My Confusion about Moral Philosophy

In mathematics, axioms are not just chosen based of what feels correct - instead, the implications of those axioms are explored, and only if those seem to match the intuition too, then the axioms have some chance of getting accepted. If a reasonably-seeming set axioms allows you to prove something that clearly should not be provable (such as - in the extreme case - a contradiction), then you know your axioms are no good.

Axiomatically stating a particular ethical framework, then exploring the consequences of the axioms in the extreme and tricky cases can serve a similar purpose - if simingly sensible ethical "axioms" lead to completely unreasonable conclusions, then you know you have to revise the stated ethical framework in some way.

Moral philosophy seems to me to be a judgement about once own utility function.

You didn't argue for that, and it seems obviously false: if I like killing people, that doesn't make it moral for me to kill people. Morality might have something to do with utility, but that in itself doesn't tell you whether extreme selfishness, extreme altruism, or something in between is correct. Trying to treat morality as rationality doesn't help either, because rationality is about optimising a UF which is not otherwise specified, so that the resulting morality could range between extreme selfishness and extreme altruism.

It's striking that, in practice, rationalism-inspired morality actually does range from extreme egoism to extreme altruism, and that rationalists think they are nonethless basically on the same page.

Mathematics can be taken in that way but there are important ways how it does't work like that. Axioms are assumed, not believed and this can make a difference. There is also the whole business whether you are pro or anti axiom of choice. This divide is an example how the axioms are not evident and intuition conflicts genuinely happen. Then there are questions about what cardinalities exist or not which suffer from there not being a favorite axiom set or reason to prefer one ovedr the other.

Philosphy is more used to there being mutiple camps and some sorts of argumentation flying in some circles and not others. Adding axioms gives you fodder to consruct proofs but it also increases threshold to find the proof compelling. You could have dialogue like "I have a neat proof. Assume that A", "I don't believe A", "Well you won't believe my proof then". You could think of mathematians starting their things with "To whomever shares these basic beliefs...", they don't argue or find commom ground but just list the prerequisite to find the material interesting. True it is more common to expect for simple explanastion to advance mathetmatical disagreements where phisophy expects for disagreements to stay lingering but the kind of moves happen on both ends.

Interesting points and important topic but there are some things I would like to challenge.

First off is your notion of a moral or ethical system based on rationality. I don’t disagree and in fact think it could make enormous difference in legal reform. It is important to realize that this is not a novel idea though. Some forms of utilitarian or consequentialist thought work toward a similar goal. See Peter Singer as an example.

Second, the idea that a rationally consistent philosophy will by definition minimize moral suffering can be disproven by experience. This is entirely anecdotal but I can recount actions even from yesterday that were rational and even compassionate, but still left me feeling morally challenged in a way I could not explain through logic. Personal rationality and personal morality are related but separate cognitive domains which are at best often in conflict with each other and, at worst, in conflict with themselves.

Finally, I would disagree that rationality is that much easier to define - at least in the clear-cut way you present it. I imagine you and I have rationalities that are very similar but rationality is not an independent concept floating around in metaphysical space. It is shaped by our epistemology and emotional cognition. For example, can you imagine the rational system of a person with eschatological beliefs? The difference in rationality between a venture capitalist based in non-renewable resources and a complex systems theorist devoted to climate management? Between someone who believes in women’s choice in abortion and someone who believes an egg is ensouled at conception? Etc. Rationality is shaped by beliefs and emotions more than the other way around.

All that said, I think you are discussing something very important. Moving away from “good-vs-evil” politics and behaviour is becoming crucial in the world and we can’t get there without these types of discussions. I suspect we would both embrace a best-practice system of ethics, separated from moral judgments. However, it is essentially important to realize rationality is not objective or unchanging, and the way to change people’s minds is not by telling them they are “wrong” but by showing them what is “right” and why. We may learn about our own rational inconsistencies in the meantime.

Have I misinterpreted you in any way? If so, my apologies. I hope this comment is helpful and look forward to a reply if you feel one is necessary.