Yeah, I've thought about this a little bit but again my math isn't so strong.
I guess approaching this more from computer science (something I'm more familiar with) you could compare with stuff like the NP Hard class of problems. And thus I offer that unproveable does not mean "wrong". We generally "know" that P=NP is wrong but we cannot prove it only because we lack omniscience. Us lacking the information (in the physics sense of the word i.e. Hawking radiation) doesn't mean the information isn't there to be quantified.