“In other words, the rules allow us to ascertain truths beyond the rules.” Gödel demonstrates nothing of the kind: humans can be _mistaken_ about their “truths

“In other words, the rules allow us to ascertain truths beyond the rules.” Gödel demonstrates nothing of the kind: humans can be _mistaken_ about their “truths”, and if you permit mistaken assertions into your formal system, well, Gödel simply doesn't apply.