Summary

Before Descartes can move on to the existence of material things, there is still one last thing he has to consider: his ideas of them. One of the most important aspects of these ideas is how they present material objects as having geometrical and mathematical properties; we picture thinks as having shapes, location, number, and so on. These properties, Descartes says, are so clear and distinct that things like numbers or triangles clearly exist in some way, even if it is as objects in the external world. Furthermore, the properties of these objects do not depend on Descartes’ own mind; the fact that a triangle’s angles sum up to 180 degrees is true independent of Descartes.

Meditating on the certainty of geometric reasoning, Descartes wonders if he can use that same kind of reasoning to give another proof that God exists. Like triangles...