quantifiern.

Brit.

/ˈkwɒntᵻfʌɪə/, U.S.

/ˈkwɑn(t)əˌfaɪər/

Origin: Formed within English, by derivation. Etymons: quantify v., -er suffix¹.

Etymology: < quantify v. + -er suffix¹.In quot. 1876 at sense 2 after quantification n. (compare quantification n. 1).

1. Something by means of which quantification is effected.

a. Logic. An expression (such as ‘(for) all’, ‘any’, ‘(for) some’, ‘there exists a‘, ‘most’) that indicates the scope of the term, variable, or proposition to which it is attached; a mathematical symbol for such an expression.existential, universal quantifier: see the first element.

ΘΚΠ

the mind > mental capacity > philosophy > logic > predicate or propositional logic > [noun] > quantification > elements of

quantifier1864

universal quantifier1931

existential quantifier1933

1864 A. De Morgan in Trans. Cambr. Philos. Soc. 10 471 We are to take in both all and some-not-all as quantifiers: that is, ‘some affirmed to be all’, and ‘some denied to be all’.

1885 C. S. Peirce in Amer. Jrnl. Math. 7 197 If the quantifying part, or Quantifier, contains Σ_x, and we wish to replace the x by a new index i, not already in the Quantifier, and such that every x is an i, we can do so at once by simply multiplying every letter of the Boolian having x as an index by x_i.

1926 Ann. Math. 28 17 A proposition which involves a change from ‘some’ to ‘every’ or from ‘every’ to ‘some’ in the quantifier, will be said to be doubly-quantified.

1956 A. Church Introd. Math. Logic 41 As the universal quantifier (when, e.g., the operator variable is x) we use the notation (∀ x) or (x)..(x)_ is true if the value of _ is truth for all values of x.

1965 B. Mates Elem. Logic x. 159 A string of universal quantifiers containing n quantifier-occurrences.

2005 Bull. Symbolic Logic 11 28 A universal theory has a model completion if and only if it first has a model companion, and second, the model companion eliminates quantifiers.

b. Linguistics. A word (usually a determiner or pronoun) or phrase expressive of quantity.

ΘΚΠ

the mind > language > linguistics > study of grammar > a part of speech > determiner > [noun] > quantifier

quantifier1924

quantitative1924

1924 O. Jespersen Philos. Gram. vi. 85 All these quantifiers, as they might be called, differ from ordinary qualifying adjectives in being capable of standing alone..as when we say ‘some (many, all, both, two) were absent’.

1933 O. Jespersen Essent. Eng. Gram. vii. 67 Little is sometimes a qualifier (a little girl), sometimes a quantifier (a little bread).

1951 S. F. Nadel Found. Social Anthropol. 43 Thus I am not considering the ‘formal’ parts of language (conjunctions, prepositions, ‘quantifiers’, etc.).

1972 J. J. Lamberts Short Introd. Eng. Usage vii. 137 These are generally taken as plural unless a ‘quantifier’ like a pair of precedes the noun.

1980 Linguistics & Philos. 4 162 ‘Most’ must be treated as a determiner, not as a quantifier. It is the NP ‘most people’ that is the quantifier.

2000 Internat. Jrnl. Amer. Linguistics 66 326 Teotongo, Tulancingo and Natívitas speakers specify plurality by adding the uninflected quantifier kie¹ ‘all’ to the singular pronouns.

2. A person who quantifies something; a person who adopts or favours quantitative methods.In quot. 1876: a person who applies the method of quantification of the predicate (see quantification n. 1).

ΘΚΠ

the world > relative properties > measurement > [noun] > a measurer

meter1336

measurer1552

metster1582

rater1823

quantifier1941

1876 Mind 1 213 Quantifiers of the predicate insert the word some, and Boole uses a special symbol V, to mark the partial character of the identity.

1941 Sociometry 4 52 That he reduced his observations to lines and numbers should satisfy the quantifiers that he is dully empirical.

1970 Computers & Humanities 5 1 ‘Quantifiers’ assemble in conferences, workshops and symposia to thrash out common problems and share research methods and findings.

1992 Australian 5 Feb. (Brisbane ed.) 16/5 [He] describes himself as, among other things, a great quantifier. ‘I retired almost a year ago after 3025 days in the job—eight years, three months and 11 days.’

Compounds

quantifier-free adj. Logic that does not use or involve quantifiers.

ΚΠ

1948 Jrnl. Symbolic Logic 13 185 F* is the associated quantifier-free formula of F.

1963 O. Wojtasiewicz tr. J. Łukasiewicz Elem. Math. Logic 95 Detachment..is the same as in the quantifier-free sentential calculus.

2004 Bull. Symbolic Logic 10 376 The system has axioms ϕ, Γ where ϕ is a true quantifier-free formula.

This entry has been updated (OED Third Edition, December 2007; most recently modified version published online March 2022).

单词	quantifier
释义	quantifiern. Brit. /ˈkwɒntᵻfʌɪə/, U.S. /ˈkwɑn(t)əˌfaɪər/ Origin: Formed within English, by derivation. Etymons: quantify v., -er suffix¹. Etymology: < quantify v. + -er suffix¹.In quot. 1876 at sense 2 after quantification n. (compare quantification n. 1). 1. Something by means of which quantification is effected. a. Logic. An expression (such as ‘(for) all’, ‘any’, ‘(for) some’, ‘there exists a‘, ‘most’) that indicates the scope of the term, variable, or proposition to which it is attached; a mathematical symbol for such an expression.existential, universal quantifier: see the first element. ΘΚΠ the mind > mental capacity > philosophy > logic > predicate or propositional logic > [noun] > quantification > elements of quantifier1864 universal quantifier1931 existential quantifier1933 1864 A. De Morgan in Trans. Cambr. Philos. Soc. 10 471 We are to take in both all and some-not-all as quantifiers: that is, ‘some affirmed to be all’, and ‘some denied to be all’. 1885 C. S. Peirce in Amer. Jrnl. Math. 7 197 If the quantifying part, or Quantifier, contains Σ_x, and we wish to replace the x by a new index i, not already in the Quantifier, and such that every x is an i, we can do so at once by simply multiplying every letter of the Boolian having x as an index by x_i. 1926 Ann. Math. 28 17 A proposition which involves a change from ‘some’ to ‘every’ or from ‘every’ to ‘some’ in the quantifier, will be said to be doubly-quantified. 1956 A. Church Introd. Math. Logic 41 As the universal quantifier (when, e.g., the operator variable is x) we use the notation (∀ x) or (x)..(x)_ is true if the value of _ is truth for all values of x. 1965 B. Mates Elem. Logic x. 159 A string of universal quantifiers containing n quantifier-occurrences. 2005 Bull. Symbolic Logic 11 28 A universal theory has a model completion if and only if it first has a model companion, and second, the model companion eliminates quantifiers. b. Linguistics. A word (usually a determiner or pronoun) or phrase expressive of quantity. ΘΚΠ the mind > language > linguistics > study of grammar > a part of speech > determiner > [noun] > quantifier quantifier1924 quantitative1924 1924 O. Jespersen Philos. Gram. vi. 85 All these quantifiers, as they might be called, differ from ordinary qualifying adjectives in being capable of standing alone..as when we say ‘some (many, all, both, two) were absent’. 1933 O. Jespersen Essent. Eng. Gram. vii. 67 Little is sometimes a qualifier (a little girl), sometimes a quantifier (a little bread). 1951 S. F. Nadel Found. Social Anthropol. 43 Thus I am not considering the ‘formal’ parts of language (conjunctions, prepositions, ‘quantifiers’, etc.). 1972 J. J. Lamberts Short Introd. Eng. Usage vii. 137 These are generally taken as plural unless a ‘quantifier’ like a pair of precedes the noun. 1980 Linguistics & Philos. 4 162 ‘Most’ must be treated as a determiner, not as a quantifier. It is the NP ‘most people’ that is the quantifier. 2000 Internat. Jrnl. Amer. Linguistics 66 326 Teotongo, Tulancingo and Natívitas speakers specify plurality by adding the uninflected quantifier kie¹ ‘all’ to the singular pronouns. 2. A person who quantifies something; a person who adopts or favours quantitative methods.In quot. 1876: a person who applies the method of quantification of the predicate (see quantification n. 1). ΘΚΠ the world > relative properties > measurement > [noun] > a measurer meter1336 measurer1552 metster1582 rater1823 quantifier1941 1876 Mind 1 213 Quantifiers of the predicate insert the word some, and Boole uses a special symbol V, to mark the partial character of the identity. 1941 Sociometry 4 52 That he reduced his observations to lines and numbers should satisfy the quantifiers that he is dully empirical. 1970 Computers & Humanities 5 1 ‘Quantifiers’ assemble in conferences, workshops and symposia to thrash out common problems and share research methods and findings. 1992 Australian 5 Feb. (Brisbane ed.) 16/5 [He] describes himself as, among other things, a great quantifier. ‘I retired almost a year ago after 3025 days in the job—eight years, three months and 11 days.’ Compounds quantifier-free adj. Logic that does not use or involve quantifiers. ΚΠ 1948 Jrnl. Symbolic Logic 13 185 F* is the associated quantifier-free formula of F. 1963 O. Wojtasiewicz tr. J. Łukasiewicz Elem. Math. Logic 95 Detachment..is the same as in the quantifier-free sentential calculus. 2004 Bull. Symbolic Logic 10 376 The system has axioms ϕ, Γ where ϕ is a true quantifier-free formula. This entry has been updated (OED Third Edition, December 2007; most recently modified version published online March 2022). < n.1864
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