, Piaget accepts, questions regarding development are unnecessary: a synchronic perspective provides much-needed insights. But, as he had previously pointed out, meaning is also contingent upon how these sources and structures came to have their meaning; one therefore needs to examine the diachronic in addition to the synchronic.
Both quotes from the same paragraph in (Piaget & Grinevald, 1973/1983, p. 74) 221 (In other words, one must decentre oneself from one's initially synchronic perspective to examine the larger structure as a whole and thereby construct a more complete understanding of the culture as a thing-in-itself.) This seemed, to Piaget, to be the point
Levi-Strauss misunderstood.
His criticism of history - history does not explain itself, history is an effect, etc. - all that was a kind of criticism of the developmental point of view. And then, most important of all, the idea to which he returned again and again in his previous works was that of an unchanging human mind. The structure of the mind was given and considered to be similar at all levels and in all civilizations.602
The result is that - in Levi-Strauss' opinion, Piaget suggests603 - either peoples are innately competent in the same way we are, or they are not. (They are human, or not.)
This is the sort of innate essentialism that Piaget argued against his entire career.
From Piaget's perspective, in contrast to Levi-Strauss', it is unproblematic to assert that there must be a progressive development in the structuring of thought.
...mine are successive levels. The idea of the prelogical is completely acceptable when it is considered as a kind of... progressive construction. A level is considered pre-logical when the thinker is not at the following stage.604
Indeed, Piaget predicts that there should therefore be whole peoples who do not - in practice - reason from a series of hypotheses to a set of necessary conclusions irrespective of whether the original hypotheses are true.
They know how to class, how to seriate things, they know how to orientate themselves in space. In other words, they are capable of all concrete operations. But I am convinced that they are not capable of formal reasoning. That is to say, a
(Piaget in Piaget & Grinevald, 1973/1983, pp. 73-74) (Piaget & Grinevald, 1973/1983, p. 75) (Piaget in Piaget & Grinevald, 1973/1983, p. 74) 222 reasoning independent of content.1
Yet Piaget also points out that whether such a prelogical people could be found is not for him or Levi-Strauss to conclude deductively; the issue is one to be settled through empirical investigation—proper scientific hypothesis testing (i.e., a formal investigation irrespective of whether the hypothesis is true).606
On most other dimensions, however, Piaget and Levi-Strauss do seem to agree.
Their method is similar, even if their interpretation of the results is different.
I remember very well that during a seminar which Levi-Strauss gave long before he was elected to the College de France, even before he was elected secretary of the International Association of the Social Sciences, he held a seminar at the Hautes Etudes to which I was invited to speak on the thought of children. I drew up a structural table of the groups of concrete operations and of the groups of four transformations at the formal level. Levi-Strauss was surprised to see how much our methods converged. He told me, "That is exactly what I do in anthropology."
The overlap is interesting. Yet the key question here, for our purposes, is whether we can use it. (This can be found in whether, and how, Levi-Strauss agreed with Piaget's characterization of his work.)
Part 2 of 2: Levi-Strauss responds. In his response, given to Grinevald in an interview conducted in Paris in December 1981, Levi-Strauss makes the point that - despite the
English subtitling of his multi-volume Mythologiques as an Introduction to a Science of
Mythology - his purpose was never intended to produce a "science."607
605 (Piaget in Piaget & Grinevald, 1973/1983, p. 74) 606 (Piaget in Piaget & Grinevald, 1973/1983, p. 75) also points to work on the Arountas of Australia that supports his perspective, but without referencing a specific source. 607 (Levi-Strauss & Grinevald, 1981/1983, p. 82) 223 I am not scientific for I do not consider ethnology a real science from what I have been able to glimpse of the scientific method, yet it has provided me with great intellectual stimulation.
For this reason, Piaget's criticisms were directed toward an otherwise productive explanatory metaphor (i.e., Levi-Strauss followed method 1 but not method 3). They are therefore deemed interesting but irrelevant.609 In addition, despite the intervening years, he is surprised that his own earlier criticisms of Piaget's general orientation had remained unaddressed:
I was surprised to discover that he [Piaget] remained faithful to the positions for which I [Levi-Strauss] had criticized him in the past: the belief in a parallelism between an individual's cognitive development during childhood and the development of thought in human history. As if a certain equivalence, a certain correspondence, existed between what happens in the first few years of a child's life and what the study of people without writing reveals to ethnologists. Piaget continued to consider this parallelism a given. And of course, an ethnologist cannot agree.610
But, as we have seen, his criticisms were addressed. The parallelism is not a result of a recapitulation in childhood of the species' evolution; rather, it is one of inventing structures that are complete relative to how they have been tested.
The point of contention is the apparent invisibility of Piaget's updating of his groupements and their replacement with a Godelian conception of levels within which organization is consistent and complete. From this newer perspective, it may be possible to find some common ground. But, even still, their disagreement was not total.
608 (Levi-Strauss & Grinevald, 1981/1983, p. 81) 609 This seems a particularly weak response, however, given that Piaget's own theory began the same way and only later shifted toward an analysis of causes. But perhaps future research could offer a more charitable interpretation of his meaning in this interview. 610 (Levi-Strauss & Grinevald, 1981/1983, p. 83) 224 Piaget generously refers to a seminar that I remember having organized.... He showed us a structural table of concrete operational groupings as well as his famous group of four transformations [the groupements replaced with levels]. However, I do not remember having said as he reports.... It seems more likely to me that I said, or ought to have said, "That's exactly what I find in myths!" And in fact, understanding is more likely that. It is less a certain formulation of the external world, because relations with the natural world in these societies are not the same as in ours; their technology, their needs, do not require their intelligence to be used to such an extent as we would. Instead, intelligence is used in mythical thought, less consciously on the one hand, more freely on the other, in order to spontaneously engender variations on myths which are, from the beginning, the products of the individuals who recount them. In any case, it is by means of individuals that myths are perpetuated and transformed. It is in this area that I find the closest similarity to the mental operations defined by Piaget.611
In this overlap of their two positions - a turn toward the tools used for "understanding," in both children and cultures, rather than the developing structure of thought itself512 - we immediately see the relevance of the experiments reported in Memory and Intelligence: how you think (function) is a reflection of how you assimilate reality, whether it be through instinct, memory, or using cultural tools (structures). And it was in fact an examination of this theme - success and understanding,613 but not learning in general (as
Beilin had originally suggested) - that then launched the "new theory" in 1974.614
611 (Levi-Strauss & Grinevald, 1981/1983, p. 83) 612 (cf. Gardner, 1972, pp. 203-205) 613 (Piaget, 1974/1978) 614 Beilin's dates are somewhat deceptive: as Ducret (2000) notes, the projects that were published starting in 1974 were actually begun in 1968. (See the full list of "new theory" works in Ducret, 2000, p. 22; for the dates of English translation, see Piaget & Smith, 2004/2006, p. 2.) 225 Organizing the Structures of Functioning615
Piaget ultimately came to describe the final Eureka-inducing stage of "understanding" as a kind of awakening into the world: a flash of insight regarding organizing structure, leading to "truer" reconstructions of the object-in-experience.616 (This goes well beyond standard conceptions learning.) The notion was then further developed in the theory of
"reflective" or, depending on the translation, "reflecting abstraction" (/ 'abstraction reflechissantef11—the cognitive motor driving the feeling of what happens when we understand, but which also leads to the production of novel behaviour.618
Traditionally a difficult concept to understand, the significance of "reflective abstraction" is that solves the problem of converting action into operation; somatic seed into mental root. Yet part of the challenge in approaching it results from a long delay in the emergence of the related ideas: as we have seen, Piaget only began to formalize his
Some of what follows in this section has been revised from a version appearing in (Burman, 2008b) 616 (Piaget, 1974/1976, 1974/1978; cf. Ploran et al., 2007) 617 As Campbell notes in the introduction to his translation, there are several different similar terms at work here: "reflective abstraction" is the standard presentation of the constructive mechanism; "reflecting abstraction" is that process as it occurs (and thus what Piaget studied in his experiments); "reflected abstraction" is the product of its occurrence, which then becomes available for comparison; and "metareflection" is reflection upon the process or comparisons. That said, however, Piaget doesn't provide a simple explanation of the underlying mechanism; the process, as presented, is metaphorical. Yet this can be remedied, at least in part, by comparing it with the perspective offered by Zelazo (2004). Building on contemporary research regarding the development of executive function, yet still informed by constructivist theory, Zelazo's new model provides a gentler introduction to the notion of reflection and abstraction through levels of consciousness. Although different from Piaget's theory in many respects, it is similar in that it is based on a related approach to cognition and is oriented toward uncovering the same functional processes (P. D. Zelazo, personal communication, 16 August 2007). The significance and added complexity of Piaget's original presentation then comes as a result of its application beyond the individual to the development of knowledge in general. As a result, further alignments between these two approaches - as we extend our growing awareness about the brain and how it comes to know something about anything - will offer enormous opportunities for enhancing value in those areas currently touched upon by research in applied psychology. 618 (Piaget, 1977/2001; but see also Piaget et al., 1990/1992) 226 framework after he had returned to update the underlying biology. The presentation
was also made more complex, in English, by a quirk of the French philosophical
tradition: an apparent pun62 on reflexion and reflechir ("to reflect"), intended to mean
both mirroring (which the translator renders "projection") and cogitation (rendered
"reflection") in a two-part process of construction.621 These steps are not new to the
theory, however; they are merely variations on the theme of assimilation and
accommodation—moments in the construction of knowledge through experimentation.
Before a new knowledge structure can be constructed, the disequilibration caused
by anomalous stimuli is "transmitted to" - which, following the explanation of Baldwin's
circular reaction (Chapters I-II), Piaget's levels model (Chapters III-V), and the
contextualization of Piaget's pun (above), can now be rephrased as "mirrored at" - a higher, but structurally-isomorphic level of cognitive processing (e.g., by realizing that
'x' and 'y' belong to a unified coordinate system instead of existing as unrelated
(starting in a talk given in 1965 1967c; then followed by three books, published in 1967/1971; 1974/1980a, 1976/1979) 6201 am indebted to Tyson Gofton (personal communication, 16 February 2007) for noting that the conflation of the two by English readers is probably not the product of a rare moment of literary flamboyance - a Piagetian "play on words," as the translator suggests (Campbell in Piaget, 1977/2001, p. 4) - but is rather the result of a fundamental incommensurability between English and French philosophy: meaning loss, resulting from the incomplete transmission of a theoretical construct ("to reflect") from one context to another. 6211 wished to make the further terminological distinction here, in addressing any potential misunderstandings, because - although it has been similarly translated elsewhere (e.g., Piaget, 1973b, pp. 81-82) - "projection" implies something more active in English than what it appears Piaget intends. Just as concepts imply their opposites as a natural consequence of their existence, so too can they be mirrored at various "levels of consciousness" (cf. Zelazo, 2004, pp. 15-16). Thus, "projection" does not require an intentional act, but is rather a natural consequence of what it means "to reflect" (see also the discussion in Kessen & Kuhlman, 1962, p. 165). In other words, for Piaget, the intended meaning is logico- mathematical; it has the same sense as our mapping of 'x' onto the domain of 'y,' in which 'x' is "projected" onto 'y' as a sort-of pseudo-empirical abstraction, with results to be filled in later (see the section, below, on dialectics). 227 domains). At this higher level of abstraction, where related conceptual schemes can be assimilated to each other (such as through the use of a shared metaphor or mathematical equation), a new set of more complex syntheses can be produced "intensionally" that then enable various effects of previously-disequilibrating stimuli to be accommodated by the new whole (i.e., as a result of "cogitation"). The result - for new observations - is an increase in "information" derived from basic stimuli, coupled with a decrease in the
"data" required to produce a perceptible signal.622 (In other words, just as the behavior of
'y' can be mapped onto the domain of 'x,' so too can the predicted behavior of 'x' be mapped onto the domain of 'y,' which yields new opportunities for observation in both domains that can serve to verify the total synthesized structure and which can then itself be abstracted and acted upon.)
2 In addition to its grounding in history and theory, this interpretation is also supported by recent neurological findings. First, the prefrontal cortex - the area implicated in Zelazo's (2004) model - appears to be responsible for the change in strategies required of reflective abstraction (Passingham, Toni, & Rushworth, 2000). Second, novel stimuli require a large amount of cortex to process, but experience and training slowly reduce this amount (Little, Klein, Shobat, McClure, & Thulborn, 2004; Goldberg, 2005). Third, findings collectively labeled the "Wisdom Paradox" show that older adults perform better on certain cognitive tests than teens having the same reasoning skills and superior cognitive power; this is hypothesized to be the result of "wisdom" in discerning a signal from noise, which pure "cognitive horsepower" is unable to do (Goldberg, 2005). Although it appears from these findings that there are at least two new innate mechanisms responsible for adaptation-as-intelligence - support for change (plasticity) and a drive for efficiency (selection) - an alternative conception is that inefficient demands on cognitive capacity can themselves become a source of disequilibration; a selection pressure, subject to our involuted-Baldwin Effect. Furthermore, developing Zelazo's model, the specialization of cortical response to stimuli suggests that the highest levels of consciousness are only necessary to "reflect upon" the newest and most complex problems and comparisons (to draw connections between them and "fit them in" to the internalized abstraction of the world's logic), the occasions for use of which diminish with increased experience. Although this has implications for the extension of Piaget's constructivism to explain some aspects of cognitive decline (i.e., senescence as well as development), a more immediate suggestion is that once efficiency takes over as a primary selection pressure, "drilling" may become the more relevant pedagogical tool: a means to reduce the amount of cortical space required to process stimuli (for an exemplar case, known to many simply as "Kumon Math," see Ukai, 1994). This issue was not addressed by Cavicchi, but certainly ought to be examined in the future. 228 From Dynamic Structures to a New Take on Dialectics623
In an as-yet-untranslated, posthumously-published book reviewing the elementary forms of dialectical construction (and attempting to provide a simpler metaphor than stages to explain his evolving perspective), Piaget concluded that the Fichtean dialectical triad of thesis-antithesis-synthesis is a good fit for, but is also overly restrictive in application to, his problem: contradiction may be sufficient to precipitate learning (via trial-and-error), but it is not necessary. Instead, he argued that the revolutionary "dialectic" is followed by a normal "discursive" phase - a continuous process of filling in details between periods of punctuated change - without which everything could otherwise be deconstructed and reduced to first principles.624 Furthermore, contra Hegel, he pointed out that concepts do not "contain" their opposite, but rather imply them as a possibility.625
In the jointly-authored follow-up, the standard dialectical triad was then replaced with nested sequences of intra-, inter-, and trans-active procedures.
This important book - begun in 1967 and later translated as Psychogenesis and the History of Science621 - synthesizes Piaget's empirical findings with his epistemological theory to present a mature statement regarding the processes that drive the social construction of knowledge. The goal for this work, which clearly builds on the transitional works, is clearly stated:
623 Some of what follows in this section has been revised from a version appearing in (Burman, 2008b) 624 (p. 214). This is what Putnam fails to understand in his commentary on the Piaget-Chomsky debate (in Piattelli-Palmarini, 1979/1980). 625 (pp. 57-61, 63, 224; see also Piaget, 1981/1987; anticipated in Piaget, 1968/1971, p. 68) 626 (Piaget & Garcia, 1983/1989) 627 (Inhelder in Piaget & Garcia, 1983/1989, p. vii) 229 .. .not to set up correspondences between historical and psychogenetic sequences in terms of content, but rather to show that the mechanisms mediating transitions from one historical period to the next are analogous to those mediating the transition from one psychogenetic stage to the next.
To achieve this goal, Piaget's earlier adopting of Baldwin's dialectical mechanisms - assimilation and accommodation, in the circular reaction - are updated and generalized following the new discursive form: intra (observations within the separate domains of 'x' and 'y'), inter (cross-mapping between 'x' and 'y'), and trans (synthesizing 'z' to accommodate anomalies in the structure of observations yielded by 'x' and 'y').
3) Trans ('z')
4 2) Inter ('y')
Figure 24. Baldwin's "circular reaction," updated to use Piaget's "new theory" dialectic. The "trans" step illustrates the reflecting of an abstraction from one level of relative completeness to the next higher one, which is then shared. (Double decentration is implicit to the "trans" phase.)
(Piaget & Garcia, 1983/1989, p. 28; contra Gould, 1977, pp. 144-147) 230 Building on the modern neurological approach, coupled with our discussion regarding
Baldwinian selection pressures, we might then say that this means an external stimulus must be "felt" before it can have a change-inducing, disequilibrating effect. But that doesn't mean that the source of such a stimulus has to be "understood" to have an impact; it may simply impinge upon the organism, as a necessary obstacle that implies - merely through its existence - a series of possible assimilatory reactions to be undertaken in the future, thereby potentiating further change. (Thus in learning and development, just as in education and science, the mere awareness of an obstacle entails the possibility of a set of solutions to address it.)630
It is clear how this conception of knowledge-as-adaptation is consistent with
Piaget's appeal to Waddington's epigenetic theory. All organisms - including humans - are located in a landscape of perturbations, which is abstracted and modeled endogenously. As a result, and as children distance themselves from their visceral experience (through decentration), it is as if they extend themselves in time and space: behaviour can respond to hypothesized selection pressures, experienced abstractly. This new epistemic level in the landscape is then itself built upon socially through the joint- construction of institutions which, through their influence on the actions of individuals, begin to function as if they were asserting their own selection pressures.
(cf. Becker, 2004; Immordino-Yang & Damasio, 2007) (Piaget, 1981/1987, 1983/1987; Piaget& Garcia, 1987/1991) 231 Figure 25. Waddington's illustration of the complex system of interactions between two levels shows part of this larger system, but must be expanded to show the interactions across the total structure.631
Through the application of the Godelian levels model, Waddington's "epigenetic" approach can be seen to apply not only to development and evolution but also to cultural evolution: each is a level in the hierarchy. In other words, each child comes increasingly to live in the same world inhabited by adults; they "grow into" it, following the same constructive processes as infants, as if becoming more deeply entrenched in reality (while at the same time, through abstraction, decentring themselves in its consideration). It is then this reality - the child's developing conception of the logics of relation between objects, as well as their representations of those relations as abstract sets of possible behaviour - that is shared in communicating their beliefs.
631 (Waddington, 1957, p. 36) 632 (cf. Wimsatt, 1999; Wimsatt & Griesemer, 2007) 232 So What?
Piaget's return to biology informs his mature theory of knowledge, which attempts to go beyond Baldwin's earlier epistemology by explaining the emergence of true novelty. As
Piaget explained near the end of this transitional period, implicitly responding to
Baldwin's apparent mutationism while putting in context the competing explanations for novelty:
From the empiricist point of view, a "discovery" is new for the person who makes it, but what is discovered was already in existence in external reality and there is therefore no construction of new realities. The nativist or apriorist maintains that the forms of knowledge are predetermined inside the subject and thus again, strictly speaking, there can be no novelty. By contrast, for the genetic epistemologist, knowledge results from continuous construction, since in each act of understanding, some degree of invention is involved; in development, the passage from one stage to the next is always characterized by the formation of new structures which did not exist before, either in the external world or in the subject's mind.
In other words, because the effects of objects are reconstructed in knowledge (via imitative looping), each act that leads to new understanding is an act of individual discovery. Such acts therefore include a creative element: new structures are created, but following a formal procedure of reflecting abstraction.
Piaget then continues, linking his explanation of novelty with the plan for the last decade of his life's work and starting with the results of the studies conducted during the transitional period:
The central problem of genetic epistemology concerns the mechanism of this construction of novelties which creates the need for the explanatory factors which we call reflexive abstraction [or "reflective abstraction," see supra, also Chapters III-IV] and self-regulation [Chapters I-II]. However, these factors have furnished only global explanations. A great deal of work remains to be done in order to
233 clarify this fundamental process of intellectual creation, which is found at all the levels of cognition, from those of earliest childhood to those culminating in the most remarkable of scientific inventions [Chapter V].633
In other words, it is clear that the plan for the works produced during what Beilin called the "new theory" period were building on the "global explanations" already produced during the earlier transitional period examined here. The key concept introduced during this transition is therefore more complex than the one implicit in the old theory, but it is still manageable: construction takes place in response to selection pressures (current or historical) and is constrained by the relevant level's ability to change its forms of organization (plasticity).
Current selection pressures are external, produced by obstacles, and can be examined synchronically; historical selection pressures are internal, as the effects of past constructions and their interactions, and must therefore be examined diachronically.
Overcoming either constraint can be achieved by acts of adaptation (in the long term) or of intelligence and the abstraction of causal relationships that can be mined for opportunities (in the short term). These relationships can also be abstracted at new levels to provide new opportunities for adaptation: the genesis of new structures to contain new content.
To put these additions in the context of our earlier extended example, we come to see childhood as a period of change in changing contexts; learning as adaptation as positioning, given the collective importance of each individual's drive to achieve a well-
(Piaget, 1970/1971, pp. 77-78) fitting place in relevant level of the general social environment that ultimately comes to be inherited.
genotypes of generation »
THE EXPLOITIVE SYSTEM
THE NATURAL SELECTIVE SYSTEM
\ THE GENETIC SYSTEM
genotypes of generation n+l
Figure 26. My modification of Waddington's illustration of the levels of action in selection.634
' This is the historically-supported version of the dialectic presented by (Gofton, 2007). 235 Thus, exploration enables the possibilities for new construction (innovation), while totem
and taboo constrain them: educational standards, and a general curriculum, indicate both what is explicitly worth learning and what is dangerous to know. Productive, non- revolutionary novelty then emerges in individuals' actions in abstracting out contemporary implications from the intersection between the results of exploration and the historical forgotten—the vast epistemic territory between "accepted knowledge" and
"purposeful ignore-ance."635 These abstractions then become opportunities for "truths," in the form of "discoveries" and the production of new "knowledge."
Where to From Here?
Before turning fully toward the "new theory," to further unpack how Piaget justifies his turn toward a logic of meanings in the construction of an "epigenetic epistemology," the final two books from the transitional period must be incorporated into the narrative presented here. (Although these are collections of studies conducted at the Centre while the transition was underway, they may have implications for future work.) The first, an untranslated work on identity (A= A'), seems to lay the foundations for abstraction through reflection across levels.636 The second, translated but rarely discussed, applies the new recognition of structural functions to a logical analysis of the thought of preoperational children.
635 (cf. Proctor & Schiebinger, 2008) 636 (Piaget et al, 1968) expanded upon in (Piaget, 1977/2001) 637 (Piaget et al., 1968/1977) was used to anchor a set of new studies by (Kamii, Miyakawa, & Kato, 2007), demonstrating that Piaget's theoretical work can still provide grist for the scientific mill. 236 Piaget's 1967 lectures at Clark University, on memory and identity, seem to link these two books to our current narrative; together, they can also be seen to lay the groundwork for Piaget's final theoretical statements, but their significance is only made manifest in the context provided by the connection we have made from the transitional forgotten works to the later new theory works. That said, however, they do not seem to fit easily into the current narrative; there is no obvious link back from the psychology they discuss to the social theory examined in Chapter V. For this reason, they might be better used as part of an introduction to a future work on the new theory itself.
More important than incorporating these collections, in terms of clarifying the larger issues examined as part of "the return," would be the inclusion of Piaget's critique of philosophical thinking. This was published in 1965 and later translated as Insights and
Illusions of Philosophy.61'9 It reflects on his early conversion to - and later deconversion from - the kind of philosophy that he had proposed for his second dissertation. Such a discussion could easily be incorporated into the narrative presented here through the addition of a new section between Chapter III (Godel) and Chapter IV (psychology), using the omitted section from Biology and Knowledge on the levels of behaviour (from instinct to intelligence) to bridge the gap. The result would be to make clearer how much his "return" was a return to his formative interests, and not just to his early biology.
In terms of basic chronology, it's worth remembering that these lectures (Piaget, 1968b) came after those introducing his return to biology in 1965 (Piaget, 1966a, 1967c) but before his lectures critiquing structuralism in February 1968 (Piaget, 1969). 639 This would have to be compared to Piaget's 1961 response to his philosophical critics, to ensure that it's not just an expanded book-length version of an essay that emerged earlier in the lineage of ideas. 237 In clarifying the overall narrative, with a view to focusing on the results of the return for laying the foundations for the new theory, it would also be desirable to incorporate a discussion of the justification for the return to biology (as well as why he covers the history of evolutionary theory in such detail when it seems obvious that it is learning that must be explained). The contents of Waddington's 1964 address, as well as of the discussion that followed, would be particularly important in addressing this need.
Yet this could only be added following detailed research at the Piaget Archive in Geneva, and perhaps the Waddington Archive in Edinburgh too.
Most important for understanding the new theory, however, will be charting the shifts in the formal logic - from "truth tables" to "logics of meaning"640 - that were beyond the scope of this thesis. These changes are tied in with issues discussed here, such as Piaget's response to Kant (via the reintroduction of "Kantian appeals to individual necessity"641 following a "repudiation" of Frege642), and would therefore also require some of his earliest arguments to be unpacked in greater detail.
For now, however, it seems sufficient simply to have pointed out that the "new theory" did not first emerge in 1974, as Beilin claimed. Rather, its roots are in the transitional period discussed; in the "forgotten works" which collectively lay the foundations for a shift from genetic to epigenetic epistemology. Only once this has been adequately excavated, and Piaget's theory fully understood, will we be in a position to
640 From the argument formalized in (Piaget, 1975/1985) to that suggested in (Piaget & Garcia, 1987/1991). 641 (Rotman, 1977, p. 156; qtd in context by Beilin, 1999, p. 121) 642 (L. Smith, 1999c) 238 most fruitfully apply his ideas to important contemporary issues such as the education of our youth.643 This thesis has been a first step toward that goal.
643 Indeed, as Deborah Seltzer-Kelly (2008) recently noted, there is presently an urgent need for a truly scientific basis upon which to ground educational theory. Since her own solution is based on pre-neo Darwinian theory, however, an update conducted from the perspective of Piaget's new (post-neo) theory would have value in fulfilling the needs she outlines (as suggested independently by Burman, 2008b, p. 166ft). 239 References
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