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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
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.
Barendregt, H.P. 1981. The Lambda Calculus, its syntax and semantics. Amsterdam: North-Holland.
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].
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.
Bishop, E., and D.S. Bridges. 1985. Constructive analysis. New York: Springer.
Murawski, R. 1999. Recursive functions and metamathematics. Dordrecht: Kluwer.
Tait, W. 1981. Finitism. Journal of Philosophy 78:524–546.
Troelstra, A.S. 1973. Metamathematical investigation of intuitionistic arithmetic and analysis. Lecture Notes in Mathematics, No. 344. Berlin: Springer.
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.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2011 Springer Science+Business Media B.V.
About this chapter
Cite this chapter
Ye, F. (2011). Strict Finitism. In: Strict Finitism and the Logic of Mathematical Applications. Synthese Library, vol 355. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1347-5_2
Download citation
DOI: https://doi.org/10.1007/978-94-007-1347-5_2
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-1346-8
Online ISBN: 978-94-007-1347-5
eBook Packages: Humanities, Social Sciences and LawPhilosophy and Religion (R0)