So...guess I'm the new guy

[discordianpope]

when you take two chestnuts and describe them as two chestnuts you have already started doing the math though. You have identified a set - a mathematical object - and assigned a cardinality to the set. I think, my maths knowledge in't too good. In the very act of carving up reality into these sets of one things, two things, and tens of things, you are already doing the math though. And then when you add these sets together to get bigger sets of things (like chestnuts) you are doing more maths, whether you use numbers to describe the process or not. All this doesn't mean that science can't confirm mathematics though. Just because we didn't begin with an empirical basis for mathematics doesn't mean we can't use the success of science to say "Gee, I guess those mathematical intuitions must have been right, cos all this physics is basically mathematics and it seems to work pretty well!" That's where Vinny is wrong. I actually, I think he is right about mathematics not being empirically testable, but I wouldn't say that it's all just assumed either.

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.