About damned time.
I have no problem with the fact that, at bottom, all reasoning, including from assumed axioms in formal systems, requires some element of faith.
Not necessarily. The Axiom of Choice is a great example. You don't have to "believe" it, you just have to say whether or not you assume it.
It's just that some reasoning is done with as much institutionalized cynically critical rigor as we can muster, and we call that natural sciences.
Oh, you can muster a little more. Just a little more.
Not necessarily. The Axiom of Choice is a great example.
Um...are you arguing with me or agreeing with me? I agree that if you are going to offer formal proofs, you have to reveal what are the assumptions of your formal system--which you accept on faith, since you don't prove axioms, and that would include the Axiom of Choice.
You don't have to "believe" it, you just have to say whether or not you assume it.
What would be the point of assuming Axioms you don't know are true? There are important meta-mathematicians that have touted formal systems entirely divorced from domains of discourse, real or ideal, but you have been touting mathematics as the uber-cover of Everything, so I would not have thought you would be going in this direction.