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

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Citations of this work BETA
Mihai Ganea (2010). Two (or Three) Notions of Finitism. Review of Symbolic Logic 3 (1):119-144.

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