identity

i·den·ti·ty

I0020300 (ī-dĕn′tĭ-tē)n. pl. i·den·ti·ties 1. a. The condition of being a certain person or thing: What is the identity of the author of the manuscript?b. The set of characteristics by which a person or thing is definitively recognizable or known: "The identity of the nation had ... been keenly contested in the period of nationalist opposition to Imperial rule" (Judith M. Brown).c. The awareness that an individual or group has of being a distinct, persisting entity: "He felt more at home thousands of miles from Britain than he did in an English village four miles from his home ... Was he losing his identity?" (Robert Fallon).2. a. The fact or condition of being the same as something else: The identity of the two handwriting samples was established by an expert.b. The fact or condition of being associated or affiliated with something else: the identity between mass and energy.3. Information, such as an identification number, used to establish or prove a person's individuality, as in providing access to a credit account.4. Mathematics a. An equation that is satisfied by any number that replaces the letter for which the equation is defined.b. Identity element.

[French identité, from Old French identite, from Late Latin identitās, from Latin idem, the same (influenced by Late Latin essentitās, being, identidem, repeatedly), from id, it; see i- in Indo-European roots.]

identity

(aɪˈdɛntɪtɪ) n, pl -ties1. the state of having unique identifying characteristics held by no other person or thing2. the individual characteristics by which a person or thing is recognized3. Also called: numerical identity the property of being one and the same individual: his loss of memory did not affect his identity. 4. Also called: qualitative identity the state of being the same in nature, quality, etc: they were linked by the identity of their tastes. 5. the state of being the same as a person or thing described or claimed: the identity of the stolen goods has not yet been established. 6. identification of oneself as: moving to London destroyed his Welsh identity. 7. (Logic) logic a. that relation that holds only between any entity and itselfb. an assertion that that relation holds, as Cicero is Tully8. (Mathematics) maths a. an equation that is valid for all values of its variables, as in (x – y)(x + y) = x² – y². Often denoted by the symbol ≡b. Also called: identity element a member of a set that when operating on another member, x, produces that member x: the identity for multiplication of numbers is 1 since x.1 = 1.x = x. See also inverse^2b9. informal Austral and NZ a well-known person, esp in a specified locality; figure (esp in the phrase an old identity)[C16: from Late Latin identitās, from Latin idem the same]

i•den•ti•ty

(aɪˈdɛn tɪ ti, ɪˈdɛn-)

n., pl. -ties. 1. the state or fact of remaining the same one, as under varying aspects or conditions. 2. the condition of being oneself or itself, and not another: He doubted his own identity. 3. condition or character as to who a person or what a thing is: a case of mistaken identity. 4. the state or fact of being the same one as described. 5. the sense of self, providing sameness and continuity in personality over time. 6. exact likeness in nature or qualities: an identity of interests. 7. an instance or point of sameness or likeness. 8. Logic. an assertion that two terms refer to the same thing. 9. Math. a. an equation that is valid for all values of its variables. b. Also called iden′tity el`ement. an element in a set such that the element operating on any other element of the set leaves the second element unchanged. [1560–70; < Late Latin identitās= Latin ident(idem) repeatedly, again and again (earlier *idem et idem) + -itās -ity]

Thesaurus

Noun	1.	identity - the distinct personality of an individual regarded as a persisting entity; "you can lose your identity when you join the army"personal identity, individualitypersonality - the complex of all the attributes--behavioral, temperamental, emotional and mental--that characterize a unique individual; "their different reactions reflected their very different personalities"; "it is his nature to help others"gender identity - your identity as it is experienced with regard to your individuality as male or female; awareness normally begin in infancy and is reinforced during adolescenceidentification - the attribution to yourself (consciously or unconsciously) of the characteristics of another person (or group of persons)personhood - being a person; "finding her own personhood as a campus activist"
	2.	identity - the individual characteristics by which a thing or person is recognized or known; "geneticists only recently discovered the identity of the gene that causes it"; "it was too dark to determine his identity"; "she guessed the identity of his lover"recognition, identification - the process of recognizing something or someone by remembering; "a politician whose recall of names was as remarkable as his recognition of faces"; "experimental psychologists measure the elapsed time from the onset of the stimulus to its recognition by the observer"
	3.	identity - an operator that leaves unchanged the element on which it operates; "the identity under numerical multiplication is 1"identity element, identity operatoroperator - (mathematics) a symbol or function representing a mathematical operation
	4.	identity - exact sameness; "they shared an identity of interests"identicalness, indistinguishabilitysameness - the quality of being alike; "sameness of purpose kept them together"oneness, unity - the quality of being united into oneselfsameness - the quality of being identical with itself

identity

noun1. name, details, specification The police soon established his true identity.2. individuality, self, character, personality, existence, distinction, originality, peculiarity, uniqueness, oneness, singularity, separateness, distinctiveness, selfhood, particularity I wanted a sense of my own identity.

identity

noun1. The set of behavioral or personal characteristics by which an individual is recognizable:individualism, individuality, selfhood.2. The quality or condition of being exactly the same as something else:identicalness, oneness, sameness, selfsameness.

Translations

身份

identity

(aiˈdentəti) noun who or what a person is. The police are still uncertain of the murderer's identity.身份iˈdentity card a card with a person's name (often also with a photograph) which is carried to show or prove who he/she is. 身份证

identity

→ 身份zhCN

identity

identity,

in philosophy, problem of distinguishing sameness from change, or unity from diversity; primarily examined in connection with personal identity, universals, and the law of identity in logic. In personal identity the concern has been to determine whether anything in the body or mind remains constant; philosophers have reached no general agreement on this point. The term identity has also become increasingly important in modern psychology, largely through the work of Erik Erikson. He has used the term to designate a sense of self that develops in the course of a man's life and that both relates him to and sets him apart from his social milieu. The terms "identity crisis" and "identity confusion," introduced by Erikson, have gained a wide usage, which often varies from their intended technical sense.

identity

the sense, and continuity, of SELF that develops first as the child differentiates from parents and family and takes a place in society.

The NEO-FREUDIAN theorist. Erik Erikson, has proposed that there is a crisis of identity in adolescence. It is at this stage of development that a young person searches for an identity, trying out different friendship groups, different lifestyles, different career plans. Ideally, by the end of adolescence the identity has stabilized and the young person accepts him/herself, feeling at ease with this identity.

In Erikson's view, therefore, identity forms as a result of social interaction, and problems with identity occur if the adolescent feels alienated from society through, for example, ethnic differences or unemployment. See also IDENTIFICATION.

There are broad similarities but some differences in the emphasis on identity and the process of identity formation in sociology compared with psychology (see MEAD, COOLEY). see also SOCIAL IDENTITY.

In some versions of psychoanalytic theory, especially the poststructuralism of LACAN, identity is altogether more problematic. Lacan challenges the central presupposition involved in the question ‘Who am I?’, the assumption that there exists a Cartesian self. Instead ‘identity’ involves a dependence on a dialectic of self and others. While such a dialectic is, of course relatively commonplace in sociology, Lacan's formulation is distinguished by the far greater radicalism of its implications for identity There is no PRESENCE, only language, and the lack of an identifiable core ‘self, according to Lacan, can only be repaired by an ‘imagined self, a ‘phantasy’ in which identity is only preserved by DEFENCE MECHANISMS such as ‘denial’.

Identity

The abstract counterpart of unity is the co-called identity (or identity element). Specifically, let the symbol * denote a (binary) operation on some set S. An element e in S is called an identity relative to the operation * if a*e = e*a =a. If * is a noncommutative operation, that is, if there are elements a and b such that a*b ≠ b*a, then we define a right identity to be an element e_r such that a*e_r for all a in S and a left identity to be an element e_r such that e_l*a = a for all a in S. If more than one operation is defined on the set S, then we speak of identities relative to the individual operations (for example, In the case of multiplication we speak of a multiplicative identity and in the case of addition of an additive identity).

Identity

a fundamental concept in logic, philosophy, and mathematics; it is used in the language of scientific theories to formulate definitions, laws, and theorems.

In mathematics, an identity is an equation that is satisfied identically—that is, an equation that holds true—for all admissible values of its variables. In logic, identity is a predicate that is represented by the formula x = y (to be read as “x is identical to y, ” or “x is the same as y”); the predicate’s corresponding logical function is true when the variables x and y denote different occurrences of “one and the same” object, and false in the opposite case. In philosophy, or epistemology, identity is a relationship based on ideas or judgments about the meaning of what it is to be “one and the same” object of reality, perception, or thought.

The logical and philosophical aspects of identity are complementary: the former provides a formal model of the concept of identity, while the latter provides grounds for the model’s application. The first aspect includes the concept of “one and the same” object, but the formal model does not depend for its meaning on the content of this concept; the method of identification is ignored, as is the dependence of the results of identification on the conditions or methods of identification and on the abstractions that are explicitly or implicitly assumed in the given case. In the second, or philosophical, aspect, applications of logical models of identity are considered in relation to the methods and tests by which objects are identified; such considerations, in effect, depend on the point of view, conditions, and means of identification.

The distinction between the logical and philosophical aspects of identity goes back to the well-known statement that identity as a concept is not one and the same as a judgment about the identity of objects (see Plato, Soch., vol. 2, Moscow, 1970, p. 36). It is essential, however, to emphasize the independence of and lack of contradiction between these two aspects. The meaning of the concept of identity is settled by its corresponding logical function; the concept is not deduced or extracted from the actual identity of objects, but rather it is an abstraction achieved under “suitable” experiential conditions or, in theory, by means of assumptions, or hypotheses, about actually allowable identifications. At the same time, in the case of a substitution carried out, as in axiom (4) below, in an appropriate domain of abstraction of identification, “within” this domain the actual identity of objects precisely coincides with identity in the logical sense.

Because of the importance of the concept of identity, the need arose for specific theories of identity. The method most commonly used in constructing these theories is the axiomatic method. For example, all or some of the following axioms may be applicable:

(1) x = x

(2) x = y ⊃ y = x

(3) x = y & y = z ⊃ x = z

(4) A(x)⊃(x = y ⊃ A(y))

Here A(x) is an arbitrary predicate containing x free and free for v, while A(x) and A(y) differ only in their occurrences (even if only one) of x and y.

Axiom (1) postulates reflexivity as a property of identity. In traditional logic, reflexivity was considered the only logical law of identity—a law to which axioms (2) and (3) were customarily added as “nonlogical postulates” (in arithmetic, algebra, and geometry). Axiom (1) may be regarded as epistemologically justified, inasmuch as it is sui generis a logical expression of individuation. It is such individuation, in turn, that forms the basis for the experiential “givenness” of objects, or makes it possible for objects to be recognized: in order to speak of an object as of a given, it is necessary to isolate it in some fashion, to distinguish it from other objects, and to maintain this distinction at all times. In this sense identity, based on axiom (1), is the particular relation of “self-identity” in which each object is bound only to itself, and not to any other object.

Axiom (2) postulates symmetry as a property of identity. According to this axiom, the result of any identification is independent of the order in pairs of objects being identified. This axiom is also justified to some extent by experience. For example, when a weight and a piece of goods are placed on weighing scales, their respective position—on the left or on the right—is different for the customer and the salesperson facing each other, but the result—in this case, equal weight—is the same for both.

Axioms (1) and (2) jointly are an abstract expression of the principle of the identity of indiscernibles—a theory in which the notion of “one and the same” object is based on the factual non-observability of differences. Essentially, this theory depends on the criteria of differentiation—the means, or instruments, that distinguish one object from another; it depends, in the final analysis, on the abstraction of indiscernibility. Inasmuch as there is an inherent dependence in practice on the “threshold of differentiation, ” the notion of identity that is satisfied by axioms (1) and (2) is the only natural result that can be obtained in any test.

Axiom (3) postulates the transitiveness of identity. It states that the composition of the identity relation with itself is again the identity relation, and it is the first nontrivial assertion concerning the identity of objects. The transitiveness of identity is either an “idealization of experience” under conditions of “decreasing accuracy” or an abstraction that expands upon experience and “creates” a new meaning of identity, other than indiscernibility. Indiscernibility is guaranteed by identity only in the domain of abstraction of indiscernibility, whereas the latter is not linked to fulfillment of axiom (3). Axioms (1), (2), and (3) jointly are an abstract expression of the theory of identity as an equivalence.

Axiom (4) postulates as a necessary condition for the identity of objects that their properties coincide. From a logical point of view, this axiom is self-evident: all the properties of an object belong to “one and the same” object. This axiom, however, is not a trivial one, inasmuch as the idea of “one and the same” object must inevitably rest on assumptions or abstractions of a particular kind. It is impossible to verify this axiom “in general”—that is, for all conceivable properties; it can only be verified in certain fixed domains of the abstractions of identification or indiscernibility. This is precisely the way in which this axiom is used in practice: objects are compared and identified not with respect to all conceivable properties, but only with respect to the fundamental (primitive) properties of a theory in which one wants to have the notion of “one and the same” object based upon these properties and on axiom (4). In such instances the scheme of axiom (4) is replaced by a finite list of “intensional” axioms of identity of the same form. For example, the Zermelo-Fraenkel axiomatic set theory substitutes the axioms

(4.1) z ∊ x ⊃ (x = y ⊃ z ∊ y)

(4.2) x ∊ z ⊃ (x = y ⊃ y ∊ z)

Assuming that the universe contains only sets, these axioms determine the domain of abstraction in the identification of sets by “the sets that belong to them” and by “the sets to which they belong, ” with the mandatory addition of axioms 1–3, determining identity as equivalence.

Axioms 1–4 belong to the category of the laws of identity. By means of the rules of logic, one can deduce from them many other laws, unknown in premathematical logic. The difference between the logical and epistemological, or philosophical, aspects of identity is not important in the context of general or abstract formulations of the laws of identity. The difference, however, is substantive when these laws are used to describe real states. In defining the concept of “one and the same” object, the axiomatics of identity necessarily influence the formation of the universe “within” the corresponding axiomatic theory.

REFERENCES

Tarski, A. Vvedenie v logiku i metodologüu deduktivnykh nauk. Moscow, 1948. (Translated from English.)
Novoselov, M. “Tozhdestvo.” In Filosofskaia entsiklopediia, vol. 5. Moscow, 1970.
Novoselov, M. “O nekotorykh poniatiiakh teorii otnoshenii.” In Kibernetika i sovremennoe nauchnoepoznanie. Moscow, 1976.
Shreider, Iu. A. Ravenstvo, skhodstvo, poriadok. Moscow, 1971.
Kleene, S. C. Matematicheskaia logika. Moscow, 1973. (Translated from English.)
Frege, G. Schriften zur Logik. Berlin, 1973.

M. M. NOVOSELOV

identity

[ī′den·ə‚dē] (mathematics) An equation satisfied for all possible choices of values for the variables involved. identity element

identity

1. Logica. that relation that holds only between any entity and itself b. an assertion that that relation holds, as Cicero is Tully 2. Mathsa. an equation that is valid for all values of its variables, as in (x -- y)(x + y) = x² -- y². Often denoted by the symbol ≡ b. a member of a set that when operating on another member, x, produces that member x: the identity for multiplication of numbers is 1 since x.1 = 1.x = x

identity

i·den·ti·ty

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i•den•ti•ty

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a case of mistaken identity

identity politics

case of mistaken identity

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REFERENCES

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i·den·ti·ty

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Synonyms for identity

noun name

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noun individuality

Synonyms

Synonyms for identity

noun the set of behavioral or personal characteristics by which an individual is recognizable

Synonyms

noun the quality or condition of being exactly the same as something else

Synonyms

Synonyms for identity

noun the distinct personality of an individual regarded as a persisting entity

Synonyms

Related Words

noun the individual characteristics by which a thing or person is recognized or known

Related Words

noun an operator that leaves unchanged the element on which it operates

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Related Words

noun exact sameness

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