Objectivity in Mathematics, without Mathematical Objects

Abstract

I identify two reasons for believing in the objectivity of mathematical knowledge: Apparent objectivity and applications in science. Focusing on arithmetic, I analyze platonism and cognitive nativism in terms of explaining these two reasons. After establishing that both theories run into difficulties, I present an alternative epistemological account that combines the theoretical frameworks of enculturation and cumulative cultural evolution. I show that this account can explain why arithmetical knowledge appears to be objective and has scientific applications. Finally, I will argue that, while this account is compatible with platonist metaphysics, it does not require postulating mind-independent mathematical objects.