> Some very intelligent people, including Gödel and Penrose, seem to think that humans have some kind of ability to arrive directly on correct propositions in ways that bypass the incompleteness theorem. Penrose seems to think this can be due to Quantum Mechanics, Göder may have thought it came frome something divine.

Did Gödel really say this? It sounds like quite a stretch of incompleteness theorem.

It's like saying because halting problem is undecidable, but humans can debug programs, therefore human brains must having some supernatural power.

Gödel mostly cared about mathematics. And he seems to have believed that human intuition could "know" propositions to be true, even if they could not be proven logically[1].

It appears that he was religious and probably believed in an immaterial and maybe even divine soul [2]. If so, that may explain why he believed that human intuition could be unburdend by the incompleteness theorem.

[1] https://philsci-archive.pitt.edu/9154/1/Nesher_Godel_on_Trut...

[2] https://en.wikipedia.org/wiki/G%C3%B6del%27s_ontological_pro...