# Modified numerals revisited: the cases of *fewer than 4* and *between 4 and 8*

## Linmin Zhang (NYU)

### Abstract

As shown in previous studies (e.g., Spector 2014, Buccola 2015a, b, Buccola and Spector 2015), (i) when non-monotone-increasing numerals such as *fewer than 4* are used along with distributive predicates (e.g., *fewer than 4 students smiled*), there is an upper-bound reading, but no existential reading, while (ii) when these numerals are used along with collective predicates (e.g., *fewer than 4 students lifted the piano together*), there is an existential reading, but no upper-bound reading. I argue that maximality-based pragmatic accounts for these data (Spector 2014, Buccola 2015a, b, Buccola and Spector 2015) are problematic: they over-generate unattested readings in the use of *fewer than 4* and cannot be extended to account for similar patterns in the use of *few*/*little* (see Solt 2007). Following Solt 2006’s decompositional account for few, I propose that, essentially, *fewer than 4* is decomposed into (i) a positive cardinality predicate and (ii) a negation operator which takes the widest possible scope. Sentences with collective predicates are accounted for with an existential closure at the DP level.