Strict Finitism

Chapter
First Online:
Part of the Synthese Library book series (SYLI, volume 355)

Abstract

This chapter presents the logical framework for strict finitism. I will first present a logical formal system for strict finitism. Then, I will introduce a system of semi-formal notations to allow the presentation of the constructions and inferences in strict finitism in a simplified and more readable format. This will allow us to state ordinary mathematics in strict finitism in an informal way and make it look very similar to classical mathematics. This includes allowing us to talk about sets and functions in strict finitism, although we are not really committed to such entities.

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References

  1. 2.
    Avigad, J., and S. Feferman. 1998. Gödel’s functional (“dialetica”) interpretation. In Handbook of proof theory, ed. S.R. Buss, 337–405. Amsterdam, The Netherlands: Elsevier.CrossRefGoogle Scholar
  2. 3.
    Barendregt, H.P. 1981. The Lambda Calculus, its syntax and semantics. Amsterdam: North-Holland.Google Scholar
  3. 4.
    Benacerraf, P. 1973. Mathematical truth. Journal of Philosophy 70:661–679. [Reprinted in Benacerraf, P., and H. Putnam. 1983. Philosophy of mathematics: Selected readings, 2nd ed. Cambridge: Cambridge University Press].CrossRefGoogle Scholar
  4. 5.
    Bishop, E. 1970. Mathematics as a numerical language. In Intuitionism and proof theory, eds. A. Kino, J. Myhill, and R.E. Vesley, 53–71. Amsterdam: North-Holland.Google Scholar
  5. 6.
    Bishop, E., and D.S. Bridges. 1985. Constructive analysis. New York: Springer.CrossRefGoogle Scholar
  6. 24.
    Murawski, R. 1999. Recursive functions and metamathematics. Dordrecht: Kluwer.CrossRefGoogle Scholar
  7. 33.
    Tait, W. 1981. Finitism. Journal of Philosophy 78:524–546.CrossRefGoogle Scholar
  8. 34.
    Troelstra, A.S. 1973. Metamathematical investigation of intuitionistic arithmetic and analysis. Lecture Notes in Mathematics, No. 344. Berlin: Springer.CrossRefGoogle Scholar
  9. 35.
    Troelstra, A.S. 1990. Introductory note to 1958 and 1972. In Kurt Gödel Collected works, volume II, ed. S. Feferman, et al. 217–239. Oxford: Oxford University Press.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of PhilosophyPeking UniversityBeijingP. R. China

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