On the Intuitionistic Background of Gentzen's 1935 and 1936 Consistency Proofs and Their Philosophical Aspects

Gentzen's three consistency proofs for elementary number theory have a common aim that originates from Hilbert's Program, namely, the aim to justify the application of classical reasoning to quantified propositions in elementary number theory. In addition to this common aim, Gentzen gave a “finitist” interpretation to every number-theoretic proposition with his 1935 and 1936 consistency proofs. In the present paper, we investigate the relationship of this interpretation with intuitionism in terms of the debate between the Hilbert School and the Brouwer School over the significance of consistency proofs. First, we argue that the interpretation had the role of responding to a Brouwer-style objection against the significance of consistency proofs. Second, we propose a way of understanding Gentzen's response to this objection from an intuitionist perspective.
Keywords proof theory  intuitionism  foundations of mathematics  philosophy of logic  history of logic
Categories (categorize this paper)
DOI 10.4288/jafpos.27.0_1
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 36,555
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

A Semantics of Evidence for Classical Arithmetic.Thierry Coquand - 1995 - Journal of Symbolic Logic 60 (1):325-337.
Notation Systems for Infinitary Derivations.Wilfried Buchholz - 1991 - Archive for Mathematical Logic 30 (5-6):277-296.
The Collected Papers of Gerhard Gentzen.M. E. Szabo - 1971 - Journal of Philosophy 68 (8):238-265.

View all 9 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Gentzen's Consistency Proof Without Heightlines.Annika Siders - 2013 - Archive for Mathematical Logic 52 (3-4):449-468.
Classical Logic, Intuitionistic Logic, and the Peirce Rule.Henry Africk - 1992 - Notre Dame Journal of Formal Logic 33 (2):229-235.
On the Philosophical Significance of Consistency Proofs.Michael D. Resnik - 1974 - Journal of Philosophical Logic 3 (1/2):133 - 147.
Consistency Proof Via Pointwise Induction.Toshiyasu Arai - 1998 - Archive for Mathematical Logic 37 (3):149-165.
Monotone Proofs of the Pigeon Hole Principle.R. Gavalda, A. Atserias & N. Galesi - 2001 - Mathematical Logic Quarterly 47 (4):461-474.
Gentzen's Proof Systems: Byproducts in a Work of Genius.Jan von Plato - 2012 - Bulletin of Symbolic Logic 18 (3):313-367.


Added to PP index

Total downloads
6 ( #691,859 of 2,302,554 )

Recent downloads (6 months)
6 ( #97,470 of 2,302,554 )

How can I increase my downloads?

Monthly downloads

My notes

Sign in to use this feature