Advertisement

Synthese

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

A platonist epistemology

  • Mark Balaguer
Article

Abstract

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.

Keywords

Mathematical Object Naturalistic Epistemology 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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

Personalised recommendations