Erik Weber

In this paper we argue that in recent literature on mechanistic explanations, authors tend to conflate two distinct features that mechanistic models can have or fail to have: plausibility and richness. By plausibility, we mean the probability that a model is correct in the assertions it makes regarding the parts and operations of the mechanism, i.e., that the model is correct as a description of the actual mechanism. By richness, we mean the amount of detail the model gives about the actual mechanism. First, we argue that there is at least a conceptual reason to keep these two features distinct, since they can vary independently from each other: models can be highly plausible while providing almost no details, while they can also be highly detailed but plainly wrong. Next, focusing on Craver's continuum of ?how-possibly,? to ?how-plausibly,? to ?how-actually? models, we argue that the conflation of plausibility and richness is harmful to the discussion because it leads to the view that both are necessary for a model to have explanatory power, while in fact, richness is only so with respect to a mechanism's activities, not its entities. This point is illustrated with two examples of functional models

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.

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