Modified Numerals as Post-Suppositions

Adrian Brasoveanu

Abstract: The paper provides a compositional account of cumulative readings with non-increasing modified numerals (aka van Benthem's puzzle), for example, Exactly 3 boys saw exactly 5 movies. The main proposal is that modified numerals make two kinds of semantic contributions. Their asserted/at-issue contribution is a maximization operator that introduces the maximal set of entities that satisfies their restrictor and nuclear scope. The second contribution is a post-supposition, that is, a cardinality constraint that needs to be satisfied relative to the context that results after the at-issue meaning is evaluated. Thus, the interpretation process ends up giving a kind of pseudo wide scope to the cardinality post-suppositions contributed by modified numerals.