At least, at most revisited

Abstract

The interaction between modified numerals and modals offers important insights into their interpretation. As pointed out by Buring (2008), not all superlative numerals interacting with modals give rise to the same interpretations: while both at least and at most interacting with universal modals give rise to authoritative/bounded-interpretations, only at most interacting with existential modals does so. In the case of interactions with at least, the readings are of speaker-insecurity/ignorance. This paper offers a new perspective on this interaction, building on a focus-based Krifka (1999)-style analysis for superlatives as well as a view of context structured by questions under discussion. The pragmatic component of the proposal makes a case for enrichment driven by considerations of speaker cooperativity and authority. The account thus differs from proposals in the literature that appeal to scalar alternatives and disjunction-style reasoning.