Splitting "at most"

Abstract

Negative quantifiers are known to give rise to split scope readings, where some other operator, in particular a modal, takes scope in between the negative and the indefinite meaning component. The fact that split scope readings are not only restricted to negative quantifiers, but arise with downward monotonic quantifiers more generally, has been taken as an argument against a decompositional analysis. This paper discusses split scope readings that arise in connection with the superlative modifier 'at most', which shows a particularly interesting pattern of interaction with modals, as it naturally combines with possibility modals to yield split scope readings, but not with necessity modals. While recent pragmatic approaches to the meaning of superlative modifiers successfully account for the interaction of at least with modals, they fail for downward monotonic 'at most'. I argue that the interaction of at most with modals can be explained if the pragmatic approach is amended with the assumption that at most is decomposed into at least plus an antonymizing operator defined in terms of degree negation.