Philosophical Investigations, Volume 45, Issue 3, Page 320-333, July 2022.

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. (shrink)

In Remarks on the Foundations of Mathematics, Wittgenstein notes that he has ‘not yet made the role of miscalculating clear’ and that ‘the role of the proposition: “I must have miscalculated”…is really the key to an understanding of the “foundations” of mathematics.’ In this paper, I hope to get clear on how this is the case. First, I will explain Wittgenstein's understanding of a ‘foundation’ for mathematics. Then, by showing how the proposition ‘I must have miscalculated’ differentiates mathematics from the (...) physical sciences, we will see how this proposition is the key to understanding the foundations of mathematics. (shrink)

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