The Importance of Cartesian Triangles: A New Look at Descartes's Ontological Argument

Abstract

In this paper, I argue that commentators have missed a significant clue given by Descartes in coming to understand his 'ontological' proof for the existence of God. In both the analytic and synthetic presentations of the proof throughout his writings, Descartes notes that the proof works 'in the same way' as a particular geometrical proof. I explore the significance of such a parallel, and conclude that Descartes could not have intended readers to think that the argument consists of some kind of intuition. I argue that for Descartes the attribute of existence is a 'second-order' attribute that is demonstrated to belong to the idea of God on the basis of 'first-order' attributes. The proof, properly understood, is in fact a demonstration. Having brought to light the geometrical parallels between the ontological and geometrical proofs, we have new evidence to resolve the 'intuition versus demonstration' controversy that has characterized much of the discussion of Descartes's ontological argument.