Gödel's Disjunction [video]
Where this all falls down is in the assumption that human minds are consistent systems. I have to wonder if anyone who thinks such a thing has ever met any actual humans. Even a brief interrogation of a typical human as to their beliefs and assumptions about the world should rapidly disabuse us of the thought.<p>Humans are perfectly capable of assuming unproved axioms, changing their set of axioms, and accepting contradictory axioms. We do these things all the time, applying one axiom in one situation, and it&#x27;s opposite in another. Just ask someone about their political beliefs for a while.<p>The fact is human intelligence is not an end in itself, it&#x27;s a tool we use to achieve goals set by our evolutionary priorities, as encoded into our emotions and needs. These are the things that drive us, not logical axioms and proven truths. Even smart people have an emotional need to be correct, and many will resist having their beliefs challenged and changed tooth and nail. It takes constant effort and self discipline to maintain an open mind to new ideas and the rejection of existing assumptions, and certainly doesn&#x27;t come naturally to us.<p>So this systematic theorising all seems somewhat beside the point. Don&#x27;t get me wrong. It&#x27;s interesting and useful philosophical work, no question, but it&#x27;s not really applicable to actual human minds.