Abstract

The so-called traditional connection—a position defended by Bob Hale and Crispin Wright—aims to account for our knowledge of arithmetic by appeal to implicit definitions and stipulations. The resulting picture is one that does not draw on epistemic support from empirical evidence or from pragmatic considerations and thus regards our arithmetical knowledge as genuinely a priori. In this paper, I will offer a general framework for a theory of implicit definitions and locate therein the main tenets of the traditional connection while also highlighting the main challenges this approach faces.