On a comparison parameter as induction (from “Two Carts and a Balloon”)

Regarding the claim that the generalization at the basis of the comparison is “not implicit at all” – I think that in concrete comparisons it is definitely implicit, that is, not really defined to the end.
When I say this frog can swim and therefore that frog can swim too, it does go through some kind of grand generalization, because there is nothing special exactly about that frog, but I don't know how to define exactly what a frog is. It is possible that tomorrow I will see a species of animal and I will think that it is “a frog” but it will not know how to swim. The generalization regarding swimming depends, for example, on body structure and place of residence. And the real set of criteria that led me to compare frog A’ to frog B’ a person does not always know how to formulate. Even when he says ‘These and those are frogs’ This does not always capture exactly the criterion he used for comparison. We are all casuistrians and not positivists as explained there in two circles.

Right?

Absolutely true in my opinion.

I still have trouble separating this argument from the first one. What you're essentially saying is that even before I even thought about Plato, by the very fact that I decided to look for a reason (or correlation or explanation) for Socrates being mortal (being human), I had already included all those for whom the reason exists (by the very fact that it is a reason or correlation, etc.) as also being mortal. But this is exactly the same generalization as the first argument. There is only one generalization here.

To insist

I disagree with you. Usually when a person makes an analogy it is because he already suspected that there was a connection between the frog and its swimming and he has already generalized in his mind. He does not yet say it explicitly out of caution. He wants to gather evidence for the generalization before he makes a general claim and acts on it and before he is sure of it. So it is just a matter of self-awareness of the operation of our cognition. But from the moment that it is clear to a person then the moment when the generalization was made (in that first case) will also be clear to the person.

(Who said that there are two generalizations at the foundation of every analogy? If you quote the passage from Two Carts where it is written, we can try to relate it.)
First, the ’blindness’ of induction when making an analogy is simply because the formulation of the analogy does not present the induction. Therefore, even if when you think about it, you see clearly as if there is an induction here, it is still called ‘latent’.
Second, induction as a sweeping rule is also essentially latent, and here I disagree with you again, although perhaps there is actually no argument. “Self-awareness of our act of cognition” is exactly the point. It is usually not possible to precisely formulate our act of cognition (i.e. to formulate a positivist rule and from now on let machines draw deductions from it). Someone who makes an analogy is not always (and sometimes not) able to explicitly and precisely formulate the induction that is in the background even though he is using it himself (because the boundaries are gray and tortuous).
Third, you wrote that it is not clear why in the first place they considered the analogy as another way of inference, etc., etc. This, for some reason, and please take me in good spirits, reminds me of the story about a certain person who stood in the rain at a loss for how to get home and prayed to God to save him and that he would take it upon himself to do this and that. A moment after he finished praying, a luxurious Mercedes stopped next to him and offered him a ride. He hurried away and said to himself, "Forget it, God bless you, I've already taken care of it," and got into the car.

That's true. These are two sides of the same coin.

I'm sorry. I really still don't understand. How are there two sides of the coin (generalization)? After all, the first side is the fact that there is a generalization at the base of the analogy, and that is understandable. The second side refers to the decision on how to generalize (and not to the fact of generalization. The rabbi there spoke about induction in that I specifically choose one parameter and not another that is not of interest (the letter that their name begins with)). How is this exactly the second side. It seems as if the rabbi said there that the fact that we decided that something is of interest and something is not is the induction (“a kind of induction”. And I didn't understand how)

I'm bothered precisely because of the feeling that I have that you are raising something here that is a real point. It really bothered me for years and only now did I remember that there is a website where I can ask this. I would be happy if the rabbi could explain it to me in more detail. I mean how the rabbi would rewrite this section there.

I won't rewrite the passage here, and I'm not sure that anything needs to be changed. My argument is simple: when you choose a relevant similarity parameter, you are essentially making an implicit generalization. This reflects, on the other hand, the fact that there is a generalization at the basis of the analogy. What is not clear?

It is not clear why the relevance of the parameter is important. Even if I choose an irrelevant parameter, I am implicitly generalizing (although it is not a good generalization, but still).