Philosophia Mathematica 16 (3):354-373 (2008)
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Abstract |
Several scholars have argued that Wittgenstein held the view that the notion of number is presupposed by the notion of one-one correlation, and that therefore Hume's principle is not a sound basis for a definition of number. I offer a new interpretation of the relevant fragments on philosophy of mathematics from Wittgenstein's Nachlass, showing that if different uses of ‘presupposition’ are understood in terms of de re and de dicto knowledge, Wittgenstein's argument against the Frege-Russell definition of number turns out to be valid on its own terms, even though it depends on two epistemological principles logicist philosophers of mathematics may find too ‘constructivist’.
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Keywords | wittgenstein mathematics hume's principle number cardinal number philosophy of mathematics Frege-Russell definition of cardinal number logicism constructivism |
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Reprint years | 2007, 2008 |
DOI | 10.1093/philmat/nkn002 |
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References found in this work BETA
Ludwig Wittgenstein the Duty of Genius.Ray Monk & Richard C. Monk - 1990 - New York, NY, USA: Penguin.
The Foundations of Arithmetic: A Logico-Mathematical Enquiry Into the Concept of Number.Gottlob Frege - 1950 - New York, NY, USA: Northwestern University Press.
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