@gorillapaws “What about his ontological argument for the existence of God?”
Descartes’ ontological argument says that once we examine our idea of God, we will see that He must exist. The necessity of our belief confirms God’s existence. But the argument doesn’t say that our idea of God causes God to exist (nor that ceasing to believe in God would cause God to cease existing, even if He were standing right before our eyes when we stopped believing). Our belief does not determine God’s existence.
If I might be allowed to get deep into the weeds here, Descartes’ argument for the existence of God is supposed to operate on the same principles as the cogito. The cogito says that once you examine your idea of thinking, you will realize that there is no way to doubt that you are both thinking and existing. Descartes’ version of the ontological argument for God, meanwhile, says that once you examine your idea of God, you will realize that there is no way to doubt that that something answering to that description must exist.
But while both of these conclusions are initially approached in the guise of a deductive argument, that aspect is ultimately discarded. In the end, the existence of the self and the existence of God are delivered by what Descartes calls the “natural light of reason.” Note that the natural light of reason is not the same as logic. It can’t be since the possibility of making an error in between steps would introduce room for doubt. Instead, the natural light of reason is some kind of pure intellectual capacity that precedes more structured forms of reasoning, and this capacity directly apprehends that “I think” cannot be separated from “I exist.”
This is clearer in the French version of the text, where the final formulation of the argument is “je pense, je suis” (“I think; I am”). The first formulation—“je pense, donc je suis” or “cogito, ergo sum”—suggests that there is a deductive move being made here, but Descartes realizes that he needs to shed that aspect of the argument (even if it is a helpful way of introducing it). As noted above, this is because the evil demon, or even just plain old incompetence, could introduce error if we had to conclude “I exist” from “I think.” The only way to avoid this is to have them be aspects of the same thought.
If this reading of the argument seems utterly unfamiliar, it’s not your fault. While it is more or less uncontroversial among Descartes scholars, my experience is that only oversimplified versions tend to be presented in any context below a graduate-level history of philosophy class. It’s a classic case of not trusting the audience, which is a tendency among academics that I rather dislike.