Metaphysics operates one level up from physics or the sciences, asking what reality has to be like for anything, including the sciences, to be possible or meaningful at all.
I know what metaphysics is (and your description isn't accurate--science is a knowledge-producing method that doesn't depend on metaphysics in order to be meaningful), but that has nothing to do with my statement. And it's called "metaphysics" because Andronicus placed that volume after the "physics" volume when he organized Aristotle's writings.
Science absolutely does depend on metaphysics. Most famously: the validity of the scientific method is ultimately a metaphysical extension of our intuitions about inductive reasoning and causality. There is no scientific proof that the scientific method is valid. ("Our intuitions" is why I said metaphysics is tautologically the domain of humans. This is essentially Kant's philosophical legacy: science will describe what it does, but humans intuitively understand reality in ways that defy noncircular scientific description, and metaphysics must be invoked to have a rational and grounded discussion about these intuitions.)
Isn't it obvious that scientific method is fallible? It's just statistically better than pure reason, which should be possible to demonstrate statistically. It's a product of trial and error, and there were many errors, I don't think there's much metaphysics there.
The problem is not that it's fallible, but that there's no noncircular explanation for why it seems to work. Inductive reasoning doesn't have a rational explanation, only an intuitive one.
I don't think your claim is possible to prove statistically - what does "pure reason" mean? And of course it's "pure reason + empirical observations": even if they're not running reproducible experiments they still see natural phenomena.
It works because humans looked for a method that works, they tried different methods and chose one that works best, actually it gradually evolved over time.
Pure reason is conjecture with little empirical input (and big intuitive or memey input) and little verification of output, i.e. a large deviation from empiricism.
I asked for proof of claims and I just get "it absolutely does" and a bunch more assertions, and word salad like "the validity of the scientific method is ultimately a metaphysical extension of our intuitions about inductive reasoning and causality" -- there's nothing "metaphysical" about it ... the scientific method is a disciplined application of an effective process of discovery. And '"Our intuitions" is why I said metaphysics is tautologically the domain of humans' is more word salad -- "tautologically" has no business in that sentence, and none of the rest of it makes any sense either. Humans have multiple domains, not just "the" domain. Metaphysics is a field of study that non humans capable of studying can also study. Metaphysical facts govern everything, not just humans. etc. I consider this sort of junk to border on bad faith ... it certainly isn't of any use to me, and I have no interest in engaging with it.
> There is no scientific proof that the scientific method is valid.
The scientific method is provably effective in a lawful world. That the scientific method isn't provably effective is because the world is not provably lawful ... it's logically possible for the "laws" of physics--which are simply regularities that we have discovered--to suddenly change, oscillate, be random, etc. But as long as they don't the scientific method works ... and we can't do better. (Not in this world, anyway ... in some other world there might be oracles (aka gods or bibles) that always have the right answer and we could simply query them. Of course, such oracles are also not provably correct.)
There is no single "scientific method" to speak of. Your epistemic position is ultimately just as faith based as you claim faith in God etc. is, the sciences (plural) just have a set of operations which, as you point out, seem to have practical utility and seem to be better than certain alternatives for building up shared epistemic structure.
The attitude of "we can't do better" is precisely the kind of attitude that would have hampered the creation of various sciences and their methods in the first place, and the production of scientific thought is often not as pure or logically consistent as all the methodological purists or Popperians seem to believe it is. Feyerabend, Quine, Von Foerster, Dataon and Gallison and several others have made this pretty clear and make the argument pretty forcefully in my opinion.
All sciences carry an ontology and value system along with them. Religion is also a rich and highly effective epistemic structure when your underlying ontological assumptions, values, and goals differ from those established and implicit in the scientific (predominantly utilitarian) Western enlightenment value system. Science is not able to found itself on some irrefutable bedrock "truth" correspondence any more than religion is. There is no basis by which we can actually solidify empiricism as somehow more privileged and more capital T true if we admit the possibility of human error.
Agnosticism is an example that nobody wants a theory that works but not empirically. If a theory works, then it must work empirically, in this sense empiricism is tautological.
You are missing the point. Let me use "fabulashinaism" which is a theory I just made up that posits that the universe is made up of little gnomes called atoms.
There is a sense in which all of my observations hence will be "theory laden". When I seek "proof" i'm likely to do so within the constraints of fabulashinaism.
Science proceeds in the same way. Only crises, which are unpredictable and may have much more than simple "new data collected" behind them actually drive theory change. Beyond the theoretical assumptions, many of which are not proven but are constraining hypotheses, there are the social value assumptions I mentioned as well. As someone else said in the thread, science cannot prove science. You can be of the opinion that it's been more effective than alternatives, and I would agree, but there is no way to prove this because it is ultimately a question of theoretical assumptions and of values.
Observable effectiveness can be demonstrated statistically. The only option I see is if it's unobservably ineffective, which can't be ruled out experimentally.