Remarks on finitism

Abstract

The background of these remarks is that in 1967, in ‘’Constructive reasoning” [27], I sketched an argument that finitist arithmetic coincides with primitive recursive arithmetic, P RA; and in 1981, in “Finitism” [28], I expanded on the argument. But some recent discussions and some of the more recent literature on the subject lead me to think that a few further remarks would be useful.

Categories

Keywords

Reprint years

Other Versions

No versions found

Links

PhilArchive

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

  • Only published works are available at libraries.

My notes

Similar books and articles

What Hilbert and Bernays Meant by “Finitism”.William Tait - 2018 - In Gabriele M. Mras, Paul Weingartner & Bernhard Ritter, Philosophy of Logic and Mathematics: Proceedings of the 41st International Ludwig Wittgenstein Symposium. Berlin, Boston: De Gruyter. pp. 249-262.
What Finitism Could Not Be.Matthias Schirn & Karl-Georg Niebergall - 2003 - Critica 35 (103):43-68.
Gödel on intuition and on Hilbert's finitism.W. W. Tait - 2010 - In Kurt Gödel, Solomon Feferman, Charles Parsons & Stephen G. Simpson, Kurt Gödel: essays for his centennial. Ithaca, NY: Association for Symbolic Logic.
Finitism = PRA? On a Thesis of W.W. Tait.Matthias Schirn & Karl-Georg Niebergall - 2005 - Reports on Mathematical Logic:3-24.
Kant and Finitism.W. W. Tait - 2016 - Journal of Philosophy 113 (5/6):261-273.
Wittgenstein and finitism.Mathieu Marion - 1995 - Synthese 105 (2):141 - 176.
Hilbert’s Finitism: Historical, Philosophical, and Metamathematical Perspectives.Richard Zach - 2001 - Dissertation, University of California, Berkeley
Some Remarks on a Difference between Gentzen's Finitist and Heyting's Intuitionist Approaches toward Intuitionistic Logic and Arithmetic.Mitsuhiro Okada - 2008 - Annals of the Japan Association for Philosophy of Science 16 (1-2):1-17.
On the Coherence of Wittgensteinian Constructivism.Amit Saad - 2016 - Acta Analytica 31 (4):455-462.
Skolem TH.. Remarks on recursive functions and relations. Det Kongelige Norske Videnskabers Selskab, Forhandlinger, vol. 17, pp. 89–92.Skolem TH.. Some remarks on recursive arithmetic. Det Kongelige Norske Videnskabers Selskab, Forhandlinger, vol. 17, pp. 103–106.Skolem TH.. A note on recursive arithmetic. Det Kongelige Norske Videnskabers Selskab, Forhandlinger, vol. 17, pp. 107–109.Skolem TH.. Some remarks on the comparison between recursive functions. Det Kongelige Norske Videnskabers Selskab, Forhandlinger, vol. 17, pp. 126–129. [REVIEW]Paul Bernays - 1946 - Journal of Symbolic Logic 11 (1):26-28.

Analytics

Added to PP
2009-01-28

Downloads
151 (#281,020)

6 months
22 (#468,057)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Photo of William W. Tait
William W. Tait
University of Chicago

Citations of this work

Arithmetical Reflection and the Provability of Soundness.Walter Dean - 2015 - Philosophia Mathematica 23 (1):31-64.
Hilbert’s Program.Richard Zach - 2012 - In Ed Zalta, Stanford Encyclopedia of Philosophy. Stanford, CA: Stanford Encyclopedia of Philosophy.
The Ways of Hilbert's Axiomatics: Structural and Formal.Wilfried Sieg - 2014 - Perspectives on Science 22 (1):133-157.
Hilbert's program then and now.Richard Zach - 2002 - In Dale Jacquette, Philosophy of Logic. Malden, Mass.: North Holland. pp. 411–447.

View all 29 citations / Add more citations

References found in this work

No references found.

Add more references