History and Philosophy of Logic 18 (4):201-209 (1997)
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Abstract |
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".
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Keywords | Hilbert Frege axiomatic method |
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DOI | 10.1080/01445349708837289 |
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References found in this work BETA
Grundlagen der Arithmetik: Studienausgabe MIT Dem Text der Centenarausgabe.Gottlob Frege - 1884 - Breslau: Wilhelm Koebner Verlag.
Die Grundlagen der Arithmetik: Eine Logische Mathematische Untersuchung Über den Begriff der Zahl.Gottlob Frege - 1988 - Felix Meiner Verlag.
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Citations of this work BETA
Frege’s ‘On the Foundations of Geometry’ and Axiomatic Metatheory.Günther Eder - 2016 - Mind 125 (497):5-40.
Frege and the Origins of Model Theory in Nineteenth Century Geometry.Günther Eder - 2019 - Synthese 198 (6):5547-5575.
Remarks on Independence Proofs and Indirect Reference.Günther Eder - 2013 - History and Philosophy of Logic 34 (1):68-78.
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