### Modified Numerals (Handbook article)

### Benjamin
Spector

To appear in the Wiley Companion to Semantics
(eds. Matthewson, Meier, Rullmann, Zimmermann)

Full
paper in pdf

**Abstract**

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.