Journal of Philosophical Logic

, Volume 41, Issue 2, pp 471–491 | Cite as

Strict Finitism and the Happy Sorites

Article

Abstract

Call an argument a ‘happy sorites’ if it is a sorites argument with true premises and a false conclusion. It is a striking fact that although most philosophers working on the sorites paradox find it at prima facie highly compelling that the premises of the sorites paradox are true and its conclusion false, few (if any) of the standard theories on the issue ultimately allow for happy sorites arguments. There is one philosophical view, however, that appears to allow for at least some happy sorites arguments: strict finitism in the philosophy of mathematics. My aim in this paper is to explore to what extent this appearance is accurate. As we shall see, this question is far from trivial. In particular, I will discuss two arguments that threaten to show that strict finitism cannot consistently accept happy sorites arguments, but I will argue that (given reasonable assumptions on strict finitistic logic) these arguments can ultimately be avoided, and the view can indeed allow for happy sorites arguments.

Keywords

Finitism Vagueness Sorites Sorites paradox Strict finitism Intuitionism Constructivism Cut Cut elimination Induction 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Boolos, G. (1984). Don’t eliminate cut. Journal of Philosophical Logic, 13, 373–378.CrossRefGoogle Scholar
  2. 2.
    Boolos, G. (1991). Zooming down the slippery slope. Nous, 25, 695–706.CrossRefGoogle Scholar
  3. 3.
    Buss, S. (1998a). An introduction to proof theory. In Buss, S. (ed.), Handbook of Proof Theory. Elsevier.Google Scholar
  4. 4.
    Buss, S. (1998b). First-order proof theory of arithmetic. In Buss, S. (ed.), Handbook of Proof Theory, Elsevier.Google Scholar
  5. 5.
    Dedekind, R. (1963) Essays on the Theory of Numbers, translated by Beman, W. Dover Publications.Google Scholar
  6. 6.
    Dummett, M. (1975). Wang’s paradox. Synthese, 30, 301–324.CrossRefGoogle Scholar
  7. 7.
    Dummett, M. (1977). Elements of Intuitionism. Oxford University Press.Google Scholar
  8. 8.
    Fara, D. (2001). Phenomenal Continua and the Sorites. Mind, 110, 905–935 (Originally published under ‘Delia Graff’).CrossRefGoogle Scholar
  9. 9.
    Frege, G. (1974). The Foundations of Arithmetic, translated by Austin, J.L. Oxford University Press.Google Scholar
  10. 10.
    Magidor, O. (2007). Strict finitism refuted? Proceedings of the Aristotelian Society, CVII, 403–411.Google Scholar
  11. 11.
    Read, S., & Wright, C. (1985). Hairier than Putnam thought. Analysis, 45, 56–58.CrossRefGoogle Scholar
  12. 12.
    Tennant, N. (1997). The Taming of the True, Oxford University Press.Google Scholar
  13. 13.
    Wright, C. (1982). Strict Finitism. Synthese, 51, 203–282.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.University of Oxford (Balliol College)OxfordUK

Personalised recommendations