What to morality, is proof to truth?

"Wow! You are right, and I was wrong. This whole time, I was wrong! For 40 years I have believed in the claims of [insert any political ideology or religion]. Yet, in 20 minutes, you and I have calmly sat here, have presented observable facts, and have deduced from them, conclusions using only reason – truly, the compassionate way to do things! I have discovered now that the reasoning of me and my people was flawed all along. I have been defeated in dialectics."

Said no one ever. Why?

We will be looking at one of the most prominent topics in philosophy – the is-ought dichotomy. I have read much and talked much about the is-ought dichotomy, but we have never read it in its original, most prominent form – from the Enlightenment philosopher David Hume's most celebrated work "A Treatise of Human Nature".

Thus, for our meeting, please read Book 3, Part 1, Section 1 of "A Treatise of Human Nature" by David Hume. The section is entitled "Moral Distinctions Not Derived From Reason" and can be accessed at https://www.gutenberg.org/files/4705/4705-h/4705-h.htm#link2H_4_0085 (if that link fails, try https://oll.libertyfund.org/title/bigge-a-treatise-of-human-nature#lf0213_label_247).

It is only 8 pages!

The last paragraph in the section is the most famous excerpt on the topic.

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There are many pithy ways of describing what the is-ought dichotomy is, all roughly equivalent to the non-fastidious.

1. You cannot derive an "ought" from an "is".
2. The prescriptive cannot be derived from the descriptive.
3. Statements of fact and statements of value are categorically distinct.

A clue to the categorical distinction is that you can violate moral law, but you cannot violate physical or mathematical law. The former is prescriptive, the latter is descriptive. I believe it was Kant who noted any moral "ought" (moral decree) presupposes the possibility to violate it. Yet, it is not possible for a circle to have three corners.

One might object at least to one of the presented restatements of the is-ought dichotomy, noting "It is wrong to murder" is a descriptive statement. However, it is often argued this is an innately prescriptive statement merely presented as if it were a descriptive statement, for how does one go about proving "It is wrong to murder" is true? No scientific experiment can determine this. It is not possible to observe, in the physical universe, the truth of murder being wrong. You can observe murder, you can observe the suffering it brings, you can observe people denouncing it, and you can even observe other people claiming it is wrong, but none of this is proof it is wrong. Nor is it a theorem of mathematics. How would one, in his wildest imagination, go from arithmetic and geometry (I toil under the thought this is what most people think mathematics is) to proving murder is wrong?

Anywho, the overall idea is, from the sum total of all that which has been proven empirically and deductively, scientifically and mathematically, you cannot even prove it is wrong to murder an innocent child, much less one wearing a nice hat. To get to a moral statement, to get what one ought or ought not do, you need a categorically distinct set of axioms not provided by a description of the physical universe or by logical deduction alone.

Given the categorical distinction between morality and epistemology, an interesting question arises. To convince someone of something true, one uses proof. What is the equivalent tool used to convince others or to change people's mind in morality?

What to morality is proof to truth?