In the simplest cases, generalization and restriction operations can be characterized as follows. Generalization of volume A is a logical operation that results in the formation of a name with volume B containing volume A.

In other words, to generalize the name A means to form another name B (genus) that would subordinate the name A (species).

The transition from A to B is carried out by discarding features belonging to objects that are included in volume A. Thus, on behalf of “ interrogative sentence”we move on to the name “sentence”, excluding from the first the indication that in the grammatical form of this type something is being asked.

Generalization processes are inherent properties scientific knowledge. Before the general name “Boyle-Mariotte law” appeared, decades of hard work by scientists had passed to study the relationship between the pressure and volume of various gases.

The cognitive role of the generalization lies, in particular, in the fact that it is permissible to assign the characteristics of the generic name B to any new item, which turns out to be within volume B. If this operation is performed incorrectly, then such a transfer leads to a deviation of cognition from the right path. For example, for a long time it was believed that a whale was a fish (this idea was entrenched in spoken languages a number of peoples: in Russian folklore there is a “fish-whale”, in German – “Walfisch”, etc.). In this regard, it is natural to ask questions like “What kind of scales does a whale have?”, “Where does it spawn?” etc., which are dead ends.

In the process of cognition, the generalizing name, in turn, can be generalized, etc. The limit of generalization in each specific case is a certain universal name. In various sciences, these are names that fix fundamental concepts(scientific categories): point, straight line, plane - in geometry; material point, mass, force, acceleration - in mechanics; atom, molecule, valency - in chemistry; labor, goods, money, value - in economic theory; subject, property, relation - in logic; law, legal norm, legal decision - in jurisprudence.

A constraint is a logical operation that is the inverse of a generalization. It consists of finding a name with volume B, which is contained in volume A. To limit the volume of A means to find another name B (species) that would be in a relationship of subordination to A (genus).

The transition from A to B under restriction is carried out by attaching features belonging to objects that are included in the volume of A.

The limit of the limitation is names whose volumes are equal to one item (single names). Thus, the limit of the limitation of the name “capital” is the names of individual states - Minsk, Moscow, Tokyo, etc.

A special type of restriction is type selection, or typification. A type is a name to which homogeneous objects correspond to one degree or another. If some objects make up the volume of the name A and among them there are those that undoubtedly (i.e. with a degree equal to 1) belong to the volume B, and others have this property to some (less than 1) degree, then the name with the volume B represents type. So, by limiting the scope of the name “person”, you can get the name “ A tall man" This will be a type, since, based on practice and reasonable considerations, it is possible to single out, of course, tall people, while the rest can be ordered according to the degree of their belonging to tall people, to the limit beyond which there are, of course, short people (the degree of their belonging to the volume the name “tall man” is 0). A type is thus a name with a fuzzy scope.

Objects that unconditionally (with a degree equal to 1) belong to the volume of a fuzzy name are called typical representatives of this genus. In a concentrated form, they contain the characteristics of related objects and serve as standards for their description and evaluation. For example, Pan Adolf Bykovsky in Y. Kupala’s play “Peacock” is a typical representative of the minor Belarusian gentry at the beginning of the twentieth century.

It is easy to see that the operations of generalization and restriction are interrelated. This relationship is characterized by the so-called. law of inverse relation: if the name B is a generalization of the name A, and A, obviously in this case, is the result of the restriction of B, then the volume of A leaves the correct part of B, and the content of B is part of the content of B.

A relevant question is: what will happen to the volume of the name (according to its content) if it is replenished with new objects with their own specific properties? Will, for example, the volume of the name “chemical element” increase in connection with the discovery of a new chemical element? Will there be any changes in the content of this name? These questions should be answered in the negative. The scope of the name “chemical element”, as well as its content, remains stable. After all, the sign according to which this volume is isolated and fixed (“a simple substance, indecomposable by ordinary chemical methods to pieces") remains unchanged.

Adding new objects to the volume that are identical to the old ones in some way is called the logical operation of expanding the volume A.

The inverse operation of expansion, i.e. The removal from volume A of objects that are identical to the remaining ones according to some characteristics is called localization of the volume of the name A. An example of localization is the removal of whales from the class of fish, carried out at one time in biology, although the volume and content of the name “fish” remained unchanged.

Logical operations with volumes of names should not be confused with mental transitions from part to whole and, conversely, from whole to part.

The specificity of the latter is most clearly revealed when they are compared with the operations of generalization and limitation.

The generalized name contains the entire content of the result of the generalization, but not vice versa. In other words, the species has all the characteristics of the genus. For example, you can generalize the name “newspaper” to get the name “periodical,” and not a single newspaper is conceivable without this generic feature.

The situation is different when moving from part to whole. After getting acquainted with the individual rooms in new apartment, you can get an idea of ​​the apartment as a whole, but you cannot transfer the properties of the entire apartment (for example, the fact that it consists of three rooms) to each part of the apartment. The part, therefore, does not have the content of the whole. Therefore, confusing the operation of generalization (limitation) with the operation of mental transition from part to whole (from whole to part) is impermissible and can serve as a source of serious misconceptions. For example, the East Slavic tribe of Krivichi can be considered sometimes as a variety, sometimes as part of the Slavs. In the first case, knowing that the Eastern Slavs worshiped Perun, we will not make the mistake of concluding that the Krivichi also worshiped Perun (limitation operation). In the second case, from the knowledge that the Eastern Slavs were subjected to raids by the steppe inhabitants, it does not at all follow that any part of them, for example, the Krivichi, were subjected to these raids (transition from the whole to the part). Otherwise, a logical error is made.

Operations of generalization and limitation play an important role in legal science. In particular, by isolating common features from many concepts, they form concepts that are broader in scope. By establishing the general characteristics of the concepts “thief”, “murderer”, “bribe taker”, etc., namely, that they are violators of the disposition of the norm and subjects in relation to whom, in principle, a sanction should be applied, the concept of “offender” is formed. Accordingly, such concepts as “subject of law”, “ normative act"etc.

When limited, the interpretation of any specific name largely depends on the understanding of the generic name. For example, knowing what features are included in the content of the name “crime” (“act”, “socially dangerous”, “illegal”), we can confidently say that “robbery”, as a type of crime, also has these (but not only these) signs.

The logic of the relationship between the whole and the part is reflected, for example, in Article 52 of the Civil Code of the Republic of Belarus: “Founders (participants) legal entity or the owner of its property is not liable for the obligations of the legal entity, and the legal entity is not liable for the obligations of the founder (participant) or owner, except for cases provided for by law or documents of the legal entity.” Exercises:

1. Find the sum of volumes A and B (AÈB) in each of the following cases:

a) poet (A), prose writer (B);

b) foreign economic activity (A), international trade(B);

c) even natural number(A), odd natural number (B);

d) the last letter of the Russian alphabet (A), the thirty-third letter of the Russian alphabet (B);

e) king (A), current king of Poland (B).

2. Find the product of volumes A and B (AÇB) from Exercise 1.

3. Let the set of people be the universal volume T. Formulate the results of complementing the volumes of the following names:

a) man;

b) minor;

c) a person 180 cm tall and above;

d) a man born on the Moon;

e) a person with a soft earlobe.

4. Which of the following names are summarized by the name “proper fraction”:

a) a fraction in which the numerator is less than the denominator;

b) natural number;

c) denominator;

f) a fraction with a denominator equal to zero?

5. Which of the following names can be restricted and which cannot:

a) the Earth's pole;

b) constellation Ursa Major;

c) Universe;

d) space (in geometry);

e) body (in mechanics)?

6. Which names from exercise 9 can be generalized and which cannot?

7. In which of the following cases does the logical operation of limiting the name A take place:

a) minute (A) – second (B);

b) part of a minute (A) – second (B);

c) part of a minute (A) – part of a second (B);

d) second (A) – part of second (B)?

9. Let A be the scope of the name “man”, B – the scope of the name “young man”, C – the scope of the name “man not older than 50 years”. What do the expressions mean:

10. Let the set of scientists be the universal volume T, and also: A – the volume of the name “ancient scientist”, B – the volume of the name “modern scientist”, C – the volume of the name “physicist”, D – the volume of the name “Einstein”. Formulate names with volumes:

a) (AÇD)¢È B;

d) (T - A) Ç C;

e) (A" - T) ÈA;

f) T - (A Ç B).

11. Of the 50 students who passed the exams in physics and mathematics, 45 successfully passed physics, 44 - mathematics, 40 - physics and mathematics. How many students failed both exams?

As a result of mastering this topic, the student should:

know

• – logical operations with concepts: generalization, limitation, definition, division,
• – ways of generalizing and limiting concepts,
• – types of definition and division of concepts,
• – types of classifications of concepts;

be able to

• – perform logical operations of limitation and generalization of concepts,
• – apply in practical activities logical rules definitions and divisions of concepts;

own

– skills of practical generalization and limitation of concepts and logical operations - definition and division of concepts.

Generalization and limitation of concepts

To generalize a concept means to move from a concept with a smaller volume, but with more content, to a concept with a larger volume, but less content, i.e. move from a specific concept to a generic concept by reducing the information content of the content, i.e. from species to genus.

Logical operations with concepts include generalization and limitation, definition and division.

Since a distinction is made between logical and factual volumes, we can talk about factual and logical generalization.

For example, the result of generalizing the concept “Moscow State University" (A) is the concept of "state university" (IN), and the result of the generalization of the latter is the concept of “university” (WITH). This can be represented schematically as follows (Fig. 4.1).

When making generalizations, you need to be careful not to make "change to another gender" error for example this error

Rice. 4.1

will take place if, in the process of generalization, a transition is made from the concept of “student” to the concept of “students” or from the concept of “textbook section” to the concept of “textbook”. In the second case we are dealing with error "transition from part to whole"" .

As for the limit of generalization, here we should distinguish between the question of the limits of generalization of a single concept within a certain system of knowledge.

If a generalization is made within the framework of a particular science, then the limit of generalization is the concepts with the widest scope - categories , for example, “matter”, “consciousness”, “form of social consciousness”. Categories have no gender, so they cannot be generalized.

If we're talking about about the generalization of a concept within the framework of everyday consciousness, then the limit of generalization of any individual concept can be the concept of “something”.

The opposite operation to generalization is restriction.

To limit a concept means to move from a concept with a larger volume, but with less content, to a concept with a smaller volume, but with more content, i.e. from genus to species.

For example, limiting the concept of “ministry” ( A), you can move on to the concept of "Ministry of Foreign Affairs" (IN). The limit of the limitation is a single concept, in this case the concept “Ministry of Foreign Affairs of Russia” (C).

This can be represented as shown in Fig. 4.2.

That is, as follows from the definition of the restriction operation and the given example, the restriction occurs by increasing the information content of the content of the original concept.

Using the operations of generalization and limitation in the practice of cognition, we carry out a sequence of mental actions: in the case of generalization, we carry out the process of ascent from the individual or particular to the general; in the case of limiting concepts, we perform the reverse process - movement from the general to the specific, to the special or separate.

Using these operations in the process of mental and practical activity, it is necessary to take into account:

• 1) when carrying out these operations, jumps in generalizations and restrictions must be avoided, i.e. in the case of generalizing concepts, each step should be transition from species to the nearest genus; in case of restriction - vice versa: transition from genus to the nearest species;
• 2) when carrying out these operations, one must also take into account the fact that the generalization and limitation of the same concept can go in different directions;
• 3) generalization and limitation are based on generic relations, which there is no need to replace the relations "part – whole";
• 4) as criterion of correctness implementation of generalization and restriction operations there is a relation of logical consequence, which can be defined as follows: “If from a statement or statement form A logically follows IN, that is A|=B, the opposite is not true, then A more informative than B", where |= – relation of logical consequence.

The following specific cases of consistency between the contents of concepts are possible.

1. From any set of features of the content of concepts connected conjunctively, any of these features or a smaller set of them follows. For example, from the content “Moscow University for the Humanities” the contents “Moscow University” and “Humanitarian University” follow.

Thus, the content of a concept can be increased by adding new informationally non-empty features using conjunction.

• 2. From every attribute follows a complex attribute formed by adding some new attribute using disjunction. For example, from the attribute “to be cheerful” follows the attribute “to be cheerful or resourceful.” Consequently, it is possible to increase the content of a concept by reducing the terms of the disjunction, if they are in the content of the concept.
• 3. In the case when a characteristic contains a general quantifier, then a characteristic follows from it, which is obtained by substituting the name of any object located in the scope of the general quantifier or by substituting the names of several objects from this field. Thus, from the attribute “knows all his teachers” the attribute “knows teachers of logic and psychology” logically follows.
• 4. If a feature contains a subject constant, then a feature with an existence quantifier (expressed using the words “some”, “part”, “most”, etc.) for the subjects of this area can follow from it. In this case, the content of the concept can be increased in the following ways:
  • a) replacing the attribute containing a common name with an existence quantifier with singular names. For example, the content of the concept will increase (and its volume will decrease) if we move from the attribute “visited some European capitals” to the attribute “visited Moscow and Paris”;
  • b) replacing a feature with an existence quantifier with a feature with a general quantifier.

For example, the content of the concept will increase (and its volume will decrease) if we move from the attribute “visited some European capitals” to the attribute “visited all European capitals”;

c) replacing a characteristic with single names with a characteristic with a common name and with a quantifier of generality (the words “all”, “every”, “each”, etc.) for subjects of the corresponding field. For example, you can increase the content of the concept (reducing its volume) by replacing the attribute “visited the European capitals of Moscow and Paris” with the attribute “visited all European capitals.”

Famous Russian logician E. B. Kuzina identifies the following ways of generalizing and limiting concepts.

Ways to generalize concepts:

"(1) By discarding a feature included in the content through conjunction.

• (2) By adding a feature to the content of the concept using disjunction.
• (3) Replacing a single name in the attribute with a general name with an existential quantifier.
• (4) Replacing the general quantifier in the attribute with the existence quantifier.
• (5) Replacing a feature with a general quantifier with a feature with singular names."

Ways to limit concepts:

"(1) The addition of an informatively non-empty attribute is conjunctive.

• (2) Rejection of an informatively non-empty attribute if it is included in the content of the concept through disjunction.
• (3) Clarification of the attribute by replacing in it a common name with an existential quantifier with singular names.
• (4) Replacement of the existence quantifier in the attribute with a general quantifier.
• (5) Replacement of a feature with singular names by features with a common name and a general quantifier."

Possible mistakes when carrying out logical operations of generalization and limitation of concepts.

"Transition from part To whole " - lies in the fact that a part does not have all the characteristics of the whole. For example, “a paragraph is a chapter of a textbook.”

"Transition to another gender." For example, " cellular telephone- telegraph."

"Transition from the whole to the part." For example, “house – floor apartment”.

"Imaginary limitation" (pleonasm). For example, “ball – round ball – largest ball.”

Logical operations of generalization and restrictions are often used in the practice of thinking, moving from the concept of one volume, we clarify the subject of our thought, the thinking process becomes more specific and consistent.

• Kuzina E. B. Logic in summary and exercises: textbook. allowance / E. B. Kuzina. M.: Moscow State University Publishing House, 2000. P. 61.
• Right there. 60.

Operations of generalization and limitation of concepts are based on the law of the inverse relationship between the volumes of concepts and their content.

Generalization of a concept is the transformation of a certain concept into a new concept with more volume but less content.

For example, the result of the generalization of the concept “hot coffee with cream” is the concept “hot coffee”, and the result of the generalization of the latter is the concept “coffee”.

Limitation of a concept is the transformation of a certain concept into a new concept with less volume but more content.

As a result, restriction is the inverse operation of generalization. The limit of limitation is a single concept.

15. Definition of concepts

Definition (in other words, “definition”) of a concept is a logical operation that reveals the content of the concept or establishes the meaning of a term.

A definition is also often called a statement that contains the result of the logical operation of defining a concept.

By defining concepts, we somehow identify the essence of the reflected objects in the concept, reveal the content of the concept and separate the defined objects from other objects.

The definitions are as follows types:

obvious:

real; nominal; genetic; implicit.

Explicit definitions are those in which d/c1 and C/n are given and an equal sign or equivalence is established between them.

The most commonly used explicit definition is that by nearest genus and specific distinction. In it, the defining part begins with indicating the generic attribute of objects, precisely the one that is available to the wider class. In this case, the essential features of the defined concept are highlighted.

For example, “Ammeter is a device for measuring the strength of electric current,” “Speedometer is a device for measuring speed of movement,” or “Moscow Federal State University of Instrument Engineering and Informatics is one of the largest and oldest universities in Russia.”

The characteristics on the basis of which a defined set of objects are distinguished from the total number of objects corresponding to the generic concept are called specific differences. When defining a concept, one or more specific characteristics (differences) can be used.

The real definition is the definition of the concept itself. If a term denoting a concept is defined, then the definition is called nominal. For example, “A teacher is a civil servant working in the field of education” is a real definition, and “When a child reaches 18 years of age is called adulthood” is a nominal definition. Nominal definitions also serve to introduce new terms and to replace complex and lengthy descriptions of objects with more succinct and concise ones. For example, “An array is a collection of elements of a certain type, each of which has its own serial number, called the element index.”

Nominal definitions introduce signs that replace terms and reveal the etymology (origin) of a particular term. Definitions of this type are characterized by the presence of the word “called” in their composition.

Genetic definition is the definition of an object by reference to the mode of formation of that object. For example, “A hydroxide is a complex substance formed from metal atoms and one or more hydroxyl groups.”

3. When defining a concept, the following rules must be observed:

the definition must comply with the principle of proportionality, i.e. the scope of the defining concept must be equal to the scope of the defined concept (Dfd=Dfn);

the definition should not contain a logical ("closed") circle. It arises in the case when the defined concept and the defining one are expressed through each other;

the definition must be clear and precise. The definition of concepts should not be ambiguous; metaphors, personifications, comparisons, etc. should be avoided in the definition.

In practice, these rules are not always followed. Thus, if the principle of proportionality is violated, the following logical errors arise:

broad definition, i.e. the defining concept is wider in scope than the concept being defined (Dfd

a narrow definition, i.e. the defining concept is narrower in scope than the concept being defined (Dfd>Dfn). Example: “The bottom is the lowest part of the vessel,” however, seas, oceans, etc. also have a bottom;

the definition is narrow in one respect and broad in another. Example: “An airplane is an aircraft for transporting people.” On the one hand, this is a broad definition, since an aircraft for transporting people can be a helicopter or an airship. On the other hand, this is a narrow definition, since the aircraft also serves to transport all kinds of cargo.

4. Implicit definitions, unlike explicit ones, are built not on the identity - Dfd, but on replacing Dfn with a context, a set of axioms or a description of the method of formation of the defined object. There are 3 main types of implicit definitions:

contextual;

inductive;

definition through axioms.

A contextual definition reveals the content of an unfamiliar word that expresses a concept through context, without resorting to a translation dictionary (if the text is in a foreign language) or an explanatory dictionary (if the text is in the native language). Inductive definition uses the term being defined in the process of expressing the concept that is attributed to it as its meaning.

Definition through axioms is widespread in mathematics, mathematical logic and other sciences. It represents the disclosure of the content of a concept on the basis of axioms, i.e., certain provisions accepted as truth that can neither be refuted nor proven.

5. Since it is impossible to define all concepts (and there is no need for this), then in science and in the education system other ways of introducing new concepts are also used:

description;

characteristic;

interpretation by example;

comparison;

discrimination, etc.

These techniques are similar to the definition of concepts, but have some differences.

The description consists of listing the external features of an object with the aim of loosely distinguishing it from a class of homogeneous objects. The description creates a sensory-visual image of an object, which a person can create through a creative or reproductive representation. The description contains both essential and non-essential features. It is often found in fiction, historical and technical literature. Biology uses descriptions of plants, animals, and nature. In criminal practice, descriptions of criminals are common: their appearance, special features, etc. Characteristics list only some essential internal features of a person, phenomenon, object, and do not provide a description of appearance. In some cases, the characteristic is given by indicating one characteristic. For example, “Lev Yashin is the greatest football goalkeeper in the world.” In literature, character characteristics are compiled based on the following characteristics:

business qualities;

moral principles and ethical principles;

✓ character traits;

✓ temperament;

✓ political and social worldview;

✓ actions;

✓ set goals and ways to achieve them.

Characteristics of literary heroes make it possible to accurately and clearly notice the typical features of a particular collective image.

In practice, description and characterization are often combined. This combination is used in the study of biology, chemistry, geography, history, etc. The essence of this method is to give the most complete and comprehensive picture of a particular subject, to reveal its internal qualities and external features.

Interpretation by example is used in cases where it is more expedient to give one or more examples to illustrate a given concept than to give a strict definition through genus and specific difference. Thus, it is easier to explain the concept of “the living world of the forest” by listing its representatives: owl, bear, wolf, woodpecker, etc. This type of explanation of the concept is widely used in law, sociology, political science, natural and other sciences.

Comparison is the identification of similarities in compared objects. Based on comparison, it is possible to identify not only the similarities, but also the differences between the objects being compared. Comparison allows you to better imagine the object at the level of figurative thinking. This technique is used in the process of scientific knowledge, in the artistic representation of reality, etc. Comparative phrases in fiction include words such as “as if,” “as if,” “as,” “exactly,” etc.

Discernment is establishment distinctive features of a given object in relation to similar objects. This allows you to distinguish an object from a mass of similar objects by identifying the differences between it and other objects. Example: “Sport is not only daily training and a strict sports regime, it is, first of all, character strengthening, education of will and spirit.”

16. Division of concepts

1. Division of concepts

2. Division rules

3. Types of division

4. Classification

1. Division is a logical operation by which the volume of the concept being divided (set) is divided into a number of subsets using a certain division basis. The basis of division is a sign by which the scope of a concept is divided.

For example, climate zones are divided into the following types.

equatorial;

subequatorial;

tropical;

subtropical;

moderate;

subarctic and subantarctic;

Arctic and Antarctic.

The division in this case is based on the climatic characteristics of each zone (humidity, temperature, etc.). The types of climatic zones in the given example are members of the division, i.e., species of a given genus, subordinate to each other.

It should be noted that although the base of division can be almost any, only one base can be taken at each stage of division.

2. In the process of dividing a concept, the following rules must be observed:

principle of proportionality. The volume of the concept being divided must be equal to the sum of the volumes of the division terms. If this rule is violated, the following errors occur:

incomplete division, i.e. not all species of a given genus are listed;

division with extra members;

division should be carried out on only one basis. If this rule is not observed, then there will be a crossing of the volumes of concepts that appeared as a result of division. For example, the division “The Olympics are divided into summer, winter, held in Montreal, held in 56, etc.” is incorrect, since it was produced on more than one basis; >>/ division members must exclude each other. They should not have common elements; must be subordinate concepts whose volumes do not intersect. This principle is directly related to the previous one, since when dividing by more than one base, the members of the division will not exclude each other; the division process must be continuous. This means that you cannot make leaps in division. If the division is not single-level, i.e., in addition to species there are subspecies, then the first level is described first, then the second, etc.

3. The following types of division of concepts are distinguished: division of the scope of a concept according to a species-forming characteristic. In this case, the basis for division is the characteristic according to which specific concepts are formed. For example, “Transport can be land, air, or water.” The basis of division here is the environment in which transport operates;

two-term (dichotomous) division. With this type of division, the scope of the concept is divided into 2 contradictory concepts: A and non-A. For example, “Chemical elements are divided into metals and non-metals.” Dichotomous division has a number of advantages:

it always meets the requirements of proportionality;

the division members exclude each other, since each object of the divisible set automatically falls into class A or not-A;

division is carried out according to only one base. Due to its advantages, dichotomous division is widespread, but there are cases when its use is impossible for certain reasons.

The operation of dividing a concept is used when it is necessary to find out what types the generic concept consists of. The division of a concept should not be confused with the mental division of a whole into parts, since parts of a whole are not types of a genus. Example: “A computer consists of a system unit, keyboard, monitor, and mouse.” We cannot say “The keyboard is a computer,” but we can only say “The keyboard is part of the computer.” Therefore, the given example is not a logical operation, but a division of the whole into parts.

4. Classification is a kind of sequential division of a concept, forming a detailed structure in which each of its members (types) is divided into subtypes, etc. Classification is characterized by a more stable nature with respect to division. Scientific classification persists for quite a long time. It may practically not change, only be replenished with new members (for example, the periodic table). During the classification process, it is necessary to follow all the rules specified for dividing concepts. Just like division, classification can be dichotomous and according to a species-forming characteristic.

During classification, special attention should be paid to the choice of the basis of classification, since the type and structure of the classification itself directly depends on this. Natural classification is made on the basis of essential characteristics, and auxiliary classification is made on the basis of non-essential characteristics.

Sometimes in the process of classification it is impossible to clearly define boundaries, since everything changes and develops. Therefore, each classification by its nature is relative, approximate and reveals the connections between the classified objects only in a generalized form. There are many transitional forms that are difficult to attribute to one group or another. It happens that such a transitional group forms an independent species (biochemistry, astrophysics, etc.).

17. Judgment

1. Judgment is a certain type of thinking through which the presence or absence of any attribute in an object (class of objects) is expressed and which can be characterized in terms of truth or falsity.

2. Each judgment consists of the following elements:

subject;

predicate;

quantifier word.

The subject is a concept that expresses the subject of thought, what is being said in a given judgment. It is designated by the letter “S” (from the Latin sibjectum - underlying). A predicate is a concept that expresses a feature of the subject of thought, what is said about the subject of judgment. Indicated. the letter “P” (from the Latin pgaedicatum - said). A connective is a relationship between a subject and a predicate that exists in a proposition. It expresses the presence or absence of any quality reflected in the predicate. The connective is indicated by the “dash” sign, it can be implied, or it can be expressed in words:

is, etc.

Quantifier is a word that denotes quantity. The quantifier indicates whether the attribute expressed in the predicate belongs to the entire scope of the concept expressed in the subject, or only to part of it. The quantifier in a judgment always comes before the subject. Its meaning is contained in the words: “all”, “none”, “some”, etc. However, the quantifier is not an obligatory part of the judgment and may be absent. Thus, the structure of the judgment has the following form: S is (is not) P.

3. The type classification of judgments is very extensive due to large quantity bases of division. All judgments are divided into:

A simple proposition is one that expresses the connection between two concepts or is expressed by one concept when the second is implied. For example, “Pavlov is a local policeman,” “Morning,” “It’s getting cold.”

A complex proposition is a proposition consisting of several simple propositions. For example, the judgment “Both designers and technologists are satisfied with the test result” consists of two simple ones: “Designers are satisfied with the test result” and “Technologists are satisfied with the test result.” Let's consider the classification of simple judgments. Depending on the volume of the subject, simple judgments are:

single;

Single judgments contain a denial or affirmation about one subject of reasoning. The formula for such a judgment.

This S is (is not) R.

For example, “Tupolev is an outstanding aircraft designer.” This judgment is singular, since the subject “Tupolev” is a specific object.

Private judgments affirm or deny something only about a part of the objects of the class. This part can be definite or indefinite. According to this, private judgments are divided into definite and indefinite. Certain private judgments contain information about both parts of the subject of judgment. They have the following formula: only some S are (are not) P.

For example, “Only some apartments in this building are three-room.”

Indefinite private judgments have the form: Some S are (are not) P.

The quantifier word “some” gives uncertainty to such judgments. Example: “Some areas of the city are industrial.”

General judgments are those in which something is denied or affirmed about all objects of a given class. They have this structure. All S are P or None S is P.

Example: “Every state has its own flag” or “No federal republic is a monarchy.”

Judgments also differ in the presence or denial of properties. They can be divided depending on the quality of the bundle into:

affirmative;

negative.

An affirmative judgment indicates that an object has some characteristic. For example, “Animals of prey have fangs.”

A negative judgment indicates the absence of any attribute in an object. For example, “This evidence has no logical basis.”

attributive (judgment of property);

relative (judgment of relation);

existential (judgment of existence).

An attributive judgment speaks about the presence or absence of a particular property or state in the object of thought. In an attributive judgment, the predicate serves as a sign - a property, and the subject is expressed by one concept. Categorical judgment. In it, the relationship between the subject and the predicate is expressed definitely, without specifying any conditions or options. Such judgments include all attributive judgments.

A relational judgment or a relative judgment affirms or denies various connections, relationships between two, three or more objects of thought depending on time, place and cause. Example: “Petrov and Medvedev were university students,” where “were university students” is a relational predicate.

The existential or existence judgment affirms or denies the fact of the existence of the object of thought. Example: “There are no ugly women.”

4. Each judgment has qualitative and quantitative characteristics. To analyze both characteristics, a combined classification is used. According to it, there are 4 types of judgments:

general affirmative;

generally negative;

privately affirmative;

Partial negatives.

A general affirmative judgment (denoted by the Latin letter “A”) is general in the scope of the subject and affirmative in the quality of the connective. His scheme: All S is R.

A general negative judgment (Latin letter “E”) is general in the volume of the subject and negative in the quality of the connective. His diagram:

No S is an R.

A particular affirmative judgment (Latin letter “I”) is private in terms of the scope of the subject and affirmative in terms of the quality of the connective. His diagram: SomeS are R.

A partial negative judgment (Latin letter “O”) is private in terms of the scope of the subject and negative in terms of the quality of the connective. His diagram:

Some S are not R.

Complex judgments are those that include simple judgments. They, just like simple ones, can be true and false. But if the truth or falsity of a simple judgment is determined by its correspondence or inconsistency with reality, then the truth or falsity of a complex judgment is determined by the truth or falsity of its components (simple judgments).

Complex judgments have a different structure than simple ones. The components here are no longer concepts, but simple judgments. As a result, the connection between them is made not through connectives “is”, “is not”, etc., but through logical conjunctions “or”, “and”, “either”, “if, then”, etc. Depending From the functions of logical connectives, complex judgments are of the following types:

conjunctive (connective). Such judgments include as constituent elements other judgments - conjunctions, which are united by the logical connective “and”. For example, “Petya threw out the trash and went to the grocery store”;

disjunctive (dividing). Such judgments include as constituent elements other judgments - disjuncts, which are united by the connective “or”. Disjunction can be weak - when the conjunction “or” acts as a connective-disjunctive link and the components of a complex judgment do not exclude each other. For example, “In the evening I will watch the news or football on TV.” There is a strong disjunction - when the conjunctions “or”, “or” have an exclusive-dividing meaning, that is, the components of a complex judgment exclude each other. For example, “Tomorrow I will go for a walk or I won’t go for a walk”;

implicative (conditional). Such judgments are formed from 2 simple judgments and a logical conjunction “if, then”. For example, “If there are clouds in the sky, then it will probably rain.” The argument that in conditional propositions begins with the word “if” is called the basis, the remaining part, starting with the word “then”, is called the consequence -,

✓ equivalence. They assert the mutual conditionality of two situations, i.e., subject and predicate. Formed from two simple propositions and the conjunction “if, and only if, then.” As in implicative judgments, here we can distinguish a basis and a consequence. In a judgment of equivalence, the event that is the effect is a necessary and sufficient condition for the event that is the reason."

✓ with external negation. Such judgments are formed using the expression “it is not true that” or “not.”

6. A truth table is a table in which different types of propositions are considered in terms of truth or falsity (see table). As mentioned above, the truth or falsity of a complex proposition is determined by the truth or falsity of its components. Each type of complex judgment has its own logical designation:

✓ conjunction (conjunctive judgment) is designated as “&” or “^”;

✓ weak disjunction is denoted as “V”, strong disjunction -

✓ implication is denoted as “→”

✓ equivalence is indicated as “o” or “i..

✓ Negation is indicated as ┐, “-” or a line over the logical letter.

Truth table

А b al еуь ЭУь a->b a«->b -.a

And And And And - l And And l

I L l I I l l l

L and l I and and and

L l l l l i i i

In this table, a, b are variables denoting judgments, the letter “I” denotes truth, the letter “L” denotes false.

Modality of judgments

Definition of modality |

Alethic modality

Deontic modality

5 Epistemic modality. Axiological modality

1. Modality is additional information about the logical, factual status of a judgment, its various characteristics, directly or indirectly expressed in the judgment itself. The following types of modality are distinguished:

✓ alethic;

✓ deontic;

✓ epistemic;

✓ axiological.

2. Alethic modality reflects the nature of the connection between the objects of thought, that is, between the subject and the predicate of the judgment. Words expressing this modality are “possibly”, “probably”, “maybe”, etc. According to this modality, there are the following types of judgments:

✓ assertoric (about a real fact). In these judgments, truth or falsity is determined by the state of affairs in reality. Example: “In Southeast Asia, indeed, a large part of the population lives below the poverty line”;

✓ problematic (about the possibility of something). Example: “The situation in Southeast Asia may improve in the future”;

✓ apodictic (about the necessity of something). Example: “The situation in Southeast Asia needs to change for the better.”

3. Deontic modality covers the sphere of human activity, social and legal norms. This modality is characterized by words such as “prohibited”, “allowed”, “obligatory”, “inadmissible”, etc. Deontic modality is divided into the following varieties:

✓ judgments about the presence (or absence) of any right;

✓ judgments about the presence (or absence) of any obligation.

4. Epistemic modality characterizes the degree of reliability

“refuted”, “unprovable”, etc. Epistemic modality has the following varieties."

✓ judgments based on faith. Example: “I believe that God will save me”;

✓ judgments based on knowledge. Example: “As we know, the square of the hypotenuse is equal to the sum of the squares of the legs.”

5. Axiological modality expresses a person’s attitude towards material and spiritual values. Characterized by words such as “good”, “bad”, “indifferent”, etc. Example: “It’s bad that we go to museums so rarely,” “He doesn’t care what her fate will be.”

Generalization and limitation of a concept are two mutually inverse logical operations that allow, on the basis of one concept, to construct (find) another - a new concept.

Generalization- an operation through which a transition is made from a concept with a smaller volume to a concept with a larger volume.

The generalization of a concept is based on the search for a generic concept in relation to the original one by discarding the specific feature of the original concept.

Let's say we have the concept of “student” as our starting point. Students differ from other students in that they study in higher or secondary specialized educational institutions. Discarding this species hallmark, we get the concept “student” - generic for the original concept. In turn, the concept of “student” can be generalized into the generic concept of “person”. To do this, it is necessary to discard the specific characteristics of the student that distinguish him from other people. The concept “human” can be generalized using the same algorithm into the concept “mammal”, and the latter concept into the concept “animal”, etc.

It is easy to notice that, by discarding the specific features of generalized concepts, we each time create (find) a concept whose volume is greater than the previous one. Obviously, in expanding the scope of a concept when generalizing it, there must be a limit beyond which it is impossible to generalize. In our example, this limit will be reached when, having generalized the concept of “animal” into the concept of “element of the biosphere,” we then move from it to the concept of “phenomenon,” which cannot be further generalized, since its content consists of one attribute - to exist . Rejection of this single attribute will lead to the destruction of the concept, since absolutely meaningless concepts do not exist. Thus, the limit of generalization of concepts is philosophical categories - “object”, “thing”, “phenomenon”, etc., which are unlimited in scope and therefore cannot be further generalized.

Limitation concepts are a logical operation inverse to generalization. Through limitation, a transition is made from a concept with a larger volume to a concept with a smaller volume (from generic to specific).

The limitation of a concept is made by adding a species-forming characteristic to the content of the concept. For example, we need to limit the concept of “building”. By adding the attribute “brick” to the content of this concept, we obtain a specific concept of “brick building” in relation to the original one. By supplementing the content of the resulting concept with the attribute “three-story,” we obtain a new concept “three-story brick building,” etc. Since the limit of a restriction is one of its elements, the limit of a limitation is a single concept, in the scope of which one of the specific items class distinguished by the original concept. In our example, we will reach the limit of the limitation if we specify the address of a specific three-story brick building.

Let us pay attention to the fact that in the logical operations of generalization and limitation there is a clearly visible connection between the content of a concept and its volume. By generalizing a concept, we consistently impoverish its content, and this steadily leads to an expansion of its scope. By limiting the concept, we see the opposite picture - enriching the content of the concept leads to a decrease in its volume. All this allows us to formulate an important logical law of the inverse relationship between the volume and content of concepts: if concepts are in a relationship of subordination to each other, then a concept with a larger volume will be poorer in content, and vice versa, a concept with a richer content will be narrower in volume.

In order to correctly generalize and limit concepts, one must be guided by simple rule: concepts obtained as a result of generalization (limitation) must be in a relationship of subordination with the original generalized (limited) concepts. In accordance with this rule, for example, in the correctness of the generalization of the concept A into the concept IN, we can be sure if we answer affirmatively to two questions: 1) is everything A are IN; 2) is there IN, which are not A. The generalization of the concept of “metal” into the concept of “chemical element” is certainly correct, since all metals are chemical elements (an affirmative answer to the first question), and among the chemical elements there are chemical elements, which are not metals (yes answer to the second question).

Violations of the generalization (restriction) rule are intersection during generalization (restriction), equivolume during generalization (restriction) and incompatibility during generalization (restriction).

Intersection under generalization (restriction) – the most common error that arises due to underestimation of the possible incomplete coincidence of the generic characteristic with the objects of the generalized (limited) concept. By limiting, for example, the concept of “young man” to the concept of “student”, we will commit this error, because we do not take into account that in reality not all students are young people.

Equivalence in generalization (limitation) – an error that arises as a result of an illusory discrepancy between the volumes of some equally voluminous concepts. An example of such an error is the generalization of the concept of “great-granddaughter” into the concept of “woman”. Since the sign of being a great-granddaughter is more specific compared to the gender characteristic of being female, the illusion arises that the first concept is narrower in scope than the second. In reality, they are equal in volume: all great-granddaughters are women, and all women are someone’s great-granddaughters.

Incompatibility in generalization (limitation)(for example, the generalization of the concept “apartment” into the concept “house” or the restriction of the concept “book” into the concept “page”) is the most gross, although, alas, quite common violation of the rule of generalization (restriction), which is a consequence of a complete misunderstanding of the fact that parts objects included in the scope of a concept are not elements of the scope of this concept (no apartment is a house, and no book is a page).

Generalization of a concept 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 “ coniferous forest", we move on to the concept of "forest". The content of this new concept is narrower, but the scope is much wider. The content decreased because we removed (removing the word “coniferous”) a number of characteristic species characteristics that reflect the characteristics of a coniferous forest. Forest is a genus in relation to the concept “coniferous forest”, which is a species. The initial concept can be either general or individual. For example, it is possible to generalize the concept of “Paris” (a single concept) by moving to the concept of “European capital”, the next step would be to move to the concept of “capital”, then “city”, “village”. Thus, gradually eliminating the characteristic features inherent in the subject, we move towards the greatest expansion of the scope of the concept, sacrificing content in favor of abstraction.

The purpose of generalization is to remove as much as possible from characteristic features. In this case, it is desirable that such a removal should occur as gradually as possible, that is, the transition from the genus should occur to the closest species (with the broadest content).

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

Limitation of a concept is a logical operation opposite to generalization. If generalization follows the path of gradual removal from the characteristics of the object, limitation, on the contrary, enriches the totality of the characteristics of the concept. Thus, a transition is made from the general to the particular, from species to genus, from individual concepts to general ones.

This logical operation is characterized by a reduction in volume by expanding the content.

The operation of limitation cannot continue further when a single concept is reached in its process. It is characterized as much as possible full content and the volume in which only one object is conceived.

Thus, the operations of limitation and generalization are a process of concretization and abstraction within the framework from 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, and their interrelations. Through generalization and limitation, thinking becomes clearer, more precise, and more consistent. However, generalization and limitation should not be confused with isolating a part from the whole and considering this part separately. For example, a car engine consists of parts (carburetor, air filter, starter), parts consist of smaller ones, and those in turn consist of even smaller ones. In this example, the concept following the previous one is not its type, but is only its component part.