A Scalar Semantics for Scalar Readings of Number Words

Number words have played a central role in debates about the relation between context and meaning for decades. While current analyses of these terms and the sentences in which they appear differ in their details, they typically agree that interpretations of sentences containing number words crucially involve pragmatic enrichment of a more basic meaning. In the first part of this paper, I present a set of challenges for existing semantic and pragmatic accounts of number word meaning. In the second part, I develop a fully semantic and compositional analysis of scalar readings of sentences containing numerals, in which number words denote generalized quantifiers over degrees, and scalar readings arise through scopal interactions between number words and other constituents, and show how it responds to these challenges.