[part 2]

> You need to establish that axiomatic claims can't be about reality in some way besides intent. The syllogism that I've asked you to provide above would do that.

You are simply missing the point. It's not a question of if it "can be about reality". That's like asking "can claims about John be about Jack?" No, they can't. And that's not for some deep reason that you seem to be looking for that somehow magically prevents claims about John from being about Jack. It's the frickin obvious fact that when I say "John has brown hair", I am not talking about Jack. That's all there is to it, and you are just obfuscating this trivial fact by trying to reinterpret what I might mean by "John", and whether I maybe am using "John" to refer to an invisible unicorn. I don't mean any of that, I simply mean John, and that is why I said "John". Your ability to be creative in your interpretation does not change what I mean by a statement.

> My point is that you don't know whether '1 < 2' has a referent or not. If you know that mathematical claims are not about reality, then you would know that '1 < 2' has no referent. If you don't know that '1 < 2' has no referent, then you don't know that mathematical claims are not about reality. I don't need to establish "'1 < 2' has a referent" to establish that you don't know whether mathematical claims are about reality.

Let me clarify: Under the definitions used by mathematicians, '1 < 2' has no referent absent the axioms defined by mathematicians, that is easy to know from the definitions used by mathematicians. If you want to propose different definitions that possibly are structurally compatible with the ones used by mathematicians, feel free to do so, but if those imply that '1 < 2' has a referent absent axioms/evaluators/..., that would be up to you to demonstrate.

> I explicitly stated it. Even if you said science is limited, as you have done, you'd still have no case because the position that "there are not explanations for some things" is self-defeating, as I have already stated.

But I have never made that claim, so what is the point of bringing it up?

> Unless your criterion assumes that everything that exists is physical, I don't see why I couldn't use your criterion.

I don't have a criterion? I don't think there is any distinction to be made, and if you think that there is, it's up to you to demonstrate some way to make the distinction.

> If you think there is a contradiction, please state it as a syllogism to highlight it. I'll rephrase to make my statement less ambiguous: It is immoral to do X if you think X is immoral even if X is moral, so you'll be better off doing any X you think is moral even if X is immoral.

For any action X, "being moral" is semantically equivalent to "being moral to do", and "immoral" is the negation of "moral". Therefore, your statement says that there exists an action that is moral and not moral at the same time.

> That being said, I have no interest in substantiating my claims regarding morality if you don't think that what I am saying could be compatible with science even in principle.

The primary problem is not what you are saying, the primary problem is the method you use to justify it.

> If I were to supplant "morality", as I have defined it, for "science", and repeated what you said as a reason to care about morality, what objections might you have to the given reason?

That you have in no way demonstrated that your version of morality does produce any of the results promised, it's just an empty assertion.