David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
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
Paul Benacerraf (1965). What Numbers Could Not Be. Philosophical Review 74 (1):47-73.
George Boolos (1998). Logic, Logic, and Logic. Harvard University Press.
George Boolos (1984). To Be is to Be a Value of a Variable (or to Be Some Values of Some Variables). Journal of Philosophy 81 (8):430-449.
Harry C. Bunt (1985). Mass Terms and Model-Theoretic Semantics. Cambridge University Press.
John P. Burgess (2004). Mathematics and Bleak House. Philosophia Mathematica 12 (1):18-36.
Citations of this work BETA
Hartley Slater (2007). Logic and Grammar. Ratio 20 (2):206–218.
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