Why it is even relevant? Godel's incompletness theorem applies to almost any strong formal system with self-referential abilities, so if you want to do a good formalization, you bound to have one that satisfy Godel's theorem requirement.

Easy: have you ever had a an epiphany how idiot you were and did not understand what all people told you for a long time? Then you realized something and everything just snapped into place. You now understand all. Paff! An axiom or condition was just changed in you by an experience. Suddenly you get now what others told you. Welcome to an other system of understanding.