In my opinion, the Rabbi is mixing up the different proofs.
If we examine the cosmological and teleological proofs, we will discover that the entire teleological proof stands only on the basis of the cosmological proof. For if the world is its own cause, then the teleological proof does not even get off the ground.
So the correct understanding of the combination of these proofs is that the cosmological proof has the power to reveal that there exists an entity Y that is its own cause and that, in a teleological way (as opposed to a deterministic one), led to the creation of the world.
Whereas the physico-theological proof has power only in characterizing entity Y—that is, whether it is an intelligent entity or not. Indeed, I agree that this argument is based on a probabilistic consideration that reveals to us what kind of entity it is most reasonable to assume caused the world before us to be as it is, or in other words: what is Y?

Therefore, once we already know that there exists an entity Y that is its own cause, then and only then can the physico-theological proof arrive and tell us which characterization of entity Y, as the entity that led to the world’s existence, is the most probable.
I claim that the reasonable conclusion from the physico-theological proof is an entity that acts in a compelled and necessary way to create the world. Because only in that way can we arrive at the conclusion that the probability that, given that Y exists, the world will be created—is 1. If Y has free choice, then we do not know what the probability is that it will in fact choose to create the world, for we are dealing with a choosing entity!!!

Also, it is important to re-emphasize that the fact that Y is a “complex” entity does not mean that it is not its own cause. Because the assumption of the cosmological proof applies only to objects in our experience, not to objects outside our experience. And I claim that perhaps Y is indeed “complex,” but it is its own cause. And the assumption that it is complex comes precisely from the physico-theological proof. And I will stop here so as not to reach a regress of explanations. It seems to me this is simple and clear.

(P.S.
Therefore, if the Rabbi notices, in some formulations of the physico-theological proof they first assume that God is the most perfect entity and the best one, and that the best thing is, among other things, to create human beings; and when nothing prevents the best entity from creating the best thing, the probability that it will choose that is 1. But the Rabbi did not mention all these pilpulim.)

I do not accept any of the arguments here, and I already explained why. You are basically arguing that the alternative is that the entity that created the world is its own cause but a deterministic mechanism. I do not see why this is more logical (the argument that if it has choice then it can also do other things is simply a mistake. There could also be other deterministic entities that create other worlds). If it is a deterministic mechanism, then there is the principle of sufficient reason, which asks why it is precisely like this. To say that it is its own cause is not an answer but an evasion one step back. By contrast, if I do not claim anything about God and only say that He chose to create the world as it is, that is an explanation.

I think the Rabbi is not right here.
Of course, according to my approach, I agree that the teleological non-volitional entity may also be able to create additional worlds. But there is a huge difference precisely on this point between my claim and the assumption of a choosing entity.
Whereas with a volitional entity I do not know the probability that it will choose to create specifically a world like ours (a perhaps-claim), with a deterministic entity designed to do so, it is certainly 1 (a definite claim).
So correct, maybe it also creates other worlds in a compelled way, just as the choosing entity might create them—but that no longer interests me. Because my probability question is: given entity Y, what is the probability that it will create the event before us? And here this is significantly preferable.

Your claim too—that if it is a deterministic mechanism, then the principle of sufficient reason asks why it created this kind of world rather than another—is not correct. Because I already prefaced that the physico-theological proof stands on the basis of the cosmological assumption that we already know there exists an entity that is its own cause and is not of the type of things in our experience.
*Only* after that understanding does the physico-theological argument come in, in order to characterize this first cause by means of a statistical calculation. And as I have argued throughout all my comments here, the claim that the primary entity is “deterministic” is significantly preferable statistically.

Also, I did not understand our Rabbi’s words at the end of the response, where he wrote that whereas he does not claim anything about God and only says that He chose to create the world as it is—that is an explanation. (As opposed to my assumption, which is not an explanation.)
A. Why is that an explanation and this is not an explanation? B. Why are you not claiming anything about God if you assume that He acts volitionally? after all you are characterizing Him.

As I explained, you cannot assume that the mechanism creates a particular world and then claim that the probability is high. It is like explaining a special result of a die by the existence of an invisible entity that creates exactly that result. Therefore there is no reason to assume that the die is not fair. This is an ad hoc explanation, and it has no value.
In other words, I too can assume that this entity is a choosing one, but its values dictate specifically a world like this (because this is the optimal world for its purposes; by the way, many argue this), and once again we have reached a probability no lower than yours. You are simply hiding the problem inside your mechanism. Therefore the claim about a deterministic entity is really not preferable in any respect.
On the contrary, even by simple reasoning I would say that an entity that is its own cause will not be deterministic (after all, even we, its simple creations, have choice, so our creator, who gave us that, would not have choice?!).

As I understand it, the physico-theological proof does not require the cosmological one in any way.

True, I characterize it as a choosing entity (probably). But you dictate its whole nature: according to your approach, it is a mechanism that is deterministically forced to create a world like ours. A machine for producing a world like ours (only once, of course).

By the way, I am not sure that if the entity is deterministic it changes anything for us. Why is that important?

I agree that I am, as it were, hiding the probabilistic problem inside the mechanism itself. But even so, I think that when you assume that there exists a choosing entity, you are speaking about two probabilistic considerations:
1. What is the probability that such an entity exists? 2. What is the probability that it will choose this?
By contrast, when I speak about a deterministic mechanism, I am speaking only about a single probabilistic consideration:
1. What is the probability that such a mechanism exists?
The second part, in my case, is already included in the first. Therefore there is indeed an advantage to my claim.

By the way, I do not understand how your example differs from the claim about God explaining the world’s existence, just as explaining a special result in a die by “the existence of an invisible entity that creates exactly that result”…

Also,
You wrote that in your understanding, the physico-theological proof does not require the cosmological one. But the Rabbi has mentioned many times that the distinction between the proofs is not correct. (If I remember right, he even used the word “didactic.”)
Because if we do not use the cosmological proof and its Leibnizian offshoots, then the question “who created God” returns with full force—which, in other words, claims: why not stop the regress at the world? So as long as the Rabbi does not use the Big Bang as an escape hatch (which is also scientifically incorrect—because although people say that the world and time were created out of quantum fields, they do not claim that those quantum fields were also created!), he must arrive at the cosmological principle that will help him not to stop at things of the kind found in our experience.

You wrote further that I characterize the entire mechanism, and therefore my explanation is weaker. But I too can claim that according to my view there is only a deterministic mechanism (in order to increase the statistics for creating a world identical to ours, as above), yet it may create other worlds as well, perhaps many times, etc. So in this part of the argument we would be equal.

As for the last line, I completely disagree. It seems to me that the basis and foundation of the pillar of religion is the belief that the world was created *volitionally* and could have not been created. If I remember correctly, even Rabbi Kook mentions that the image of God in man is choice, and so on and so forth. According to your view, does God not have free choice?

You are once again hiding the probabilistic problems inside a mechanism and a mere definition. There is no difference at all between the possibilities. You split it into the probability that there is an entity and the probability that it will create specifically a world like this. That is a meaningless division. Overall, if you look at the whole process, it is the same thing. In other words: the probability of each stage changes, and now the probability of the first stage contains the probabilistic problems of the two stages.

The connection to the cosmological proof is incorrect. “Who created God?” is not a relevant question because He is His own cause. Otherwise we are back to an infinite regress. That is said within the physico-theological framework itself as well.

I do not know what the foundation of religion is or where you derive it from. It is not clear to me why it is important that He have choice. Though as I wrote, I tend to think that He indeed has choice on intuitive grounds.

I am not sure that this is correct, but it may indeed be that in the absence of information about the statistical distribution, one can relate to them as equal.

Here this is already a mistake. Because although it is true that within the physico-theological discussion too there is a regress-stopping stage called “self-cause,” the difference is that the Rabbi did not notice that from the standpoint of the physico-theological proof there is no reason not to stop the regress here rather than at God. And that is why in the notebooks and in the responsa it seems that the Rabbi always used the assumption of why it is not reasonable to stop it at our world—by means of the cosmological proof, which revealed to us that there is a first cause different from the world and that the world is created, and so on.

I do not recall using that in the notebooks, and I do not agree with it and see no need for it. I do not see in what way the cosmological proof is preferable to the physico-theological one in this context.

I will copy your words:
“But again, the answer here will be the same answer (that is, as in the cosmological proof). If one keeps extending it further, one arrives at an infinite chain, or really at the conclusion that this information is primordial (eternal). It existed forever. Where was it? We have already seen that according to modern physics our universe is not primordial. So where was this information? The place where it was will be called by us God. Who or what created it? Nobody.”
As can be seen in this paragraph, the Rabbi uses the Big Bang as proof for faith. (Even though, as I already wrote, this is not scientifically correct: science does not say that the quantum fields that caused the creation of the world were also created.)

Let us continue to the next contradiction later in paragraph 2:
“The assumption that complexity does not arise on its own, or that there is no primordial complexity, is correct only for our universe and for the entities within it, about which we have experience. We should not apply this to other entities. On the contrary, there must be some existent to which this does not apply, for otherwise we necessarily fall into an infinite regress. Exactly as we saw in the parallel discussion in the notebook on the cosmological argument. The second law of thermodynamics, which is part of physics, also does not apply to entities that are not part of physics, and the intuition underlying it is likewise not relevant to transcendental entities and cannot be applicable to them (if we wish to avoid an infinite regress).”
Here the Rabbi contradicted what he explicitly mentioned in the first answer in our present discussion. As you wrote: “The claim that a complex thing requires a composer is not connected to our experience. It is a probabilistic consideration (of entropy).”

Let us continue to see the use of the cosmological proof as a basis in the final paragraph—3:
“It can be formulated more precisely: God always existed, and therefore the principle of causality does not require positing a prior cause for His complexity. There was no change of entropy over time here. This complexity always existed.”
Here the Rabbi is already using the assumption and conclusion of the cosmological proof—that the world did not always exist, and since God always existed, one can stop the principle of causality with Him, and consequently we have also found a good place to stop the physico-theological proof.

I do not use the Big Bang theory but the fact that there was a Big Bang. Nobody is dealing with the question whether the quantum fields were created or not, so I do not know where you are getting your physical claims from.

The claim that a complex thing requires a composer is a probabilistic claim on the assumption that it was indeed created and is not its own cause. But at the end of the chain there must be a primary link that is not like that, otherwise we are back to the problem of infinite regress.

That is no more a conclusion of the cosmological proof than of the physico-theological one. And you have not brought any statement of mine that the physico-theological proof is based on the cosmological one.

I think we are repeating ourselves. The positions have been clarified, and the chooser may choose.

If the Rabbi agrees that scientifically the quantum fields were not created, then it is not clear how the Big Bang advances us on the question of breaking the regress. After all, the only thing the Big Bang shows is that there is a change in entropy over a defined period of time.

Here, this is not precise, because there are two kinds of regress-stoppers:
1. A brute fact—as a plain, arbitrary first source.
2. A first cause that is essentially different from the other causes, such that it is not even in the category of the question at all.
The regress-breaker of the cosmological proof falls under 2. By contrast, the regress-breaker of the physico-theological proof falls under 1. Therefore there is no reason not to stop at the world.
The Rabbi wrote this explicitly with us at the beginning of the discussion:
“The claim that a complex thing requires a composer is not connected to our experience. It is a probabilistic consideration (of entropy). The cosmological argument depends on objects in our experience.”
So there is no reason to stop at God rather than at the world. Unless, that is, we know that the world is not its own cause (following the cosmological proof), and therefore we are left with no choice but to stop at God.

That is true—I indeed did not bring a direct statement that the physico-theological proof is based on the cosmological one, only a hint to that effect, but it was said orally. And there was at least indirect evidence in something you said—that the separation between the proofs is artificial—and, if I remember correctly, that was in connection with this question.

I do not agree with a single word, and everything has already been explained.