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33Russell's paradox in consistent fragments of Frege's Grundgesetze der ArithmetikIn Godehard Link (ed.), One Hundred Years of Russell's Paradox: Mathematics, Logic, Philosophy, De Gruyter. 2004.We provide an overview of consistent fragments of the theory of Frege’s Grundgesetze der Arithmetik that arise by restricting the second-order comprehension schema. We discuss how such theories avoid inconsistency and show how the reasoning underlying Russell’s paradox can be put to use in an investigation of these fragments.
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180Aspekte der Frege–Hilbert-KorrespondenzHistory 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…Read more
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