The role of pragmatic considerations during mathematical derivation in the applicability of mathematics

Abstract

The conditions involved in the applicability of mathematics in science are the subject of ongoing debates. One of the best-received approaches is the inferential account, which involves structural mappings and pragmatic considerations in a three-step model. According to the inferential account, these pragmatic considerations happen in the immersion and interpretation stages, but not during derivation (symbol-pushing in a mathematical formalism). In this work, I draw inspiration from the later Wittgenstein and make the case that the applicability of mathematics also rests on pragmatic considerations at the mathematical derivation level. I make the further case that pragmatic considerations at the mathematical derivation level may substitute pragmatic considerations in the other two stages, thus showing how they are holistically interrelated. I illustrate these two points with the solution of a simple geometrical problem.