David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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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|
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Günther Eder (2013). Remarks on Independence Proofs and Indirect Reference. History and Philosophy of Logic 34 (1):68-78.
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