To skim things down, let's get more formal.
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Could you please state your argument, regarding things being testable as they relate to science, in the form of a syllogism that ends with the conclusion "Therefore if X is a claim about reality and X is not testable, then X is not compatible with science" to establish that a claim about reality not being testable is "about as incompatible with science as you can get"?
A preemptive question to the syllogism that you may give (to possibly help its formulation): Are all aspects of reality testable by science?
Much of our discussion can be omitted as it ties back to our main contention which is "what constitutes compatibility with science". If there is a need to resume something previously discussed it will likely resurface from here. I apologize if I am making you restate things, I am making my best attempt to understand your position (you have no idea how nice it would be for me to ditch my Catholic faith if it could be shown that it wasn't true), hopefully that's been evident by the amount of time I've left between some responses. Again I've included things that interest me which don't necessarily contribute to our "compatibility with science" dispute.
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> By testing whether the predictions made by whatever method is suggested as part of scientific methodology do come true with a probability higher than chance, preferably much higher than chance.
Testing by a method other than science? How do you know that method is reliable?
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Could you please provide a syllogism that ends with the conclusion "Therefore formal claims are not about reality" to establish that mathematical/grammatical claims are not about reality?
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> So, what would you point to for mathematics if you wanted to point to mathematics while avoiding pointing to the concept of mathematics? I don't see what could possibly be meant by that, so if you want to make the claim that there is something there, it's up to you to demonstrate that there is.
That's what I'm asking, I'm not claiming one way or the other. If you know what it points to please let me know, and how you know. If you don't know, then you can't rule out the non-physical without knowing whether it points to something physical or not.
> It is just completely normal and not the slightest bit of a problem that you generalize when talking about groups of people, when it is just completely irrelevant whether some small minority of that group deviates from what otherwise defines that group.
Except your saying that it all depends upon intent and you'd need to take into account intents that don't agree if that is the case. But now you've stated that it depends upon the intent of the majority. If the majority of mathematicians say that they are making claims about reality, then you'd likely say (correct me if I am wrong) that "anyone can obviously redefine words however they want but that doesn't make the claims they are making about reality" even though you've made it about the majority's intent. 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.
> I guess so? I mean, I would say it's pretty obvious that the way we know them they are an artificial construct of humans (like, the axioms were formulated by humans). If you think there is more to it than that, that would be for you to demonstrate.
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.
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> You implicitly claimed that there would be explanations for all things we have no explanations for yet.
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.
> You have specified no criterion by which we could distinguish whether that potential is physical or not.
Unless your criterion assumes that everything that exists is physical, I don't see why I couldn't use your criterion.
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> "It is immoral to do [something] even if it is moral [...]". How is it not blatantly obvious to you that that is just a nonsense statement due to a couldn't-be-more-obvious self-contradiction?
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.
> You are again shifting the burden of proof. Seriously, stop it, it's annoying! No one claimed that your claim wasn't true. ...
Your question seemed snarky, so I gave it the snarky response I thought it deserved. I apologize if it was a genuine question, and if so my answer would be "No there is a reason, but not one I care to defend at the moment".
I thought I could give part of a reason, even if not fully formed, because I didn't want to be a bad host of the questions that lead to this side conversation. 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. I don't mind getting deeper into it, but substantiating, not worth the effort at the moment.
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> If you care about being able to better achieve your goals (as you probably do, because that's a thing humans almost universally do), you should care about using the most reliable methodology known so far that enables that, up to the point where we possibly find a demonstrably more reliable methodology.
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?