Comparative vs. superlative quantifiers Superlative and comparative ...

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Superlative vs. comparative Indefinites, numerals, and scales Comparative modifiers Superlative modifiers Experimental evidence Indefinites and numerals ◮ Nouns and number words denote properties: ◮ ‖book‖ = λx[book(x)] ◮ ‖three‖ = λx[#x = 3] = λx[3(x)] ✐ Note that this is an ‘exact’ reading. ◮ ‖three books‖ = λx[3(x) ∧ book(x)] ◮ Existential closure turns a predicate into a quantifier: ◮ ‖∅[three books]‖ = λP∃x[3(x) ∧ book(x) ∧ P(x)] ◮ ‖Betty read [∅[three books]]‖ = ∃x[3(x) ∧ book(x) ∧ read(b, x)] ✐ Note that this is an ‘at least’ reading. ◮ Implicature: ◮ ¬∃x[#x > 3 ∧ book(x) ∧ read(b, x)] ◮ Specificity requires existential closure. ◮ Betty has read three books. [May be specific.] ◮ These are three books. [Non-specific only.] Bart Geurts & Rick Nouwen: Comparative vs. superlative quantifiers Superlative vs. comparative Indefinites, numerals, and scales Comparative modifiers Superlative modifiers Experimental evidence Digression on number terms How are we to account for the fact that number terms behave differently from bona fide scalar expressions? Some of the options: ◮ Short-circuited implicature (whatever that may be). ◮ Existential closure comes in several flavours, and the ‘exactly’ flavour is the default for expressions like ‘three’, ‘half of’, etc. ◮ The lexical meaning of a number term is quantificational and ‘exact’: type shifting yields first a predicative, and then a quantificational (‘at least’) sense. ♥ Number terms are polysemous between predicative and quantificational senses, and both are exact, so the ‘at least’ reading must still be derived. This view is recommended by experts in Germany and the Netherlands. Bart Geurts & Rick Nouwen: Comparative vs. superlative quantifiers
Superlative vs. comparative Indefinites, numerals, and scales Comparative modifiers Superlative modifiers Experimental evidence Scales Krifka (1999) ◮ Focus-induced alternatives are ordered. ◮ E.g., if ‘three’ is in focus, we get: . . . λx[3(x)] ⊲ λx[2(x)] ⊲ λx[1(x)] ✐ Note: this is not an entailment scale. ◮ This ordering is propagated up the derivation tree. Hence, the alternatives for ‘[three] F books’ are ordered thus: . . . λx[3(x) ∧ book(x)] ⊲ λx[2(x) ∧ book(x)] ⊲ λx[1(x) ∧ book(x)] ◮ Scalar modifiers operate on such ordered alternatives (cf. ‘only’). ◮ Example: When applied to ‖three‖, ‖more than‖ returns the union of all the properties that are ‘higher’ than λx[3(x)], i.e. λx[4(x) ∨ 5(x) ∨ . . .] = λx[#x > 3]. Bart Geurts & Rick Nouwen: Comparative vs. superlative quantifiers Superlative vs. comparative Indefinites, numerals, and scales Comparative modifiers Superlative modifiers Experimental evidence Comparative modifiers Bart Geurts & Rick Nouwen: Comparative vs. superlative quantifiers
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Comparative vs. superlative quantifiers Superlative and comparative ...

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