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An account of distinctively mathematical explanation (DME) should satisfy three desiderata: it should account for the modal import of some DMEs; it should distinguish uses of mathematics in explanation that are distinctively mathematical from those that are not (Baron [2016]); and it should also account for the directionality of DMEs (Craver and Povich [2017]). Baron’s (forthcoming) deductive-mathematical account, because it is modeled on the deductive-nomological account, is unlikely to satisfy these desiderata. I provide a counterfactual account of DME, the Narrow Ontic Counterfactual Account (NOCA), that can satisfy all three desiderata. NOCA appeals to ontic considerations to account for explanatory asymmetry and ground the relevant counterfactuals. NOCA provides a unification of the causal and the non-causal, the ontic and the modal, by identifying a common core that all explanations share and in virtue of which they are explanatory.

Mechanistic explanations satisfy widely held norms of explanation: the ability to control and answer counterfactual questions about the explanandum. A currently debated issue is whether any non-mechanistic explanations can satisfy these explanatory norms. Weiskopf (2011) argues that the models of object recognition and categorization, JIM, SUSTAIN, and ALCOVE, are not mechanistic, yet satisfy these norms of explanation. In this paper I will argue that these models are sketches of mechanisms. My argument will make use of model-based fMRI, a novel neuroimaging approach whose significance for current debates on psychological models and mechanistic explanation has yet to be explored.