At the beginning of your answer you wrote, by way of analogy, that even regarding sight, you know that your eyes are reliable, and that’s it.
But even with respect to that analogy, the question arises: how exactly do you *know* that? After all, in the analogy you were never exposed to the object you are observing. True, people don’t usually ask skeptical questions about vision, but your analogy really is similar. (And in truth, all our cognition by its very nature is never identical with the object being observed.)
Rather, the most you can conclude, on your view, is that you know that you are convinced that you *see* an object out there. But not that you know that this object really exists.
The same question also arises regarding the next ruling you wrote—that lack of certainty should not be identified with doubt, but rather as some possibility, while at the end of the day most opinions in the world still differ from one another. And if so, it is easy to see that what people understand as truth is, more precisely, the truth *in their eyes*. But that is not truth itself.
It seems that you sharpened this very well: that there is some kind of leap that cannot be bridged at all between me and the object.

What truth are you referring to?
Do you mean a certain proposition like: “The truth is X,” which everyone agrees to?
Or a certain experience Y that you experience?

Obviously,
By the concept of truth I mean, of course, a claim that “the truth is X,” or in the analogy in the answer (the claim X is correct/exists).
But I’m saying that the most one can claim, from that perspective, is that we perceive a certain experience Y as being true for us.
And there is an unbridgeable gap between Y and “X.”
As a result, and as a further source for this distinction, there are the many contradictory opinions that plainly show this insight: that we do not have access to truth itself, but only to what we perceive as truth.
Postmodernism completely neglected “X” and remained only with Y. But the Rabbi strongly opposes postmodernism, and as an expert on the matter I’d be glad to know what he thinks. How can one connect between Y and “X,” without throwing the baby out with the bathwater and identifying them so that “Y==X,” but rather they are separate and yet both are correct. (Or at the very least have some degree of probability P>0).

There are two answers to this:
If you want a justification for everything, you’ll never find one, because every guarantor needs a guarantor. Whatever justification is given, you’ll ask how we know that. The very demand for justification assumes that there are reasons that won’t require something outside themselves (basic assumptions, axioms). Axioms are self-evident principles, and regarding their truth I do not hesitate. If you do hesitate, then of course that’s legitimate. But by the same token, it’s legitimate not to hesitate.
Put differently: together with the perception of the various cognitions, assumption A is accompanied by the understanding B that these cognitions reflect an external world and are reliable. Your very distinction between cognition and the external world, or accepting assumption A while rejecting B, is itself not necessary. In your terminology, for some reason you accept X but reject Y. I accept both of them as my basic assumptions (not arbitrary, but true).
Your claim itself is also based on a form of thinking that has not been justified. How do you know that if I am aware only of what is inside me, I cannot infer from that something about the external world? Maybe my cognition is an exact and reliable expression of what is outside. You too assume certain principles without justification.
Bottom line: this is simply the question of skepticism. If someone is a skeptic—good for him (and as is known, there is no possible answer to a true skeptic). And if someone isn’t—good for him too.

Thank you very much for the broad reply,
In the end, the two answers you mentioned are quite similar and are built like a kind of fork: either every claim requires a system of axioms and there is no legitimate problem with expanding them, or, to the extent that you are skeptical, you can even doubt the axioms you accept.
But I didn’t understand exactly what basic assumption I have. After all, it is clear to me that I experience something—for example, in your analogy I experience sight. Even if I am an extreme skeptic who accepts no basic assumption, there is no way for me to doubt here. This is not a basic assumption but a clear experience. It is a fact.
You can of course doubt whether I experience something (other selves). But I cannot doubt that I experience sight.

First of all, you can. The fact that right now you think that an hour ago you experienced something could be a memory illusion. Second, the assumption that even if there is an experience it is not clear that it says something about the world—that is an additional assumption too (which is of course obvious in your view, just as in my view it is obvious that it does say something about the world).

I agree with both.
But that’s not exactly the question I asked,
Is the claim that I experience *something* before me an assumption? It seems to me to be a fact that I can’t undermine.

Right, so what?

So how is that called an assumption? An assumption is something that can be challenged.
Maybe you could call it the necessity of an assumption. And if so, it is not a question for anything, because it is a different level in the status of its assumption. And therefore it is not correct to compare it to the distinction between Y and “X”.

A basic assumption is an assumption that you do not challenge. Such as the fact that you see something or hear something.
The problem begins with language. Without language you would not have been able to ask what truth is.
But imagine that you had never learned language. There would be no room for the question.

That is, the truth is that the whole question of truth arises because of your ability to think thoughts. In other words, the truth is: “I think.” And if you were not able to speak, then indeed you would not ask the question what truth is, but you would still know that you see.

In other words, the truth is all the things that you experience, and not only what you think.

Everything that you do not experience belongs to the realm of belief and worldview.