David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
History and Philosophy of Logic 18 (4):201-209 (1997)
In a letter to Frege of 29 December 1899, Hilbert advances his formalist doctrine, according to which consistency of an arbitrary set of mathematical sentences is a sufficient condition for its truth and for the existence of the concepts described by it. This paper discusses Frege's analysis, as carried out in the context of the Frege-Hilbert correspondence, of the formalist approach in particular and the axiomatic method in general. We close with a speculation about Frege's influence on Hilbert's later work in foundations, which we consider to have been greater than previously assumed. This conjecture is based on a hitherto neglected revision of Hilbert's talk "Über den Zahlbegriff".
|Keywords||Hilbert Frege axiomatic method|
|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
Günther Eder (2013). Remarks on Independence Proofs and Indirect Reference. History and Philosophy of Logic 34 (1):68-78.
Similar books and articles
William Demopoulos (1994). Frege, Hilbert, and the Conceptual Structure of Model Theory. History and Philosophy of Logic 15 (2):211-225.
G. Aldo Antonelli & Robert C. May (2000). Frege's New Science. Notre Dame Journal of Formal Logic 41 (3):242-270.
David Hilbert (1899). Letter to Frege, 29.Xii.1899. In Gottfried Gabriel, Hans Hermes, Friedrich Kambartel, Christian Thiel, Albert Veraart, Brian McGuinness & Hans Kaal (eds.), Gottlob Frege: Philosophical and Mathematical Correspondence. 38--41.
Patricia Blanchette, The Frege-Hilbert Controversy. The Stanford Encyclopedia of Philosophy.
Patricia A. Blanchette (2007). Frege on Consistency and Conceptual Analysis. Philosophia Mathematica 15 (3):321-346.
Michael Stoeltzner, How Metaphysical is "Deepening the Foundations"? - Hahn and Frank on Hilbert's Axiomatic Method.
Enrico Moriconi (2003). On the Meaning of Hilbert's Consistency Problem (Paris, 1900). Synthese 137 (1-2):129 - 139.
Gottlob Frege (1895). The Frege-Hilbert Correspondence. In Gottfried Gabriel, Hans Hermes, Friedrich Kambartel, Christian Thiel, Albert Veraart, Brian McGuinness & Hans Kaal (eds.), Gottlob Frege: Philosophical and Mathematical Correspondence. Blackwell. 33--51.
Richard Zach (2006). Hilbert's Program Then and Now. In Dale Jacquette (ed.), Philosophy of Logic. North Holland. 5--411.
Volker Peckhaus (1995). Hilberts Logik. Von der Axiomatik zur Beweistheorie. NTM International Journal of History and Ethics of Natural Sciences, Technology and Medicine 3 (1):65-86.
Stewart Shapiro (2005). Categories, Structures, and the Frege-Hilbert Controversy: The Status of Meta-Mathematics. Philosophia Mathematica 13 (1):61-77.
Richard Zach (2004). Hilbert's 'Verunglückter Beweis', the First Epsilon Theorem, and Consistency Proofs. History and Philosophy of Logic 25 (2):79-94.
Ansten Klev (2011). Dedekind and Hilbert on the Foundations of the Deductive Sciences. Review of Symbolic Logic 4 (4):645-681.
Added to index2010-09-02
Total downloads22 ( #79,499 of 1,102,917 )
Recent downloads (6 months)5 ( #62,002 of 1,102,917 )
How can I increase my downloads?