Modified Numerals as Post-Suppositions

The paper provides a compositional account of cumulative readings with non-increasing modified numerals (aka van Benthem's puzzle), e.g., Exactly three boys saw exactly five 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, i.e., a cardinality constraint that needs to be satisfied relative to the context that results after the at-issue meaning is evaluated. We take contexts to be sets of variable assignments relative to which quantificational expressions are interpreted and which are updated as a result of their interpretation. 1 Cumulativity and Modified Numerals The goal of the paper is to provide a compositional account of cumulative readings with non-increasing modified numerals (aka van Benthem's puzzle, van Benthem 1986), ex...

• Type: Journal
• Year: 2009
• Where: AMSTERDAM
• Authors: Adrian Brasoveanu
• Keywords: AMSTERDAM 2009, Cumulative Reading, Logical Reasoning, Non-increasing Modified Numerals, Van Benthem