Dissociation and Exemplarity. Proposing a Mathematical Alternative to Heideggerian Questioning

Abstract

Within the philosophy of Martin Heidegger, the role of modern mathematics and modern natural science is largely limited to that of “producing results” (rather than “thinking”), because, he argues, science is always ontologically founded on a being—for example, the transcendental subject—which itself remains unelucidated as to its ontological bearings. At the same time, however, the usefulness of Heidegger's alternative to scientific inquiry, philosophical questioning, is seemingly limited to the vague “pondering of essences.” I argue that the work of Albert Lautman, a French philosopher of mathematics active for only a few years on the eve of the Second World War, offers a way out of this impasse. His conception of the dissociative movement by which mathematics progresses can be understood as a mode of Heideggerian questioning, and his notion of exemplarity, by which he interprets the relation of being and beings, provides mathematics with a foundation that escapes Heidegger’s conception of modern science. This means that the activity of mathematics thus understood is not reducible to thoughtless result-production, but is in fact deeply philosophical—even in Heidegger's sense.