Sure, and see also https://en.wikipedia.org/wiki/BLIT_(short_story)
But, uh, any evidence that that's real? We should be careful with Gödel's results here; the Gödelian incompleteness of the human mind is that a human cannot consistently believe that everything they believe is true. It has nothing to do with sanity and perception: https://en.wikipedia.org/wiki/Doxastic_logic