Abstract

The question of how and why the application of mathematics to physical reality is possible has occupied philosophers for many centuries. In contemporary discussions, Philip Kitcher’s attack on a priorist approaches to the question is particularly interesting, for it suggests that there is no global answer (Kitcher 1983, Chapters 1-4). In this essay, I would like to develop his insight by arguing, first, that the problem of how mathematics relates to physical reality should be addressed by an appeal to the history of mathematics and the sciences in the form of case studies which analyze the peculiar and changing ways in which these domains interact. Generalizations about such interaction should be made carefully, in a kind of local and piecemeal retrospective; I believe that the historical record will show that the grounds of justification and the form of applied mathematics changes dramatically from one historical era to the next.