Mapping-Based Accounts of Applicability and Converse Applications

While the problem of the applicability of mathematics in science has been the object of much philosophical discussion, the converse issue of accounting for the successful application of science in mathematics is still in its exploratory stages. In this paper I focus on the latter issue and I discuss it in connection with the mapping view of applied mathematics, which is currently the most influential approach adopted by philosophers to account for the applicability of mathematics in the empirical sciences. More specifically, I address the question of whether the mapping view works for cases of converse applications (i.e., successful applications of the empirical sciences in mathematics). By focusing on some case studies, I argue that the answer to this question is negative and the mapping account of applied mathematics, as it is usually presented in the literature on the applicability of mathematics, does not have the resources to handle the converse applicability issue. To make my point, I will proceed in the following way: first, I will maintain that we can distinguish two types of converse applications, which I name in-argument and in-result converse applications; next, I will assess the mapping account on these types of converse applications and I will point to the reasons why such view cannot accommodate converse applications within its framework.