Plural descriptions and many-valued functions

Mind 114 (456):1039-1068 (2005)
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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DOI 10.1093/mind/fzi1039
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Superplurals in English.Øystein Linnebo & David Nicolas - 2008 - Analysis 68 (299):186–197.
Can Semantics Guide Ontology?Katherine Ritchie - 2016 - Australasian Journal of Philosophy 94 (1):24-41.
A Modest Logic of Plurals.Alex Oliver & Timothy Smiley - 2006 - Journal of Philosophical Logic 35 (3):317-348.
Term Limits Revisited.Stephen Neale - 2008 - Philosophical Perspectives 22 (1):375-442.

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