Proportional readings of many and few : the case for an underspecified measure function
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Proportional readings of many and few: the case for an underspecified measure function Alan Bale1
· Bernhard Schwarz2
© Springer Nature B.V. 2019
Abstract In the so-called reverse proportional reading (Herburger in Nat Lang Semant 5(1):53, 1997), the truth conditions of statements of the form many/few φ ψ appear to make reference to the ratio of the individuals that are in the extensions of both φ and ψ to the individuals that are in the extension of ψ. The analysis of such readings is controversial. One prominent approach assumes they are a symptom of many and few making reference to a context dependent standard of comparison. We observe that this initially attractive approach systematically undergenerates, failing to capture pervasive reverse proportionality in environments that remove context dependency of the standard. Instead, we propose that reverse proportionality in such cases can arise from the underspecification of the measure function underlying the meanings of many and few. Keywords Proportional quantifiers · many and few · Reverse proportionality · Comparatives · Degree constructions · Measure functions · Context dependency
For comments and discussion, we would like to thank the audience at Sinn und Bedeutung 23 in Barcelona (in particular Ora Matushansky, Maribel Romero, Stephanie Solt, and Rob van Rooij), the members of the Semantics Research Group at McGill University (in particular Aron Hirsch), the members of SemanticsBabble at UCSD, three anonymous reviewers for Linguistics and Philosophy, and David Shanks. The authors acknowledge support from the Social Sciences and Humanities Research Council of Canada (SSHRC), Insight Grant #435-2016-1376 (Bale, Schwarz), and Insight Grants #435-2016-1448 and #435-2013-0592 (Schwarz).
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Bernhard Schwarz [email protected] http://www.mcgill.ca/linguistics/people/faculty/schwarz/ Alan Bale [email protected] http://linguistics.concordia.ca/bale/
1
FB-1030, Linguistics Program, CMLL Department, Concordia University, 1455 de Maisonneuve Ouest, Montreal, QC H3G 1M8, Canada
2
Department of Linguistics, McGill University, 1085 Avenue du Docteur Penfield, Montreal, QC H3A 1A7, Canada
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A. Bale, B. Schwarz
1 Introduction Since Partee (1989), much work has assumed that many and few are lexically ambiguous between a cardinal and a proportional sense. Under the cardinal meaning, the truth of many/few φ ψ requires that the cardinality of φ ∩ ψ , the intersection of the extensions of φ and ψ, be above/below a contextually determined standard cardinality; under the proportional meaning, it requires that the ratio of individuals in φ ∩ ψ to individuals in φ be above/below a contextually determined standard proportion. This lexical ambiguity is posited to capture the range of interpretations that is illustrated for few by Partee’s examples in (1). (1)
a. There were few faculty children at the 1980 picnic. b. Few egg-laying mammals suckle their young.
Partee presents (1a) as illustrating the cardinal sense of few. The sentence c
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