and mathematicians, which are tautologies, are "empty", "empty",
"do not say anything about reality" and are admissible in science only as special
former syntactic expressions (logical syntax elements) - see:
R. Carnap. Logical syntax of language. London, New York. 1937; Int-
production to Semantics. Cambridge, Mass., 1942.
In contrast to this understanding, J. Piaget defends the view
according to which the laws of logic and the principles of mathematics are
real constructions of the subject; their structure J. Piaget
lurking to find out within the framework of his operational concept of intellectual
that. It should be noted that against the concept of "emptiness" for-
many modern logicians act as the cons of logic; see for example:
P. V. Tavanets. On the so-called tautological character of logic.
"Questions of Philosophy", 1957, No. 2; G.Frey. Die Logic als empirische
Wissenschaft, in book. "La Theorie de l "argumentation". Louvain-Paris, 1963,
pp.240-2(32; however, in this case, the criticism proceeds according to its own logical
(and not like J. Piaget - on psychological and logical grounds).
The antinomy of the class of all classes. Antinomies (paradoxes, aporias) -
contradictions in reasoning that arise when all conditions are met
viy logically correct reasoning. An example of an antinomy is
serve as the antinomy “Liar” formulated in ancient philosophy:
“One Cretan said: “All Cretans lie.” What did he say - the truth or
False?". If his statement is true, then it must be false.
if it is false, then the Cretan has spoken the truth.
The antinomy of the class of all classes (or the set of all normal
sets, that is, those that are not elements of themselves)
discovered by B. Russell in 1902 (W. Russell. On finite and infinite car-
dinal numbers. "American journal of mathematics", 1902, pp. 378-383;
see also: S. K. Klini. Introduction to metamathematics. M., IIL,
1957, p. 40). Translating this antinomy into ordinary language, Ras-
sat gives the example of a village barber who shaves
all those and only those inhabitants of their village who do not shave themselves.
Should he shave himself? Both positive and negative
the answers to this question are equally provable.
Paradoxes like Russell's paradox arise with a certain form
malization of the reasoning process, the change of which (for example, through
the theory of types, distributing various objects - individuals, properties
va individuals, properties of properties, etc. by type) makes it possible to avoid
these paradoxes. J. Piaget refers to this paradox as
argument in favor of an operational interpretation of logic and mathematics.
Logistics is a term proposed in 1901 by L. Couture, Itel-
son and A. Lalande to designate a new, mathematical logic.
At present, the term "mathematical logic" is more common.
ka" (sometimes "symbolic logic"), but French and some
other researchers often use the term "logistics". Wide
uses this term in his works and J. Piaget.
Axiomatic method in logic. In the concept of J. Piaget, it is essential
important role belongs to the proof of the impossibility of using
for the psychological study of axiomatic constructions of logic.
This problem, in particular, is raised by him in the second chapter of "Psychology

Creator of the most profound and influential theories of the development of intelligence became a Swiss scientist Jean Piaget(1896-1980). He transformed the basic concepts of other schools: behaviorism (instead of the concept of reaction, he put forward the concept of operation), gestaltism (gestalt gave way to the concept of structure) and Jean (taking over from him the principle of interiorization, which goes back to Sechenov).

Piaget puts forward the provision on the genetic method as the guiding methodological principle of psychological research.

Focusing on the formation of the child's intelligence, Piaget emphasized that in scientific psychology any research should begin with the study of development and that it is the formation of mental mechanisms in a child that best explains their nature and functioning in an adult. On a genetic basis, according to Piaget, not only separate sciences, but also the theory of knowledge should be built. This idea became the basis for the creation genetic epistemology, those. the sciences of the mechanisms and conditions for the formation in humans of various forms and types of knowledge, concepts, cognitive operations, etc.

It is known that representatives of different approaches differently understood the essence of the development of the psyche. Supporters of the idealistic, introspective approach took as their starting point the psychic world closed in itself; Representatives of behavioral psychology understood the development of the psyche, according to M.G. Yaroshevsky, “as filling the originally“ empty ”organism with skills, associations, etc. under the influence of environmental conditions. Both of these approaches Piaget rejected both in genetic and functional terms, i.e. in relation to the consciousness, mental life of an adult.

Piaget's starting point for his analysis was interactionaction of a holistic individual- and not the psyche or consciousness - with the surrounding world. He defined intelligence as a property of a living organism, which is formed in the process of material contacts with the environment.

According to Piaget, in the course of ontogenetic development, the external world begins to appear before the child in the form of objects not immediately, but as a result of active interaction with him. In the course of an ever more complete and deep interaction between the subject and the object, as the author believed, their mutual enrichment takes place: more and more new aspects and characteristics are distinguished in the object, and the subject develops more and more adequate, subtle and complex ways of influencing the world with the aim of knowledge and achievement of consciously set goals.

In his experimental and theoretical studies of the genesis of intelligence, Piaget studied only the elementary forms of activity of a developing person. The main material of the study was various forms of the child's behavior in the surrounding world. But unlike representatives of the behaviorist trend, Piaget did not confine himself to describing actions, but tried to reconstruct on their basis those mental structures that behavior is a manifestation of. Piaget's many years of research on the reconstruction of the psyche on the basis of behavior also led him to the conclusion that the mental processes themselves, not only intellectual, but also perceptual, represent a specific activity.

Piaget's main task was to study human structuressky intellect. He considered its structure as a natural development in the course of the evolution of less organized organic structures. However, the psychological views of J. Piaget were formed on the basis of a general biological understanding of the development process as a relationship assimilation and accommodation. During assimilation, the organism, as it were, imposes its own patterns of behavior on the environment, while during accommodation, it rearranges them in accordance with the characteristics of the environment. In this regard, the development of the intellect was conceived as a unity of assimilation and accommodation, because through these acts the organism adapts to its environment.

Piaget's first books were published in the 1920s: The Child's Speech and Thinking (1923), The Child's Judgment and Inference (1924), and The Child's Representation of the World (1926).

M.G. Yaroshevsky, analyzing these initial views of Piaget, writes the following: “On the way from an infant to an adult, thought undergoes a number of qualitative transformations - stages, each of which has its own characteristics. In an attempt to uncover them, Piaget initially focused on children's utterances. He used the method of free conversation with the child, trying to make the questions asked by the little subjects as close as possible to their spontaneous statements: what makes clouds, water, wind move? where do dreams come from? why is the boat floating? etc. It was not easy to find in many children's judgments, stories, retellings, replicas unifying principle, giving grounds to delimit "what the child has" from the cognitive activity of an adult.

So common denominator Piaget considered child's egocentrism. A small child is the unconscious center of his own world. He is not able to take the position of another, to take a critical look at himself from the outside, to understand that other people see things differently.

Therefore, he confuses the objective and the subjective, the experienced and the real. He attributes his personal motives to physical things, endows all objects with consciousness and will. This is reflected in children's speech. In the presence of others, the child talks aloud as if he were alone. He is not interested in whether he will be understood by others. His speech, expressing his desires, dreams, "the logic of feelings", serves as a kind of companion, an accompaniment to his real behavior. But life forces the child to leave the world of dreams, to adapt to the environment ... And then the child's thought loses its originality, deforms and begins to obey a different, "adult" logic drawn from the social environment, i.e. from the process of verbal communication with other human beings” [Yaroshevsky M.G.].

In the 1930s, Piaget's approach to the problems of the development of the psyche underwent a radical change. In order to describe the structure of intellectual acts, he develops a special logical and mathematical apparatus.

Piaget defined the stages of development of the intellect, their content and meaning differently. Now he believed that not communication with other people, but an operation (a logical-mathematical structure) determines the cognitive development of a child. In 1941, in collaboration with A. Sheminskaya, J. Piaget's book "The Genesis of Number in a Child" was published, and in the same year, together with B. Inelder, "The Development of the Concept of Quantity in a Child." In the center of the second work is the question of how the child discovers the invariance (constancy) of certain properties of objects, how his thinking learns the principle of conservation of matter, weight and volume of objects. Piaget found out that the principle of conservation is formed in children gradually, first they begin to understand the invariance of mass (8-10 years), then weight (10-12 years) and, finally, volume (about 12 years).

To arrive at the idea of ​​preservation, the child's mind, according to Piaget, must develop logical schemes representing the level (stage) of specific operations. These particular operations in turn have a long history. A mental action (arising from an external objective action) is not yet an operation. To become such, it must acquire very special characteristics. Operations are reversible and coordinated into a system. For each operation there is an opposite or inverse operation, by means of which the initial position is restored and equilibrium is reached. The interconnection of operations creates stable and, at the same time, mobile integral structures. Gradually, the child's ability to draw conclusions and build hypotheses increases. After the age of 11, the child's thinking enters a new stage - formal operations, which ends by the age of 15.

When studying intelligence, Piaget used the so-called slicing method: he presented the same task to children of different ages and compared the results of solving it. This method made it possible to catch certain shifts in the intellectual activity of the child, to see in the previous stage the emergence of the prerequisites and some elements of the subsequent stage. However, this method could not ensure the disclosure of the psychological formation in the child of a new intellectual device, concept, knowledge.

Piaget's main idea is that the child's understanding of reality is a coherent and consistent whole that allows him to adapt to his environment. As the child grows, he several stages, on each of which "equilibrium" is reached:

1. The first turning point, at about one and a half to two years, is also the end of the "sensomotor period". At this age, the child is able to solve various non-verbal tasks: looking for objects that have disappeared from the field of view, i.e. understands that the external world exists constantly, even when it is not perceived. The child can find the way by making a detour, uses the simplest tools to get the desired object, can foresee the consequences of external influences (for example, that the ball will roll downhill, and if you push the swing, they will swing back to their previous position).

2. The next stage is the “pre-operational stage”, characterized by a conceptual understanding of the world and is associated with language acquisition.

3. By about the age of seven, the child reaches the stage of "concrete operations", for example, he understands that the number of objects does not depend on whether they are laid out in a long row or in a compact pile; earlier he could decide that there were more objects in a long row.

4. The last stage occurs in early adolescence and is called the "formal operations" stage. At this stage, a purely symbolic representation of objects and their relationships becomes available, the ability to mentally manipulate symbols appears.

<...>How does the first awareness of the quantitative side of a group of objects arise in a child? In response to this question, there is still a dispute between representatives of opposing views aloud. Although this controversy, as mentioned, has already lost its sharpness, it has not yet received its final solution. One point of view believes that awareness of quantity arises as the result of direct perception of different groups of objects and naming each group with the appropriate word. It is, as it were, a sensual image simultaneously (simultaneously) of a given set of objects, groups of things, their collection.

Representatives of the other point of view believe that awareness of quantity arises as expressed in the word the result of a consistent(successive) interrupting elements a specific set, the selection of single objects from a given set of them.

Some authors put forward a compressor solution to this issue. In Soviet psychological and methodological literature, it was initiated by K. F. Lebedintsev (1923). Based on observations of the development of numerical representations in his two children, he came to the conclusion that the awareness of the first numbers (up to 5 inclusive) arises by contemplating groups of objects, simultaneously grasping them, and the concept of numbers greater than 5 is formed by sequential selection elements of the set, their counts.<...>

It is easy to trace the connection of these points of view with the discussion about the genetic priority of a quantitative or ordinal number. Without entering into a consideration of its results, let us point out the general shortcoming of the points of view manifested in it: in each of them, one of the psychological conditions for the formation of the concept of number is taken as the essence of this process.

In reality, neither a single process of direct perception of simultaneously given groups of objects, nor the successive selection of their individual elements associated with a certain word, by themselves can lead and do not lead to the formation of the concept of number.

Awareness of quantity, even at first, concerning numbers within 5, turns out to be a much more complex process than the representatives of the above views considered. Like any act of awareness, it is a solution to a new task for the child, requiring the abstraction of quantitative relations from the rest of the properties of sets of objects.

The need to abstract these relationships is generated by the needs of the child's activity itself and by the conditions under which it takes place.

The joint activity of the child with other people, his relationships and communication with adults become the main source of those tasks, the solution of which puts him before the need to reflect in his mind the quantitative composition of groups of objects. However, as we have seen, even a child's adequate handling of these sets of objects does not, under all conditions, lead him to realize their quantitative relations. Latest become the subject of his consciousness where the performance of an action with a multitude of objects encounters difficulties due to discrepancy between the quantitative composition and other properties of these sets. In such a situation, the methods available to the child for estimating the number of objects, based on the perception of their spatial and other features, turn out to be not only insufficient, but also erroneous. The contradiction that arises between the new tasks, in the solution of which the child is involved, and the visual methods available to him specific

setsitems, encourages him to the disclosure of new aspects in those objects with which he deals.

The child takes the first steps towards understanding the quantitative relationship of these objects in the process of communication with adults, overcoming difficulties in performing practical actions with groups of objects caused by the discrepancy between the majestic and other properties of these groups. Overcoming these difficulties, the child comes to the realization of the fact that there are identical quantitative groups or sets of objects with their different appearance and different qualitative composition. This awareness arises in the child not before solving a new task for him, but in the process of solving it. As we shall see later, the child experiences it as a solution to a task that is genuinely new to him.

<...>Most children complete the task “Take the same amount and put it on a ruler” in two steps: first, taking one cube at a time, they reproduce the figure of a given set in the ways we described above, and then arrange its elements in a row along the ruler.

Some children resort to a more perfect method: they only “apply” each taken cube to each element of a given set, as if noting that this element has already been taken, and immediately put it on a ruler. For smaller quantities, this method gives an adequate result, and for large quantities, it leads to errors.

The most perfect way that some kids resorted to when completing these tasks was the following: they took two cubes at once, put them on a ruler, then added the remaining cubes to them, carefully comparing the amount they got with a given group of objects. As we will show below, this way of performing a task becomes possible where the child has already developed a fairly clear idea of ​​the deuce. He speaks of a higher stage in the child's awareness of the number of things.

Looking closely at these ways of performing a task, we are convinced that they all boil down to a comparison one by one elements formed set of objects with each element of their given set.

This action appears complex and dual by its structure an act. It includes opposite operations developed by the child in his previous activity, namely, the selection of individual elements of the group and their combination, their sequential examination and simultaneous grasping, the comparison of each element of one set with each element of another, sorting one by one, transferring together, etc. .

These operations appear more differentiated at the first stages of awareness of quantities, standing out under certain conditions even in separate actions in the future, they are combined into one integral act, they become more sketchy and economical, with the complication of the task (for example, with an increase in a given set), they are again differentiated, appear in a more expanded form. With the help of this action, the child reveals relations between two compared sets of objects that are not directly given to him, establishes their quantitative similarity with their different qualitative composition and different grouping. This action is the primary way to establish a one-to-one

correspondence between visually given sets of objects. Containing the possibility of further modification and improvement, it eventually becomes the main operation with the help of which the concept of number is formed in the child. Therefore, if anyone had any doubt as to whether it is worthwhile to engage in such a detailed psychological analysis of the methods of operating with a variety of objects in babies of 2-3 years of age, then about this doubt one could say,

That the significance of this analysis goes far beyond the limits of the psychology of an early age: here we are present at birth in the ontogenetic development of human consciousness of that basic operation on which all arithmetic is based, once called by K. Gauss the “QUEEN OF MATHEMATICS”.

<...>The generalization of the first quantitative estimates of aggregates arises in the child as a result of the solution of new cognitive tasks, requiring in developing better ways abstraction of quantity from other properties of sets. An essential role in this process is played, first of all, by the expansion of those specific sets of different objects that the child learns through his effective connections with the outside world. The child's comparison of sets of different objects, in different conditions, in their different positions and groupings, creates experimental prerequisites for generalizing their quantitative assessment. As well as the first awareness of the quantitative relationship of things, so the generalization of their quantitative assessment arises in the child in the process of communicating with adults. His handling of multitudes of objects and the knowledge of their quantitative relations from a very early age is imbued with language. Even his first diffuse ideas about a multitude of objects, as we have seen, take shape in speech. In speech, the first judgments about the quantitative similarity of the compared groups of objects also appear. They are pure judgment in action only in those children who lag far behind their peers in the development of active speech. For these reasons, the word becomes a means of generalizing the first quantitative judgments of the child.

The child soon proceeds to a generalized reflection of the concrete sets of objects known to him. The use of words - numerals, which often occurs in the child as an imitative act and is early included in the process of formation by him of these multitudes of objects, further becomes a form of awareness of their quantitative composition.

The child does not have to develop this form himself, as humanity had to do. He learns from adults a system of words - numerals. But this assimilation does not come down to a simple memorization of their series, to the formation of an association between a word and an image of a group of objects, as is often thought, to the reproduction of a memorized series of words. This is a generalization of the classes of sets of objects cognized by the child, carried out in speech form.

Such a generalization requires a restructuring of the ways in which a one-to-one correspondence between specific sets of objects has hitherto been established.

As we have seen, the act of comparing one by one the members of these sets, which children resort to at their first steps on the way to the concept of number, is a complex motor-speech action. First, this is a practical action carried out in the usual ways developed in the previous activity (For "right-handers" - with the right hand). With further restructuring of this action, the leading role soon passes to its speech side. Used words, learned from adults, become the carrier of a standard set, with the help of which the plurality of certain groups of specific objects begins to be determined. The task of determining their quantitative composition is solved by establishing a one-to-one correspondence between the evaluated specific group of objects and the standard set fixed in speech acts. In other words, the child's primary way of understanding the quantitative composition of groups of objects turns into counting.

The child has an account as a qualitative modification of his ways of knowing sets of objects, carried out in a public setting. Its emergence is prepared by the child's previous actions with a variety of objects. The counting includes these actions as its own operations (selecting the elements of the set, iterating over them, establishing a correspondence, etc.). At the same time, it differs from the previous methods of determining the number of objects by its great perfection. The difference is also manifested in the consequences of this action. Its consequence is a generalized mental result, acquiring a new, namely verbal, form of its existence in which it can only be born.

verbal his form, being neutral in relation to the defined sets of objects, makes it easier to abstract the quantitative sidefrom their other properties, generalize the results of abstraction andapply to the evaluation of new types of concrete populations. Thus, it becomes possible for the child to gradually move from figurative, situational judgments about the quantitative similarity of specific sets of objects to the first concepts about their classes.

Thus, the genesis of the concept of number in a child, even at the first stages, is a complex process. A child's awareness of the quantitative side of a multitude of objects arises in the process of his communication with adults. The necessary abstraction of the quantitative composition of sets of objects from their other features is carried out in the process of operating with these objects. It occurs not before the action, but in the very process of the action and represents the solution of a new task for the child, carried out in ways developed in his previous activity.

The child's awareness of the number of objects arises not simply as an image of directly perceived sets, but as a judgment about the quantitative similarity of the compared sets with their different qualitative composition and different form of their spatial distribution. The child arrives at this judgment by comparing, one by one, the elements of the evaluated sets of objects. This is how that basic operation is born, which in theoretical arithmetic is called the establishment of a one-to-one correspondence between the compared sets. In the process of further effective knowledge of various groups by the child

objects and generalizing its results with the help of numerals learned from adults, this operation turns into a count. The latter does not arise as some "artificial" a way of determining the quantities of things, supposedly displacing “purely childish”, “natural” arithmetic, but as a natural modification and improvement in the social conditions of the child's development of his original ways of recognizing sets of things. It mediates this process of their recognition very early.

The study of the first steps of children on the way to the formation of the concept of number indicates erroneous attempts to find the sources of the formation of this concept in one or another separately taken side of the process of cognition: in contemplation of groups of objects or in thought, in the simultaneity of impressions or their successive change, in distinguishing objects or their identification, in their grouping or decomposition, etc. The concept of number arises in a child in the process of active, directly or indirectly directed by adults, cognition of sets of objects, which includes these various aspects in their contradictory unity. In the formation of the concept of number, the child has the same processes and operations that take place in the formation of his other concepts of objects and phenomena of the external world. Only here they acquire their differences depending on the specific tasks in the solution of which they meet.

Contrary to the statements of some authors that there are different ways in which a child can and does reach the assimilation of the first numerical concepts, the study of this process convinces us that this path is one. It acquires its own characteristics depending on the direction of the process of formation of the concept of number in the child. The management that successfully copes with its tasks is the leadership that, at these preparatory stages of formation, takes care of the development of the child's cognitive activity as a whole, the education of his curiosity, the enrichment of his life experience and the development of the operations necessary for the birth of his arithmetic thought. The assimilation of numerals also plays an important role, but it gives its effect only in combination with the effective knowledge of the child of various sets of objects and the generalization of it.

G.S. Kostyuk. Selected psychological works. M.: Pedagogy, 1988, p. 170-194.

J. Piaget “Psychology of the intellect. The genesis of the number in a child. Logic and psychology» The main provisions of the theory of J. Piaget. According to Jean Piaget's theory of intelligence, human intelligence goes through several main stages in its development: From birth to 2 years, it continues sensorimotor intelligence period; from 2 to 11 years - the period of preparation and organization of specific operations, in which sub-period of pre-operational representations(from 2 to 7 years old) and sub-period of specific operations(from 7 to 11 years); from 11 years old to about 15 lasts period of formal operations. The problem of children's thinking was formulated as qualitatively unique, having unique advantages, the activity of the child himself was singled out, the genesis was traced from "action to thought", the phenomena of children's thinking were discovered, and methods for its research were developed. ^ Definition of intelligence Intelligence is a global cognitive system consisting of a number of subsystems (perceptual, mnemonic, mental), the purpose of which is to provide information support for the interaction of the individual with the external environment. Intelligence is the totality of all cognitive functions of an individual.

Intelligence is thinking, the highest cognitive process.

Intelligence- flexible at the same time stable structural balance of behavior, which in essence is a system of the most vital and active operations. Being the most perfect of mental adaptations, the intellect serves, so to speak, as the most necessary and effective tool in the interactions of the subject with the outside world, interactions that are realized in the most complex ways and go far beyond the limits of direct and instantaneous contacts in order to achieve pre-established and stable relations. ^ The main stages in the development of a child's thinking Piaget identified the following stages in the development of intelligence. Sensorimotor intelligence (0-2 years) During the period of sensory-motor intelligence, the organization of perceptual and motor interactions with the outside world gradually develops. This development proceeds from being limited by innate reflexes to the associated organization of sensory-motor actions in relation to the immediate environment. At this stage, only direct manipulations with things are possible, but not actions with symbols, representations in the internal plan. ^ Preparation and organization of specific operations (2-11 years old) Sub-period of pre-operational representations (2-7 years) At the stage of pre-operational representations, a transition is made from sensory-motor functions to internal - symbolic, that is, to actions with representations, and not with external objects. This stage of intelligence development is characterized by dominance assumptions and transductive reasoning; egocentrism; centralization on the conspicuous features of the subject and neglect in reasoning of its other features; focusing attention on the states of a thing and inattention to its transformations. ^ Sub-period of specific operations (7-11 years) At the stage of specific operations, actions with representations begin to be combined, coordinated with each other, forming systems of integrated actions called operations. The child develops special cognitive structures called factions(for example, classification^ Formal operations (11-15 years old) The main ability that appears at the stage of formal operations (from 11 to about 15 years old) is the ability to deal with possible, with the hypothetical, and perceive external reality as a special case of what is possible, what could be. Knowledge becomes hypothetical-deductive. The child acquires the ability to think in sentences and establish formal relationships (inclusion, conjunction, disjunction, etc.) between them. The child at this stage is also able to systematically identify all the variables that are essential for solving the problem, and systematically sort through all possible combinations these variables. ^ 5. The main mechanisms of cognitive development of the child 1) the mechanism of assimilation: the individual adapts new information (situation, object) to his existing schemes (structures), without changing them in principle, that is, he includes a new object in his existing schemes of actions or structures. 2) the mechanism of accommodation, when an individual adapts his previously formed reactions to new information (situation, object), that is, he is forced to rebuild (modify) old schemes (structures) in order to adapt them to new information (situation, object). According to the operational concept of intellect, the development and functioning of mental phenomena is, on the one hand, the assimilation or assimilation of this material by existing patterns of behavior, and on the other, the accommodation of these patterns to a specific situation. Piaget considers the adaptation of the organism to the environment as a balancing of the subject and the object. The concepts of assimilation and accommodation play the main role in Piaget's proposed explanation of the genesis of mental functions. In essence, this genesis acts as a succession of various stages of balancing assimilation and accommodation. . ^ 6. Egocentrism of children's thinking. Experimental studies of the phenomenon of egocentrism Egocentrism of children's thinking - a special cognitive position taken by the subject in relation to the surrounding world, when the objects and phenomena of the surrounding world are considered from their own point of view. The egocentrism of thinking causes such features of children's thinking as syncretism, the inability to focus on changes in the object, the irreversibility of thinking, transduction (from particular to particular), insensitivity to contradiction, the cumulative effect of which prevents the formation of logical thinking. Piaget's well-known experiments are an example of this effect. If, in front of the child's eyes, equal amounts of water are poured into two identical glasses, then the child will confirm the equality of volumes. But if in his presence you pour water from one glass into another, narrower one, then the child will confidently tell you that there is more water in the narrow glass. - There are many variations of such experiences, but they all demonstrated the same thing - the child's inability to focus on changes in the object. The latter means that the baby fixes well in memory only stable situations, but at the same time the process of transformation eludes him. In the case of glasses, the child sees only the result - two identical glasses with water at the beginning and two different glasses with the same water at the end, but he is not able to catch the moment of change. Another effect of egocentrism consists in the irreversibility of thinking, i.e., the inability of the child to mentally return to the starting point of his reasoning. It is the irreversibility of thinking that does not allow our baby to follow the course of his own reasoning and, returning to their beginning, imagine the glasses in their original position. The lack of reversibility is a direct manifestation of the child's egocentric thinking. ^ 7. The concept of "subject", "object", "action" in the concept of J. Piaget Subject is an organism endowed with the functional activity of an adaptation, which is hereditarily fixed and inherent in any living organism. ^ An object- it's just material to manipulate, it's just "food" for action. Scheme actions- this is the most general thing that remains in action when it is repeated many times in different circumstances. The scheme of action, in the broad sense of the word, is a structure at a certain level of mental development. ^ 8. The concept of "operation" and its place in the concept of J. Piaget Operation - a cognitive scheme that ensures, at the end of the preoperational stage of the development of the intellect, the child's assimilation of the idea of ​​preserving quantity. Operations are formed in the period from 2 to 12 years. - At the stage of specific operations (from 8 to 11 years), various types of mental activity that arose during the previous period finally reach the state of "mobile equilibrium", i.e., acquire the character of reversibility. In the same period, the basic concepts of conservation are formed, the child is capable of logically specific operations. It can form both relations and classes from concrete objects. ^ 9. Laws of grouping and the operational development of the intellect The construction of operational groupings and groups of thought requires inversion, but the paths of movement in this area are infinitely more complicated. We are talking about the decentering of thought not only in relation to the actual perceptual centering, but also in relation to one's own action as a whole. Indeed, thought born out of action is egocentric in its very starting point, precisely for the reasons that the sensorimotor intellect is first centered on the actual perceptions or movements from which it develops. The development of thought comes, first of all, to a repetition, on the basis of a wide system of displacements, of that evolution that, on the sensory-motor plane, seemed already complete, until it unfolded with renewed vigor in an infinitely wider space and in an infinitely more temporally mobile sphere, in order to reach before structuring the operations themselves. ^ 10. The concept of structure in the concept of J. Piaget Structure, according to Piaget, it is a mental system or integrity, the principles of activity of which are different from the principles of activity of the parts that make up this structure. Structure- self-regulating system. New mental structures are formed on the basis of action. During the entire ontogenetic development, Piaget believes, the main functions (adaptation, assimilation, accommodation) as dynamic processes are unchanged, hereditarily fixed, independent of content and experience. Unlike functions, structures are formed in the process of life, depend on the content of experience, and differ qualitatively at different stages of development. Such a relationship between function and structure ensures the continuity, succession of development and its quality. . ^ 11. Skills and sensorimotor intelligence ‑­ Skill- the primary factor explaining intelligence; from the point of view of the trial and error method, the skill is interpreted as the automation of movements selected after a blind search, and the search itself is considered as a sign of intelligence; from the point of view of assimilation, intellect yields as a form of equilibrium to the same assimilation of activity, the initial forms of which form a habit. ^ Sensorimotor intelligence- the type of thinking that characterizes the pre-verbal period of a child's life. The concept of sensorimotor intelligence is one of the main concepts in Jean Piaget's theory of the development of the child's intellect. Piaget called this type, or level of development of thinking, sensorimotor, since the child's behavior during this period is based on the coordination of perception and movement. J. Piaget outlined six stages of the sensorimotor development of the intellect: 1) exercise of reflexes (from 0 to 1 month); 2) the first skills and primary circular reactions (from 1 to 4-6 months); 3) coordination of vision and grasping and secondary circular reactions (from 4 - b to 8-9 months) - the beginning of the emergence of one's own intelligence; 4) stage of "practical" intellect (from 8 to 11 months); 5) tertiary circular reactions and the search for new means to achieve the goal, which the child finds through external material samples (from 11-12 to 18 months); 6) the child can find new means of solving the problem through internalized combinations of action schemes that lead to sudden insight or insight (from 18 to 24 months). ^ 12. Stages of intuitive (visual) thinking. Conservation Phenomena Intuitive (visual) thinking- a type of thinking in which we directly perceive the conclusion, that is, we feel its obligatory nature, without even being able to restore all the reasoning and premises by which it is conditioned; its opposite is discursive thinking. Intuitive thinking is characterized by the fact that it lacks clearly defined stages. It is usually based on a folded perception of the whole problem at once. The person in this case arrives at an answer, which may or may not be right, with little or no awareness of the process by which he got that answer. As a rule, intuitive thinking is based on familiarity with the basic knowledge in a given area and with their structure, and this gives it the opportunity to be carried out in the form of jumps, quick transitions, with the omission of individual links. Therefore, the conclusions of intuitive thinking need to be verified by analytical means. Picture of conservation in the concept of J. Piaget acts as a criterion for the emergence of logical operations. It characterizes the understanding of the principle of conservation of the amount of matter when changing the shape of an object. The concept of preservation develops in the child under the condition that the egocentricity of thinking is weakened, which allows him to discover the points of view of other people and find in them what they have in common. As a result, children's ideas, which were previously absolute for him (for example, he always considers large things heavy, and small things light), now become relative (a pebble seems light to a child, but turns out to be heavy for water). ^ 13. The concept of invariance and mental development of the child Invariance- knowledge about the object in relation to one or another subjective "perspective" is provided by the real interaction of the subject and the object, is associated with the action of the subject and is quite unambiguously determined by the object's own properties. The invariance of knowledge progresses with intellectual development, being directly dependent on the subject's experience of operating with real objects. In the system of genetic psychology of J. Piaget, mastering the principle of "preservation" (invariance, constancy) is an important stage in the intellectual development of the child. The concept of preservation means that an object or a set of objects is recognized as unchanged in terms of the composition of elements or in any other physical parameter, despite changes in their shape or external location, but on the condition that nothing is taken away or added to them. According to Piaget, mastery of the conservation principle serves as a psychological criterion for the emergence of the main logical characteristic of thought - reversibility, which indicates the child's transition to a new, concrete-operational thinking. The mastery of this principle is also a necessary condition for the formation of scientific concepts in the child. ‑­ ^ 14. Stage of concrete operations Stage of specific operations(7-11 years old). At the stage of specific operations, actions with representations begin to be combined, coordinated with each other, forming systems of integrated actions called operations. The child develops special cognitive structures called factions(for example, classification), thanks to which the child acquires the ability to perform operations with classes and establish logical relationships between classes, uniting them in hierarchies, whereas earlier his abilities were limited to transduction and the establishment of associative links. The limitation of this stage is that operations can be performed only with concrete objects, but not with statements. Operations logically structure the performed external actions, but they cannot yet structure verbal reasoning in a similar way. ^ 15. Stage of formal-logical operations Stage of formally - logical operations (11-15 years). The main ability that appears at the stage of formal operations is the ability to deal with the possible, with the hypothetical, and perceive external reality as a special case of what is possible, what could be. Cognition becomes hypothetical-deductive. The child acquires the ability to think in sentences and establish formal relationships (inclusion, conjunction, disjunction, etc.) between them. The child at this stage is also able to systematically identify all the variables that are essential for solving the problem, and systematically sort through all possible combinations these variables. ^ 16. Social factors of intellectual development Manifestations of intelligence lies in: language (signs) the content of the subject's interactions with objects (intellectual values) the rules prescribed for thinking (collective logical or pre-logical norms). On the basis of language acquisition, that is, with the onset of the symbolic and intuitive periods, new social relations appear that enrich and transform the thinking of the individual. But there are three different aspects to this problem. Already in the sensorimotor period, the infant is the object of numerous social influences: he is given the maximum pleasures available to his little experience - from feeding to the manifestation of certain feelings (he is surrounded by care, he is smiled at, he is entertained, soothed); he is also instilled with skills and regulations associated with signals and words, adults forbid him certain types of behavior and grumble at him. At pre-operational levels, covering the period from the appearance of language to approximately 7-8 years, the structures inherent in the emerging thinking exclude the possibility of the formation of social relations of cooperation, which alone can lead to the construction of logic. ^ 17. Research methods proposed by J. Piaget Piaget critically analyzed the methods that were used before him, and showed their failure to elucidate the mechanisms of mental activity. In order to identify these mechanisms, hidden, but determining everything, Piaget developed a new method of psychological research - the method of clinical conversation, when not symptoms (external signs of a phenomenon) are studied, but the processes leading to their occurrence. This method is extremely difficult. It gives the necessary results only in the hands of an experienced psychologist. ^ clinical method- this is a carefully conducted statement of facts, an age cut of speech and mental development. The researcher asks a question, listens to the child's reasoning, and then formulates additional questions, each of which depends on the child's previous answer. He expects to find out what determines the position of the child and what is the structure of his cognitive activity. In the course of a clinical conversation, there is always a danger of misinterpreting the child's reaction, getting confused, not finding the right question at the moment, or, conversely, suggesting the desired answer. Clinical conversation is a kind of art, "the art of asking." ^ 18. Correlation between logic and psychology in the study of intellectual development- Logic is the axiomatics of the mind, in relation to which the psychology of intelligence is the corresponding experimental science. Axiomatics is an exclusively hypothetical-deductive science, that is, one that reduces reference to experience to a minimum (and even seeks to completely eliminate it), in order to freely build its subject on the basis of unprovable statements (axioms) and combine them between in all possible ways and with the utmost rigor. The problem of the relationship between formal logic and the psychology of the intellect receives a solution similar to that which, after centuries of discussion, put an end to the conflict between deductive geometry and real or physical geometry. As in the case of these two disciplines, the logic and psychology of thought initially coincided without being differentiated. Due to the preserved influence of the original indivisibility, they still continued to consider logic as a science of reality, which, despite its normative nature, lies on the same plane as psychology, but deals exclusively with “true thinking”, in contrast to thinking in general, taken in abstraction from no matter what the rules. Hence the illusory perspective of the "psychology of thinking", according to which thinking as a psychological phenomenon is a reflection of the laws of logic. On the contrary, as soon as we understand that logic is an axiomatic, immediately - as a result of a simple reversal of the original position - the false solution to the problem of the relationship between logic and thinking disappears. Logic schemes, if skillfully constructed, always help the analysis of psychologists; a good example of this is the psychology of thinking

Period 1925-1929 is important in the formation of the psychological concept of J. Piaget. At this time, J. Piaget moved from the analysis of verbal thinking to a direct study of the active side of the thinking process ( It took some time, Piaget later wrote, to understand that the roots of logical operations lie deeper than linguistic connections and that my early research on thinking was too much focused on the linguistic aspect (See J. Piaget. Comments on Vygotsky's critical remarks)). Research materials 1925-1929. were published by J. Piaget in the books: "The Emergence of Intellect in a Child" (1936), "The Construction of Reality in a Child" (1937), "Formation of a Symbol in a Child" (1945), as well as in a number of articles. Research center in the period 1925-1929. was focused around the analysis of the structure of the intellect in the initial, pre-symbolic sensorimotor period of its development and in the period of symbolic thinking following it.

In 1929, Piaget began a new cycle of research (it ended approximately in 1939). In the course of these studies, Piaget, firstly, continuing the main line of work of 1925-1929, supplemented the analysis of the intellect of young children with a study of intellectual development in middle age (primarily on the basis of the analysis of the genesis of number and the concept of quantity), and secondly, he formulated the main ideas of his psychological theory of thinking (the operational concept of intelligence), and, thirdly, he built his logical concept. The results of these studies were published by Piaget in the books Genesis of Number in a Child (together with A. Sheminskaya, 1941), Development of Quantity in a Child (together with B. Inelder, 1941), Psychology of Intellect (1946), Logic and psychology" (1953). The works "Classes, Relations and Numbers" (1942), "Tractatus Logique" (1949) and others are devoted to a special presentation of the logical theory of J. Piaget. psychological and logical concept.

According to the operational concept of intellect, the development and functioning of mental phenomena is, on the one hand, the assimilation or assimilation of this material by existing patterns of behavior, and on the other, the accommodation of these patterns to a specific situation. Piaget considers the adaptation of the organism to the environment as a balancing of the subject and the object. The concepts of assimilation and accommodation play the main role in Piaget's proposed explanation of the genesis of mental functions. In essence, this genesis acts as a successive change of various stages of balancing assimilation and accommodation ( See J. Piaget. La psychologic de l "intelligence. Paris, 1952, p. 13-15).

Piaget emphasizes the great difficulties in developing a theory of the development of mental functions. The main one is the extreme difficulty of separating the internal factors of development4 (maturation) from its external factors (environmental influences). Classical psychology, Piaget notes, operated on three main factors of development - heredity, physical environment and social environment, but it could neither single them out in a "pure" form, nor establish the nature of the relationship between them.

Consideration of the fundamental dependence of external and internal factors of development, Piaget continues further, leads to the conclusion that any behavior is the assimilation of the given by pre-created schemes and, at the same time, the accommodation of these schemes to the present situation. It follows from this that "the theory of development must necessarily turn to the concept of equilibrium, for any behavior essentially expresses a balance between internal and external factors or, more generally, between assimilation and accommodation" ( J. Piaget. Le role de la notion d "equilibre dans l" explication en psychologie. - "Actes du quinzienie congres Internationale de psychologic. Bruxelles, 1957". Amsterdam, 1959, p. 53).

Piaget proposes to consider the balance factor as the fourth main factor of development. It does not join the three antecedent factors simply additively, for none of them can, strictly speaking, be separated from the others. At the same time, equilibrium as a fourth factor has an important advantage over others: according to Piaget, equilibrium is a more general factor and can be analyzed relatively independently ( Ibid., pp. 53-54).

Piaget emphasizes that equilibrium can be understood in two ways - as a result and as a process of balancing. Moreover, equilibrium as a process is rigidly associated by Piaget with the principle of activity. Any changes external to the organism can be compensated only through activity. Because of this, the maximum value of equilibrium corresponds not to the state of rest, but to the maximum value of activity, which compensates for both actual and virtual changes ( Ibid., p. 53).

The concept of equilibrium, according to Piaget, should be used as an explanatory principle of all mental functions of the body. The intellect, or thinking, is one of these functions, the most developed and perfect (in the sense of the possibility of mastering the external world), moreover, it has such forms of balance to which all other mental structures gravitate.

Raising the question of the genesis of the intellect and its relationship with other mental functions, Piaget clearly formulates the principle, prepared by his early studies, of the derivativeness of internalized mental structures from external objective actions.

From Piaget's point of view, it is meaningless to talk about the "starting point" of mental development, at which the intellect first appears. On the other hand, it makes sense to talk about various intellectual structures that replace one another in the process of development, one can compare these structures with each other and use the concept of "degree of intellectuality", it can be argued that in the process of development, behavior becomes more and more intellectual.

Intelligence cannot be defined by specifying its "limits," Piaget argues. The definition of intellect can be given only through an indication of its development in the direction of the greatest balance of cognitive structures. From this it follows, in particular, that the method of studying the intellect can only be the genetic method, since the intellectual structure, torn out of the chain of development, taken outside of its relation to the previous and subsequent forms of balancing, cannot be correctly understood.

The genesis of intelligence is expressed in the formation of such intellectual structures, each of which can be considered as a special form of equilibrium between the organism and the environment, and intellectual development leads to the formation of more and more stable forms of equilibrium.

According to Piaget, the analysis of the successive formation of the intellect should begin with elementary sensorimotor actions. The latter, as they become more complex and differentiated, lead to the formation of a pre-operational form of intellect associated with representation, and then to thinking of a concrete-operational type, and, finally, to intellect proper, i.e., to the ability to manipulate formal operations.

The task of psychology, according to Piaget, is to give a detailed description of this process, to show how external objective actions are gradually internalized, leading to the formation of intellect.

The essence of the intellect, according to Piaget, lies in the system of operations that form it. The highest forms of balancing the organism and the environment are expressed in the formation of operational intellectual structures.

According to Piaget, an operation is an internal action of the subject, derived from an external, objective action and coordinated with other operations in such a way that together they form a certain structural whole, a system.

The system of operations is characterized by the fact that in it some operations are balanced by others, inverse to the first (the reverse is the operation that, based on the results of the first operation, restores the original position). Depending on the complexity of the operating system, the forms of reversibility that take place between operations change. The psychological criterion for the emergence of operational systems is the construction of invariants, or concepts of conservation (for example, for the appearance of operations A + A "= B and A = B-A" it is necessary to realize the conservation of B) ( See J. Piaget. La psychologie de l "intelligence, p. 53-55).

Thus, the principles of activity and derivativeness of internalized mental structures from external objective actions, the ideas of genesis and the operational (systemic) nature of the intellect form the initial foundations of the psychological theory of J. Piaget.

The way in which Piaget attempts to uncover the essential connections of the intellect is through the analysis of mental operations and their systems. How is such an analysis carried out?

Psychological and logical ways of studying intelligence

In the analysis of intelligence, it is necessary, Piaget believes, to combine psychological and logical research plans. In this statement and in its clear implementation is one of the most important features of Piaget's theory of thinking.

Although already when writing his early works, J. Piaget was well aware of the principles of the new logic - mathematical, or logistics, he, striving for the "purity" of psychological analysis, believed that attempts at a hasty deductive presentation of experimental data easily lead to the fact that the researcher finds himself " dominated by preconceived ideas, superficial analogies suggested by the history of science and the psychology of primitive peoples, or, even more dangerously, by the prejudices of the logical or epistemological system" ( J. Piaget. Speech and thinking of the child, p. 64) (our detente. - V. L. and V. S.). "Classical logic (that is, the logic of textbooks) and the naive realism of common sense," he wrote, "two mortal enemies of a healthy psychology of knowledge..." ( Ibid).

The critical attitude of J. Piaget to the "logic of textbooks" is, to a large extent, a reaction against the logicization of the psychology of thinking, which was widespread in the 19th century. Piaget himself characterizes the situation that took place at that time as follows. Classical formal logic (i.e., pre-mathematical logic) believed that it was possible to reveal the actual structures of thought processes, and classical philosophical psychology, in turn, believed that the laws of logic are implicit in the mental functioning of every normal individual. There were no grounds for disagreement between these two disciplines at that time ( J. Piaget. Logic and psychology. Manchester University Press, 1953, p. one).

However, in the subsequent development of experimental psychology, logical factors were excluded from it as "alien" for the subject studied in it. Attempts to preserve the unity of psychological and logical research, as they took place, for example, among the supporters of the Würzburg psychological school, were not crowned with success. The use of logic in the "causal explanation of psychological facts proper" ( J. Piaget. Logic and psychology, p. one) was called "logicism" in psychological research and, since the end of the 19th century, was considered as one of the most important dangers that an experimental psychologist must avoid. “Most modern psychologists,” writes J. Piaget, “are trying to explain intelligence without any recourse to logical theory” ( Ibid., p. 2).

This state of affairs was also facilitated by changes in the theoretical interpretation of logic that occurred at the end of the 19th century. Instead of understanding logic as a part of psychology, the laws of which are derived from the empirical facts of the intellectual life of people (“psychologism” in logic), the dominant view of logic has become a set of formal calculus that establishes the rules for transforming one language form into another, which are independent of empirical psychological material and do not are related to the analysis of the process of thinking. Piaget quite rightly notes that "most modern logicians no longer concern themselves with the question of whether the laws and structures of logic have any kind of relation to psychological structures" ( Ibid). Between the psychology of thinking and modern formal logic, a seemingly insurmountable wall has formed since the beginning of the 20th century.

Speaking in his early works for the "purity" of psychological analysis, against the introduction of elements of logic into psychological research, J. Piaget undoubtedly paid tribute to the views prevailing at that time. But his position, even at that time, should by no means be regarded as accepting the point of view of the absolute separation of psychological and logical research. Piaget fought against the introduction of elementary, "school" logic into psychology and against the interpretation of a child's thinking in terms of the logical structures of an adult's thinking, and not against the use of logic in psychology in general. In his early works, he proceeds from the fact that adult thinking is logical thinking, i.e., subject to a set of skills "used by the mind in the general conduct of operations" ( J. Piaget. Speech and thinking of the child, page 97), and Piaget turns his main attention to the analysis of the specific features of the child's logic, which is not reducible to the logical thinking of an adult ( Ibid., pp. 370-408).

Thus, already the early works of J. Piaget were characterized in fact by the desire for the unity of psychological and logical analysis. However, the real implementation of such a unified analysis was given by Piaget only in the 1930s.

The main task that J. Piaget solves in his studies of the problems of logic is to decide whether there is a correspondence between the logical structures and the operational structures of psychology. In the case of a positive solution to this issue, the real development of mental operations receives a logical justification.

According to J. Piaget, three main difficulties arise when comparing axiomatic logical theories with a psychological description of the real development of the intellect: 1) adult thinking is not formalized; 2) the deployment of axiomatic logic is in a certain respect opposite to the genetic order of the construction of operations (for example, in axiomatic construction, the logic of classes is derived from the logic of propositions, while from the genetic point of view, propositional operations are derived from the logic of classes and relations; 3) axiomatic logic has an atomic character (it is based on atomic elements) and the method of proof used in it is of necessity linear; the real operations of the intellect, on the contrary, are organized into some integral, structural formations, and only within this framework do they act as operations of thinking ( See J. Piaget. Logic and psychology, p. 24).

The axiomatic construction of logic is not, however, the starting point for logic itself. Both historically and theoretically, it is preceded by some meaningful consideration of logical concepts - in the form of an analysis of systems of logical operations (algebra of logic). It is these operational-algebraic structures that, according to J. Piaget, can act as an intermediate link between psychological and logical structures.

Given the above, Piaget believes that logic and its relation to the psychology of thinking can be given the following interpretation ( See J. Piaget. La psychologic de l "intelligence, p. 37-43).

Modern formal logic, for all its formalized and highly abstract nature, is ultimately a specific reflection of actually occurring thinking. This means that logic can be regarded as the axiomatics of thinking, and the psychology of thinking as an experimental science corresponding to logic. Axiomatics is a hypothetical-deductive science that tries to minimize the appeal to experience and reproduces the object with the help of a series of unprovable statements (axioms), from which it deduces all possible consequences using predetermined, strictly fixed rules. Axiomatics can be regarded as a kind of "scheme" of a real object. But precisely because of the "schematic" nature of any axiomatics, it can neither replace the corresponding experimental science, nor be considered the "basis" of the latter, since the "schematism" of axiomatics is evidence of its obvious limitations.

Logic, being an ideal model of thinking, does not feel any need to appeal to psychological facts, since the hypothetical-deductive theory does not directly analyze facts, but only at some extreme point comes into contact with experimental data. However, since a certain connection with actual data is nevertheless inherent in any hypothetical-deductive theory, since any axiomatic is a "scheme" of some really existing object, there must be some correspondence between psychology and logic (although there is never any parallelism between them). This correspondence between logic and psychology takes place to the extent that psychology analyzes the final positions of equilibrium reached by a developed intellect.

In order for the data of modern formal logic to be used for the purpose of explanation in psychology, it is necessary to single out the operational-algebraic structures of logic. The solution to this problem is given in a number of works by Piaget ( See J. Piaget. Classes, relations and nombres. Essai sur les groupements de la logistique et sur la reversibilite de la pensee. Paris, 1942; J. Pia-get. Traite de logique. Paris, 1949).

The most important role in these studies by Piaget is played by the concept of grouping, which is derived from the concept of a group. A group in algebra is understood as a set of elements that satisfy the following conditions: 1) the combination of two elements of the set gives a new element of the given set; 2) each operation applied to the elements of a set can be canceled by an inverse (inverse) operation; 3) set operations are associative, for example: (x+x")+y =x+(x"+y); 4) there is one and only one identical operator (0), which, when applied to an operation, does not change it, and which is the result of applying the inverse (x+0=x; x-x=0) to the direct operation. Grouping is obtained by adding a fifth condition to the four conditions of the group: 5) the presence of a tautology: x+x=x; y+y=y.

Consider, for example, a simple classification, where B is divided by A and not \u003d A (A "), C - by B and B", etc. Schematically, a simple classification can be represented as follows:

The laws of formation of a simple classification are as follows:

The fulfillment of the first four conditions shows that a simple classification is a group. But it also fulfills the fifth condition, which can be interpreted as follows: the group operation "+" means the union of all elements of two sets connected by this operation into one set, in which all elements are included once (if any element is contained in both sets, then this element appears in the resulting set only once). By virtue of what has been said, it is clear that A + A = A, because all elements of the second set are contained in the first. Thus, a simple classification is a grouping, more precisely, one of the elementary groupings of class logic.

Piaget establishes eight such elementary groupings of the logic of classes and relations. Each of these groupings has a well-defined structure; some of these structures are rather elementary (as in the example given with a simple classification), the rest are more complex. For relations there is a grouping (additive grouping of asymmetric relations), an isomorphic grouping of a simple classification. Let's characterize this group.

Let A->B be the relation "B is greater than A", which is asymmetric and transitive. We will write it like this: A a -> B, where a is the difference between B and A; respectively: A b -> C, B a " -> C, C b" -> D, C c " -> D, etc.

The addition of asymmetric relationships forms a grouping:

Logical groupings of classes and relations represent, according to Piaget, certain structures that serve as a standard to which the real operations of thinking "aspire" at a certain level of their development (the so-called level of concrete operations). Psychologically, therefore, they can be seen as defining a form of equilibrium of the intellect. At the same time, each grouping condition receives a corresponding psychological interpretation: the first condition indicates the possibility of coordinating the actions of the subject, the second asserts a certain freedom of direction of action (associativity condition), the third (the presence of a reverse operation) - the ability to cancel the result of the previous action (what is in the intellect and what not, for example, in perception), etc.

According to Piaget, the subject's mastery of the corresponding logical operations is the criterion of his intellectual development. All eight groupings of the logic of classes and relations belong to Piaget's so-called concrete-operational level of development of the intellect. A fourth level is built on top of it and from it is formed - the stage of formal operations, where the subject masters the logical connections that take place in the logic of propositions.

In this regard, Piaget is faced with the question of the logical structures of this higher level of development of the intellect - the stage of formal operations. In the study of this problem, carried out, in particular, in the Logical Treatise, Piaget came to the following conclusions ( See J. Piaget. Traite de logique, ch. V, Paris, 1949).

1. For each propositional calculus operation, there is an inverse operation (N), which is the complement to the full statement. Thus, for р∨q, whose normal form is pq∨pg∨pq, the operation pq will be inverse; for p⊃q - pq, etc.

2. For each operation there is a reciprocal operation (R), i.e. the same operation, but performed on statements of inverse signs: for p∨q - p∨, for pq-pq, etc.

3. For each operation there is a correlative operation (C), which is obtained by replacing the sign V with a sign in the corresponding normal form; and back. For p∨q, the correlative operation is p q, and vice versa.

4. Finally, if we add to N, R and C the identical operation (I), i.e., the operation that leaves the expression the same, then the set of transformations (N, R, C and I) form a communicative group given by the equalities

N=RC(=CR); R=NC(=CN); C⇔NR(=RN); I=RCN

or table

The RCNI group, however, does not cover the entire two-valued propositional calculus; it expresses only part of it. The problem of the logical organization of the propositional calculus as a whole - the most important component of the stage of formal operations - is solved by Piaget on the way of generalizing the concept of grouping introduced by him. In particular, he constructs a special grouping that expresses the logical structure of the propositional calculus ( See ibid., §§36-40). At the same time, Piaget shows that the two-valued logic of propositions is based solely on the relationship of the part to the whole and the complement of the part to the whole. Thus, it considers the relation of the parts to each other, but only through the relation to the whole and does not take into account the direct relation of the parts to each other ( Ibid., pp. 355-356. See also: F. Kroner. Zur Logik von J. Pia-get.- "Dialectica", 1950, vol. 4, N 1).

The constructed logic gives Piaget an important criterion for psychological research. As soon as the logical structures of the intellect have been established, which must be developed in the individual, the task of psychological research now is to show how, in what way this process occurs, what is its mechanism. In this case, logical structures will always act as the final links that must be formed in the individual.

Successive stages of the formation of intelligence

The central core of the genesis of intelligence, according to Piaget, forms the formation of logical thinking, the ability for which, according to Piaget, is neither innate nor preformed in the human spirit. Logical thinking is a product of the growing activity of the subject in his relationship with the outside world.

J. Piaget identified four main stages in the development of logical thinking: sensorimotor, pre-operational intelligence, specific operations and formal operations ( When presenting the stages of the formation of intelligence, we rely mainly on the final work of J. Piaget and B. Inelder: J. Piaget und B. Inhelder. Die Psychologic der Friihen Kindheit. Die geistige Entwicklung von der Geburt bis zum 7 Lebensjahr. - In: "Handbuch der Psychologic" hrsg. D. and R. Katz. Basel - Stuttgart, 1960, S. 275-314).

I. Intellectual acts at the stage of sensorimotor intelligence (up to two years) are based on the coordination of movements and perceptions and are performed without any idea. Although the sensorimotor intellect is not yet logical, it forms a "functional" preparation for proper logical thinking.

II. Pre-operational intelligence (from two to seven years) is characterized by well-formed speech, ideas, internalization of action into thought (action is replaced by some kind of sign: word, image, symbol).

At a year and a half, the child begins to gradually master the language of the people around him. Initially, however, the mutual relation of designation and thing is still indeterminate for the child. At first it does not form concepts in a logical sense. His visual concepts, or "concepts," do not yet have any precisely described meaning. A small child does not conclude either deductively or inductively. His thinking is based primarily on inferences by analogy. By the age of seven, the child thinks well visually, that is, he experiments internally with the help of ideas. However, in contrast to logical-operational thinking, these thought experiments are still irreversible. At the stage of pre-operational intelligence, the child is not able to apply the previously acquired scheme of action with constant objects either to distant objects or to certain sets and quantities. The child lacks reversible operations and conservation concepts applicable to actions of a higher level than sensorimotor actions. The quantitative judgments of the child during this period, notes J. Piaget, lack systematic transitivity. If we take the quantities A and B, and then B and C, then each pair is recognized as equal - (A \u003d B) and (B \u003d C) - without establishing the equality of A and C ( J. Piaget. La psychologie de l "intelligence, p. 102).

III. At the stage of concrete operations (from 8 to 11 years), various types of mental activity that arose during the previous period finally reach a state of "mobile equilibrium", i.e., acquire the character of reversibility. In the same period, the basic concepts of conservation are formed, the child is capable of logically specific operations. It can form both relations and classes from concrete objects. The child is able during this period: to arrange the sticks in a continuous sequence from smallest to largest or vice versa; correctly establish an asymmetric sequence (A

“However, all logical operations at this age still depend on specific areas of application. If, for example, a child already at the age of seven manages to arrange sticks along their length, then only at nine and a half years old is he able to perform similar operations with weights, and with volumes - only at 11-12 years old" ( J. Piaget and B. Inhelder. Die Psychologie der friihen Kindheit, S. 284). Logical operations have not yet become generalized. At this stage, children cannot construct logically correct speech, regardless of the actual action.

IV. At the stage of formal operations (from 11-12 to 14-15 years old), the genesis of intelligence is completed. During this period, the ability to think hypothetically-deductively appears, theoretically, a system of operations of propositional logic (propositional logic) is formed. With equal success, the subject can now operate both with objects and with statements. Along with the operations of propositional logic, the child during this period forms new groups of operations that are not directly related to the logic of propositions (the ability to perform combinatorial operations of any kind, to operate extensively with proportions); there are operational schemes related to probability, multiplicative compositions, etc. The appearance of such systems of operations indicates, according to J. Piaget, that the intellect is formed.

Although the development of logical thinking forms the most important aspect of the genesis of the intellect, it does not, however, completely exhaust this process. In the course and on the basis of the formation of operational structures of varying complexity, the child gradually masters the reality around him. “During the first seven years of life,” write Piaget and Inelder, “the child gradually discovers the elementary principles of invariance relating to the object, quantity, number, space and time, which give his picture of the world an objective structure” ( J. Piaget and B. Inhelder. Die Psychologic der fruhen Kindheit, S. 285). The most important components in the interpretation of this process proposed by Piaget are: 1) analysis of the construction of reality by the child depending on his activity; 2) the spiritual development of the child as an ever-increasing system of invariants mastered by him; 3) the formation of logical thinking as the basis of the entire intellectual development of the child.

Piaget, together with his collaborators, subjected many aspects of this process to a detailed experimental analysis, the results of which are presented in a whole series of monographs. Without being able to enter into the subtleties of these studies, we will give a summary of the results of these studies.

The formation of the concept of an object and the basic physical principles of invariance in a child goes through the same four main stages as in the case of the development of logical thinking. At the first stage (sensory-motor intelligence) the sensory-motor scheme of the object is formed. Initially, the world of children's ideas consists of appearing and disappearing images; there is no constant object here (first and second steps). But gradually the child begins to distinguish known situations from unknown ones, pleasant from unpleasant.

During the second stage (pre-operational intelligence), the child develops a visual concept of set and quantity. He is not yet able to apply the previously acquired scheme of action with a constant object either to individual objects or to sets and quantities. Multiple objects (for example, a mountain) appear to the child of this phase to increase or decrease depending on their spatial arrangement. If a child is given two plasticine balls of equal shape and mass and one of them is deformed, then he believes that the amount of matter has increased (“the ball has now become so long”) or decreased (“it is now so thin”). Thus, children at this stage deny both the invariance of matter and the invariance of the quantity of matter.

At the stage of operational-concrete thinking, the child forms the logical-operational concepts of set and quantity. This process ends at the stage of formal-operational intelligence. During this period, the child is able to mentally process the perceived changes in Plurality and Quantity; thus, he confidently asserts that, despite the change in shape, there is an equal amount of plasticine (in the example just considered). This is the result of thinking operations, more precisely, of coordinating reversible relations ( See ibid., p. 288).

Piaget traces the process of the child's mastery of the concepts of number, space, and time in a similar way. The main thing in this genesis is the formation of certain logical structures, and on their basis - the possibility of constructing an appropriate concept. In this case, the experimental technique usual for Piaget is used: special tasks for children are selected, the degree of mastery of these tasks by them is established, then the task is complicated in such a way that it makes it possible to establish the subsequent stage of the child's spiritual development. On this basis, the entire analyzed process is divided into phases, stages, sub-stages, etc.

So, for example, when analyzing the genesis of a number in a child, it is established that the arithmetic concept of a number is not reduced to separate logical operations, but is based on the synthesis of the inclusion of classes (A + A "= B) and asymmetric relations (A Ibid., pp. 289-290; see J. Piaget et A. Szeminska for details. La genese du nombre chez l "enfant. Neuchatel, 1941).

In his research, J. Piaget considers not only the actual development of the child's intellect, but also the genesis of his emotional sphere. Feelings are seen by Piaget (as opposed to Freud) as developing, as a result of active spiritual construction.

In this regard, the genesis of feelings is divided into three phases corresponding to the main phases of the development of the intellect: sensorimotor intelligence corresponds to the formation of elementary feelings, visual-symbolic thinking - the formation of moral consciousness, which depends on the judgment of adults and on the changing influences of the environment, and, finally, logically concrete thinking corresponds to the formation of will and moral independence ( J. Piaget. Le jugement moral chez l "enfant. Paris, 1932). During this last period, life in a children's society develops independence of moral judgment and a sense of mutual responsibility. Piaget emphasizes the fact that "the will develops together with moral independence and with the ability to think consistently logically." "The will really plays a role in the sensory life of the child, similar to the role of the operations of thinking in intellectual cognition: it preserves the equilibrium and constancy of behavior" ( J. Piaget and B. Inhelder. Die Psychologic der fruhen Kindheit, S. 312). Thus, a single principle of analysis is consistently carried through the entire system.

Problems of interpretation of the operational concept of intelligence

We have outlined the main principles of the psychological concept of J. Piaget. We now turn to the consideration of issues that arise in connection with the interpretation of the operational concept of intelligence.

Attempts to construct such interpretations appeared ( See A. G. Comm. Problems of the psychology of intelligence in the works of J. Piaget; V. A. Lektorsky, V. N. Sadovsky. The main "ideas of "genetic epistemology" by J. Piaget. - "Questions of Psychology", 1961, No. 4, etc.), and it is natural to assume that work in this direction will be continued. Below we will try to offer an interpretation of a number of important aspects of Piaget's concept.

To build an interpretation of the operational concept of intelligence means, firstly, to reconstruct its subject matter, secondly, to establish the fundamental results obtained in the course of its deployment, and, thirdly, to correlate the theoretical representation of the subject studied by J. Piaget with the modern understanding of this object.

For the reconstruction of the subject studied in the operational concept of intelligence, it is necessary to single out the starting point of the psychological research of J. Piaget. As such, as already noted, is the task of analyzing the mental development of the individual depending on changes in the forms of social life. Schematically, such a subject of research can be represented as follows:

where ⇓ means the direct impact of various forms of social life on individual mental development.

With regard to the subject of research highlighted in scheme (1), the following should be emphasized.

1. The mental development of the individual from the very beginning is understood by J. Piaget, firstly, as a certain specific form of activity and, secondly, as something derived from external non-psychic (objective) activity.

2. In a real study (as, for example, it was carried out in the first books of J. Piaget), not the entire structure depicted in diagram (1) is subjected to analysis, but its relatively narrow "cut".

3. When studying the subject (1), the understanding of the psyche as a specific activity derived from objective activity, being accepted in principle, is actually replaced by consideration of only verbal activity (children's conversations), which, as is well known, Piaget himself was forced to soon abandon.

Distracting for the time being from the fact of the evolution of Piaget's concept (i.e., from the modification of the object studied within the framework of this concept, we consider it necessary to pay special attention to the initial structure, the analysis of which Piaget tried to give in his first works. Singling out the subject (1) in as an object of psychological analysis puts Piaget at the forefront of contemporary psychological science.Moreover, this structure contains all the fundamental elements necessary to build a psychology of thinking from the point of view of today's theoretical ideas on this subject.Special mention should be made of the awareness of the fact that mental development depends on changes social reality and the principle of activity, that is, the understanding of the psyche not as some kind of static internal state of the individual, but as a product of a special form of activity of the subject.

However, having given the structure (1) as the initial object of study, Piaget essentially found himself in an unsolvable (at least for the period of the 1920s) situation. The fact is that such a subject of research is an extremely complex structural formation, the research methods of which have not been sufficiently developed even today. The success of the analysis of the subject (1) is possible only in the case of constructing detailed theories of the genesis of mental functions and the evolution of forms of social activity, and already on this basis - a detailed presentation of the ways in which social reality influences the psyche of the individual.

Piaget had neither the first, nor the second, nor the third. At that time, he did not have a specific apparatus for analyzing each of these components.

In this situation, Piaget's perfect transition from the original subject of research to its essential modification, which is much simpler in structure and therefore amenable to detailed analysis, seems quite natural. This modification concerned primarily three points:

1. The connection between the generation of the mental states of the individual by the forms of social activity is replaced by the relation of mutual expression of the first in the second, and vice versa.

2. For a rigorous representation of the various stages of the intellectual development of an individual, the apparatus of modern formal logic is used in such a way that the logical structures correspond to certain intellectual structures identified in psychology, and vice versa. As a result, a relationship of mutual expression is established not only between mental and social structures, but also between social structures and logical structures.

3. In the genetic plan, intellectual structures are generated by external objective actions; for its part, the form of organization of intellectual structures clearly expresses the organization towards which the structures of external objective actions strive, in other words, the structure of systems of external actions anticipates (expresses in an implicit form) the logical organization of the intellect.

Taking into account these modifications, we can give the following image of the subject of research in the works of J. Piaget:

In scheme (2), the arrow ↔ represents the relationship of mutual expression of one component of the object in another, the dotted arrow

--> characterizes the relation of the generation of intellectual structures by systems of external actions, and the arrow ⇒ indicates the field of science from which Piaget proceeds in his research when constructing in one case the theory of logical structures, and in the other - the theory of the genesis of intelligence.

The multicomponent nature of structure (2) is largely imaginary. By introducing the relationship of mutual expression, J. Piaget essentially reduces the structure (1) to an object in which each component is only a different form of expression of the other, i.e., to an object in which there is only a different expression of the same structure. Thus, a real simplification of the subject of analysis is carried out; it is reduced to a structure that lends itself - at the present level of development - to detailed study.

To understand the position defended by Piaget about the relationship between social structures and structures of the intellect (both logical and actually mental), it is extremely interesting to pay attention to the formulation of this problem by him in the book "Psychology of Intellect". The question here is posed as follows: is logical grouping a cause or a result of socialization? ( See J. Piaget. La psychologie de l "intelligence, p. 195) According to Piaget, two different, but complementary, answers should be given to it. First, it should be noted that without the exchange of thoughts and without cooperation with other people, the individual could never co-organize his mental operations into a single whole - "in this sense, operational grouping presupposes social life" ( Ibid). But, on the other hand, the exchange of thoughts itself obeys the law of equilibrium, which is nothing more than a logical grouping - in this sense, social life presupposes a logical grouping. Thus, grouping acts as a form of balance of actions - both interindividual and individual. In other words, the grouping is a certain structure that is contained in both individual mental and social activity.

That is why, Piaget continues, the operational structure of thought can be isolated both from the study of the thought of the individual at the highest stage of its development and from the analysis of the ways in which thoughts are exchanged between members of society (cooperation) ( See J. Piaget. La psychologic de l "mtelligence, p. 197). "Internal operational activity and external cooperation ... are only two additional aspects of one whole, that is, the balance of one depends on the balance of the other" ( Ibid., p. 198).

The central link of the subject presented in the diagram (2) undoubtedly lies in the nature of the relationship between logical and real mental structures. This problem and the way to solve it, proposed in the operational concept of intelligence, express the most specific features of Piaget's approach to the study of the psyche.

If structure (1) is adopted, the researcher has two possible ways of further analysis - either in terms of elucidating the impact of forms of social activity on individual mental development (which, as we found out, significantly exceeded the real possibilities of psychology in the 1920s and 1930s), or in terms of direction of the opening of the patterns of "internal" mental activity. The transition to structure (2) indicates that Piaget solves the problem in favor of the second term of the alternative, which inevitably raises the question of the apparatus of such research.

Like any special scientific study, Piaget's analysis of the psychology of the formation of intelligence relies on some - perhaps not always clearly formulated - prerequisites. In this regard, we should first of all name the concretization of the idea of ​​intellect as an activity (intelligence as a certain set of operations, i.e., the acceptance of the thesis that an operation is an element of activity). The next step is to define what an operation is. This question is solved by referring the operation to some integral system, only as a result of entering into which the action is an operation. Finally, the last premise is to adopt a genetic approach to the analysis of intellectual activity as different systems of operations.

These prerequisites for Piaget's psychological studies represent a certain abstraction from the experimental material accumulated in the psychology of thinking (including in Piaget's works), and as such they should serve as means of further theoretical analysis. But at the same time - and this is no less obvious - these principles are not directly contained in the experimental psychological material itself: the process of their identification (and especially further development) is necessarily connected with the involvement of a special apparatus, which may not be directly related to psychology. child, but, however, must be able to clearly express these principles and have sufficient "opportunities" to concretize them.

Now we can clearly formulate, following J. Piaget, the main premises of his approach to the analysis of the psychology of intelligence only because the author of this concept "found" such an apparatus, and the choice turned out to be very promising.

Thus, in terms of the formation of the very concept of J. Piaget, the following relationship of its logical and psychological aspects took place:

The logical structures included in the operational concept of intelligence are a special reformulation of the content of certain sections of formal logic. The nature of this reformulation is determined, however, not only and not so much by the corresponding formal logical theories, but by the structure of those intuitively singled out mental structures, which, in the end, logical structures must act as a special way of describing. Therefore, in the construction of Piaget's concept, along with the relation "formal logic ⇒ logical structures", the most important role was played by the influence of intuitively distinguished mental structures on the formulation of the theory of logical structures non-intuitive representation) of the first. A similar mechanism for the formation of the concept led to the fact that in the created theory between the logical and psychological structures the relationship of mutual expression was established. The "become" theory removes the processes that led to its creation, and leaves only the final result - the correspondence of some structures to others.

In this regard, how is the problem of the status of logic and the psychology of thinking solved within the framework of Piaget's concept? In contrast to various interpretations of the subject of logic, which refuse to be a way of describing thinking - Platonism, conventionalism, etc. ( See J. Piaget. Logic and psychology. Manchester, 1953), Piaget puts forward the thesis that both traditional and modern formal logic ultimately describe certain patterns of thinking. Depending on the method of construction, the degree of formalization, axiomatization, the relation of logical systems to the real process of thinking varies. This relatedness is very indirect in the case, for example, of the axiomatic calculus of modern formal logic, and is much closer to the operational interpretation of logic.

To the extent that psychology analyzes the final states of equilibrium of thought, there is, Piaget argues, a correspondence between psychological experimental knowledge and logistics, just as there is a correspondence between a schema and the reality it represents ( See J. Piaget. La psychologic de 1 "intelligence, p. 40). At the same time, the particular parallelism between logic and psychology does not mean that logical rules are the psychological laws of thought, and one cannot without ceremony apply the laws of logic to the laws of thought ( J. Piaget, E. Beth, J. Dieudonne, A. Lichnerowicz, G. Choquet, C. Gattengo. L "enseignement des Mathematiques. Neuchatel - Paris, 1955).

Thus, there is no parallelism, understood literally, between logic and psychology. The relationship of mutual expression, correspondence of logical structures takes place only for those final states of equilibrium that are formed in the course of individual mental development. In all other respects, the psychology of thinking and logic belong to different areas and solve problems that differ from each other.

On the basis of what has been said, it is necessary to introduce the following concretization into the structure (2) (we take only one fragment of the whole subject):

Logical structures S 1 S 2 , S 3 .... included in the operational concept of intellect are a set of algebraic formations between which logical-mathematical relations are established, ultimately based on the use of deductive inference techniques. There is nothing specifically psychological, therefore, in this area. Structures S 1 , S 2 , S 3 ,... describe certain ideal conditions of equilibrium and as such correspond (with proper psychological interpretation) to real intellectual structures S 1 ", S 2 ", S 3 ",..., formed in the course of Particular parallelism, or rather mutual expression, the correspondence of certain "final products" - such is the real meaning of the connection between logic and psychology in the works of J. Piaget.

There is no doubt that the idea of ​​the unity of psychological and logical research is the most important merit of J. Piaget and his most significant contribution to the development of the psychology of thinking ( See V. A. Lektorsky, V. N. Sadovsky. The main ideas of the "genetic epistemology" of Jean Piaget. - "Questions of Psychology", 1961, No. 4, pp. 167-171, 176-178; G. P. Shchedrovitsky. The place of logic in psychological and pedagogical research. - "Abstracts of reports at the II Congress of the Society of Psychologists", vol. 2. M., 1963). Only as a result of the wide involvement of the logical apparatus in psychological research, Piaget was able to make great progress in the analysis of the most important problems of modern psychology: the idea of ​​the activity and genesis of the psyche, questions of the derivativeness of intellectual structures from external objective actions, and the systemic nature of mental formations.

It is well known that the concept of activity underlies many modern psychological interpretations of thinking.

However, as a rule, this concept is taken as intuitively obvious and further undefined, which inevitably leads to the fact that, in fact, it falls out of the analysis. Piaget, starting with such an intuitively accepted concept of activity, then, through the prism of his logical apparatus, introduced a certain rigor and certainty into this concept. The logical apparatus in his concept serves precisely to give a breakdown of activity and to turn this concept into a real means of psychological analysis. But, following the path to achieve this goal, Piaget - by virtue of the logical apparatus he uses - gives only an extremely one-sided presentation of activity. The activity analyzed within the framework of the operational concept of intelligence is an object built on the basis of the application of logical structures, and as such, on the one hand, it can be analyzed within the framework of the possibilities inherent in psychologically interpreted logical structures, and on the other hand, in no way can serve as a picture of the activity as a whole. After all, even for Piaget himself, logic is just some ideal scheme that never represents reality in its entirety.

The foregoing was very clearly manifested in the nature of Piaget's genetic research. To reveal the causal mechanism of genesis, this means, according to Piaget, "firstly, to restore the initial data of this genesis ... and, secondly, to show how and under the influence of what factors these initial structures are transformed into structures that are the subject of our study "( J. Piaget and B Inelder. Genesis of elementary logical structures. M., 1963, p. 10).

Giving a more detailed presentation of the criteria for genetic analysis, B. Inelder writes that the development of intelligence goes through a number of stages. At the same time: 1) each stage includes a period of formation of genesis and a period of "maturity"; the latter is characterized by a progressive organization of the structure of mental operations; 2) each structure is at the same time the existence of one stage and the starting point of the next stage, a new evolutionary process; 3) the sequence of stages is constant, the age at which one or another stage is reached varies within certain limits depending on the experience of the cultural environment, etc.; 4) the transition from the early stages to the later ones takes place through special integration: the previous structures become part of the subsequent ones ( W. Inholder. Some aspects of Piaget's genetic approach to cognition. - In: "Thought in the Young Child", p. 23).

What is really obtained as a result of research built on such principles? Fixing the successive stages that, according to this concept, the child goes through in his development, both in the field of logical thinking and mastering reality, and in the field of affective life. In this case, logical structures again act as the only working criterion. They not only correspond to real mental structures, but also predetermine - at each stage of development - what should be formed in the individual.

The genetic study of intelligence, therefore, acts as a fixation of the stages of achieving the corresponding logical structures. As a result, analysis of the internal mechanisms of the developmental process falls out of the study, and genetic consideration at best gives an idea of ​​pseudogenesis, built in accordance with the requirements arising from the system of logical structures.

The same difficulty, but in a somewhat different form, appears when considering the process of generation of primary intellectual structures by external objective actions. Sensorimotor intelligence, according to Piaget, is an undeveloped form of balance. But in this case, as noted by A. Vallon, there is an error of anticipating the investigation. Unable to derive intelligence, personality from the system of actions, Piaget, according to Wallon, introduced intellectual structures into the actions themselves ( See A. Vallon. From action to thought. M., 1956, pp. 43, 46-50). To a large extent, this argument is justified. It should not, of course, be understood in the sense that the very idea of ​​deriving intellectual structures from sensorimotorism is false. The systematic consideration of this possibility contains the most important positive part of Piaget's work. The point is different - normative logical requirements here again act as the only real research principle, thereby reducing genetic analysis to a deliberately one-sided pseudogenetic reconstruction.

Great difficulties remain with Piaget in his interpretation of the intellect as a system of operations. Piaget shares with a number of other modern researchers the merit of putting forward the problem of consistency as one of the central problems of science. Much has also been done on the concrete application of this idea to the analysis of the psyche. Piaget repeatedly emphasizes the idea of ​​constructing a "logic of integrity" in the form of logical-algebraic structures: "... it is necessary to construct a logic of integrity if they want it to serve as an adequate scheme for the equilibrium states of the spirit, and to analyze operations without returning to isolated elements, insufficient in terms of psychological requirements" ( J. Piaget. La psychologie de l "intelligence, p. 43; J. Piaget. Methode ixiomatique et metiiode operationnelle. - "Synthese", vol. X, 1957, N 1).

The algebraic apparatus used by Piaget in this connection undoubtedly acts, within certain limits, as a systemic alternative to atomized axiomatics. Group, grouping and other algebraic structures define elements, their connections and relations depending on the whole. But it is obvious that in the case of algebraic systems we are dealing with a very narrow and simplest class of system formations.

Piaget sees the intellect only through the prism of these algebraic structures, the inadequacy of which in terms of the analysis of mental activity does not require even a detailed justification.

Thus, the extremely important problem of the systemic nature of mental functions received in Piaget the first real results, which, however, essentially led to the need for a new "entry" in its analysis.

Concluding the consideration of the interpretation of the psychological theory of J. Piaget, it must be emphasized that the reconstruction of the subject studied in this theory helped us to establish both the real area subjected to analysis and the conceptual apparatus used for this, as well as the main difficulties in constructing the psychology of thinking that J. Piaget. Additional considerations on this score we can get in the course of the analysis of the principles of "genetic epistemology".