Hume's Conception of Geometry and the Role of Contradiction

Abstract

David Hume’s account of geometry can seem puzzling as he claims that geometry is inexact and demonstrable. Graciela de Pierris argues for an interpretation that explains why Hume sees geometry as inexact and, yet, demonstrable. However, she doesn’t consider Hume’s description of relations of ideas found in the Enquiry. Hume distinguishes between matters of fact and relations of idea by checking to see if there is a contradiction with the denial of a proposition. Geometry is categorized as relations of idea, so the denials of geometric propositions cannot be conceivable and must imply a contradiction. I will argue that De Pierris’ account depicts definitions of geometric objects in such a way as to leave open the possibility for some relations of ideas where the denial of their proposition does not imply a contradiction, something Hume clearly did not intend.