Answer

You are mistaken in your understanding of the naturalistic fallacy. The fallacy does not say that there is no connection between facts and norms, but rather that in addition to facts you need something else in order to derive norms.
For example, the fact that hitting causes pain and suffering is connected to the principle that one may not hit. But in addition to that fact, you also need the principle that whatever causes pain is forbidden. The fact that a painting is made up of certain colors and shapes is connected to its beauty, but the facts by themselves are not enough (you also need principles of aesthetic evaluation).
The same is true regarding the revelation at Mount Sinai. If historically it did not happen, then there is no reason to keep commandments, because they were not given. The fact that someone dreamed up a collection of commandments does not seem to me to be a reason to observe them. True, even if such a revelation did occur, that still would not necessarily create obligation. The historicity of the event is a necessary condition for obligation, but not a sufficient one.
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Questioner:

If I understand the argument correctly, then according to your view one can justify accepting Torah and commandments on the basis of the following assumptions:
1. One should fulfill the word of God — that is the evaluative assumption.
2. The Torah is the word of God — that is the factual claim supported by the occurrence of the revelation at Mount Sinai.
As I understand it, the occurrence of the revelation at Mount Sinai is not enough even for claim 2 alone (and it is not necessary either). Does an impressive pyrotechnic display at the end of which someone arrives with a few commands turn those commands into the word of God?
In my view, the question of what counts as the word of God is an evaluative question. It is my judgment as to how I decide that something is the word of the Holy One, blessed be He. The factual infrastructure is less relevant here.
As an analogy: when I say that a certain painting is beautiful in my eyes, then the claims relevant to me are that the painting exists and the feelings it arouses in me. It may be that I think the painter used brush x to paint the picture, whereas in fact he used brush y. The question of how the painting was created is not relevant to my judgment of it.
Similarly, it seems to me that one could say that the way the Torah was transmitted is not relevant to the question of our obligation toward it.

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Rabbi:
Of course the method is irrelevant if you think this really is a Torah transmitted from the Holy One, blessed be He. I just do not understand how you arrive at the conclusion that something was transmitted by the Holy One, blessed be He, if there was no event of transmission. If you trust hallucinations, then good for you. My assumption is that without an event of transmission there is no justification for assuming that a Torah was given to us.
Of course, even if there was a revelation at Mount Sinai, you can still doubt it and say it was a performance and not divine revelation (just as if you ask someone what time it is, you can doubt his answer and wonder whether he is lying). But without revelation, I do not see how you would decide that a Torah was given. As I said, revelation is a necessary condition, even if not a sufficient one. And that is what I wrote in the previous message.
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Questioner:
I still don’t understand how the revelation at Mount Sinai advances us toward the conclusion that the Torah was given by the Holy One, blessed be He.
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Rabbi:
I don’t understand the question. If the Holy One, blessed be He, gave the Torah at Mount Sinai, then the Torah was given at Mount Sinai.

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Questioner:
What in the revelation proves that the Holy One, blessed be He, was present at Mount Sinai?
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Rabbi:
The revelation at Mount Sinai is a revelation of the Holy One, blessed be He. That is its definition. To say there was such a revelation without the Holy One, blessed be He, means there was no revelation. You can of course wonder whether such a revelation occurred, but then you are simply asking a historical question (how do we know such an event happened, and how do we know it was not an illusion). What does that have to do with the naturalistic fallacy with which you began? That is a completely different discussion.
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Questioner:
My claim is that saying the Holy One, blessed be He, was present at the revelation is an evaluative claim, whereas what was seen at the revelation was a collection of facts.
In other words, inferring from some pyrotechnic display that the Holy One, blessed be He, was present there and giving us the Torah — that is deriving a value from facts.
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Rabbi:
At this point I’ve completely lost you. It is like saying that the fact that I met you does not mean that you were present at the meeting. This is just skepticism, perhaps legitimate, but I do not see what it has to do with the naturalistic fallacy. The assertion that the Holy One, blessed be He, was present there is a factual assertion, whether true or false.
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Questioner:
Unlike a meeting with a person, which can be confirmed through the basic senses, our meeting with the Holy One, blessed be He, is experienced with the “eyes of the intellect.” From that standpoint, I would classify the claim that the Holy One, blessed be He, is in a certain place as an evaluative claim (just as in evaluative claims we use the eyes of the intellect). Empirically, what was observed at the revelation were some effects on some mountain.
If I understood correctly, you are making the following claims:
1. The Holy One, blessed be He, was present at the revelation.
2. The revelation is a unique event of disclosure, and any other form of revelation is problematic.
Accordingly, my questions are:
1. What in the description of the event indicates that the Holy One, blessed be He, was there?
2. What is unique about that revelation as compared to other forms of revelation?

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Rabbi:
By that logic, you could ask what the proof is that if I see a wall in front of me, there really is a wall there. The assumption that my senses are in fact reliable is an assumption of the intellect, not an observational assumption.
As stated, this question, just like your own question, has not even the slightest connection to the naturalistic fallacy. What you are asking is the standard question of why one should believe in the revelation at Mount Sinai. I tried to answer that in my fifth booklet. The accumulation of evidence together seems sufficiently reasonable to me. I have nothing to add beyond that.

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Questioner:
The difference is that unlike a wall, the Holy One, blessed be He, cannot be seen.
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Rabbi:
Correct. But as I wrote here, even what can be seen can be doubted — maybe I am not seeing it correctly. And the assumption that I am seeing correctly is intelligible, not sensory, and therefore again it is exposed to the same skeptical attack. There is no principled difference between the two.
My book Science of Freedom opens with a prologue on Descartes and also ends with him. Descartes showed that our trust in the senses is based on the intellect, not that trust in the intellect is supposed to be based on the senses. And that is exactly my point.

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Questioner:
My question is not how we know the revelation at Mount Sinai occurred, but what is unique about it compared to another revelation.
Why is a story in which the Holy One, blessed be He, performed tricks on some mountain specifically the form of revelation on which one can rely?
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Rabbi:
The Holy One, blessed be He, also spoke there before the eyes of all Israel. The tricks did not come without context. And again, you may reject these testimonies or part of them, but that is an entirely different discussion.
I am not familiar with parallel revelations, so I cannot compare. Also see the entire discussion here:
https://mikyab.net/%D7%A9%D7%95%D7%AA/%D7%A2%D7%96%D7%A8%D7%94-%D7%91%D7%A9%D7%99%D7%A2%D7%95%D7%A8-%D7%A2%D7%9C-%D7%9E%D7%A2%D7%9E%D7%93-%D7%94%D7%A8-%D7%A1%D7%99%D7%A0%D7%99/
 
At the very bottom of the page there is also a discussion of other revelations.

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Questioner:

I feel like I’m repeating myself and you probably feel that way too… Apparently I didn’t explain myself well.
 
My question is not casting doubt on the existence of the revelation — for the sake of discussion I accept that there was some sort of event with “hocus-pocus.” My question is why the “hocus-pocus” that happened there is supposed to prove/confirm the claim that the Holy One, blessed be He, was revealed.

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Rabbi:
Indeed we are repeating ourselves. The event described in the tradition was not hocus-pocus, but rather God spoke to the entire people (with pyrotechnics in the background). If you accept the existence of the revelation, then what is the question? That maybe some demon spoke to them through its belly? And if you doubt that, then we are back to the previous point.
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Questioner:
How, in your view, did the whole people know that God was speaking to them?
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Rabbi:
Since I have never gone through that experience myself, I have no idea. Like a blind person asking how I know that I see something. If he has not gone through the experience, it is impossible to explain it to him. So he can always ask whether it is an illusion. Try explaining to him that it isn’t.
How do you know that someone is speaking to you? They understood it from the situation.

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Questioner:

That seems strange to me. You assume that some group experienced some experience that you do not know, and on that you rely?
It sounds strange to me that we do not know what it means to have an experience in which God reveals Himself to us, and yet we still rely on it. It reminds me of what I read from you against expressions like “things beyond reason” (what does that even mean, etc.).
A note:
Following this exchange, I’ve now started reading your fifth booklet (naively I thought the quartet and my Yedioth Ahronoth books were enough, but I’m finding new things there that I hadn’t known). It may be that you feel that if I read it I’ll find the answer there. If that’s how you feel, then tell me and I’ll stop bothering you until I finish reading…
Unrelatedly, I think there may be an editing mistake at the end of page 12 (of the fifth booklet) — it should say “critical importance” and not “critical thinking.”

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Rabbi:
There is nothing here that is beyond reason. People report to me that they encountered something, and I believe them. What is beyond reason here? Maybe you should read there.
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Questioner:

Okay, I read the booklet. It added something, but I still have objections…
Here there is a group of people reporting a phenomenon whose meaning I have no idea about. That really sounds to me like “an experience that is beyond reason.”
If I understand correctly, the argument is something like this:
You do not understand how someone arrives at the conclusion that God is revealing Himself to him (like a blind person who does not understand what seeing is), but the fact that they managed to convince many people of this makes the claim reasonable.
If my analysis is correct, then the actual occurrence of the revelation at Mount Sinai does not seem significant to me. It is enough that they managed to convince many people to observe Torah and commandments, and it is not critical to understand how the Holy One, blessed be He, managed to convince them.

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Rabbi:
Like any other event. For example, they managed to convince many people that they saw clouds in the sky. Should I believe that? I don’t know. And even if I am one of those who saw the clouds, the question still arises whether I should believe what I see or not. That too is an argument “beyond reason,” because I have no way of knowing that my sight is reliable and not deceptive except through sight itself.
Alternatively, a scientist reports to me about an unfamiliar event (a supernova, quantum tunneling). Should I believe him? No one has ever actually seen that. That too is an argument beyond reason. In the end, you have to decide whether you trust the judgment of other people, or of yourself, or not.

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Questioner:
When someone reports a supernova to me, he explains to me what he saw and why he inferred from it that there is a supernova.
In the case at hand, it is not at all clear to me how they arrived at the conclusion that they encountered God. 
Do you think that an encounter with the Holy One, blessed be He, and an empirical sensory observation belong to the same genre of experiences?

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Rabbi:
They too would explain everything to you. We met God and He said to us, “I am the Lord your God.” How do you know? Because we experienced it clearly. Exactly like the explanation of a sighted person to a blind person. When you see clouds, do you have some different explanation for that? You saw clouds, and that’s it.
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Questioner:
Are you saying that they heard some voice and had an intuition that it was the Holy One, blessed be He?
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Rabbi:

When you see me, do you see an image and then have an intuition that this is an encounter with me?

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Questioner:

Absolutely. The senses give me information, and then through considerations of intuition and common sense I interpret it.

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Rabbi:
So it is the same thing as the encounter with God. There too they had an experience of encounter, and intuition told them that it was an encounter with Him.
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Questioner:

Fine, the difference is that this time people are telling about an experience that I have no idea how to grasp.
That is, we do not really understand what happened there at that revelation, only that in the end a substantial number of people took upon themselves the yoke of Torah and commandments.
Which brings me back again to the claim that it is enough to recognize that many people accepted Jewish law, and it is not critical to define when, how, and where that happened.

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Rabbi:
A baseless claim. Why should I accept something just because there are people who accepted it? If those people claim that the Holy One, blessed be He, revealed Himself to them and I believe them — then there is a reason to take that obligation upon myself. But if a group of people decides to run a marathon, does that mean I have to do so too?
I think we’ve exhausted this.
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Questioner:
It’s a bit of a shame, because I feel I didn’t manage to make my position clear, and I wasn’t convinced by your position.
 
With your permission, in order to check that I understood you correctly — tell me if the following statements are correct in your eyes:
 
1. At Mount Sinai, the children of Israel experienced a revelation of the Holy One, blessed be He.
2. Just as a blind person does not know what sight is, so we do not know what revelation is.
3. In the terms of people who do not know what revelation is — the meaning of the revelation at Mount Sinai is that afterward the children of Israel took upon themselves the yoke of Torah and commandments.
 
 
Thank you for the time you devoted.
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Rabbi:
Statement 3 requires correction: the meaning of the revelation at Mount Sinai is that those people reached the conclusion that the Holy One, blessed be He, had revealed Himself and given them a Torah, and then they accepted the obligation toward it. That is exactly what I explained in the previous message. I still think we are repeating ourselves.