> I don't know bout incompleteness theorem, but I'd say it's pretty obvious (both in introspection and in observation of others) that people don't naturally use formal logic for anything, they only painstakingly emulate it when forced to.

Indeed, this is one reason why I assert that Wittgenstein was wrong about the nature of human thought when writing:

"""If there were a verb meaning "to believe falsely," it would not have any significant first person, present indicative."""

Sure, it's logically incoherent for us to have such a word, but there's what seems like several different ways for us to hold contradictory and incoherent beliefs within our minds.