Platonism and Anti-Platonism in MathematicsOxford University Press, 20 août 1998 - 240 pages In this highly absorbing work, Balaguer demonstrates that no good arguments exist either for or against mathematical platonism-for example, the view that abstract mathematical objects do exist and that mathematical theories are descriptions of such objects. Balaguer does this by establishing that both platonism and anti-platonism are justifiable views. Introducing a form of platonism, called "full-blooded platonism," that solves all problems traditionally associated with the view, he proceeds to defend anti-platonism (in particular, mathematical fictionalism) against various attacks-most notably the Quine-Putnam indispensability attack. He concludes by arguing that it is not simply that we do not currently have any good arguments for or against platonism but that we could never have such an argument. This lucid and accessible book breaks new ground in its area of engagement and makes vital reading for both specialists and all those intrigued by the philosophy of mathematics, or metaphysics in general. |
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abstract mathematical objects abstract objects acquire knowledge anti-platonists anti-realism anti-realistic appeal applications of mathematics argue arithmetic axiom Benacerraf's Benacerrafian causally chapter claim consistent purely mathematical ematical empirical science empirical theories endorse entails epistemological explain externalist fact false FBP-ists and fictionalists Field's Gödel Hilbert spaces instance Kitcher logical Maddy math mathematical beliefs mathematical intuition mathematical knowledge mathematical platonism mathematical practice mathematical realm mathematical singular mathematicians matical natural numbers no-contact nominalistic content nominalization non-spatiotemporal non-uniqueness notion of consistency Ockham's razor orthomodular lattice philosophy of mathematics physical objects physical world platonists possible worlds possible-world-style truth conditions propensities purely mathematical theories quantum system question real number reason Resnik response seems semantic sentence sequence set theory Shapiro simply sort spacetime standard model strategy structuralists structure sub-section theorem theories are true theories truly describe thesis things unique version of anti-platonism version of platonism w-sequences worry