The semantics and pragmatics of directional numeral modifiers

Abstract

Directional prepositions that can be used as numeral modifiers (directional numeral modifiers or DNMs) are different from other numeral modifiers that set an upper bound in that they set a non-cancellable lower bound, their upper bound is cancellable, they are incompatible with the numeral at the bottom of the scale they quantify over, they are not downward monotone and do not license NPIs, and they interact differently with evaluative adverbs. This paper argues that the cause of all these differences is that DNMs assert a lower bound and implicate an upper bound, and that all class B numeral modifiers require quantification over a range of values. Crosslinguistic data support these claims.