Thank you very much for the comments. I understood some of them; I’ll try to clarify the parts I didn’t understand.
2. Indeed, I was also asking about that point. It seems that anyone who is not a skeptic agrees that there must be some connecting factor between the world and the phenomena (say, the eyes and light in example 1). But if all our cognition is built only on the basis of an a priori principle like causality, it can still be interpreted through countless possible causes for how sensory impressions were formed. Even Descartes’ demon is a cause in this broad sense; but most of us do not think it is the correct cause. So it seems that the principle of causality alone is not enough, but requires something more, even though of course it does seem to stand in the background.

3. I did not mean the question about events or entities, though of course there is a connection, but mainly about first premises and claims. For example, the definition of a first premise is that it has no cause. I assume that only by means of this can one place trust in something, in a kind of view that God is the anchor of causes in the world. But if we do not cast doubt on first premises, how can we say that something is not certain but also has a probabilistic dimension? After all, the whole assumption of probability presupposes in the background that doubt can be cast on it.
3. Also, by contrast, the skeptic in his own view is indeed willing to cast doubt on first premises. But if so, he can also cast doubt on the assumption that one ought to cast doubt on first premises, or that anything without a cause is false. If so, doesn’t it seem that he is sawing off the branch he is sitting on? No?
5/4 I meant as in the first part of 3.

3. You are using the term "cause" in a way I don’t understand. Do you mean a rationale/justification?
A first premise indeed has no justification that grounds it. But it is not true that I do not cast doubt on first premises. No claim, assumption, or conclusion is certain in my view.

Yes, I do mean in the sense of rationale/justification.
First, regarding 2: do you agree that we simply have a first premise that what we see is true? Because it does not seem that just any a priori principle, whatever it may be, can *by itself* bridge the gap to accepting the material world.

So if that is the case, how are you able to accept a first premise but in a non-certain way? That is what is very unclear to me.
And even if you say that is possible—relative to what would it be uncertain? Relative to some other challenge or some other doubt? Presumably that doubt too assumes that there exists another, more basic explanation, and that too—or the beginning of the system of explanations at its base—is axiomatic. But then that just means that the assumption we thought was a first premise is not really one, but rather a conclusion from something more basic.
Unless you are a skeptic and claim that one can cast doubt on first premises—but then where does probability enter the picture? Because from that perspective everything is arbitrary to the same degree. (And the assumption that everything is arbitrary is arbitrary too…)

And if so, insofar as you accept skeptical claims, then there is also no validity at all to the idea that something seems probable to me, because all probability is only on the level of subjective probability, but there is no connection between that and the objective world, and one can never bridge that gap, as in the opening point you presented in 2 regarding the objection to Kant.
And if you are not a skeptic, then in any case you do not challenge first premises…

"An electromagnetic wave in the world is translated into light"
The wave is translated into neural signals. Which are translated into something else which is translated into something else… somehow in the end there is light.
There is no direct connection between the light and the wave. The connection is very, very indirect.

I’ve completely lost you. You keep mixing categories again and again, and not addressing what I answered. I already answered everything.

Posek, it is a direct connection. One causes the other, even if this happens through several stages. If you break down the process from striking the match to lighting the fire, you’ll find several intermediate stages there too. So what? One causes the other. What difference does it make that there are intermediate stages? Are we dealing with the Talmudic topic of indirect force upon indirect force?

If you lost me, then how did you answer?…

What is unclear to me is that everyone agrees that the definition of a first premise is that there is no justification grounding it.
But if so, how can one cast doubt on a first premise without using some prior first premise? As you claimed you do.
So on the other side, if you accept that one can cast doubt on first premises, then how can you assume that something is more or less probable? After all, you can cast further doubt on that very sense of probability too… And then your probable conclusion would be to be a solipsist. Or you would cast doubt on the assumption that one can cast doubt and be stuck.
Rather, one must say that at the beginning of thought there is some *certain* assumption, however small it may be.
For example, the assumption that what we think is probable really is objectively probable (even if it is not objectively certain). Because only from there onward can one say that we are working with probabilities, etc. But if you say that all our first premises forever have some percentage of doubt built into them, then that doubt must arise because of skeptical claims external to them—and insofar as you are a skeptic, you can never claim that anything is probable in the slightest…

And therefore I want to say that you too agree that, in your approach, there is some initial certainty and not everything is only probability. Or else probability is certain.
In any case, if I’m right, then what is nice to see is that you prefer to be a postmodernist rather than a fundamentalist 😉

And even though there is no proof of the matter, there is a hint to it in the introduction to the Notebooks of Faith:
"To the best of my understanding, a person has no possibility of arriving at certainty in any area…. If he has found a way to reach such certainty, he has apparently made a mistake (certainly! 🙂 )."
That implies that there is something certain and fundamentalist at the bottom of our thinking, at the end of the day, which says that there is a correspondence between probability and the world; otherwise we would have to be condemned to skepticism.

Meshiv, I’ve now lost you too (what do you want now), since I already answered everything earlier.

Must there also, according to your approach, be some first premise (even a very limited one) that we accept with certainty and not merely on the basis of probability?
And I think that this first premise is that what seems probable to us really is probable, and that there is a correspondence to that. Only that way, I think, can my questions be resolved without falling into full skepticism and, on the other hand, without claiming that everything is certain.
By contrast, earlier you claimed that you do indeed "cast doubt on first premises. No claim, assumption, or conclusion is certain in my view."
But if you really meant what you wrote, then you must have the ability to distinguish which first premise is correct and which is not (because you are not a skeptic….), but that ability too is a kind of first premise, and with regard to it as well you will cast doubt, and so on ad infinitum—and then you must be a skeptic.
I think these things are simple, but since I see that you are already the second philosopher who says similar things while both of you declare yourselves not to be postmodernists, I wanted to test whether I am in fact right or perhaps my words are not sharp enough. Maybe one can have one’s cake and eat it too.

Because he too accepts that according to Kant there is no connection at all between first premises and their truth in the world, and that all of them should be doubted, and yet in other areas there are probable conclusions… It’s not exactly your claim, but in the end it is fairly similar to the line of thought I presented here.

I’m answering for the third time: no. There is nothing at all that is certain in my eyes. And I repeat for the seventeenth time: uncertainty is not skepticism. Skepticism means that a certain position is no better than its opposite. By contrast, uncertainty means only that I am not sure.
That’s it. I’m done.

And what about a geometric series that converges to 0. Something seems probable to me. It seems probable to me that what seems probable to me is probable. It seems probable to me that what seems probable to me to be probable, is probable. If we quantify the probability as 99.99% certainty, then every claim rolls down in the limit to 0% certainty.

I wrote what I understood from the question. Because if the answer is that "something seems probable to me," and when quantified let us say it is 99.99, then it is 99.99 after all the calculations in the world, and that is a direct claim about the world and not a claim about myself—then that means we are fixing the rigid relation between probability and certainty with certainty.

How does this miracle happen—that there is no certainty, but that does not lead to skepticism?
Because the whole idea of uncertainty and remaining with probability assumes that there is a second option, but you have no ability to assess what is probable, because that itself is another assumption that you would then also ask whether it is probable…

This wondrous miracle lies in the difference between, say, 90% doubt and 50% doubt (if we insist on quantifying it). True, it is really amazing and incomprehensible, but it can still happen. I roll a die six million times. I bet that the result will be uniformly distributed and there will be about a million results for each face. I have some doubt (it’s not 100%), but still that is probably what will happen. Amazing.
And I have an intuitive ability also to assess the value of intuition. This circularity is just sophistry. It’s like asking how do you know you’re right, after all you yourself are the one who decides that you are right. How is this different from an ordinary skeptical argument?
We have really exhausted these sophistries to the point of blood.

What does this have to do with an ordinary skeptical argument? Here they are not asking "how do you know," but are accepting everything the person says and discussing only his own view. If he says he is one hundred percent sure that something is true, and he is also one hundred percent sure that in cases where he is one hundred percent sure that something is true, then one hundred percent that thing is true—then everything is fine, because one to whatever power remains one. But if he has only only only probability, then through iterative circularity he decays to zero. Very simple. In any case, it seems very probable to me, for example, that there is no one here on the site besides you who knows how to answer this. And even if you have an implicit answer, it cannot be found here in the thread. Apparently the gatekeeper is to blame and got the comment mixed up with the answer.

Indeed. I agree that this is so simple that in the end the intuition’s ability to assess itself is a first premise that you must accept with *certainty*, even if within the intuition there is included the possibility that it is not certain—but that does not come from external doubt, rather from *internal* doubt, which is part of the definition of that first premise. The main thing is that there is some certain foundation here.

This point is important, because I wanted to make sure that these things, which seemed entirely obvious to me, are indeed correct. Because as I said at the beginning, there is an important person who is also such a philosopher who completely denies this point, yet strongly claims on the other hand that he is not a skeptic—which sounds completely implausible.
And so too throughout the discussion here it seemed that you were also going in his direction, and therefore I could not see how one could produce this miracle, especially since in my previous understanding of you, where the doubt was external to the first premise, the difficulty arises as to why it is only 10% doubt and not 50% methodological doubt. But I see that you agree with the approach I presented here.

Indeed, it may be that B.T. offered an explanation that explains that philosopher by using an integration of an infinite number of explanations, such that even though every explanation itself requires an explanation, it still has a small weight. Personally, that sounds very strange to me, if it is even possible at all. But it is the only way out I found.

This question is also critical for your opposition to fundamentalist claims on the one hand and the possibility of uncertainty on the other. But you could say that this is a kind of tautology. Although I think it does sharpen the difference between external doubt (postmodernism) and internal doubt (your synthetic approach).

No, not with certainty. That too is not certain.

Do you accept the difference between your claim that first premises themselves contain the assumption that they are not certain, and casting doubt that is external to the first premises themselves? (Because then either you accept some other control system as a first premise, or you are condemned as a skeptic.)

Otherwise I really do not understand how you are not a skeptic if you cast doubt on first premises even by small percentages (as long as this is not part of that same first premise which is itself not certain).

It seems to me that there is some distinction here that I’m probably not grasping, because if it’s not as I said then I completely do not understand how you claim that you are not a skeptic. Maybe you can explain this little point.

I truly cannot grasp where the problem is here. I am saying very simple and clear things. My first premises are not certain in my view. Not because there are refutations against them, but because I am not sure whether they are correct (there are possible alternatives). I don’t know what external doubt is. I cast a certain amount of doubt on my assumptions. That’s all.

By external doubt I mean that the doubt comes from a negative place, as a kind of challenge external to thought, and not inherently as part of the first premise of thought—for example one that says it is accurate only in 90% of cases.

But the moment you wrote: "My first premises are not certain in my view…. because I am not sure whether they are correct (there are possible alternatives)," that sounds like negative doubt altogether. And if so, you can keep pushing it back and back:

Because that implies that there is "you the discerner," and external to them you observe the first premises. For example, this can be understood from your parable about the eyes of the intellect that observe distant ideas.
But if so, you must admit that you, the discerner (= the eyes?), are themselves endowed with complete certainty regarding your ability to discern the first premises, so that even if you do not accept their level of accuracy as fully complete, you still must accept with certainty that they have some level of accuracy—for example, that it depends on several parameters like the distance of the idea, the inclinations, and so on. So with respect to that level you cast no doubt at all, because even their lack of accuracy is inherent in that first premise.
But if you once again cast negative doubt on them:
1. then you will never be able to get out of the circle of casting doubt. 2. there is no reason at all to assume that the statistical quantification of doubt is only 10%, say, and not 50%. And that is already full skepticism. 3. it will produce a loop of skepticism that in the end yields that the truth of your subjective truths approaches zero through multiplication of probabilities. 4. you could also cast doubt on the principle of casting negative doubts.