Event Detail

For over two millennia, Euclid’s Elements was seen as a paradigm of a priori reasoning. With the discovery of non-Euclidean geometries, and the eventual realization that our own universe is itself non-Euclidean, the status of our geometrical knowledge was radically undermined. In the wake of this upheaval, philosophers adopted two revisionary interpretations of Euclidean proof. Some suggested that we understand Euclidean proof as a purely formal system of deductive logic – one not concerned with specifically geometrical content at all. Others suggested that Euclidean proof employs concepts derived from our sensory experience or imagination. I argue that both interpretations fail to capture the true nature of our geometrical reasoning. Euclidean proof is not a purely formal system of deductive logic, but one in which our grasp of the content of geometrical concepts plays a central role; moreover, our grasp of this content is a priori, rather than being derived from experience.