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Unity and PluralityLogic, Philosophy, and Linguistics$
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Massimiliano Carrara, Alexandra Arapinis, and Friederike Moltmann

Print publication date: 2016

Print ISBN-13: 9780198716327

Published to Oxford Scholarship Online: June 2016

DOI: 10.1093/acprof:oso/9780198716327.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 26 February 2021

Singularist Predicative Analyses and Boolos’s Second-Order Pluralism

Singularist Predicative Analyses and Boolos’s Second-Order Pluralism

Chapter:
(p.33) 3 Singularist Predicative Analyses and Boolos’s Second-Order Pluralism
Source:
Unity and Plurality
Author(s):

Alex Oliver

Timothy Smiley

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198716327.003.0003

This chapter argues against predicative analyses of plurality, which force plurals into the familiar mold of singular logic by turning an apparently plural term standing for several objects into a singular predicate standing for a concept or property. Michael Dummett enlists support from Fregean semantics in favor of a predicative analysis, but his arguments do not stand up, either as exegesis of Frege or on their own merits. As well as facing difficulties in eliminating plural content, predicative analyses are sunk by the equivocity objection: they misrepresent single English predicates as equivocal, by treating the predicate differently according as it combines with singular or plural arguments. Although George Boolos does not offer a predicative analysis, it is argued that his second-order treatment of plurals is also sunk by the equivocity objection. And Ian Rumfitt fails in his attempt to avoid the objection by modifying Boolos’s scheme.

Keywords:   Boolos, Dummett, equivocity objection, Frege, plural term, pluralist, predicative analysis, second-order logic, singularist, Rumfitt

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