The thing is that the proof for Gödel’s theorem is constructive. We have an algorithm to construct Gödel sentences from Axioms. So basically the only way we can be unable to recognize our Gödel sentences is being unable to recognize our axioms.
The thing is that the proof for Gödel’s theorem is constructive. We have an algorithm to construct Gödel sentences from Axioms. So basically the only way we can be unable to recognize our Gödel sentences is being unable to recognize our axioms.