Hilbert's 'Verunglückter Beweis', the first epsilon theorem, and consistency proofs
History and Philosophy of Logic 25 (2):79-94 (2004)
| Abstract | 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 | ||||||||||
| Options |
|
|||||||||
Download options| PhilPapers Archive |
Upload a copy of this paper Check publisher's policy on self-archival Papers currently archived: 5,653 |
| External links |
 |
| Through your library | Configure |
Similar books and articlesNorwood Russell Hanson (1964). Stability Proofs and Consistency Proofs: A Loose Analogy. Philosophy of Science 31 (4):301-318.
Grigori Mints (1996). Strong Termination for the Epsilon Substitution Method. Journal of Symbolic Logic 61 (4):1193-1205.
G. Kreisel (1953). A Variant to Hilbert's Theory of the Foundations of Arithmetic. British Journal for the Philosophy of Science 4 (14):107-129.
Gregory H. Moore (1997). Hilbert and the Emergence of Modern Mathematical Logic. Theoria 12 (1):65-90.
Enrico Moriconi (2003). On the Meaning of Hilbert's Consistency Problem (Paris, 1900). Synthese 137 (1-2):129 - 139.
Georg Moser & Richard Zach (2006). The Epsilon Calculus and Herbrand Complexity. Studia Logica 82 (1):133 - 155.
Richard Zach (2003). The Practice of Finitism: Epsilon Calculus and Consistency Proofs in Hilbert's Program. Synthese 137 (1-2):211 - 259.
Analytics
Monthly downloads |
Added to index2010-08-10Total downloads5 ( #160,204 of 548,984 )Recent downloads (6 months)1 ( #63,327 of 548,984 )How can I increase my downloads? |
My notes
Discussion
