The Unreasonable Effectiveness. The Philosophical Problem of the Applicability of Mathematics

Abstract

In this article I will sketch a general introduction to the problem of the applicability of mathematics as it is conceived in contemporary philosophy of mathematics. After some brief considerations concerning the historical reason why this problem was dismissed by the philosophical analysis during the first half of 20th century, I will expound Wigner’s puzzle, and I will make some theoretical considerations about it. In particular, I will show that the problem of applicability is independent from the ontological framework we can eventually assume and that it depends rather on the existence of an epistemological gap between mathematics and physics. Finally, I will try to sketch a possible line of inquiry for understanding the applicability of mathematics in physics.