> This is the classical "who shaves the barber" paradox I don't think it is. Simply because a set contains things that cannot be represented by a symbol, does

> This is the classical "who shaves the barber" paradox I don't think it is. Simply because a set contains things that cannot be represented by a symbol, does not mean that the set itself cannot be represented by a symbol. And since it can, the set is not a member of itself. No paradoxes. Also, I propose to you all that everything can be represented by a symbol. Thus, the set in question is the empty set. And here is the requested symbol: ∅