That makes sense, because it could explain why a mirage appears to be an error. And people who hallucinate are often aware of the hallucination of one of the senses, for example. So let’s take one step back to the concept called "intuition."
But even if intuition is a cognitive faculty, the question then arises about it too: is the source of intuition something that fits the term a priori? Or is it something else (in which case the question of circularity comes up, of course)?
And the way it is used is more reflective and even not fully conscious, right?

I read Truth and Unstable and also a bit of Two Carts, but in Two Carts there were two formulations: is it correct to say that intuition is in fact a cognitive tool that looks inward or outward?

Also,
do you connect intuition with the soul and judgment/discretion (which is the soul’s free decision)? I just didn’t see that stated explicitly.
That is, is intuition the soul’s glasses, and judgment the choice of the correct opinion?
(By analogy to free choice of actions: intuition is the eyes, the choosing person is the soul, and the movement of the hand is parallel to an act of judgment.)

It’s just that the terms aren’t always clear to me, and sometimes I read things like reflective thinking versus introspective thinking, etc.

I do not understand these questions.
You cannot ground intuition on anything but itself. Otherwise you fall into an infinite regress. In the end there will always be something that has no grounding outside itself. In that sense, this is an a priori principle, as I explained.

The distinction between looking inward and outward is completely equivalent. Because when looking inward, you still have to assume a correspondence between what you find inside and the world (otherwise looking inward cannot yield insights about the world), and therefore de facto it is the same thing as looking outward.

I connect everything to the soul: will, intuition, intellect, emotion, and all mental faculties. But that is not important for the discussion.

The basis for your willingness to rely on your senses is that when you were a baby, you learned that if you don’t use the information from your eyes, you crash into a wall and it hurts.
And if you use your eyes, then the pain disappears because you don’t crash into the wall.

Okay, thank you very much! Indeed, that point isn’t important for the discussion, but I was just wondering whether everything is a characteristic of the soul or whether there is something additional.
As for the middle part, I דווקא don’t think it is entirely correct. It is possible to think of practical differences between the approaches, such as the existence of objective concepts. So I wanted to ask what you think. And there could also be practical differences with respect to the method of justification.
For example, do I assume that there is a coordinating factor directly, like a direct revelatory inference? Or only through a revelatory inference that "teaches"? Not that I discover that there is God, but that I learn through it that there is God.

By the way, apropos the last comment:
What does the Rabbi think about these "materialist" approaches that like to understand the sources of reason in relation to the understanding and psychology of a small child and so on? Some even take it a step further and say that the truest truths are what a small child believes, and so forth. Usually this comes out of despair over the current situation of the multiplicity of methods and opinions.

You didn’t understand.
So if you want to understand, drop a heavy stone on your foot.
It will hurt.

While you’re groaning in pain, try to figure out whether this is a priori pain, or maybe there is some intuition here that this is the appropriate time to feel pain. Or perhaps this is really a materialist approach and it doesn’t hurt you at all.

After you do all that, you’ll understand. Right now, instead of trying to understand, you’re busy arranging words in a puzzle game that some bored people invented so you could talk to them in their made-up language.

But apparently you don’t want to understand, so go on with the discussions about the puzzle game and think that because of it you understand something.

I didn’t understand the last question. What is the connection between materialism and small children?