Was Wittgenstein really a Constructivist about Mathematics?

Abstract

It will be argued that Wittgenstein did not outright reject the law of excluded middle for mathematics or the proof-techniques that constructivists reject in connection with the law of excluded middle. Wittgenstein can be seen to be critical of the dogmatic claims of Brouwer and Weyl concerning how proofs should be constructed. Rather than himself laying down a requirement concerning what is and is not a proof, Wittgenstein can be read as exploring the differences between constructive and non-constructive proofs. I will read Wittgenstein as arguing that Brouwer’s rejection of excluded middle is based upon an over-extension from examples that Wittgenstein reads as special cases. Wittgenstein is certainly interested in the difference between constructive and non-constructive proof but only for the purposes of exploring the easily-missed differences between the two, not in order to reject non-constructive approaches.