ABSTRACT
This chapter is concerned with the nature of a priori statements, for example mathematical and logical propositions, and in particular, it critically discusses John Stuart Mill’s, Immanuel Kant’s and Gottlob Frege’s accounts of them. Traditionally a priori statements pose a problem for empiricists since empiricism holds that all knowledge is based on experience, but a priori propositions precisely are not based on experience. One response to the traditional problem that a priori knowledge presents empiricism with is Mill’s, which involves denying that mathematical truths are really a priori after all. Mill has two main arguments for denying the necessity of mathematical truths. First, he argues they are known by experience after all, and he holds this because he notes they are known through examples drawn from experience. The second argument that Mill offers against the necessity of mathematics is that mathematical truths are not necessary truths because they are not always even true.
