Gödel's incompleteness theorems are proof though contradiction which as I said can be interesting. (Or I should say they are part of the set of proofs though contradiction.) However, the paradox is not interesting it's just paradox = bad assumption.

So, don't read to much into Gödel, you also can't prove 1 + 1 = 2 except by making an equivalent assumption. Yet, that does not mean what you think it means.

PS: I don't think HN has jumped the shark, but I do try and keep it clean. IMO, it was fairly close to the acceptable line but to close to the HN equivalent of a funny cat photo, (hey look a paradox how cute), but a longer post taking about a well defined paradox and it's implications would have been acceptable and had a much cleaner discussion.