Modified numerals and maximality

Abstract

In this article, we describe and attempt to solve a puzzle arising from the interpretation of modified numerals like less than five and between two and five. The puzzle is this: such modified numerals seem to mean different things depending on whether they combine with distributive or non-distributive predicates. When they combine with distributive predicates, they intuitively impose a kind of upper bound, whereas when they combine with non-distributive predicates, they do not (they sometimes even impose a lower bound). We propose and explore in detail four solutions to this puzzle, each involving some notion of maximality, but differing in the type of maximality involved (‘standard’ maximality versus ‘informativity-based’ maximality) and in the source of maximality (lexically encoded in the meaning of the numeral modifier versus non-lexical). While the full range of data we consider do not conclusively favor one theory over the other three, we do argue that overall the evidence (i) goes against the view that modified numerals lexically encode a ‘standard’ maximality operator, and (ii) suggests the need for a pragmatic blocking mechanism that filters out readings (logical forms) of sentences that are generated by the grammar but intuitively unavailable.