A concept is the result of a generalization of a set of homogeneous objects according to their common essential features. For example, the concept of “building” is formed as a result of abstraction from the individual characteristics of individual buildings, which is achieved using logical techniques: comparison, analysis, synthesis, abstraction and generalization.
The concept is inextricably linked with the linguistic unit - the word. Concepts are expressed and consolidated in words and phrases called names. Simple names: “building”, “table”, complex names: “unknown area”, “famous person”, etc. are the material, linguistic basis of the corresponding concepts, without which it is impossible to form concepts or operate with them.
However, the unity of language and thinking, words and concepts does not mean their identity. For example, in any language there are synonymous words and homonym words. Synonyms are words that are close or identical in meaning, expressing the same thing, but differing in shades of meaning or stylistic coloring (“labor” and “work”). Homonyms are words that have the same sound, the same form, but express different concepts (for example: fist - hand and fist - rich peasant). Many words have multiple meanings. The polysemy of words (polysemy) often leads to confusion of concepts, and, consequently, to errors in reasoning. Therefore, it is necessary to establish the exact meaning of words in order to use them in a strictly defined sense.
Concept– this is the result of generalizing a set of homogeneous objects according to their essential characteristics. Essential features are stable, necessary features, without which a given object cannot exist in its qualitative certainty. The main logical methods of concept formation are: comparison, analysis, synthesis, abstraction and generalization.
Any concept can be characterized in terms of its content and scope. Scope of concept- this is a set of objects that are thought of in a given concept. For example, the concept “student” includes all students who were, are and will be. Contents of the concept- this is a set of essential features of an object that are thought of in a given concept. For example, the content of the concept “student” includes the property of being a student of a higher educational institution. The content of the concept “square” includes the following characteristics: “to be a quadrilateral”, to have “equal sides” and “equal angles”.
Content and volume are related to each other on the basis of the formal-logical principle of the inverse relationship: the greater the content of a concept, the smaller its volume, and vice versa. For example, if we add the attribute “fiction” to the content of the concept “literature,” we will reduce the scope of this concept, since we will exclude scientific and popular science literature from it, but we will increase its content with the additional attribute “fiction.”
The transition from a concept of a greater degree of generality to a concept of a lesser degree of generality is called limitation. With this operation, the content increases, but the volume decreases. For example, “law – criminal law”. The transition from a concept of a lesser degree of generality to a concept of a greater degree of generality is called generalization, that is, we increase the volume, but reduce the content. For example, “civil law is law.”
Logic also operates with the concepts of “class” (“set”), “subclass” (“subset”) and “class element”.
By class, or by many a certain set of objects that have some common characteristics is called. Such, for example, is a class of students, higher educational institutions, etc. Based on the study of a certain class of objects, the concept of this class is formed. A set can be reflected not in one, but in several concepts. For example, many athletes and many students can be combined into one set: students and athletes. This set is reflected in two concepts.
A class may include a subclass. For example, the class of students includes a subclass of law students.
Classes consist of a set of this class. Class element - this is an item included in this class. Thus, elements of many educational institutions will be schools, institutes, technical schools, etc.
Types of concepts
By volume concepts are divided into general, single and empty. Empty concepts do not designate any object. Examples of an empty concept are "centaur", "the time of year between December and January". Single concepts designate only one object: for example, “planet Earth”. Are common concepts denote more than one object, such as, for example, the concepts “student”, “teacher”, “person”, “table”. General concepts include registering and non-registration. Registering concepts have a finite volume of objects included in a given concept. Non-registering have no finite volume. General and individual concepts are collective and non-collective (dividing) Collective- those in which homogeneous objects are thought of as one whole. For example, “collective” is a collective general concept, “the constellation Ursa Minor” is a collective individual concept. Non-collective (separation) concepts refer to each object that is thought of in a given concept: “hand”, “light bulb”, “bird”. Thus, if the statement refers to each element of the class, then such a use of the concept will be disjunctive; if the statement refers to all elements taken in unity, and is not applicable to each object separately, then the use of the concept will be collective. For example: “students of our institute study logic,” we use the concept “students of our institute” in a divisive sense, since This statement applies to every student. In the statement “students of our institute held a theoretical conference,” here the concept “students of our institute” is used in a collective sense. The word “everyone” is not applicable to this judgment.
By content concepts are divided into concrete and abstract. Specific concepts denote a separate object, thing or person. For example, “house”, “tree”, “building”. Abstract concepts denote a property or relationship between objects. Examples of abstract concepts are “justice”, “truth”, “good”. Contrasting abstract concepts with concrete ones is necessary to prevent one of the fairly common errors called the “hypostatization error,” that is, finding in the real world a thing that corresponds to an abstract concept. The distinction between concrete and abstract concepts is based on the difference between an object, which is thought of as a whole, and a property of an object, abstracted from the object itself and not existing separately from the object. Abstract concepts are formed as a result of abstraction, abstraction of a certain feature of an object from the object itself; these signs are thought of as independent objects of thought. Thus, the concept of “courage” reflects a trait that does not exist on its own, in isolation from the persons possessing this trait. This is an abstract concept.
Relative concepts that presuppose the existence of another object are called: “north pole - south pole”, “father - son”. IN irrelevant Concepts conceive of objects that exist on their own, regardless of other objects: “house”, “city”, “village”. Positive concepts speak of the presence of some attribute of an object. Negative– about the absence of this sign. For example, positive concepts are the concepts of “wonderful person”, “sublime feeling”, and negative concepts are “injustice”, “slowness”. Negative concepts in Russian are most often expressed by the particles “ne”, “bes”, “bez”, but not always. For example, the concepts “slob” and “bad weather” are positive. In foreign words, mainly of Greek origin, negative concepts are expressed by the negative prefix “a” “immoral”, “asymmetry”, etc.
One should not confuse concrete concepts with individual ones, and abstract ones with general ones. General concepts can be both concrete and abstract (“crime” - general, concrete; “crime” - general, abstract).
To determine what type a concept belongs to means to give it a logical characterization. Thus, giving a logical characterization of the concept “house”, it is necessary to indicate that this concept is general, specific, positive, and irrespective.
The logical characterization of concepts helps to clarify their content and scope, and to develop a more precise use of the words that express them.
Relationships between concepts
Concepts are in certain relationships with each other. The relationships between the volumes of concepts are depicted on Euler circles. First of all, concepts are divided into comparable and non-comparable. Comparable concepts have common characteristics, which makes it possible to compare them. Incomparable do not have such characteristics, so their comparison does not make sense. An example of the latter is the concepts “deputy” and “stone”.
The compared concepts are compatible and incompatible. Compatible– these are those whose volumes completely or partially coincide. Incompatible– the volumes do not match. Compatible concepts are equivalent, intersecting, subordinate. Concepts where the volumes, but not the contents, completely coincide are called equivalent. For example, “grandson” and “great-grandson”, they do not coincide in content, but are equivalent in scope, since every grandson is a great-grandson, and every great-grandson is a grandson. Equivalence is depicted by one circle:
1. Grandson 2. Great-grandson
Intersecting concepts are concepts whose scopes overlap. For example: “student” and “musician”, since some students are musicians, and some musicians are students. On circles, this type of relationship is depicted in the form of two intersecting circles (if two concepts are related), where the intersecting part symbolizes the coincidence of volume.
1. Student. 2. Musician.
In a relationship submission there are concepts, the scope of one of which is included in the scope of the other. A concept with a larger volume is called subordinating. The concept with a smaller volume is subordinate. For example, the concepts of “man” and “father”. “Man” is a subordinate concept, and “father” is a subordinate concept. Because all fathers are men, but not all men are fathers. On circles this is depicted as two circles, one of which is included in the other circle.
1. Man. 2. Father.
There are three types of incompatible concepts. Subordination- this is the relationship between the volumes of two or more concepts that exclude each other, but belong to some generic concept. For example, “law”, “civil law”, “criminal law”. On circles they are depicted as separate non-overlapping circles within one, larger circle, which represents the generic concept.
1. Law 2. Civil law 3. Criminal law
Opposite concepts: volumes exclude each other, without adding up to the entire volume of the generic concept. Opposite concepts are the concepts of “love” and “hate”, “beautiful” and “ugly”.
1. Hate 2. Love
Contradictory concepts - volumes exclude each other, and together they constitute the volume of the generic concept. For example, the concepts of “love” and “dislike”. These concepts exhaust the scope of the generic concept – feeling.
1. Love 2. Dislike
Circular diagrams can be used to simultaneously represent the three-dimensional relationships of many concepts. For example, the concepts “woman”, “woman with children”, “woman without children”, “mother” are depicted by one circle denoting the concept “woman”, one part of the circle constitutes the concept “woman without children”, the other part circle means two equivalent concepts “a woman with children” and “mother”.
1. Woman 2. Woman with children
3. Woman without children 4. Mother
Definition of concepts
A definition, or definition, is a logical operation that reveals the content of a concept.
Types of definition. There are nominal and real definitions.
Nominal a definition is called, through which, instead of describing an object, a new term is introduced, the meaning of the term, its origin, etc. is explained. For example: “The field of science related to space flights is called astronautics”; “The term “legal” means relating to jurisprudence, legal.” Real is a definition that reveals the essential features of an object. For example: “Evidence is proof of the guilt of the accused in committing a crime.”
There are also explicit and implicit definitions. To the obvious include definitions containing a direct indication of the essential features inherent in the subject. They consist of two clearly expressed concepts: defined and defining. Implicit are definitions in which the content of the defined concept is revealed in a certain context.
The main type of explicit definition is definition through genus and specific difference.
Definition through genus and species difference. Genetic determination. The logical determination operation includes two successive steps.
The first stage is subsuming what is being defined under a broader generic concept. The generic concept contains part of the characteristics of the defined concept; in addition, it indicates the circle of objects that includes the defined object. For example, for the concept “logic” the generic concept will be “philosophical science”.
Usually they indicate the closest genus, which, compared to a more distant genus, contains more characteristics that are common to the characteristics of the concept being defined. By subsuming, for example, the concept of “taking a bribe” under the concept of a crime or “act,” we will complicate our task. Given this circumstance, this type of definition is sometimes called definition through the nearest genus and species difference.
But subsuming a defined concept under a generic one does not mean defining it. It is necessary to indicate a feature that distinguishes the object being defined from other objects belonging to the same genus. This operation is carried out at the second stage, which consists of indicating the distinctive feature of the object being defined. This feature will be a species difference. Species difference belongs only to a given species and distinguishes it from other species included in a given genus. So for logic, a species difference will be a sign indicating the subject of this science - the forms in which human thinking occurs and the laws to which it obeys. This feature reveals the essence of logic and distinguishes it from other sciences: political economy, theory of state, criminology, etc.
Thus, in order to define any concept, it is necessary, firstly, to find the genus, i.e., to perform a generalization operation, and, secondly, to indicate the specific difference, i.e., a feature that distinguishes this concept from other concepts included in this genus. Definition through the genus and specific concept is expressed by the formula A = Bc, where A is the concept being defined, Bc is the defining concept, c is the specific difference.
It must, however, be borne in mind that when indicating species differences it is not always possible to limit oneself to one characteristic. For example, in criminal law, a gang is characterized by a combination of three characteristics: 1) an association of two or more individuals, 2) the presence of weapons in at least one of them, 3) the cohesion of the group, the stability of the criminal ties of its members.
Determination through genus and specific difference is the most common type of definition, widely used in all sciences, including legal ones. Thus, in the theory of state and law, the following definition of a republic is given: a republic is a form of government (genus), in which the highest state power is vested in an elected body elected for a certain term (specific distinction). In civil proceedings, a decision is defined as a procedural document (genus) issued by the court of first instance when considering a civil case on the merits (specific distinction).
Genetic- is a definition that indicates the origin of an object, the method of its formation. For example: “A ball is a body formed by the rotation of a circle around one of its diameters.
Revealing the method of formation of an object, its origin, genetic origin plays an important cognitive role and is widely used in a number of sciences. Being a variety, defined through genus and specific difference, it has the same logical structure and is subject to the same rules.
Determination rules. The definition must be not only true in content, but also correct in its construction and form. If the truth of a definition is determined by the correspondence of the characteristics specified in it to the actual property of the defined object, then the correctness of the definition depends on its structure, which is regulated by a number of logical rules.
1. The definition must be proportionate.
The rule of proportionality requires that the volume of the defined concept be equal to the volume of the defining concept. In other words, these concepts must be in a relation of identity (A=Bc). For example, the definition “Recidivist is a person who committed a crime after being convicted of a previously committed crime” is proportionate. If a “recidivist” is defined as a person who has committed a crime, then the rule of proportionality will be violated: the scope of the defining concept (“person who committed a crime”) is wider than the scope of the defined concept (“recidivist”).
This violation of the rule of proportionality is called mistake of too broad a definition(A An error will occur if the defining concept turns out to be an already defined concept in its scope. Such an error will be made if, for example, the victim is defined as a person who has been physically harmed by a crime. In this example, the defining concept does not cover the characteristics of a victim who may suffer not only physical, but also moral and property harm. This error is called error of too narrow a definition(A>Bc). 2. The definition should not include a circle.
If, when defining a concept, we resort to another concept, which, in turn, is defined using the first, then such a definition contains a circle. For example, rotation is defined as movement around an axis, and an axis is defined as a straight line around which rotation occurs. A type of circle in the definition is tautologistsI- an erroneous definition in which the defining concept determines the defined. For example, an idealist is a person with idealistic beliefs. Such erroneous definitions are called “the same through the same.” Such concepts do not reveal the content of the concept. If we do not know what an idealist is, then indicating that a person has idealistic beliefs will not add anything to our knowledge. A tautology differs from a circle in its definition by being less complex in its construction. The defining concept is a simple repetition of the defined. 3. The definition must be clear.
The definition must indicate known characteristics that do not require definition and do not contain ambiguity. If a concept is defined through another concept, the characteristics of which are not known, and it itself needs definition, then this leads to an error called defining the unknown through the unknown or definition X through at. For example, Hegel defines the state as follows. “The state is the political manifestation of the world spirit.” However, the definition of the state with the help of the mystical concept of “world spirit”, which corresponds to the empty class, cannot be clear. The rule of clarity of definition requires that definitions not be replaced by metaphors, comparisons, etc., which, although they are important for characterizing the subject, are not definitions. 4. The definition does not have to be negative. The specific difference should indicate a characteristic that belongs to the object, and not one that is absent from it. True, this rule has exceptions. There are definitions, the specific difference of which is a negative attribute: an atheist is a person who does not recognize the existence of God; disobedience is a military crime consisting of deliberate failure to comply with the order of a superior. Negative concepts are widely used in mathematics. This means that this requirement is not a strict logical rule that is mandatory when defining any concept. Implicit definitions. Techniques that replace definition. Using definitions through genus and species difference, most concepts can be defined. However, for some concepts this technique is not suitable. It is impossible to define extremely broad concepts (categories) through genus and specific difference, since they do not have a genus, and individual concepts, since they do not have specific difference. In these cases, they resort to implicit definitions, as well as to techniques that replace the definition. Implicit definitions include definition through an indication of the relationship of an object to its opposite. This technique is widely used in defining philosophical categories. For example, “Freedom is a recognized necessity,” etc. Techniques that replace definition include; description, characterization, comparison, discrimination, ostensive definition. Task descriptions consists in more accurately and completely indicating the characteristics of an object, and, as a rule, external characteristics are listed. Characteristic consists of indicating the distinctive, characteristic features of a single object (persons, objects, etc.) A technique that replaces definition is also comparison, with the help of which one object is compared with another that is similar to it in some respect. This technique is used to figuratively characterize an object. By using distinctions signs are established that distinguish one object from other objects similar to it. For example, when searching for stolen property, “special features” play an important role: a monogram or engraving on a watch, etc. In some cases, ostensive definitions are widely used. Ostensive is a definition that establishes the meaning of a term by demonstrating the thing denoted by the term. These definitions are used to characterize objects accessible to direct perception. The ostensive definition is also used to characterize the simplest properties of things: color, smell, etc. A definition cannot provide comprehensive knowledge about a subject. Revealing the content of the concept, the definition indicates the general, essential features of the object reflected in it, abstracting from all its other features. However, revealing the main thing in a subject, a definition allows you to highlight a given subject, distinguish it from other subjects, and warns against confusion of concepts and confusion in reasoning. And this is the enormous value of definitions in knowledge and practical activity. Division of concepts By division is called a logical operation that reveals the scope of a concept, called division. In the division operation it is necessary to distinguish divisible concept, i.e. the scope of the concept that needs to be revealed, division members, i.e. subordinate types into which the concept is divided (they represent the result of division), and base of division- the sign by which division is made. The essence of division is that objects included in the scope of the concept being divided are distributed into groups. The divisible concept is considered as a generic one, and its volume is divided into subordinate types. Thus, the concept of “literature” is a genus, and the members of the division are “scientific literature”, “fiction”, “popular science literature”, etc. The division of concepts should not be confused with the mental division of the whole into parts. Its members of division are independent species; when divided, the individual parts of the object from which it consists are separated. But the parts of the whole are not species that are formed as a result of the operation of dividing the concept. If it were necessary to divide the concept of “aircraft,” it would be necessary to indicate the types of aircraft according to some characteristic, for example, by engine type. The following types of division are distinguished: division by modification of a characteristic and dichotomous division, which is often considered as its subtype. Division by modification of a characteristic.
The basis of division is a feature, when changed, specific concepts are formed that are included in the scope of the thing being divided (generic concept). For example, a socio-economic formation, depending on the method of production, is divided into subordinate types: primitive communal, slaveholding, feudal, etc.; the right in the form of its expression - to legal custom, legal precedent and normative act. Various features of the divisible concept can be used as a basis. It is possible to divide states according to their historical type, according to forms of government, according to forms of government; the population of a country - according to its membership in social classes, nationality, education, etc. The choice of attribute depends on the purpose of division and practical tasks. At the same time, certain requirements must be imposed on the foundation, the most important of which is the objectivity of the foundation. For example, science should not be divided into easy and difficult, books into interesting and uninteresting. This division is subjective: the same sciences can be easy for some people and difficult for others. Division rules.
In the process of dividing a concept, it is necessary to follow a number of rules that ensure clarity and completeness of the division. 1. The division must be proportionate.
The task of division is to list all types of the concept being divided. Therefore, the volume of division terms must be equal in their sum to the volume of the concept being divided. This rule requires that no division terms be omitted. If, for example, when dividing socio-economic formations only slaveholding, feudal and capitalist formations are indicated, then the rule of division of proportionality will be violated, since the member of the division (primitive communal) is not indicated. This division is called incomplete. The rule of proportionality will also be violated if we indicate unnecessary division members, that is, concepts that are not species of a given genus. Such an error will occur if, for example, when dividing the concept of “punishment,” in addition to all types, a warning is indicated, which is not included in the list of penalties in criminal law, but is a type of administrative penalty. This division is called division with extra members.
2. Division must be carried out using only one base.
Throughout the entire division, the feature we have chosen must remain the same and not be replaced by another feature. 3. Division terms must be mutually exclusive.
This rule follows from the previous one. When mixing bases, the division members - species concepts - will be in a relationship of partial coincidence. We get this result when dividing crimes into intentional, military and careless. If the division is made on one basis, then the members of the division will exclude each other, each object covered by the dividing concept will, as a result of the division, be included in only one of the subordinate species. 4. Division must be continuous.
This means that in the process of dividing a generic concept, you need to move on to the closest species without skipping them. For example, the concept of “literature” can be divided into fiction, scientific, popular science, etc. Each of these types can be divided, in turn, into subspecies. But one cannot move from division into species to division into subspecies. This division is devoid of sequence, it is called jump in division.
Dichotomous division (dichotomy). Represents the division of the volume of a divisible concept into two contradictory concepts. Dichotomous division is used in various sciences. For example, reflexes are divided into conditioned and unconditioned; wars - just and unjust. A dichotomous division does not always end with the establishment of two contradictory concepts. Sometimes a negative concept is again divided into two concepts, which helps to isolate from a large circle of objects a group of objects that interests us in some respect. Compared to division by modification of a characteristic, dichotomous division has a number of advantages. In a dichotomy, there is no need to list all the species of the dividing genus: we single out one species, and then form a contradictory concept that includes all other species. The members of division are two contradictory concepts that exhaust the entire scope of the concept being divided. Therefore, division is always proportionate. The division is made on one basis - depending on the presence or absence of a certain attribute in the object. The members of a dichotomous division are always each other; any object can be thought of only in one of the contradictory concepts that cannot be intersecting. Classification.–
This multi-stage, branched division represents the distribution of objects into groups (classes), where each class has its own permanent, specific place. The purpose of classification is to systematize our knowledge, therefore it differs from the usual division in its relatively stable nature and persists for a more or less long time. In addition, the classification forms an expanded system, where each member of the division is again divided into new members, branching into new classes, usually fixed in tables, diagrams, etc. Knowledge of this operation helps to correctly distribute objects into groups, study them, and, therefore, get to know the whole class as a whole. Knowledge of the types and rules of division is of great importance in the work of a lawyer, especially in investigative practice; planning, crime investigation, drawing up diagrams in the planning process, classification of investigative leads and a number of other investigative actions have as their main logical operation the division of concepts. There are natural classifications, made on the basis of an essential characteristic, and artificial (based on any non-essential characteristic). An example of a natural classification is the periodic system of D. Mendeleev. An example of an artificial one is library catalogs. CONCEPT Through dept. P. and P. systems display fragments of reality studied by various sciences and scientific theories. F. Engels pointed out that “... the results in which his data are summarized (natural sciences. - Ed.) experience, the essence of the concept..." (Marx K. and Engels F., Works, T. 20, With. 14)
. P. often reflects such objects and their properties that cannot be represented in the form of a visual image. With the help of P., both fragments of reality, considered in abstraction from change and development, and the process of constant change and development of the reality being studied, the process of deepening our knowledge about it, are displayed. Lenin emphasized: “Concepts are not immovable, but - in themselves, by their nature - before” (PSS, T. 29, With. 206-07)
; “... human concepts... are forever moving, transforming into each other, pouring one into another, but this does not reflect living life” (ibid., With. 226-27)
. Often, knowledge systems are understood as knowledge systems that are fragments of certain scientific theories. Such knowledge systems require definitions of knowledge and the establishment of their connections with other knowledge systems. From the totality of such knowledge, new knowledge about the objects under study can be logically derived. So, eg, K. Marx, defining as social-economic. formation, specific a feature of which is commodity relations of the highest type (when labor acts as a commodity), showed how the contradictions of goods explain the specifics of capitalism. relations, and logically deduced from the correspondence relations. "P. contradictions of capitalist society. This body of knowledge characterizes P. about capitalism as a system. The refined formulation of the inverse relation law looks like this: WaA(a) cWaB(a), if and only if Г, (a) |= В(а) and Г, Β(α)μΑ(α). In light of the distinction made in modern logic between the actual and logical volumes and contents of a concept, this formulation is valid in the case when WaA(oi) and WaB(a) represent the actual volumes of the concept, and Α(α) and B(a) are records of their actual contents in the applied language of predicate logic. The inverse relation law also applies to logical volumes and contents: WaA(a) with WaB(a) if and only if A(a)|=B(a) and B(a)|,tA(a). In this case, the set Г is empty, A(a) and B(a) represent linguistic expressions corresponding to the contents of the concepts under study, and WaA(a) and WaB(a) are their logical volumes, i.e. subsets of the universe of abstractly possible objects, generated on the basis of the information contained in the specified logical forms. Concepts used in science and in other spheres of human activity are extremely diverse in their structure, types of objects generalized in them and other characteristics. The typologization of concepts, i.e., the identification and systematization of their various types, can be carried out on different grounds - they are divided into types, firstly, based on the characteristics of the contents and, secondly, taking into account the specifics of their volumes and elements of volumes. Depending on the nature of the attribute by means of which the generalization of objects in a concept is carried out, they are divided into simple (their content indicates the inherent or non-inherent nature of a particular property, for example, “intelligent being”) and complex (their content fixes the connection between properties, for example, “creature” , capable of flying and swimming”), into non-relative (the object is characterized by itself, for example, “an ancient city”) and relative (the object is characterized through its relationship to other objects, for example, “a city located south of Moscow”). Based on the number of volume elements, a distinction is made between empty concepts (not containing volume elements) and non-empty concepts. (the volume of which has at least one element). A concept may turn out to be empty for various reasons: firstly, due to prevailing circumstances (for example, “the king who ruled France in the 20th century”) or due to the laws of nature (for example, “perpetual motion machine”), such concepts are actually called empty; secondly, due to the logical contradiction of its content (for example, “the director who staged all of Chekhov’s plays and did not stage Chekhov’s “The Seagull””), they are called logically empty. Non-empty concepts are single (their volume contains exactly one element) and general (their volume contains more than one element), and general ones are divided into registering and non-registering (depending on whether the number of elements of their volumes can be accurately counted in practice). Based on the ratio of the volumes of concepts to their genera (universes), universal and non-universal concepts are distinguished (the volumes of the former coincide with the genus, for the latter they are already genera). There are actually and logically universal concepts. The volumes of the former coincide with the genus due to circumstances of an illogical nature (for example, “metal that conducts heat”), the contents of the latter are logically necessary signs, the logical form of which is represented by a generally valid formula (for example, “a person who is stronger than anyone or not stronger than anyone else”). something"). According to the structure of volume elements, non-collective concepts are distinguished, the volume elements of which are individual objects (for example, “a person born in 1900”) or their tuples - pairs, triplets, etc. (for example, “people born in one and the same year”), similar concepts have the form ai... c(„A(c(i,..., α„)), and , their volume elements are collections of objects, conceived as one whole (for example, “political party”). According to the nature of the generalized objects, concepts are divided into concrete and abstract. Concrete concepts are generalized by individuals (for example, “electrically conductive substance”), tuples of individuals (for example, “isotopes”) or sets of individuals (for example, “beam parallel lines"). Abstract concepts generalize individual characteristics of individuals - properties, relationships, etc. (for example, “the ability of a substance to conduct electricity”), tuples of characteristics (for example, “mutually inverse relations”) or sets of characteristics (for example ., the concept of phenotype is “the totality of all properties of the structure and vital activity of an organism, determined by the interaction of its genotype with environmental conditions”). Concepts can be in different logical relationships to each other. Relations are established between concepts of the same gender (between comparable concepts) by comparing either their volumes or contents. Three fundamental relationships can be distinguished between the two concepts in scope: compatibility (in the scope of the concept there is at least one common element), exhaustiveness (the combination of volumes coincides with the genus), inclusion (each element of the scope of the first concept is included in the scope of the second). All other volumetric relations can be considered as combinations of fundamental ones. Among them, the relations between non-empty and non-universal concepts are particularly representative. They are used as model diagrams in traditional syllogistics. There are only seven of this kind of relationship: equal volume, subordination (the first concept is included in the second, but not vice versa), reverse subordination, crossing (compatibility, lack of inclusion on both sides and inexhaustibility of the genus), complementarity (compatibility, lack of inclusion on both sides and exhaustiveness kind), subordination (incompatibility and inexhaustibility), contradiction (incompatibility and exhaustibility). The classification of relations between concepts by content is less developed. One of the possible approaches is as follows: to establish this kind of relationship between the concepts αΑ(α) and aB(a), using the means of predicate logic, they find out in what relation the propositional forms A(a) and B(a) are located. If, for example, the latter are contraries (compatible in falsity and incompatible in truth), then the concepts themselves are in a relation of opposition; if B(a) logically follows from A(a), but not vice versa, then the first concept is more informative than the second, etc. Various operations can be performed on concepts. The most important of them are the operations of division, generalization and restriction. The division of concepts is a procedure for moving from a given concept to a set of subordinate ones from the point of view of a certain characteristic, which is called the basis of division. During this operation, the elements of the volume of the original divisible concept are distributed into subclasses, which form the volumes of the resulting concepts - members of the division. The basis for division can be, firstly, the presence or absence of some attribute B(a) in the volume elements of the dividing concept oA(a) (in this case, two subclasses of objects are distinguished in the original set - those with and without this attribute, members of the division are the concepts α(Α(α)&Β(α)) and α(Α(α)&-ιΒ(α)), and itself is called dichotomous); secondly, an object-functional characteristic (for example, height, age, color, nationality), modifying its meaning as a result of application to various objects of the original class (this type of division is called division by modification of the base). In logic, a number of rules have been developed for the correct implementation of this operation: the requirements of proportionality (equal volume of the divisible concept and the totality of division members), non-emptiness of division members, their mutual incompatibility in volume, uniqueness of the basis. The operation of dividing a concept should be distinguished from the procedure of mentally dividing an object into parts (for example, “A sentence consists of a subject, predicate and secondary members”), the latter is sometimes called mereological division. The division of a concept is a necessary element of the most important and widely used cognitive procedure in science - classification, which can be interpreted as a system of nested divisions. Generalization of a concept is a transition from a concept with a given scope to a concept with a wider scope, but of the same kind (for example, the concept of “a novel written by a Russian writer” can be generalized to the concept of “a novel written by a Russian or Ukrainian writer”). The reverse transition from a concept with a given scope to a non-empty concept that is narrower in scope is called a restriction (as a result of restricting the concept “a novel written by a Russian writer,” one can obtain, for example, the concept “a novel written by a Russian writer in the 19th century”). The limit of limitation is individual concepts, and the limit of generalization is universal concepts (the scope of which coincides with the genus). Operations of generalization and limitation can be carried out by modifying the content of a concept, relying on the law of the inverse relationship between the containing and the scope of concepts: in order to generalize, it is necessary to move to a less informative concept, and in order to limit, to a more informative concept. Since the volumes of concepts are sets, the same operations can be performed on them as on sets. The peculiarity of applying the concepts of Boolean operations to volumes (see Algebra of Logic) - union, intersection, difference of sets, taking the complement of a set - is that the result is a set, which is the volume of a new, complex concept formed from the contents of the original ones. Thus, the addition to the scope of the concept αΑ(α) is the scope of the negative concept α-ιΑ(α). The union of the volumes of the concept αΑ(α) and аВ(а) gives the volume of the dividing concept α(Α(α)νΒ(α)), the intersection of their volumes gives the volume of the connecting concept The doctrine of the concept was one of the most fundamental sections in traditional logic. However, after the creation of mathematical logic, this issue faded into the background for a long time, which was explained both by the dominance of the nominalistic attitude in modern logic and by the insufficient development of the doctrine of the concept itself, which in its traditional form did not meet the new logical criteria of rigor, contained a lot of gaps and internal inconsistencies. The modern version of the logical theory of the concept was created through the efforts of E. K. Voishvillo, who managed to inscribe the doctrine of the concept into symbolic logic, applying such means as formalized languages, precise methods of semantic analysis, and modern deductive systems to the analysis of the concept. As a result, in particular, the specificity of the concept as a special type of thought, its logical, was clarified, the distinction between logical and factual volumes and contents was introduced, which made it possible to explicate the meaning of the law of the inverse relation, precise criteria for typologizing the concept were identified, and a special, close to natural, expression was constructed which are formed using conceptual constructions. Recently, there has been a growing interest in concept theory in connection with the problem of knowledge representation, which is being developed within the framework of the artificial intelligence program. In line with this direction of science, a number of researchers (E. Orlovskaya, Z. Pavlyak, P. Materna, etc.) have proposed original explications of the conceptual form. Concepts play an important role both in science and in everyday practice. Rational cognition differs from sensory cognition, in particular, in that at this stage of cognition not only individual objects are identified, but also what is common to various objects is highlighted, that is, concepts are formed with the help of which general statements and scientific laws are formulated. Abstract thinking is the process of operating with concepts. In many areas of human activity (in science, in various fields of law, in medicine, etc.) special attention is paid to the accuracy of the terminology used. To achieve this goal, the meanings of the terms used are clearly recorded, i.e., the concepts of objects represented (represented) by these terms. An adequate understanding of various language contexts presupposes precise knowledge of what types of objects are being discussed in them, that is, knowledge of the concepts associated with linguistic expressions in these contexts. See what “CONCEPT” is in other dictionaries: 1. Types of concepts by volume………………………………………………………3 2. Types of concepts by content………………………………………………………...4 Task No. 1………………………………………………………………………………………7 Task No. 2…………………………………………………………………………………8 References……………………………………………………………..9 Types of concepts by volume. By scope, concepts are divided into: Single; The scope of a single concept is a single-element class (for example, “the great Russian writer Alexander Nikolaevich Ostrovsky”; “the capital of Russia”, etc.). The scope of a general concept includes a number of elements greater than one (for example, “car”, “briefcase”, “state”, etc.). Among general concepts, concepts with a volume equal to the universal class are especially distinguished, i.e. a class that includes all objects considered in a given field of knowledge or within the limits of given reasoning (these concepts are called universal). For example, natural numbers are in arithmetic; plants - in botany; constructive objects - in constructive mathematics, etc. In addition to general and single concepts, empty concepts (with zero volume) are distinguished by volume, i.e. those whose volume represents an empty set (for example, “perpetual motion machine”, “Baba Yaga”, “caloric”, “a person who lived 300 years” ", "Snow Maiden", "Santa Claus", characters from fairy tales, fables, etc.). Types of concepts by content. 1) Concrete and abstract concepts. Concrete concepts are those that reflect single-element or multi-element classes of objects (both material and ideal). These include the concepts: “house”, “witness”, “romance”, “Vladimir Mayakovsky’s poem “Good!”, “earthquake”, etc. Abstract are those concepts in which not the whole object is conceived, but one of the characteristics of the object, taken separately from the object itself (for example, “whiteness”, “injustice”, “honesty”). In reality, there are white clothes, unjust wars, honest people, but “whiteness” and “injustice” do not exist as separate sensory things. Abstract concepts, in addition to individual properties of an object, also reflect relationships between objects (for example, “inequality”, “similarity”, “identity”, “similarity”, etc.). 2) Relative and non-relative concepts. Relative - such concepts in which objects are conceived, the existence of one of which presupposes the existence of another (“children” - “parents”, “student” - “teacher”, “boss” - “subordinate”, “north pole of a magnet” - “south pole”) magnet pole", "base" - "superstructure"). Irrelative - such concepts in which objects are conceived that exist independently, regardless of another object (“house”, “person”, “blast furnace”, “village”). 3) Positive and negative concepts. Positive concepts characterize the presence of a particular quality or attitude in an object. For example, a literate person, greed, a lagging student, a beautiful deed, an exploiter, etc. If the particle “not” or “without” (“demon”) has merged with the word and the word is not used without them (for example, “bad weather”, “outrage”, “carelessness”, “impeccability”, “hatred”, “slob”) , then the concepts expressed in such words are also called positive. In the Russian language there are no concepts of “reproach” or “nastya”, and the particle “not” in the given examples does not perform the function of negation, and therefore the concepts “bad weather”, “slob” and others are positive, since they characterize the presence of a certain quality in an object (maybe even bad - “slob”, “carelessness”). Negative concepts are those that mean that the specified quality is absent in objects (for example, “an illiterate person”, “an ugly act”, “an abnormal regime”, “selfless help”). These concepts in language are expressed by a word or phrase containing a negative particle “not” or “without” (“demon”) attached to the corresponding positive concept and performing the function of negation. Positive (A) and negative (not-A) are contradictory concepts. 4) Collective and non-collective concepts. Collective concepts are those in which a group of homogeneous objects is thought of as a single whole (for example, “regiment”, “herd”, “flock”, “constellation”). Let's check it like this. For example, about one tree we cannot say that it is a forest; one ship is not a fleet. Collective concepts can be general (for example, “grove”, “student construction team”) and individual (“the constellation Ursa Major”, “Russian State Library”, “the crew of a spaceship that carried out a joint flight for the first time”). In judgments (statements), general and individual concepts can be used both in a non-collective (separation) and in a collective sense. In the judgment “Students of this group successfully passed the exam in pedagogy,” the concept “student of this group” is general and is used in a divisive (non-collective) sense, since the statement about successfully passing the exam in pedagogy refers to each student of this group. In the judgment “Students of this group held a general meeting,” the concept “students of this group” is used in a collective sense, since the students of this group are taken as a single collective and this concept is singular, because this set of students (of this particular group) is one of the other such collective No. For clarification purposes, we provide the following examples. Let us give a logical description of the concepts “team”, “bad faith”, “poem”: “Collective” - general, specific, irrespective, positive, collective. “Bad faith” is general, abstract, irrespective, negative, non-collective. “Poem” - general, specific, irrespective, positive, non-collective. Task No. 1 Determine which of the five answers given on the right are correct: a) Indicate the type of concept “civil courage” by volume. 1. Positive. 3. Negative. 4. Specific. 5. Single. b) Indicate the type of concept “air fleet” in terms of content. 2. Collective. 3. Irrelevant. 4. Abstract. 5. Single. a) The concept of “civil courage” is general in scope. b) The concept of “air fleet” in content is collective and irrespective. Problem No. 2 Give a complete logical description of the concepts: a) the western border of the state; b) insolvency; c) legality; d) team; e) dismantling; f) privatization; h) insanity; i) economic crime. a) the western border of the state - singular, specific, irrespective, positive, non-collective. b) insolvency - general, abstract, irrespective, negative, non-collective. c) legality - general, abstract, irrespective, positive, non-collective. d) collective - general, specific, irrespective, positive, collective. e) dismantling - general, specific, irrespective, positive, non-collective. f) privatization - general, specific, irrespective, positive, non-collective. g) museum - general, specific, irrespective, positive, non-collective. h) insanity - general, abstract, irrelevant, negative, non-collective. i) economic crime - general, specific, irrespective, negative, collective. Bibliography 1. Voishvillo E.K. Concept. – M., 1967. 2. Zherebkin V.E. Logical analysis of the concepts of law. – Kyiv, 1976. 3. Ivanov E.A. Logics. – M., 1996. 4. Kirillov V.I., Starchenko A.A. Logic: Textbook for law schools. – M., 1995. Related information. Most likely, few people think about the fact that they think and reason using concepts. Concepts are like air: we don’t notice them, but at the same time we cannot think without them. Every child naturally learns to think with their help at the age of seven or eight, moving from operating with concrete objects to operating with ideas. However, this does not mean that everyone knows how to use them correctly, and without this skill the path to logical reasoning is closed. That's why in this lesson, we'll tell you what concepts are, what types of concepts there are, how different concepts relate to each other, and how to handle them correctly. What is a concept? It seems intuitively clear. Perhaps many will say: a concept is the same as a word or term. However, this definition is incorrect. Concepts are expressed in words and terms, but are not identical to them. Let us recall that in the last lesson we said that all the words of our language are signs that have two characteristics: meaning and meaning. Usually we use language intuitively, without thinking about meaning and meaning. We simply call some objects apples, others pears, and others oranges. Often we choose a particular word based on the context, that is, the boundaries of its use are blurred. Meanwhile, there are often situations when such intuitive use of words is unacceptable or leads to unpleasant consequences. Imagine, for example, that your whole family is going on vacation abroad. You apply for a visa together, and for this you need your spouse to take a salary certificate from work. You tell him: “Don’t forget to take the necessary paper.” In the evening he brings you a pack of beautiful A4 paper. In this situation, each of you understood the word “paper” in your own way, and this became the cause of mutual misunderstanding. In many areas (legislation, legal proceedings, job and technical instructions, science, etc.) such ambiguity should be eliminated. Concepts are designed to combat it. From the point of view of logic, to understand a word means to be able to indicate exactly what objects it denotes, that is, to be able to establish in relation to any object whether it can be called by a given word or not. How to achieve this? Through concept formation. Concept is a logical mental operation that, based on certain characteristics, selects objects from a set and combines them into one class. Thus, three components are involved in the formation of a concept: a word or phrase (sign), a set of objects that it denotes (meaning), and some idea or distinctive feature that connects the word with the objects falling under it (meaning). It is this distinctive feature that acts as the heart of the concept, because it connects the word and objects. An example is the concept of a square. “Square” is a term, a distinctive feature is “a regular quadrilateral in which all angles and sides are equal,” objects are a set of geometric shapes that have this feature. What does the concept of a square do? From the entire set of geometric shapes, it singles out a certain group of shapes, because they have a set of some special characteristics. It is important not to confuse the concept and the word by which it is designated. Sometimes different concepts can be associated with one word, depending on what is taken as a distinctive feature. For example, the following concepts can be associated with the word “man”: “a social being”, “a being with intelligence”, “a being capable of creating tools”, “a being with articulate speech”, etc. However, it must be taken into account that, for the sake of brevity, people most often simply talk about the concept of a square or the concept of a person, without specifying what specific distinguishing feature forms the basis for identifying this concept. This often leads to disagreements and so-called disputes over words. Therefore, before entering into an argument, it is useful to clarify exactly what concept your interlocutor puts into this or that word. Each concept has two characteristics: content and volume. Contents of the concept- this is the set of distinctive features on the basis of which objects are distinguished from the universe and generalized into one group. Scope of concept- this is the totality of all objects that have distinctive features. It is important to note that the scope of a concept is always specified relative to a certain universe of consideration, that is, a set of objects that, in principle, may have certain distinctive features. The universe of consideration can be people, living beings, numbers, chemical compounds, household appliances, science, food products, etc. Thus, the concept of “elephants” is given in the universe of living beings, the concept of “physics” - in the universe of sciences, the concept of “even numbers” - in the universe of numbers, the concept of “cheese” - in the universe of food products. Depending on volume concepts are divided into empty and non-empty. The volume of empty concepts does not contain a single element. The scope of non-empty concepts contains at least one element. If there is only one element, then we are talking about a single concept (the author of “War and Peace”), if there are many of them, then we are talking about general concepts (“French kings”). If the scope of a concept coincides with the universe of consideration, then we speak of universal concepts (“numbers”, “people”) Let's talk in more detail about empty concepts. We don't always notice it, but people use empty concepts quite often. This may happen unconsciously, but sometimes they try to mislead us with their help. We already encountered one example of an empty concept in the last lesson: “the current king of France.” In the entire universe of people there is not a single person who has the distinction of being the current king of France. It should be noted that in this case the concept turned out to be empty due to historical circumstances. If history had gone differently, this concept might not be empty. Another example of an empty concept is “perpetual motion machine”. Here the emptiness is not due to historical reasons, but to the laws of nature. As for scientific concepts, it is unknown for many of them whether they are empty or not. A good illustration of this is the concept of the “Higgs boson”, the non-emptiness of which was confirmed only recently with the discovery of a new particle that satisfies the distinctive features of this concept. A concept can also be empty due to the laws of logic. These are so-called self-contradictory concepts, for example, “round square”. Depending on the types of generalized objects concepts are divided into collective and non-collective, abstract and concrete. Collective concepts include concepts about sets of objects or people. Such concepts usually contain the following terms: “set”, “class”, “collection”, “group”, “flock”, etc. Examples of collective concepts: “factory workers”, “rock band”, “constellation”. Non-collective concepts refer to single objects: “computer”, “tree”, “star”. Concepts are considered concrete if the elements of their scope are individuals or collections of individuals. It is important to note that individuals here are understood not as people, but as individual objects, even if these objects are abstract entities. Therefore, an example of a specific concept could be “Solar system”, “natural numbers”. Abstract concepts include concepts whose volume elements are properties, subject-functional characteristics, relationships, for example: “beauty”, “hardness”. By content type concepts are divided into positive and negative, relative and non-relative. Negative concepts contain a logical negation sign, positive concepts, accordingly, do not contain it. All the examples of concepts we gave were positive. An example of a negative concept: “odd numbers.” Relative concepts take so-called relational properties, that is, properties formed from some relation, as a distinctive feature of the objects falling under it. An example of a relative concept would be man as “a being capable of producing tools.” Among the relative concepts, we can distinguish pairs of interrelated concepts that presuppose each other: “teacher” and “student”, “seller” and “buyer”. Concepts about objects whose distinctive feature is not a relational property are called non-relative, for example: “citrus fruits”. This entire rather complex typology of concepts is needed so that we can easily perform operations on concepts and determine the relationships they have to each other. Concepts are not isolated from each other; on the contrary, they are in many connections with other concepts. The ability to identify these connections is very important, since it allows us to identify when our interlocutor or the author of the text is mistaken in the use of concepts or even consciously manipulates them. Examples of such manipulation include the use of concepts whose volumes are not equal as interchangeable, an imperceptible transition to a concept with a smaller volume to facilitate the proof of one’s position, etc. Before finding out the relationship between two concepts, it is necessary to determine whether they are comparable at all or not. Roughly speaking, the concept of “dogs” and the concept of “natural numbers” cannot be in any relation, because they refer to different universes of consideration: in the first case, animals, and in the second, numbers. Although if, for example, our universe of consideration is the things that people are interested in, then these two concepts become comparable, since people are interested in both. Thus, before comparing concepts, you need to make sure that, figuratively speaking, they have the same denominator - they refer to the same universe. Logicians divide relations between concepts into fundamental and derivative. Fundamental relations are primary; with the help of their various combinations, all other relations can be defined. There are three fundamental relationships: compatibility, inclusion and exhaustion. Concepts compatible, if the intersection of their volumes is non-empty. Accordingly, if the intersection of their volumes is empty, then the concepts are incompatible. Concept A turns on into the concept B if every element of volume A is also an element of volume B. Concepts are in relation exhaustion, if and only if each object from the universe of consideration is an element of the scope of either the first or second concept. By combining these fundamental relationships, fifteen derived relationships between concepts can be defined. We will only talk about those that operate with non-empty and non-universal concepts. There are only six of them. This is a relationship in which the volumes of two concepts completely coincide. With equal volume, the concepts A and B live in the same circle. An example is the pair of concepts: “triangle with equal sides” and “triangle with equal angles.” Both of these concepts denote the same set of objects. It occurs when the scope of one concept is completely included in the scope of another concept. Circle B is completely located in circle A, and at the same time circle A is larger than B in volume, that is, A includes objects that are not included in B. An illustration of subordination is the relationship between the concepts “citrus fruits” (A) and “oranges” ( IN). This is a relationship in which the scopes of concepts intersect, but do not completely coincide. An example of intersection is the relationship between the concepts of “women” and “leaders”. There are people who have both the first and second characteristics. This is a relationship when two concepts intersect and at the same time exhaust the entire universe of consideration. I specifically depicted concepts A and B in different colors so that it would be clear that the circle in the center is not a separate concept, but the result of their intersection. The complementarity relation exists, for example, between the concepts “temperature above 0°C” and “temperature below 30°C”. The volumes of these concepts intersect, and at the same time the volume of their addition is equal to the volume of the universe of consideration. This is a relationship in which the volumes of concepts do not intersect and exhaust the entire universe. If, for example, the universe of consideration is people, then A can be the concept “employed”, and B can be “unemployed”. Every person can be either employed or unemployed, but not both of them and not something third. It arises when the scopes of concepts do not intersect, but at the same time do not exhaust the entire universe of consideration. I’ll say right away that I don’t know what motivated those who called this relationship subordination. In my opinion, it is more about independence from each other. Apparently, what is meant is that both concepts are in a relationship of subordination to some third concept - in this case, the entire universe of consideration. Let us assume that the universe of consideration is animals. Then concept A is “lizards”, concept B is “cats”. Both lizards and cats are animals. The scopes of these concepts do not overlap. At the same time, the scope of the universal concept “animals” contains many elements that do not fall under A and B. At the very beginning, we said that a concept has two characteristics: content and volume. Accordingly, when we determine the relationship between concepts, not only their volumetric characteristics matter, but also their content. In particular, logicians have discovered that there is a so-called inverse relation law between the volume and content of concepts. The essence of this law is as follows: if the first concept is narrower in scope than the second concept, then the first concept is richer in content than the second. By and large, this law operates when we are faced with a relationship of subordination between concepts. Suppose the first concept is “flowers”, the second concept is “daisies”. The concept of “daisies” is narrower in scope than the concept of “flowers,” that is, it includes fewer elements. But it is richer in content. This means that we can extract more information from the concept “daisies” than from the concept “flowers.” If a certain object falls under the concept of “daisy,” then we automatically know that it will also fall under the concept of “flowers,” but a conclusion in the opposite direction cannot be made. If a certain object is an element of the concept “flowers,” this does not mean at all that it will also be an element of the concept “daisy.” It could well be peony, rose, lavender, etc. The main goal of operations on concepts is the formation of a new concept, with its own volume and content, from existing other or more concepts. The basic operations performed on concepts are called Boolean operations. They received this name in honor of the English mathematician and logician J. Boole, who developed a kind of logical mathematics. True, the operations performed on concepts are similar to the operations that we learned to perform with numbers in elementary school. These include: intersection, union, subtraction, symmetric difference, addition. Conception is an operation during which two or more concepts are taken and, as it were, superimposed on each other. As a result, at the intersection of their volumes, a new concept is formed, the elements of which will be those objects that simultaneously possess the distinctive features of all intersected concepts. To visualize this, let's look at the pictures: The result of the intersection is a shaded area. For example, if we take the concept of “police officers” and the concept of “corrupt officials” and perform an intersection operation on them, then the shaded area will contain only those people who are both police officers and corrupt officials. This is how we formed a new concept of “corrupt police officers.” As you can see, the intersection operation is based on the intersection relation. This means that if two concepts are in an intersection relationship, then we can easily form a new concept with their help. An association concepts is similar to addition: we take several concepts, combine their volumes and thereby form a new concept, the elements of which will be those objects that have at least one of the distinctive features of the combined concepts. To illustrate, we can take the concepts of “smokers” and “people who drink alcohol” and, by combining, form the concept of “people who smoke or drink alcohol.” In this case, the concept will include not only those people who both smoke and drink, but all those who have at least one of these bad habits. Therefore, we shaded both circles. Subtraction concepts are again very similar to mathematical subtraction. When subtracting, two or more concepts are taken and the volumes of the remaining ones are subtracted from the volume of one. Thus, a new concept is formed, the elements of which will be objects that have a distinctive feature of the first concept, but do not have the distinctive features of those concepts that were subtracted from it. Let's assume that concept A is “people with diabetes” and concept B is “people who are overweight.” If we subtract concept B from concept A, we get the new concept “people who have diabetes but are not overweight.” It is shown as a shaded area. This is an operation, in a sense, the opposite of intersection. It is also necessary to take two or more concepts and superimpose them on each other, but the new concept formed as a result of this superposition will contain only those elements that have no more than one distinctive feature of the original concepts. The shaded area shows this new concept. Items falling under this concept must have attribute A or B, but not both. Let A be the concept of “doctor”, B - “man”. Then we get the following concept: “to be a doctor, but not to be a man, or to be a man, but not to be a doctor.” This is an operation during which a concept is taken, and then its volume is subtracted, as it were, from the entire universe of consideration. This creates a new concept, the elements of which will be only those objects that do not have the distinctive feature of the initially taken concept. The new concept A’ is an addition to the concept A. If the universe of our consideration is animals, the concept A is “mammals,” then A’ is “animals that are not mammals.” The complement operation should not be confused with the complementarity relation. In addition to Boolean operations, a whole series of operations can be performed on concepts: restriction, generalization, division. This is an operation that represents, as it were, a narrowing of a concept. To limit the concept A means to move to the concept B, such that its scope will be strictly included in the scope of the concept A. Moreover, this transition from A to B represents a transition from a generic concept to a specific one. As can be seen from the picture, as a result of the restriction, the circle representing the volume of the concept becomes smaller. We restrict concept A to concept B, and then concept B to concept C. We can assume that concept A is “fish”. We can limit it to the concept B - “sharks”. The scope of concept A is broader, since fish are different, they include many species - not just sharks. In this case, the scope of concept B is completely included in the scope of concept A, because all sharks are fish. The concept of “sharks” can be limited to the concept C - “white sharks”. Again, the concept of “white sharks” is fully included in the concept of “sharks”, but is smaller in scope. The limit of limitation of a concept is a single concept. In our drawing it would represent a point in the center that can no longer be narrowed. The operation of limiting concepts is often accompanied by errors. Most often, they are due to the fact that the limitation of concepts is confused with the division of objects, that is, a concept is limited not on the basis of generic characteristics, but on the basis of those parts into which the elements of their volumes are divided. For example, let’s take the concept of “cars”. Based on generic characteristics, we can limit it to the concepts of “cars with manual transmission” or “electric cars”. And this is the right limitation. However, a car consists of many components: headlights, wheels, steering wheel, windshield wipers, engine, etc. Therefore, you can come across this option: the concept A - “cars” is limited to the concept B - “wheels”. Although wheels are part of a car, this limitation is incorrect. There is an easy way to avoid this mistake. Given the correct restriction of concept A to concept B, the statement “All B is A” must be true: “All sharks are fish,” “All electric cars are cars.” If we apply this formula to cars and wheels, it turns out: “All wheels are cars.” The statement is incorrect, which means that the restriction operation was carried out incorrectly. This is the inverse operation of a constraint. This time we are not narrowing, but expanding the concept. To generalize concept B means to move to concept A, so that the scope of concept B will be strictly included in the scope of concept A. Here a transition is made from a specific concept to a generic one. We generalize the concept C, represented by the smallest circle, to the concept B, which in turn we can further generalize to the concept A, and C is completely included in B, and B is completely included in A. Let C be the concept “gold”, then we can generalize it to the concept B - “metals”, and the concept B - to the concept A - “chemical elements”. The limit of generalization is a universal concept, that is, a concept whose scope coincides with the universe of consideration. In our example, the concept of “chemical elements” can be considered as universal. The operation of generalizing concepts can be subject to the same error as restriction: often people generalize concepts based not on generic characteristics, but on their constituent parts. In particular, the concept of “wings” is generalized to the concept of “birds,” which is incorrect. The way to check is the same: see if the statement “All B is A” is correct. Obviously, the statement “All wings are birds” is incorrect. Division- this is an operation consisting of taking a concept, highlighting some characteristic and, based on varying this characteristic, the original concept is divided into several parts, resulting in a set of new concepts. The original concept is called a divisible concept. Those concepts that are formed after division are members of division. The characteristic on the basis of which division is carried out - the basis of division. The entire circle is the volume of the concept of the divisible concept A. B, C, D and E are division members, that is, concepts formed as a result of dividing concept A. For illustration, let’s assume that concept A is “months”. The basis of division is belonging to the season. Then the newly formed concepts B, C, D and E are “winter months”, “spring months”, “summer months” and “autumn months”. Obviously, as a result of division, a different number of concepts can be obtained: everything depends on the concept being divided and the basis of division. For the division to be correct, the following conditions must be met: There are two types of division: dichotomous division and division by modification of the base. The word “dichotomous” is literally translated from Greek as “dividing into two.” When it is implemented, the original concept is divided into only two new concepts. Any basis of division, that is, a sign, is selected, and depending on the presence or absence of this sign, all volume elements are divided into two parts. Let the divisible concept be the concept of “people”; let the division be based on the presence of higher education. In this case, our initial concept will be divided into two: “people with higher education” and “people without higher education.” Another example: let’s take the concept of “dog”, the basis of division is thoroughbred. As a result of the dichotomous division we get the concepts: “pedigreed dogs”, “mongrel dogs”. The second type of division is division by modification of the base. As a result, we can get more than two new concepts. Here, any subject-functional characteristic of the elements of the scope of the original concept is chosen as the basis. In our example with months, this characteristic was belonging to the season. If our divisible concept is “people,” then we can take eye color, hair color, nationality, etc. as the basis for division. If the concept being divided is “poems,” then the basis for the division may be their genre. To illustrate, let’s take the concept of “playing cards”, and use the suit as the basis for the division: The division operation underlies the compilation of classifications and typologies. Classification is carried out by sequentially dividing a concept into its types, types into subspecies, etc. Classification, first of all, is important in scientific knowledge. It can act as both a result of studying a certain subject area (Carl Linnaeus’s general classification of plants and animals) and a driver of research (Mendeleev’s periodic table of chemical elements). In addition, classifications are very important in learning: people perceive information much easier if it is organized into categories. Often, without even noticing it, we use classifications in everyday life: ranking employees in the office, organizing clothes in a closet, distributing goods into departments in a store - these are just a few examples. Correctly done classification is like an upside-down tree (in my opinion, more like an upside-down bush). The top of the classification - the original divisible concept - is called the root. The lines radiating from it are like branches. They lead to division members, from which, in turn, branches also diverge to new concepts. Each concept in the classification is called a taxon. Taxa are grouped into tiers. On the first tier is the root of the classification A. On the second tier are the taxa B 1 -B n, formed using the first division operation. On the third tier are taxa C 1 -C n, formed as a result of the second division operation, etc. Each tier can contain any number of taxa. When constructing classifications, both types of division are used: dichotomous and by modification of the base. Moreover, they can coexist even in the same classification. The fact is that within the classification, each individual division operation can be performed according to its own basis. Let's give an example. Let’s take the concept of “writers” as the root of the classification, the basis of the division - whether the writer was Russian or not. Accordingly, we make a dichotomous division, as a result of which we obtain two new concepts at the second level: “Russian writers” and “foreign writers”. Then we can divide the concept of “Russian writers” according to the modification of the basis. As a basis, let’s take the characteristic: “in what century did the writer live?” We get new concepts: “Russian writers of the 11th century,” “Russian writers of the 12th century,” and so on up to “Russian writers of the 21st century.” As for the concept of “foreign writers,” it can also be divided according to the modification of the basis, but take the nationality of the writers as the basis. Thus, we get: “Spanish writers”, “French writers”, “German writers”, etc. The sign [...] indicates missing division terms. Further, each taxon can be divided according to some other characteristic. The main thing in each individual division is to follow the rules listed above. It should be noted that drawing up classifications is not as simple a task as it might seem at first glance. Situations are not uncommon when it is difficult or impossible to determine which taxon a particular item should be classified as. In our example with writers, in particular, cases are possible when a writer was born and began to create in one century, and died in another, like Chekhov. Where should he be classified - among the writers of the 19th century or the 20th century? Sometimes there are objects that, in principle, do not fit anywhere. Then a separate taxon is created for them or they are placed in the so-called “settlement tank”. It can be designated by the words “everything else,” and the objects located in it are not connected by anything other than the fact that they cannot be defined anywhere. Borges in one of his works cites an excerpt from a mysterious Chinese encyclopedia. This “divine repository of beneficial knowledge” says that “animals are divided into: a) those belonging to the Emperor, b) embalmed, c) tamed, d) suckling pigs, e) sirens, f) fairy tales, g) stray dogs, h) included in real classification, i) raging, as if in madness, j) innumerable, k) painted with a very thin brush of camel hair, m) and others, p) having just broken a jug, o) from afar seeming like flies" (Borges H.L. Analytical the language of John Wilkins // Works in 3 volumes, Vol. 2. Riga: Polaris, 1997, p. 85). Try to imagine this classification of animals as a tree. Do you think it was done correctly? If yes, then prove that none of the rules of division are violated. If not, then explain exactly what rules were violated. How could this classification be corrected? Cat. Please forgive me for my indiscretion. This is what I've been wanting to ask you for a long time... Cat. How can you eat thorns? Donkey. And what? Cat. There are, however, edible stems in the grass. And the thorns... so dry! Donkey. Nothing. I love it spicy. Cat. What about meat? Donkey. What - meat? Cat. Have you tried eating it? Donkey. Meat is not food. Meat is luggage. They put him in the cart, you fool. (E. Schwartz, “Dragon”) Define the relationships between the concepts of “food”, “sharp objects”, “spicy food”, “thorns”, “meat” and “luggage”. Depict these relationships using graphical diagrams. Remember that concepts can only be compared if they belong to the same universe of consideration. Husband: Honey, you're wrong. Wife: Oh, I'm wrong. So I'm lying. I'm lying, which means I'm a bad person, that is, a non-human. Are you saying that I'm an animal? Mom, he called me a beast! Determine whether the transition between the concepts “a person who is wrong”, “a liar”, “a bad person”, “a non-human”, “animal”, “a brute” was made correctly. Justify your position. What operations on concepts were used during this transition? What are the relationships between these concepts? Depict them using graphic diagrams. If you want to test your knowledge on the topic of this lesson, you can take a short test consisting of several questions. For each question, only 1 option can be correct. After you select one of the options, the system automatically moves on to the next question. The points you receive are affected by the correctness of your answers and the time spent on completion. Please note that the questions are different each time and the options are mixed. one of the logical forms of thinking, the highest level of generalization, characteristic of verbal-logical thinking. A concept can be concrete or abstract. Empirical and theoretical concepts are distinguished. The most abstract concepts are called categories. Psychology studies the development of concepts in humans. There is a difference between the assimilation of concepts developed by other people and the independent development of new concepts. In empirical studies of thinking, methods of defining concepts, comparing concepts, classifying concepts, and forming artificial concepts (-> generalization) are widely used. The degree of systematization of concepts is studied, the formation of concepts about the objective world, about other people, about oneself is studied. Everyday and scientific concepts, spontaneous and controlled development of concepts are differentiated. The possibility of earlier, in comparison with spontaneous, formation of conceptual structures in a child in the conditions of special education has been proven. One of the forms of thinking characterized by a high level of generalization. P. can be concrete and abstract; the most abstract P. are designated as categories. P. is expressed in words and exists only in this form. English concept) is a form of knowledge that reflects the individual and the particular, which is at the same time universal. P. acts both as a form of reflection of a material object, and as a means of its mental reproduction and construction, that is, as a special mental action. The first moment is a passive, contemplative prerequisite for activity, dependent on the objective content. At the same time, there is an internal connection between the true content of P. and the method of its construction and idealization (abstraction and generalization). Through P. the realization of meaningful generalization occurs, the transition from essence to phenomenon occurs. It fixes in itself the conditions and means of such a transition and the removal of the particular from the general. Behind each P. there is hidden a special objective action (or their system) that reproduces the object of knowledge. P. historically developed in society objectively exist in the forms of human activity and in its results—purposefully created objects. The individual assimilates them before he learns to act with particular manifestations. The learned general is the prototype, measure, scale for assessing empirically encountered things. P., depending on the type of abstraction and generalization underlying its cognition, acts as empirical or theoretical. Empirical P. fixes something identical in each individual subject of the class on the basis of comparison. The specific content of theoretical philosophy is the objective connection between the universal and the individual (whole and different); it reflects the transition, the identification of the different in the unified, which occurs in reality itself, reproduces the development, the formation of a system of integrity of the concrete, and only within this reveals the features and interconnection of individual objects (see Theory). developed form of generalization. Empirical P. - fixes something identical in each individual subject of the class on the basis of comparison. Theoretical P. is built on the basis of an analysis of the origin (genesis) of a phenomenon or object. Specificity. Each concept contains a special objective action that reproduces the object of knowledge through the use of certain tools. Kinds. Empirical and theoretical concepts are distinguished. 1. A complex of objects that have some common properties or characteristics. 2. Internal, psychological representation of general properties. Strictly speaking, the term should be used only in the latter sense, since it is the mental representation that is the concept and the mental representation is ultimately responsible for behavior in relation to the external world. Of course, there are things in the world that are chairs, but the concept of a chair is "in the head" and not in the external world. However, we can say about the first meaning that in order for a concept to “end up in the head,” there must be a complex of objects endowed with properties that are ultimately represented cognitively. In psychology, a concept is often viewed in terms of its place on the abstract-concrete continuum, where the chair is seen as concrete, easily identifiable, easy to represent, and (relatively) easy to conceptualize and classify, while control is seen as abstract, difficult to identify poorly representable and (relatively) difficult to easily classify. For more information about these problems (which present a certain difficulty for both philosophy and cognitive psychology), see class and related terms. one of the forms of reflection of the world in the human psyche, revealing with the help of language the essential properties, connections and relationships of objects and phenomena. The main logical function of P. is the identification of the general, which is achieved by abstracting from the characteristics of individual objects of a given class. P. has the greater scientific significance, the more significant the characteristics by which objects are generalized. The development of knowledge is expressed in the deepening of P., in transitions from some P. to others, which capture the deeper essence of objects, etc. representing a more adequate reflection of them. Each science operates with a specific P. system; the knowledge accumulated by science is concentrated in them. The value of a product is determined by how accurately and deeply it reflects objective reality (E.K. Voishvillo, 2001). The most general and fundamental categories are called categories. The category acts as a system-forming factor for the group of P. The system of P. and the categories of conflictology forms its conceptual-categorical apparatus. Conflictology so far mainly borrows concepts from other sciences that study conflicts. She also produces her own P. A generalization that arises on the basis of a synthesis of the most significant sensations and ideas. It arises as a result of abstraction and logical conclusions. Concepts can be everyday (furniture, transport, etc.) and scientific (matter, energy, etc.). As thinking develops, more and more abstract concepts are created. The most general concepts that allow one to reach the highest level of abstraction are called categories. 1. a thought expressed in words, which contains knowledge about the general and abstract properties of objects, phenomena, events. There are different approaches to distinguishing and systematizing concepts, For example: 1. specific concepts; 2. collective concepts; 3. general concepts; 4. abstract concepts; 5. conjunctive concepts; 6. disjunctive concepts, etc.; 2. a complex of objects that have some common properties or characteristics; 3. in philosophy - a form of thought that generally reflects objects and phenomena by fixing their essential properties. Each concept is characterized in terms of its content (a certain feature) and volume (the number of objects with such a feature), both of these aspects are connected by the law of the inverse relationship between the volume and the content of the concept: the smaller the volume, the greater its content, and vice versa. Entering into connections with each other in a person’s consciousness, concepts form various types of logical relations (incompatibility, identity, causation, etc.). Knowledge of the relationships between concepts allows you to avoid logical errors, but, alas, not misconceptions. An individual can formally adequately identify concepts and relationships between them in a neutral environment, but in a real situation he often does this completely differently; 3. in psychopathology – a) a thought in which some specific knowledge about a mental disorder or a certain theoretical idea is recorded (“Pirogov’s symptom”, “oligophrenia”, “symptom”, syndrome”, “course of the disease”, “pathokinesis, etc. .); b) the result of the process of disruption of the formation and assimilation of concepts due to a mental disorder (mental retardation, dementia, schizophrenia, affective and other psychiatric pathologies), that is, from a phenomenological point of view, how this or that concept is represented in the mind of a psychiatric patient; 4. in psychoanalysis - a way of organizing facts into theoretical formulations, “violence” over the facts of human life, which seems to be the result of the action of speculative impersonal forces. The differences are: a) basic concepts - those concepts that assume that usually mental life is driven by a conflict between opposing forces (Eros and Thanatos, sex and aggression, the reality principle and the pleasure principle); b) structural concepts - such concepts that assume that mental processes are functions of an organism or apparatus consisting of interconnected parts (for example, the mental apparatus is formed by the Id, Ego and Super-Ego); c) topographical concepts - concepts that proceed from the fact that mental processes can be localized according to the principle of a diagram (these parts of the mental apparatus can be presented as layers of mental content; their presence suggests that memories, impulses, fantasies, etc. are located at different distances from the surface; d) economic concepts - concepts that presuppose the presence of mental energy, quanta of which can be attached to structures (bound energy), move from one psychological structure to another (free energy) or receive a release in action; e) dynamic concepts - concepts that describe mental activity from the point of view of process, drive and development (for example, instinct, impulse, sublimation, etc.); f) the concept of abilities - such “pre-Freudian” concepts as memory, insight, thinking, etc., which can be reformulated in the spirit of dynamic psychology (“memory, forgetting and, possibly, introspection”).
What is a concept?
Types of concepts
Relationships between concepts
The law of the inverse relationship between the content and volume of a concept
Operations on concepts
Exercises
Chinese Encyclopedia
Meat is not food
Conversation between husband and wife
Test your knowledge
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