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.

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.