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

• Main Author: Christopher Kennedy
• Format: Article
• Language: English
• Published: Linguistic Society of America 2015-05-01
• Series: Semantics and Pragmatics
• Subjects: Numerals, implicature, ignorance, free choice, degree quantification
• Online Access: http://semprag.org/article/view/3004

A challenge for the semantic and pragmatic analysis of modified numerals is how to account for ignorance implications about exact quantity. Superlative-modified numerals (<em>at least/most six</em>) systematically give rise to such implications while their comparative-modified counterparts (<em>more/fewer than sixggy</em>) 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 &quot;de-Fregean&quot; 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 <a href="http://semantics-online.org/sp-bib/kennedy-2015-defregean.bib">BibTeX info</a>