Philosophical Studies

, Volume 129, Issue 3, pp 545–574 | Cite as

Epistemological Challenges to Mathematical Platonism

Article

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

  1. Benacerraf P. (1973) ‘Mathematical Truth’, reprinted in Benacerraf and Putnam (1983).Google Scholar
  2. Benacerraf, P.Hilary, P. eds. 1983Philosophy of Mathematics. Selected Readings 2nd edn.Cambridge University PressCambridgeGoogle Scholar
  3. Boolos, G. 1984‘To Be Is To Be a Value of a Variable (or to Be Some Values of Some Variables)’Journal of Philosophy81430450CrossRefGoogle Scholar
  4. Boolos, G. 1985‘Nominalist Platonism’Philosophical Review94327344CrossRefGoogle Scholar
  5. Burgess, J., Gideon, R. 1997A Subject with No Object. Strategies for Nominalistic Interpretation of MathematicsClarendon PressOxfordGoogle Scholar
  6. Dummett, M. 1991The Logical Basis of MetaphysicsHarvard University PressCambridge MAGoogle Scholar
  7. Field, H. 1989Realism Mathematics, and ModalityBasil BlackwellOxfordGoogle Scholar
  8. Field, H. 1994‘Deflationist Views of Meaning and Content’Mind103249285Google Scholar
  9. 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.Google Scholar
  10. Horwich, P. 1990/98TruthBasil BlackwellOxfordGoogle Scholar
  11. Lewis, D.K. 1986On the Plurality of WorldsBasil BlackwellOxfordGoogle Scholar
  12. Linnebo, Ø. (2002) Science with Numbers: A Naturalistic Defence of Platonism, Ph.D. Dissertation, Harvard University.Google Scholar
  13. Linnebo, Ø 2003‘Plural Quantification Exposed’Nous377192CrossRefGoogle Scholar
  14. Linnebo, Ø. Forthcoming. ‘Reference and Frege’s Context Principle’, In Proceedings of Uppsala Conference on the Philosophy of Mathematics.Google Scholar
  15. Maddy, P. 1997Naturalism in MathematicsClarendonOxfordGoogle Scholar
  16. McGee, V. 1997‘How We Learn Mathematical Language’Philosophical Review1063568CrossRefGoogle Scholar
  17. Stalnaker R. (2001) ‘On Considering a Possible World as Actual’, Proceedings of the Aristotelian Society Suppl. 65:141–56.Google Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Merton CollegeOxfordUK

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