Mathematical Explanation In Biology

Biology has proved to be a rich source of examples in which mathematics plays a role in explaining some physical phenomena. In this paper, two examples from evolutionary biology, one involving periodical cicadas and one involving bee honeycomb, are examined in detail. I discuss the use of such examples to defend platonism about mathematical objects, and then go on to distinguish several different varieties of mathematical explanation in biology. I also connect these discussions to issues concerning generality in biological explanation, and to the question of how to pick out which mathematical properties are explanatorily relevant

Are Dynamic Mechanistic Explanations Still Mechanistic?

International audienceA major type of explanation in biology consists of mechanistic explanations (e.g. Machamer et al. 2000, Kaplan and Craver 2011). The explanatory force of mechanisms is apparent in such typical cases as the functioning of an ion channel or the molecular activation of a receptor: it includes the specification of a model of mechanism and the rehearsing of a causal story that tells how the explanandum phenomenon is produced by the mechanism. It is however much less clear how mechanisms explain in the case of complex and non-linear biomolecular networks such as those that underlie the action of hormones and the regulation of genes. While dynamic mechanistic explanations have been proposed as an extension of mechanistic explanations (e.g. Bechtel and Abrahamsen 2010), we argue that the former depart from the latter in that they do not draw their explanatory force from a causal story but from the mathematical warrants they give that the explanandum phenomenon follows from a mathematical model. By analyzing the explanatory force of mechanistic explanation and of dynamic mechanistic explanation, we show that the two types of explanations can be construed as limit cases of a more general pattern of explanation-Causally Interpreted Model Explanations-that draws its explanatory force from a model, a causal interpretation that links the model to biological reality, and a mathematical derivation that links the model to the explanandum phenomenon