Erik Weber

Although there is a consensus among philosophers of mathematics and mathematicians that mathematical explanations exist, only a few authors have proposed accounts of explanation in mathematics. These accounts fit into the unificationist or top-down approach to explanation. We argue that these models can be complemented by a bottom-up approach to explanation in mathematics. We introduce the mechanistic model of explanation in science and discuss the possibility of using this model in mathematics, arguing that using it does not presuppose a Platonist view of mathematics and allows one to gain insight into why a theorem is true by answering what-if-things-had-been-different questions

If dispositions are conceived as properties of systems that refer to possible causal relations, dispositions can be used in singular causal explanations. By means of these dispositional explanations, we can explain behavior B of a system x by (i) referring to a situation of type S that triggered B, given that x has a disposition D to do B in S, or (ii) by referring to a disposition D of x to do B in S, given that x is in a situation of type S. Dispositional explanations are adequate and indispensable explanations: they can explain behavior B without explicitly referring to the underlying causal basis in x that constitutes a disposition to do B. Radical Behaviorist explanations are a sort of dispositional explanations, but the dispositional model is not restricted to these explanations. The dispositional model is compatible with, or can be applied to, several research programs.

Among philosophers of science, there is now a widespread agreement that the DN model of explanation is poorly equipped to account for explanations in biology. Rather than identifying laws, so the consensus goes, researchers explain biological capacities by constructing a model of the underlying mechanism.We think that the dichotomy between DN explanations and mechanistic explanations is misleading. In this article, we argue that there are cases in which biological capacities are explained without constructing a model of the underlying mechanism. Although these explanations do not conform to Hempel’s DN model, they do invoke more or less stable generalisations. Because they invoke generalisations and have the form of an argument, we call them inferential explanations. We support this claim by considering two examples of explanations of biological capacities: pigeon navigation and photoperiodism. Next, we will argue that these non-mechanistic explanations are crucial to biology in three ways: sometimes, they are the only thing we have, they are heuristically useful, and they provide genuine understanding and so are interesting in their own right.In the last sections we discuss the relation between types of explanations and types of experiments and situate our views within some relevant debates on explanatory power and explanatory virtues.

In a recent paper on realism and pragmatism published in this journal, Osmo Kivinen and Tero Piiroinen have been pleading for more methodological work in the philosophy of the social sciences—refining the conceptual tools of social scientists—and less philosophically ontological theories. Following this de-ontologizing approach, we scrutinize the debates on social explanation and contribute to the development of a pragmatic social science methodology. Analyzing four classic debates concerning explanation in the social sciences, we propose to shift the debate away from (a) the ontologizing defenses of forms of social explanation, and (b) a winner-takes-all-approach. Instead, we advocate (c) a pragmatic approach towards social explanation, elaborating a rigorous framework for explanatory pluralism detached from the debates on social ontology.