Philippe Huneman, CNRS/Université Paris 1 Sorbonne

About the concept of structural explanations.

Abstract. I argue that in some scientific explanations mathematics are playing an explanatory rather than a representational role, and that this feature unifies many types of non-causal or non-mechanistic explanation that some philosophers of science have been recently exploring under various names (mathematical, topological, etc.). I'll start by illustrating how mathematics can play either a representational or an explanatory role through the consideration of two alternative explanations of a same biological pattern - "Bergmann's rule" -.
Then I account for the way mathematical properties may function in an explanatory way within an explanation by arguing that some mathematical facts involving variables non directly referring to the target system constitute constraints to which a whole class of systems should comply. According to this "constraint account", those mathematical facts are directly entailing the explanandum (often a limit regime, a robustness property or a steady state), as a consequence of such constraints. I call those explanations "structural", because here properties of mathematical structures are accounting for the explanandum; various kinds of mathematical structures (algebraic, graph-theoretical, etc.) thereby define various types of structural explanations. This account makes sense of particular features of all these families of explanations, and above all their genericity.