Plural descriptions and many-valued functions

Mind 114 (456):1039-1068 (2005)
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Abstract

Russell had two theories of definite descriptions: one for singular descriptions, another for plural descriptions. We chart its development, in which ‘On Denoting’ plays a part but not the part one might expect, before explaining why it eventually fails. We go on to consider many-valued functions, since they too bring in plural terms—terms such as ‘4’ or the descriptive ‘the inhabitants of London’ which, like plain plural descriptions, stand for more than one thing. Logicians need to take plural reference seriously if only because mathematicians take many-valued functions seriously. We assess the objection (by Russell, Frege and others) that many-valued functions are illegitimate because the corresponding terms are ambiguous. We also assess the various methods proposed for getting rid of them. Finding the objection ill-founded and the methods ineffective, we introduce a logical framework that admits plural reference, and use it to answer some earlier questions and to raise some more.

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Author Profiles

Alex Oliver
Cambridge University
Timothy Smiley
Cambridge University

Citations of this work

Plural quantification.Ø Linnebo - 2008 - Stanford Encyclopedia of Philosophy.
Superplurals in English.Øystein Linnebo & David Nicolas - 2008 - Analysis 68 (3):186–197.
Pluralities, counterparts, and groups.Isaac Wilhelm - 2022 - Philosophical Studies 179 (7):2133-2153.
Ontological Collectivism.Raul Saucedo - 2022 - Philosophical Perspectives 36 (1):233-269.

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References found in this work

Introduction to metamathematics.Stephen Cole Kleene - 1952 - Groningen: P. Noordhoff N.V..
Introduction to mathematical logic.Alonzo Church - 1944 - Princeton,: Princeton University Press. Edited by C. Truesdell.
Frege: Philosophy of Mathematics.Michael DUMMETT - 1991 - Philosophy 68 (265):405-411.

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