LECTURE No. 7. Relations between concepts

1. General characteristics of the relationship between concepts

The world around us by its nature is a very complex system. This nature is manifested in the fact that all objects that we can only imagine are always in relationship with some other objects. The existence of one is conditioned by the existence of the other. Considering the relationship between concepts, it is necessary to define the concepts comparable и incomparable. Incomparable concepts are far from each other in their content and do not have common features. Thus, “nail” and “vacuum” will be incomparable concepts. All concepts that cannot be called incomparable are comparable. They have some common features that allow us to determine the degree of proximity of one concept to another, the degree of their similarity and differences.

Comparable concepts are divided into compatible и incompatible. This division is carried out based on the scope of these concepts. The scopes of compatible concepts coincide in whole or in part, and the content of these concepts has no features that exclude the coincidence of their scopes. Scope of incompatible concepts do not have common elements.

For the sake of greater clarity and better assimilation of the relationship between concepts, it is customary to depict using circular diagrams, called Euler circles. Each circle denotes the volume of the concept, and each of its points - the object contained in its volume. Circular diagrams allow you to represent the relationship between different concepts.

2. Compatible concepts

Compatibility relationships can be of three types. This includes equivalence, overlap и subordination.

Equivalence. The relation of equivalence is otherwise called the identity of concepts. It arises between concepts containing the same object. The scope of these concepts coincides completely with different contents. In these concepts, one thinks of either one object or a class of objects containing more than one element. To put it more simply, the relation of equivalence refers to concepts in which one and the same object is conceived.

As an example illustrating the relationship of equivalence, we can cite the concepts of "equilateral rectangle" and "square". These concepts contain a reflection of the same object - a square, which means that the volumes of these concepts completely coincide. However, their content is different, because each of them contains different features that characterize the square. The relationship between two similar concepts on the circular diagram is reflected in the form of two completely coinciding circles (Fig. 1).

Intersection (crossing). Concepts in relation to intersection are those whose volumes partially coincide. The volume of one, thus, is partially included in the volume of the other and vice versa. The content of such concepts will be different. The intersection relationship is schematically reflected in the form of two partially combined circles (Fig. 2). The intersection in the diagram is shaded for convenience. An example is the concepts of “villager” and “tractor driver”; "mathematician" and "tutor". That part of circle A that is not intersected with circle B contains the reflection of all villagers - not tractor drivers. That part of circle B that is not intersected with circle A contains the reflection of all tractor drivers who are not villagers. At the intersection of circles A and B, villagers-tractor drivers are imagined. Thus, it turns out that not all villagers are tractor drivers and not all tractor drivers are villagers.

Subordination (subordination). The relationship of subordination is characterized by the fact that the scope of one concept is completely included in the scope of the other, but does not exhaust it, but forms only a part.

This relationship is genus -> species -> individual.

In this relation are, for example, the concepts of "planet" and "Earth"; "athlete" and "boxer"; "scientist" and "physicist". As you can easily see, here the scope of some concepts is wider than others. After all, the Earth is a planet, but not every planet is the Earth. In addition to the Earth, there are also Mars, Venus, Mercury and many more planets, including those unknown to man. The same situation occurs in the other examples given. Not every athlete is a boxer, but a boxer is always an athlete; any physicist is a scientist, but speaking of a scientist, we do not always mean a physicist, etc. Here one of the concepts is subordinate, the other is subordinate. Obviously, it subordinates a concept that has a larger volume. The subordinate concept is denoted by the letter A, the subordinate - by the letter B.

In the diagram, the relationship of subordination is displayed as two circles, one of which is inscribed in the other (Fig. 3).

When two concepts enter into a subordination relation, each of which is general (but not singular), concept A (subordinate) becomes a genus, and B (subordinate) becomes a species. That is, the concept of "planet" will be a genus for the concept of "Earth", and the latter is a species. There are cases when a single concept can be both a genus and a species. This occurs if the concept of the genus, which contains the concept of the species, refers to the third concept, which is wider than the last in scope. It turns out a triple subordination, when a more general concept subordinates a less general one, but at the same time is in a relationship of subordination with another, which has a larger volume. The following concepts can be cited as an example: "biologist", "microbiologist" and "scientist". The concept of "biologist" is subordinate to the concept of "microbiologist", but is subordinate to the concept of "scientist".

A situation is possible when the general and singular concepts enter into the relationship of subordination. In this case, the general and concurrently subordinating concept is a species. The individual concept becomes an individual in relation to the general. This type of relationship illustrates the subordination of the concept of "Earth" to the concept of "planet". You can also give the following example: "Russian writer" - "N. G. Chernyshevsky".

Thus, the relationship of subordination can be simplified in linear diagrams: "genus -> species -> species".

Looking ahead, it can be noted that the relation -> view -> individual" is used in logical operations with concepts such as generalization, restriction, definition and division.

3. Incompatible concepts

Incompatible are concepts whose volumes do not coincide either completely or partially. This happens as a result of the fact that the content of these concepts contains signs that completely exclude the coincidence of their volumes.

Incompatibility relations are usually divided into three types, among which there are subordination, opposition and contradiction.

Subordination. A relationship of subordination arises in the case when several concepts are considered that exclude each other, but at the same time have subordination to another, common to them, broader (generic) concept. Since such concepts exclude each other, it is quite natural that they do not intersect. For example, the concept of “firearm” includes in its scope “revolver”, “machine gun”, “rifle”, etc. Considering these concepts, it can be noted that not a single revolver can be a machine gun, just as not a single rifle is a revolver. Despite their mutual exclusion, these concepts are subordinated to the general. In a circular diagram, the relationship of subordination is depicted in the form of several circles (their number corresponds to non-overlapping concepts) inscribed in one, larger circle (Fig. 4). Concepts that are in a relationship of subordination to a more general concept for them, but do not intersect, are called subordinate.

Subordinate concepts are types of a generic concept.

When defining the concepts included in the relationship of subordination, an error is sometimes possible. It lies in the fact that instead of mutually exclusive concepts, as an example, concepts are given that are subordinate to one another (for example, "writer" - "Russian writer" - "N.V. Gogol"). As a result, the relationship of subordination is replaced by a relationship of subordination, which is unacceptable.

Opposite (contrast). Concepts that are in a relationship of opposition can be called such types of the same genus, the contents of each of which reflect certain characteristics that are not only mutually exclusive, but also replace each other.

The volumes of two opposite concepts in their totality constitute only a part of the volume of the generic concept common to them, the types of which they are and to which they are subordinated.

Each of these concepts in the content has features that, when superimposed on the opposite concept, overlap (replace) the features of the latter.

It is characteristic that these concepts, by their linguistic nature, are antonymous words. These words reflect the contrast well, as a result of which they are widely used in the educational process. Antonym words expressing opposite concepts are: "top" - "bottom", "black" - "white", "heavy projectile" - "light projectile", etc.

On the circular scheme, the relationship of opposites is depicted as a circle divided into several parts by opposite concepts. Opposite concepts, say "white" and "black", are on different sides of this circle and are separated from each other by other concepts, among which are, for example, "gray" and "green" (Fig. 5).

Contradiction (contradiction). A relation of contradiction arises between two concepts, one of which contains certain characteristics, and the other denies (excludes) these characteristics without replacing them with others.

In this regard, two specific concepts that are in relation to contradiction occupy the entire scope of the concept that is generic for them. It should be especially noted that between two contradictory concepts there can be no other concept.

Positive and negative concepts enter into the relation of contradiction. Words that make up contradictory concepts are also antonyms. Thus, on a linear diagram, the contradiction relation formula can be depicted as follows: a positive concept should be marked with the letter A, and a negative one (contradictory to the latter) should be designated as non-A. The concepts of "loud" and "quiet", "high" and "low", "pleasant" and "unpleasant" perfectly illustrate the relationship of contradiction. That is, the house can be large and small; chair comfortable and uncomfortable; bread fresh and stale, etc.

When using Euler circles for clarity, the contradiction relation is depicted as a circle divided into two parts, A and B (not-A) (Fig. 6).

Author: Shadrin D.A.

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