Question about faith

And another note. Even if it were possible to build a computer program that would rule on a law, that would say nothing about its validity and consistency. Certainly if it were machine learning and not a classical program, since then the program would imitate human judgment, and would probably also make mistakes from time to time. But even humans make mistakes from time to time.
In principle, it is possible to build a computer program that would treat a person psychologically. This is not very far from a realistic application. This is despite the fact that psychology not only does not pass consistency tests, but it is not a science and is not systematic at all.

"In short, this is a really childish argument. A kind of youthful enthusiasm for a new field that is revealed to you (mathematics and logic). I would take a short breath before drawing rash conclusions from this enthusiasm. If this is the main problem that makes you hesitate about faith and halakha, we are in an excellent situation."

This question arose in my youth, but I have not yet received a satisfactory answer. For that matter, I am close to completing a master's degree in computer science and this question still bothers me. I believe in the existence of God, and can also accommodate the fact that empirical observations are not absolute truth, i.e., the fact that given a contradiction between science and Torah, it will not be possible to prove with absolute certainty who is right. But for the sake of consistency, this is a necessary condition. Proving the correctness of a system from outside the system would be impossible (as in all Torah), but at the very least I would expect it to be possible to prove the correctness from within, otherwise it would be possible to prove one thing and the other. Likewise, it is not possible to judge whether the ruling throughout the generations was correct at all. Perhaps religious figures throughout the generations invented things out of personal interests, etc.

"When the halakhic solution comes in, it will eliminate the contradiction and eliminate the proof of the system's contradiction."

Why is there a need to create a solution every time? Isn't the Torah absolute, but changes from time to time? Isn't the Torah that G-d revealed to the people of Israel from Sinai exactly the same Torah that we learn today? And if the Torah is truly absolute and only new things are "discovered" and not "invented," why do you think it is not possible to define some area from the foundation and judge it mathematically?

"There is a feeling that if this is the nature of Halakha, then this is not a serious system. In my opinion, the situation is the opposite: if it could be proven and its consistency proven, it would not be serious. It also does not mean in any way that it was not given by God. There are different interpretations of what was given by Him. Contrary to your naive assumption and expectation, the Halacha was created by humans and not by God. The basis on which it was built was what we received from Him. But that does not mean that it is not binding. The authenticity of Halacha is not a condition for its validity."

I'm sorry, but I believe that a system of rulings must be consistent, otherwise there is simply no guarantee of its correctness. According to my worldview, there is only one thing in this world that can be proven with absolute certainty, and that is the consistency of a system and the laws within it.

And if you think that consistency cannot be proven at all, why did you believe in something that cannot be proven to be true at least in itself?

Do you believe that this cannot be done at all?

"Here I will prove to you the consistency of a subsystem of Halacha (you said you are satisfied with a subsystem)"

The system proposed by the L.A.D. is not rich enough, I am looking for something rich enough.

Again, sorry, but you insist on just that.

I explained to you why this demand is unfounded. So it doesn't help to repeat it unless you come up with some kind of argument against what I wrote. You are talking about proofs for or against, and I claim that the format of mathematical or logical proofs is irrelevant to this type of material. I showed you the problematic nature of even the simplest systems that I demonstrated, which you called insufficiently rich. Even there, you will not be able to truly prove consistency or refute it. You will not be able to prove anything in them or their opposite, since proofs are not the format for dealing with such a system.
It is not about creating a solution every time. When there is a problem, a solution is sought. When you have a problem in science or logic, you do not seek a solution? Don't understand this strange claim. Do you want a system that will not create problems or a system that has no problems? The fact that it creates problems is our business, not the system's.
It is not that I think that the field of halakhic law cannot be described logically or mathematically. This is not possible in the fields of natural sciences either (Tarski tried to do this partially. Very weakly), and certainly not in more ‘soft’ fields.
There is nothing to be sorry about. A person makes mistakes sometimes. Legitimate. There are mathematical systems whose consistency cannot be proven. Are you willing to accept them or use them? If not, I don't know what you are doing in the field you mentioned. Not to mention systems whose consistency has not yet been proven (even if it exists). If you believe in any values, not necessarily religious or halakha, or in any legal field or in findings of psychology, physics, chemistry, and the like, I don't see how you do it if their consistency has not been proven. There is almost no field of knowledge whose logical consistency has been proven, except for a few simple mathematical systems. So if you only accept that, good luck to you.
You didn't understand my argument. I showed you that even in this simple system your requirement is not well defined.