"In the Magnificrab, some unusual powers of the Crab's mind are revealed. His own version of his powers is merely that he listens to music and distinguishes the

"In the Magnificrab, some unusual powers of the Crab's mind are revealed. His own version of his powers is merely that he listens to music and distinguishes the beautiful from the non-beautiful. Now Achilles finds another way to describe the Crab's abilities: the Crab divides the statements of number theory into the categories true and false. But the Crab maintains that, if he chances to do so, it is only by the purest accident, since he is, by his own admission, incompetent in mathematics, What makes the Crab's performances all the more mystifying to Achilles, however, is that they seem to be in direct violation of a celebrated result of metamathematics with which Achilles is familiar."