Wholes, Parts, and Numbers (1997)

Nathan Salmon

in Metaphysics, Mathematics, and Meaning

Published in print November 2005 | ISBN: 9780199284719
Published online February 2006 | e-ISBN: 9780191603235 | DOI:
 Wholes, Parts, and Numbers (1997)

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It would appear to be provable that there cannot be exactly exactly two and a half oranges on the table. For the orange-half on the table is itself not an orange. An orange is a whole orange (or nearly enough so), whereas an orange-half, whatever else it is, is not a whole orange (nor even nearly so). Thus, there are only two oranges on the table, together with a third thing that (despite its color, taste, etc.) is no orange. This paradoxical conclusion is rejected. Instead a non-classical understanding is adopted on which the numerical quantifier ‘there are exactly n’, surprisingly, creates a nonextensional context.

Keywords: fraction; number; part; plurality; whole

Chapter.  8570 words. 

Subjects: Philosophy

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