So...guess I'm the new guy

[Vincenzo Vinny G.]

I'm not saying mathematical truths cannot be confirmed or supported by science. Or more properly, a posteriori knowledge or empirical observation (is science isotropic to empirical observation? I don't think so, but that's another subject).

But so far as "proving numbers and mathematical relations are valid through science", as Hoodie wants to prove, there has to be a hypothesis first. And you cannot make this hypothesis simply by observing the world. Numbers and mathematical relations don't exist in the world in the same way as the objects of scientific inquiry exist.

From this it's almost commonsensical to say that "proving math" lies outside the realm of science, because science, at least hard science, is fundamentally physical, and mathematical quantities and relations are non-physical.

I thought this was fundamental, commonsense knowledge. I can't believe it's being denied that science makes assumptions it cannot prove.

Thing is, your view of the way science works is wrong. Our scientific knowledge is not a set of individual hypotheses which face the tribunal of experience alone. It is a complex network of beliefs, including all that outlying auxillary seemingly non-empirical stuff like maths, logic and metaphysical assumptions. Anything that feeds in to science is indirectly tested by the success or failure of science as a whole. The success of science is thereby an indirect confirmation of those mathematical assumptions you mention. Or so the argument goes. It's called epistemological holism. I don't actually buy it myself (well, not the maths and logic part anyway), but, like much of common sense, the idea that these things are "unprovable" by science is not at all certain.

This is a serious point. I have to concede that the way I understand your point, I agree that "anything that feeds into science is tested". But properly, scientifically tested? No, of course not. This claim is about as valid as "paper is valid because it works when used as intended in scientific experiments". But it never was, properly the subject of scientific inquiry in the first place.

Do computers carry philosophical validity because many journal articles are written using computers? Or calculators carry mathematical validity because mathematicians use them? Seeing as they don't even meet the criteria of of being the subject of inquiry in the relevant field, this is a highly tenuous claim that only epistemological holism can assess, seeing as it turns all assumptions into mini-hypotheses that themselves are tested.

I can see the value in e-h given some limited situations where it would be useful, but to use it to justify the validity or rational justification of using math in science, I don't think so. The validity of extant assumptions will never be as well-examined, or even properly examined under e-h as if it were the subject of inquiry itself, ie the focus of testing.

Using epistemological holism to validate or justify mathematics would be an abuse of the theory, in my opinion.

edit: PS- I'm aware that there are some people going around calling me an idiot. It's an unfortunate part and parcel of the situation, when atheism has become more of a religious dogma, and skepticism expressed towards some foundational beliefs of atheists can make them very offended.

I'm of the opinion that skepticism should be equally applicable to all sides.