A Response to Dehnel's ‘Defending Wittgenstein’

Abstract

This is a reply to ‘Defending Wittgenstein’, Piotr Dehnel's critique of my article, ‘Defending Wittgenstein's Remarks on Cantor from Putnam’. I first show that my position is much more in agreement with Felix Mühlhölzer than Dehnel takes it to be, and that his criticism of me is nothing more than a failure to recognize this. I then show how Dehnel incorrectly reads Wittgenstein as rejecting set theory as false. It is an overemphasis on and a much too narrow picture of ‘applicability’ which leads him to this view. Finally, I conclude by rejecting Dehnel's view that Wittgenstein was a finitist about mathematics.