The Nature of Mathematical Knowledge

Abstract The Nature of Mathematical Knowledge develops and defends an empiricist approach to mathematical knowledge. After offering an account of a priori knowledge, it argues that none of the available accounts of a priori mathematical knowledge is viable. It then constructs an approach to the content of mathematical statements, viewing mathematics as grounded in our manipulations of physical reality. From these crude beginnings, mathematics unfolds through the successive modifications of mathematical practice, spurred by the presence of unsolved problems. This process of unfolding is considered in general, and illustrated by considering the historical development of analysis from the seventeenth century to the end of the nineteenth.