A certain thought about a subject. It expresses the essential characteristics of an object.

A concept is a form that is formed by abstracted (identified) characteristics of objects, expressed in a general form. At the same time, specific features of the object in which a sign characteristic of many others was seen were not indicated.

A concept is a form that can be used in relation to any object, process of reality, phenomenon. The thought is also applicable to ideas about objects, to images of human fantasy.

Features of objects

A concept is a construct that includes a number of components. Features of objects are considered an integral part of this form. They, in essence, determine the characteristics of the concept itself. Signs can be expressed in the form of similarities or differences between objects. In the first case, the characteristics are called general. The second characteristics are called distinctive. Both characteristics can reflect insignificant or essential features of objects. In the second case, we mean the importance of the feature of one object over the features of another. So, for example, an essential characteristic of fruit juice is the presence of beneficial microelements and vitamins. In this case, the color of the liquid is considered a secondary sign. The property that determines the character, direction and nature of the development of an object is considered irrespective of its significance for other features.

Examples.

Enterprise concept

This term in Russian is usually used in two meanings. In the first case, there is an establishment, for example, a plant, factory, workshop. In the second case, the definition refers to some kind of thing conceived by someone. This term thus contains It should be said that the term “enterprise” is considered somewhat vague and relatively broad. It includes not only economic and legal, but also social, technological and other components. The ambiguity of the term shows that in each case of its use it is necessary to consider the meaning in a specific context. It must be said that in the legal literature the definition of “enterprise” is of an economic nature. Therefore, it is considered an economic category in the first place.

Competition concept

This term refers to the rivalry of economic structures, during which the independent activities of each of them are limited or the ability to unilaterally influence the conditions of circulation of products on the relevant market is excluded. In accordance with the Law, the legal and organizational framework is established to ensure the protection of competition. Among the measures taken for this purpose, it should be noted the suppression and prevention of monopolistic activities, restrictions by government bodies, federal executive structures and other organizations and funds.

Classification of concepts

In everyday life, and even in science, the meaning of the word “concept” may differ from its meaning in philosophy or formal logic.

The concept is considered composite, if it relies on other concepts, and elementary otherwise (for example: "Elementary Concepts of Statistics")

Concepts can be divided into abstract and concrete, and, in each of them, into empirical and theoretical.

The concept is called empirical, if it is developed on the basis of a direct comparison of the general properties of a certain class of existing (available for study) objects or phenomena, and theoretical, if it is developed on the basis of an indirect analysis of a certain class of phenomena (or objects) using previously developed concepts, concepts and formalisms.

The concept is called specific, if it refers to a specific object in the surrounding world, and abstract, if it refers to properties of a wide class of objects.

The name of any material object is at the same time a concrete empirical concept. Specific theoretical concepts include, in particular, state laws.

Abstract empirical concepts reflect an accepted style of thinking or judgment, for example: “In the context of logotherapy, the concept spiritual has no religious connotation and relates to the strictly human dimension of existence.”

Abstract empirical concepts include, in particular, the unwritten and sometimes rather vague code of conduct of a social group (often criminal or even criminal), which general outline defines what actions are considered “right” or “wrong”). To see the difference between theoretical and empirical concepts, compare 2 phrases:
« Sentences... were passed in accordance with those in force at that time laws »

« Sentences...were passed in accordance with the concepts in force at that time»

In more specific cases, the concept is considered concrete (although it may remain completely theoretical), for example: " Electron- stable elementary particle with charge −1.6021892(46)×10−19 C, mass 9.109554(906)×10−31 kg and spin 1/2. ".

Concepts in a broad sense and scientific concepts

There are concepts in in a broad sense And scientific concepts. The first formally identify common (similar) characteristics of objects and phenomena and enshrine them in words. Scientific concepts reflect essential and necessary features, and the words and signs (formulas) that express them are scientific terms. The concept distinguishes its content and volume. The set of objects generalized in a concept is called the scope of the concept, and the set of essential features by which objects in the concept are generalized and distinguished is its content. So, for example, the content of the concept “parallelogram” is a geometric figure, flat, closed, bounded by four straight lines, having mutually parallel sides, and the volume is the set of all possible parallelograms. The development of a concept involves a change in its volume and content.

Origin of concepts

The transition from the sensory stage of cognition to logical thinking is characterized primarily as a transition from perceptions and ideas to reflection in the form of concepts. By its origin, the concept is the result of a long process of development of knowledge, a concentrated expression of historically achieved knowledge. The formation of a concept is a complex dialectical process, which is carried out using methods such as comparison, analysis, synthesis, abstraction, idealization, generalization, experiment, etc. A concept is a non-figurative reflection of reality expressed in a word. It acquires its real mental and speech existence only in the development of definitions, in judgments, as part of a certain theory.

The concept highlights and fixes, first of all, the general, which is achieved by abstracting from all the features of individual objects of a given class. But it does not exclude the individual and special. On the basis of the general, it is only possible to isolate and recognize the particular and the individual. A scientific concept is the unity of the general, the particular and the individual, that is, concretely universal (see Universal). Moreover, the general in a concept refers not simply to the number of instances of a given class that have common properties, not only to the set of homogeneous objects and phenomena, but to the very nature of the content of the concept, expressing something essential in the subject.

see also

Concept in the history of philosophy

In the approach to the concept in the history of philosophy, two opposing lines have emerged - the materialist, which believes that concepts are objective in their content, and the idealist, according to which the concept is a spontaneously arising mental entity, absolutely independent of objective reality. For example, for the objective idealist G. Hegel, concepts are primary, and objects and nature are only pale copies of them. Phenomenalism considers the concept as the last reality, not related to objective reality. Some idealists view concepts as fictions created by the “free play of the forces of the spirit” (see Fictionalism). Neopositivists, reducing concepts to auxiliary logical-linguistic means, deny the objectivity of their content.

Being a reflection objective reality, concepts are as plastic as reality itself, of which they are a generalization. They “... must also be hewn, broken, flexible, mobile, relative, interconnected, united in opposites in order to embrace the world” (ibid., p. 131). Scientific concepts are not something complete and complete; on the contrary, it contains the possibility further development. The main content of the concept changes only at certain stages of the development of science. Such changes in the concept are qualitative and are associated with a transition from one level of knowledge to another, to knowledge of the deeper essence of objects and phenomena conceivable in the concept. The movement of reality can only be reflected in dialectically developing concepts.

Kant's definition of a concept

By concept Kant meant any general idea, since the latter is fixed by the term. Hence its definition: “A concept... is a general representation or representation of what is common to many objects, therefore, a representation that can be contained in various objects”

Hegel's definition of a concept

Concept in formal logic

A concept in formal logic is an elementary unit of mental activity, possessing a certain integrity and stability and taken in abstraction from the verbal expression of this activity. A concept is something that is expressed (or denoted) by any meaningful (independent) part of speech (except for pronouns), and if we move from the scale of the language as a whole to the “micro level”, then as a member of a sentence. To interpret the problem of the concept (in its formal logical aspect), you can use the ready-made arsenal of three areas of modern knowledge: 1) general algebra, 2) logical semantics, 3) mathematical logic.

1. The result of the process of name (concept) formation is naturally described in terms of homomorphism; dividing the set of objects of interest to us into classes of elements “equivalent” in some respect (that is, ignoring all the differences between elements of the same class that are not of interest to us at the moment), we obtain a new set, homomorphic to the original one (the so-called factor set ) according to the equivalence relation we have identified. A factor set can contain only 2 classes (name elements and all other elements), then it is natural to call it a name, or a larger number of classes, then it is natural to call it a property. For example: name - house, property - color. In the case of a name, the homomorphism described above is usually called the characteristic function of the subset corresponding to the volume of the name. The elements of this new set (equivalence classes) can now be thought of as single, indivisible objects obtained as a result of “gluing” all the original objects, indistinguishable in the relations we have fixed, into one “lump”. These “clumps” of initial objects (images) identified with each other are what we call names (concepts), obtained as a result of the mental replacement of a class of closely related ideas with one “generic” name. In this sense, the name is the same as the (binary) property. The collection of names and properties defines the tolerance relation. Concepts thus constitute a subset of names or properties, selected due to their proven practical importance for the process of cognition. It is this definition that was formalized within the framework of the theory of problem solving; it is described below in the corresponding section. It is worth emphasizing that the above considerations are not related to the very process of formation of a name or concept, and do not provide a clear, mathematically accurate algorithm for it. The search for such algorithms relates to the topic of pattern recognition.
2. When considering the semantic aspect of the problem of a concept, it is necessary to distinguish between a concept as some abstract object and the word that names it (which is a completely concrete object), name, term. The volume of the name is the same set of elements “glued” into it, which is mentioned above, and the content of the name is the list of characteristics (properties) on the basis of which this “gluing” was carried out. Thus, the scope of a concept is the denotation (meaning) of the name denoting it, and the content is the concept (meaning) that this name expresses. The more extensive the set of characteristics, the greater the class of objects that satisfy these characteristics, and vice versa, the greater the content of the concept, the wider its scope; this obvious fact is often called inverse relation law.
3. Formalological problems associated with the theory of concepts can be presented based on the well-developed apparatus of predicate calculus (see Predicate Logic). The semantics of this calculus is such that it easily describes the subject-predicate structure of judgments considered in traditional logic (subject, that is, the subject, is what is said in the sentence expressing this judgment; predicate, that is, the predicate, is what is said about the subject), and far-reaching, albeit quite natural, generalizations are possible. First of all, it is allowed (as in ordinary grammar) more than one subject in a sentence, and (unlike grammatical canons) the role of subjects is played not only by subjects, but also by complements - “objects”; The role of predicates includes not only the predicates themselves (including those expressed by multiplace predicates that describe relations between several subjects), but also definitions. Circumstances and adverbial phrases, depending on their grammatical structure, can always be attributed to one of these two groups (subjects and predicates), and a review of the entire vocabulary of any language “mobilized” to express a concept shows that it is all divided into these two categories (cardinal numerals, as well as words like “every”, “any”, “some”, “exists”, etc., which are not included in this distribution into two classes, play the role of quantifiers in natural language, allowing one to form and distinguish each other general, particular and individual judgments from each other). In this case, subjects (expressed through the so-called terms of languages ​​based on predicate calculus) and predicates act as names of concepts: the latter in the most literal way, and the former, being variables, “run through” some “subject areas” that serve as volumes of concepts, and if they are permanent (constants), then they are proper names denoting specific objects from these subject areas. Thus, predicates are the contents of concepts, and the classes of objects on which these predicates are true are volumes; As for terms, they are either generic names for arbitrary “representatives” of some concepts, or names of specific representatives. In other words, all formal logical problems associated with the theory of concepts turn out to be a fragment of predicate calculus. Thus, the law of the inverse relation turns out to be a paraphrase of the tautology (identically true formula) of the logic of statements A & B -> A (here & is the sign of conjunction, -> is the sign of implication) or its generalization from the logic of predicates x C (x) -> C ( x)( - universal quantifier).

Concept in problem solving theory

Problem solving theory - a theoretical branch of research on artificial intelligence - offers a fairly mathematically rigorous and at the same time visual interpretation of the term “concept”. A complete mathematically rigorous description can be found in Benerjee's monograph

A less strict but more concise description can be given as follows:

1. Concepts are formed on the basis of properties.
2. There are two main classes of properties - internal and external. External properties are revealed directly, their existence is postulated, and the question of their origin is not raised. Intrinsic properties are an unobservable logical function of extrinsic properties.
3. When solving problems, internal properties are mainly used. This use consists in the fact that, depending on the value of the property, one or another operation is selected, leading to the solution of the problem.
4. A concept in its traditional sense is a special type of internal properties obtained as a result of a logical conjunction (logical AND) of external properties.
5. Any internal property can be represented as a disjunction (logical OR) of concepts.

In this interpretation, the law of the inverse relation really turns out to be a trivial consequence of the definition and one of the laws of absorption A&B->A. It is worth noting that the inverse relation law does not hold for an arbitrary property.

Benerjee considers a problem model in which a certain set of situations and a set of transformations (operations) of one situation into another are specified. A subset of situations that are the goal of the solution is also identified. “In doing so, we seek to transform a given situation into another feasible situation by applying a sequence of transformations to ultimately arrive at a target situation.” The concepts in Benerjee's model are used to describe both the target subset and the strategy for selecting transformations.

According to Benerjee, it would be logical to call concepts “proto-concepts”, since in the general scientific sense, concepts are identified and fixed using the term in the course of solving a wide class of homogeneous problems in which their application has proven useful.

Concept in psychology

Psychology allows you to approach the study of concepts empirically, exploring the relationships between concepts existing in the mind (semantic clusters, groups, networks), including using mathematical methods (cluster and factor analysis); processes of concept formation, including using the method of forming artificial concepts; age-related development of concepts, etc.

Concept research methods

Psychology has developed many methods for studying concepts, such as associative experiment, classification method, subjective scaling method, semantic differential, method of forming artificial concepts.

In some cases, such as the semantic radical method, physiological measurements are also used.

Age-related development of concepts

Psychological research has made it possible to establish that concepts are not unchangeable entities in nature, independent of the age of the subject operating them. Mastery of concepts occurs gradually, and the concepts that a child uses differ from those of an adult. Different types of concepts corresponding to different age stages were identified.

Preconceptions

J. Piaget discovered that at the pre-operational stage of cognitive development (2-7 years), the child’s concepts are not yet true concepts, but pre-concepts. Concepts are figurative and concrete, do not relate to individual objects or classes of things and are connected with each other through transductive reasoning, which is a transition from particular to particular.

Vygotsky-Sakharov Study

L. S. Vygotsky and L. S. Sakharov in their classic study, using their own methodology, which is a modification of N. Ach’s methodology, established types (they are also age stages of development) of concepts.

Everyday and scientific concepts

Main article: Everyday and scientific concepts

L. S. Vygotsky, exploring the development of concepts in childhood, wrote about everyday (spontaneous) and scientific concepts. Everyday concepts are words acquired and used in everyday life, in everyday communication, such as “table”, “cat”, “house”. Scientific concepts are words that a child learns at school, terms built into a system of knowledge, associated with other terms.

When using everyday concepts child for a long time (up to 11-12 years old) only realizes the subject, which they point to, but not the concepts themselves, not their meaning. Only gradually does the child master the meaning of concepts. According to Vygotsky's views, the development of spontaneous and scientific concepts goes in opposite directions: spontaneous - towards a gradual awareness of their meaning, scientific - in the opposite direction.

The awareness of meanings that comes with age is associated with the emerging systematicity of concepts, that is, with the establishment of logical relationships between them. And since the scientific concepts that a child acquires during the learning process are fundamentally different from everyday concepts precisely in that by their very nature they must be organized into a system, then, Vygotsky believes, their meanings are recognized first. Awareness of the meanings of scientific concepts gradually extends to everyday ones.

see also

Links

• Voishvillo E.K. Concept. - M.: Moscow State University Publishing House, 1967. - 284 p.
• Voishvillo E.K. Concept as a form of thinking: logical and epistemological analysis. - M.: Moscow State University Publishing House, 1989. - 239 p.
• Vlasov D. V. Logical and philosophical approaches to constructing a theoretical model of concept formation // Electronic journal "

On this basis, concepts are divided into:

concrete and abstract;

positive and negative;

correlative and non-relative;

collective and non-collective.

Specific concept– a concept reflecting the object or phenomenon itself, which has a relative independent existence (diamond, oak, lawyer).

Abstract concept- a concept in which a property of objects or a relationship between objects is conceived that does not exist independently, without these objects (hardness, durability, competence).

Positive concept– a concept that reflects the presence of some property or quality in the object of thought (“metal”, “living”, “action”, “order”).

Negative concept– a concept characterizing the absence of any quality or property in the object of thought. Such concepts in the language are denoted using negative particles (“not”), prefixes (“without-” and “bes-”), etc., for example, “non-metal”, “inanimate”, “inaction”, “disorder”.

The logical characterization of concepts as negative and positive should not be confused with the axiological assessment of the phenomena and objects they designate. For example, the concept “innocent” is logically negative, but reflects a positively assessed situation.

Correlate- a concept that inevitably presupposes the existence of another concept (“parents” - “children”, “teacher” - “student”).

Irrelevant concept- a concept in which an object is conceived that exists to a certain extent independently, separately from others: “nature”, “plant”, “animal”, “man”.

Collective concept- a concept that is correlated with a group of objects as a whole, but not correlated with an individual object from this group.

For example, the concept of “fleet” denotes a collection of vessels, but is not applicable to an individual vessel, a “collegium” consists of individuals, but one person is not a collegium.

Non-collective concept– refers not only to the group of objects as a whole, but also to each individual object of this group.

For example, a “tree” is the entire collection of trees in general, and birch, pine, oak in particular, and this particular tree individually.

The distinction between collective and non-collective (distinctive) concepts is important when drawing conclusions.

For example:

The conclusion is correct because the concept “law students” is used in a divisive sense: every student at the faculty studies logic.

The conclusion is incorrect because in this case the concept of “law students” is used in a collective sense, and what is true in relation to the entire population of students as a whole may not be true in relation to individual of them.

2.2. Types of concepts according to their scope

If the types of concepts by their content characterize the qualitative differences of objects, then the division of concepts by volume characterizes their quantitative differences.

Empty and non-empty concepts. They are characterized depending on whether they relate to non-existent or really existing objects of thought.

Empty concepts – concepts with zero volume, i.e. representing the empty class “ideal gas”.

Empty concepts include concepts that denote really non-existent objects - both fantastic, fairy-tale images (“centaur”, “mermaid”), and some scientific concepts that denote or hypothetically assumed objects, whose existence can later be refuted (“caloric”, “magnetic fluid”, “perpetual motion machine”), either confirmed, or idealized objects playing an auxiliary role in the sciences (“ideal gas”, “pure matter”, “absolutely black body”, “ideal state”).

Non-empty concepts have a volume that includes at least one real object.

The division of concepts into empty and non-empty is to some extent relative, since the boundary between the existing and the non-existent is mobile. For example, before the appearance of the first real spaceship, the concept of “spaceship”, which necessarily appeared at the stage of human creative process, was logically empty.

Single and general concepts.

Single concept - a concept whose scope is only one object of thought (a single object, or a set of objects, conceived as a single whole).

For example, “Sun”, “Earth”, “Faceted Chamber of the Moscow Kremlin” are single objects; “solar system”, “humanity” are individual concepts used in a collective sense.

General concept - a concept whose scope is a group of objects, moreover, such a concept is applicable to each element of this group, i.e. used in a disjunctive sense.

For example: “star”, “planet”, “state”, etc.

E.A. Ivanov 1 notes that the formal-logical division of concepts into types is necessary, but has significant drawbacks:

the convention of dividing concepts into concrete and abstract; every concept is real at the same time both concrete (has a completely definite content) and abstract (as a result of abstraction);

Therefore E.A. Ivanov proposes to proceed from the division of objects of thought into things, their properties, as well as connections and relationships, accepted in dialectical-materialist philosophy. Then we can distinguish the following types of concepts according to their content:

substantial concepts (from Latin substantia - the fundamental principle, the deepest essence of things), or the concept of the objects themselves in the narrow, proper sense of the word (“man”);

attributive concepts (from the Latin atributium - added), or concepts of properties (“reasonableness” of a person);

relational concepts (from Latin relativus - relative) (“equality” of people).

The formal-logical division of concepts into concrete and abstract does not make it possible to understand why concepts are less abstract and more abstract, less concrete and more concrete, how the abstract and the concrete are related to each other in the same concept. The answer to these questions is given by dialectical logic.

1. Concept as a form of thinking. Content and scope of the concept.

2.Types of concepts.

3. Relationships between concepts.

4. Limitation and generalization of concepts.

5. Definition of concepts.

6. Division of concepts. Classification and its types.

A-priory, a concept is a form of thinking that reflects objects in their essential characteristics. When studying this topic, we necessarily turn to general philosophical problems: what is a sign? what signs are essential? Which ones are unimportant? What signs are called single? which ones are common?

Linguistic forms of expressing concepts are words and phrases. For example, “book”, “man who laughs”, “first-class athlete”.

The main methods of concept formation are: analysis– mental dissection of objects into their component parts, properties, characteristics, synthesis– mental connection into a single whole of parts of an object or its features; comparison– install

identification of similarities or differences between the objects under consideration; abstraction- mental distraction from some signs and highlighting others; generalization- a technique by which individual objects, based on their inherent similarities,

characteristics are combined into groups of homogeneous objects.

Every concept has volume and content. Scope of concept – this is a set (class) of objects conceivable in it, and content is a set of essential features on the basis of which this class is formed. The scope and content of the concept are closely related. Clearly defined content leads to a clear idea of ​​scope. Conversely, unclear content leads to uncertain scope. This connection is expressed in the law of the inverse relationship between volume and content: an increase in the content of a concept leads to the formation of a concept with a smaller volume, and vice versa. For example, the scope of the concept “student” includes all objects that have the attribute “to be a university student.” Having added the attribute “excellent student” to the content of the concept, we see that the scope of the concept has been significantly reduced.

Types of concepts are distinguished on two grounds: content and volume.

By volume (quantity) there are:

1)single concepts, the scope of which includes only one object (the first president of Russia, the United Nations); 2) general concepts, the scope of which includes more than one object (school, state, lake); 3) zero (empty) concepts, the scope of which does not include a single really existing object (Baba Yaga, centaur, goblin). Zero concepts include not only fantastic creations of human consciousness, but also scientifically significant ones, such as “ideal gas”, “absolutely solid body”, “incompressible liquid”, etc.

General concepts can be registering, the volume of which is finite, the set of objects included in it can, in principle, be taken into account (planet of the solar system, science, student of St. Petersburg Technological Institute) and non-registering, the volume of which is infinite (atom, creature, grain of sand)

1)specific concepts, in which an independently existing object (a person, a building, a pencil) is conceived and abstract, in which it is not the whole object that is thought of, but one of the attributes of the object, taken separately from the object itself (whiteness, injustice, honesty);

2)positive concepts, in which the present in the object is thought of

sign (greed, a lagging student, a literate person) and negative, in which the absence of a sign is imagined in an object (an illiterate person, an ugly

act).

3)correlative concepts, in which objects are conceived, the existence of one of which presupposes the existence of another (parents - children, boss - subordinate, student - teacher) and irrelevant, in which objects are thought,

existing independently, regardless of another object (house, book, country);

4)collective concepts, in which a group of homogeneous objects is thought of as a single whole (flock, constellation, student group) and non-collective, the content of which can be attributed to each subject of a given class (river, notebook, institute); collective concepts can be general (grove, regiment, herd) and individual (the constellation Ursa Major).

Concepts whose content includes some general characteristics are called comparable(student and man, black and red, birch and plant). Incomparable concepts Dont Have common features(music and brick, carelessness and home). Comparables are divided into compatible, the volumes of which partially or completely coincide, and incompatible, the volumes of which do not coincide in any element.

Compatibility Types: equivolume (identity), intersection and subordination. In relation to identity, there are concepts whose volumes completely coincide with each other (the Volga River and the longest river in Europe, a square and a rectangular rhombus). Concepts whose scopes partially coincide are in a relationship of intersection (student and athlete, schoolchild and philatelist). In relation to subordination there are concepts, the scope of one of which is completely included in the scope of the other, but does not exhaust it (cat and mammal, MSU student and student).

Types of incompatibility: subordination, opposition and contradiction.

In relation to subordination there are concepts that exclude each other, but belong to some more general generic concept (spruce, birch, linden belong to the scope of the concept tree). In relation to opposition there are two concepts belonging to the same genus, one of which contains some

signs, and the other not only denies these signs, but also replaces them with other, exclusive signs (bravery - cowardice, white - black). Words expressing opposite concepts are antonyms. Regarding the contradiction, we find

There are two concepts that are species of the same genus, one of which indicates some characteristics, and the other denies these characteristics, without replacing them with any other characteristics (honest - dishonest, literate student - illiterate student). The relationships between the volumes of concepts are schematically depicted using circular diagrams.

Comparable Incomparable

Compatible Incompatible

identity intersection subordination subordination opposite contradiction

Operations on concepts are the most complex and important part of the doctrine of concepts.

Summarize the concept- means moving from a concept with a smaller volume. but with more content, to a concept with more volume, but less content (school - educational institution). Generalization cannot be unlimited. The limit of generalization is philosophical categories.

Limit concept- means to move from a concept with a larger volume to a concept with a smaller volume by increasing its content ( geometric figure– rectangle) The limit of the restriction is a single concept (lawyer – investigator – investigator of the prosecutor’s office – investigator of the prosecutor’s office of the Vyborg district of St. Petersburg I.P. Mikhalchenko)

A logical operation that reveals the content of a concept or establishes the meaning of a term is called definition. If the content of a concept is revealed, then the definition is called real, for example, “A barometer is a device for measuring atmospheric pressure.” If a term is defined, then the definition will be nominal, for example, “The word “philosophy” is translated from Greek as “love of wisdom.”

According to the method of identifying the content of concepts, definitions are divided into obvious And implicit. Explicit definitions are those in which the scopes of the defined and defining concepts are in relation to equality and equivalence. The most common explicit definition is definition through genus and species difference. The definition operation itself includes two stages: 1) subsuming the defined concept under a broader generic concept and 2) indicating the specific difference, that is, a feature that distinguishes the defined object from other objects included in the given genus. “A trapezoid is a quadrilateral in which two sides are parallel and the other two are not.” The generic concept in this case is “quadrangle”.

Explicit definitions include genetic definitions, which indicate the method of education and construction of a given subject. For example, “A cylinder is a geometric figure formed by rotating a rectangle relative to

one of the parties"

Explicit definition rules.

1) The definition must be proportionate, that is, the scope of the defined concept must be equal to the scope of the defining concept. If this rule is violated, errors occur:

a) too broad a definition, when the scope of the defining concept is greater

volume determined;

b) too narrow a definition, when the scope of the defining concept is less than the scope of the defined concept.

c) the definition is broad in one respect and narrow in another.

2) The definition should not contain a circle. A type of circle in the definition is a tautology.

3) the definition must be clear, precise, and must not contain any ambiguity. A mistake would be the substitution of definitions with metaphors, comparisons, etc. There is also such a mistake as defining the unknown through the unknown

4) the definition should not be negative.

Most concepts can be defined using definitions through genus and species difference. But what about definitions of categories? general concepts, since they have no gender? Single concepts cannot be defined in this way, since they do not have specific differences. In these cases, they resort to implicit definitions or techniques that replace definitions.

Implicit definitions include: contextual, ostensive, axiomatic, definition through relation to its opposite and some others. For example, the concept of “categorical” can be established in the context of “In my letters, I ask you only for a categorical, direct answer - yes or no.”

(A.P. Chekhov). Ostensive is a definition that establishes the meaning of a term by demonstrating the thing denoted by the term. You can take him to the table and say: “This is a table, and all the things that look like it.” Ostensive, like

contextual definitions are incomplete and inconclusive. The fundamental difference between axiomatic definitions is that the axiomatic context is strictly limited and fixed. Axioms are statements accepted without proof. “Force is equal to mass times acceleration” - this provision is not an explicit definition, but the connection of this concept with other concepts of mechanics is indicated here. Philosophical categories are often defined through their relationship to their opposite: “Reality is a realized possibility.”

In a number of cases, techniques are used that replace the definition: description, characterization, comparison, explanation through examples.

A logical operation that reveals the scope of a concept is called division. In the division operation, one should distinguish between the concept being divided - the volume of which should be

reveal, the members of the division are the subordinate types into which the concept is divided (the result of the division), and the basis of the division is the characteristic by which the division is made. The essence of division is that objects included in the scope of the concept being divided are distributed into groups.

There are two types of division: 1) by species-forming trait and 2) dichotomous division. In the first case, the basis for division is the characteristic by which species concepts are formed: “Depending on the form

The state structure of the state is divided into unitary and federal.” The choice of the basis for the division depends on the purpose of the division and on practical tasks. But in any case, only an objective sign should act as a basis. For example, books should not be divided into interesting and uninteresting. This division is subjective: the same book is interesting for one and uninteresting for another.

Dichotomous division- this is a division of the scope of the divisible concept into two contradictory concepts: “All modern states can be divided into democratic and non-democratic.” Here there is no need to list all the types of the divisible concept: we single out one type, and then form a contradictory concept, which includes all other types. But this type of division has disadvantages. Firstly, the scope of the negative concept turns out to be too broad and vague. Secondly

Of course, only the first two contradictory concepts are essentially strict and consistent, and then this strictness and certainty can be violated.