 Is \(R\) a member of itself? If it is, then it must satisfy the condition of not being a member of itself and so it is not. If it is not, then it must not satisfy the condition of not being a member of itself, and so it must be a member of itself. Since by classical logic one case or the other must hold – either \(R\) is a member of itself or it is not – it follows that the theory implies a contradiction.