David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
In Kurt Gödel, Solomon Feferman, Charles Parsons & Stephen G. Simpson (eds.), Kurt Gödel: Essays for His Centennial. Association for Symbolic Logic (2010)
There are some puzzles about G¨ odel’s published and unpublished remarks concerning finitism that have led some commentators to believe that his conception of it was unstable, that he oscillated back and forth between different accounts of it. I want to discuss these puzzles and argue that, on the contrary, G¨ odel’s writings represent a smooth evolution, with just one rather small double-reversal, of his view of finitism. He used the term “finit” (in German) or “finitary” or “finitistic” primarily to refer to Hilbert’s conception of finitary mathematics. On two occasions (only, as far as I know), the lecture notes for his lecture at Zilsel’s [G¨ odel, 1938a] and the lecture notes for a lecture at Yale [G¨ odel, *1941], he used it in a way that he knew—in the second case, explicitly—went beyond what Hilbert meant. Early in his career, he believed that finitism (in Hilbert’s sense) is openended, in the sense that no correct formal system can be known to formalize all finitist proofs and, in particular, all possible finitist proofs of consistency of first-order number theory, P A; but starting in the Dialectica paper..
|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
Matthias Wille (2011). 'Metamathematics' in Transition. History and Philosophy of Logic 32 (4):333 - 358.
Similar books and articles
Richard Zach (2006). Hilbert's Program Then and Now. In Dale Jacquette (ed.), Philosophy of Logic. North Holland. 5--411.
Kurt Gödel, Solomon Feferman, Charles Parsons & Stephen G. Simpson (eds.) (2010). Kurt Gödel: Essays for His Centennial. Association for Symbolic Logic.
Matthias Schirn & Karl-Georg Niebergall (2003). What Finitism Could Not Be (Lo Que El Finitismo No Podría Ser). Critica 35 (103):43 - 68.
Thomas Hofweber (2000). Proof-Theoretic Reduction as a Philosopher's Tool. Erkenntnis 53 (1-2):127-146.
Yvon Gauthier (1994). Hilbert and the Internal Logic of Mathematics. Synthese 101 (1):1 - 14.
Richard Zach, Hilbert's Program. Stanford Encyclopedia of Philosophy.
Richard Zach (2003). The Practice of Finitism: Epsilon Calculus and Consistency Proofs in Hilbert's Program. Synthese 137 (1-2):211 - 259.
Wilfried Sieg (1999). Hilbert's Programs: 1917-1922. Bulletin of Symbolic Logic 5 (1):1-44.
Matthias Schirn & Karl-Georg Niebergall (2001). Extensions of the Finitist Point of View. History and Philosophy of Logic 22 (3):135-161.
Solomon Feferman (2008). Lieber Herr Bernays!, Lieber Herr Gödel! Gödel on Finitism, Constructivity and Hilbert's Program. Dialectica 62 (2: Table of Contents"/> Select):179–203.
Added to index2009-01-28
Total downloads45 ( #44,993 of 1,684,082 )
Recent downloads (6 months)9 ( #26,028 of 1,684,082 )
How can I increase my downloads?