Anti-Realism and Objectivity in Wittgenstein's Philosophy of Mathematics

In the first section, I characterize realism and illustrate the sense in which Wittgenstein's account of mathematics is anti-realist. In the second section, I spell out the above notion of objectivity and show how and anti-realist account of truth, namely, Putnam's idealized rational acceptability, preserves objectivity. In the third section, I discuss the "majority argument" and illustrate how Wittgenstein's anti-realism can also account for the objectivity of mathematics. What Putnam's and Wittgenstein's anti-realisms ultimately show is that this notion of objectivity is distinct from the notion of realism and that an account of objectivity is no reason to be either realist or anti-realist.