LECTURE No. 8. Generalization and limitation; definition of concepts

1. Generalization and restriction of concepts

Generalization of the concept - this is the transition from a concept with a smaller volume, but more content to a concept with a larger volume and less content. When generalizing, a transition is made from a specific concept to a generic one.

For example, generalizing the concept of "coniferous forest", we turn to the concept of "forest". The content of this new concept is narrower, but the scope is much broader. The content has decreased because we removed (removing the word "coniferous") a number of characteristic species features that reflect the characteristics of a coniferous forest. Forest is a genus in relation to the concept of "coniferous forest", which is a species. The initial concept can be both general and singular. For example, you can generalize the concept of "Paris" (single concept) by moving to the concept of "European capital", the next step will be the transition to the concept of "capital", then "city", "village". Thus, gradually excluding the characteristic features inherent in the subject, we are moving towards the greatest expansion of the scope of the concept, sacrificing content in favor of abstraction.

Purpose of generalization - the maximum removal from the characteristic features. At the same time, it is desirable that such a removal should occur as gradually as possible, i.e., the transition from the genus should occur to the closest species (with the widest content).

The generalization of concepts is not unlimited, and the limit of generalization is philosophical categories, for example, "being" and "consciousness", "matter" and "idea". Since the categories are devoid of a generic concept, their generalization is impossible.

Concept constraint is a logical operation, the opposite of generalization. If the generalization follows the path of gradual removal from the attributes of the object, the restriction, on the contrary, enriches the totality of the attributes of the concept. Thus, there is a transition from the general to the particular, from species to genus, from single concepts to general ones.

This logical operation is characterized by a decrease in volume due to the expansion of content.

The operation of limitation cannot continue any further when a single concept is reached in its process. It is characterized by the most complete content and volume, in which only one object is conceived.

In this way, restriction and generalization operations is a process of concretization and abstraction within the framework of a single concept to philosophical categories. These operations teach a person to think more correctly, contribute to the knowledge of objects, phenomena, processes of the surrounding world, their relationships. Through generalization and limitation, thinking becomes clearer, more precise, and more consistent. However, one should not confuse generalization and limitation with the selection of a part from the whole and consideration of this part separately. For example, a car engine consists of parts (carburetor, air filter, starter), parts consist of smaller ones, and those, in turn, of even smaller ones. In this example, the concept following the previous one is not its kind, but is only its component.

2. Definition

The word "definition" comes from the Latin word definition. In the process of communication, work, just everyday life, a person often has problems understanding information and transferring this information to other people. This is due to the lack or ignorance of the definition of the subject given in the available information. Simply put, a person often does not understand the meaning of a particular concept. It is not necessary for the person who encountered the problem to explain a complex concept, to reveal its essence, but this can be done by a person whose profession the problem under consideration belongs to. To implement the interpretation, the logical operation of defining the concept is called upon.

Definition of concept is a logical operation aimed at identifying the correct meaning of a term or the content of a concept.

To define a concept means to fully reveal its content and to distinguish the scope of this concept from the scope of other concepts (that is, to determine the objects included in the concept and separate them from other objects).

It is necessary to say about the relationship between definition and definition. Some scientists identify them, but some researchers separate the definition from the definition and call the latter a judgment that reveals the content of the concept. Thus, it turns out that definition is a logical operation, and definition - judgment.

The concept, the content of which is required to be disclosed, is called the defined concept and denoted by Dfd (definendum). To reveal the content of this concept, a defining concept is used, denoted by Dfn (definence). The goal of a person who reveals the content of Dfd, using Dfn, is to achieve equivalence (equality) of both sides of the definition, i.e., the defined and the defining concept.

The definition of a concept as a logical operation plays an important role in human activity, no matter what he does. At first glance, knowledge of the content of a particular concept is not necessary for people who are not involved in science. However, this is not so, because accurate knowledge of the signs of a concept not only increases the mass of a person’s knowledge, but also helps to avoid misunderstandings, incidents, and mistakes. The logical fallacy is all the more dangerous because at present the law plays a special role. Ignorance of the signs (content) of certain legal concepts makes a person vulnerable in legal relations.

Needless to say, for science, the definition of concepts plays an even more significant role, because it is within the framework of science that new concepts appear and old ones are interpreted. And if we are talking about legal science, then we understand that the life of the state, society and the individual depends on how clear and correct the definitions are.

The definition of a concept can be explicit and implicit.

Explicit definitions contain the defined and the defining concept, with their equal volumes. In this form, the closest genus and species (species difference) containing the characteristic features of the concept being defined are used for definition.

A variation of the definition through the genus and species difference is the genetic (from the Greek. genesis - "origin") definition. It indicates only the method of formation of this subject, its origin. The genetic definition plays a very important role for the sciences, where, due to their specificity, many concepts can be defined only through the method of formation or origin. Such sciences include mathematics, chemistry, physics. A genetic definition is a kind of definition through genus and specific difference, therefore it obeys the same rules and has a similar logical structure. As a separate type of definition through genus and species, nominal definitions can be called. They define a term denoting a concept, or introduce signs that replace it. Usually in such a definition there is the word "called".

The definition through genus and specific difference is made in two steps. The first step of such a definition is the relation (submission) of the defined concept under a generic concept, characterized by a greater degree of generalization. In the second step, the concept being defined is separated from others belonging to the same genus, with the help of specific differences. The attributes of both the genus and the species, on the basis of which the concept is defined, are contained in the defining concept. For example: "A square is a rectangle with equal sides." The concept being defined here is "square"; generic - "rectangle"; specific difference - "with equal sides".

For example: "The custom of business turnover is considered to be a rule of conduct that has developed and is widely used in any area of ​​business activity, not provided for by law, regardless of whether it is recorded in any document." In this case, the concept of "usual business practice" is a defined concept. Generic for him will be the "rule of conduct" contained at the very beginning of the defining concept. Thus, we bring the defined concept under a more general one. Since the "rule of conduct" contains in its scope not only the custom of business turnover, but a whole set of rules, it becomes necessary to single out the latter from the general mass. To do this, we add signs of this phenomenon, thereby expanding the content and reducing the volume. The custom of business turnover is not enshrined in law, but may or may not be reflected in any document. Pointing to this characteristic feature, we reduce the number of objects contained in the volume to the desired ones. The signs by which we delimit the concept being defined from others corresponding to the generic concept are called species difference (kind). In the definition of species differences, there may be one or more.

The definition through the genus and species difference can be reflected in the form of a formula A = Sun. Under А in this case, the concept being defined is implied, В is a genus, с - view.

В и с taken together are the defining concept. Another way to reflect such a definition looks like this: Dfd = Dfn.

Definition through the genus and specific difference is also called classical. It is the most common and widely used in various branches of scientific knowledge.

Implicit Definitions. Definition through genus and species difference is a very convenient and effective tool for revealing the content of concepts. However, like any other tool, this type of definition has limitations. Thus, it is impossible to determine by referring to genus and species concepts that have no genus at all, such as general philosophical categories. Single concepts do not have a form, and, accordingly, also cannot be defined, because if we used only the genus to define a concept, we would get too many elements in its scope, which would also include this concept itself, which is impossible (for example, the concept “N. G. Chernyshevsky” cannot be defined only as “Russian writer”).

When this situation arises, researchers use implicit definitions and techniques that replace definitions.

In contrast to explicit definitions, where there are defined and defining concepts that are equal to each other, in implicit definitions, context, axioms, or a description of the way the defined object arises are substituted for the defining concept.

There are several types of implicit definitions: contextual, inductive, ostensive, through axioms.

contextual (from lat. contextus - "connection", "connection") definition characterized by the fact that it allows us to find out the essence, the meaning of a word, the meaning of which we do not know, through context, i.e. through a relatively complete piece of information that accompanies a given word, relates to it and contains its characteristics. Sometimes during a conversation we come across a situation where the interlocutor uses a word that is unfamiliar to us. Without asking again, we try to determine the meaning of this word, relying on the words accompanying it. This is definition through context. An example of such a definition is the following sentence: "...you will take a check there. It will be personal - in your name. You will receive money from it." Thus, even without knowing what a check is, you can understand from the context that this is a document by which funds are received. With some ingenuity, you can guess that there are also checks payable to bearer.

Inductive definitions reveal the meaning of the term with the help of this term itself, through the concepts that contain its meaning. An example of this is the definition of natural numbers. So, if 1 is a natural number and n is a natural number, then 1 + n is also a natural number.

Ostensive definition establishes the meaning of the term by resorting to the demonstration of the subject denoted by this term. Such definitions are used in revealing the essence of the objects of the sensory world, in other words, objects that are available for direct perception. Such a definition often focuses on the simplest properties of objects, such as taste, color, smell, texture, weight, etc. It is often used when learning a foreign language or explaining the meaning of an incomprehensible word.

Sometimes, to characterize concepts, techniques are used that replace definitions.

An axiom is a position that is accepted without logical proof due to direct persuasiveness.

The definition through axioms is based on their quality. Characterization through axioms is widely used in mathematics.

Comparison is a technique that allows you to quite clearly characterize an object by comparing its characteristic features and features with another, homogeneous object. Such a comparison leads to a fairly clear delimitation of the compared objects from each other by identifying not only similarities, but also differences in their features. When a comparison is used to define a concept, it will be defined the more fully, the more homogeneous objects the scope of this concept will be compared with. Comparison leads to the formation of an imaginary image of an object that has characteristic features.

Description as a technique is simpler than comparison. The task of the researcher using the description is to consolidate as much information as possible about the subject, containing an indication of its characteristic features. In other words, when describing the image of an object directly perceived by the researcher, it is fixed in one form or another (drawing, diagram, text, etc.). When describing various kinds of characteristic features (weight, shape, size, etc.) should be reflected most fully and reliably.

Characterization is the creation of an idea of ​​an object by indicating some of its characteristic features. In this case, only one important sign is revealed. An example of a characteristic could be: “Gianfranco Pederzoli is the best Italian engraver of our time”; “According to K. Marx, Aristotle is “the greatest thinker of antiquity.”

You can also find combinations of description and characteristics. Often used in both science and fiction.

An example is used in cases where it is difficult to give a definition by genus and species difference, but you can resort to describing events, processes, phenomena, etc., illustrating this concept. An explanation with the help of an example is also the reflection of a complex concept through the enumeration of its elements. For example, the concept of "army" can be explained through the enumeration of its constituent units. Explanation by example is often used in the educational process of elementary grades.

3. Definition rules

The truth of a definition depends not only on the correct presentation of its content, but also on how harmoniously and consistently its form will be built. If the truth of a definition depends on whether its content accurately reflects all the necessary features of the concept being defined, there is only one rational way to obtain such a definition - when formulating, strictly follow the requirements of the logical rules for the formation of definitions.

Proportionality. The determination must be proportionate. This means that the defined concept must be equal to the defined one, that is, the defined and defining concepts must have equal volumes. If this rule is violated, a logical error occurs due to an incomplete definition or an overly broad interpretation of the subject.

The definition in making such a mistake may be either too broad or too narrow; sometimes there are definitions that are both too narrow and too broad.

Broader Definitions. They are characterized by the fact that the scope of the concept they define is greater than that of the one they define. In the form of a formula, this can be reflected as follows: Dfd ‹ Dfn. An example of a too broad definition would be the following: “a television is a means of satisfying the hunger for information” and “a chandelier is a source of light,” as well as “a wheel is a rubber circle.” In connection with this issue, we can recall the incident that occurred with the ancient Greek philosopher Plato, when he defined man as a “two-legged animal without feathers.” Subsequently, he had to admit the mistake and add the phrase “and with broad nails,” since Diogenes, another thinker of antiquity, brought a plucked chicken to a lecture at Plato’s school with the words: “Here is Plato’s man.”

Too narrow a definition. This is a definition in which the scope of the defined concept is wider than the scope of the defining concept (Dfd › Dfn). This error is contained in the following definition: “an immovable thing is a house or other structure.” The mistake here is that a structure (including a house) does not exhaust the scope of the concept of “immovable thing”, since the latter also includes land plots, subsoil plots, separate water bodies, etc. The definition of “indivisible” is also too narrow a thing is a thing the division of which in kind is impossible.” One feature was not indicated here, namely, that the division of such a thing is impossible only if it changes its functional purpose.

A definition that is too broad and at the same time narrow. They are characterized by a certain ambiguity. The same definition, depending on the direction in which its research is directed, becomes either too narrow or broader. For example, the concept of “a car is a device for transporting people” is broad, because a car is far from the only device for transporting people. However, on the other hand, the above concept is narrow, because a car can be used not only for transporting people (after all, you can also transport animals, building materials, for example, and other things).

Absence in the definition of a circle. The circle in the definition arises in two cases. The first is called tautology and is characterized by the definition of a concept through the concept itself. In the second case, a circle is formed if the content of the defined concept is revealed through a concept that was previously (in a previous definition) defined through the concept being defined at the moment.

Tautology - this is a simpler, in terms of structure and construction, erroneous definition. It is characterized by absolute uselessness, since it does not perform the main function of the definition - the disclosure of the content of the concept. In other words, after the definition-tautology, the concept remains as incomprehensible as it was before it. There are many examples of tautologies. You can often hear tautologies in colloquial speech, wherever you are - in line, at the market, at the circus and even the theater. People resort to tautology, often without noticing it. The following definitions are tautologies: "engine oil is an oily liquid with a pungent odor"; "an old person is one who has grown old in the process of life"; "funny is what causes laughter"; "an idealist is a person with idealistic convictions"; "a reminder is a reminder of something," etc. This shows that if we did not know the meaning of a concept and it was defined through itself, the meaning of this concept will not become clear, therefore, such a definition is useless.

From a logical position, the expressions "given task" or, for example, "assigned task" are incorrect. It often happens that one person says to another: "Butter is oily, sugar is sugary." This is also a tautology, but in this context it is used to highlight the tautology in the speech of another person.

Another case of a definition containing a circle is definition of the first concept by the second concept, which was previously defined first (the concept A is defined through the concept B, and then B is defined through A). A longer chain of definitions is possible, closing in a vicious circle. An example of such a circle is a definition derived from the proposition “the definition must be correct.” Here it is: “a correct definition is a definition that does not contain any signs of an incorrect definition.” This definition will be correct if we reveal the content of the concept “incorrect definition” (“this is a definition that contradicts the correct one”). The fact that there is a logical error here leads to the fact that this definition reveals something that does not reveal anything.

Clarity of definition. The definition must discard ambiguity and use only true concepts that have been previously proven or do not need definition. If this rule is violated, that is, if the content of the defined concept is allowed to be revealed through a defining element, the meaning of which is also unknown, the logical error “defining the unknown through the unknown” arises. A definition that complies with the rule of clarity should not contain metaphors or comparisons. There are a number of aphorisms and metaphors that are true judgments, which, although they effectively convey information, serve instructive purposes and often play an important role in shaping a person’s worldview, are not definitions of the concepts they contain. For example, the following judgment does not define the concept: “The death of one person is a tragedy, the death of a thousand people is a statistic” (I.V. Stalin).

Inadmissibility of negativity. This rule is due to the fact that a negative definition does not reveal the content of the concept being defined. An example of a negative definition would be the following proposition: “A car is not a carriage.” This judgment does not reveal the characteristics of a car, but only indicates that “car” and “carriage” are different concepts. Naturally, such an indication is not enough for a full definition.

This rule does not apply to the definition of negative concepts, the content of which is revealed mainly through negative definitions: "an incomparable work is a work that has no equal."

Author: Shadrin D.A.

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