Thank you.
But even if I am not thinking anything, I cannot know that. And from the moment I “know” that, it is a sign that I am thinking. I also may not exist, and then the conclusion “I exist” is not correct. But logically I don’t understand how one can say such a thing. Because the moment you make any claim, you are assuming your own ability to make claims. How can one argue with that logically? Can you give me a logical argument? You necessarily contradict yourself, no? That is, even logically this seems like a winning argument. So why not say that logically too this is a proof? I didn’t understand exactly how one can escape this with logical tricks. Any attempt to get out of the premise that I think entails that I think.

And why, then, do you see this proof as an explanation that is merely “reasonable” and not certain? After all, it is self-evident and so intuitive—why not adopt it as something completely certain?

Descartes merely wanted to show that one cannot cast doubt on one’s own existence. And in that he was right, since one has to exist in order to doubt.
His argument is correct, as long as one understands what he was trying to do and what he was not.

For me, the feeling that I exist is sufficiently certain even on its own, if you are looking for something very intuitive. But if that is not enough and I need the cogito, that is because one is looking for absolute logical certainty and not intuition—that is, an argument that is certainly true and not based on premises. The cogito is not such a thing.
I explained that logically it is possible that I am not thinking (the claim that I am thinking is a factual claim, and therefore subject to all the problems of a factual claim).

Roni, what you mean to say is that it is still possible that I am not thinking (and also not doubting) and do not exist. That is exactly what I said.

Until now I thought that this is not a necessary proposition (“I think, therefore I exist”) because there is the option that I simply do not think and also do not exist. But my question is: so what actually happens when I think? You might say that perhaps I simply don’t. That’s what I also thought, but I would still ask: then what is happening? Because I do in any case feel that I am thinking, and it is not like “I walk,” where it could be that I am imagining it, because thinking is the foundation. The reason “I walk, therefore I exist” is not correct is that maybe I am imagining it—that is, thinking it. But thought itself is the foundation; I really do feel that I am thinking, and seemingly it cannot be denied (because then what did happen when I thought? You can’t say simply “nothing,” because something did happen—maybe you have another explanation for what that something is, but there is something).

What do you mean, what happens? On the logical level it is always possible to say that nothing happens. From logic alone you can derive nothing about the world; nothing will help.
By the way, it seems to me that Descartes did not mean to say that there is logical certainty; he does not mention logic at all with respect to the cogito. He is looking for a certainty that is not based on logic, and his claim is that the fact that I think is a fact that is certain for me (although the concept of “certain” is not so well-defined, since ostensibly this is not an objective state of the proposition but a psychological state of the speaker), and therefore one can infer from it that I exist. Note well: this is an inference. The certain state is the very feeling that I think; at this stage there is still no meaningful statement here, only immediate perception. From that perception one can extract and infer an ontological proposition that claims that I exist.

I have a column on the cogito. You are asking what you feel, and by that you are already in effect saying that you exist. In fact, there is an observational premise here that you exist (from introspection), and the conclusion follows from it. Nothing special.