A "de-Fregean" semantics (and neo-Gricean pragmatics) for modified and unmodified numerals

Abstract

A challenge for the semantic and pragmatic analysis of modified numerals is how to account for ignorance implications about exact quantity. Superlative-modified numerals (at least/most six) systematically give rise to such implications while their comparative-modified counterparts (more/fewer than sixggy) do not, but the distribution of ignorance implications with superlative modifiers is sensitive to how the numeral interacts with modals and other operators. In this paper, I demonstrate that a "de-Fregean" semantic analysis of modified and unmodified numerals as second-order properties of degrees that differ only in the kind of ordering relation they introduce supports a neo-Gricean pragmatic account of ignorance implications as Quantity implicatures, and derives the pattern of interaction with modals as a scopal phenomenon.

http://dx.doi.org/10.3765/sp.8.10

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