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...