Grammar and sets

Australasian Journal of Philosophy 84 (1):59 – 73 (2006)
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Abstract

'Philosophy arises through misconceptions of grammar', said Wittgenstein. Few people have believed him, and probably none, therefore, working in the area of the philosophy of mathematics. Yet his assertion is most evidently the case in the philosophy of Set Theory, as this paper demonstrates (see also Rodych 2000). The motivation for twentieth century Set Theory has rested on the belief that everything in Mathematics can be defined in terms of sets [Maddy 1994: 4]. But not only are there notable items which cannot be so defined, including numbers and mereological sums, the very notion of a set, as formalized within this tradition, is based on a series of grammatical confusions.

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Citations of this work

Logic and grammar.Hartley Slater - 2007 - Ratio 20 (2):206–218.

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References found in this work

What numbers could not be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
Realism in mathematics.Penelope Maddy - 1990 - New York: Oxford University Prress.
Parts of Classes.David K. Lewis - 1991 - Mind 100 (3):394-397.

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