Types of concepts. Abstract and concrete terms

Generalization and restriction

We would not be able to cope with the abundance of impressions that flood over us every hour, every minute, every second, if we did not continuously combine them, generalize and fix them by means of language. In order to reveal the general, it is necessary to abstract from what obscures it, veils it, and sometimes even distorts it. Scientific generalization is not just the selection and synthesis of similar features, but the penetration into the essence of a thing: the perception of the single in the diverse, the general in the singular, the regular in the random.

The mental transition from the more general to the less general is a process of limitation. There is no theory without generalization. The theory is created in order to apply it in practice to the solution specific tasks. For example, for the measurement of objects, the creation of technical structures, a transition from the more general to the less general and individual is always necessary, that is, the process of limitation is always necessary.

The term "concrete" is used in two senses. First, as a directly given, sensually perceived and represented whole. Secondly, in theoretical thinking, the concrete already acts as a system of scientific definitions that reveal the essential connections and relationships of things, events, unity in the manifold.

If initially the concrete is given to the subject in the form of a sensuously visual image of the whole object, “hovering in the representation”, mentally not yet divided and incomprehensible in its regular connections and mediations, then at the level of theoretical thinking, the concrete acts as an internal differentiated whole, understood in its contradictions. If the sensory-concrete is a poor reflection of phenomena, then the concrete in thinking is a richer, essential knowledge. The concrete is opposed to the abstract as one of the moments of the process of cognition and is comprehended in relation to it. Abstraction is most often understood as something "mental", "conceptual" as opposed to sensually visual. The abstract is also thought of as something one-sided, poor, incomplete, abstracted from the connection of the whole - a property, relation, form, etc. And in this sense, not only a concept can be abstract, but also the most visual image, for example, any scheme, drawing, stylization, symbol. Knowledge is also abstract in the sense that it reflects, as it were, a fragment of reality that has been purified, refined and, thus, a dinner. The phenomenon of abstraction is contradictory: it is one-sided, divorced from the phenomenon that trembles with life, but it is only a necessary step towards the cognition of a concrete, life-filled fact.

Abstraction is a kind of "splintering" of integral objects. And our thinking works with this kind of "splinters". From individual abstractions, thought constantly returns to the restoration of concreteness, but already on a new, more highly based. This is the concreteness of concepts, categories, theories, reflecting unity in diversity.

This is the essence of the method of ascent from the abstract to the concrete. The process of abstraction in this light acts as a kind of implementation of the principle: move away in order to hit more accurately. The dialectics of cognition of reality consists in the fact that, “flying away” from this sensually given reality on the “wings” of abstraction, it is better to “survey” the essence of the object under study from the height of concrete theoretical thinking. That's history and logic scientific knowledge. The principle of concreteness, taken in its inextricable connection with the abstract, requires that the facts of natural and social life be approached not with general formulas and diagrams, but with an accurate account of all the real conditions in which the object of knowledge is located, highlighting its main, essential properties, connections, trends that determine its other aspects.

Concepts can be classifiedby volume and content. According to the volume of concepts are divided into single, general and empty.

Volume singleconcepts constitutes a one-element class (for example, "the great American writer Theodore Dreiser"; "Kama river"). Volumegeneralthe concept includes the number of elements greater than one (for example, "bicycle", "computer", etc.).

Exercise: Give examples of general and singular concepts.

Among general concepts, concepts with a volume equal to the universal class are especially singled out, i.e. a class that includes all subjects considered in a given field of knowledge or within given reasoning (these concepts are called universal). For example, integers- in arithmetic, plants - in botany, etc.

In addition to general and single concepts, empty concepts (with zero volume) are distinguished by volume, i.e., those whose volume represents an empty class (for example, “perpetual motion machine”, “a person who has lived 300 years”, “Snow Maiden”, “Santa Claus ”, characters of fairy tales, fables, etc.).

Exercise: Give examples of empty concepts.

What is the volume of concepts (general, singular or empty):"capital of Russia"; "capital", "city",
« famous commander”, “infinity”, “Snake-Gorynych” .

By contentthe following four pairs of concepts can be distinguished.

Concrete and abstract concepts

specificare called concepts that reflect single-element or multi-element classes of objects (both material and ideal). These include the concepts of "school", "opera", "Alexander the Great", "earthquake", etc.

Concrete - these are concepts in which an object or a set of objects is conceived as something independently existing: "academy", "student", "romance", "house", "A. Blok's poem "The Twelve", etc.

abstractare called concepts in which not an object is conceived, but some of the attributes of the object, taken separately from the object itself (for example, "whiteness", "injustice", "honesty"). In reality there are white clothes, unjust actions, honest people, but "whiteness" and "injustice" as separate sensible things do not exist. Abstract concepts, in addition to individual properties of an object, also reflect relations between objects (for example, “inequality”, “similarity”, “identity”, “similarity”, etc.).

Exercise : Give examples of abstract concepts.

Relative and non-relative concepts

relative- these are concepts in which objects are thought, the existence of one of which implies the existence of the other ("children" - "parents", "student" - "teacher", "boss" - "slave", "north pole of the magnet" - "south pole of a magnet).

Irrelevant - these are concepts in which objects are thought that exist independently, regardless of another object (“pencil”, “city”, “sheep”, “strong flood”).

Positive and negative concepts

Positiveconcepts characterize the presence of a particular property or relation in an object. For example, “literate person”, “greed”, “lagging student”, “beautiful deed”, etc.

negativethose concepts are called that mean that the specified property is absent in objects (for example, "an illiterate person", "an ugly act", "abnormal mode", "disinterested help"). These concepts are expressed in the language by a word or phrase containing a negative particle “not” or “without” (“devil”), attached to the corresponding positive concept and performing the function of negation.

In Russian, negative concepts are usually expressed by words with negative prefixes “not” or “without” (“demon”): “illiterate”, “unbeliever”, “lawlessness”, “disorder”, etc. If the particle is “not” or “without "(" demon ") merged with the word and the word is not used without them (for example, "bad weather", "carelessness", "impeccability", "hatred", "slob"), then the concepts expressed by such words are called positive. The Russian language does not have the concept of “hatred” or “nastya”, and the particle “not” in the examples given does not perform the function of negation, and therefore the concepts of “bad weather”, “hatred” and others are positive, since they characterize the presence of a certain quality in an object (maybe even bad - "sloppy", "carelessness"). In words of foreign origin - most often words with a negative prefix "a": "agnosticism", "immoral", etc.

Positive (A) and negative (non-A) are contradictory concepts.

Collective and non-collective concepts

Collective concepts are those in which a group of homogeneous objects is thought of as a single whole (for example, "regiment", "herd", "flock", "constellation"). For example, we cannot say about one tree that it is a forest; one ship is not a fleet, and one football player is not a football team. Collective concepts are general (for example, "grove", "children's choir") and singular ("constellation Big Dipper"," State Scientific Pedagogical Library. K.D. Ushinsky Russian Academy education").

In judgments (statements), general and singular concepts can be used both in a non-collective (separative) and in a collective sense. Take the judgment: "All the apples in this basket are ripe." In it, the concept of "an apple in this basket" is general and is used in a non-collective sense, that is, each individual apple is ripe. In the statement "All the apples in this basket weigh 5 kg", the term "apples in this basket" is used in a collective sense, since they weigh 5 kg together, and not individually.

Exercise:Give examples of empty and concrete concepts.

Give examples of a negative specific concept.

Give examples of a negative abstract concept.

Give examples of a negative empty concept.

Give examples of a negative singular concept.

Give examples of a positive singular concept.

To determine to which of the indicated types a particular concept belongs means to give itlogical characteristic . For example, the concept of "carelessness" is general, non-collective, abstract, negative, irrelevant. The logical characterization of concepts helps to clarify their content and scope, develops skills for more accurate use of concepts in the process of reasoning.

Thus, the logical characteristic of concepts may look, for example, as follows:

"collection" - general, specific, irrelevant, positive, collective;

"indecision" - general, abstract, irrelevant, negative, non-collective;

"poem" - general, concrete, irrelevant, positive, non-collective.

Exercises:

Write down the logical characteristic of the following concepts (indicate the volume, expand the content - you can use the dictionary), determine their type and indicate any elements of the volume:

a) a person who has a brother but no sister;

b) a settlement located north of Novgorod and south of Moscow;

c) a liquid that boils at normal atmospheric pressure at 1000 ° WITH;

d) the state;

d) the capital.

abstract(lat. abstractio - distraction) - side, part of the whole, one-sided, simple, undeveloped; specific(lat. condensed, fused) - multilateral, complex, developed, holistic.

The definition of knowledge as concrete or abstract is relative and makes sense only in comparing two knowledge related to the same reality. Getting more and more specific knowledge is the goal of research. The ascent from the abstract to the concrete as a research method is applicable only to the study of the whole, represented as an organic system of connections. The first step in this case is the selection of the main or initial connection and its study while abstracting - isolating - this connection from other significant connections. The subsequent study of the connections - the concretization of the subject of study - is no longer carried out in isolation, but taking into account the results of the previous analysis. The method of taking into account and the sequence of links involved in the analysis are always determined by the specifics of the subject being studied.

Specific concepts - these are concepts that denote integral objects or their classes that have independence. Reflect objects, processes, phenomena: things "table", living beings "Human", fantasy products "centaur", events "war", natural phenomena "earthquake". In Russian, words expressing specific concepts, as a rule, can be used in the plural: diamonds, oaks, lawyers, explosions, wars. Designats (volume) are not difficult to determine. If a set of features that make up the semantic meaning is known, then it is possible to point to objects that have these features.

abstract concepts - these are concepts that denote properties or relations abstracted from objects, conceivable as independent objects. That is, we do not think of the object itself, but of any of the signs, taken separately. Properties of objects or relations between objects do not exist independently, without these objects. Properties: "hardness"(diamond), "durability"(oak), "competence"(lawyer) "blue"(seas); relations: " equality"(women and men), social partnership"(between employees and employers) citizenship"(a stable legal relationship of a person with the state, expressed in the totality of their mutual rights and obligations)," friendship"(between people). In Russian, words expressing abstract concepts do not have a plural: they do not say: "A diamond has a lot of hardness" or "Oak has a lot of durability", a "A lawyer has a lot of all sorts of competencies."

One should not confuse concrete concepts with singular ones, and abstract ones with general ones. General concepts can be both concrete and abstract: "intermediary"- general, specific; a "mediation» - general, abstract. A single concept can be abstract: "United Nations"- single, concrete; "Courage of Captain Gastello" singular, abstract.

It is not difficult to determine the designates of specific concepts, if a set of features that make up the semantic meaning is known, then you can point to the objects that this concept denotes. But with abstract concepts, everything is different, what is denoted by them does not exist in material form, they, having a semantic meaning, have no objective meaning. It is believed that the content of an abstract concept is the property or relation that it denotes, and the volume is the set of objects that have this property, or the set of objects between which there is a certain relationship. Therefore, the whiteness of the snow and the whiteness of the tablecloth should be considered as designata of the concept "white", and the equality of the values ​​X and Y and the equality of the citizens of the country before the law - as designata of the concept "equality".

The division of concepts into concrete and abstract - relatively. If an abstract concept reflecting a property is used in relation to the objects themselves that have this property, then it acquires plural. The concept of " sweetness"- abstract, if only property is conceived in it, and "oriental sweets"- this is a specific concept applied to the products themselves that have this property. Abstract concepts can be part of more complex concrete ones and vice versa. They are distinguished by the leading concept: "lawyer incompetence"- abstract, although it includes concrete as an element - "lawyer", a "a victim of incompetence"- concrete, although it contains the abstract - "incompetence".

Examples concrete and abstract concepts: "citizen" - "citizenship", "employee" - "professionalism", " wage"- "payment", "court" - "conviction".

Concepts irrelative and correlative

Irrelevant concepts – these are such concepts that designate objects in themselves, regardless of the relation they are to other objects: "farmer", "rule", "village", "justice", "nature". An irrelevant concept is retained by the object from the moment of its naming until the moment of its disappearance (“man” in relation to a separate human individual is retained by him from birth to death).

Correlative concepts – these are concepts that designate not independent objects, but objects as members of a relationship. One object of thought presupposes the existence of another and is impossible without it, therefore they have meaning as long as this relation exists, and lose it as soon as this relation is destroyed: concepts "parents" and "children": one cannot be a son or daughter without parents, in turn, it is children who make us fathers or mothers; "groom - bride", "boss - subordinate", "plaintiff - defendant", "right - duty", "judge - defendant", "plaintiff - defendant".

Example: concepts "three" and "five"- irrelevant, but if you draw a horizontal line between them, you get three-fifths fraction- 3 is the “numerator”, and the number 5 is the “denominator” - these are already correlative concepts. In order to revive them as independent numbers, it is necessary to destroy the relation, as a result of which its moments - the numerator and denominator - will cease to exist. The terms "generation" and "destruction", to characterize correlative concepts, have not a physical, but a logical meaning.

An illustration of the nature of correlative concepts is a joke: when asked who gives birth to whom, "father - son" or "son of father" follows a paradoxical, at first glance, answer: "son begets father" and this answer is correct. If you ask a man whose first child had a son when he became a father, he will give the date of birth of his first child.

The concepts acquired by a person as a result of education are not correlative ("lawyer", "engineer").

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Evlannikova G.E
E 17 Logic: textbook. Allowance / G.E. Evlannikov. - St. Petersburg: SPbGIEU, 2011. - 235. S. ISBN The study guide highlights the basic concepts and problems

Subject of logic
Logic (from the Greek logos - thought, speech, mind) is the science of the laws and forms of thinking, aimed at understanding the objective world. One of the main tasks of logic is the search for truth, i.e. she is izu

Righteousness and Truth
As mentioned above, logic studies not all thinking, but only that which is aimed at finding and substantiating truth. The distinction between the concepts of "truth" and "correctness" is associated with the allocation in thought

Logic in Ancient China
Logic in China appeared during the development of various schools, competition and discussions between them. A contemporary of Confucius Mo-tzu, teacher Mo (V-IV centuries BC) founded the Mo-chia school,

Indian logic
The origins of logic in India can be traced back to the grammatical texts of the 5th century B.C.

The logic of antiquity
Despite the fact that the first teachings about reasoning, about the forms and methods of thinking arose in ancient india, China, the basis of modern logic is the Aristotelian doctrine. Adopted precisely by Aristotle (3

Logic in the Middle Ages
In the Middle Ages in Europe, the state Christian ideology subjugated science, politics, culture, and logic becomes the servant of theology, and only in Arab countries, the logic still retains

Logic in the Renaissance and Modern Times
During the Renaissance, experimenters began to contrast the experience of deduction associated with scholasticism and Aristotle. Leonardo da Vinci, G. Galilei with his logic "

Modern logic
In the 20th century, mathematical logic took shape as an independent discipline within the framework of logical science, both theories and practices of "machine thinking" are rapidly developing, and computational

Logic in Russia
The first Russian who wrote only three pages on logic was Prince A.M. Kurbsky (1528-1583). He prepared for publication the first in Russian printed book logically

Thinking and language
Thinking - highest form active reflection, expressed in the purposeful knowledge of the essential connections and relations of the objective world by a person, the production

Language as a sign system
Language emerges at the same time as human society during labor activity primitive people. In the course of its development and functioning, it is determined by a set of processes

Concept and name
The main forms of correct thinking are - concept, judgment and conclusion. Human speech is made up of words. Words are necessary in order to designate, names

Concept structure
In the structure of the concept, content and volume are distinguished, each concept or name associated with it has volume and content. As an integral form of thought, the concept is a natural unity of these two

Education and the role of concepts
The emergence of concepts is an objective pattern of the formation and development of human thinking. At first, a man thought figuratively, for him the “beast” is a deer,

Types of concepts by volume
Concepts are simple, complex and descriptive Simple concepts- these are concepts expressed in one word: “table”, “factory”, “tree”, “cosmonaut”,

The concepts of general, single and zero
Concepts are divided into non-empty and empty concepts, depending on the relationship to existing or non-existent real objects of thought. Non-empty concepts

The concepts of collective and non-collective
Collective concepts are concepts that denote a certain set of objects, constitute a certain integrity, considered as an independent object. Content collected

Concepts positive and negative
Positive concepts are such concepts that reflect the presence of any qualities, properties in objects of thought, i.e. their content is made up of properties inherent in the subject: "n

Relationship between concepts
The considered types of concepts can be among themselves in certain relations, and first of all in relation to comparability and incomparability. Incomparability - relation

Compatibility relation between concepts
The volume of a concept represents a certain set of objects, and the ratio of concepts in terms of volume is represented as a relationship between sets. The relationship in volume between concepts, as well as in content

Equivalence relation between concepts
In relation to the equivolume (equivalence) of concepts, the volumes of which completely coincide. Their content may be the same or different (“rectangular rhombus” and “equilateral

Intersection relation between concepts
In relation to the intersection, the volumes of two or more concepts that partially coincide with each other are found. DIAGRAM: The intersection relation is represented by two partially

Subordination relationship between concepts
In relation to subordination (subordination), there are concepts, the scope of one fully includes the scope of the other, but is not covered by it entirely.

Subordination relationship between concepts
In relation to subordination, there are two or more single-order species of the same genus. Single-order views are views that belong to the same horizontal level.

Relation of opposites between concepts
In relation to the opposite, there are correlative concepts formed as a result of comparing the intensities of a certain quantity. The subjects of such concepts are combined

The relation of contradiction between concepts
Contradictory concepts exclude each other, but do not presuppose as opposites. One of these concepts indicates some signs, and the other denies them. Thus, one of the contradictions

Limitation and generalization of concepts
Generalization is an operation in which, by excluding a species-forming feature from the content this concept get a generic concept from a specific one, thus

Division of concepts
When studying a concept, the task often arises to reveal its scope, i.e. to distribute the objects that are conceived in the concept into separate groups. In theoretical and practical areas

Definition of concepts
The definition of a concept (definition) is an operation consisting in revealing the content, finding the essential general features of a certain class of objects, conceivable in a given concept.

Structure of an attributive judgment
S - P, an attributive judgment consists of a subject, a predicate, which are terms, a connective, and a quantifier. S - the subject of the judgment, the concept of the subject

Conjunctive (connective) "L" - judgments united by ligaments "and", "but", "yes", "a", "and also", "although", "however". Р L q
Example: "Nights are lunar and moonless." Consists of judgments: "Nights are moonlit" and "Nights are moonless." A judgment is true if and only if

S is P → aS is aP
Example: "All cats are predators" → "All domestic cats are domestic predators". As a rule, restrictions are generally unjustified, not always judgments obtained with p

From attributive
If the premise is a judgment of the form A, E, I or O, then a direct conclusion can be drawn by inference on a logical square, The contradiction relation

From relational
The logical basis is the nature of the relationship R between objects X and Y. Symmetry relation If X=Y, then Y=X, then from the premise

Immediate output via transformation
The transformation of judgments takes place in the forms of conversion, transformation and opposition of S and P, which we have already considered in the topic “Judgment”. umozaklyu

From attribute judgments
A typical form of a mediated conclusion is a simple categorical syllogism, consisting of two premises and a new judgment - the conclusion. Example

I II III IV
M R R M M R R M S M S M M S M S The I figure includes syllogisms in which the middle term takes the place of S in the major premise and the place of P in the minor

Modes of a simple categorical syllogism
Syllogism modes are varieties of figures that differ from each other in the quality and quantity of judgments that are premises and conclusions. Since a simple categorical syllogism includes

Bramantip, Camenes, Dimaris, Fesapo, Fresison
The vowels included in the names of the modes correspond to the symbolic designation of the premises and the conclusion, so there are only three vowels in the name of each mode. Consonants boo

SaM; SIM; MaS; MiS
Conclusion: SeP; SOP; SOP; SOP. Relations in the minor premise excluding the possibility of conclusions: SeM; SOM; MeS, MoS. 8. Relationship of terms in large

From relational judgments
Non-syllogistic deductive mediated inferences. They may have a certain resemblance to syllogisms. Example: "B. Mayakovsky - a contemporary of M. Gorkog

Indirect inference from complex judgments
The logical following of the conclusion is determined not by subject-predicate relations, but by the logical connection between the components of a complex judgment. There are two types of indirect minds

Types of induction
Complete induction if the premises exhaust the entire class of subjects subject to inductive generalization. Scheme of reliable induction: S1 is P S

Inductive Methods for Establishing Causality
Cause - a phenomenon (a set of phenomena), in the event of which another action must be caused - a consequence, and when it disappears, inevitably

Conditions for the validity of inductive inferences
1. For an inductive generalization, it is necessary that the number of cases registered in the premises be as large as possible. As a rule, the cause of delusion is not an insufficient number of

Logical fallacies in inductive reasoning
It increases the likelihood of inference by avoiding the following common mistakes: "hasty generalization" and "after this, therefore because of this." "Hasty Generalizations"

Types of analogy
Attributive analogy Conclusions by analogy - the transfer of information from one object (model) to another (prototype, sample). The model in the process of cognition acts as a deputy

The difference between induction and analogy
These are inferences from particulars, but the difference between them is that induction comes to the general, and inference by analogy comes again to particulars. Inference by analogy does not refer to the definition

Conditions for the legitimacy of conclusions by analogy
Structure different forms conclusions by analogy are different, therefore general rules no, we are talking only about the rules of individual forms of inference by analogy. Let's start with an analogy of the paradeigma type.

Role of analogy
The less scientific and practical knowledge, the more often a person judges new phenomena by analogy with previously encountered ones. If there are no experimental generalizations, then the consideration of phenomena according to similar characteristics

Logical fallacies in analogy
The analogy is sometimes superficial and leads to a deliberately erroneous conclusion, or even lead to a dead end. Many prejudices still prevailing - belief in omens, divination - are based on erroneous analogies.

Evidence is a way of substantiating the truth
Obtaining mediated, inferential knowledge occurs not only in the form of inference. The proof is based on inferences, but is not reduced to them. Revealing the truth, man

Structure of the proof
In any proof, three parts are distinguished: the position being proved, or the thesis - that which must be proved or made obvious, is expressed in the form of a judgment; ground proof

Refutation
Refutation is the denial of evidence, the justification of the falsity or inconsistency of either elements or the evidence as a whole. A refutation is structurally not much different from a proof. O

Thesis rules
The provable thesis must be true, the truth of the thesis is not born, but only established, revealed. All attempts to break this rule, which follows from the very essence of truths

Argument rules
Arguments must be true and their truth must not be in doubt. This rule is inextricably linked with the first rule of the thesis. East

deductive way of reasoning
Precise definition in a larger premise that acts as an argument, an initial position, which makes it possible to convincingly demonstrate the scientific positions or practical considerations that

Errors in relation to the thesis
The loss of the thesis is manifested in the fact that, having formulated the thesis, the proponent forgets it and moves on to another, directly or indirectly related to the first, but in principle a different position. Further

Errors with Arguments
Violation of the requirement of reliability, truth and proof of arguments leads to two errors. The main fallacy is the acceptance of a false argument as the truth. Causes -

Logic of questions and answers
The development of knowledge is the transition from previously established judgments to new, more accurate and rich in content. This transition consists of stages: 1) posing a question, 2) searching new information, 3) construct

Whether questions - clarifying
These questions are divided into simple unconditional - "Is it true that" and simple conditional - "Is it true that if ... then" and complex: conjunctive, disjunctive and implicative. The answers to them may

Simple and difficult questions
Simple Questions are those which do not include as constituent parts other questions. Difficult questions are those that involve

Substantive and non-substantive answers
Answer on the merits of the question - such an answer, the content and structure of which is built in accordance with the question posed. Only in this case is it considered relevant,

Short and long answers
Short - these are monosyllabic affirmative or negative answers: "yes" or "no". Expanded - these are answers in which repeat

Accurate and inaccurate answers
Under the accuracy and certainty understand the logical, ie. conceptual and structural characteristics of the issue. It is expressed in the accuracy of the concepts used.

Logical norms for posing a question and answer
1. The question must be correctly posed. Tricky, provocative and vague questions are unacceptable. 2. The question should be simple, short, clear, precise. Long, confusing question

Problem
A problem is a form of thought that reflects knowledge of the unknown in the form of a question, and its formulation requires the theoretical or practical overcoming of this uncertainty, i.e.

Problem types
1. By their nature, the problems are divided into empirical, related to the resolution of the contradiction between facts and their interpretation, and theoretical, arising from pr

problem statement requirements
1. The premises of the problem must be true. 2. The prerequisites must be necessary and sufficient to raise the problem. 3. The problem itself must be exactly

Hypothesis
A hypothesis is an assumption that is believed to be true. A hypothesis is resorted to when there are a number of facts that are not explained due to the fact that in the immediate op

Types of hypotheses
1. By function in cognitive process hypotheses are distinguished: a) descriptive - this is an assumption about the properties inherent in the object under study

Conclusion
AT study guide the main problems that logic solves are considered. It is inextricably linked with thinking and with what is available to it, so logic finds practical use in science, art

Bibliographic list
References: 1. Guts A.K. Mathematical logic and theory of algorithms. M., 2009. 2. Evlannikov V.P., Evlannikova G.E. Logic and the theory of argumentation. consp

Terminological dictionary
AXIOM - a true judgment that is accepted without evidence as a starting point. ALTERNATIVE - each of two or more mutually exclusive possibilities.

Abstract terms are such terms that serve to designate qualities or properties, states, actions of things. They denote qualities that are considered by themselves, without things. When we use abstract terms, we do not at all mean to indicate that the qualities or properties corresponding to these terms, the states of things, exist somewhere in a certain space or in a certain moment time, but, on the contrary, they are conceived by us without things, and therefore without a definite space and time. An example of abstract terms can be such terms as "heaviness", "volume", "shape", "color", "intensity", "hardness", "pleasantness", "weight", "humanity". In fact, "gravity" is not something that has an existence in this moment time: it exists not only in some particular place, but also wherever there are heavy things. These terms are called abstract because the properties or qualities they denote can be thought of without the things to which they belong: we can abstract, abstract (abstrahere) from certain things.
Abstract, in a different sense, are sometimes also called the concepts of such things that cannot be perceived by us as a known definite thing, for example, “universe”, “star system”, “millennial”, “mankind”, etc.
Concrete are the concepts of things, objects, persons, facts, events, states, consciousness, if we consider them to have a definite existence, for example, "square", "flame", "house", "battle", "fear" (1), etc. The relation between abstract concepts and concrete ones is as follows. The abstract concept is derived from the concrete; we single out by analysis some quality, or property, of a thing, for example, whiteness from chalk. On the other hand, a concrete concept can be viewed as a synthesis of abstractly conceivable qualities. For example, the concept of "stone" is a synthesis of the qualities "heaviness", "roughness", "hardness", etc.
It should be noted that adjectives are always concrete and not abstract terms; when we use the adjective "white", we always think of a thing; property or quality we think in the case when we use the noun "whiteness".
In the language, sometimes abstract and concrete terms are used in pairs. For example, the specific term "white" corresponds to the abstract concept "whiteness", the specific term "strict" corresponds to the abstract concept "strictness", the term "square" - "squareness", "man" - "humanity".
The terms are positive and negative. Positive terms are characterized by the fact that they serve to denote the presence of one or another quality. For example, using the terms "beautiful", "divisible", "final", we want to indicate that in objects there are qualities denoted by these words; the corresponding negative terms “ugly”, “indivisible”, “infinite” will mean that these qualities are absent in objects. Other examples of negative terms are "timeless", "supersensual", "abnormal", "careless", "meaningless".
Relative and absolute terms. Finally, there are relative and absolute terms. What does absolute mean? By absolute we mean that which is not connected with anything else, that which does not depend on anything else; By relative we mean that which is related to something
1. It can be said about the feeling of fear that it has a certain quality, for example, a certain strength or intensity, that it has the property of paralyzing mental activity, etc. In a word, it can be considered as something consisting of a combination of properties or qualities.

others; An absolute term is one that in its meaning does not contain any relation to anything else, it does not force us to think about any other things than those that it designates. For example, the term "house" is an absolute term. Thinking about the house, we can not think about anything else. A relative term, on the other hand, is a term that, in addition to the object that it means, implies the existence of another object as well. For example, the term "parents" necessarily presupposes the existence of children: one cannot think of parents without at the same time not thinking of children. If we say about any person that he is strict, then we can limit our attention only to this person; but if we speak of him as a friend, then we must think of another person who stands towards him in relation to friendship. Other examples: "companion", "partner", "similar", "equal", "close", "king-subjects", "cause - effect", "north - south". Each of such a pair of terms is called correlative to another term.
Review questions
What is the relationship between the consideration of terms and concepts? Which terms are general and which are specific? Which terms do we say that they are used in a collective sense, and which ones - in a divisive sense? What is the difference between collective terms and general terms? Which terms are called abstract and which are specific? Which terms are called positive and which are negative? What are relative and absolute terms?