To clarify, when I say “trying to establish” I don’t mean “trying to establish in a rigorous way,” I just mean that that the goal of the informal reasoning should be the informal conclusion “we won’t be able to find a way around this problem.” It’s also not a literal universal quantifier, in the same way that cryptography isn’t up against against a literal universal quantifier, so I was doubly sloppy.
I don’t think that a mathematical proof is likely to be convincing on its own (as you point out, there is a lot of slack in the choice of formalization). It might be helpful as part of an argument, though I doubt that’s going to be where the action is.
To clarify, when I say “trying to establish” I don’t mean “trying to establish in a rigorous way,” I just mean that that the goal of the informal reasoning should be the informal conclusion “we won’t be able to find a way around this problem.” It’s also not a literal universal quantifier, in the same way that cryptography isn’t up against against a literal universal quantifier, so I was doubly sloppy.
I don’t think that a mathematical proof is likely to be convincing on its own (as you point out, there is a lot of slack in the choice of formalization). It might be helpful as part of an argument, though I doubt that’s going to be where the action is.