David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Australasian Journal of Philosophy 84 (1):59 – 73 (2006)
'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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References found in this work BETA
David Lewis (1991). Parts of Classes. Blackwell.
Paul Benacerraf (1965). What Numbers Could Not Be. Philosophical Review 74 (1):47-73.
Bob Hale (ed.) (2001). The Reason's Proper Study: Essays Towards a Neo-Fregean Philosophy of Mathematics. Oxford University Press.
George Boolos (1998). Logic, Logic, and Logic. Harvard University Press.
Penelope Maddy (1990). Realism in Mathematics. Oxford University Prress.
Citations of this work BETA
Hartley Slater (2007). Logic and Grammar. Ratio 20 (2):206–218.
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