> Not just axioms, but all mathematical proofs are not testable by science.
By virtue of being derived from axioms?
> Are you saying that math on its own doesn't pertain to reality at all?
No, I am saying exactly what I am saying: Axioms, and thus all of mathematics, because all of mathematics is derived from axioms, do/does not make claims about reality. "1 + 9 = 10" is not a claim about reality, it's simply a statement that is consistent with the Peano axioms.
> Either way I'd imagine you find math useful
Yes, very much so. Because it so happens that it can be used to describe models of reality. But whether given mathematical structure is a good fit for describing some aspect of reality is testable. In fact ,that is the only reason why it is rational to believe that mathematics can be used to model reality.
While "1 + 9 = 10" is not a claim about reality, "1 apple + 9 apples = 10 apples" is, and a very testable one at that.
> It would be a category error to test all religious claims with science
Why?
> and unless a religion has made an explicit scientific claim that IS false, whether known or not
How do you decide whether a given claim made by a religion is a scientific claim? Is it "not scientific" just because they say so? Or is there come criterion by which to distinguish scientific religious claims from "not scientific" religious claims?
By virtue of being derived from axioms?
> Are you saying that math on its own doesn't pertain to reality at all?
No, I am saying exactly what I am saying: Axioms, and thus all of mathematics, because all of mathematics is derived from axioms, do/does not make claims about reality. "1 + 9 = 10" is not a claim about reality, it's simply a statement that is consistent with the Peano axioms.
> Either way I'd imagine you find math useful
Yes, very much so. Because it so happens that it can be used to describe models of reality. But whether given mathematical structure is a good fit for describing some aspect of reality is testable. In fact ,that is the only reason why it is rational to believe that mathematics can be used to model reality.
While "1 + 9 = 10" is not a claim about reality, "1 apple + 9 apples = 10 apples" is, and a very testable one at that.
> It would be a category error to test all religious claims with science
Why?
> and unless a religion has made an explicit scientific claim that IS false, whether known or not
How do you decide whether a given claim made by a religion is a scientific claim? Is it "not scientific" just because they say so? Or is there come criterion by which to distinguish scientific religious claims from "not scientific" religious claims?