Modified numerals revisited: The cases of fewer than 4 and between 4 and 8

Abstract

There seems an interplay between (i) the interpretation of sentences containing non-increasing modified numerals (e.g., fewer than 4, between 4 and 8) and (ii) the type of predicates in those sentences. For example, (i) fewer than 4 boys smiled, where the predicate is distributive, has no existential entailment, but an upper-bound reading; while (ii) fewer than 4 boys lifted the piano together, where the predicate is collective, has an existential entailment, but no upper-bound reading. Following Brasoveanu (2013)’s post-supposition-style account for modified numerals, here I propose that (I) the semantic contribution of non-increasing modified numerals is twofold: (i) introducing a maximal referent as at-issue meaning in the derivation, and (ii) adding a cardinality constraint as a secondary dimension of meaning, and that (II) it is the type of predicates (distributive vs. collective) that determines the scope of maximization and where to evaluate this secondary dimension of meaning – at the sentential level or within a group-denoting DP.