"If p were provable, then Bew(G(p)) would be provable, as argued above. But p asserts the negation of Bew(G(p)). Thus the system would be inconsistent, proving both a statement and its negation."Fuck Gödel. Let's just assume that the system he used is inconsistent, that he has proven an inconsistency (p ∧¬p) in his inconsistent system, and lets concentrate on complete and consistent logics.
[1]: http://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_theorems
