paradox of omniscience an objection to the possibility of omniscience, developed by Patrick Grim, that appeals to an application of Cantor’s power set theorem. Omniscience requires knowing all truths; according to Grim, that means knowing every truth in the set of all truths. But there is no set of all truths. Suppose that there were a set T of all truths. Consider all the subsets of T, that is, all members of the power set 3T. Take some truth T1. For each member of 3T either T1 is a member of that set or T1 is not a member of that set. There will thus correspond to each member of 3T a further truth specifying whether T1 is or is not a member of that set. Therefore there are at least as many truths as there are members of 3T. By the power set theorem, there are more members of 3T than there are of T. So T is not the set of all truths. By a parallel argument, no other set is, either. So there is no set of all truths, after all, and therefore no one who knows every member of that set. The objection may be countered by denying that the claim ‘for every proposition p, if p is true God knows that p’ requires that there be a set of all true propositions. See also CANTOR, DIVINE ATTRI- BUTE. E.R.W.