[Diogenesian]

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.)

[GoblinSlayer]

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.

[Diogenesian]

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.

[GoblinSlayer]

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.