At Least Et Al.: the Semantics of Scalar Modifiers

On the naive account of scalar modifiers like more than and at least, At least three girls snored is synonymous with More than two girls snored, and both sentences mean that the number of snoring girls exceeded two (the same, mutatis mutandis, for sentences with at most and less/fewer than). We show that this is false and propose an alternative theory, according to which superlative modifiers (at least/most) are quite different from comparative ones (more/less/fewer than). Whereas the naive theory is basically right about comparative modifiers, it is wrong about superlative modifiers, which we claim have a MODAL meaning: an utterance of At least three girls snored conveys two things: first, that it is CERTAIN that there was a group of three snoring girls, and second, that more than four girls MAY have snored. We argue that this analysis explains various facts that are problematic for the naive view, which have to do with specificity, distributional differences between superlative and comparative modifiers, differential patterns of inference licensed by these expressions, and the way they interact with various operators, like modals and negation.* 1. INTRODUCTION. We are concerned in this article with what we propose to call SCALAR MODIFIERS. Expressions falling under this rubric come in two types: SUPERLATIVE (at least, at most) and COMPARATIVE (more than, less/fewer than). Our focus of attention is on superlative and comparative quantifiers, like at most three beers and more than two vodkas, though other uses of scalar modifiers are taken into account as well. It might seem that the semantics of scalar modifiers is a fairly straightforward matter, but readers of Kay 1992 and Krifka 1999 will be aware that it is not. The problems we concentrate on all have to do with the fact that the distinction between comparative and superlative modifiers runs much deeper than is generally acknowledged. Our aim in this article is twofold: to establish that the differences between comparative and superlative modifiers are profound, and then to explain them. The keystone in our proposal is that superlative but not comparative modifiers are modal expressions. For a long time, semantic research on quantification has concentrated its attention on commonalities between quantifying expressions and has tended to gloss over the internal makeup of composite quantifiers like the ones treated here. Recently, however, there has been an increasing awareness that all quantifiers are special (e.g. Ariel 2004 and Hackl & Acland 2006 …