"is false" doesn't mean anything in Godel's system. That's too high level and imprecise. We're dealing with only symbol manipulation here. We only have provabil

"is false" doesn't mean anything in Godel's system. That's too high level and imprecise. We're dealing with only symbol manipulation here. We only have provability (which really is "there exists a derivation for") - we don't have "truth".