Abstract
Since Benacerraf’s “Mathematical Truth” a number of epistemological challenges have been launched against mathematical platonism. I first argue that these challenges fail because they unduely assimilate mathematics to empirical science. Then I develop an improved challenge which is immune to this criticism. Very roughly, what I demand is an account of how people’s mathematical beliefs are responsive to the truth of these beliefs. Finally I argue that if we employ a semantic truth-predicate rather than just a deflationary one, there surprisingly turns out to be logical space for a response to the improved challenge where no such space appeared to exist.
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References
Benacerraf P. (1973) ‘Mathematical Truth’, reprinted in Benacerraf and Putnam (1983).
P. Benacerraf P. Hilary (Eds) (1983) Philosophy of Mathematics. Selected Readings 2nd edn. Cambridge University Press Cambridge
G. Boolos (1984) ArticleTitle‘To Be Is To Be a Value of a Variable (or to Be Some Values of Some Variables)’ Journal of Philosophy 81 430–450 Occurrence Handle10.2307/2026308
G. Boolos (1985) ArticleTitle‘Nominalist Platonism’ Philosophical Review 94 327–344 Occurrence Handle10.2307/2185003
J. Burgess R. Gideon (1997) A Subject with No Object. Strategies for Nominalistic Interpretation of Mathematics Clarendon Press Oxford
M. Dummett (1991) The Logical Basis of Metaphysics Harvard University Press Cambridge MA
H. Field (1989) Realism Mathematics, and Modality Basil Blackwell Oxford
H. Field (1994) ArticleTitle‘Deflationist Views of Meaning and Content’ Mind 103 249–285
Goldman A. (1967) ‘A Causal Theory of Knowing’, Journal of Philosophy 64:355–372. Hazen A.P. (1993) ‘Against Pluralism’, Australasian Journal of Philosophy 81:132–144.
P. Horwich (1990/98) Truth Basil Blackwell Oxford
D.K. Lewis (1986) On the Plurality of Worlds Basil Blackwell Oxford
Linnebo, Ø. (2002) Science with Numbers: A Naturalistic Defence of Platonism, Ph.D. Dissertation, Harvard University.
Ø Linnebo (2003) ArticleTitle‘Plural Quantification Exposed’ Nous 37 71–92 Occurrence Handle10.1111/1468-0068.00429
Linnebo, Ø. Forthcoming. ‘Reference and Frege’s Context Principle’, In Proceedings of Uppsala Conference on the Philosophy of Mathematics.
P. Maddy (1997) Naturalism in Mathematics Clarendon Oxford
V. McGee (1997) ArticleTitle‘How We Learn Mathematical Language’ Philosophical Review 106 35–68 Occurrence Handle10.2307/2998341
Stalnaker R. (2001) ‘On Considering a Possible World as Actual’, Proceedings of the Aristotelian Society Suppl. 65:141–56.
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Linnebo, Ø. Epistemological Challenges to Mathematical Platonism. Philos Stud 129, 545–574 (2006). https://doi.org/10.1007/s11098-004-3388-1
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DOI: https://doi.org/10.1007/s11098-004-3388-1