I didn’t understand point 2. This “probable” comes from my intellect. It makes sense to say that if the sun rose yesterday, it will rise today; it has nothing to do with habit. In short,
“Isn’t it just your habit?” Answer: no, it’s my logic. So there’s no problem.

You can say anything about anything. Saying it solves nothing.
Induction is a form of thinking you have, not an observation about the world. That way of thinking is a product of how you are built. So it doesn’t matter that we call it logic. The question is: what connection is there between your logic and the way the world behaves? We’re also afraid at night for no reason, and afraid of heights for no reason too (even when there are safe railings). What is ingrained in us in no way testifies to the nature of the world. Hume raised his questions long before the discovery of evolution, although that doesn’t solve the problem either.

This is not a problem of induction but a problem of projection.
And the solution to the problem is simple; all you need to do is internalize the following sentence:
Just because you think and believe that something will happen doesn’t mean it will happen.

After you internalize that, there won’t be any problem.

Rabbi, there’s something I didn’t understand. By definition, induction is not a valid argument but a strong one. And the problem of induction says, “Wait a second, I have a problem: you can’t rely on induction because it isn’t valid.” But right—that’s its definition. So what’s the problem?

And besides, just incidentally: is a presumption in Talmudic terminology (not in the sense of acquisition, but in the sense that what was true once remains true, such as “better to dwell as two”) basically exactly induction or not?

The problem is not that it isn’t valid, but that it lacks a basis (it isn’t logical). Beyond that, even if you define induction as something invalid, that doesn’t make it something one can rely on. You can give any illogical argument a name. So now we can accept it?
The Talmud is not exempt from the difficulties involved in general logical and philosophical arguments.

I asked: the fact that intuition operated and worked in the past (“empirical confirmation from the history of science”) is no guarantee that it will operate in the future!
And you told me: “The claim is that the past proves intuition is reliable. The successes show that this faculty we have is not just arbitrary, and the success is not accidental. The claim that something in us has changed since then is not plausible.”
(Let’s continue here because again I don’t need to reject images.)

Several times in the book Truth and Unstable, and in Two Carts, following Hume, you brought up that the fact that the sun has always risen does not constitute a reason that it will also rise tomorrow (= the problem of induction, what was is not necessarily what will be). What’s the difference between that and what you said now?

In other words, what you wrote to justify intuition—“the claim that the past proves intuition is reliable (and therefore one can rely on it)”—is itself based on intuition.

That is exactly what Hume asks, and my answer is that intuitively it is clear to us that it is true, and intuition is a kind of cognition. Now we ask what the justification is—how did this come about? Because of the Holy One, blessed be He.
As for intuition, obviously you can’t answer the question of where we know that intuition is reliable except by means of intuition. We have no other tool. You can talk about second-order intuition and continue to an infinite regress, but I prefer the formulation that it validates itself. It is self-evident.
The fact is that these arguments were not enough for Hume, because he did not accept God as the source of that reliability.

Is the problem of induction based on the fallacy of affirming the consequent (inferring the antecedent of a conditional statement from its consequent), or is it a different problem in the path toward validating a scientific theory?

Definitely. The cases can be derived from the theory by logical deduction (that is Carl Hempel’s deductive-nomological schema), but the theory cannot be derived from the cases.
But like any logical fallacy, that only means the argument is not logically necessary, not that it is false, and not even that it is improbable.

Therefore Popper held that a theory cannot be proven, only refuted. If one case does not fit, then the theory is nullified. That is denying the consequent (modus tollens), which is indeed a valid argument.

If I understood correctly, then the problem of induction includes, among other things:
The fact that it isn’t logical to rely on a set of cases I’ve seen, because maybe I haven’t seen everything;
And that even if a set of cases were logical, it still wouldn’t mean anything at all because of the fallacy of affirming the consequent.

Right?

Right. But not that it doesn’t mean anything at all, only that it does not necessarily imply the conclusion.

Are you familiar with Uri Belkind from Tel Aviv University? Do you know about his solution to the problem of induction, which he called Newtonian transduction?

Not familiar.