No recursive axiomatization of arithmetic is complete.
[...] Now one day while Joshu and another monk were standing together in the monastery, a dog wandered by. The monk asked Joshu, “Does a dog have Buddha-nature, or not?”
Whatever that is. So tell me—what did Joshu reply?
‘MU’? What is this ‘MU’? What about the dog? What about Buddha-nature? [...]
Mumon Has the Last Word
Has a dog Buddha-nature?
This is the most serious question of all.
If you say yes or no,
You lose your own Buddha-nature.
Excerpt from Douglas R. Hofstadter, Gödel, Escher, Bach - an Eternal Golden Braid (20th anniversary edition), Penguin Books, 2000, p233, p272