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Plural Descriptions and Many-valued Functions

Plural Descriptions and Many-valued Functions 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mind Oxford University Press

Plural Descriptions and Many-valued Functions

Oliver, Alex; Smiley, Timothy
Mind , Volume 114 (456) – Oct 1, 2005
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References (53)

Publisher
Oxford University Press
Copyright
© Oliver and Smiley 2005
ISSN
0026-4423
eISSN
1460-2113
DOI
10.1093/mind/fzi1039
Publisher site
See Article on Publisher Site

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.

Journal

Mind – Oxford University Press

Published: Oct 1, 2005

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