Identity
the relationship between objects (real or abstract), which allows us to speak of them as indistinguishable from each other, in some set of characteristics (for example, properties). In reality, all objects (things) usually differ from each other according to some characteristics. This does not exclude the fact that they also have common characteristics. In the process of cognition, we identify separate things in their general characteristics, combine them into sets according to these characteristics, form concepts about them on the basis of the abstraction of identification (see: Abstraction). Objects that are combined into sets according to some properties common to them cease to differ from each other, since in the process of such association we abstract from their differences. In other words, they become indistinguishable, identical in these properties. If all the characteristics of two objects a and b turned out to be identical, the objects would turn into the same object. But this does not happen, because in the process of cognition we identify objects that are different from each other not according to all characteristics, but only according to some. Without the establishment of identities and differences between objects, no knowledge of the world around us, no orientation in the environment around us is possible.
For the first time, in the most general and idealized formulation, the concept of t. of two objects was given by G. V. Leibniz. Leibniz's law can be stated as follows: "x = y if and only if x has every property that y has and y has every property that x has." In other words, an object x can be identified with an object y when absolutely all of their properties are the same. The concept of T. is widely used in various sciences: in mathematics, logic, and natural science. However, in all cases
its application, the identity of the studied subjects is determined not by absolutely all general characteristics, but only by some, which is connected with the goals of their study, with the context of the scientific theory within which these subjects are studied.
Dictionary of logic. - M.: Tumanit, ed. center VLADOS. A.A. Ivin, A.L. Nikiforov. 1997 .
Synonyms:See what "identity" is in other dictionaries:
Identity- Identity ♦ Identité Coincidence, the property of being the same. Same as what? The same as the same, otherwise it will no longer be an identity. Thus, identity is primarily a relation of oneself to oneself (my identity is myself) or ... Philosophical Dictionary of Sponville
A concept that expresses the limiting case of the equality of objects, when not only all generic, but also all their individual properties coincide. The coincidence of generic properties (similarity), generally speaking, does not limit the number of equated ... ... Philosophical Encyclopedia
Cm … Synonym dictionary
The relationship between objects (objects of reality, perception, thought) considered as one and the same; limiting case of the relation of equality. In mathematics, an identity is an equation that is satisfied identically, that is, valid for ... ... Big Encyclopedic Dictionary
IDENTITY, a and IDENTITY, a, cf. 1. Complete similarity, coincidence. T. looks. 2. (identity). In mathematics: an equality that is valid for any numerical values of its constituent quantities. | adj. identical, oh, oh and identical, oh, oh (to 1 ... ... Explanatory dictionary of Ozhegov
identity- IDENTITY is a concept usually represented in natural language either in the form "I (is) the same as b, or "a is identical to b", which can be symbolized as "a = b" (such a statement is usually called absolute T.) , or in the form of ... ... Encyclopedia of Epistemology and Philosophy of Science
identity- (wrong identity) and obsolete identity (preserved in the speech of mathematicians, physicists) ... Dictionary of pronunciation and stress difficulties in modern Russian
AND DIFFERENCE are two interrelated categories of philosophy and logic. When defining the concepts of T. and R., two fundamental principles are used: the principle of individuation and the principle of T. indistinguishable. According to the principle of individuation, which has been substantively developed ... History of Philosophy: Encyclopedia
English identity; German identity. 1. In mathematics, an equation that is valid for all admissible values of the arguments. 2. The limiting case of equality of objects, when not only all generic, but also all their individual properties coincide. Antinazi.… … Encyclopedia of Sociology
- (notation ≡) (identity, symbol ≡) An equation that is true for any values of its constituent variables. So, z ≡ x + y means that z is always the sum of x and y. Many economists are sometimes inconsistent and use the common sign even then... Economic dictionary
identity- identity identity identification ID - [] Topics information security Synonyms identity identity identification ID EN identityID ... Technical Translator's Handbook
Books
- Difference and Identity in Greek and Medieval Ontology, R. A. Loshakov. The monograph explores the main issues of Greek (Aristotelian) and medieval ontology in the light of understanding being as Difference. Thus, a derivative, secondary, ...
Explanatory dictionary of the Russian language. S.I. Ozhegov, N.Yu. Shvedova.
identity
A and IDENTITY. -a, cf.
adv. In the same way, just like anyone else. You are tired, I
union. Same as also. Are you leaving, brother? - T.
Full similarity, coincidence. G. views.
(identity). In mathematics: an equality that is valid for any numerical values of its constituent quantities. || adj. identical, -th, -th and identical, -th, -th (to 1 value). Identity algebraic expressions. ALSO [do not mix with a combination of the pronoun "that" and the particle "same"].
particle. Expresses distrustful or negative, ironic attitude (simple). *T. smart guy found! He is a poet. - Poet comrade (to me)!
New explanatory and derivational dictionary of the Russian language, T. F. Efremova.
identity
-
Absolute coincidence with smth., smth. both in its essence and in external signs and manifestations.
An exact match. something
cf. An equality that is valid for all the numerical values of the letters included in it (in mathematics).
Encyclopedic Dictionary, 1998
identity
the relationship between objects (objects of reality, perception, thought) considered as "one and the same"; "limiting" case of the relation of equality. In mathematics, an identity is an equation that is satisfied identically, i.e. is valid for any admissible values of the variables included in it.
Identity
the basic concept of logic, philosophy and mathematics; used in the languages of scientific theories to formulate defining relations, laws and theorems. In mathematics, T. ≈ is an equation that is satisfied identically, that is, it is valid for any admissible values of the variables included in it. From a logical point of view, T. ≈ is a predicate represented by the formula x \u003d y (read: "x is identical to y", "x is the same as y"), which corresponds to a logical function that is true when the variables x and y mean different occurrences of the "same" item, and false otherwise. From a philosophical (epistemological) point of view, T. is an attitude based on ideas or judgments about what the “one and the same” object of reality, perception, thought is. The logical and philosophical aspects of T. are additional: the first gives a formal model of the concept of T., the second - the basis for the application of this model. The first aspect includes the concept of “one and the same” subject, but the meaning of the formal model does not depend on the content of this concept: the procedures of identifications and the dependence of the results of identifications on the conditions or methods of identifications, on explicitly or implicitly accepted abstractions are ignored. In the second (philosophical) aspect of consideration, the grounds for applying the logical models of T. are associated with how objects are identified, by what signs, and already depend on the point of view, on the conditions and means of identification. The distinction between the logical and philosophical aspects of T. goes back to the well-known position that the judgment of the identity of objects and T. as a concept is not the same thing (see Platon, Soch., vol. 2, M., 1970, p. 36) . It is essential, however, to emphasize the independence and consistency of these aspects: the concept of logic is exhausted by the meaning of the logical function corresponding to it; it is not deduced from the actual identity of objects, “is not extracted” from it, but is an abstraction replenished under “suitable” conditions of experience or, in theory, by assumptions (hypotheses) about actually admissible identifications; at the same time, when substitution (see axiom 4 below) is fulfilled in the corresponding interval of the abstraction of identification, "inside" this interval, the actual T. of objects coincides exactly with T. in the logical sense. The importance of the concept of T. has led to the need for special theories of T. The most common way of constructing these theories is axiomatic. As axioms, you can specify, for example, the following (not necessarily all):
x = y É y = x,
x = y & y = z É x = z,
A (x) É (x = y É A (y)),
where A (x) ≈ an arbitrary predicate containing x freely and free for y, and A (x) and A (y) differ only in the occurrences (at least one) of the variables x and y.
Axiom 1 postulates the property of reflexivity of T. In traditional logic, it was considered the only logical law of T., to which, usually (in arithmetic, algebra, geometry), axioms 2 and Z were added as “non-logical postulates”. Axiom 1 can be considered epistemologically justified, since it is a kind of logical expression of individuation, on which, in turn, the “givenness” of objects in experience, the possibility of recognizing them, is based: in order to speak of an object “as given”, it is necessary to somehow single it out, distinguish it from other objects, and in the future not to be confused with them. In this sense, T., based on Axiom 1, is a special relation of "self-identity" that connects each object only with itself ≈ and with no other object.
Axiom 2 postulates the symmetry property T. It asserts the independence of the result of identification from the order in pairs of identified objects. This axiom also has a certain justification in experience. For example, the order of the weights and goods on the scales is different, when viewed from left to right, for the buyer and seller facing each other, but the result is ≈ this case the equilibrium is the same for both.
Axioms 1 and 2 together serve as an abstract expression of T. as indistinguishability, a theory in which the idea of the “same” object is based on the facts of the non-observability of differences and essentially depends on the criteria of distinguishability, on the means (devices) that distinguish one object from another , ultimately ≈ from the abstraction of indistinguishability. Since the dependence on the “threshold of distinguishability” cannot be eliminated in principle in practice, the idea of a temperature that satisfies axioms 1 and 2 is the only natural result that can be obtained experimentally.
Axiom 3 postulates the transitivity of T. It states that the superposition of T. is also T. and is the first non-trivial statement about the identity of objects. The transitivity of T. is either an “idealization of experience” under conditions of “decreasing accuracy,” or an abstraction that replenishes experience and “creates” a new, different from indistinguishability, meaning of T.: indistinguishability guarantees only T. in the interval of abstraction of indistinguishability, and this latter does not connected with the fulfillment of Axiom 3. Axioms 1, 2, and 3 together serve as an abstract expression of the theory of T. as an equivalence.
Axiom 4 postulates that a necessary condition for the typology of objects is the coincidence of their characteristics. From a logical point of view, this axiom is obvious: “one and the same” object has all its features. But since the notion of "the same" thing is inevitably based on certain kinds of assumptions or abstractions, this axiom is not trivial. It cannot be verified "in general" - according to all conceivable signs, but only in certain fixed intervals of abstractions of identification or indistinguishability. This is exactly how it is used in practice: objects are compared and identified not according to all conceivable signs, but only according to some - the main (initial) signs of the theory in which they want to have a concept of the "same" object based on these signs and on axiom 4. In these cases, the scheme of axioms 4 is replaced by a finite list of its alloforms ≈ "meaningful" axioms T congruent to it. For example, in the axiomatic set theory of Zermelo ≈ Frenkel ≈ axioms:
4.1 z О x О (x = y О z О y),
4.2 x Î z É (x = y É y Î z),
defining, provided that the universe contains only sets, the interval of abstraction of the identification of sets according to their “membership in them” and according to their “own membership”, with the obligatory addition of axioms 1≈3, defining T. as equivalence.
The axioms 1≈4 listed above refer to the so-called laws of T. From them, using the rules of logic, one can derive many other laws that are unknown in pre-mathematical logic. The distinction between the logical and epistemological (philosophical) aspects of theory is irrelevant as long as we are talking about general abstract formulations of the laws of theory. The matter, however, changes significantly when these laws are used to describe realities. Defining the concept of “one and the same” subject, the axiomatics of theory necessarily influence the formation of the universe “within” the corresponding axiomatic theory.
Lit .: Tarsky A., Introduction to the logic and methodology of deductive sciences, trans. from English, M., 1948; Novoselov M., Identity, in the book: Philosophical Encyclopedia, v. 5, M., 1970; his, On some concepts of the theory of relations, in the book: Cybernetics and modern scientific knowledge, M., 1976; Shreyder Yu. A., Equality, similarity, order, M., 1971; Klini S. K., Mathematical logic, trans. from English, M., 1973; Frege G., Schriften zur Logik, B., 1973.
M. M. Novoselov.
Wikipedia
Identity (mathematics)
Identity(in mathematics) - equality, which is satisfied on the entire set of values of the variables included in it, for example:
a − b = (a + b)(a − b) (a + b) = a + 2ab + betc. Sometimes an identity is also called an equality that does not contain any variables; e.g. 25 = 625.
Identical equality, when they want to emphasize it especially, is indicated by the symbol " ≡ ".
Identity
Identity, identity- polysemantic terms.
- An identity is an equality that holds on the entire set of values of its constituent variables.
- Identity is a complete coincidence of the properties of objects.
- Identity in physics is a characteristic of objects, in which the replacement of one of the objects with another does not change the state of the system while maintaining these conditions.
- The law of identity is one of the laws of logic.
- The principle of identity is the principle of quantum mechanics, according to which the states of a system of particles, obtained from each other by rearranging identical particles in places, cannot be distinguished in any experiment, and such states should be considered as one physical state.
- "Identity and Reality" - a book by E. Meyerson.
Identity (philosophy)
Identity- a philosophical category that expresses equality, the sameness of an object, phenomenon with itself or the equality of several objects. Objects A and B are said to be identical, the same, if and only if all properties. This means that identity is inextricably linked with difference and is relative. Any identity of things is temporary, transient, while their development, change is absolute. In the exact sciences, however, abstract identity, i.e., abstracted from the development of things, in accordance with Leibniz's law, is used because in the process of cognition, idealization and simplification of reality are possible and necessary under certain conditions. The logical law of identity is also formulated with similar restrictions.
Identity should be distinguished from similarity, similarity and unity.
Similar we call objects that have one or more common properties; the more objects have common properties, the closer their similarity comes to identity. Two objects are considered identical if their qualities are exactly the same.
However, it should be remembered that in the objective world there can be no identity, since two objects, no matter how similar they are in quality, still differ in number and the space they occupy; only where material nature rises to spirituality does the possibility of identity appear.
The necessary condition for identity is unity: where there is no unity, there can be no identity. The material world, divisible to infinity, does not possess unity; unity comes with life, especially with spiritual life. We speak of the identity of an organism in the sense that its one life persists despite the constant change of particles that make up the organism; where there is life, there is unity, but in the true meaning of the word there is still no identity, since life waxes and wanes, remaining unchanged only in the idea.
The same can be said about personalities- the highest manifestation of life and consciousness; and in personality we only assume identity, but in reality there is none, since the very content of personality is constantly changing. True identity is possible only in thinking; a properly formed concept has an eternal value regardless of the conditions of time and space in which it is conceived.
Leibniz, with his principium indiscernibilium, established the idea that two things cannot exist that are completely similar in qualitative and quantitative respects, since such similarity would be nothing but identity.
The philosophy of identity is the central idea in the works of Friedrich Schelling.
Examples of the use of the word identity in the literature.
This is precisely the great psychological merit of both ancient and medieval nominalism, that it thoroughly dissolved the primitive magical or mystical identity words with an object are too thorough even for a type whose foundation is not to cling tightly to things, but to abstract the idea and put it above things.
it identity subjectivity and objectivity, and constitutes precisely the universality now attained by self-consciousness, which rises above the two sides or particularities mentioned above and dissolves them in itself.
At this stage, self-conscious subjects correlated with each other have risen, therefore, through the removal of their unequal singularity of individuality, to the consciousness of their real universality - their inherent freedom - and thereby to the contemplation of a certain identities them with each other.
A century and a half later, Inta, the great-great-great-granddaughter of the woman who was given a seat in the spaceship by Sarp, amazed by her inexplicable identity with Vella.
But when it turned out that before his death, the good writer Kamanin read the manuscript of KRASNOGOROV, and at the same time the very one whose candidacy was discussed by the ferocious physicist Sherstnev a second before his, Sherstnev’s, SIMILAR death, - then, you know, it smelled on me of not simple coincidence, it smells IDENTITY!
The merit of Klossowski is that he showed that these three forms are now connected forever, but not due to dialectical transformation and identity opposites, but through their dispersion over the surface of things.
In these works, Klossowski develops the theory of the sign, meaning and nonsense, and also gives a deeply original interpretation of Nietzsche's idea of the eternal return, understood as an eccentric ability to assert divergences and disjunctions, leaving no room for identity me, neither identity peace or identity God.
As in any other type of identification of a person by appearance, in a photo-portrait examination, the identified object in all cases is a specific individual, identity which is being installed.
Now a teacher has emerged from the student, and above all, as a teacher, he coped with the great task of the first period of his master's degree, having won the struggle for authority and full identity person and position.
But in the early classics it identity thinking and conceivable was interpreted only intuitively and only descriptively.
For Schelling identity Nature and Spirit is a natural-philosophical principle that precedes empirical knowledge and determines the understanding of the results of the latter.
Based on this identities mineral features and it is concluded that this Scottish formation is contemporary with the lowest formations of Wallis, because the amount of available paleontological data is too small to confirm or refute this kind of position.
Now it is no longer the origin that gives place to historicity, but the very fabric of historicity reveals the need for the origin, which would be both internal and external, like some hypothetical apex of a cone, where all differences, all scattering, all discontinuities are compressed into a single point. identities, into that incorporeal image of the Identical, capable, however, of splitting and turning into the Other.
It is known that there are often cases when an object to be identified from memory does not have a sufficient number of noticeable features that would allow it to be identified. identity.
It is clear, therefore, that veche, or uprisings, in Moscow against people who wanted to flee from the Tatars, in Rostov against the Tatars, in Kostroma, Nizhny, Torzhok against the boyars, veches convened by all the bells, should not, one by one. identity names, mixed with the vechas of Novgorod and other old cities: Smolensk, Kyiv, Polotsk, Rostov, where the inhabitants, according to the chronicler, converged as if on a thought, for a vecha, and that the elders decided, the suburbs agreed to that.
Law of Identity- the principle of constancy or the principle of preservation of the subject and semantic meanings of judgments (statements) in some known or implied context (in conclusion, proof, theory). It is one of the laws of classical logic.
In the process of reasoning, each concept, judgment must be used in the same sense. A prerequisite for this is the possibility of distinguishing and identifying the objects in question. . A thought about an object must have a definite, stable content, no matter how many times it is repeated. The most important property of thinking is its certainty- is expressed by the given logical law.
Application
In everyday life
Any of our acquaintances changes every year, but we still distinguish him from other people we know and do not know (there is a possibility of distinction), because he retains the main features that act as the same throughout the life of our acquaintance (there is a possibility of identification ). That is, in accordance with Leibniz's law(defining the concept of identity) we say that our acquaintance has changed. However, in accordance with identity law we argue that this is one and the same person, since the definition is based on the concept of personality. The law of identity requires that we always use the same expression (name) to describe the same concept. Thus, we simultaneously consider one object (familiar) at two different levels of abstraction. The possibility of distinction and identification is determined in accordance with the law of sufficient reason. In this case, our sensory perception is used as a sufficient basis (see identification).
In jurisprudence
In formal logic
Under the identity of thought to itself in formal logic is understood the identity of its volume. This means that instead of a boolean variable A (\displaystyle A) into the formula " A (\displaystyle A) there is A (\displaystyle A)"can be substituted thoughts of different specific content, if they have the same volume. Instead of the first A (\displaystyle A) in the formula " A (\displaystyle A) there is A (\displaystyle A)» we can substitute the concept "animal; having a soft earlobe", and instead of the second - the concept "an animal with the ability to produce tools"(both of these thoughts from the point of view of formal logic are considered equivalent, indistinguishable, since they have the same scope, namely, the signs reflected in these concepts refer only to the class of people), and at the same time a true judgment is obtained "An animal with a soft earlobe is an animal with the ability to produce tools".
In mathematics
In mathematical logic, the law of identity is the identically true implication of a logical variable with itself X ⇒ X (\displaystyle X\Rightarrow X) .
In algebra, the concept of arithmetic equality of numbers is considered as a special case of the general concept of logical identity. However, there are mathematicians who, contrary to this point of view, do not identify the symbol " = (\displaystyle =)”, found in arithmetic, with a symbol of logical identity; they do not consider that equal numbers are necessarily identical, and therefore consider the concept of numerical equality as a specifically arithmetic concept. That is, they believe that the very fact of the presence or absence of a special case of logical identity should be determined within the framework of logic. .
Violations of the Law of Identity
When the law of identity is violated involuntarily, out of ignorance, then logical errors arise, which are called
Identity - a relationship between objects (real or abstract), which allows us to speak of them as indistinguishable from each other, in some set of characteristics (eg, properties). In reality, all objects (things) usually differ from each other according to some characteristics. This does not exclude the fact that they also have common characteristics. In the process of cognition, we identify separate things in their general characteristics, combine them into sets according to these characteristics, form concepts about them on the basis of the abstraction of identification (see: Abstraction). Objects that are combined into sets according to some properties common to them cease to differ from each other, since in the process of such association we abstract from their differences. In other words, they become indistinguishable, identical in these properties. If all the characteristics of two objects a and b turned out to be identical, the objects would turn into the same object. But this does not happen, because in the process of cognition we identify objects that are different from each other not according to all characteristics, but only according to some. Without the establishment of identities and differences between objects, no knowledge of the world around us, no orientation in the environment around us is possible. For the first time, in the most general and idealized formulation, the concept of t. of two objects was given by G. V. Leibniz. Leibniz's law can be stated as follows: "x = y if and only if x has every property that y has, and y has every property that x has." In other words, an object x can be identified with an object y when absolutely all of their properties are the same. The concept of T. is widely used in various sciences: in mathematics, logic, and natural science. However, in all cases of its application, the identity of the subjects under study is determined not by absolutely all general characteristics, but only by some, which is related to the goals of their study, with the context of the scientific theory within which these subjects are studied.
Definitions, meanings of the word in other dictionaries:
Philosophical Dictionary
The relationship between objects (real or abstract), which allows us to speak of them as indistinguishable from each other, in some set of characteristics (eg, properties). In reality, all objects (things) usually differ from each other by us in some ...
What is Identity? Meaning and interpretation of the word tozhdestvo, definition of the term
1) Identity- - the relationship between objects (real or abstract), which allows us to speak of them as indistinguishable from each other, in some set of characteristics (for example, properties). In reality, all objects (things) usually differ from each other according to some characteristics. This does not exclude the fact that they also have common characteristics. In the process of cognition, we identify separate things in their general characteristics, combine them into sets according to these characteristics, form concepts about them on the basis of the abstraction of identification (see: Abstraction). Objects that are combined into sets according to some properties common to them cease to differ from each other, since in the process of such association we abstract from their differences. In other words, they become indistinguishable, identical in these properties. If all the characteristics of two objects a and b turned out to be identical, the objects would turn into the same object. But this does not happen, because in the process of cognition we identify objects that are different from each other not according to all characteristics, but only according to some. Without the establishment of identities and differences between objects, no knowledge of the world around us, no orientation in the environment around us is possible. For the first time, in the most general and idealized formulation, the concept of t. of two objects was given by G. V. Leibniz. Leibniz's law can be stated as follows: "x = y if and only if x has every property that y has and y has every property that x has." In other words, an object x can be identified with an object y when absolutely all of their properties are the same. The concept of T. is widely used in various sciences: in mathematics, logic, and natural science. However, in all cases of its application, the identity of the subjects under study is determined not by absolutely all general characteristics, but only by some, which is related to the goals of their study, with the context of the scientific theory within which these subjects are studied.
2) Identity- a philosophical category expressing: a) equality, the sameness of an object, phenomenon with itself or the equality of several objects (abstract identity); b) the unity of similarity and dissimilarity, identity (in the first sense) and difference, due to the change, development of the subject (concrete identity). Both types of identity in the process of cognition are mutually connected and pass into each other: the first of them expresses the moment of stability, the second - variability.
3) Identity- - coincidence, suggesting numerical unity.
4) Identity- - see Identity.
5) Identity- - a category expressing equality, the sameness of an object, a phenomenon with itself, or the equality of several objects. Objects A and B are said to be identical, the same, indistinguishable if and only if all properties (and relations) that characterize A characterize B as well, and vice versa (Leibniz's law). However, since the material reality is constantly changing, objects that are absolutely identical to themselves, even in their essential, fundamentals. properties does not exist. T. is not abstract, but concrete, that is, containing internal differences, contradictions, constantly “removing” itself in the process of development, depending on these conditions. The very identification of individual objects requires their preliminary distinction from other objects; on the other hand, it is often necessary to identify various objects (for example, in order to create their classifications). This means that T. is inextricably linked with difference and is relative. Every change of things is temporary, transitory, while their development and change is absolute. In mathematics, where we operate with abstractions (numbers, figures) considered outside of time, outside of their measurement, Leibniz's law operates without special restrictions. In the exact experimental sciences, on the other hand, the abstract, i.e., abstraction from the development of things, is used with limitations, and then only because in the process of cognition we resort, under certain conditions, to idealization and simplification of reality. The logical identity law is formulated with similar restrictions.
Identity
The relationship between objects (real or abstract), which allows us to speak of them as indistinguishable from each other, in some set of characteristics (eg, properties). In reality, all objects (things) usually differ from each other according to some characteristics. This does not exclude the fact that they also have common characteristics. In the process of cognition, we identify separate things in their general characteristics, combine them into sets according to these characteristics, form concepts about them on the basis of the abstraction of identification (see: Abstraction). Objects that are combined into sets according to some properties common to them cease to differ from each other, since in the process of such association we abstract from their differences. In other words, they become indistinguishable, identical in these properties. If all the characteristics of two objects a and b turned out to be identical, the objects would turn into the same object. But this does not happen, because in the process of cognition we identify objects that are different from each other not according to all characteristics, but only according to some. Without the establishment of identities and differences between objects, no knowledge of the world around us, no orientation in the environment around us is possible. For the first time, in the most general and idealized formulation, the concept of t. of two objects was given by G. V. Leibniz. Leibniz's law can be stated as follows: "x = y if and only if x has every property that y has and y has every property that x has." In other words, an object x can be identified with an object y when absolutely all of their properties are the same. The concept of T. is widely used in various sciences: in mathematics, logic, and natural science. However, in all cases of its application, the identity of the subjects under study is determined not by absolutely all general characteristics, but only by some, which is related to the goals of their study, with the context of the scientific theory within which these subjects are studied.
a philosophical category expressing: a) equality, the sameness of an object, phenomenon with itself or the equality of several objects (abstract identity); b) the unity of similarity and dissimilarity, identity (in the first sense) and difference, due to the change, development of the subject (concrete identity). Both types of identity in the process of cognition are mutually connected and pass into each other: the first of them expresses the moment of stability, the second - variability.
Coincidence suggesting numerical unity.
See Identity.
A category that expresses equality, the sameness of an object, a phenomenon with itself, or the equality of several objects. Objects A and B are said to be identical, the same, indistinguishable if and only if all properties (and relations) that characterize A characterize B as well, and vice versa (Leibniz's law). However, since the material reality is constantly changing, objects that are absolutely identical to themselves, even in their essential, fundamentals. properties does not exist. T. is not abstract, but concrete, that is, containing internal differences, contradictions, constantly “removing” itself in the process of development, depending on these conditions. The very identification of individual objects requires their preliminary distinction from other objects; on the other hand, it is often necessary to identify various objects (for example, in order to create their classifications). This means that T. is inextricably linked with difference and is relative. Every change of things is temporary, transitory, while their development and change is absolute. In mathematics, where we operate with abstractions (numbers, figures) considered outside of time, outside of their measurement, Leibniz's law operates without special restrictions. In the exact experimental sciences, on the other hand, the abstract, i.e., abstraction from the development of things, is used with limitations, and then only because in the process of cognition we resort, under certain conditions, to idealization and simplification of reality. The logical identity law is formulated with similar restrictions.
