Problem-Driven Mathematical Explanations In Science

Document Type

Book Chapter

Publication Date

2025

Published In

The Heuristic View: Logic, Mathematics, and Science

Series Title

Synthese Library

Abstract

In his recent book, The Making of Mathematics, Carol Celucci raises three objections to the possibility of mathematical explanations in science; the Problem of Aboutness, the Problem of Abstraction, and the Problem of Arbitrariness. I argue that only the last of these raises any serious concerns. The current mainstream view on how mathematics is applied in science is that this involves the mapping of physical phenomena onto mathematical apparatus. The mapping is supposed to relate physical structure to mathematical structure, but arbitrariness occurs because any given physical phenomenon exhibits a myriad of different structures. To illustrate, I discuss the well-known bridges of Königsberg example, and the less well-known river crossings of Manhattan example. I explore a possible solution to this problem that involves linking mathematics not to phenomena but to problems. The idea is that a problem may naturally prioritize one physical structure over others, thus picking out a unique structure for the mapping relation.

Keywords

Mathematical explanation, Bridges of Königsberg, Abstraction

Published By

Springer

Editor(s)

E. Ippoliti and F. Sterpetti

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