, Volume 103, Issue 3, pp 303–325 | Cite as

A platonist epistemology

  • Mark Balaguer


A response is given here to Benacerraf's 1973 argument that mathematical platonism is incompatible with a naturalistic epistemology. Unlike almost all previous platonist responses to Benacerraf, the response given here is positive rather than negative; that is, rather than trying to find a problem with Benacerraf's argument, I accept his challenge and meet it head on by constructing an epistemology of abstract (i.e., aspatial and atemporal) mathematical objects. Thus, I show that spatio-temporal creatures like ourselves can attain knowledge about mathematical objects by simply explaininghow they can do this. My argument is based upon the adoption of a particular version of platonism — full-blooded platonism — which asserts that any mathematical object which possiblycould exist actuallydoes exist.


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  1. Balaguer, M.: 1994, ‘Against (Maddian) Naturalized Platonism’,Philosophia Mathematica 2, 97–108.Google Scholar
  2. Balaguer, M.: in progress,Platonism and Anti-Platonism in Mathematics.Google Scholar
  3. Benacerraf, P.: 1973, ‘Mathematical Truth’,Journal of Philosophy 70, 661–79.Google Scholar
  4. Field, H.: 1989,Realism, Mathematics, and Modality, Basil Blackwell, New York.Google Scholar
  5. Field, H.: 1991, ‘Metalogic and Modality’,Philosophical Studies 62, 1–22.Google Scholar
  6. Frege, G.: 1980,Philosophical and Mathematical Correspondence, University of Chicago Press, Chicago.Google Scholar
  7. Gödel, K.: 1964, ‘What is Cantor's Continuum Problem?’, reprinted in Benacerraf and Putnam (eds.),Philosophy of Mathematics, 2nd ed., 1983, Cambridge University Press, Cambridge, pp. 470–85.Google Scholar
  8. Katz, J.: 1981,Language and Other Abstract Objects, Rowman and Littlefield, Totowa, NJ.Google Scholar
  9. Kreisel, G.: 1967, ‘Informal Rigor and Completeness Proofs’, in Lakatos (ed.),Problems in the Philosophy of Mathematics, North-Holland, Amsterdam, pp. 138–71.Google Scholar
  10. Lewis, D.: 1986,On the Plurality of Worlds, Basil Blackwell, Oxford.Google Scholar
  11. Maddy, P.: 1990,Realism in Mathematics, Oxford University Press, Oxford.Google Scholar
  12. Resnik, M.: 1982, ‘Mathematics as a Science of Patterns: Epistemology’,Noûs 16, 95–105.Google Scholar

Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Mark Balaguer
    • 1
  1. 1.Department of PhilosophyCalifornia State University, Los AngelesLos AngelesUSA

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