The semantics of scalar modifiers

On the naive account of scalar modifiers like ‘more than’ and ‘at most’, ‘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 secondly, 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. To appear in Language.