Wittgenstein on Circularity in the Frege-Russell Definition of Cardinal Number

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Samenvatting

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 from Wittgenstein's Nachlass, showing that if different uses of 'pre-supposition' 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 the logicist may find too 'constructivist'.

Originele taal-2English
Pagina's (van-tot)354-373
Aantal pagina's20
TijdschriftPhilosophia Mathematica
Volume16
Nummer van het tijdschrift3
DOI's
StatusPublished - okt-2008

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