Wittgenstein on circularity in the frege-russell definition of cardinal number

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 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 the logicist may find too 'constructivist'. © The Author [2008]. Published by Oxford University Press. All rights reserved.