2.
A) As I understand it, if synthetic thinking is based on the assumption that nothing is certain, and therefore we can also be mistaken about what we base our opinion on, then in other words this is *something open to refutation*.

B) That sounds blatantly unreasonable. And that’s why I’m asking whether it even makes sense to say that synthetic thinking is being used here.

Anything that can be refuted is not certain, but there can be things that are uncertain and still cannot be refuted (every square is a quadrilateral, but not every quadrilateral is a square). For example: was the world created such-and-such a number of years ago, or was it created this very moment in a way that perfectly simulates creation such-and-such a number of years ago?
And in particular, even things that are refutable in a very theoretical sense are sometimes not refutable in practice, like the claim that yesterday morning there were two toads on Mars for a fraction of a second. Or the claim that there is a person in the world whose actions, once a day, are controlled by aliens.

The word intuition is somewhat misleading, and it is used incorrectly in the language. There is something a bit sneaky about using that word.

Usually people use it to refer to beliefs that are correct even though they did not pass the scrutiny of thought at the time they were formed.

Once you are asking about whether things are actually true, you should use the word belief and not the word intuition.

Forest of Lebanon answered nicely.

Rabbi, don’t you find the option of “if a tradition of another revelation were to arise” to be something that is refutable in a very theoretical sense, but not in practice?

I wrote that this is a principled possibility, and it is possible. But as I said, none of this matters for our issue.

Why is it very theoretical? It is entirely possible that tomorrow at noon God will reveal Himself to a particular group of six hundred thousand and give it tablets of the covenant written by His glorious finger.

Rabbi, I didn’t understand why this doesn’t matter for our issue.

Forest of Lebanon, I agree that it is possible, but not exactly likely. Why? Because from our experience, there is only one tradition out of thousands of traditions that reports such a thing, so the chance that it will happen again is quite rare. After all, this is part of Rabbi Michi’s argument, that he rejects Hume’s criticism of the witness argument because it “mentally locks things in”—since although such things do not happen often, that is not enough to completely rule out the possibility that they happen. Learn from this that it really is rare. And if it’s that rare, then saying that this is what could refute my claim is mainly theoretical and very, very strained to call it realistic.

I’m not against the idea of synthetic thinking in general, but I’m wondering here how relevant it is in something that is so rare to begin with.

Okay, I’m trying again.
In chapter 20 of the book “Truth and Not Stable” you present the Talmudic a fortiori argument as a synthetic tool.
I’m presenting here a short summary I wrote about it to make sure I understood, and I’d be happy if you could confirm that I understood correctly:

“Summary of a fortiori as a synthetic tool — basically, if I succeed in literature but not in English, then all the more so Daniel, who succeeds in English, should also succeed in literature (the hierarchical assumption is that he is smarter than me). The refutation would be if we brought another English test in which Daniel did not succeed and I did—then in fact we are equal, and you can no longer infer the hidden assumption. Basically, if we had not received another piece of data, we would be sure that Daniel is smarter than me, even though maybe that’s a mistake. In other words, it isn’t certain, but it is quite plausible to say so until proven otherwise. For analytic thinking this tool is not relevant.”

In principle, correct. But a more accepted refutation would be to bring a third subject in which Daniel did not succeed and you did. What you brought is a refutation of one of the data points (proof that Daniel is not necessarily better than you in English). A regular refutation refutes the hierarchical relation.

Rabbi, can’t we say that we accept testimony as the default, and only if it sounds puzzling do we not accept testimony?
And if so, since it is strong, we would accept it anyway.

Okay, so there is a reasonable chance that at some point we will discover that we were mistaken in our distinctions (because suddenly they brought a third subject that I succeeded in but Daniel did not), and therefore we will have to change the conclusion accordingly. So although the conclusions are never certain, we find that in a substantial majority of cases we do in fact advance in our understanding of the world thanks to these tools—and therefore there is justification for using synthetic tools and synthetic thinking in general.

Now if we say that such a third test (/another English test) happens once every few thousand years, and even that is not certain—would it still be correct to say that the conclusion we reached (that Daniel will also succeed in literature) is highly reasonable? After all, the chance that more data will come is very, very low, so how do I know that I am reasonably right? These are just three isolated events (my English test + my literature test + Daniel’s English test).
Is synthetic thinking even relevant in such a situation?

I’ll add one more thing to clarify what I mean—after all, Newton’s second law is also not certain, but because of our intuition we want regularity (and understand that a straight line passes through all the points on the graph). And after all, we can keep doing more experiments all the time and see that the points continue to form a straight line—bingo! It’s not just an isolated event, and therefore saying it is very plausible is much more relevant; synthetic thinking fits.

I hope I managed to explain this time.

Sh,
This may perhaps have the status of a report, not testimony. And there are those to whom it sounds dubious (the content of the “testimony” is divine revelation, not everyday events. And there certainly could be a mistake here, hallucination, and the like).

Roi,
Your analogy to tradition is weak. Our intuition distinguishes between testimony about a tradition and an analogy between success in different subjects. See my reply to Sh.

I wasn’t able to understand what you mean, and I still haven’t made the analogy—because before I make an analogy I want to understand whether there is even anything to compare.
I’d like to go back again to the question I asked at the end of the previous comment— is synthetic thinking relevant in this isolated case of the tests?

I don’t understand the question.

You already saw the analogy I’m thinking of making between my question about the tests and the revelation argument, and you answered me that the analogy is weak, without answering the question I asked there. And before discussing whether it is relevant to make that analogy at all, I am still looking for an answer to the question I asked:

“If we say that such a third test occurs (/another English test) once every few thousand years, and even that is not certain—would it still be correct to say that the conclusion we reached (that Daniel will also succeed in literature) is highly reasonable? After all, the chance that more data will come is very, very low, so how do I know that I am reasonably right? These are just three isolated events (my English test + my literature test + Daniel’s English test).
Is synthetic thinking even relevant in such a situation?”

I don’t understand this whole discussion. There is an a fortiori inference, and I assume you understand it well. If a refutation arises, it knocks down the a fortiori argument. How do you know? Ask yourself. I have nothing to answer.

Even though for some reason that’s what you answered, I didn’t ask whether there can be a refutation that knocks down an a fortiori argument…

I asked: given a situation in which the refutation that could knock down an a fortiori argument is very uncommon—is working with the tool of a fortiori itself relevant?
After all, we already said that an a fortiori argument is an argument with the character of synthetic thinking, and because of that I would expect a minimum number of trials before I become convinced that a certain direction is more plausible.
After all, I can rely on the a fortiori argument even though sometimes it is not the most “precise” tool, precisely because I know that if there is an error in what I’m saying, it will fall. If it is also by nature an imprecise tool + there are almost no opportunities to test the conclusion drawn from it—then is the very use of this tool in such a case relevant??

If I’m mistaken in what I’m saying (perhaps even in a major way), it would be nice if you could help me sharpen my point and correct what I’m not understanding properly.
Of course you don’t have to, but if you’ve already written books and you allow people to ask you questions and people want to learn…

The validity of an a fortiori argument does not depend on the number of refutations against it, but on its internal logic. If A is more stringent than B, then when there is a stringency in B it will certainly also be in A. As long as this has not been refuted, it is logical. And if there are no refutations, then all the better.