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
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DOI 10.1080/01445340310001606930
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References found in this work BETA
A Survey of Proof Theory.G. Kreisel - 1968 - Journal of Symbolic Logic 33 (3):321-388.
Hilbert's Epistemology.Philip Kitcher - 1976 - Philosophy of Science 43 (1):99-115.
Hilbert's Philosophy of Mathematics.Marcus Giaquinto - 1983 - British Journal for the Philosophy of Science 34 (2):119-132.
On the Interpretation of Non-Finitist Proofs--Part I.G. Kreisel - 1951 - Journal of Symbolic Logic 16 (4):241-267.

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

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