>> Not just axioms, but all mathematical proofs are not testable by science.
> By virtue of being derived from axioms?
No, but by virtue of not being able to perform scientific observation on a mathematical proof. Math has no color, smell, taste, feel, nor affect on other material objects from which we can observe.
> "1 + 9 = 10" is not a claim about reality
This is wrong. If "1 + 9 = 10" is true and truth is that which pertains to reality, then "1 + 9 = 10" is a claim about reality albeit a mathematical one (i.e. science is not the only way to talk about reality). I'd agree that it's not a claim about PHYSICAL reality though.
>> It would be a category error to test all religious claims with science
> Why?
Because not all religious claims are claims about physical reality, some are about moral reality. Just like "1 apple + 9 apples = 10 apples" is not a claim about physical reality, but is an application of mathematics to physical reality, "You must not steal" is not a claim about physical reality, but is an application of morals to persons in physical reality.
Moral claims are not testable by science. It would be a categorical error to try to discover the color, smell, taste, feel, or affect of morality.
> 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?
If you can perform direct or indirect physical observation to verify a religious claim, then it is a claim that science can deal with.
> By virtue of being derived from axioms?
No, but by virtue of not being able to perform scientific observation on a mathematical proof. Math has no color, smell, taste, feel, nor affect on other material objects from which we can observe.
> "1 + 9 = 10" is not a claim about reality
This is wrong. If "1 + 9 = 10" is true and truth is that which pertains to reality, then "1 + 9 = 10" is a claim about reality albeit a mathematical one (i.e. science is not the only way to talk about reality). I'd agree that it's not a claim about PHYSICAL reality though.
>> It would be a category error to test all religious claims with science
> Why?
Because not all religious claims are claims about physical reality, some are about moral reality. Just like "1 apple + 9 apples = 10 apples" is not a claim about physical reality, but is an application of mathematics to physical reality, "You must not steal" is not a claim about physical reality, but is an application of morals to persons in physical reality.
Moral claims are not testable by science. It would be a categorical error to try to discover the color, smell, taste, feel, or affect of morality.
> 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?
If you can perform direct or indirect physical observation to verify a religious claim, then it is a claim that science can deal with.