Extensions of the Finitist Point of View

History and Philosophy of Logic 22 (3):135-161 (2001)
Hilbert developed his famous finitist point of view in several essays in the 1920s. In this paper, we discuss various extensions of it, with particular emphasis on those suggested by Hilbert and Bernays in Grundlagen der Mathematik (vol. I 1934, vol. II 1939). The paper is in three sections. The first deals with Hilbert's introduction of a restricted ? -rule in his 1931 paper ?Die Grundlegung der elementaren Zahlenlehre?. The main question we discuss here is whether the finitist (meta-)mathematician would be entitled to accept this rule as a finitary rule of inference. In the second section, we assess the strength of finitist metamathematics in Hilbert and Bernays 1934. The third and final section is devoted to the second volume of Grundlagen der Mathematik. For preparatory reasons, we first discuss Gentzen's proposal of expanding the range of what can be admitted as finitary in his esssay ?Die Widerspruchsfreiheit der reinen Zahlentheorie? (1936). As to Hilbert and Bernays 1939, we end on a ?critical? note: however considerable the impact of this work may have been on subsequent developments in metamathematics, there can be no doubt that in it the ideals of Hilbert's original finitism have fallen victim to sheer proof-theoretic pragmatism
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1080/01445340210154295
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history
Request removal from index
Download options
Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 27,613
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA
Proof Theory.Gaisi Takeuti - 1987 - Elsevier.
The Collected Papers of Gerhard Gentzen.Gerhard Gentzen - 1969 - Amsterdam: North-Holland Pub. Co..
Finitism.W. W. Tait - 1981 - Journal of Philosophy 78 (9):524-546.
Encyclopedia of Philosophy.Leonard Linsky - 1970 - Ethics 80 (4):322-323.

View all 17 references / Add more references

Citations of this work BETA
Consistency, Models, and Soundness.Matthias Schirn - 2010 - Axiomathes 20 (2-3):153-207.

Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

27 ( #189,174 of 2,168,639 )

Recent downloads (6 months)

1 ( #346,816 of 2,168,639 )

How can I increase my downloads?

My notes
Sign in to use this feature

There  are no threads in this forum
Nothing in this forum yet.

Other forums