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Mind 2005 114(456):1039-1068; doi:10.1093/mind/fzi1039
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© Oliver and Smiley 2005

Plural Descriptions and Many-valued Functions

Alex Oliver1 and Timothy Smiley2

1 Faculty of Philosophy, University of Cambridge, Cambridge CB3 9DA, UK ado10{at}cam.ac.uk, 2 Clare College, Cambridge CB2 1TL, UK tjs1002{at}cam.ac.uk

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 ‘{surd}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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