Bare numerals, collectivity, and genericity: A new puzzle
Brian Buccola
May 2017

The semantics of number words (or numerals), like three, has been the subject of intense research, and controversy, over the last few decades. The classic approach to numerical interpretation, pioneered by Horn (1972), contends that the basic, literal meaning of three in a sentence like Three people attended is ‘at least three’ (a one-sided meaning), and that the upper bound it typically implies arises by way of scalar implicature. More recent approaches argue that the literal meaning of three is ‘exactly three’ (a two-sided meaning), implemented in one of a variety of ways (e.g. Geurts 2006; Breheny 2008; Kennedy 2015). With a few exceptions, the primary data set has, up to now, consisted of simple existential sentences with distributive predicates, as well as modal sentences. The goal of this article is to reassess these two basic approaches to numerals (the ‘at least’ approach and a representative family of ‘exactly’ approaches) in light of a broader range of data that includes existential sentences with collective predicates, such as Three people lifted the piano together (cf. Koenig 1991), Four players formed a team, and Five students have the same name, and sentences with generically interpreted numerical indefinites, such as Three people can fit in the car and Three people can lift the piano (cf. Link 1987, 1991). I show that a brand new puzzle emerges: on the one hand, (a version of) the classic account gets the collective facts exactly right, but it fails to predict a previously unnoticed asymmetry in the distribution of two-sided readings of numerical indefinites embedded under a downward-entailing operator; on the other hand, (a version of) the ‘exactly’ approach beautifully predicts the embedding facts, but overgenerates in the collective domain. I conclude by offering some speculation as to how the puzzle might be resolved in favor of the classic account.
Format: [ pdf ]
Reference: lingbuzz/003400
(please use that when you cite this article)
Published in: Submitted
keywords: numerals, plurality, distributivity, collectivity, genericity, scalar implicature, semantics
previous versions: v1 [April 2017]
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