Chapter III

Signs of concepts. Concepts in psychology are derived from comparisons of similar concepts. Representations, in turn, are composed of individual elements. The constituent elements of a representation or concept are usually called signs. Signs are what distinguishes one idea or concept from another. For example, we consider the signs of gold to be “metal”, “precious”, “having a certain specific gravity”, etc. These are all the ways in which gold differs from other things, from non-metals, from base metals, etc.

Not all signs should be considered equal. Each concept has many different characteristics, but when thinking about it, we primarily think only about the known characteristics. These signs are, as it were, the main ones, around which other signs are grouped. The first signs are called essential, or basic, and the rest - secondary. Basic features are those features without which we cannot think of a known concept and which outline the nature of the object. For example, for a rhombus, the essential feature is that it is a quadrilateral with parallel and equal sides, etc.; An insignificant feature for the concept of a rhombus is that it has one or another size of sides, one or another size of angles.

Since the time of Aristotle, the signs of concepts are usually divided into the following 5 classes:

1. Generic sign. If we say that chemistry is a science, That science will be a generic attribute for the concept of “chemistry”; among other features inherent in the concept of “chemistry”, There is and the sign “science”; this feature distinguishes chemistry from everything that is not science. Genus( genus )or a generic characteristic is the concept of a class into which we introduce another concept we are considering.

2. Species difference. If we say What chemistry is a science that studies the structure of matter, That adding the attribute “studying the structure of matter” will serve to indicate how this science differs from other sciences. Such a attribute, which serves to distinguish a concept from a number of similar concepts, is called species difference ( differentiaspecifica ). Let’s take the concepts “Russian sailor”, “French sailor”, “English sailor”. In this case, “Russian”, “French”, “English” are a specific difference; it serves for Togo, to distinguish a sailor of one nation from sailors of all other nations.

3. View(species ). If you add a specific difference to a generic character, you get a species. For example, “building for a weapons depot” == arsenal; “building for grain storage” = barn. In this case, “building” is a genus, “for storing weapons” is a specific distinction; the addition of a species difference to the genus gives the species “arsenal”. Adding to the concept “building” the specific attribute “serving for storing bread” gives the form “barn”. A species can be a Sign because it can be attributed to an understanding. For example, “this science is chemistry.”

4. Own sign (proprium ).A proper attribute is a attribute that is inherent in all things of a given class, which is not contained among the essential characteristics, but which can be inferred from them. For example, an essential feature of a person is his “reasonableness.” From this property follows his ability to speak. This last sign is its own sign. The main feature of a triangle is a rectilinear flat figure with three sides. As for the characteristic of a triangle, that the sum of its angles is equal to two straight lines, this is its own characteristic, because it follows or is derived from the main characteristics.” We don’t think of this sign when we think about a triangle, so it is inferential.

5. Improper attribute (accidens ).Improper fit is a feature that cannot be derived from an essential feature, although it may be inherent in all things of a given class. For example, the black color of a raven is accidens . If the black color of the raven were deducible from the basic properties, then it could be called proprium , but we don’t deduce it, since we don’t know why crows have the black color of Yuryev. He is, therefore, accidens.

Improper characteristics are divided into two groups: inseparable improper characteristics ( accidensinsepara ble ) and separable improper features ( accidensseparabile ). The latter are those characteristics that are inherent only in some things of one class or another, but not in all, while the former are inherent in all things of a given class. For example, the black color of a raven is accidensinseparabile . Black hair color for humans is accidens separabile because there are people who don't have black hair. In relation to individual individuals, a non-proper attribute can also be separable and inseparable. Separable characteristics are those that are present at one time and not present at another time. For example, Balfour is the First Minister of England. After some time he may not be the first minister. This is a separable sign. "Leo Tolstoy was born in Yasnaya Polyana." In this sentence, the attribute “born in Yasnaya Polyana” is an inseparable attribute.

The content of a concept is what is thought in the concept. For example, in the concept of “sugar” the following signs are thought of: sweet, white, rough, heavy, etc.; These features together constitute the content of the concept “sugar”. The content of a concept, in other words, is the sum of its attributes; therefore, each concept can be decomposed into a number of characteristics inherent to it. The content of a concept can be very variable depending on the point of view adopted, the amount of knowledge, etc. For example, in the concept “sugar” a chemist thinks of one content, and a non-chemist thinks of another.

The scope of a concept is what is thought through the concept, i.e. the scope of a concept is the sum of those classes, groups, genera, species, etc., to which a given concept can be applied. For example, the scope of the concept “animal”: bird, fish, insect, person, etc.; scope of the concept “element”: oxygen, hydrogen, carbon, nitrogen, etc.; scope of the concept “quadrangle”: square, rectangle, rhombus, trapezoid;

Thus, the difference between the scope of a concept and the content of a concept comes down to the following: the scope of the concept means a group of objects to which a given concept should be attached, and the content denotes those characteristics that are attributed to one or another concept.

For a clearer representation of the scope of concepts and the relationship of volumes, there is a special technique called “logical symbolism.”

In Fig. 1 large circle symbolizes the concept of “element”, and the smaller circles located in it symbolize the concepts included in its volume. If we depict a circle inside another circle, then we symbolize that the scope of one concept is included in the scope of another. From Fig. 2 it is clear that the concept “tree” contains in its scope the concepts “oak”, “spruce”, etc. Individual points in the circle “spruce” symbolize individual, or single, spruce trees.

A concept with a larger scope is called a genus in relation to the concept with a smaller scope that is included in its scope. A concept with a smaller volume in this case is called a type. Concepts with a larger volume can also be called broader or more general concepts.

Any species can become a genus. For example, the concept “palm tree” relates to the concept “tree”, as a species relates to a genus, but in turn it relates as a genus to its species - “coconut palm tree”, “fig palm tree”, etc. In general, a more general concept is genus for a less general concept; a more general concept is a generic concept for a less general one, a less general one itself becomes a genus for an even less general one, etc., until we come to a concept that can no longer contain any other species in its scope, but can be subdivided only into separate individuals.

Rice. 3.

Rice. 3 a.

It is worth mentioning the attempt of the Greek philosopher Porphyria(233-304) with the help of a diagram to facilitate understanding of the relationship between concepts that embrace each other, that is, concepts of which one is included in the scope of the other. This diagram is called the “Porphyry tree”. The concept of “being” (i.e., that which exists in general) includes the concept of “corporeal being” and “incorporeal being.” The body contains in its volume an animate body, or organism, and an inanimate body. The concept of “organism” contains in its scope sentient and non-sentient organisms (plants). Sensing organisms contain in their volume intelligent and irrational beings, etc. (Fig. 3).

Being is the highest genus, which can no longer be a species for another genus. This kind is called summumgenus ; man is the lowest species. Its scope no longer includes concepts with a smaller scope, but only individual individuals. This concept is called infimaspecies (the lowest type). The nearest highest class (or genus) of a species is called proximumgenus (closest genus). The relationship between broader and narrower concepts can be depicted in another way, namely, by placing circles that serve to designate concepts with a smaller scope inside circles that serve to designate concepts with a larger scope (Figure 3a).

Limitation and generalization. The process of forming less general concepts from more general ones is called limitation( determlnatio ). To form a less general concept, we must add several features to the more general one, thanks to which the concept is clarified ( determinatur ). For example, in order to obtain the less general concept of “palm tree” from the concept “tree”, it is necessary to add to the characteristics of a tree the special characteristics of a palm tree: the type of its leaves, the straightness of the trunk, etc. The reverse process of the formation of a more general concept from a less general one, in which, on the contrary , a certain number of features are taken away from a given concept, called generalization( generalisatio).

A genus is formed from species by a process of generalization, and, conversely, species are formed from genera by a process of limitation. We can depict these processes using the following diagram:

Suppose we have the concept A(the science). From it, using species differences A we can form a species Ahh(mathematics); adding to the concept Ahh species difference B (definition of spatial relationships), we obtain the geometry Aaa. By adding to this type the feature c (determination of spatial relationships on a plane), we obtain planimetry Aabc.

The reverse process - obtaining more general concepts by discarding individual features - will be called generalization. Both processes can be depicted using the following diagram, in which the arrows show either a descent from more general concepts to less general ones or, conversely, an ascent from less general to more general concepts.

The relationship between the volume and content of a concept. In order to answer the question, what is the relationship between the volume and content of a concept, let’s take an example. The scope of the concept “person” is broader than, for example, the scope of the concept “Negro”. When we use the concept “person,” we think about all people, we think about people living in all five parts of the world, including in Africa, among other things. When we use the term “Negro,” we think only of those people who live in Africa. But exactly the opposite should be said about the content of these two concepts: the content of the concept “Negro” will be broader than the content of the concept “man.” When we talk about a Negro, we can find in him all the signs of the concept of “man” plus some more special signs, such as black skin color, curly hair, flattened nose, thick lips, etc.

So, as the content of a concept increases, its volume decreases, and vice versa.

Review questions

What are the signs of concepts? What signs of concepts do we distinguish? What is a generic sign? What is species difference? What is a species? What is a proper sign? What is an improper attribute? What is the content of a concept? What is the scope of a concept? What's happened summumgenus? What are infimaspecies ? What is a generalization? What is a restriction? What is the relationship between the volume and content of a concept?

Any concept has content and scope.

Scope of concept constitutes a collection or set of objects that is thought of in a concept.

Sufficient content for the formation of the concept “isosceles right triangle” will be an indication of the presence in the geometric figure of two angles equal to 45°. The volume of such a concept will be the entire set of possible isosceles triangles.

Any concept can be fully characterized by defining its content (in other words, meaning) and establishing the objects with which this concept has certain connections.

Intensity of concepts. Most often, in the process of interpreting the term “content of a concept,” it is defined as a concept as such. In this case, it is implied that the content of a concept is a system of attributes through which the objects contained in the concept are generalized and distinguished from the mass of others. Sometimes content is understood as the meaning of a concept or all the essential features of an object contained in the concept taken together. In some studies, the content of a concept is identified with the entire complex of information that is known about a given subject.

Extensionality of concepts. Any concept reflects an object and contains features that characterize and separate it from other objects. This object is always associated with other objects that are not included in the content of this concept, but have characteristics that partially repeat the characteristics of the object reflected in the concept. These items form a special group. Such a group can be defined as a set of objects characterized by the presence of common features, fixed by at least one concept.

Types of concepts

In modern logic, it is customary to divide concepts into: clear and vague; single and general; collective and non-collective; concrete and abstract; positive and negative; non-relative and correlative. Let's move on to consider each type of concept separately.

Clear and blurry. Depending on the content of concepts, they can reflect reality more or less accurately. It is this quality that forms the basis for the division of concepts into clear and vague. As you might guess, the clarity of reflection is much higher for clear concepts, while blurred ones often reflect the subject with insufficient completeness. For example, the clear concept of “inflation” contains in its characteristics a fairly clear indication of the degree of economic destabilization in the country.

Single and general concepts. This division is related to whether they involve one element or several. As you might guess, concepts in which only one element is implied are called single (for example, "Venice", "J. London", "Paris"). Concepts in which several elements are thought of are called general (for example,“country”, “writer”, “capital”).

General concepts can be registering or non-registering. They differ in that they registering In concepts, many implied elements can be taken into account and can be recorded. Not registering concepts are characterized by the fact that the multitude of their elements cannot be counted; they have an infinite volume.

Collective and non-collective concepts. Concepts containing signs of a certain set of elements included in one complex are usually called collective. As example collective concepts can be bring concepts"team", "pack", "squad". It should be noted that the content of a single concept cannot be attributed to a separate element included in its scope, since it applies to all elements at once. Collective concepts are common(“team”, “pack”) and single(“Team “Falcon””, “Team “Alpha””).

Concepts that contain characteristics not of a whole set, but of individual elements, are called non-collective. If the use of such a concept in speech refers to each of the elements that make up its scope, such an expression is called a dividing expression. If all the elements are mentioned in a complex (totality) and without regard to each of the elements taken separately, such an expression is called a collective expression.

Concrete and abstract concepts. This division of concepts depends on the subject reflected in the content of the concept. This may be an object, or a certain set of objects, or a sign of this object (the relationship between objects). Accordingly, the concept, the content of which is information about the attribute of an object or the relationship between objects, is called abstract concept. On the contrary, the concept of an object or a set of objects called concrete.

The main feature, the line by which concepts are divided into concrete and abstract, is the relationship between the object and its characteristics. In other words, although the attributes of an object cannot exist without the latter, as a result of the logical technique of “abstraction” they are isolated into an independent object of thought and are considered without regard to their object. Accordingly, the concept is called abstract.

We must not forget that concrete and individual concepts are not synonymous, just as abstract ones must be separated from general ones. Thus, general concepts can be both concrete and abstract. For example, the concept of "merchant" is general and specific, and the concept of “mediation” - general and abstract.

Positive and negative concepts. The classification of these concepts is based on the properties of an object, phenomenon or process. The type of concept here is made dependent on the presence or absence of characterizing properties of the object. In other words, the concept is called positive, if it contains an indication of the presence of properties inherent in the subject. In contrast to the positive ones are negative concepts, which imply the absence of such properties. Thus, the positive concept will be “strong”, and the negative concept will be “weak”; positive - “calm”, negative - “restless”.

Non-relative and correlative concepts. This classification is based on the presence or absence of a connection between the object that makes up the scope of the concept and other objects of the material world. Thus, irrelevant there will be concepts that exist separately from each other and do not have a significant impact on the existence of each of them. Such concepts For example, there can be “nail” and “button”. Each of these objects exists separately and independently of the other.

Based on the above, we can determine correlative concepts as having a connection with each other, embedded in the characteristics of the objects that make up their volume. Such concepts will be: “suzerain” - “vassal” or “brother” - “sister”.

Test

in the subject "Logic"

on the topic of:

“Concept: general characteristics, content and scope, types”

1. General characteristics of the concept

Types of concepts

Relationships between concepts

Literature

1. General characteristics of the concept

Signs of objects. Essential and non-essential features.

The characteristic of an object is that in which objects are similar to each other or in which they differ from each other.

Any properties, features, states of an object that in one way or another characterize the object, distinguish it, help to recognize it among other objects, constitute its characteristics. Signs can be not only properties belonging to an object; an absent property (trait, state) is also considered as its sign. For example, a passenger does not have a ticket or a criminal does not have a weapon; a sign of ownerless property is that it has no owner or its owner is unknown.

Any object has many different characteristics. Some of them characterize a separate subject, are single,others belong to a certain group of objects and are general.Thus, each person has characteristics, some of which (for example, facial features, physique, gait, gestures, facial expressions, so-called special signs) belong only to this person and distinguish him from other people; others (profession, nationality, social affiliation, etc.) are common to a certain group of people; Finally, there are signs common to all people. They are inherent in every person and at the same time distinguish him from other living beings. These include the ability to create tools, the ability for abstract thinking and articulate speech.

In addition to single (individual) and general characteristics, logic distinguishes essential and non-essential characteristics.

Signs that necessarily belong to an object, express its internal nature, its essence, are called significant.Features that may or may not belong to an object and that do not express its essence are called insignificant.

Essential features are crucial for the formation of concepts. The concept reflects objects in essential characteristics, which can be both general and individual. Concepts that reflect a variety of subjects include general essential features.For example, the general characteristics of a person (the ability to create tools, etc.) are at the same time essential. A concept that reflects one subject (for example, “Aristotle”), along with general essential features (man, ancient Greek philosopher) includes single essential features(founder of logic, author of Analytics), without which it is impossible to distinguish Aristotle from other people and philosophers of Ancient Greece.

Reflecting objects in essential features, the concept is qualitatively different from the forms of sensory knowledge: perceptions and ideas that exist in the human mind in the form of visual images of individual objects. We cannot, for example, imagine, much less perceive, a building at all. Perception or representation is a sensory-visual image of a specific building, for example, the main building of Moscow State University on the Lenin Hills. The concept is not clear. The concept of “building” is characterized by the absence of individual characteristics of individual buildings; it reflects the characteristics that necessarily belong to any of them and are common to all buildings.

A concept is the result of a generalization of a set of homogeneous objects based on their essential features.

So, a concept is a form of thinking that reflects objects in their essential characteristics.

The concept is one of the main forms of scientific knowledge of reality. By forming concepts, science reflects in them the objects, phenomena, and processes it studies. For example, political economy has formed such concepts as “commodity”, “capital”, “cost”; legal sciences - the concepts of “crime”, “punishment”, “guilt”, “intention”, “legal capacity”, etc.

Reflecting the essential, concepts do not contain all the wealth of individual characteristics of objects, and in this sense they are poorer than the forms of sensory knowledge - perceptions and ideas. At the same time, abstracting from the unimportant and random, they allow us to penetrate deeper into reality and reflect it with greater completeness, which sensory knowledge is not capable of.

“Thinking, ascending from the concrete to the abstract, does not move away - if it correct...from the truth, but approaches it. Abstraction matter, lawnature, abstraction costetc.; in a word, all scientific... abstractions reflect nature more deeply, or rather, fuller."

Logical methods of concept formation.To form a concept, it is necessary to identify the essential features of an object. But the essential does not lie on the surface. To reveal it, you need to compare objects with each other, establish what is common to them, separate them from the individual, etc. This is achieved using logical techniques: comparison, analysis, synthesis, abstraction and generalization.

To form a concept about an object, you must first compare this object with other objects, find the signs that make it similar to one and distinguish it from other objects. A logical technique that establishes the similarity or difference between objects of reality is called comparison.By comparing a number of objects, we establish that they have some common features inherent in a certain group of objects.

To highlight the characteristics of an object, you need to mentally dissect objects into their component parts, elements, sides. The mental breakdown of an object into its component parts is called analysis.Having identified certain signs, we can study each of them separately.

Having studied individual details, it is necessary to restore the subject as a whole in thinking. The mental connection of parts of an object dissected by analysis is called synthesis.Synthesis is the opposite of analysis. At the same time, both methods presuppose and complement each other.

Having identified the characteristics of an object using analysis, we find out that some of these characteristics are of significant importance, while others do not have such significance. By focusing our attention on the essential, we abstract from the unimportant. The mental isolation of individual features of an object and distraction from other features is called abstraction.To consider any feature abstractly means to distract (abstract) from other features.

We can extend the characteristics of the objects being studied to all similar objects. This operation is carried out by generalizationsthat is, a technique with the help of which individual objects, on the basis of their inherent identical properties, are combined into groups of homogeneous objects. Thanks to generalization, the essential features identified in individual objects are considered as signs of all objects to which this concept is applicable.

Thus, establishing similarities (or differences) between objects (comparison), dividing similar objects into elements (analysis), highlighting essential features and abstracting from non-essential ones (abstraction), connecting essential features (synthesis) and extending them to all homogeneous objects (generalization) ), we form one of the main forms of abstract thinking - the concept.

Concept and word. The concept is inextricably linked with the linguistic unit - in a word, concepts are expressed and fixed in words and phrases, for example “right”, “law”, “complicity”, “Council of People’s Deputies”, “socialist self-government of the people”, etc. Words are material , the linguistic basis of concepts, without which neither their formation nor their manipulation is possible.

However, the unity of language and thinking, words and concepts does not mean their identity. Unlike concepts, words are different in all languages: the same concept is expressed differently in different languages. In addition, in one language there is also no identity of concept and word. For example, in any language there are synonymous words and homonym words.

Synonymsare words that are close or identical in meaning, expressing the same concept, but differing from each other in shades of meaning or stylistic coloring. For example, “labor” and “work”; "homeland" and "fatherland"; “socialism” and “the first phase of communism”; “agreement” and “contract”, and many others.

Homonyms- these are words that match in sound, are the same in form, but express different concepts (for example, drummer is part of the bolt of a rifle and drummer is an advanced worker of socialist production; fist is a hand with clenched fingers and fist is a rich peasant owner exploiting the labor of others ).

Many words have multiple meanings. The polysemy of words (polysemy) often leads to confusion of concepts and, consequently, to errors in reasoning. Therefore, it is necessary to accurately establish the meaning of words in order to use them in a strictly defined sense.

In various fields of science and technology, special terminology is developed - a system of terms used in a given field of knowledge. Term -This is a word or phrase that denotes a strictly defined concept and is characterized by unambiguity, at least within the boundaries of a given science or a related group of sciences. Legal sciences, which, as a rule, provide an explanation of the terms used in a certain branch of law, attach great importance to the development and clarification of terminology.

Any concept has content and scope.

The totality of objects that is thought of in a concept is called the volume of the concept.The scope of the concept “crime” covers all crimes, since they have common essential features.

Thus, increasing the content of the concept of “state” by adding a new feature - “modern”, we move on to the concept of “modern state”, which has a smaller scope. Increasing the scope of the concept of “textbook on the theory of state and law,” we move on to the concept of “textbook,” which has less content, since it does not include the features that characterize a textbook on the theory of state and law.

Similar relationships between volume and content take place in the concepts of “crime” and “economic crime” (the first concept is wider in scope, but narrower in content), “prosecutor general” and “prosecutor”, where the first concept is narrower in scope, but wider by content.

The law of the inverse relationship between the volume and content of a concept underlies a number of logical operations that will be discussed below.

Logic also operates with the concepts of “class” (“set”), “subclass” (“subset of a set”) and “class element”.

A class, or set, is a certain collection of objects that have some common characteristics.These are, for example, classes (sets) of higher educational institutions, students, legal laws, crimes, etc. Based on the study of a certain class of objects, the concept of this class is formed. Thus, based on the study of a class (set) of legal laws, the concept of legal law is formed.

A class (set) may include subclass or subset.For example, the class of students includes a subclass of law students, the class of crimes includes a subclass of malfeasance.

The relationship between a class (set) and a subclass (subset) is expressed using the sign “ Ì ": A Ì B. This expression reads as follows: A is a subclass of B. Thus, if A are investigators and B are lawyers, then A will be a subclass of class B.

Classes (sets) consist of elements. A class element is an item included in a given class.Thus, elements of many higher educational institutions will be Moscow State University. M. V. Lomonosova, All-Union Legal Correspondence Institute. Kharkov Law Institute, etc.

The relationship of an element to a class is expressed using the sign “ Î ": A Î B (A is an element of class B).

If, for example, A is lawyer Ivanov, and B are lawyers, then A will be an element of class B.

There is a universal class, a unit class, and a null or empty class.

The class consisting of all elements of the study area is called universal class(for example, the class of planets in the solar system). If a class consists of one single element, then it will be unit class(for example, the planet Jupiter), finally, a class that does not contain a single element is called zero (empty) class.Empty classes are, for example, perpetual motion machine, god, goblin, etc. The number of elements of an empty class is zero.

. Types of concepts

Concepts are usually divided into the following types: (1) individual and general, (2) concrete and abstract, (3) positive and negative, (4) non-relative and correlative.

Concepts are divided into singleAnd are commondepending on whether one element or many elements are thought of in them. The concept in which one element is thought is called singular(for example, “Moscow”, “Supreme Court of Russia”,). A concept in which many elements are thought of is called general(for example, “capital”, “court”, “country of the socialist community”). They contain many elements that have common essential features.

General concepts can be registeringAnd non-registering. Registering concepts are those in which the set of elements conceivable in it can be taken into account and registered.(at least in principle). For example, “participant of the Great Patriotic War”, “planet of the solar system”. Registering concepts have a finite scope.

A general concept that refers to an indefinite number of items is called non-registering.Thus, in the concepts of “person”, “investigator”, “decree”, the multitude of elements conceivable in them cannot be taken into account; in them all people, investigators, decrees of the past, present and future are thought of. Non-registering concepts have an infinite scope.

A special group is allocated collective concepts,in which the signs of a set of elements that make up a single whole are conceived, for example, “team”, “regiment”, “constellation”. These concepts, as well as general ones, reflect many elements (team members, soldiers and regiment commanders, stars), however, as in individual concepts, this multitude is thought of as a single whole.

The content of a collective concept cannot be attributed to each individual element included in its scope; it refers to the entire set of elements. For example, the essential characteristics of a team (a group of people united by common work, common interests) are not applicable to each individual member of the team. Collective concepts can be general (“team”, “regiment”, “constellation”) and individual (“the team of our institute”, “86th rifle regiment”, “constellation Ursa Major”).

In the process of reasoning, general concepts can be used in a separate and collective sense.

If the statement refers to each element of the class, then this use of the concept will be dividing;if the statement refers to all elements taken in unity, and is not applicable to each element separately, then such a use of the concept is collective.For example, when expressing the thought “Students of our institute are studying logic,” we use the concept “students of our institute” in a disjunctive sense, since this statement applies to each student of the institute. In the statement “Students of our institute held a theoretical conference,” the statement refers to all students of our institute as a whole. Here the concept of “students of our institute” is used in a collective sense. The word “everyone” is not applicable to this judgment.

Concepts are divided into specificAnd abstractdepending on what they reflect: an object (a class of objects) or its property (the relationship between objects).

The concept in which an object or a set of objects is conceived as something independently existing is called concrete; a concept in which a property of an object or a relationship between objects is conceived is called abstract.Thus, the concepts “book”, “witness”, “state” are specific; the concepts of “whiteness”, “courage”, “responsibility” are abstract.

The difference between concrete and abstract concepts is based on the difference between an object, which is thought of as a whole, and a property of an object, abstracted from the latter and not existing separately from it. Abstract concepts are formed as a result of distraction, abstraction of a certain feature of an object; these signs are thought of as independent objects of thought. Thus, the concepts of “courage”, “disability”, “insanity” reflect characteristics that do not exist on their own, in isolation from the persons possessing these characteristics. These are abstract concepts.

One should not confuse concrete concepts with individual ones, and abstract ones with general ones. General concepts can be both concrete and abstract (for example, the concept of “crime” is general, concrete; the concept of “crime” is general, abstract). A single concept can be both concrete and abstract (for example, the concept “Great October Socialist Revolution” is single, concrete; the concept “the courage of the vigilante Smirnov” is single, abstract).

Concepts are divided into positiveAnd negativedepending on whether their content consists of properties inherent in the object or properties absent from it.

Concepts whose content consists of properties inherent in an object are called positive. Concepts whose content indicates the absence of certain properties in an object are called negative.Thus, the concepts “literate”, “order”, “believer” are positive; the concepts of “illiterate”, “disorder”, “non-believer” are negative.

In Russian, negative concepts are expressed by words with negative prefixes “not” and “without”: “independence”, “negligence”, “inaction”; in words of foreign origin - most often with words with a negative prefix “a”: “immoral”, “apolitical”, “asymmetry”, etc.

One should not confuse the logical characterization of concepts as positive and negative with the political, moral, legal assessment of the phenomena that they reflect. Thus, the concepts of “national enmity”, “remnants of capitalism”, “crime” are positive: their content consists of properties belonging to the subject. However, the phenomena reflected in these concepts cause us a negative assessment.

Concepts are divided into irrelevantAnd correlativedepending on whether objects are thought of as existing separately or in relation to other objects.

Irrelative concepts reflect objects that exist separately and therefore are thought of outside of relation to other objects.These are the concepts of “student”, “state”, “victim”, “crime scene”, etc. Correlative concepts reflect objects whose signs are their relationships to each other.For example: “parents” and “children”, “boss” and “subordinate”, “receiving a bribe” and “giving a bribe”. These concepts reflect objects, the existence of one of which is not conceivable outside of its relationship to the other.

To determine what type a concept belongs to means to give it a logical characterization. Thus, giving a logical characterization of the concept “Soviet Union”, it is necessary to indicate that this concept is singular, concrete, positive, and irrespective. When characterizing the concept of “insanity,” it must be indicated that it is general (non-registering), abstract, negative, and irrelevant.

Logical characterization of concepts helps clarify their content and scope, develops skills for more accurate use of concepts in the process of reasoning.

concept logical class

4. Relationships between concepts

When considering the relationships between concepts, one should first distinguish between the concepts comparableAnd incomparable.

Comparableare concepts that have some common characteristics that allow these concepts to be compared with each other. For example, “Union of Soviet Socialist Republics” and “People’s Republic of Bulgaria” are comparable concepts; they have common features that characterize any socialist country.

Incomparableconcepts are called that do not have common characteristics, so it is impossible to compare these concepts. For example: “square” and “public censure”, “crime” and “outer space”, “state” and “symphonic music”. They belong to different, very distant areas of reality and have no characteristics on the basis of which they could be compared with each other.

Only comparable concepts can exist in logical relations. There are comparable concepts compatibleAnd incompatible.

Concepts whose scopes completely or partially coincide are called compatible.There are no signs in the content of these concepts that exclude the coincidence of their volumes. There are three types of compatibility relationships: (1) equivalence, (2) intersection (crossing), and (3) subordination (subordination).

1.In a relationship equivalencethere are concepts in which one and the same object is conceived. The scope of these concepts completely coincides (although the content is different). In relation to equivalence, there are, for example, the concepts of “the last exploitative system” and “a social system based on the exploitation of wage labor.” These concepts reflect one subject of thought - capitalism, their volumes completely coincide, but the content is different, since each of them contains different signs of capitalism.

Relationships between concepts are usually depicted using circular diagrams (Euler circles), where each circle denotes the volume of the concept, and each point represents an object included in its volume. Circular diagrams allow you to visualize the relationship between various concepts, to better understand and assimilate these relationships.

Thus, the relationship between two equivalent concepts “the last exploitative system” (A) and “a social system based on the exploitation of wage labor” (B) should be depicted in the form of two completely coinciding circles (Fig. 1).

2.In a relationship intersections(crossing) there are concepts, the scope of one of which is partially included in the scope of the other. The content of these concepts is different.

In relation to the intersection there are the concepts of “lawyer” (A) and “deputy of the Supreme Soviet of the USSR” (B): some lawyers are deputies of the Supreme Soviet of the USSR (as some deputies of the Supreme Soviet of the USSR are lawyers). With the help of circular diagrams, this relationship is depicted in the form of two intersecting circles (Fig. 2).

In the combined part of circles A and B (the shaded part of the circles) we think of those lawyers who are deputies of the Supreme Soviet of the USSR, in the non-combined part of circle A - lawyers who are not deputies of the Supreme Soviet of the USSR, in the non-combined part of circle B - deputies of the Supreme Soviet of the USSR - not lawyers.

Rice. 1 Fig. 2

In a relationship submission(subordination) there are concepts, the scope of one of which is completely included in the scope of the other, constituting its part.

In this relationship are, for example, the concepts of “crime” (A) and “offense of office” (B). The scope of the first concept is wider than the scope of the second concept: in addition to official crimes, there are other types of crimes: state, economic, etc. The concept of “official crime” is fully included in the scope of the concept of “crime” (Fig. 3).

A concept that has a larger scope and includes the scope of another concept (A) is called subjugatingand a concept that has a smaller scope and forms part of the scope of another concept (B) - subordinates.

If there are two general concepts in relation to subordination, then the subordinating concept is called originally fromsubordinate - view.Thus, the concept of “official crime” will be a type in relation to the concept of “crime”. A concept can be both a species (in relation to a more general concept) and a genus (in relation to a less general concept). For example, the concept of “official crime” is a genus in relation to the concept of “official forgery” and at the same time a type in relation to the concept of “crime”. The relationship between three subordinate concepts is depicted in Fig. 4.

Rice. 3 Fig. 4

If in relation to subordination there are general and individual (individual) concepts, then the general (subordinating) concept is view,and the individual (subordinate) - individual.In this relationship there will be, for example, the concepts “lawyer” and “F. N. Plevako.”

The relations “genus” - “species” - “individual” are widely used in logical operations with concepts - in generalization, limitation, definition and division.

Concepts whose volumes do not coincide either completely or partially are called incompatible (or external).These concepts contain features that exclude the coincidence of their volumes.

There are three types of incompatibility relations: (1) subordination (coordination), (2) opposition (contrary) and (3) contradiction (contradictory).

1.In a relationship subordination(coordination) there are two or more non-overlapping concepts subordinate to a common concept for them. For example: “law institute”, “medical institute”, “higher educational institution”; “regional court”, “city court”, “court”. Concepts that are in a relationship of subordination to a common concept for them are called subordinates.

In circular diagrams, this relationship is depicted as follows (Fig. 5.).

2.In a relationship opposites(contrary) there are concepts, one of which contains some features, and the other contains features that are incompatible with them. Such concepts are called opposite(contrary). The volumes of two opposite concepts constitute in their sum only a part of the volume of the generic concept common to them, of which they are species and to which they are subordinate. Such are, for example, the relationships between the concepts of “black” and “white”, “excellent student” and “underachiever”, “socialist state” and “capitalist state” (Fig. 6).

The dotted line depicts the generic concept of “state”.

Concept B contains features that are incompatible with the features of concept A. The scope of these concepts does not exhaust the total scope of the generic concept “state”: there are other types of states.

Rice. 5 Fig. 6 Rice. 7

In a relationship contradictions(contradictory) there are concepts, one of which contains some features, and the other excludes these same features. The volumes of two contradictory concepts constitute the entire volume of the genus of which they are species and to which they are subordinate.

In relation to the contradiction there are positive and negative concepts: “black” and “non-black”, “successful” and “unsuccessful”, “socialist state” and “non-socialist state”.

The relationship between contradictory concepts is depicted in Fig. 7.

From the diagram it is clear that the positive concept Aand negative concept not-Aexhaust the entire scope of the concept of “state”; any state is socialist or non-socialist. Between two contradictory concepts there can be no third concept. The relationships between concepts can be represented by the following diagram (Fig. 8).

Literature

1.Ivin A.A. Logics. M., 1997

2.Ivanov E.A. Logics. M., 1996

3.Toftul L.G. Logic. Handbook for VNZ students. Kiev, 1999.

.IN AND. Kirillov, A.A. Starchenko. Logics. M., 1991

5.O.M. Bandurka, O.V. Tax. Logic course. Kiev, 2002.

6.Ivin A.A., Nikiforov A.D. Dictionary of logic. M., 1998

7.Zherebkin V.E. Logic. Kiev, 2001.

8.Ivin O.A. Logic. Kiev, 1996.

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A concept is a form of thinking that reflects objects in their essential characteristics.

The characteristic of an object is that in which objects are similar to each other or in which they differ from each other.

Any properties, features, states of an object that in one way or another characterize the object, distinguish it, help to recognize it among other objects, constitute its characteristics. Signs can be not only properties belonging to an object; an absent property (trait, state) is also considered as its sign. For example, a passenger does not have a ticket or a criminal does not have a weapon. A sign of ownerless property is that it has no owner or its owner is unknown.

The concept as a form of thinking reflects objects and their aggregates in an abstract, generalized form based on their essential features.

Concept is one of the main forms of scientific knowledge. By forming concepts, science reflects in them the objects, phenomena, and processes it studies. For example, economic theory has formed such concepts as “commodity”, “capital”, “cost”; legal sciences - the concepts of “crime”, “punishment”, “guilt”, “intention”, “legal capacity”, etc.

Reflecting the essential, concepts do not contain all the wealth of individual characteristics of objects, and in this sense they are poorer than the forms of sensory knowledge - perceptions and ideas. At the same time, abstracting from the unimportant and random, they allow us to penetrate deeper into reality and reflect it with greater completeness, which sensory knowledge is not capable of.

To form a concept, it is necessary to identify the essential features of the subject, using a number of logical techniques for this purpose: comparison, analysis, synthesis, abstraction, generalization. These techniques are widely used in cognition. They play an important role in the formation of concepts based on the identification of essential features.

To form a concept about an object, you need to compare this object with other objects, find signs of similarity and difference. A logical technique that establishes the similarity or difference of objects is called comparison.

The identification of features is associated with the mental division of an object into its constituent parts, sides, and elements. The mental dissection of an object into parts is called analysis.

Isolation using feature analysis allows you to distinguish essential features from unimportant ones and to distract yourself and abstract from the latter. Mentally highlighting the features of one object and distracting from other features is called abstraction.

Elements, sides, characteristics of an object, identified through analysis, must be combined into a single whole. This is achieved using a technique opposite to analysis - synthesis, which is a mental connection of parts of an object dissected by analysis.

The characteristics of the objects being studied apply to all similar objects. This operation is carried out by generalizations- a technique with the help of which individual objects, on the basis of their inherent identical properties, are combined into groups of homogeneous objects. Thanks to generalization, the essential features identified in individual objects are considered as signs of all objects to which this concept is applicable.

Thus, establishing similarities (or differences) between objects (comparison), dividing similar objects into elements (analysis), highlighting essential features and abstracting from non-essential ones (abstraction), connecting essential features (synthesis) and extending them to all homogeneous objects (generalization) ), we form one of the main forms of thinking - the concept.

The set of objects that is thought of in a concept is called the volume of the concept.

Logic also operates with the concepts of “class” (“set”), “subclass” (“subset”) and “class element”.

By class, or by many, is a certain collection of objects that have some common characteristics. These are, for example, classes (sets) of higher educational institutions, students, legal laws, etc. Based on the study of a certain class of objects, a concept about this class is formed.

A class (set) may include a subclass, or subset. For example, the class of students includes a subclass of law students, the class of crimes includes a subclass of economic crimes.

The relationship between a class (set) and a subclass (subset) is a relation of inclusion and is expressed using the sign c: A with B. This expression reads: A is a subclass of B. So, if A are investigators and B are lawyers, then A will be a subclass class B.

Classes (sets) consist of elements. A class element is an item included in a given class. Thus, elements of many higher educational institutions will be Moscow State University. M.V. Lomonosov, Moscow State Law Academy, etc.

The relationship of an element to a class is expressed using the signÎ : A Î B (A is an element of class B).

If, for example, A is teacher Ivanov, and B is a teacher, then A will be an element of class B.

There is a universal class, a unit class, and a null or empty class.

The class consisting of all elements of the study area is called universal class(for example, the class of planets in the solar system). If a class consists of one element, then it will be a single class (for example, the planet Jupiter); finally, a class that does not contain a single element is called a null (empty) class. Empty classes are, for example, perpetual motion machine, round square, mermaid, goblin, etc. The number of elements of an empty class is zero.

Thus, increasing the content of the concept of “state” by adding a new feature - “modern”, we move on to the concept of “modern state”, which has a smaller scope. Increasing the scope of the concept “textbook on cultural studies”, we move on to the concept “textbook”, which has less content, since it does not include the features that characterize a textbook on cultural studies.

The law of the inverse relationship between the volume and content of a concept states: if the volume of a concept increases, then its content decreases, and vice versa, with an increase in the content of the concept, its volume decreases.
_

If we agree to depict the scope of a concept in the form of a circle, and the content in the form of letters, then the diagram will look as follows (Fig.), where A is a textbook, B is a logic textbook, C is a logic textbook for universities.

generalization and limitation of concepts

Using the law of the inverse relationship between the volume and content of a concept, one can produce generalization and limitation of the scope of concepts.

To generalize a concept means to increase its volume.

And in accordance with the law of the inverse relationship, an increase in volume can be achieved by reducing the number of features in its content. Against,- the limitation of concepts, again in accordance with the formulation of the law, can be achieved by adding signs to the content of a certain concept.

For example, the limitation of the concept “work” will be the following concepts - “work of art”, “literary work”, “story”, “story by A.P. Chekhov” and so on. Reading this example in reverse order, we have a generalization of the concept: “story by A.P. Chekhov” - “story” - “literary work” - “work of art”.

However, you need to be careful. The formation of complex features using the conjunction “or” occurs in a different way. The conjunction “or” indicates that a certain feature is not inherent in all elements of a certain volume, but in some part. Therefore, the addition of a simple feature using the conjunction “or” does not lead to a decrease, but to an increase in volume, and, on the contrary, the exclusion of a disjunctive feature leads to a decrease in the volume of the concept.

1. In relation to equivolume, there are concepts in which one and the same object is conceived. The scope of these concepts completely coincides (although the content is different). In relation to equivolume, there are, for example, the concepts “geometric figure with three equal angles” and “geometric figure with three equal sides.” These concepts reflect one subject of thought: an equiangular (equilateral) triangle, their volumes completely coincide, but the content is different, since each of them contains different characteristics of a triangle.

The relationship between concepts is usually depicted using circular diagrams (Euler circles), where each circle denotes the volume of the concept, and each of its points represents an object conceivable in its volume. Circular diagrams allow you to visualize the relationship between various concepts, to better understand and assimilate these relationships.

Thus, the relationship between two equal concepts should be depicted in the form of two completely coinciding circles A and B.

2. Regarding intersections (crossing) there are concepts, the scope of one of which is partially included in the scope of the other. The content of these concepts is different.

3. In relation to subordination (subordination) there are concepts, the scope of one of which is completely included in the scope of the other, constituting its part.

A concept that has a larger scope and includes the scope of another concept is called subordinate. ( A), a concept that has a smaller scope and forms part of the scope of another concept, - subordinates (IN).

If there are two general concepts in relation to subordination, then the subordinating concept is called a genus, the subordinate - view. A concept can be both a species (in relation to a more general concept) and a genus (in relation to a less general concept).

If in a relation of subordination there are general and individual (individual) concepts, then the general (subordinate) concept is a species, and the individual (subordinate) individual.

The relations “genus” - “species” - “individual” are widely used in logical operations with concepts - in generalization, limitation, definition and division.

Concepts whose volumes do not coincide either completely or partially are called incompatible (or external). These concepts contain features that exclude the coincidence of their volumes.

There are three types of incompatibility relations: 1) subordination (coordination), 2) opposition (contrary), 3) contradiction (contradictory).

Incompatible concepts

1. In relation to subordination (coordination) there are two or more non-overlapping concepts subordinate to a common concept for them. Concepts that are in a relationship of subordination to a common concept for them are called subordinate.

2. In relation to opposition (contrary) there are concepts, one of which contains some characteristics, and the other - characteristics that are incompatible with them. Such concepts are called opposite (contrary). The volumes of two opposite concepts constitute in their sum only a part of the volume of the generic concept common to them, of which they are species and to which they are subordinate. Such, for example, are the relationships between the concepts “black” and “white,” “excellent student” and “underachiever,” “friendly state” and “hostile state.”

Concept IN contains features that are incompatible with the features of the concept A. The scope of these concepts does not exhaust the total scope of the generic concept of “state”: there are other interstate relations.

3. Regarding contradictions (contradictions) There are concepts, one of which contains some features, and the other excludes these same features.

The volumes of two contradictory concepts constitute the entire volume of the genus of which they are species and to which they are subordinate.

In relation to the contradiction there are positive and negative concepts: “even” and “odd”, “successful” and “unsuccessful”, “friendly state” and “unfriendly state”.

2. JUDGMENT AS A FORM OF THINKING. COMPOSITION OF JUDGMENT

Cognizing the objective world, a person reveals connections between objects and their characteristics, establishes relationships between objects, affirms or denies the fact of the existence of an object. These connections and relationships are reflected in thinking in the form of judgments, which are connection of concepts. For example, when expressing the judgment “Semyonov is a teacher,” we connect the concepts “Semyonov” and “teacher,” reflecting the real connection between a specific person and his attribute. In the judgment “Vladimir is Alexei’s brother”, in connection with the concepts “Vladimir” and “Alexey”, the family relationship between two persons is expressed.

Connections and relationships are expressed in judgment through statements or denial. In the judgment “Citizens of the Russian Federation have the right to education,” the connection between citizens of Russia and their right to education is affirmed

Any judgment can be either true or false, i.e. correspond to reality or not correspond to it. If a judgment affirms a connection that actually exists, or denies a connection that actually does not exist, then such a judgment will be true. For example, “Astrology is not a science” are true judgments. If a judgment asserts a connection that does not actually exist, or denies an existing connection, then such a judgment is false. “Astrology is a science” are false judgments; they contradict the real state of affairs.

There are judgments whose truth or falsity is obvious or can be easily established (for example, “Today is a sunny day”), but often they need justification. The truth or falsity of such judgments must be confirmed by other judgments whose truth has been established.

So, judgment is a form of thinking in which the connection between an object and its attribute, the relationship between Objects, or the fact of the existence of an object is affirmed or denied; a proposition can be either true or false.

The linguistic form of expressing a judgment is a sentence. Just as concepts cannot arise and exist outside of words and phrases, so judgments cannot arise and exist outside of sentences. However, the unity of judgment and proposal does not mean their complete coincidence. And if every judgment is expressed in a sentence, then it does not follow that every sentence expresses a judgment. The judgment is expressed declarative sentence, it contains a message about something.

Judgment and proposal differ in their composition. A judgment about the connection between an object and its attribute consists of two concepts (terms) of the judgment: the subject (from the Latin subjekta), reflecting the subject of the judgment, and the predicate (from the Latin praedikatum), reflecting the attribute of the object. Subject and predicate are denoted by Latin letters S And R. In addition to the subject and predicate, a judgment includes bunch- an element of judgment that connects both terms of judgment, affirming or denying that an object belongs to a certain attribute. The connective is expressed by the words “is” (“is not”), “is” (“is not”), etc. In Russian, the copula is usually implied or replaced by a dash.

Judgments are divided into simple And complex.

A proposition that does not include other propositions is called simple. A judgment consisting of several simple judgments is called complex.

In logical literature, along with the term “judgment”, the term “statement” is used, which can be considered equivalent.

Simple judgments. Types and composition of simple judgments

Depending on what is affirmed or denied in judgments—the attribute belonging to an object, the relationship between objects, or the fact of the existence of an object—they are divided into 1) attributive judgments, 2) judgments with relations, and 3) judgments of existence (existential).

Attributive (from the Latin atrributio - “property”, “sign”) is a judgment about the attribute of an object. It reflects the connection between an object and its attribute; this connection is affirmed or denied.

Attributive judgments are also called categorical (from the Greek kategorikos - “clear”, “unconditional”, “not allowing other interpretations”).

Categorical judgments are divided into 1) by quality and 2) in count. And since any judgment has both quantitative and qualitative characteristics, they are usually divided into 3) unified classification.

The subject of judgment is the concept of the subject of judgment. The concept of an attribute of an object is called a predicate of a judgment. The connective expresses the relationship between the subject and the predicate.

The subject and predicate are called terms of judgment. Each of them plays a special cognitive role. The subject of judgment reflects what we judge, i.e. subject of judgment. It contains the original knowledge. The predicate reflects the attribute of the subject, what is said about the subject of the judgment; it contains new knowledge about him. For example, in the judgment “Russia ( S) - sovereign state ( R)” knowledge about Russia is expressed in a predicate that reveals one of its characteristics. Therefore, the main semantic load is carried by the predicate.

The subject and predicate form a proposition through a connective. By establishing whether a feature belongs or not to an object, the connective unites the terms of judgment into a single whole. Thanks to this function, the copula is a necessary element of judgment.

1. Dividing judgments by quality. Based on the quality of judgments, they are divided into affirmative and negative. An affirmative is a judgment that expresses that an object belongs to a certain attribute. A judgment expressing the absence of a certain attribute in an object is called negative. For example, “The author of a work is recognized as the citizen whose creative work it was created” is an affirmative judgment. Its logic circuit is "S is P".

The logical scheme of a negative judgment is “S is not P.”

Affirmative and negative judgments differ in the nature of the connective and its quality. The affirmative connective (“is”) indicates that the attribute belongs to an object. A proposition with a negative predicate but with an affirmative connective “S is not-P” is considered affirmative. For example: “Religion is a non-scientific worldview.”

It is important to emphasize that “is” and “is not” are logical connectives. In language they can be expressed in other words: “is”, “is not”, “is”, “does not represent”, “recognised”, “is not recognized”, as well as with a dash or implied.

2. Dividing judgments by quantity. You can affirm or deny something about one object, about part of the objects of a certain class, and about all objects of the class. In accordance with this, judgments by quantity are divided into individual, particular and general.

A singular judgment is a judgment in which something is affirmed or denied about one subject. For example: “This building is an architectural monument.” Schemes of single judgments: “This S is P” and “This S is not P.”

A particular judgment is a judgment in which something is affirmed or denied about a part of objects of a certain class. Particular judgments are expressed in sentences containing the words: “some”, “many”, “few”, “most”, “minority”, “part”. For example, “Most students in our course do not have academic debt.” Schemes of private judgments: “Some S are P” and “Some S are not P.”

Depending on the meaning in which the word “some” is used, two types of private judgments are distinguished: indefinite particulars and definite particulars.

In an indefinite private judgment, the word “some” is used in the sense of “Some, and maybe all,” “at least some.” For example, the judgment “Some people told about this” may have the following meaning: some of the people known to us told, but we cannot say anything definite about the other part of them, since our knowledge about this fact is incomplete. The word "some" means "some, maybe all."

In a certain private judgment, the word “some” is used to mean “only some.” If, for example, we know that not all, but only some of the witnesses testified, then another part of them did not testify. Therefore, a certain private judgment contains knowledge about both parts of the witnesses and can be considered as a complex judgment: “some witnesses testified, and some did not testify.” Schemes of a definite particular proposition: “Only some S are P” and “Only some S are not P.”

A general judgment is a judgment in which something is affirmed or denied about all objects of a certain class.

General judgments are expressed in sentences, which, as a rule, include the words “all” and “none”, as well as other words close to them in meaning, indicating that a certain attribute belongs or does not belong to all objects of a given class: “every”, “anyone”, “nobody”, etc. However, these words may be missing. For example: “Indifference humiliates.” In meaning, such judgments are general; the predicate refers to each element of the class: “All indifference...”.

Each of the considered types of judgments has a certain cognitive value. Knowledge about individual phenomena, events, and persons is expressed in the form of single judgments. Such knowledge plays an important role, for example, in the historical sciences when describing historical figures and events.

Unlike individual judgments, private judgments contain generalized knowledge. In an indefinite private judgment, this knowledge is characterized by incompleteness: it is known that a certain attribute belongs (or does not belong) to at least some part of the elements of the class. Complete knowledge is expressed in the form of certain private judgments, which have greater cognitive value compared to indefinite private judgments.

Knowledge contained in general judgments is characterized by generality and completeness. General judgments express the laws of science, laws established by the state, etc. For example, the fundamental rights in the Universal Declaration of Human Rights are formulated in the form of general judgments.

3. Combined classification of judgments. Combining quantitative and qualitative characteristics, judgments are divided into general affirmative, general negative, particular affirmative, and particular negative.

A generally affirmative judgment is a judgment that is general in quantity and affirmative in quality.

Scheme of a general affirmative judgment “All S are P”, where the quantifier word “all” characterizes the quantity, the affirmative connective “essence” - the quality of the judgment.

A general negative judgment is a judgment that is general in quantity and negative in quality.

Scheme of the generally negative proposition “No S is P.” The quantifier word “not one” characterizes the quantity, the negative connective “is not” characterizes the quality of the judgment.

A partial affirmative judgment is a judgment that is particular in quantity and affirmative in quality. For example: “Some court verdicts (S) are guilty (P).” The schema of these propositions is “Some S are P.” The quantity of judgments is characterized by the quantifier word “some”, the quality is characterized by the affirmative connective expressed by the word “essence”.

A partial negative judgment is a judgment that is particular in quantity and negative in quality.

Complex judgments can also be comparable and incomparable.

Incomparable are judgments that do not have common propositional variables.

Comparable- these are judgments that have the same prepositional variables (components) and differ in logical connectives, including negation. For example, the following two propositions are comparable: “Norway or Sweden have access to the Baltic Sea”; “Neither Norway nor Sweden have access to the Baltic Sea.” Although these judgments are different in logical form (the first of them is a disjunctive judgment, and the second is a conjunction of negations), at the same time they are comparable, since they include the same components.

Complex comparable judgments can be compatible And incompatible.

Compatibility relationship.

TO compatible These are comparable propositions that can simultaneously be true. As in the case of simple judgments, there are three types of compatibility of complex judgments: equivalence, partial compatibility and subordination.

1. Equivalent are judgments that take the same values, i.e. are simultaneously either true or false.

The equivalence relation allows one to express complex judgments through others - conjunction through disjunction or implication, and vice versa.

2. Partial compatibility is characteristic of judgments that can be simultaneously true, but cannot be false at the same time.

3. Subordination between judgments occurs in the case when, if the subordinate is true, the subordinate will always be true.

The relation of logical subordination, which allows us to determine the truth of the subordinate judgment based on the truth of the subordinating judgment, forms the basis of the fundamental concept of logical implication in the science of logic, which regulates all types of reasoning.

Relationship of incompatibility.

Judgments that cannot be true at the same time are incompatible. Of the two types of incompatibility, one is opposite, another- contradiction.

Opposite- a relationship between judgments that cannot simultaneously be true, but may be temporarily false.

2. Contradiction - a relationship between judgments that can be neither true nor false at the same time. If one of them is true, the other will be false, and if the first is false, the second will be true.

To obtain a complex judgment, the latter must be negated if it contradicts the original one.

3. DIRECT CONCLUSIONS. THEIR TYPES

In the process of understanding reality, we acquire new knowledge. Some of them are direct, as a result of the influence of objects of the external world on the senses. But we obtain most of our knowledge by deriving new knowledge from existing knowledge. This knowledge is called mediated, or inferential.

The logical form of obtaining inferential knowledge is inference.

Inference is a form of thinking by which a new judgment is derived from one or more propositions.

Any conclusion consists of premises, conclusion and conclusion. Parcels inferences are the initial judgments from which a new judgment is derived. Conclusion is a new proposition obtained logically from premises. The logical transition from premises to conclusion is called conclusion.

When analyzing a conclusion, it is customary to write the premises and conclusion separately, placing them one below the other. The conclusion is written under a horizontal line separating it from the premises and indicating logical consequence. The words “therefore” and similar ones in meaning (“means”, “therefore”, etc.) are usually not written under the line. In accordance with this, the example given will take the following form:

The relationship of logical consequence between the premises and the conclusion presupposes a connection between the premises in content. If judgments are not related in content, then a conclusion from them is impossible.

If there is a meaningful connection between the premises, we can obtain new true knowledge in the process of reasoning if two conditions are met: firstly, the initial judgments - the premises of the inference must be true; secondly, in the process of reasoning one must observe the rules of inference, which determine the logical correctness of the conclusion.

Inferences are divided into the following types.

1. Depending on the severity of the inference rules, there are demonstrative(necessary) and non-demonstrative(plausible) inferences. Demonstrative inferences are characterized by the fact that the conclusion necessarily follows from the premises, i.e. logical consequence in such conclusions is a logical law. In non-demonstrative inferences, the rules of inference provide only the probabilistic conclusion of the conclusion from the premises.

2. The classification of inferences according to the direction of logical consequence is important, i.e. by the nature of the connection between knowledge of varying degrees of generality, expressed in premises and conclusion. From this point of view, three types of inferences are distinguished: deductive(from general knowledge to specific), inductive(from private knowledge to in general), inferences by analogy(from private knowledge to private knowledge).

This classification will form the basis for further presentation.

Let's look at deductive reasoning.

Deductive(from Latin deductio- "removal") called an inference in which the transition from general knowledge to specific knowledge is logically necessary.

The rules of deductive inference are determined by the nature of the premises, which can be simple (categorical) or complex propositions. Depending on the number of premises, deductive conclusions from categorical judgments are divided into immediate, in which the conclusion is derived from one premise, and mediated, in which the conclusion is derived from two premises.

TASK 1

From the group of these concepts, select the one that has the largest volume and the greatest content: a) house, residential building, cottage; b) person, student, student psychologist; c) book, textbook, history textbook.

Answer.

a) house, residential building, cottage;

the concept with the largest volume is house;

the concept with the greatest content is cottage;

b) person, student, student psychologist;

the concept with the largest scope is human;

the concept with the greatest content is a student psychologist;

c) book, textbook, history textbook

the concept with the largest volume is a book;

The concept with the most content is a history textbook.

TASK 2

Identify the subject and predicate in the following propositions: all students take exams; Mexico is home to many cacti; Cholerics are characterized by unbalanced behavior.

ANSWER

All students take exams

Subject – students; predicate – exams;

Mexico is the birthplace of many cacti

Subject – Mexico; predicate – home to many cacti

Cholerics are characterized by unbalanced behavior

Subject – choleric; predicate – unbalanced behavior.

TASK 3

Carry out inversion, transformation and opposition to the predicate with the proposition “All metals are electrically conductive.”

ANSWER

Appeal

All metals are electrically conductive

Transformation

None of the metals are non-electrically conductive.

Opposition

Anything that is not electrically conductive is not metal.

TASK 4

Find definitions of any psychological term (two or more) and give their comparative logical characteristics.

ANSWER

Personality is a specific person in the totality of those spiritual, mental characteristics, qualities that characterize him as an object (product, result) of social (and other) development and as a subject of transformation of reality on the basis of its knowledge and attitude towards it.

Abilities are individual psychological characteristics of a person that ensure success in activity, communication and ease of mastering them.

Both of these definitions are logical definitions that reveal the content of the concept. In the first case, the concept of personality is revealed, in the second case - abilities. These concepts are called definitionendum, and the concept itself, which reveals the content, is definition.
The concept, essence and content of property relations regulated by Russian civil law PRINCIPLES AND CONCEPTS OF EINSTEIN'S GENERAL THEORY OF RELATIVITY (THORY OF GRAVITY)

Any concept has content and scope.

Scope of concept constitutes a collection or set of objects that is thought of in a concept.

Sufficient content for the formation of the concept “isosceles right triangle” will be an indication of the presence in the geometric figure of two angles equal to 45°. The volume of such a concept will be the entire set of possible isosceles triangles.

Any concept can be fully characterized by defining its content (in other words, meaning) and establishing the objects with which this concept has certain connections.

Regardless of human consciousness, there are various objects in the world around us. These items are characterized by many. A set can be finite or infinite. If the number of objects included in a set can be counted, the set is considered finite. If such objects cannot be counted, the set is called infinite. It is necessary to mention the relations of inclusion, belonging and identity.

The relation of inclusion is the relation of species and genus. A bunch of A is a part or subset of set B if each element A there is an element B. Reflected as a formula A with B(set A is included in set B). In relation to affiliation class A belongs to class A and is written as and with A. The identity relation implies that sets A And IN match up. This is fixed as A = B.

Intensity of concepts. Most often, in the process of interpreting the term “content of a concept,” it is defined as a concept as such. In this case, it is implied that the content of a concept is a system of attributes through which the objects contained in the concept are generalized and distinguished from the mass of others. Sometimes content is understood as the meaning of a concept or all the essential features of an object contained in the concept taken together. In some studies, the content of a concept is identified with the entire complex of information that is known about a given subject.

From the above it is clear that the content of a concept is some information containing information about objects, phenomena, processes included in this concept. This information is necessary for the formation of a concept, determination of its form and rational consideration. Such information can be any information about an object that allows it to be distinguished from the mass of homogeneous (and heterogeneous) objects and clearly determine its characteristics. In other words, this is information about the essential and other characteristics of the subject.

In the process of communication, from the point of view of the effectiveness of information transfer, such an element of the content of the concept as connotation is of particular interest. It is more or less characteristic of the languages ​​of different countries and, to a very large extent, of the Russian language. These are all kinds of variations in pronunciation, intonation, emphasis on individual words, ethical, aesthetic, ethnic, professional, diminutive and other shades and colors of concepts used in speech. Such variations can lead to a change in the meaning of a concept without changing its verbal form, and a change in the verbal form most often leads to a change in meaning. For example, the words “book” - “little book”; “grandmother” – “grandmother” – “grandmother” fully illustrate the connotation.

It is necessary to say something about the so-called value of the content of concepts. It is inextricably linked with their volume. In this case, we mean the ability of some concepts to be broader than others, and thereby, as it were, “overlap” them. For example, the concept of “science” is much larger in content than the concept of “logic” and overlaps the latter. When characterizing the first concept, you can use or not use the second, but replace it with another or even make do with other means. However, when characterizing the concept of “logic,” we will inevitably have to use the concept of “science.” The concept of “science” in this case is subordinate, and “logic” is subordinate. Let's take for example two other concepts - “helicopter” and “airplane”. These concepts in relation to each other are not subordinate and subordinate. It is almost impossible to define one of them using the other. The only sign connecting these two concepts is that their objects are devices for flight. The subordinate concept for both the first and the second will be “aircraft”.

Thus, only subordinate and subordinating concepts can be compared in terms of volume content.

Extensionality of concepts. Any concept reflects an object and contains features that characterize and separate it from other objects. This object is always associated with other objects that are not included in the content of this concept, but have characteristics that partially repeat the characteristics of the object reflected in the concept. These items form a special group. Such a group can be defined as a set of objects characterized by the presence of common features, fixed by at least one concept.

However, simply reflecting an object with one or another concept is not enough. An object that really exists and an object as an object of thought are not identical. This is associated with the representation of an abstract (imaginary, conceivable) and real (having a real embodiment) object. Abstract subject is a mental construction that can accurately reflect the characteristics and properties of an object, but may also contain an error or inaccuracy. In this context, we can define the scope of a concept as a set of abstract objects related to it.

Thus, a real object is an object of the material world that has characteristic features unique to it. An abstract object has no material embodiment and is characterized only by information about its belonging to any concept.

There are two approaches to the question of belonging to a concept, according to which the scope of a concept can be the scope of diversity or quantitative. The first approach implies that the scope of a concept includes several other concepts. Accordingly, this last concept is common to all incoming ones. For example, the concept of “aircraft” includes “airplane”, “helicopter”, “airship” and others, so it is general. This approach shows the presence of a sufficient number of elements included in the volume of the subject; accordingly, such a volume is called the volume of diversity.

Not only the objects themselves, but also the categories inherent in these objects are related to the concept. The scope of a concept is the entire set of objects associated with it. The concept, and, accordingly, the content and scope that characterize it, are mental formations. Therefore, the scope of a concept cannot consist of real objects, just as the thought of water cannot consist of water itself. It consists of mental reflections of these objects and their properties. The main condition is that such reflections, thoughts about objects, must fall under the characteristics implied in the concept. The concept and the objects included in its scope are made real by the idea of ​​the reality of these objects. Thus, the quantitative volume of a concept can be called a volume composed of mental reflections of real-life objects corresponding to a given concept.

You should always remember to use any logical categories correctly. Thus, there may be an error related to the scope of concepts. It is unacceptable to identify parts of an object and parts of the scope of the concept of this object. Otherwise, part of a physical object (a car wheel, an airplane wing, a weapon firing pin) is identified with independent objects, the mental reflections of which are included in the scope of the corresponding concept.

It is also necessary to mention empty volumes. In some cases there may be so-called empty volumes. There are two options for the appearance of an empty volume: let us remember that the concept does not include the object itself, but only its mental reflection. Therefore, if an object reflected in a concept contradicts objective physical laws, the scope of such a concept is considered empty. This happens either with concepts containing fantastic objects, or with concepts about objects whose existence is impossible (for example, a perpetual motion machine). In another case, self-contradictory (false) concepts are implied. They have content when the volumes are empty.

Studies different cases of the existence of volumes formal logic. She considers thinking from the point of view of its extensionality. Or, in other words, in an extensional context. Within the framework of formal logic, thinking is represented as a process of carrying out various operations with the volumes of concepts without considering the content of these concepts. Purpose of formal logic– determine the truth or falsity of concepts, relying only on their volumes.

If there is a formal logic that studies only the scope of concepts, it would be reasonable to assume the existence of a logic of content that would study the content side of concepts and judgments. The object of consideration is the logic of content there must be an intensional part of thinking, the interaction of the content of various concepts and the degree of correctness of reflection of the objective world in concepts and judgments.

Logic studies concepts and judgments about objects in the real world. Concepts are only mental reflections of really existing objects. However, a concept implies the existence of its subject. This is where the concept of modality arises. Modality is the way of existence of a certain object or process (ontological modality). There is also the concept of logical modality. This is a way of understanding, obtaining a conclusion about an object, phenomenon or process.

Logical existence can be called absolute, since this concept defines existence in itself, existence as it is, without reference to any specific object.

Existence can be of the following types:

1) sensual. This is the existence of objects, processes and phenomena perceived by man. Sensory existence can be objective and subjective. The first implies the real existence of an object reflected in human perception. Such an object exists independently of the perceiver. The second (subjective) existence does not reflect real objects, processes and phenomena, but only imaginary ones. This could be a person’s fantasy, his thought about something, a dream, an image;

2) hidden existence. It is interesting that his objects are hidden from human perception for certain reasons. Can be objective and subjective.

Objective. The reason for the impossibility of perceiving real-life objects is the inability of the human senses to perceive microscopic objects, various kinds of waves, electromagnetic fields and other similar phenomena.

Subjective. This should include the existence of unconscious psychological characteristics that are part of and constitute the subconscious. These are various aspirations, instincts, drives, complexes, etc.

The scope of a concept can exist either in a sensory or in a hidden form of existence, regardless of whether it is objective or not. However, such a dependence arises when a mistake is made. Being determined not to its type of existence, the volume becomes empty.

At the same time, we must not forget that types of existence sometimes do not have clear boundaries. Depending on the circumstances, one of these types can flow into another - hidden existence can become sensual, objective - subjective. Therefore, often the scope of a concept may not be empty. It is necessary to consider the scope of the concept separately in each case.

The relationship of categories within a concept is subject to logical laws and has its own specifics. Thus, the peculiarities of the effect of the content and scope of a concept on each other are reflected in the law of the inverse relationship between the content and scope of concepts. This law is based on the logical nature of concepts. Taking two concepts, we can notice that one of them is wider than the other in scope, while the other is included in the scope of the first. However, a concept that is included in the scope of another (having, accordingly, a smaller volume) in its content reflects more features and is more saturated with them. It is this phenomenon that forms the basis of the feedback law, which goes like this: the wider the scope of a concept, the narrower its content; the richer the content, the smaller the volume. The essence of this law is that the less information about an object is reflected in the content of the concept, the wider the class of objects and the more uncertain the composition. For example, the concept “airplane” is poor in content, but at the same time it includes aircraft of various types, brands and designs. Expanding the content, we add one more characterizing word and get the concept of “passenger aircraft”. Now the scope of the concept has narrowed significantly, but still contains a significant number of objects. The concept of “Boeing passenger aircraft” has almost the broadest possible content, but the class of objects included in the scope is now clearly defined and few in number. In this way, it is possible to narrow the scope of a concept by expanding its content down to one subject.