Introduction

Summary

In this Introduction, I distinguish between two a posteriori views with respect to mathematical knowledge. According to the epistemological a posteriori position, mathematical knowledge is acquired empirically. According to the methodological a posteriori approach, empirical research is important for understanding what mathematical knowledge is like. I emphasise the need for the latter in the epistemology of arithmetic, while also accepting the importance of a priori methodology. However, empirical researchers and philosophers of mathematics do not share a common conceptual framework, which makes successful interdisciplinary research difficult. After pointing out some of the key problems, I provide a coherent conceptual framework and consistent terminology.