You proved that we have no option to rely on proofs without intuition. But what is the connection between the claim that there is no other option and the claim that it is reasonable to rely on intuition as a detector of truths about the world?

I said that if you are a skeptic, I have no answer for you. I am not a skeptic. After all, for any explanation I give you, you can ask the same thing about it. So what kind of explanation are you expecting?

I only meant to ask what role the conclusion plays that there is no option to rely only on proofs and logical arguments without intuition. Is that just a point you happened to think was worth noting in this thread, or what?

Oh, maybe that is (only) an empirical proof that all people rely on intuitions, since they obviously act in accordance with some beliefs, and underneath every such belief there sits an intuition.

I understood, and I answered. Someone who is a skeptic remains a skeptic, and someone who is not a skeptic has no choice but to rely on intuition and axioms.

Now I understand (both what you wrote throughout the thread and the tone in which to read the answer beginning with "I said that if you are a skeptic"), thank you.

There is no limit to axioms, and there is no limit to skepticism.
It's just an arbitrary / personal / emotional / curiosity-driven matter of what you choose to invest energy and time in during life, whether out of choice or interest or any other motive.
In the end, both the skeptic and the one who posits axioms return to dust. So it doesn't matter all that much.

Last Decisor,
Or perhaps the skeptic and the one who posits axioms do not return to dust, or perhaps only one of them returns to dust, or perhaps only one of them exists, or perhaps there is no such thing as "dust" and only the illusion of dust. Or perhaps there is not even an illusion of "dust."

In modern mathematics, an axiom is an arbitrary statement taken as a foundational assumption on which the mathematical theory is built. You can determine that between 2 points there can also pass a billion straight lines.
That of course changes the way things are viewed.
The axioms can be based on intuitions and hold in the real world, or be detached from it, or hold in an imagined world.

It seems that even skeptics are not really skeptics, because if someone throws a stone at them, they will trust their intuition and it will not occur to them to entertain doubts such as maybe they are hallucinating and imagining the stone flying toward them. Psychologically, a true skeptic ought to lose any taste for life. Because why should he suffer all this imaginary suffering? And even if his life is very good, maybe that isn't real either… Does anyone actually live like that?

Dvir, that is very true. And therefore all those who divide the world between skeptics and believers, and all kinds of such shallow classifications, do not understand what is really going on.