Nō reira, ko te kāinga o ngā tuhinga kāore anō a Gödel e tohu ana he mana tōtika tētahi pūnaha whai arithmetic taketake, mēnā he oro (ko te tikanga he pono ngā tautuhinga katoa ka taea te whakamatara), kāore i te oti rawa (arā he kuputuhi pono e kore e taea te whakamatau i roto i taua pūnaha).