CEPA eprint 2782

A systemic interpretation of Piaget’s theory of knowledge

García R. (1999) A systemic interpretation of Piaget’s theory of knowledge. In: Scholnick E. K., Nelson C., Gerlman S. & Miller P. (eds.) Conceptual development: Piaget’s legacy. LEA, Mahwah NJ: 165–184. Available at http://cepa.info/2782
Table of Contents
Epistemology and the Foundation of Science
Constructivism and Contemporary Developments in Science
The Stratified Universe
The Nonlinear Universe
Complexity
Complexity and Complex Systems
Systems and Complex Systems: Some Definitions
Principles of Organization
Principles of Evolution
The Cognitive System as a Complex System
The Components of C at the Elementary Levels
The Boundary Conditions of the Cognitive System in Strict Sense (C)
The Boundary Conditions at the Interface C/B
The Internal Dynamics of the Cognitive System
The Role of Boundary Conditions at C/S Interface
Concluding Remarks
References
Epistemology and the Foundation of Science
The history of the development of thought in the individual – which genetic psychology attempts to systematize – and the history of the development of knowledge accumulated by society over time – systematized by the historicocritical analysis of science – have the objective of achieving a coherent conceptualization of the type of activity that leads us to known reality.
But what is reality? The immediate response obtained when this question is asked is that what we call reality is the set of observables that correspond to our perceptions. One of the artificers of the scientific revolution brought about by quantum mechanics expressed this concept in the following terms: ’’The set of invariants of our sense impressions is the physical reality which our minds construct in a perfectly unconscious way.” He added: “Science is nothing else than the endeavour to construct these invariants where they are not obvious” (Born, 1948, p. 104). According to this formulation, reality is what is there, directly given in our experience. The table on which I work, the lamp that gives me light, the people I speak to, myself, we are reality. And what is it that we observe when we observe reality?
“There is no pure reading of experience,”[Note 1] said Piaget. “Every observable is theory laden,”[Note 2] repeated the teachers of philosophy of science after Russell Hanson.
I see the table, I touch it, I lean on it. What is the basis of the statement that there are no pure readings of experience? Where is the theory that these observables are laden with?
Although it would appear that they made similar statements, the responses of Piaget and of Russell Hanson are fundamentally different.
Hanson’s dictum is based on the analysis of numerous examples, which he used to show that what appears as a direct observation already contains an interpretation belonging to the observer and varying from one observer to another depending on the previous knowledge of each. Quine responded to this statement by indicating: “What counts as an observation sentence varies with the width of community considered. But we can also get an absolute standard by taking in all speakers of the language, or most” (Quine, 1969, p. 88).
Quine was right insofar as the statement in question is concerned. However, what is important for us is that Russell Hanson did not touch at all the basic epistemological problem that is involved in Piaget’s dictum, as we shall see. Curiously enough, Quine did not mention the epistemological problem in his remark to Hanson although he was quite aware of it, and he said so emphatically: “The notion of observation as the impartial and objective source of evidence for science is bankrupt” (Quine, 1969, p. 88).
Quine was, without doubt, the empiricist who most thoroughly analyzed the presuppositions of empiricism. These analyses led him to profound revision of the epistemological creed that he had proclaimed for a long period and that led Putnam to describe him as “The Greatest Logical Positivist.”[Note 3]
I submit that the radical change of Quine’s epistemological position may be considered one of the most transcendental events in the philosophy of science. It deserves a profound analysis that goes far beyond the limits of this presentation. For our purposes, it suffices to quote a few statements in which the transit to a new epistemology was registered with his characteristic sharpness: ”[W]e gave up trying to justify our knowledge of the external world by rational reconstruction… we have stopped dreaming of deducing science from sense data” (Quine, 1969, p. 84).
Quite right. But what did Quine offer in its place? Let us follow his line of thought:
The only information that can reach our sensory surfaces from external objects must be limited to two dimensional optical projections and various impacts from air waves on the ear drums and some gaseous reactions in the nasal passages and a few kindred odds and ends. How could one hope to find about the external world from such meager traces? In short, if our science were true, how could we know it? Clearly, in confronting this challenge, _ the epistemologist may make free use of all scientific theory. His problem is that of finding ways, in keeping with natural sciences, whereby the human mind can have projected this same science, from the sensory information that could reach him, according to this science. (Quine, 1973, p. 2)
From here onward, Quine was to concern himself with demonstrating that although circular, his proposal does not contain a vicious circle. It is inmaking free use of all scientific theory that he located the point of transition between what he called “the old epistemology” and the new formulation of the problem. Where did Quine break the circle so that is not a vicious one? I do not repeat his journey here. I just state his surprising conclusion: “Our liberated epistemologist ends up as an empirical psychologist, scientifically investigating man’s acquisition of science” (Quine, 1973, p. 3).
In his famous essay Epistemology Naturalized (1969), already cited, Quine was even more explicit: “The old epistemology aspired to contain, in a
sense, natural science; it would construct it somehow from sense data. Epistemology in its new setting, conversely, is contained in natural science, as a chapter of psychology” (p.83). And again another surprising statement: “In the old anti-psychologist days the question of epistemological priority was moot… Now that we are permitted to appeal to physical stimulation, the problem dissolves” (pp. 84–85).
The greatest logical positivist, recognizing his “old anti-psychologist days,” made considerable progress with respect to the old empiricist epistemology, but the end of his road remained dramatically in the shadow because the psychology he turned to ended up being purely speculative.[Note 4]
Why have the century’s great empiricists reached a dead end and stayed there without exploring other paths? Let us remember that only in the last paragraph of the last chapter of his last book on philosophy, did the great Bertrand Russell confess: “It must be admitted, empiricism as a theory of knowledge has proven inadequate, though less so than any other previous theory of knowledge” (Russell, 1948, p. 507).
Why did they not try what appears an obvious alternative to many of us, that is, constructivism?
Let us return to Piaget and Russell Hanson. In my view, Quine’s comment with regard to Hanson was sufficiently conclusive and showed that, contrary to what is usually argued, Hanson’s dictum fit in a wide conception of empiricism, but he did not go beyond.
Thus, there remains only Piaget’s position with respect to the reading experience. What was this position based on? Genetic psychology has given us the verdict: The reconstruction of the development of knowledge of an individual shows that to reach his or her conception of the world with objects and properties distributed in a space and participating in a process of a certain duration, the individual must pass through a long process that takes place throughout childhood and that culminates in adolescence.
An empiricist à la Quine would say: Very good! But finally everyone recognizes that there are tables, lamps, and people. What is the fuss about? Is this not a process of learning? Once a child learns to distinguish between a table and a lamp and between a real dog and a stuffed dog, where is the theory? Why do we say that the reading of experience is not pure? Is it not on the basis of this shared experience that science begins?
Strangely enough, Quine’s position has some points of contact with constructivism. For Quine, the problem faced by the epistemologist was to understand how to move from observations to science, once we have renounced the deduction of science from sense data. To this end, Quine considered the use of knowledge acquired through science as legitimate. He then looked for the science that links observations with conceptualizations and arrived at psychology. At this point, his impeccable logic ceased, and his empiricist ideology took over: Quine’s psychology can be none other than behaviorism. His argument remained at the level of how, in behavioral terms, the child learns the language of objects and of space and time. In this respect, Quine seemed to take the psychology prevalent at a certain time and in a certain geographical area as being thepsychology and could not find a way out of empiricism.
What did Quine do to epistemology? Did he kill, it or did he let it escape? This area was Quine’s Achilles’ heel and the Achilles’ heel of those contemporary philosophers who recognized the collapse of empiricism and tried to save it. To put it briefly, they had no epistemology left! By turning, in extremis, to behavioral psychology, they showed that they found themselves at a dead end. From this point, I return empty-handed to my original question: What is reality? How do we know?
I maintain that in renouncing the answers to these questions, philosophers of science resigned their main function (to account for the foundation of scientific knowledge), turned to sociology of science, and left out the theory of knowledge.
Piaget entered the scene of this discussion with a complete reformulation of the problem and took the only direction left after the collapse of empiricism: constructivism.
A very condensed formulation of Piagetian answers to the previous questions may be reduced (with great risk of oversimplifications) to a few basic tenets of genetic epistemology:
Experience starts from actions and their coordinations in action schemes. The organization of experience data begins with rudimentary relations of implications between actions. The framework of relations, based on inferences, which are constructed by the subject, arrives at the constitution of logic and logico-mathematical structures, which are the necessary forms of all knowledge.The interdependence of subject’s constructions and the experience data is shown at the most elementary levels by the common indistinguishable origin of logic and causal relations. Such interdependence is the foundation of a conception of causality leading to a new conceptualization of the traditional problem of scientific explanation.There is an implicit ontology in the organization of experience data, which assumes that the qualitative changes, the displacements, the changes of movements are none other than external manifestations of relations between inferred objects. The relations themselves run over the frontiers of the observable. They are reconstructed by the subject on the basis of inferences and attributed to the inferred objects. The resulting ontology is what we call reality.
These four points have a heavy content of epistemological theory. Their justification and validation cannot be meaningfully made statement by statement out of the context of the whole theory. In these respects, I adhere strongly to the well-known Duhem-Quine thesis according to which a theory confronts the tribunal of experience as an organized totality, not piecemeal (Quine, 1951). It is this thesis I refer to when I find myself faced with the surprisingly superficial opinion that dismisses Piaget’s theory of knowledge as dépassé on the basis of some new findings in developmental psychology.[Note 5]
It must be admitted, however that the application of the Duhem-Quine thesis in this case is confronted with a serious obstacle. We find in the monumental production left by Piaget all the elements of his theory of knowledge. However, it must be admitted that Piaget did not present a totally integrated theory (when I say integrated, I do not mean a closed and finished theory, because the characteristic of his scientific epistemology is precisely that of being subject to modifications and extensions, like any scientific theory). The integration of his theory is the task left to those of us who feel that we are disciples of his school and who do not have the psychoanalytic inclination “to kill the father.”
As a contribution to this task, I am working toward an integrative proposal that includes the plurality of elements found in the Piagetian conception of epistemology: the psychogenetic, biological, and social components; the logical and empirical components; the historical, cultural, and scientific components. In my view, the only conceptual methodological analysis capable of carrying out this integration must be based on a theory of development of knowledge as a complex system. To this end, I consider it necessary to show how we conceive of the analysis of complex systems today. I am going to argue, against the majority of his critics, that Piaget was a brilliant precursor of ideas that have arisen in contemporary science in recent decades.
Constructivism and Contemporary Developments in Science
Much has happened and much is happening in the science of the second half of the century and thus much is offered for epistemological reflection. The profound changes that have taken place in the conception of the universe in this period have led to the conviction that we are witnessing a new scientific revolution. I refer to only three conceptual changes that are closely linked to our interpretation of Piagetian conceptions of the construction of knowledge. Such interpretation is based on a general theory of complex systems, a theory that I have developed in connection with other studies.[Note 6]
The Stratified Universe
As a starting point, I take a statement made by Einstein at the beginning of this century enunciating a belief that he maintained throughout his life: “The supreme object of the physicist is to arrive at those universal elementary laws from which the cosmos can be built by pure deduction.” Today we know that this ideal cannot be achieved, because such conception implies a universe in which the same laws, the same forms of organization, the same dynamics of development rule in all domains and for all scales of phenomena. One of the surprising facts in the recent history of science is that in physics itself – the discipline par excellence in which Einstein’s conception had become most rooted – the demonstration that the universe cannot be conceived of in this way has arisen. I can reduce this part of the new conceptions to two points:
The physical world presents itself as constituted by semiautonomous levels of organizations, with different structures. They are semiautonomous in the sense of having different dynamics, but interact in such a way that they integrate totalities.Different levels can be decoupled in the sense that the theory developed at one of the levels can have sufficient stability so that it is not perturbed by discoveries or developments at another level.
This second point is most important, and I would like to illustrate it with an example contributed by an incisive physicist and historian of science:
High energy physics and condensed matter physics have become essentially decoupled in the sense that the existence of a top quark or any new heavy particle is irrelevant to the concerns of condensed matter physicists – no matter how great their intellectual interest in it may be. (Schweber, 1993)
This organization by levels, and this decoupling of the levels, had already been shown in other domains before this conclusion from microphysics. If I go back to my years of research on atmospheric dynamics, I can state that meteorology had already found that atmospheric movements, which apparently cover a continuous spectrum of frequencies, are distributed in levels of organization with characteristic dynamics in each level.
On the other hand, Herbert Simon, who has explored science in many directions, has frequently insisted on the hierarchic organization adopted by what he called “the organization of complex systems” (Simon, 1977, sect. 4.4). The typical example given by Simon is the hierarchic structure of biological systems: “If we look at the cell as if it were building brick, we find cells organized in tissue, tissues in organs, organs in systems.”
Simon’s hierarchic systems are similar to the Chinese boxes that fit inside each other so that each box contains another, which in turn is contained in a larger one (except perhaps the first and the last). I should point out that my conception of stratified systems does not correspond to Chinese boxes. Likewise, Simon gives the name subsystems to the structures that correspond to each of the levels of organization in the hierarchy, whereas I use such terms with a different meaning.
The terminology of hierarchic systems and of the corresponding subsystems is very widely encountered – in view of the authority of Simon – and corresponds to the notions that have points of contact with other systemic conceptions of development. But I must warn of the possibility of confusion in the case of the same term used with meanings that can be markedly different.
The Nonlinear Universe
In recent decades, a vast literature on what is usually called – to my mind, erroneously – the sciences of complexity has accumulated. As is known, the explosive growth of this literature was to a large extent due to the introduction of extraordinarily fast computers, which allowed the solution of problems that were previously beyond the possibilities of mathematical methods. On this basis, what is more appropriately called nonlinear sciencewas developed.
The problems that were taken on in very diverse disciplines and the quantity of spectacular results obtained led to statements that I consider to be illegitimate mathematical extrapolations.
Those who presented themselves as participants in this revolution tended to invoke methods of analysis of complex phenomena, which, it is said, “are capable of breaking down the barriers between disciplines.” Quite a number of authors have made assertions of this type (Prigogine, 1994; Thom, 1993, among them). These statements may lead us to think that we are faced with a new attempt to unify the sciences.
In the past, the “breaking down of the barriers between disciplines” was invoked by those with reductionist positions. The most characteristic historical examples are the mechanistic thinking of the 18th century and the program of the Encyclopedia of Unified Science launched by logical empiricism. Are we now faced with a new form of reductionism?
The current situation is different. We are not dealing with the ontological and nomological unification of the ultimate constituent of reality – as mechanistic thinking attempted – or the logicolinguistic unity of all sciences, proclaimed by the school of Vienna. The focus of attention has changed and is now centered on what I might call “the dynamics of the change.” Here there has effectively been very clear progress, which I can sum up in the following statement: Phenomena of very diverse natures, which belong to the domain of different disciplines and which from the point of view of a purely phenomenological description appear to have nothing in common, present, however, similar characteristics in their temporal evolution.
From this perspective, which goes far beyond the models of dynamic systems, it can be legitimately stated that the developments that have occurred around the problems of complexity not only contribute to a better understanding of a large number of phenomena from multiple disciplines, but also allow the establishment of a conceptual framework for the interdisciplinary study of complex systems.
I think is necessary to say, however, that there has been frequent abuse of the new concepts and methods. There is a sort of imperialism of computers in this trying to apply mathematical modeling with systems of nonlinear differential equations to all types of phenomena. On the other hand, the fact that similar dynamic equations are applied to problems of physics, biology, demography does not break down barriers between disciplines or initiate a new dialogue between them.
What I would like to recover from all the work carried out in this domain is the fact that much has been learned about the dynamics of change of complex systems. In particular, I refer to what appears to be the most general law: nonlinear and structurally discontinuous evolution that proceeds by successive reorganizations.
The principle of stratification and the nonlinearity of evolutionary processes fall into line with the tenets of genetic epistemology. The so much criticized stages in the construction of knowledge (often referred to as the myth of stages) and the assertion that the development of the cognitive system is neither a continuous growth nor a linear process but proceeds by successive reorganizations turned out to be special cases of quite general laws governing processes in all domains.
Complexity
The third conceptual development that is relevant to my study comes under the somewhat misleading title of complexity and requires a more detailed analysis.
Complexity and Complex Systems
First, I am going to make a declaration of faith: I do not believe it is possible to give a satisfactory definition of the noun complexity. What can be defined is the adjective complex. More precisely, I believe there are phenomena, situations, behaviors, models that may be described as complex, but in each case, the word has a different meaning. This does not mean that the term complexity cannot be used meaningfully. It implies withdrawing legitimacy from the question “What is complexity?” and it implies also calling into question the expression theories of complexity, which is, more often than not, restricted to the applications of dynamic systems.
The use and abuse of dynamic systems, as well as the fetishism of the computer, had led many writers, some of them well-known, to formulate problems of complexity in such a way that implies that phenomena or situations not admitting some form of mathematization are relegated to the level of vague intuitive ideas. This proposition leaves aside the possibility of rationally studying, among others, the great social, economic, and political themes that profoundly concern the contemporary world. Is not environmental deterioration at a global level, for example, a problem of
great complexity? Which notion of complexity applies to it? Dynamic equations, information theory, deterministic chaos, neuronal networks could hardly have direct application here (except in the modeling of very partial aspects, the results of which may be used as inputs for the study of the general problem). I am going to argue, however, that we have sufficiently solid bases today to approach the study of these themes in such a way that a high degree of rigor and precision can be achieved even though the work is not based on a mathematical model. The systemic conception of Piagetian constructivism falls in these considerations.
Systems and Complex Systems: Some Definitions
I use the term system in a specific sense, applied to the representation of a set of situations, phenomena, processes, cut out from reality, which can be modeled as an organized totality with a characteristic form of function-ing. Here the term functioning designates the set of activities that the system can carry out (or allows to be carried out) as a result of the coordination of the functions fulfilled by its parts.[Note 7]
Two major categories are contained in this general concept:
Decomposable systems. Their parts can be isolated and modified independently of each other. A house is an example of a system that can be decomposed. As a system, a house has properties and functioning characteristic of a totality, but its elements (electrical systems, water supply, floors, windows) can be modified without the modifications of the other elements. Systems of this sort can be called complicated but not complex.Complex systems. Here the adjective complex acquires a very specific meaning qualifying a kind of system in which the processes that determine their functioning are the result of the confluence of multiple factors interacting in such a way that they cannot be isolated. Consequently, the system cannot be described by merely adding together partial perspectives from independent studies of each of its components (i.e., they are not decomposable).
The study of a complex system thus defined presents serious difficulties, but a systematic study can be carried out by taking into account the considerations made previously. The extension and application of these considerations to complex systems can be condensed in the following principles.
Principles of Organization
Stratification. The factors that directly or indirectly determine the functioning of a complex system are distributed in structurally differentiated levels with their own dynamics. The levels are not interdefinable, but the interactions between levels are such that each level determines the boundary conditions of the adjacent levels in a precise sense that I specify later.
Internal Articulation. The study of a complex system generally starts with a particular situation or a set of phenomena, which occur at a given level of organization that I call base level. The intervening factors correspond to certain scales of phenomena and certain processes, which can be grouped in subsystemsconstituted by elements between which there is a greater degree of interconnection that with the other elements of the system. These subsystems function as subtotalities, which are articulated by relations that together constitute the structure of the system.
Boundary Conditions. The phenomena that occur at the base level are not independent of the other processes located at different levels, although as I have said, each level has its own dynamics. They interact, sometimes weakly, but, in other cases, in such a way that one level may condition the evolution of the next level. The interactions take place by means of fluxes (of matter, energy, information, policies, etc.). The set of fluxes at one level, with respect to the others, constitutes the boundary conditions of the system defined at that level.
Because it is a matter of ingoing and outgoing fluxes, that is, interactions in a strong sense, the boundary conditions are not rigid conditions imposing on the system; they are not direct or unidirectional. Their role in the structuring of the system is fundamental in that they condition the development of the internal structure of the system but do not determine it.[Note 8]
Principles of Evolution
As I indicated at the outset, the developments that have taken place in a wide diversity of themes and disciplines and that are usually grouped under the generic heading of complexity converge on the fact that the evolution of very dissimilar phenomena and processes presents common characteristics.
The complex systems I am considering suffer transformations across time, which are peculiar to open systems. The evolution of such systems does not take place by means of processes that modify gradually and continuously, but proceeds by a succession of processes of disequilibration. Each restructuring leads to a period of relative dynamic equilibrium during which the system maintains these structures with fluctuations in certain limits.
The Cognitive System as a Complex System
The overall range of studies involved in the Piagetian researches about knowledge may be organized in three levels of analysis:[Note 9]
The first level _includes the material provided by empirical research in two distinct areas: the psychogenesis of concepts from childhood to adolescence (which gave rise to a new discipline: genetic psychology) and the historical development of scientific ideas, concepts, and theories.
At the second level _is the formulation of the theory of knowledge that accounts for the findings at the first level. This is the domain of genetic epistemology in a strict sense.
The third level _of analysis is concerned with the applications of the theory as a tool for the analysis and interpretation of foundational problems in the theory of science.
My proposal of a systemic approach to the cognitive system refers to the second level of analysis (genetic epistemology).
I define the cognitive system in a wide sense as the set of interrelated activities pertaining to three different domains: biological, psychological (mental), and social. The activities in each domain have their own specific organizations defining levels of organization of the overall system. With this terminology, I consider the cognitive system in a wide sense, as a complex system having components from three levels of organization: the biological level, the psychological level (mental), and the social level. I call these components, taken together, system ∑.
System ∑ is therefore a complex system with three semiautonomous levels of organization, each of which has its own dynamics and is in permanent interaction with the others. The psychological or mental level by itself constitutes a system (subsystem of ∑), which I call cognitive system in a strict sense or System C. To start with, I center my analysis on System C, which thus is the base level defined earlier.
To establish the characteristics that qualify System C as a complex system, it is necessary to define its elements (or subsystems that are subsubsystems of ∑) with their interactions and to identify the boundary conditions through which the biological and social levels of System ∑ interact with System C.
System C presents specific problems not found in other fields. In dealing with physical, biological, and social systems, we may focus attention on the elements (chemical elements, solid bodies, biological organisms, people, institutions), or on the structure (the set of relations among the elements or the functioning of the system as a whole). In the case of cognition, the system, the elements, and the relations are all sets of interrelated structures. This composition of C increases the difficulties of the analysis and makes unavoidable a constructionistic approach. There are therefore two kinds of problems to be considered: the organization of the system at one given level (stage) and the structuring processes in the succession of developmental levels. (The second is point b dealt with later.)
Here I consider the organization of the system only at the psychogenetic levels.[Note 10] _
The Components of C at the Elementary Levels
At the elementary levels of cognitive development, a convenient way of defining the elements of C is found in Piaget’s well-known diagram of equilibration (introduced in Piaget, 1975, p. 59). The four elements of the system are:[Note 11]
Obs O: Observables related to the objects.
Obs S: Observables related to the subject’s actions.
Coord S: Coordinations inferred from the subject’s actions.
Coord O: Coordinations inferred between objects.
The interdefinibility of the elements or subsystems – an essential part of the definition of a complex system – is clearly illustrated in the cyclic sequence of the arrows and their merging in the progression from level to level.[Note 12]
The Boundary Conditions of the Cognitive System in Strict Sense (C)
The knowing subject whose mental activities are the elements of System C is, at the same time, a biological organism and a social protagonist. The definition of C as a subsystem of ∑ implies that it interacts with the other subsystems: the biological (B) and the social (S). Thus, there are two interfaces in the System ∑: C/B and C/S. There are therefore two types of boundary[Note 13] conditions to be considered.
The Boundary Conditions at the Interface C/B
In his extended studies on the interrelations between psychogenetic and biological development, Piaget anticipated some findings that the development of neurobiology was to demonstrate, particularly in regard to the interactions between neuronal development and perceptive activity in newborn infants. I take the following reference from the seminar on biology and knowledge held in Mexico during the celebration of the centennial anniversary of Jean Piaget in April 1996 (Aréchiga, 1997):
It is known that in some neuronal circuits, spontaneous activity while intrinsic to the neuronal system can be modulated by external influences. Since 1962, Torsten Wiesel and David Hubel had demonstrated that in experimental animals (cats), the suppression of visual information from one eye prevented the maturation of the connections in the visual cortex of the eye, leaving the animal without visual neurons with binocular entry, essential for the integration of stereoscopic vision. Deprivation of visual binocular entry has to take place during a fixed period of time in order to produce this difference, a little after birth, which is precisely when the interneuronal connections of the visual system mature. These experiments led to the discovery of the explanation of a fact observed from many years in medicine. In case of strabismus in children, there is full recovery of the binocular function when it is corrected surgically at an early age, whereas when a surgery is delayed, recovery does not occur. It is also possible to explain why the late recovery of visual sensibility in those blind from birth does not allow them to develop normal vision.
I want to emphasize the distinction made by Aréchiga between the activity intrinsic to a system and its modulation by external influences. This example is a typical and clear formulation of the way that the effects of boundary conditions are exerted. This example may also illustrate and clarify the distinction made earlier between to determine and to condition when I referred in the section on complexity to the action of boundary conditions on the structuring process in a system.
The Internal Dynamics of the Cognitive System
The systemic character of genetic epistemology becomes evident when we analyze Piaget’s discovery of the stages in psychogenesis as well as his theory of equilibration. The controversies about the very concept of stage and the supposed refutations by prominent logicians[Note 14] cannot be sustained anymore: The nonlinear character of evolution by successive reorganizations is a common feature in quite different domains (physical, biological, social).
Nevertheless, evolution by successive reorganizations in the case of the cognitive system has very distinctive characteristics.
My definition of a complex system involves the concept of an open system (the reciprocal is not true!). It is well known today (particularly because of the work of Prigogine’s school) that open systems are far from equilibrium conditions, that they can be kept stationary by the action of boundary conditions, and that they evolve by reorganizations fed by exchanges with the environment.[Note 15] However, it should be kept in mind that the classic models of open systems found in the literature are not complex systems in my sense and therefore the conclusions of such studies should be applied to my cognitive system with caution.
In the analysis of the development of Cognitive System C, it is necessary to make a clear distinction between the internal development processes of C, which I call its internal dynamics, and the role played by the boundary conditions.
As for the internal dynamics at the most elementary levels, the two predominant processes are the coordination of actions, leading to the generation of logic, and the coordination of observables, leading to causality. Here I must introduce two important specifications.
First, it should be noticed that coordinations of actions and coordinations of observables were referred to previously as elements of System C. Now I refer to them as dynamic processes. This dual utilization of these terms is connected with my remark that the special nature of the cognitive system consists of the fact that the system, the elements, the relations, and the internal processes are all structures (or structuring processes). At a given level of organization, the already structured coordinations are elements of the system, whereas the coordinations among them are structuringprocesses.
Action schemes are primitive structures. Such structures are forms depending very much on their contents. The logic starts at a gradual process of development that goes from coordinations of actions to inferential anticipation of results and to coordination of inferences. This process was shown in detail in various chapters of Piaget and García (1991/1987) and García (1992b). The important fact, with reference to my present analysis, is that ’’from the beginning, forms partially depend upon contents while remaining necessary for assimilating them” (Piaget & García, 1991/1987, p. 29).
This fact leads to the second specification. The interaction between forms and content is the raw material with which we proceed to the organization
of experience data leading to the knowledge of the empirical world. Knowledge means here, in short, the capacity of providing causal explanations. The common sources of logic and causality[Note 16] as well as the role of logic and logico-mathematical structures in causal explanations (Piaget & García, 1974/1971) are, I submit, the core of Piaget’s epistemological theory.
An important aspect (often overlooked) of Piaget’s theory of knowledge is the clear distinction, in the analysis of the development of cognition, between the logic (deductivistic) phases of the stabilized system and the dialectic character of the developmental processes (Piaget, 1980). The latter led the heterodox Marxist Lucien Goldman to assert that Piagetian theory was “the only existing dialectic epistemology.”[Note 17]
The Role of Boundary Conditions at C/S Interface
When applied to the specific case of cognition, the theory of complex systems outlined here leads to a consideration of the social subsystem of System ∑, as a boundary condition of System C, that may be summarized as follows:
System C possesses an activity generated by the inner dynamics, referred to earlier.This dynamics determines possible paths of development, which can take multiple directions.The boundary conditions that interact with System C in the total System ∑ perform functions that act either to favor or inhibit the realization of one of these possible directions and at the same time to contribute to the content that such direction takes. In this sense the interactions S/C condition the structure adopted by the system, but do not determine the structure as such.The specific way in which the social subsystem of ∑ operates in establishing boundary conditions of C has characteristic features at different levels of development. In Piaget and García, 1983), this problem was taken up in connection with the history of science without any reference to systemic analysis. The concepts of epistemic frame and changes in epistemic frames – introduced to explain profound conceptual differences in different cultures and in different historical periods[Note 18] – are embedded in my present conception of boundary conditions.System C is not a passive recipient of ingoing fluxes but interacts with them and modifies their action.
It should be clear that the five preceding points refer only to the mechanisms through which the Interactions C/S intervene in the construction of knowledge. I have not touched here the problem of the sociogenesis of concepts and theories treated in Piaget (1980).
Concluding Remarks
The kind of system analysis I have presented here, although in a very sketchy form, is meant to show the way for a comprehensive interpretation of genetic epistemology taking into account the multiplicity of factors that intervene in the construction of knowledge. These factors have been studied by Piaget throughout his monumental production, but he never put them together into an integrated theory.
There is, of course, L’Équilibration des structures cognitives (Piaget, 1975) and also the three epistemological syntheses referred to by Bärbel Inhelder in the preface of Psychogenesis and History of Science (Piaget & García, 1983). What is lacking, in my opinion, is the formulation of a constructivistic theory of knowledge as an organized totality, in the sense of the Duhem-Quine thesis, detached from the description of the experimental case studies that the theory is supposed to explain. My proposal for the study of the cognitive system as a complex system that was outlined here goes in that direction.
However, my aim goes beyond the theoretical requirement of having a well-formulated theory that could provide a solid basis for the analysis of its foundations and its scope. My aim points in another direction. Piaget’s conception of the construction of knowledge has been subjected to much criticism. The analysis of much of what I have heard and read by way of criticism and dismissal seems to me to be based on misinterpretations and deformations. Nevertheless, and without lack of respect to the master, I must admit that Piaget was partially guilty. Like any true scientist, he was always exploring ideas and was not afraid to venture into new territories and to advance interpretations that were left floating in the air and that in some cases he himself would have to reject.
My contention is that genetic epistemology, built by him through a monumental effort of interpretation of an immense amount of psychogenetic and historical material, has all the elements of a consistent and self-contained theory of knowledge. I further venture to say that there is at present no alternative theory of knowledge having the same degree of consistency and empirical support with which it can be confronted.
Let us go back to the misunderstandings that have served as the basis to discredit Piagetian constructivism. What is needed is a formulation of the theory through which the sources of such misinterpretations become evident. The systemic interpretation outlined earlier (on which I am now working) has such an objective. Its elaboration exceeds the scope of this presentation. Here I only point out very briefly three areas in which much of the misunderstanding has been concentrated.
The first two have to do with the assumed biologism of the theory and the supposed consequent neglect of the role of social and cultural factors in the construction of knowledge. From the perspective of the systemic approach to both problems, it becomes clear that the total System ∑ involves three levels of organization with different dynamics but interacting at the interfaces B/C and C/S. These interactions neither overemphasize the action of Subsystem B nor neglect or diminish the role of Subsystem S. The analysis of the overall System ∑ brings up the peculiarity of the interactions in both cases (B/C and S/C) because they take place between subsystems that differ in their own organization insofar as they pertain to different domains of phenomena. There is no question that the subsystems interact. The problem is what the mechanisms of interaction are. As an example, I previously summarized a way of operating at the interactions S/C.
The third area of misunderstanding has to do with the structuralism (tout court, without qualification) attributed to Piaget. The polemic on structuralism versus historicism culminating in France toward the middle of the 20th century was surpassed by Piaget with his genetic structuralismthat he condensed in his well-known formula: neither structure without history, nor history without structure. Such structuralism is an unavoidable consequence of constructivism.
Piaget concentrated his efforts on the clarification of the internal dynamics of System C, which is an absolute requirement for the functioning of the overall System ∑. The interactions between the subsystems cannot be properly analyzed without taking into account the way in which System C performs its functions. In short, what C does is to incorporate the raw material of experience into an organizational frame. The cognitive activity of C becomes an exploration in the organizability of experience. And organization implies structure.
References
Apostel, L. (1992). The future of Piagetian logic. In L. Smith (Ed.), Critical assessments (pp. ). London: Routledge. (Original work published 1982)
Aréchiga, H. (1997). Los fundamentos neurobiológicos de la teoría de Piaget sobre la génesis del conocimiento. In R. García (Ed.), Epistemología genética y la ciencia contemporanea. Buenos Aires, Argentina: Gedisa.
Born, M. (1948). Natural philosophy of cause and chance. Oxford, England: Clarendon Press.
Bruner, J. S., Bresson, F., Morf, A., & Piaget, J. (1958). Logique et perception [Logic and perception]: Études d’épistémologie génétique, Vol. 6. Paris: Press Universitaires de France.
García, R. (1984). Food systems and society. A conceptual and methodological challenge. Geneva, Switzerland: United Nations Research Institute for Social Development.
García, R. (1992a). Cambiamenti strutturali nei sistemi aperti: Il caso della cognizione. In M. Ceruti (Ed.), Evoluzione e conoscenza:L’Epistemologie genetica di Jean Piaget e le prospettive del costruttivismo. Bergamo, Italy: Pierluigi Lubrina Editore.
García, R. (1992b). The structures of knowledge and the knowledge of structures. In H. Beilin & P.B. Pufall (Eds), Piaget’s theory: Prospects andpossibilitie. Hillsdale, NJ: Lawrence Erlbaum Associates.
García, R. (1993). From planning to evaluation: A systems approach to sustainable development. Rome: International Fund for Agricultural Development.
Jonckheere, A., Mandelbrot, B., & Piaget, J. (1958). La Lecture de l’expérience [The reading of experience]: Études d’épistémologie génétique, Vol. 5. Paris: Press Universitaires de France.
Piaget, J. (1975). L’Équilibration des structures cognitives: Problème central du dévelopement [Equilibration of cognitive structures: The central problem of development]. Paris: Press Universitaires de France.
Piaget, J. (1980). Les Formes élémentaires de la dialectique [The elementary forms of dialectic]. Paris: Gallimard.
Piaget, J., & García, R. (1974). Understanding causality. New York: Norton. (Original work published 1971)
Piaget, R., & García, R. (1983). Psychogenèse et histoire des sciences [Psychogenesis and history of science]. Paris: Flammarion.
Piaget, J., & García, R. (1991). Toward a logic of meanings. Hillsdale, NJ: Lawrence Erlbaum Associates. (Original work published 1987)
Prigogine, I. (1994). Les Lois du chaos [The laws of chaos]. Paris: Flammarion.
Putnam, H. (1990). Realism with a human face. Cambridge, MA: Harvard University Press. Quine, W. V. (1951). Two dogmas of empiricism. Philosophical Review, 60, 2043.
Quine, W. V. (1969). Ontological relativity and other essays. New York: Columbia University Press.
Quine, W. V. (1973). The roots of reference. Chicago: Open Court.
Russell, B. (1948). Human knowledge: Its scope and limits. New York: Simon & Schuster.
Russell Hanson, N. (1965). Patterns of discovery. Cambridge, England: Cambridge University Press.
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Endnotes
1
This idea is developed in Jonckheer, Mandelbrot, and Piaget (1958) and Bruner, Bresson, Morf, and Piaget (1958)
2
This sentence is the leitmotiv of Russell Hanson (1965).
3
The expression quoted is the title of chap. 20 in Putnam (1990).
4
See for example, Quine, 1973, and especially the section Psychogenesis Summed Up (p. 123).
5
See the later section The Stratified Universe.
6
My publications in this area are in Spanish, with the exceptions of García 1984 and 1993.
7
The distinction between the functioning of a system and the functions of its parts was introduced by Piaget (1975).
8
This distinction is clarified in the section on internal dynamics of the cognitive system.
9
Unfortunately, the term level is used in the literature with a variety of meanings. I use it in three different contexts: level of analysis (as defined here); level of organization (referring to the structure of a system); developmental level (such as a stage in psychogenesis).
10
The organization of the system at the prescientific and scientific levels cannot be treated in the limits of this chapter.
11
There are no ultimate elements of the system. Depending on the purpose of the analysis, I can consider Obs S as a subsystem whose elements are action schemes.
12
Piaget (1975), diagram, p. 62.
13
I use the term boundary for want of a better word and know the risk of misunderstanding. It should be clear that I am not referring to any entity, physical or otherwise. The term is just a convenient way of talking about interactions between subsystems of different natures.
14
See in particular Apostel (1992/1982) and my answer in Piaget and García (1991/1987), chap. 10).
15
I have dealt with the application of the concept of self-organizing system to the cognitive system (García, 1992a, 1992b).
16
As explained by Piaget in a number of his books and articles. See in particular Piaget & García (1991/1987) and Piaget (1980).
17
Mentioned by Piaget in his obituary to Goldman.
18
See in particular Piaget and García (1983), chap. 9.
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