Of course there is a connection between the phenomenon and the noumenon.
But even so, you too agree that understandings that are not of sensory and empirical origin cannot be projected onto the noumenon; rather, their whole basis lies in the phenomenon—for example the principles of causality and induction, and so on. If so, why does the principle of sufficient reason for complex objects not suffer from these problems?

Exactly the opposite. I argue that you can project them, including induction and causality. My whole argument in True and Stable and In Two Carts and And at Which Is Present is against Hume. I claim that his skepticism is correct from an empiricist point of view, and therefore I propose syntheticity—the blurring between cognition and thought—as the only possible option if one is not to be a skeptic, and in order to justify induction and causality (and likewise the principle of sufficient reason).

Are you saying that everything you wrote in those books was only to answer David Hume, but that you are actually a rationalist? ????
Or are you claiming that this principle of sufficient reason too is cognitive?

Everything is correct except the "but" (and also the "actually"): everything I wrote was to answer David Hume, because I am a rationalist.
In fact, my claim is that the distinction between cognition and thought is not sharp, because we have intellectual cognition—a part of the intellect that cognizes and does not merely think—through which we grasp things, though not like facts that are directly absorbed through the senses. That is called rationalism, and every empiricist has to admit it. That is the whole essence of my books, not some side clarification.
In that sense, the principle of sufficient reason is "cognitive" (grasped through the cognizing intellect), like every other correct rationalist idea. There are, of course, hallucinations too, but that is something else. There are cognitions of this kind that are contradicted by facts—and with respect to those too one should not insist. But cognitions that are not based on facts (= sensory, empirical) certainly do exist, and it is right to rely on them.

Thank you very much! I calmed down… haha

I just wanted to know whether I understood your line of argument correctly up to this point, because otherwise it's a shame to argue about the assumptions through a dialogue of the deaf (especially after arguments with other people about understanding the depth of what you mean). And especially since it seems quite clear from many of the comments on the site that many people did not manage to get to the depth of your view on the subject. With God's help, this time I hope I have uncovered the depth of the matter.
As I understand it, your approach contains two hidden assumptions:
P1. A complex thing requires a sufficient reason.
P2. Complexity is an objective property and absolutely not subjective (in contrast to Y in column 144), but in order to continue with the physico-theological argument we only need to check a side condition: whether the complex event is also statistically rare. If so, we will look for an explanation for it—as a continuation of section 1. But if not, then we have no reason to assume an additional explanation for the complex event.

If that is indeed what you mean, then it explains a great many of the difficulties that arise when reading your words.
A. Why, according to your view, a creature that lacks the properties needed to identify complexity is mistaken when it sees a complex thing and does not stand on its cause.
B. Likewise, it explains why we have no reason to assume that there is a component in a random sequence, because it does not require an attempt at a reason at all (P1).
C. It explains why we must assume at the head of the chain of reasons either a being that acts randomly (in order to evade P1), or assume a rational/willing being. But it is impossible to posit a being that necessarily acts in complexity, because then the same question would apply to it as well.
D. It explains why you repeatedly emphasize that you are not assuming anything about the nature of the generating factor. (Because otherwise we would to some extent be begging the question.)
E. Likewise, it explains why there is no reason to ask Dawkins's famous question: who created God? Because of both clauses together: (1) God is Himself the reason; (2) God is defined as unified and simple, and it is not clear that it is even a well-defined discussion whether He is also statistically rare.

I would be happy for a response,
K

I sign every word (I just didn't understand B).
I will only repeat again that this is not a clarification. It is the whole essence of my books, and I am a bit surprised that someone who read them did not understand them that way. It gives me rather gloomy thoughts about my ability to explain.

First of all, who is a pioneer like our master, who opened the channels of wisdom and thought to all our people, and did so much to teach understanding to the simple folk, and like a sifter separated straw from grain for us.
Regarding assumption P2, I indeed did not manage to express it properly, but in practice it is divided into an assumption and a claim built on it:
It seems that you repeatedly return, both in the third notebook and in column 144, to the idea that you regard the concept of "complexity" as having objective meaning. It is not merely a subjective concept that is pleasing to our human eyes, but a concept that really exists and is realized in reality, just like good and evil.
And if so, that explains, for example, why a creature that lacks the capacity to distinguish between a complex thing and a non-complex one is mistaken if it does not infer from a complex thing that it requires a designer.
Likewise, there is a condition attached to this assumption: when do we claim that a complex thing requires a component? Only when the probability of it is low. But when the probability is high (for example, there are not many alternative options), then we would not claim that. And this is where the discussion in column 144 begins. Although in the background there is still another assumption, P1. But in order to ignore it you assumed that the world was created (though as I wrote in the comments, that was not really sufficient, because you also sidestepped the possibility of explaining the creation of the world by a natural factor that is neither rational nor willing).

1. A creature that does not perceive complexity will not require an explanation for a complex thing, whether I am right or not. That is, even if complexity is not objective—in that case I too would be mistaken in requiring an explanation.
2. By definition, a complex thing means that there are many alternative possibilities. That is the objective definition of complexity (via entropy).
All right, I think we've exhausted it.

Interesting,
If complexity is not objective, don't you see a problem with the principle of sufficient reason for a complex thing (P1)? After all, there too you wrote explicitly not as you did here, and I will quote:
"But if it appears only before him,
then at least from his perspective there really is no indication that it has an intelligent cause. He thinks there isn't, and rightly so in terms of the data before him, but he is mistaken. I compared this to a blind person who, from his perspective, thinks there is no wall before him, but I, as someone who sees, know that there is a wall. That creature is blind to the specialness of the phenomenon and therefore does not infer conclusions from it. He is right from his perspective but mistaken with respect to the world."
2. Agreed; that was only to make it easier to grasp. And perhaps one could set up an interpretation of "complex" as bound and asleep 😉

Of course I see a problem. That is exactly what I wrote: if complexity is not objective, then one who does not distinguish complexity will not require a cause—which is obvious—but in that situation, whoever does require a cause is also mistaken.

After, thank God and with good luck, in a good week fresh as a watered garden, with the agreement of both sides, all your hidden assumptions that were said in the matter have come to light, I would be happy to ask about the assumptions themselves.
Because of this, since "the principle of sufficient reason for a complex thing" sounds ad hoc—but according to your view one cannot deny the evident—I will try here to uproot the second assumption (P2), because you too agreed that the two depend on each other.
You argued that complexity is an objective property. But this sounds very puzzling in two ways:
1. First of all, from where would one even get the idea to claim that complexity is an objective property? Even if we can quantify it in some way, like entropy, since when do we assume that concepts are objective? We assume that only when there is not much choice, like with "good and evil," but not just like that. Is the Greek language also an objective language? A text written in it is coherent and ordered by all opinions, yet we have no doubt that it was created and is not worthy of being called "objective." Likewise, beauty is, as is well known, a subjective property, even though it causes us wonder, just as complexity does. As the poet said, there is no arguing about taste and smell.

Second, even if complexity is an objective property, you will probably claim that there are many other objective properties too, like height, width, weight, color, curvature, concavity, connectedness, and so on. So it sounds puzzling to claim that this very property, out of all the others, specifically requires a reason—and not just a cause, but an intelligent cause. Why not assume that something very heavy requires a reason? Or something very beautiful / low / curved / convex / colorful / round, etc. etc., requires a reason?
And on this I already anticipated in the column itself that at most one might claim that something good requires a cause of will behind it, in line with the ancient Greeks who argued that the only thing that can arouse desire intrinsically is morality. But a complex thing is not a prescriptive property but a descriptive one, like all the many other properties that exist!!
This seems to me clear and simple as the sunlight, sevenfold bright as the morning light.

And:
"I thank God, examiner of hearts,
when together the morning stars sing."

First, there were no hidden assumptions here at all. Everything was plain as the morning light.
Second, I did not argue that complexity is objective because it can be quantified. I argued that it is objective because the quantified magnitude is a magnitude in physics (entropy), and it acts and is acted upon within the laws of physics. If it were only a way we look at things, there would be no sense in its appearing in the laws of physics—unless you want to say that the laws of physics too are our own subjective constructs.
I do not see what the distinction between prescriptive and descriptive has to do with our issue. There are several kinds of things that require a source, among them: moral laws and a complex fact. Perhaps there are more properties that require this. So what? Any other property that requires a reason could also serve as a basis for a physico-theological argument, and then you would have another proof for the existence of God. Does that contradict this proof?

I am not a scientist, but from what appears from reading Wikipedia there is no direct connection between entropy and complexity. And even if such a connection does exist, it is still not clear to me what makes this property one that requires an explanation.
Maybe you would argue that in our world there is the concept of "speed," and it appears in physics, so something fast requires an explanation. Obviously there is no connection between something's appearing in physics and its requiring an explanation. Likewise, sometimes directions like left and right also appear in physics… and we do not assume that every right hand requires an explanation. But of course the laws of physics are descriptions in our language of a reflection that exists in objective reality.

The question is why assume that a property like complexity requires a reason—and the fact is that you have not found any other properties that require a reason. (Good requires a reason because the very concept of good is itself of divine origin.)

I don't know what Wikipedia says, but entropy is the measure of uniqueness, and uniqueness requires an explanation. Complexity is a type of uniqueness.
As for its appearance in the world, I keep explaining this again and again and you simply do not understand. Apparently my explanations are deficient, but I do not know how to improve them any further. I'll try one last time.
Complexity requires an explanation. But that is only with respect to objective complexity. Complexity that is not objective does not require an explanation, because it is an illusion. Entropy is objective complexity because it is a physical magnitude. Physics does not deal with our illusions. The appearance of complexity in physics is not the reason that it requires an explanation, but the reason that it is objective. What does that have to do with speed?
I have not found other properties that require explanation because I have not looked, and I do not see any need to look. But offhand I would say that anything requiring explanation is a kind of complex thing. There is something unique about it, and therefore it requires explanation.
That's it—forgive me, but I'm tired and I've had enough.

I will try to clarify what I mean:
Why shouldn't you argue that speed or acceleration requires an explanation? After all, it is measured as the ratio of position to a unit of time, so it is an objective property, and the formulas of physics also show that it is not subjective.
Of course I do not think that because it appears in physics it therefore requires an explanation; I am only showing that it is an objective property.
But why not assume that a very fast body requires an explanation? Especially since most bodies will not be very fast, so a very fast body is also unique.

You really don't give up, do you? 🙂
Very fast is not unique/complex. Just as a particular sequence of results from a thousand die rolls is not unique, whereas a thousand times 6 is unique. The probability of every such sequence of outcomes is very small, but every thousand rolls will yield some kind of result. The difference is not in the probability but in the entropy. But this has already been explained dozens of times on the site and also in the notebooks.
That's it. My strength has failed me.

It is established for us that Rabbi Nachman "cried out in his holy voice: Gevald! Do not despair! and he drew out the word Gevald at great length, in order to teach and hint to every person for all generations that one must never despair under any circumstances in the world, no matter what one goes through."
I'll try to look for another suitable example.

Rabbi Nachman himself despaired of despairing.