To appear in the Wiley Companion to Semantics (eds. Matthewson, Meier, Rullmann, Zimmermann)
Modified numerals are expressions such as 'more than three', 'less/fewer than three', 'at least three', 'at most three', 'up to ten, between three and ten', 'approximately ten', 'about ten', 'exactly ten', etc. At first sight, their semantic contribution seems pretty easy to describe. However, this impression is deceptive. Modified numerals do in fact raise very serious challenges for formal semantics and pragmatics, many of which have yet to be addressed in a fully satisfactorily way. These challenges relate to two broad questions: first, what is the linguistically encoded meaning of modified numerals? Second, how can we make sense of all the inferences they give rise to, and how should we divide the work between compositional semantics and pragmatics in order to account for all these effects? These are the two questions we will address in this chapter, focusing on a few striking puzzles, mostly in the domain of comparative and superlative modified numerals.