On the Shanghai metro yesterday, we saw a man with a T-shirt bearing the caption
ANTI SOCIAL SOCIAL CLUB
Do I smell a trace of Cantor’s diagonal argument here? Perhaps even Russell’s paradox? Suppose that every social club is named after a person, and a person X is antisocial if X is not a member of the X club. Then let the club of antisocial people be the Y club, and ask: Is Y social or antisocial?
Perhaps you would like to formalise this …