David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
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)|
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
No references found.
Citations of this work BETA
Mihai Ganea (2010). Two (or Three) Notions of Finitism. Review of Symbolic Logic 3 (1):119-144.
Similar books and articles
Norwood 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, Hilbert's Program. Stanford Encyclopedia of Philosophy.
Richard Zach (2006). Hilbert's Program Then and Now. In Dale Jacquette (ed.), Philosophy of Logic. North Holland. 5--411.
Richard Zach (2003). The Practice of Finitism: Epsilon Calculus and Consistency Proofs in Hilbert's Program. Synthese 137 (1-2):211 - 259.
Added to index2010-08-10
Total downloads5 ( #234,982 of 1,100,145 )
Recent downloads (6 months)1 ( #304,144 of 1,100,145 )
How can I increase my downloads?