Not just axioms, but all mathematical proofs are not testable by science.
> ... that's simply a category error because axioms are not claims about reality.
Are you saying that math on its own doesn't pertain to reality at all?
Either way I'd imagine you find math useful, and if you take it as a category error to test mathematics with science, then you've stumbled across my exact point. It would be a category error to test all religious claims with science, and unless a religion has made an explicit scientific claim that IS false, whether known or not, then that religion can't be said to be incompatible with science without making a categorical error.
Not just axioms, but all mathematical proofs are not testable by science.
> ... that's simply a category error because axioms are not claims about reality.
Are you saying that math on its own doesn't pertain to reality at all?
Either way I'd imagine you find math useful, and if you take it as a category error to test mathematics with science, then you've stumbled across my exact point. It would be a category error to test all religious claims with science, and unless a religion has made an explicit scientific claim that IS false, whether known or not, then that religion can't be said to be incompatible with science without making a categorical error.