quantifier
Informally, a quantifier is an expression that reports a quantity of times that a predicate is satisfied in some class of things (i.e. in a ‘domain’). Thus, thinking about a class of children and their diets, one might report that some eat cake, or that all eat cake, or that not all eat cake, or that none eat cake. ‘Some’ and ‘all’ are represented in modern logic by the quantifiers. The important point is that the treatment fends off thinking of ‘something’, ‘nothing’, and their kin as kinds of names.
In classical logic the two interdefinable quantifiers are the existential quantifier (∃x )… x, read as saying that something is…, and the universal quantifier (∀x )… x, read as saying that all things are…. Existential propositions, claiming that things of some kind exist, are represented by the existential quantifier. Less common quantifiers include the plurality quantifiers ‘many…’ and ‘few…’, and there are definable mathematical quantifiers such as ‘more than half…’, ‘exactly one…’.
More formally, a quantifier will bind a variable, turning an open sentence with n distinct free variables into one with n – 1 (an individual letter counts as one variable, although it may recur several times in a formula). When no variables remain free we have a closed sentence, i.e. one that can be evaluated as true or false within a domain. For example, from the open sentence F x & G x we can form (∃x )(F x & G x ), meaning that something is both F and G. The one variable x is bound on each occurrence.

Philosophy dictionary. . 2011.

Look at other dictionaries:

  • quantifier — [ kɑ̃tifje ] v. tr. <conjug. : 7> • 1897; angl. to quantify (1840); lat. médiév. quantificare 1 ♦ Log. Attribuer une quantité à (un terme). 2 ♦ Attribuer une grandeur mesurable à (un phénomène). Quantifier le coût d une mesure sociale. 3 ♦… …   Encyclopédie Universelle

  • quantifier — [kwänt′ə fī΄ər] n. Logic a word, term, prefix, symbol, etc. that quantifies …   English World dictionary

  • quantifier — noun 1. (logic) a word (such as some or all or no ) that binds the variables in a logical proposition • Syn: ↑logical quantifier • Topics: ↑logic • Hypernyms: ↑word …   Useful english dictionary

  • quantifier — /kwon teuh fuy euhr/, n. 1. Logic. an expression, as all or some, that indicates the quantity of a proposition. Cf. existential quantifier, universal quantifier. 2. a word, esp. a modifier, that indicates the quantity of something. [1875 80;… …   Universalium

  • quantifier — noun a) A word, such as all or many, that expresses a quantity b) The operator, represented by either of the symbols ∀ (universal quantifier) or ∃ (existential quantifier), used in …   Wiktionary

  • quantifier — UK [ˈkwɒntɪˌfaɪə(r)] / US [ˈkwɑntəˌfaɪər] noun [countable] Word forms quantifier : singular quantifier plural quantifiers linguistics a word or phrase such as much or a few that is used with another word to show quantity …   English dictionary

  • quantifier — quan•ti•fi•er [[t]ˈkwɒn təˌfaɪ ər[/t]] n. 1) pho logic an expression, as “all” or “some,” that indicates the quantity of a proposition Compare existential quantifier universal quantifier 2) gram. a word or phrase, usu. modifying a noun, that… …   From formal English to slang

  • quantifier — kvantorius statusas T sritis automatika atitikmenys: angl. quantifier vok. Quantor, m rus. квантор, m pranc. quantifier, m …   Automatikos terminų žodynas

  • quantifier — [[t]kwɒ̱ntɪfaɪə(r)[/t]] quantifiers N COUNT In grammar, a quantifier is a word or phrase such as plenty or a lot which you use to refer to a quantity of something without being precise. It is often followed by of , as in a lot of money …   English dictionary

  • quantifier — noun Date: 1876 one that quantifies: as a. a prefixed operator that binds the variables in a logical formula by specifying their quantity b. a limiting noun modifier (as five in “the five young men”) expressive of quantity and characterized by… …   New Collegiate Dictionary

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