Philosophy of Mathematics seminar

William D’Alessandro, Oxford

Explanation in mathematics: a noetic account (based on joint work with Ellen Lehet)  

We defend a noetic account of intramathematical explanation. On this view, a piece of mathematics is explanatory just in case it produces understanding of an appropriate type. We begin by discussing and criticizing the most prominent extant version of noeticism, due to Matthew Inglis and Juan-Pablo Mejía-Ramos, which identifies explanatory understanding with the possession of well-organized cognitive schemas. We then present a novel noetic account. On our view, explanatory understanding arises from meeting specific “explanatory objectives”. We defend a cluster-concept account of explanatory objectives and identify four important subfamilies within the relevant network of resemblance relations. The resulting view is objectivist (in the sense that it takes explanatory success to be a matter of observer-independent fact), broader in scope than why-question-based accounts, and capable of generalizing to scientific explanation as a whole. It thus fulfills Friedman’s half-century-old demand for a general and objectivist theory which accounts for the link between explanation and understanding.