Where Does the Idea of a Triangle Come From

Descartes’ Conception of Geometrical Figures Between Innate Ideas, Eternal Essences, and Universals

Abstract

In the Fifth Meditation, Descartes argues that people have innate ideas of geometric figures, such as triangles. At the same time, he writes in a problematic passage that there are eternal essences that correspond to innate ideas. Although some scholars have tried to reduce the ontological status of these essences to exsistence in the human mind, in this article, I argue that such a reading is not justified and that innate ideas and eternal essences are two separate entities, with ideas referring to eternal essences.

Additionally, Descartes discusses ideas of geometric figures in the first part of the Principles of Philosophy, where he places them within the framework of the theory of universals. However, the tone here is quite different: universal ideas of figures in the Principles are formed, not innate. This contradiction can be resolved by considering that universals are not innate ideas: rather, the universals from the Principles are ideas (or names) in a broader sense, which we form in imagination and use to categorize sensory material. He was likely influenced in this conception by the discussion in the Third and Fifth Objections and Replies to the Meditations. However, Descartes’ theory of universals was not fully developed: in his later works, Descartes also experimented with other models, such as a new theory of intellectual memory. Therefore, we can conclude that Descartes’ theory of knowledge of geometric objects, such as figures, is complex and can only be fully understood from a diachronic perspective.