Dummett on Wittgenstein’s Philosophy of Mathematics

Abstract

In his paper “Wittgenstein’s philosophy of mathematics” Michael Dummett critically represents the main Wittgenstein theses both on philosophy of mathematics and mathematics itself. Dummett mainly concentrates on Wittgenstein’s philosophy of mathematics from his “Remarks on the Foundation of Mathematics”, in which an antirealist view is endorsed. According to Dummett, Wittgenstein’s main reason for denying the objectivity of mathematical truth is his denial of the objectivity of proof in mathematics. According to Wittgenstein, we reject or accept a proof arbitrarily. Nevertheless, Wittgenstein sustains that mathematics appears to us both as a collection of rules and as the natural history of the domain of numbers. Dummett’s interpretation doesn’t include the latter thought.