Superlative Modifiers as Modified Superlatives

The superlative modifiers at least and at most are quite famous, but their cousins at best, at the latest, at the highest, etc., are less well-known. This paper is devoted to the entire family. New data is presented illustrating the productivity of the pattern, identifying a generalization delimiting it, and showing that the cousins, too, have the pragmatic effects that have attracted so much attention to at least and at most. To capture the productivity, I present a new decomposition of at least into recombinable parts. Most notable is the at-component (silent in some languages), which takes advantage of the comparison class argument of the superlative to produce the set of possibilities involved in the ignorance implicatures that superlative modifiers are known for. A side-effect is a new view on gradable predicates, accounting for uses like 88 degrees is too hot