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Events and Semantic Architecture$
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Paul M. Pietroski

Print publication date: 2004

Print ISBN-13: 9780199244300

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780199244300.001.0001

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Quantification and Plurality

Quantification and Plurality

Chapter:
(p.88) 2 Quantification and Plurality
Source:
Events and Semantic Architecture
Author(s):

Paul M. Pietroski (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199244300.003.0002

In principle, Conjunctivists can treat determiners, like ‘every’, as predicates satisfied by ordered pairs of sets. But this recapitulates standard Functionist accounts, which fail to explain various constraints on determiner meanings. A better option is to allow for plural predicates, which can be satisfied by some things without being satisfied by any one of those things, and say that determiners are plural predicates satisfied by ordered pairs consisting of an entity and a truth value. Spelling out the details requires a discussion of second-order variables, but this is required in any case. The net result is a relatively simple Conjunctivist account that explains the conservativity of determiners, while retaining the descriptive adequacy of generalized quantifier theories. The proposal, which dovetails with the idea that determiner phrases often raise, extends smoothly to an account of plural noun phrases that also avoids some undesirable implications of Functionist approaches, which invoke quantification over collections. A moral is that predicates can have many values relative to any assignment of values to variables, and that associating each predicate with a single set-like value is a distortion.

Keywords:   quantification, plurality, extensions, collections, second-order variables, assignments, determiners, conservativity

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