“The incompleteness theorem is a mathematical theorem precisely because the relevant notions of truth and provability are mathematically definable. Nonmathematical “Gödel sentences” and Liar sentences give rise to prolonged (or endless) discussions of just what is meant by a proof, by a true statement, by sound reasoning, by showing something to be true, by convincing oneself of something, by believing something, by a meaningful statement, and so on.”