A New Role for Mathematics in Empirical Sciences

A New Role for Mathematics in Empirical Sciences

Kasirzadeh, A forthcoming, ‘A New Role for Mathematics in Empirical Sciences’, Philosophy of Science.

Mathematics is often taken to play one of two roles in the empirical sciences: either it represents empirical phenomena, or it explains these phenomena by imposing constraints on them. This paper identifies a third and distinct role which has not been fully appreciated in the literature, and may be pervasive (in varying degrees) in scientific practice. I call this the "bridging'' role of mathematics, according to which mathematics acts as a connecting scheme in our explanatory reasoning about why and how two different descriptions of an empirical phenomenon relate to each other. I argue that this role differs from both the representational and the constraining - explanatory roles. I justify my claim by analysing two bridging roles for mathematics appearing in biological and physical explanations. This discussion has implications for the roles of mathematics in building ethical algorithms.