Variable monotonicity and "less than": when Van Benthem's problem is not a problem
Brian Buccola
May 2015

In this paper I describe, and provide a solution to, a novel puzzle concerning the interpretation of non-upward-monotone quantifiers, focusing in particular on modified numerals of the form "less than n". The puzzle is this: "less than n" seems to mean different things (and, in particular, have different monotonicity properties) depending on whether its nominal and verbal arguments are distributive or non-distributive, and while it is easy to formulate a lexical entry that works for each of the two individual cases, it does not seem possible to formulate a single entry that works for both cases. The solution I propose is to adopt a flexible syntax-semantics system that overgenerates readings using one and the same entry for "less than", coupled with a pragmatic blocking mechanism that filters out unavailable readings. The puzzle and proposed solution together shed light on the roles that maximality and distributivity crucially play in shaping the monotonicity properties of modified numerals, as well as the division of labor between semantics and pragmatics.
Format: [ pdf ]
Reference: lingbuzz/002512
(please use that when you cite this article)
Published in: Proceedings of NELS 45
keywords: monotonicity, downward monotonicity, modified numerals, plurality, quantification, distributivity, collectivity, semantics
previous versions: v2 [May 2015]
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