 E. J. Lowe (2013, 192) argues on behalf of the fool: Two sets are identical exactly if they have the same members. So the identity of a set is grounded on the identity conditions of its members. In the absence of members, the set is ill-defined. Mathematicians may wield it as a useful fiction. But utility should not be confused with truth. Since mathematical statements such as ‘The first prime number after 1,000,000 is 1,000,003’ are necessary truths and can only be rendered true by the existence of a contingent being, such as Cameron Winklevoss, Lowe concludes that there necessarily exists at least one contingent being. Consequently, the empty world is impossible even if there are no necessary beings.