Cantor's set theorem is often used to argue against the possibility of divine omniscience and therefore against the existence of God. It can be stated:
1. If God exists, then God is omniscient.However, this argument is false. The non-existence of a set of all truths does not entail that it is impossible for God to know all truths. The consistency of a plausible theistic position can be established relative to a widely accepted understanding of the standard model of Cantorian set theorem. The metaphysical Cantorian premises imply that Cantor’s theorem is inapplicable to the things that God knows. A set of all truths, if it exists, must be non-Cantorian.
2. If God is omniscient, then, by
definition, God knows the set of all truths.
3. If Cantor's theorem is true,
then there is no set of all truths.
4. But Cantor’s theorem is true.
5. Therefore, God does not exist.