Hilbert's 'Verunglückter Beweis', the first epsilon theorem, and consistency proofs

History and Philosophy of Logic 25 (2):79-94 (2004)
In the 1920s, Ackermann and von Neumann, in pursuit of Hilbert's programme, were working on consistency proofs for arithmetical systems. One proposed method of giving such proofs is Hilbert's epsilon-substitution method. There was, however, a second approach which was not reflected in the publications of the Hilbert school in the 1920s, and which is a direct precursor of Hilbert's first epsilon theorem and a certain ?general consistency result? due to Bernays. An analysis of the form of this so-called ?failed proof? sheds further light on an interpretation of Hilbert's programme as an instrumentalist enterprise with the aim of showing that whenever a ?real? proposition can be proved by ?ideal? means, it can also be proved by ?real?, finitary means
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1080/01445340310001606930
 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
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 24,479
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
G. Kreisel (1968). A Survey of Proof Theory. Journal of Symbolic Logic 33 (3):321-388.
Philip Kitcher (1976). Hilbert's Epistemology. Philosophy of Science 43 (1):99-115.
Marcus Giaquinto (1983). Hilbert's Philosophy of Mathematics. British Journal for the Philosophy of Science 34 (2):119-132.

View all 8 references / Add more references

Citations of this work BETA
Mihai Ganea (2010). Two (or Three) Notions of Finitism. Review of Symbolic Logic 3 (1):119-144.
Dirk Schlimm (2005). History and Philosophy of Logic. Bulletin of Symbolic Logic 11 (2):247-248.

Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

13 ( #333,277 of 1,925,752 )

Recent downloads (6 months)

5 ( #187,096 of 1,925,752 )

How can I increase my downloads?

My notes
Sign in to use this feature

Start a new thread
There  are no threads in this forum
Nothing in this forum yet.