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QUANTIFIER

QUANTIFIER. A category of DETERMINER or PRONOUN used to express quantity. Most quantifiers have a limited distribution that depends on the countability of the nouns they relate to. Many, a few, few, and several relate only to plural countable nouns (many newspapers, a few drinks, few people, several men), in contrast to much, a little, and little, which relate to uncountable nouns (much confusion, a little information, little news). Enough can relate to both types of noun (enough newspapers, enough information), as can some and any (some help, any houses). However, some and any can also be used with singular countable nouns with non-quantitative functions: Some chicken! means ‘What a poor chicken!’ or ‘What a wonderful chicken!’, depending on tone and emphasis; Any fool knows that means ‘There is nothing special about knowing that’. Distinctions in the use of certain quantifiers are contrastive and subtle: few newspapers (not many newspapers), a few newspapers (some newspapers); little help (virtually no help at all), a little help (some help but not much). It is useful to treat a few and a little as distinct quantifiers and not simply as the indefinite article followed by few and little. Neither is used with a singular countable noun (a few raisins, a little rice, but not *a raisins, *a rice, *a few raisin, *a little raisin). In addition, both little and a little have to be distinguished from the ordinary adjective little (small). Ambiguity is possible with nouns that can be both countable and uncountable: out of obvious context, a little chicken could mean either a small bird or a small quantity of the meat of a chicken.

Few and little have negative force, as is shown by the fact that, like negatives, they take positive question tags: Few of us really think that, do we? Contrast: A few people believe that, don't they? Few and little have comparative and superlative forms (fewer, fewest; less, least), while much and many share more and most. Traditionally, fewer and fewest have been described as modifying only countable nouns (fewer houses, the fewest men possible) and less and least as modifying only uncountable nouns (less wine, the least fuel possible), and many people regard this as the only acceptable USAGE in STANDARD ENGLISH. However, widely throughout the English-speaking world less and least are used with countable nouns (less people, the least working hours), regardless of criticism and in many instances without the least awareness of the basis for the criticism. Much tends to be non-assertive in informal English; it prefers negative or interrogative contexts: We don't have much money, How much money do you need? In affirmative statements, a quantitative phrase such as a lot (of) and a great deal (of) is often preferred: That explains a lot (of what I've heard) or That explains a great deal rather than That explains much. Quantifiers can be pre-modified by very, so, too, as, as in very few people, so little help, too many cooks, and as much work as possible. Some words and phrases used as quantifiers can also be used as intensifiers, as in: much nicer; much less; many more; a little better; a lot older; a lot too old; a bit too much. Some of these words are also used for duration and frequency: We waited a little; They eat a lot. This can lead to ambiguity; in She eats a lot and He doesn't read much, if the items are quantifying pronouns, the meaning is a lot of food and a lot of books, but if they are adverbs of frequency, the meaning is She's constantly eating and He doesn't often read. Compare NUMBER 1.

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quantifier

quantifier One of the two symbols ∀ or ∃ used in predicate calculus. ∀ is the universal quantifier and is read “for all”. ∃ is the existential quantifier and is read “there exists” or “for some”. In either case the reference is to possible values of the variable v that the quantifier introduces. ∀v . F means that the formula F is true for all values of v, while ∃v . F means that F is true for at least one value of v. As an example, suppose that P(x,y) is the predicate “x is less than or equal to y”. Then the following expression ∃x . y . P(x,y)

says that there exists an x that is less than or equal to all y. This statement is true if values range over the natural numbers, since x can be taken to be 0. It becomes false however if values are allowed to range over negative integers as well. Note also that it would be false even for natural numbers if the predicate were “x is less than y”. Other notations such as (∀v)F in place of ∀v . F are also found.

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quantifier

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