From the second edition (1989):
(aɪˈdɛntɪtɪ) Also 6 idemptitie. [ad. F. identité (Oresme, 14th c.), ad. late L. identitās (Martianus Capella, c425), peculiarly formed from ident(i)-, for L. idem ‘same’ + -tās, -tātem: see -ty.
Various suggestions have been offered as to the formation. Need was evidently felt of a noun of condition or quality from idem to express the notion of ‘sameness’, side by side with those of ‘likeness’ and ‘oneness’ expressed by similitās and ūnitās: hence the form of the suffix. But idem had no combining stem. Some have thought that ident(i)- was taken from the L. adv. identidem ‘over and over again, repeatedly’, connexion with which appears to be suggested by Du Cange's explanation of identitās as ‘quævis actio repetita’. Meyer-Lübke suggests that in the formation there was present some association between idem and id ens ‘that being’, whence identitās like entitās. But assimilation to entitās may have been merely to avoid the solecism of *idemitās or *idemtās. However originated, ident(i)- became the combining stem of idem, and the series ūnitās, ūnicus, ūnificus, ūnificāre, was paralleled by identitās, identicus, identificus, identificāre: see identic, identific, identify above.]

1. a. The quality or condition of being the same in substance, composition, nature, properties, or in particular qualities under consideration; absolute or essential sameness; oneness.
absolute identity, that asserted in the metaphysical doctrine of Schelling that mind and matter are phenomenal modifications of the same substance.

1570 Billingsley Euclid v. def. iv. 129 This likenes, idemptitie, or equallitie of proportion is called proportionallitie. 1603 Holland Plutarch's Mor. 65 That the soule of this universall world, is not simple, uniforme and uncompounded, but mixed‥of a certaine power of Identitie and of Diversity. 1654 Z. Coke Logick (1657) 88 Causall Identity is of them which agree in the causes. Ibid., Accidentall Identity is of them that agree in Accidents. 1669 Gale Crt. Gentiles i. i. iii. 21 That the Phenicians were originally Canaanites, is manifest from the Identitie of their Languages. 1751 Harris Hermes Wks. (1841) 233 Is it not marvellous, there should be so exact an identity of our ideas? 1839 Murchison Silur. Syst. i. xxxv. 474 The organic remains are of great interest in establishing the geological identity between the coal measures of the Dudley district and those of distant parts of Great Britain. 1855 H. Spencer Princ. Psychol. (1872) II. vi. vi. 59 Resemblance when it exists in the highest degree of all‥is often called identity. 1863 Fawcett Pol. Econ. ii. ix. 265 There is no identity of interests between the employers and employed. 1876 Tait Rec. Adv. Phys. Sc. viii. (ed. 2) 203 The identity of radiant light and heat. 1879 Froude Cæsar xviii. 298 United‥by identity of conviction.

b. with an and pl. An instance of this quality.

1664 H. More Myst. Iniq. 264 How fully assured must we needs be of these Identities, the Agreements of these two Parallelisms. 1775 Harris Philos. Arrangem. Wks. (1841) 309 It is by a contrary power of composition that we recognise their identities. 1861 Wright Ess. Archæol. I. vi. 91 The taking of resemblances of words for identities is one of the great stumbling-blocks of the philologist.

c. Recurrence of the same; repetition. Obs.

1611 Bible Transl. Pref. 11 Wee haue not tyed our selues to an vniformitie of phrasing, or to an identitie of words. a1619 M. Fotherby Atheom. ii. xi. §6 (1622) 325 The soule is delighted with variety. It is dulled with identity.

2. a. The sameness of a person or thing at all times or in all circumstances; the condition or fact that a person or thing is itself and not something else; individuality, personality.
personal identity (in Psychology), the condition or fact of remaining the same person throughout the various phases of existence; continuity of the personality.

1638 Rawley tr. Bacon's Life & Death §5 The Duration of Bodies is Twofold; One in Identity, or the selfe-same Substance; the other by a Renovation or Reparation. 1690 Locke Hum. Und. ii. xxvii. §6 The Identity of the same Man consists‥in nothing but a participation of the same continued Life, by constantly fleeting Particles of Matter, in succession vitally united to the same organized Body. Ibid. §9 Consciousness always accompanies thinking,‥in this alone consists personal Identity, i.e. the Sameness of a rational Being. 1739 Hume Hum. Nat. i. v. (1874) I. 323 Of all relations the most universal is that of identity, being common to every being whose existence has any duration. 1820 W. Irving Sketch Bk. I. 85 He doubted his own identity, and whether he was himself or another man. 1832 G. Downes Lett. Cont. Countries I. 469 The fair city almost forfeits its identity, when disguised in a misty and murky atmosphere. 1885 ‘E. Garrett’ At Any Cost v. 89 Tom‥had such a curious feeling of having lost his identity, that he wanted to reassure himself by the sight of his little belongings.

b. Personal or individual existence. rare. ?Obs.

1683 Dryden Life Plutarch 31 [Plutarch] doubtless beleiv'd the identity of one supream intellectual being which we call God. 1824 Byron Juan xvi. cxx, How odd, a single hobgoblin's non-entity Should cause more fear than a whole host's identity.

3. ‘The self-same thing.’ Obs. rare.

1616 Bullokar, Identitie, the selfe same thing. a1619 M. Fotherby Atheom. ii. iii. §2 (1622) 216 Life is not the cause of its owne liuing, but the very same identity with its liuing.

4. Alg. a. The equality of two expressions for all values of the literal quantities: distinctively denoted by the sign ≡. b. An equation expressing identity, an identical equation (identical 4a).

1859 Barn. Smith Arith. & Algebra (ed. 6) 338 Such an expression as (x + 1)2 = x2 + 2x + 1, where one of the quantities, between which the sign of equality is placed, results from performing the operations indicated in the other, is called an Identity.

5. The condition of being identified in feeling, interest, etc. rare.

1868 Gladstone Juv. Mundi i. (1870) 5 He is in truth in visible identity with the age.

6. Logic. Law or Principle of Identity, the principle expressed in the identical proposition A is A. Also attrib., as identity formula, identity relation, identity sentence.

1846 Sir W. Hamilton Reid's Wks. 767 The four logical laws of Identity, Contradiction, Excluded Middle, and Reason and Consequent. 1851 Mansel Proleg. Log. (1860) 196 This law of thought is expressed by the Principle of Identity ‘Every A is A’. 1860 Abp. Thomson Laws Th. (ed. 5) §114. 212 Criteria of Truth. 2nd Criterium. The Principle of Identity. 1889 Fowler Induct. Logic Pref. (ed. 5) 19 note, Amongst the assumptions or pre-suppositions of reasoning, I have not included the so-called Law of Identity; as to say that all A is A, or a thing is the same as itself, appears to me to be an utterly unmeaning proposition. 1940 W. V. Quine Math. Logic 232 I is‥the identity relation x^y^ (x = y). 1965 B. Mates Elem. Logic ix. 146 It will be useful to introduce a couple of obvious conventions for writing identity-formulas. Ibid. 149 The identity relation among the elements of one domain will be different from that among the elements of another. Ibid., Thus every identity-sentence would be either trivial or absurd. 1967 Encycl. Philos. IV. 123/1 When we utter an identity sentence such as ‘Venus is the morning star’, what we wish to express‥is that the terms ‘Venus’ and ‘the morning star’ both mean the same thing. 1970 J. D. Carney Introd. Symbolic Logic vii. 160 The identity relation has some rather special properties.

7. (old) identity: a person long resident or well known in a place. N.Z. and Austral.

1862 Otago, Its Goldfields & Resources 9 The exclusive spirit of the ‘old identity’. 1874 A. Bathgate Colonial Experiences iii. 26 The term ‘old identities’ took its origin from an expression in a speech made by one of the members of the Provincial Council, Mr E. B. Cargill, who, in speaking of the new arrivals, said that the early settlers should endeavour to preserve their old identity.‥ A comic singer [R. Thatcher] helped to perpetuate the name by writing a song. 1879 W. J. Barry Up & Down xx. 197 The ‘old identities’ were beginning to be alive to the situation. 1889 Bulletin (Sydney) 28 Sept. 8/1 Many of the old identities of '52 and '53 will remember the license-hunting and shanty-raiding days. 1893 Auckland Weekly News 9 Dec. 7 Both these old identities are in possession of all their faculties to a wonderful degree. Ibid. 28 Another old identity passed away on Dec. 1 in the person of Mr. Thomas Hunt. 1929 ‘M. B. Eldershaw’ House Is Built (1945) v. 111 He was the sort of man who becomes an old identity almost at once, so that the residents of the Parramatta Road‥soon thought they had been seeing him drive past in his indescribably sailorly fashion all their lives. 1942 ‘M. Innes’ Daffodil Affair ii. ii. 46 Ron's dad was a well-known identity Cobdogla-way. 1944 Mod. Jun. Dict. (Whitcombe & Tombs) 205 In Australia and New Zealand a very old resident in a place is called an ‘old identity’. 1962 J. R. Bernard in Southerly XXII. ii. 97 We [Australians] add to‥identity that of outstanding local citizen. 1970 N.Z. Woman's Weekly 9 Nov. 19/1 Havelock North identity Mrs C. E. Turner-Williams‥at 98 stitches happily on.

8. Math. a. An element of a set which, if combined with any element by a (specified) binary operation, leaves the latter element unchanged.

1894 Bull. Amer. Math. Soc. I. 61 Given an (abstract) group Gn‥with elements s1 = identity, s2, sn. 1937 R. D. Carmichael Introd. Theory Groups of Finite Order xiii. 395 For every a we have ai = a = ia. Then we call i an identity with respect to the rule of combination of the group. Ibid. i. 17 Since the identity plays the role of unity in multiplication, it is often denoted by the symbol 1. 1941 Birkhoff & MacLane Surv. Mod. Algebra i. 2 The number zero has the characteristic property that it leaves unaltered any number to which it is added; hence we say that zero is an ‘identity element’ for addition. By formal analogy, the ‘unity’ 1 is an identity for multiplication. 1966 Meyer & Hanlon Fun with New Math i. 12 The number one is the multiplicative identity, for the product of it and any other number leaves the second number unchanged. 1971 E. C. Dade in Powell & Higman Finite Simple Groups viii. 254 The associativity in G easily implies that of multiplication in FG, and the identity 1G of G is also the identity for FG.

b. A transformation that gives rise to the same elements as those to which it is applied.

1910 Veblen & Young Projective Geom. I. iii. 65 The correspondence which makes every element of the system correspond to itself is called the identical correspondence or simply the identity, and is denoted by the symbol 1. 1959 E. M. Patterson Topology (ed. 2) ii. 20 If AB, the transformation i: AB defined by i(a) = a is a one–one transformation called an inclusion; in particular, if A = B, the inclusion i: AA is called the identity. 1961 H. S. M. Coxeter Introd. Geom. ii. 29 If the product of two transformations is the identity, each is called the inverse of the other, and their product in the reverse order is again the identity.

9. S. Afr. (See quot. 1924.)

1924 E. H. Brookes Hist. Native Policy S. Afr. iii. 62 Most modern thinkers on the Native question argue as if there were no via media between the principle which refuses to acknowledge any real difference between Europeans and Natives, the policy of identity as we may call it,‥and the principle which insists on the subordinate position of the Native in the body politic, the policy of subordination. 1961 Listener 30 Nov. 898/2 These influences‥led in South Africa to the policy sometimes known as ‘identity’, of regarding all men as much the same. Ibid., The earlier British policy of identity broke down.

10. a. attrib. and Comb. with the meaning ‘that serves to identify the holder or wearer’, as identity bracelet, identity card, identity certificate, identity disc, identity papers, identity patch; also identity element Math. = identity 8a; identity matrix Math., a matrix in which all the elements of the principal diagonal are one and the remainder zero, so that its product with another matrix gives that matrix; identity parade = identification parade.

1968 J. Ironside Fashion Alphabet 167 Identity bracelet, a gold or silver chain with a flat space for the owner's name. 1973 G. Sims Hunters Point xiii. 124 On his wrists a gold watch and a gold identity bracelet. 1900 Westm. Gaz. 2 Jan. 3/1 When troops are going on service each man has issued to him what is known as a field dressing and an identity card. 1931 Times Lit. Suppl. 1 Jan. 2/2 He‥forged an identity card, and procured a pistol. 1940 Ann. Reg. 1939 101 Some 65,000 enumerators, who‥issued identity cards for all the persons mentioned in the forms. 1953 C. Day Lewis Italian Visit i. 14 The identity cards that inform us Not who we are or might be, but how we are interchangeable. 1961 Daily Mail 20 July 9/3 Millions of people may soon have to carry special medical identity cards.‥ A card‥would contain information about their illnesses‥any special drugs they were taking. 1972 Daily Tel. 23 Nov. 6 The BBC is to tighten up security at its London studios and offices by issuing identity cards to staff. 1918 Act 8 Geo. V c. 6 §11 Every person who receives, detains or has in his possession any identity certificate, life certificate, or other certificate. 1909 Daily Chron. 15 June 5/5 Rations for three days, ammunition, field bandages, and identity discs were issued to the men. 1911 Punch 15 Mar. 181/1 By the March Army Orders the identity discs issued to officers and men in war time are in future to be issued to the former in peace time. 1915 ‘I. Hay’ First Hundred Thousand vi, Its called an Identity Disc. Every soldier on active service wears one. 1919 J. B. Morton Barber of Putney i, In due course came vaccination and inoculation, and identity discs. 1956 R. St. B. Baker Dance of Trees vi. 79 When the top soil of Tel Fara was excavated we found modern spurs, identity discs, even a copy of the Tatler‥reminders of the days of Allenby. 1902 Trans. Amer. Math. Soc. III. 486 There exists a left-hand identity element, that is, an element il such that, for every element a, ila = a. 1966 May & Moss New Math for Adults Only vi. 33/2 Zero is the identity element in addition and one is the identity element in multiplication. 1941 Birkhoff & MacLane Surv. Mod. Algebra viii. 197 Corresponding to the identity transformation yi = xi is the n × n identity matrix I, which has entries 1 along the principal diagonal (upper left to lower right) and zeros elsewhere. 1908 Daily Chron. 21 Feb. 4/6 The ‘identity papers’, which every man and woman in Prussia must carry about with them. 1955 ‘A. Gilbert’ Is she Dead Too? viii. 141 Put a gorilla in a set of ginger reach-me-downs and you could put up the pair of 'em in an identity parade and no one could tell the difference. 1973 E. Lemarchand Let or Hindrance vii. 69 We may ask you to come along to an identity parade. 1959 M. Levin Eva 37 The Ukrainians didn't have to wear identity patches, since the Germans considered them allies.

b. Philos. attrib. and Comb. as identity doctrine, identity sign, identity thesis; identity theory, the materialist theory that physiological and mental perceptions are identical; hence identity theorist, a person professing belief in the identity theory.

1920 S. Alexander Space, Time & Deity II. 9 The statement‥is a species of the identity doctrine of mind and body, maintaining that there are not two processes, one neural, the other mental, but one. 1950 W. V. Quine Methods of Logic (1952) 211 It is the use of the identity sign between variables, rather than between singular terms, that is fundamental. 1965 Hughes & Londey Elem. Formal Logic xxxvii. 258 We need one further symbol, which is written ‘=’ and is known as the identity sign. 1951 G. Humphrey Thinking viii. 245 Inspired by the behaviourists one group of advocates of what may be called the ‘identity theory’ has stressed the importance of the so-called implicit speech movements which occur during thinking. 1966 Amer. Philos. Q. III. 227/2 Some philosophers‥infer that the Identity Theory is an empirical theory. Ibid. 233/2 Some Identity Theorists are anxious to eliminate mental properties. 1967 Encycl. Philos. V. 339/1 The identity theorist uses the familiar philosophical distinction between significance and reference‥to make the claim that mentalistic and physicalistic expressions‥will turn out as a matter of empirical fact to refer to or denote one and the same thing, namely physical phenomena. 1954 H. Feigl in P. A. Schilpp Philos. R. Carnap (1963) 259 The prima facie implausibility of the identity thesis arises‥mainly from the psychological incompatibility of images such as of nervous tissue‥with the qualities of some data of consciousness. 1967 Philos. Rev. LXXVI. 201 In recent years, a number of philosophers have argued in favor of materialism in the form of an identity thesis—that is, a thesis to the effect that mental events are identical with certain physiological events.

c. Belonging or relating to identity (sense 2), as in identity crisis, a phase of varying severity undergone by an individual in his need to establish his identity in relation to his associates and society as part of the process of maturing. Also transf.

1954 Jrnl. Amer. Psychoanal. Assoc. II. Apr. 327 George Bernard Shaw arranged for himself a psycho-social moratorium at the age of twenty when his identity crisis led him to leave‥his family, friends and familiar work. 1959 Listener 29 Oct. 746/2 The prolonged identity crisis of this great young man. 1965 Times Lit. Suppl. 25 Nov. 1078/4 A sympathetic study of ‘identity crisis’ might appear peculiarly relevant to many Americans. 1968 Internat. Encycl. Social Sci. VII. 63/2 An era's identity crisis is least severe in that segment of youth which is able to invest its fidelity in an expanding technology. 1971 R. A. Carter Manhattan Primitive (1972) xv. 137 Girl is on the verge of a breakdown, in deep identity crisis. 1971 M. McCarthy Birds of America 110 His college tutor, a stupid Freudian, had advised his mother that Peter had an ‘identity problem’. 1974 Times Lit. Suppl. 19 Apr. 409/1 A middle-aged cuckold with piles and an identity crisis.