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p Some modern adherents of the interpretation of the cognitive relation as a special type of interaction between two natural systems believe that the defects of epistemological conceptions criticised in the previous section are not determined by cognition being regarded as a purely natural process but by a one-sided view of the subject-object interaction: the action of the object on the subject is studied but the reverse action of the subject on the object is not. In this connection it is believed that proper attention to the subject’s own activity in the analysis of cognition, in particular to his external material activity, would allow to overcome the fundamental shortcomings of the epistemological conception of metaphysical materialism: the normative nature of cognition, for instance, will then be explained. It should be stressed that the activity the necessity of studying which is asserted is in this case understood in 28 the spirit of natural philosophy, as a purely natural characteristic of a specific body—the cognizing subject. This approach to the analysis of activity is quite acceptable to the adherents of this view. In fact, it does not in principle go beyond the interpretation of the cognitive relation as a natural interaction of a special type. Although its adherents analyse some cognitive problems with greater discrimination and precision than Locke and the other theoreticians who stressed the one-sided action of the object on the subject, it is still in principle impossible to construct an adequate epistemological conception in the framework of a modernised naturalist model of cognition. The theoreticians who interpret the subject’s cognitive activity in a naturalistic fashion, either stick to the positions of metaphysical materialism or accept the standpoint of subjective idealism, or even assimilate both of these positions.

p An illustration of this conception of the cognitive relation is the system of the so-called genetic epistemology of Jean Piaget, one of the most prominent Western psychologists. "Genetic epistemology”, which is extremely influential abroad, has arisen as an attempt to philosophically interpret the extensive results of experimental and theoretical psychological studies carried out by Piaget and his collaborators during several decades. In analysing "genetic epistemology”, we shall endeavour to separate the actual facts discovered by Piaget (we shall return to these facts, characterising important aspects of the process of cognition, in. our positive inquiry into the problem) from his theoretical interpretation, which is largely untenable in its philosophical aspects.

p Two features distinguish the approach of the Swiss psychologist. First, he recognises the subject’s active role at all levels of the cognitive process, beginning with perception and ending with complex intellectual structures. This activeness of the subject is expressed in the transformation of the object, in the fact that the latter can only affect the subject in the course of his activity, which varies in character at different intellectual levels. Second, the cognitive relation is interpreted in the framework of the system- structural approach: various cognitive formations are viewed as integral structures; and the subject-object relation itself is regarded as a special type of system in which subject and object are mutually “balanced”.

p The main ideas of the operational conception of intelligence (as Piaget refers to his psychological theory) are as follows:

p 1. Intelligence is defined in the context of behaviour, 29 that is, of specific exchange (interaction) between the external world and the subject.

p “...Unlike physiological interactions, which are of a material nature and involve an internal change in the bodies which are present, the responses studied by psychology are of a functional nature and are achieved at greater and greater distances in space (perception, etc.) and in time (memory, etc.) besides following more and more complex paths (reversals, detours, etc.).”^^4^^ According to Piaget, intelligence is a definite form of the cognitive aspect of behaviour, whose functional purpose is the structuring of relations between environment and the organism.

p 2. Intelligence, just as all the other biological processes and functions, is of adaptive nature, in Piaget’s view. Adaptation is in this case understood as equilibrium between assimilation (of the given material by the existing systems of behaviour) and accommodation (of these schemes to a definite situation). Adaptation may obviously vary quite extensively in its nature. It may be material, with equilibrium attained by "interpenetration between some part of the living body and some sector of the external environment”,^^5^^ or functional, which is not reducible to such material interpenetration (or exchange). A most important element in this understanding of the nature of intelligence is the assertion of the specifically functional nature of adaptation in the intellectual sphere.

p 3. Cognition realised by intelligence is not, according to Piaget, a static copy of reality. To cognize an object means to act on it, to reproduce it dynamically, and that is why the essence of intelligence lies in its active nature. Psychical and, consequently, intellectual life begins "with functional interaction, that is to say from the point at which assimilation no longer alters assimilated objects in a physico-chemical manner but simply incorporates them in its own forms of activity (and when accommodation only modifies this activity)".”

p 4. Intellectual activity is derivative from the subject’s material actions; its elements, or operations, are interiorised actions which prove to be operations in the proper sense of the word only if they are mutually coordinated, forming reversible, stable, and at the same time mobile integral structures.

p 5. These integral structures may differ essentially both in the degree of their reversibility and the nature of mobility, and in their being related to a given sphere of objects. Moreover, other cognitive functions (for example, perception) are also characterised by structural organisation. The problems of genetic affinity between cognitive functions 30 (and behaviour as a whole) and the specificity of intelligence are solved by Piaget in the following manner. Intelligence "is an extension and a perfection of all adaptive processes. Organic adaptation, in fact, only ensures an immediate and consequently limited equilibrium between the individual and the present environment. Elementary cognitive functions, such as perception, habit and memory, extend it in the direction of present space (perceptual contact with distant objects) and of short-range reconstructions and anticipations. Only intelligence ... tends towards an all-embracing equilibrium by aiming at the assimilation of the whole of reality and the accommodation to it of action, which it thereby frees from its dependence on the initial hie and nunc."i Hence the principle of genetic deduction of the intellectual operations, the reverse side of this principle being the impossibility of indicating the strict boundaries of intelligence: the latter has to be defined only "by the direction towards which its development is turned".^^8^^

p Thus intelligence is, according to Piaget, a special form of interaction between subject and object, specific activity which, being derivative from external object-related activity, emerges as the totality of interiorised operations mutually coordinated and forming reversible, stable, and at the same time mobile integral structures. Intelligence, says Piaget, may be defined "in terms of the progressive reversibility of the mobile structures" or, which is the same, as "the state of equilibrium towards which tend all the successive adaptations of a sensori-motor and cognitive nature, as well as all assimilatory and accommodatory interactions between the organism and the environment".^^9^^

p Piaget’s psychological and epistemological conception thus proves to be derivative from his interpretation of the interrelation between the organism and the environment, showing distinct biological orientation. We shall later see that Piaget endeavours to interpret the biological processes of assimilation and accommodation, in their turn, in terms of a physical and mechanistic theory of equilibrium.

p The core of the genesis of intelligence is, according to Piaget, the formation of logical thinking, ability for which is neither innate nor preformed in the human mind. Logical thinking is the product of the subject’s growing activity in his relations with the external world.

p Piaget singled out four basic stages in the development of logical reasoning: sensori-motor, pre-operational intelligence, concrete operations, and formal operations.^^10^^

p I. Intellectual acts at the stage of sensori-motor 31 intelligence (up to the age of two) are based on coordination of movements and perceptions and do not involve any notions. Although sensori-motor intelligence is not yet logical, it “functionally” prepares logical reasoning proper.

p II. Pre-operational intelligence (between two and seven years) is characterised by well-formed speech, notions, interiorisation of action in thought (action is replaced by some sign: word, image, or symbol).

p At the stage of pre-operational intelligence, the child is not yet capable of applying an earlier acquired scheme of action with constant objects either to remote objects or to definite sets and quantities. The child does not yet have reversible operations and the concepts of retaining applicable to actions at a level higher than sensori-motor actions.

p III. At the stage of concrete operations (between eight and eleven), different types of intellectual activity that have appeared during the previous period finally reach a state of "mobile equilibrium”, that is, they become reversible. At the same time, the basic concepts of retention are formed, the child is capable of concrete logical operations. He can form both relations and classes out of concrete things. But the logical operations have not yet become generalised. At this stage children cannot construct correct speech independently of real action.

p IV. At the formal operations stage (between 11-12 and 14-15) the genesis of intelligence is completed. The ability to reason hypothetically and deductively develops at this stage, and the system of operations of prepositional logic is formed. The subject can equally well operate with both objects and propositions. The emergence of these systems of operations shows, in Piaget’s view, that intelligence has been formed.

p Although the development of logical reasoning forms an important aspect of the genesis of intelligence, it does not fully exhaust this process. In the course and on the basis of formation of operational structures of varying degrees of complexity, the child gradually masters the reality surrounding him. "During the first seven years of life f write Piaget and Inhelderj the child gradually discovers the elementary principles of invariance pertaining to the object, quantity, number, space and time, which lend his picture of the world an objective structure.”^^11^^ The most important components in the interpretation of this process, as suggested by Piaget, are (1) dependence of the analysis of the reality as constructed by the child on his activity; (2) the child’s spiritual development as a growing system of invariants mastered by him; (3) development of logical 32 reasoning as the basis for the child’s entire intellectual development.

p Piaget’s psychological and logical conception was the concrete material on which the conception of "genetic epistemology" developed.^^12^^

p Piaget believes that the numerous attempts at constructing a scientific epistemology in the past have been fruitless, because they proceeded from a static standpoint.

p Piaget’s "genetic epistemology" substantiates the existence of a "dialectical connection" between the subject and the object, the indivisibility of the subject S and the object O. It is, writes Piaget, from the interaction S ^= O that action, the source of cognition, follows. The starting point of this cognition is neither S nor O but the interconnection =?*, characteristic of action. It is on the basis of this dialectical interaction that the object and its properties gradually come to light—through decentration, which frees cognition from external illusions. Starting from this interaction ^=, the subject discovers and cognizes the object, organising actions in a consistent system constituting the operations of his intellect or reasoning.^^13^^

p The development of cognition, Piaget believes, leads to the subject’s knowledge of the object becoming increasingly more invariant relative to the changing conditions of experience and the subject’s position relative to the object. On this path the author of "genetic epistemology" arrives at the idea of applying the theory of invariants (in particular, of the mathematical theory of groups) to the study of the processes of cognition. Piaget presents in mathematical form the cognitive entities taking shape at various stages in the development of intelligence as different structures, namely, as algebraic groups (and groupings), order structures, and topological structures. From Piaget’s standpoint, the invariant of a transformation group in an intellectual structure is knowledge about the object itself, about its own properties, irrespective of any particular reference frame in which these properties are discovered. The reversibility of operations in the intellectual structures is directly linked with the presence of invariants in them.

p In Piaget’s theory, in variance of knowledge about an object relative to some subjective “perspective” is ensured by the actual interaction of subject and object, connected with the subject’s action and quite unambiguously defined by the properties of the object itself which exists objectively and actually. In Piaget’s discussion of this problem, materialism as the basic philosophical premise of his conception stands out particularly clearly.

p The appearance of stable and reversible operational 33 structures does not, of course, mean, in Piaget’s view, that situations of instability cannot henceforth arise at all in the subject’s knowledge. Knowledge is always knowledge of an external object, whose properties are inexhaustible: it presents to the subject ever new aspects and poses ever new problems. When Piaget points out the growth in the stability of knowledge of the object in intellectual development, he has in mind, first of all, the formation of reversible structures of intellectual operations, that is, of logical instruments which permit the subject to solve those tasks which reality poses before him. Inasmuch as Piaget believes that the solution of tasks is based on well- formedness of operational structures permitting to solve classes of problems of the same type, the growth in the stability of intelligence structures also indicates a growth in the stability and invariance of the subject’s knowledge as a whole.

p But it is a well-known fact that, however important the invariance criterion may be as an indicator of the objectiveness of knowledge, it is not the only or the main criterion, and that becomes quite clear at the highest stages of the development of cognition, particularly in the construction of scientific knowledge.

p It is this variety of forms which the invariance criterion can assume, and its derivation from other, more fundamental criteria, that are not taken into account in Piaget’s works. He singles out mostly those aspects of the formation of invariant knowledge of the obiect which may be adequately described by the available mathematical apparatus and, in the first place, by group theory. The proposition concerning the role of reversibility of operations as a means of attaining invariant knowledge is also derived by Piaget from group theory. But if one takes into account the diversity of forms which invariance of knowledge assumes, one will have to admit that reversibility of cognitive operations is not apparently the kind of universal indicator of objectiveness of knowledge which Piaget believes it to be.

p Attempts to solve the problem of objectiveness of knowledge with the help of the invariance concept are numerous in the foreign literature on epistemology and the methodology of science. Thus Max Born, one of the prominent modern physicists, points out in his discourse on the nature of "physical reality" that the concept of invariant of a group of transformations is a key to the concept of reality not only in physics but also in any aspect of the world.

p “Invariants are the concepts of which science speaks in the same way as ordinary language speaks of ‘things’, and 34 which it provides with names as if they were ordinary things.”^^14^^ Most measurements in physics, Born believes, do not pertain to objects themselves but to their projections on other objects. "The projection... is defined in relation to a system of reference... There are in general many equivalent systems of reference. In every physical theory there is a rule which connects the projections of the same object on different systems of reference.”^^15^^

p However, the attempts to identify construction of objective knowledge with establishment of the object’s invariant characteristics run into serious philosophical difficulties. The apparatus used by the physicist during experiments function in this aspect as quite real physical bodies interacting with other bodies according to objective laws, so that the results of interaction, just as, generally speaking, the properties arising from the relation of one object to other objects, the so-called projections, must exist objectively and really. Besides, invariance is not an absolute characteristic of a given property, being established only in a definite system of relations, and that which is invariant in one system may be non-invariant in another, to say nothing of all possible systems. Thus, the theory of invariants cannot have that fundamental epistemological significance which Piaget and other researchers abroad ascribe to it.^^16^^

p Piaget’s "genetic epistemology" endeavours to link up the theory of invariants with the theory of equilibrium. Here the fundamental philosophical weakness of Piaget’s conceptions comes to light most clearly.

p Piaget believes that the emergence of invariants in the structure of intelligence (and, consequently, the appearance of reversible operations) is directly connected with mutual balancing of operations and, as a result of this, with the subject-object equilibrium. The theory of equilibrium must therefore provide a key to understanding intellectual development. Equilibrium is interpreted by Piaget as the maximum magnitude of the subject’s activity compensating for certain external changes, rather than as balance of forces in the state of rest.

p In building the model of subject-object equilibrium on the analogy of the equilibrium between a physical system and its environment, and later on the analogy of the equilibrium of the biological organism with the environment, Piaget cannot deduce from this model the specific properties of the kind of “equilibrium” between subject and object and is therefore compelled to introduce these properties into his system from the outside, in apparent discord with his own basic model.

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p In mechanics, a closed system is believed to be in equilibrium if the sum of all possible types of work within the system equals zero.

p Using the term “equilibrium” in his theoretical arguments, Piaget at first understood it in the sense that is close to the above. The subject-object system (and by “ object” he means, first of all, that part of the subject’s environment with which he directly interacts, practically and cognitively) may be regarded as being in equilibrium if the sum of all possible interactions between the subject and the object equals zero (that means that the subject can always perform an action reversing the first action thus regaining the original situation). The external equilibrium between the subject and the object is ensured by establishing an equilibrium within the operational structure: the existence in this structure of an operation that is the reverse of the basic one gives precisely this effect that the sum of all possible operations within the structure equals zero.^^17^^

p It soon turned out, however, that Piaget’s analogy between equilibrium in a mechanical system and equilibrium in the structure of intellectual operations is extremely imprecise. First, the mechanical principle deals with a closed system, that is, one that is isolated from the influence of the environment, whereas the whole purpose of the “ balancing” of intellectual operations of which Piaget speaks is the attainment of stability of the knowledge about the object relative to the mutable experience. In other words, Piaget deals with an “open” rather than “closed” system. Second, it came to light that in physics itself system equilibrium is only rarely expressed by the above principle. In the more general cases of system equilibrium, considered, e.g., in thermodynamics, there is a minimum of potential energy in the system (which is conditioned by the attainment of the most probable state by the system). Mechanical equilibrium proves to be only a special case of the more general equilibrium state. In recent years, a number of physicists and mathematicians (I. Prigozhin and others) have generalised the concept of equilibrium to include "dynamic equilibrium”. It proved to be possible to apply the mathematical theory of dynamic equilibrium of a system to the study of "open systems”, i.e., systems exchanging matter and energy with the environment. Some biologists have made attempts to apply the theory of dynamic equilibrium to the study of living organisms as "open systems”.

p Piaget speaks of “balancing” operations within a cognitive structure, believing this “balance” attainable due 36 to complete reversibility of operations. Endeavouring to get rid of teleology in explaining the inner trend of the subject’s actions towards mutual balancing, Piaget aims at constructing his conception on the basis of the physical theory of equilibrium. As we know, the tendency of a closed physical system towards the most probable state is explained by the action of statistical laws, without any reference to hidden goals. However, equilibrium in physical systems is very often achieved by attaining some irreversible state rather than by increasing the reversibility of processes within the system.

p Finding it impossible to deduce from the physical model of equilibrium cognitive “equilibrium” of subject and object, which is of fundamental importance for his psychological and epistemological conception, Piaget was compelled to stress more and more the specific character of psychical equilibrium.

p Piaget believes it necessary to distinguish between " instrumentally possible" and "structurally possible" operations. The former operations are those which the subject himself regards at a given moment as possible, that is, as operations he might perform. Although from the standpoint of the subject himself "instrumentally possible" operations are not those actually performed by him, an outsider (e.g., the psychologist studying the given person) may regard them as real, for the subject’s contemplation of his possible actions is just as real a psychological process as an external activity. "Structurally possible" are those operations of the subject which he himself does not regard at the given moment as possible (or he may even be unaware of his ability to perform them) but which he is nevertheless capable of performing, for he has at his disposal an objectively formed operational structure including these operations. The basis of all operations of the subject is thus "structurally possible" operations, coinciding in fact with the operational structure itself. Piaget asserts that in the intellectual operational structure the equilibrium of actual and possible changes is expressed in a manner quite different from a physical system. While in the intellectual structure there exist "instrumentally possible" operations that are mediating links, as it were, between real and possible changes, in a physical system there can only be a sharp dichotomy between real and possible changes. So the analogy between intellectual and physical equilibrium cannot be taken very far.

p Analysis of the actual “equilibrium” between the subject and the object in the process of cognition led Piaget to a recognition of such characteristics of this equilibrium 37 which can in no way be deduced from the model of equilibrium of a physical system or a biological organism. Referring to “instrumentally” and “structurally” possible operations, Piaget is compelled to speak of consciousness, of contemplation by the subject of his possible actions and of other specifically psychical states as the necessary component of the subject-object equilibrium.

p Recognising the insufficiency of the physical theory of equilibrium for understanding the subject-object equilibrium, Piaget demonstrated, in fact, the weakness of his own epistemological stand, although he failed to work out a conception that would adequately explain the facts which he analysed.

p Characteristically, when Piaget had to define the concept of “reversibility” of an action (i.e., the concept of operation, for an operation is a reversible action), he could not restrict himself to pointing out the connection between reversibility and the possibility of performing an action in two opposite directions and had to indicate the importance of realisation of the fact that the action remains the same as it is performed in either of the directions.^^18^^ Naturally, the concept of reversibility cannot be defined in this way in physics.

p Piaget admits that the reversibility of intellectual operations of which he speaks has nothing to do with the reversibility of actual physical processes. Thus, speaking of the formation of the concept of time, he remarks that reversibility of time does not mean for the subject that actual physical time can flow in the opposite direction (actual time is irreversible) but merely the fact that the subject can mentally proceed not only from the previous moment of time to the subsequent one but also from the subsequent to the preceding (i.e., he can not only perform the operation A -> B but also the operation B -> A), realising, however, that the actual sequence of moments does not change (i.e., A precedes B). "Constructing time ... is an excellent example of joint action of the reversible processes of the subject and the irreversible processes of the object,” remarks Piaget.^^19^^

Thus Piaget fails to deduce in the framework of his conception the normative character of cognitive structures without resorting to the phenomena of consciousness, those phenomena whose study cannot be carried out by interpreting the subject-object interrelations in terms of mechanics, physics, and biology, and thus does not accord with the fundamental approach of "genetic epistemology”. It proves impossible to explain objectiveness of knowledge and other fundamental characteristics of cognition by the 38 theory of “balancing” the subject and the object interpreted as bodies given by nature.