The Genetic Epistemologist

Volume 25, Number 2 (Spring 1997)

1. Inhelder’s Valedictory (Terrance Brown)

2. Announcement of 15th Advanced Course, Archives Piaget

3. An Interpretation of Operational Thought as Internalised Transformations (Andre Hopper)

4. Minutes of the Annual Business Meeting

5. Minutes of the June Board of Directors Meeting

6. Editor’s Note (Chris Lalonde)

by Terrance Brown

In planning this memorial edition of the GE, Chris Lalonde, its editor, asked me, Edith Ackermann, and Michel Ferrari to provide excerpts from the translation of Le Cheminement des Découvertes de l’Enfant (Inhelder & Cellérier, 1992), Bärbel Inhelder’s last book. The publisher of the English edition, Lawrence Erlbaum Associates, has graciously granted us permission to do so. In order for me to orient you quickly, let me first offer some brief remarks that I recently put together for a memorial issue of Human Development.

That said, I think it will be evident why I have selected the following sections from Chapter 1 and the Final Remarks. The title of that chapter is "Toward a Psychological Constructivism: Structures? Procedures?–Two Indissociables"; the excerpt chosen is subtitled "What Subject for Psychology?"

WHAT SUBJECT FOR PSYCHOLOGY?

by Bärbel Inhelder and Denys de Caprona

It is possible to distinguish the way a problem is understood in terms of the child’s general interpretation of reality from the means and the specific knowledge the child uses to solve it. The interpretation of reality derives from the child’s natural epistemology. That epistemology engenders "world views" focused either on understanding the world or on understanding oneself as a thinking subject. For example, young children have world views about why clouds move (Piaget, 1927) as well as world views about where words and thoughts are located (Piaget, 1926). When there is a particular problem to be solved, however, a world view is not enough. In such instances, the knowledge brought into play is essentially specific, and the way it is used is highly individual. This difference constitutes a significant dividing line within genetic psychology.

We began our research in the strong belief that genetic psychology had, up to that point, provided a remarkable description of people’s spontaneous epistemology and of the structures that organize their knowledge. It had sketched out a general architecture of knowledge in terms of a given epistemic subject’s structures. At the same time, we were convinced that it had not really analyzed individual know-how and that this left a vast field of conduct to be studied. Individual know-how involves a variety of cognitive schemes that are more heuristic than general knowledge structures are.

Piaget used the term "epistemic subject" to emphasize the focus of his studies and to mark the reflected and formal nature of structures. He defined the epistemic subject as the nucleus common to every individual’s knowledge at a given developmental level. He conceived subjects, therefore, in terms of their nomothetic rather than their idiosyncratic characteristics. This has led to important misunderstandings that make it essential to distinguish between the epistemic and the psychological subject. Certain psychologists have reproached Piaget and his school for studying a "disembodied" subject devoid of life, but this misses the deep and enduring meaning of Piaget’s approach. Because of Piaget, the epistemic subject is no longer the subject of philosophical knowledge. Rather, it is the subject of rational knowledge, of scientific knowledge broadly construed to include the rationality of intuition or common-sense (just as one speaks of formal and intuitive geometry).

One of the most original aspects of Piaget’s work is that it was centered on basic categories of knowledge without which there can be no adaptation to reality and no coherent thought. Piaget created the foundations of a psychology dealing with the construction of constitutive notions like space, time, causality, etc. That is why the epistemic subject becomes the subject of normative knowledge. Any psychology that would study the epistemic subject must deal with norms and, in doing so, must use models drawn from scientific thought. What interests us about all of this is how the epistemic subject’s normative framework functions, how it allows the psychological subject to grasp reality and organize his activities. Individual conduct can only unfold within the limits of the connections inherent within the categories of the cognitive system. In order to study individual psychological subjects, therefore, focus must be shifted to a different set of categories dealing with these connections (Inhelder, Ackermann-Valladão, Blanchet, Karmiloff-Smith, Kilcher-Hagedorn, Montangero, & Robert, 1976; Inhelder & Piaget, 1979). The observer must try to uncover the dynamics of subject’s cognitive behavior: their goals, the means they choose, how they monitor the results of their actions and estimate progress toward their goal, and the specific heuristics they use to reach goals that may be attained by several different paths. The aim of all of this is to unlock the secrets of the subject’s psychological functioning and to tease out the general characteristics of his procedures. In other words, it is to discern the organization and finality of his action sequences.

Does this mean that these two types of subjects, epistemic and psychological, require completely different psychological approaches? We believe that the distinction between them is by no means absolute. In general, functional psychologies try to preserve the subject as a whole by taking into account everything that might help elucidate cognitive functioning. They cannot, of course, ever do this completely, since they can only study what is accessible at a given moment. Admitting and accepting this limitation, we nevertheless attempt to consider the knowing subject in global and comprehensive fashion. At the same time, the differences in questions and methods, so striking when one moves from structural to functional analysis, should not conceal the fact that it is always the knowing subject in his totality who is being studied. The heuristic distinction between epistemic subject and psychological subject merely reflects complementary ways in which researchers elaborate what the subject knows. In the first case, the emphasis is on normative knowledge; in the second case, it is on pragmatic and empirical knowledge.

To avoid misunderstanding, we need a shared approach to and a common conception of the knowing subject. Within such an approach, categorical analysis of the epistemic subject and functional analysis of the psychological subject must both be accepted as legitimate and complementary. The idea of a subject, active and constructive, engaged in knowing not only the world but also itself must be acknowledged. Such a conception cannot, of course, just be decreed a presupposition for all research; it has to be spelled out and justified. When that is done, it provides a rich ground for research centered on the psychological subject, while at the same time fully recognizing the existence of epistemic functioning.

Once the necessary conjuncture of the two approaches was accepted, we had to figure out what the specific features of the functional perspective were. We realized early on that teleonomy and axiology have a great deal to do with how knowledge becomes individualized. The psychological subject interested us as a knowing subjects, but one with intentions and values. This led us to put special emphasis on the teleonomic and axiological aspects of cognitive activity and to study subjects from the point of view of the goals they set themselves and the values they attributed to things.

The differences between the epistemic subject’s structures and the psychological subject’s functioning arise from the fact that "structure . . . was (and remains) for Piaget an instrument that is both efficient and adequate for characterizing epistemologically what is `universal’ in various subjects’ knowledge, but not for characterizing the individual functioning of the knowing subject’s mind" (Cellérier, 1987). In other words, Piaget’s search for "universals" was an index of his interest in the norms of what he called "the society of minds," a community based on a cooperative exchange of ideas. There can be no doubt that genetic epistemology has helped us understand how existing knowledge has been constructed, but it does not tell the whole story. We wanted to go a bit further and look at subjects as they used and constructed their knowledge something along the lines of Boesch (1991, p. 366) who, in the context of contemporary cultural psychology, has developed a theory of action in which "human-beings interact with their environment in a dynamic way, thereby structuring the object and its social world, as well as the self and its action- potentialities."

This new orientation implies that interest, a cognitive conduct central to functional studies, is no longer (or not always) the same as what passes for interest in studies of the epistemic subject. In fact, the conduct focused on in the studies reported here lies outside the epistemological and psychological fields chosen by Piaget. We no longer study the construction of the great concepts underlying knowledge of reality nor do we describe the structural organization specific to each epistemic domain. Rather, we attempt to shed light on the procedures elaborated in ordinary practical contexts. To that end, we ask ourselves, "How does the child make sense of the task? How does he select and specify the cognitive tools he will use? Are there different representations of each situation and does their adequacy vary? How does the child monitor and evaluate his progress?"

And in the Final Remarks of the book, Inhelder (along with Guy Cellérier, Denys de Caprona, and Jean-Jacques Ducret) concludes:

Table of Contents

15th advanced course of the Archives Jean Piaget

University of Geneva, September 21-24, 1998

The name of Bärbel Inhelder is generally associated with Jean Piaget, the founder of genetic epistemology. For about 40 years, Bärbel Inhelder collaborated with the "patron" providing him with an important part of the experimental data on which he built his theory. However, her specific and determinant contribution to the development of Piagetian theory has not yet received the credit it deserves. Very few people know, for instance, that she was at the origin of the discovery of the stage of formal operations.

Her attachment and admiration for Piaget led her to create, in 1974, the Fondation Archives Jean Piaget, a research center whose aim is to study Piagetian theory. It is within this framework that Bärbel Inhelder organized, for many years, a series of advanced courses for researchers and advanced students. Thus it is natural that, one year after her death, the Archives Jean Piaget have decided to honor her in their next course entitled: Working with Piaget. In memoriam. Bärbel Inhelder. This course aims at bringing to the fore Bärbel Inhelder’s works, not only the ones she co-authored with Piaget, but also all those, that were personal and have partly remained unknown. Following the chronological order of these works, the advanced course will deal with various topics such as conservation, mental handicap, perspective taking, formal thought, longitudinal and intercultural research, learning of cognitive structures and strategies in problem solving. Each topic will be addressed by a researcher of international renown, who will highlight Bärbel Inhelder’s contribution, as well as the actual state of the domain. In addition, 4 workshops developing the different presentations of the conference will give the opportunity to the participants to discuss and exchange actively their ideas. Finally, an afternoon will be devoted to poster presentations.

Table of Contents

An Interpretation of Operational Thought as Internalised Transformations

Piaget’s descriptions and definitions of operational thought were based upon the idea of an operation conceived as an internalised action where the latter appears little different to that of a physical and motor movement of a limb, albeit internal to the mind and immediately reversible and mobile. This essay is an attempt to enhance and "correct" the conception of operations in the hope that our understanding will benefit if we redefine the operation as an internalised transformation that constitutes an already-abstracted attribute. The analysis attempts to resolve some apparent paradoxes presented by Piaget’s descriptions of concrete operations, and also to reject Seltman & Seltman’s (1985) main criticism of his work.

Piaget repeatedly defined operations as internalised actions, and often went so far as to say they derive directly from the subject’s physical actions as enacted in sensorimotor behaviour. The emphasis upon physical action created a terminology that is perhaps more metaphorical than exact when it comes to describing the activity of operational thought. For example, with the operation defined as an "action" enacted in thought, the grouping structure of operations (where each operation is always implicitly bound up with a whole system or structure of inter-related operations), together with the emphasis upon the operation as a reversible action, leads one to imagine the mind as comprising a system of extremely rapid and "machine-like" executions of these actions quite literally. However, this kind of terminology should be treated more as a metaphor or analogy, which, as such, leads to its own problems.

Piaget’s treatment of concrete operations, as actions, also leads to the problem of defining the qualitative difference between the two types of reversibility. On the one hand, we have operations where the reversibility is characterised by direct negation: for example, the action to place an object is negated by the action to remove the object. And on the other hand, we have operations where the reversibility is characterised by reciprocity: the relation of "bigger than" is not put in opposition to the relation of "not bigger than", but to the relation of "smaller than". However, this last statement in itself shows us the difficulty of realising operations of reciprocity as deriving from physical actions enacted by the subject: what is the action of "bigger than"? Rather, the relation of "bigger than" is just that–a relation–and not necessarily the direct result of a physical action.

If Piaget’s apparent reduction of operations to physical actions is difficult to sustain, it would be wrong to conclude that he did indeed reduce operations to actions. In fact, one can argue that Piaget made a number of attempts to provide different qualitative descriptions of operational thought. In "The Origin of Intelligence in the Child" (Piaget, 1985) , in the table in the introduction, we see the function of assimilation, not accommodation, as leading to the operations. For another, in "Possibility and Necessity", Piaget (1987) elaborated upon the functions of differentiation and integration as the mechanism for abstracting from the concrete to the abstract. And, in the various essays on equilibration, Piaget attempted to describe operational structures not so much in terms of systems of actions, but rather as systems of dynamic equilibrium. Of course, all these different perspectives amount to the same thing, not to a change of view. Piaget was attempting to describe better and better what he saw as the (rather difficult) truth, and was not simply changing his mind.

Moreover, with the difficulty of maintaining Piaget’s apparent reduction of operations to physical actions, it would be wrong to go to the other extreme of relying only upon notions of passive perceptions of physical relations. Perception, when conceived as the rather inert function of mere assimilation, does not sufficiently allow for the fact that cognitive structures develop. More significantly, preoperational and operational structures do not just change, but undergo profound qualitative advances in their capabilities. To get from one level to the next, the subject has to be active within the milieu of those relations, the internalisation of which precisely defines the next level over the previous. The definition of an operation as an action retains the sense of active and constructive participation by the subject, whereas some notion of simply "seeing" (i.e. perceiving) these relations fails to address these necessary attributes.

So, concluding with the claim that to define operations as internalised actions leads to difficulties we could do without (and more such examples will be described below), we now have to suggest a more useful terminology that does not suffer the deficiencies Piaget’s own terminology sought to overcome. In what follows, we introduce terms which do not change in any way the logic of Piaget’s description of operations–they only change (and hopefully assist) in our understanding of them.

The subject, as a centre of activity, stands in opposition to the object, which, initially (and practically), is external to the subject. Through the functions of assimilation and accommodation, and through the differentiation and integration of the subject’s structures; through the reciprocal adaptation of structures producing greater and greater abstractions; the subject eventually comes to abstract all the defining properties and determinants of that object. This process of abstraction results, on the one hand, in the subject’s internalisation of that object, and on the other hand, in the subject’s ability to produce that object. For example, in the case of sensorimotor development, the sensorimotor object is one upon which the infant physically acts; and at the culmination of sensorimotor development, the subject has internalised the object to the extent that objects can now be mentally produced as representations.

Within the perspective of a qualitative development, there is, then, a unique relationship between the subject and the object. But the real usefulness of this description is in the identification of the object as such. When sensorimotor development concludes, there is the two-fold conquest of both the internalisation and produce-ability of the (sensorimotor) object. What this means is that the subject’s intelligence conserves the object (at that qualitative level of activity–i.e. physical) despite whatever transformations are imposed upon the object. Alternatively, we can say that the object gains permanence from the subject’s point of view; and yet another way of saying the same thing is to state that the subject’s intelligence compensates for disturbances and perturbances imposed upon (or perceived from) the object. With this terminology, we are then introducing a model whereby the subject becomes able to produce a mental model of the object internally; which means the subject can manipulate (e. operate upon) that mental object with complete conservation of it.

Sensorimotor development concludes with the complete internalisation of the sensorimotor object. The type of object appropriate to the level of sensorimotor development is that upon which the subject can both sense and physically act upon, together. In contrast, there is a qualitatively higher set of objects which can either be sensed, or acted upon, but not both together. Examples of this set of objects includes colour (which can be sensed but not sucked, grasped, kicked or rattled), and simple ordinal counting (appropriate to action but not sensation). It takes a whole further qualitative stage of development to construct and internalise these latter types of objects: this stage is that of preoperational, or intuitive, intelligence.

The intuitive object is therefore qualitatively more advanced than the sensorimotor object, and of course subsumes it too. When it comes to understanding the nature of concrete operations, it is the precise nature of the intuitive object (which includes comprehending the limitations of the sensorimotor object) which must be grasped. Concrete operations operate upon the internalised intuitive object. When intuitive (preoperational) development completes, the subject is in possession of mental faculties whereby the concrete physical object gains an independence of its perceivable transformations through the ability to enact those transformations (and hence compensate for them) in thought.

It is in the descriptions of concrete operations where Piaget was most emphatic upon the property of reversibility. In helping us understand how the reversibility of operations is to be conceived, Chapman (1988) focused on the distinction between reversibility as such (mobile, internalised and immediate) with the relatively static attribute of revertibility. With a direct action that has not been internalised, one may indeed re-enact that action in the opposite direction, thus achieving revertibility of that action. But this is only to have "travelled" the relation circumscribed by that action in the two directions–it is not equivalent to having "seen" that action as an entity in itself. Only when the action is internalised does it become an immediately reversible operation. However, this terminology needs to be widened to comprehend the reversibility of all relations, as internalised transformations, and the restrictions implied by the notion of a physical action as such.

Without wanting to get into the task of deriving a full explanation of operations, it should nevertheless be apparent how this model of intelligence (at a certain qualitative level), where the object is internally produced (i.e. represented), no longer requires a description of thought only in terms of actions. For when the subject becomes powerful enough to represent the object, it also follows that the subject has internalised (or can at least mentally enact) all the relations and determinants of that object. Thus, it is not hard to foresee how the mental representation of the object will soon be followed by not so much the internalisation of mere actions upon the object, but of all transformations and relations of that object.

Now, the key to understanding the nature of concrete operations is to develop this model such that mental structures are seen to have been constructed which can than assimilate, directly, even passively, the inter- and intra- object relations that constitute transformations upon the object. Concrete operations where the reversibility is characterised by reciprocity are then easily understood as the internalised enactment of a transformation of a mental object. To judge one apple as "bigger than" another is mentally equivalent to performing the transformation of expanding the smaller apple to the size of the other, except that such a relation is only properly maintained in thought (i.e. conservable, with identity, permanence and compensations) when that relation is itself an object of thought–hence its immediate and instantaneous reversibility. What has happened is that the attribute of "bigger than" has been abstracted in itself, and becomes a schema in its own right: therefore, that schema assimilates (or produces) the relation independently to any actual and physical instance of that relation. For example, the representation of the colour yellow can only be representatively understood when it is also understood to be a "separate thing" to any particular object which happens to be yellow. If relations like bigger than" also become internalised in the same sense, then mental transformations within such relations can be understood precisely as transformations, and there is no need to try to reduce the relations to some notion of physical actions.

Concrete operations where the reversibility is characterised by negation are again understood as mental transformations of the objects mentally represented. In the paradigm of the two sets of coloured beads, the child is asked to compare the quantity of beads of one colour against the quantity of all the (wooden) beads, but the question is phrased in such a way as to force the actions of the positing and removing of the qualifying attributes of the beads as mental transformations.

It then becomes true to state that there are two sort of transformations that can be applied upon the concrete object. In the first place, the concrete object can be "placed" and "taken away", which amounts to the same thing as willfully assimilating the object to a particular schema (e.g. to permit a particular bead into the mobile schema of yellow beads), or denying that assimilation (e.g. to take a particular bead out of the set of yellow beads), which means that the transformation of this type is characterised by the reversibility of negation. And in the second place, the object in itself can be transformed: it can be made bigger or smaller, longer or shorter, thicker or thinner, brighter or duller, hotter or colder, lighter or heavier, etc. In contrast to classificatory operations, such relational transformations do not negate the object, but rather relate it to another object, both of which are being assimilated upon the same attribute. Note that the transformation of making the object longer, for example, is qualitatively the same as comparing two objects treated as identical except for their length: they are both being assimilated to the one attribute of length, but such that that attribute is conserved despite the fact it is being transformed.

Classificatory operations (reversed by negation) assimilate or reject the object according to the attribute. Relational operations (reversed by reciprocity) transform the object within the attribute. In respect to a single particular attribute (e.g. colour), classificatory operations determine how the object is the same as other objects, while relational operations determine how the object is different to other objects. [NB: Even the relation of symmetry (grouping VI) is to consider how the object may or may not be different to others in terms of the one attribute.] It is the fact that thought operates upon objects as such, and the manner in which such objects undergo transformations with respect to their abstracted attributes, that leads directly to the split between the two types of reversibility.

At the level of concrete operations the issue of number and basic arithmetic gives rise to many paradoxes due to the manner in which Piaget presented his theory of operations. First and foremost, number itself is an operational construction and is not in itself sufficiently permanent, conserved or objective, unless also included in the basic operations of addition and subtraction. In other words, if one is to sensibly talk about number, a basic understanding of addition and subtraction necessarily goes hand-in-hand with it.

In Piaget’s description of number, the arithmetic operations are reversible actions, just as for the eight groupings of intensive logic, except that this time they form an algebraic group rather than a grouping. However, Piaget also described number as a synthesis, or fusing, of the intensive operations of classifications and relations. In particular, addition and subtraction might be seen as "reducible" to a synthesis of groupings I (primary addition of classes) and V (simple seriations). Herein lies the first paradox: how can number and arithmetic be described, on the one hand, as their own system of operations, as internalised and reversible actions of thought, and on the other hand, as a "synthesis" of other types of internalised action?

A second paradox arises from Piaget’s description for how classificatory and relational operations, at the concrete level, must remain separate systems (because classificatory and relational operations cannot be operationally combined with each other), and yet number is described as a "synthesis" of these two types of reversibility. If the two types of reversibility cannot be concretely "combined", what does it mean to talk of their "synthesis"?

I would argue that the above paradoxes arise, not because the theory is particularly wrong, but because of Piaget’s insistence of talking about operations as internalised actions. The terminology of operations, as such, is probably extremely apt for the logico-mathematical analysis and presentation which Piaget made (coming from the concerns epistemology), but is not so apt when the concern is primarily psychological. Seltman & Seltman (1985) published a work in which Piaget was criticised for conflating a logical analysis with a psychological one (among others), and came to the conclusion that Piaget’s entire theory must therefore be fundamentally flawed. However, I would contend that such a conclusion is premature and unhelpful, especially as Seltman & Seltman provided no evidence of comprehending the difficult problems which Piaget was tackling. Instead, I am contending that Piaget’s theory is fundamentally correct, and that the problem is to clarify the "conflations" and confusions of terminology, and to improve the theory, not to dispense with it.

Let us first justify Piaget’s claim that the two systems of concrete operations of classifications and relations cannot be combined within a single system (operationally) at the concrete level. The solution gains a little clarity if we use our model of the internalised, mental (and still concrete) object, produced in thought. The answer is that it is simply meaningless to both posit the object according to the attribute and transform (i.e. relate) the object within that attribute at the same time. Either the object is there or it isn’t (hence the classification); if it is not there then it can’t be transformed; and if it is there, then any attempt to transform it prohibits the possibility of removing it (i.e. at the same time as transforming it). One can perform the operation of including the class of red beads within the class of wooden beads (as a concrete and directly presented configuration), but then within the same concrete context, to start taking about each bead as being "more red" or "less wooden" than another (i.e., performing operations of reciprocity) simply has no bearing or meaning upon the classificatory operations, or vice versa. For this reason, the two types of reversibility — negation and reciprocity, as described above — cannot operationally combine among themselves in any concretely meaningful way.

Then, to explain the paradox where number appears as a "synthesis" of the "un-combineable" operations of classifications and relations, we have to understand the qualitative nature of the object which intelligence has abstracted and internalised at the point by which concrete operations become active. This, however, is a task of immense proportions, and which I have begun to take on, but which cannot be properly presented in this essay. Instead, the following notes will have to suffice. In the paradigms of the conservation of basic quantity (i.e. pouring a quantity of liquid from a tall, thin glass to a short, wide glass; and changing the shape and size of a ball of modeling clay), intuitive intelligence concludes by having abstracted all the perceivable attributes of the object (e.g. length, width, colour) from the object itself. Well, if all the perceivable attributes have gained an independence from the physical object, what is left to constitute the physical object in itself? The answer is some notion of basic "substance" and "quantity". These latter abstractions are what remain permanent in the face of perceived (but judged to be irrelevant!) transformations of the object.

If all perceivable transformations and attributes of the intuitive object have been abstracted (and become independent of) that object, then intelligence has developed to the level of having produced the concrete object. The concrete object becomes, for the first time, a true abstract concept, since it is no longer reducible to its sensible (and motor) components. But what this level of abstraction also means is that intelligence can now operate upon the object either according to transformations of its (represented) attributes (hence the eight groupings of intensive logic) or according to the concrete object in the absence of all such attributes–leading to number. As Piaget wrote, number involves the production of a unit which is both identical to (i.e. same as) and separate from (i.e. different to) any other unit. The concrete object can constitute such a unit thanks to the level of abstraction achieved.

In this context, the way to resolve the aforementioned paradox (without providing a comprehensive treatment here), is to consider the subject and its schemata as a unity (in the Kantian sense) which has all these different ways upon which it can manipulate and transform the concrete object. As a unity, the subject’s schemata produce number simultaneously with intensive logical operations, since the whole thing derives from the general qualitative nature of the abstractions made. There is then no need to "synthesise" classificatory operations with relational ones to produce number (since thought, as a unit, operates upon the same objects), and number can indeed engender its own operations without them having to be reducible in some way to intensive operations.

From the point of view of (late) intuitive and (early) concrete intelligence, an attribute of an object is a perceivable entity which has become an abstracted object of though in itself. As such, an attribute has, representatively, become "liberated" from any actual object bearing that attribute. Operations, then, are apparent in the sense that the subject is able to represent those attributes which, in fact, can only be objectified as perceived transformations of the object. For example, sensorimotor development cannot understand colour, despite being able to perceive it, because sensorimotor schemata are not sufficiently advanced as to be able to transform colour independently to the coloured object. Cognitive development throughout the preoperational (or intuitive) period serves precisely to abstract such attributes from the objects to which they pertain, ready for concrete operations to make use of in their own right.

However, if (some of) Piaget’s rather one-sided terminology is to be adhered to, a concrete operation would become an action that is enacted somewhere in the subject’s mind, and immediately reversed (as an identical action in the opposite direction), every time the particular relation in question has to be thought about. Clearly, this model is too mechanical and primitive, and Piaget himself insisted upon the simultaneous integration of any operation within an immediate and co-existent system of multiple operations. Instead, if one considers how the subject’s intelligence has internalised, objectified and abstracted those relations upon which operations are supposed to bear, then one has a model whereby thought becomes more akin to assimilation (though also production) and less laborious–at least for those relations already comprehended.

I would also contend this latter model is more intuitively acceptable to ourselves (as adults who constructed all these abstractions many years ago). For example, in the various conservation of quantity paradigms mentioned above, the fact that the quantity of water remains the same despite its transformations appears to us to be "obvious" and instantaneous; we do not feel the labour of having to perform mental actions.

Saturday, June 21, 1997

Santa Monica, CA