Reflections on the Empirical Applicability of Mathematics

Abstract

This paper addresses the not infrequently voiced view that the immense usefulness of mathematics in the physical sciences constitutes a deep philosophical mystery, with potentially far-reaching implications concerning the relationship between the inquiring mind and the material world. It grants the broadly Humean point that the very possibility of inductive projection from past to future, by whatever intellectual means, must be considered a remarkable and perhaps inexplicable fact, but calls into question the idea that the utility of mathematics in this regard is especially baffling. While the aims pursued in pure mathematics may differ radically from those of engineers and scientists, in their development of concepts and theories mathematicians are nevertheless beholden to the same fundamental standards of simplicity and similarity that must govern any reasonable inductive projection; and this fact, it is suggested, may go a considerable way towards explaining why many mathematical constructs lend themselves to empirical application.