LECTURE No. 9. Division of concepts

1. General characteristics

Definition - a very effective tool in the hands of the researcher. It allows you to get an idea of ​​the content of the concept, i.e., reveals it. It is undeniable that the definition of concepts is one of the most important logical techniques. However, the application of the definition does not provide complete information about the concept under study, because, in addition to content, any concept also has volume.

Division is a logical operation by which the volume of a concept, called a set, is divided into a number of subsets. With the help of this operation, the scope of the concept is revealed, while the definition reveals its content.

The division operation contains a number of concepts: a shared concept, division members, division base. As the name implies, the divisible concept is the concept, the scope of which needs to be disclosed. Members of the division make up the scope of the divisible concept, but at the same time they are delimited from each other. These are the types into which the scope of the concept is divided. The base of the division is the basis by which the division is made. The presence of a division base is not required.

Speaking about the performance of the operation of division, we mean the division of the volume of the concept subjected to division (generic concept) into the entire set of species contained in it. The shared concept is considered as a genus in relation to the elements of its scope related to this concept as species.

Division allows you to understand the belonging of a certain species to a particular genus, to put several species in one row, based on various grounds, including generic affiliation. All this contributes both to a more effective knowledge of various kinds of information, and to its correct consolidation.

2. Rules for the division of concepts

Dividing is an important and often difficult process. As a result, this process does not always lead to the correct result. It happens that the latter contains an element erroneously added not to its class. All this can lead to confusion, confusion, which deprives the division of the clarity inherent in any important tool of science. From what has been said, it is clear that it is necessary to establish rules that are mandatory for use in the process of the logical device "division". Such rules exist, there are four of them, and they effectively contribute to the elimination of logical errors in the process of division.

Continuity of division. The main thing in the division process, from the point of view of this rule, is sequence. This means that when dividing the volume of a divisible (generic) concept into types, it is necessary to gradually move from one type, revealed last, to the next one, located closest to all the others. In this case, it is unacceptable to move from disclosing species of one order to species belonging to another order. This division leads to errors and omissions of certain types. It lacks consistency. In this case, a so-called division jump occurs. For example, you cannot divide sausage into smoked, raw smoked, “Doctor’s”, “Amateur”, etc. This is due to the fact that in the first level of division we had to indicate smoked, raw smoked and boiled. Only after this can you move on to dividing into types of a lower level and, among the types of boiled sausage, indicate “Doctoral” and “Amateur”. This error can be well illustrated by applying the Criminal Code, since it has a convenient generic structure. If we divide the concept of “crime” into crimes against the constitutional rights and freedoms of man and citizen, crimes against family and minors, against life and health, murder, beatings, leaving in danger, etc., it becomes obvious that the last three types are included in the scope of the generic The concepts of “crimes against life and health” are articles of the Criminal Code of the Russian Federation. They should be considered only after listing all the concepts of the same level, which are essentially chapters of the Criminal Code of the Russian Federation.

Proportionality of division. It consists in fully revealing the scope of the concept under consideration, without omitting a single element, but without adding a single one. This is possible only in the case when the totality of the volumes of specific concepts is equal to the volume of the generic concept. This can be illustrated using the following example: all weapons are divided into bladed and firearms. The scope of the concept “weapon” is limited to these two types, each of which in turn is divided into types of the following series. The volume of the generic concept here is equal to the volume of the totality of species.

If there are many species and their number is long or impractical to enumerate in their entirety, in order to avoid a logical error, the unfinished series is supplemented with the words "etc", "etc", "etc". Violation of the rule of proportionality of division leads to such errors as incomplete division and division with extra members.

One base rule. A division base is a characteristic feature that is used in the division process to distinguish one division member from another. Having chosen a certain basis for division, the researcher must adhere to this basis until he fully reveals the terms delimited by this basis. Using several bases of division at the same time is unacceptable, as it leads to the crossing of the scope of concepts. An example of an incorrect division with crossing volumes is the following: “Bread can be wheat, rye, fresh and stale.” Two bases are used here - according to the grain from which the bread is made, and according to its condition.

Mutual exclusion of division members. Division terms must always be mutually exclusive. Neither of them should be in an intersection relationship with the other (that is, it should not contain in its volume elements contained in the volume of another member). This result (partial intersection of the volumes of members (types) of division) is caused by a violation of the rule of division based on only one base, which determines the strong relationship between these two rules. An example of a correct division according to this rule is the following: “A substance can be in the following states: liquid, solid and gaseous.” Incorrect division with the same example: “A substance can be in the following states: liquid, solid, heated, gaseous, frozen.” Here the division members do not exclude each other precisely because the rule of one basis was violated.

3. Dichotomy

Dichotomy (from Latin dichotomia - "dividing into two parts") - this is a very effective type of division. It is characterized by the fact that the members of the division do not intersect (i.e., exclude each other), such a division is made only on one basis, and the rule of proportionality is also observed. However, despite the indisputable convenience of dichotomous division, it has a serious drawback - the dichotomy is not always applicable. In cases where it is impossible to clearly set the criterion for division, this type of division does not fulfill its function. This happens when trying to divide concepts with a "fuzzy" volume.

The division operation is used in cases where it is necessary to determine the types of generic concepts. The examples given in the previous questions are divisions based on species-forming characteristics. This name is associated with the process of division itself, which is carried out on the basis of a characteristic, from which new species concepts are derived. For example: “Crimes can be against life and health, against family and minors, against sexual integrity and sexual freedom of the individual, etc.” The basis of division here and, accordingly, the species-forming feature is the object at which the criminal act is directed.

The dichotomy is significantly different from the specified type of division, which determines the scope of its application. Dichotomy is the division of the volume of a certain concept into two contradictory (not having intersection) concepts. With the literal designation of the process of dichotomous division, the following picture arises: the concept A (the concept over which the division is made) is divided into two - В и not = B. This is a simple type of dichotomous division that is limited to one stage. In more “complicated” cases, division is possible not = B on С и not = C etc. An example of a dichotomous division is the division of crimes into intentional and unintentional; citizens for adults and minors; animals on vertebrates and invertebrates, etc.

As can be seen, dichotomous division has a number of advantages. Thus, for example, there is no need to enumerate all types of a divisible concept, but it is enough just to single out one type and a concept that contradicts it. The latter includes all other species. It follows that the two concepts formed by the dichotomy exhaust the entire volume of the divisible concept, therefore the subject under consideration is reflected only in one of them.

At the same time, the scope of the negative concept is too wide, which implies the appearance of vagueness and uncertainty. As already mentioned, the dichotomy is characterized by a strict and consistent character. However, the second and subsequent stages of the dichotomous division, to a greater or lesser extent, lose their rigor and consistency. In this regard, researchers most often limit themselves to the first stage of division.

It is necessary to mention the problem that arises when identifying the division of concepts and their mental division into parts. The main difference between division and dismemberment is that parts of the whole are not types of a divisible (generic) concept. It is impossible to recognize as a division the division of the concept "ship" into bow, stern, mast, bottom, etc., just as the latter cannot be called types of the specified generic concept. Here we are dealing only with parts of the whole. Also parts, but not types of the concept of "computer" are the monitor, system unit, keyboard and mouse. The above can be illustrated in the following way: imagine that the indicated parts of the whole are members of the division, and therefore, types of a generic concept. In this case, we can say that, for example, the monitor is a computer (kind of computer). It is obvious that this is not the case.

Despite what has been said above, the operation of dismemberment of concepts cannot be neglected. It is widely used in the educational process of both senior and junior high schools. This operation is used in botany, biology, physics, chemistry, etc.

Purpose of division - getting an idea about the constituent parts of an object. For example, you can divide the human skeleton into parts, and also divide these parts into smaller ones. You can also divide, say, an egg into shell, protein and yolk. The application of dismemberment, of course, is not limited to the educational process of secondary schools, but is used in universities, in science and in everyday life. For example, in medicine, the human body is divided into the thoracic and abdominal sections.

4. Classification

One of the special divisions is classification. This is a systematic, consistent division of concepts with the distribution of types into an interdependent system, within which the latter are divided into subspecies, subspecies are also divided into division members, etc.

Classification is of great importance and is used for the most part for the purposes of science, and it is precisely because of this that it has existed for a long time. Classifications, often used in science, are subject to changes, additions, but, despite this, are more permanent than a simple division. The purpose of classification is to systematize and preserve knowledge. Therefore, it has high precision, clarity and stability. Members of the division are usually reflected in various tables, charts and codes.

There are classifications of plants, animals, legal classifications. Often classifications have a huge number of elements. These elements within the framework of the classification are combined into a single system, which makes it convenient and quick to access its individual parts and elements. The lack of classification would lead to chaos in a large array of unsystematized information.

It is impossible not to note the relativity of any classification, which is associated with the ambiguity of many objects, phenomena, processes. Therefore, it is often not possible to attribute this or that phenomenon to one group. From the question of the ambiguity of phenomena follows the problem of choosing the basis of classification. One and the same concept can, depending on the chosen basis, express various objects, phenomena, or be interpreted from one side or another.

Scientific classification is always an evolving system. It changes, as information accumulates, its structure improves. It happens that a new, more complete and developed classification replaces the previous one. Therefore, it is impossible to allow the limitation of operations on classifications by their formation alone. It is necessary to take into account the change in the body of knowledge about the subject, the dynamics of social relations, and many other factors, since any information, including that which is fixed within the framework of various classifications, is obtained by a person exclusively from the outside world. Accordingly, it is necessary to make the necessary changes in a timely manner.

As an example of an ambiguous phenomenon, one can cite a family. Despite the fact that this institution is called social, it is impossible to limit it to only one or two areas of social life.

Classification can be carried out according to a species-forming feature, or it can be dichotomous. The classification of animals, numbering more than one and a half million species, is obviously based on the use of a species-forming trait. The dichotomous classification is based on the features of the dichotomous division of concepts.

The classification is also natural и auxiliary. The difference between them is that the first is carried out on essential grounds, while the second - on non-essential ones. Natural classification allows you to determine the properties of an individual classification element, knowing the general characteristics of this classification or another element. Auxiliary classification is needed so that you can quickly and correctly solve emerging problems. This requires prompt, quick access to one or another classification element. Convenient search and selection of the desired item often serves as the basis for effective activities. It is the achievement of the goals of efficiency, speed and convenience that determines the use of non-essential grounds. Such a classification does not give us any idea about the properties of the object. We are all familiar with such classifications. There are many of them and they are widely used in human life. How often do we take a notebook with telephone numbers, designated alphabetically by the names of acquaintances. This is an auxiliary classification. Having picked up a book dedicated to a particular subject of science, first of all we open the alphabetical subject index. This is also an auxiliary classification.

When creating classifications, operations on classes are used. They allow you to achieve the desired result and get the classification that is needed at the moment. There are operations of addition, subtraction, multiplication and negation.

Addition (combining classes). When using this operation, several groups (classes) are combined into one classification containing all the elements of those classes that are combined.

Subtraction extracts separate classes from a larger class. The result is a class from which the elements of the selected class are removed.

Multiplication (intersection of classes). There is a class of elements that are common to several classes. They are determined using the multiplication operation.

Denial (education, addition). With the help of this operation, a new class of objects is derived from a more general class and considered separately as a new one.

Author: Shadrin D.A.

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