Yes, strictly speaking that's true, but then if the universe were slightly bigger, or you used a different encoding, you'd get different results. It feels kind

Yes, strictly speaking that's true, but then if the universe were slightly bigger, or you used a different encoding, you'd get different results. It feels kind of arbitrary to stop thinking about what would happen if the universe contained just one more bit. Philosophically, I think it's also more interesting that Gödel's theorem would continue to produce such sentences, regardless of how large our universe happens to be. You could never have a universe that is so big that it could contain all Gödel sentences, even if our universe were bigger. This is a much more fundamental limitation. Gödel's theorem gives you a sentence S where you can prove neither S nor its negation from the current axioms P. Of course, if you then add S (or its negation) as an axiom, then you CAN prove it. But then Gödel's theorem will just give you another sentence S', ad infinitum. You can never win this game.