The USS Clueless, IsThere is a post here that describes Russell’s paradox in set theory. The writer then generalizes that this proves that statements like “Can God create a stone that he cannot lift?” can be put on a firm mathematical foundation and not dismissed as imprecise language.
He is more-or-less correct, but I have several comments:
- He describes this mathematics as “esoteric”, which it is not. It is rather sophomore level simple set theory.
- His discussion of the paradox is rather hideous, I am glad I never had him as a teacher.
- His proof has nothing whatsoever to do with God, or God’s omnipotence, or anything theological.
To ask the question “Can God create a stone that he cannot lift?” is to ask whether God can violate the Law of Contradiction. He cannot. One can safely say, without being sacrilegious, that this is a limitation on God. Not even God can be both A and not A at the same time and in the same relationship. It is a question of logic, not of set theory.