I was thinking about Patrick Grim’s Cantorian argument against omniscience this week, and it was after I read the exchange between him and Alvin Plantinga (which I admit required too much familiarity with set-theoretic semantics for me to follow with any ease), and while I was reading William Lane Craig’s review of Jordan Howard Sobel’s book Logic and Theism, that I thought perhaps one could use a Cantorian argument against the Leibnizian Cosmological argument as Alexander Pruss articulates it.
Pruss formulates a cosmological argument in this way:
- Every contingent fact has an explanation.
- There is a contingent fact that includes all other contingent facts.
- Therefore, there is an explanation of this fact.
- This explanation must involve a necessary being.
- This necessary being is God.
Perhaps premise 2 could be called into question, since it seems to require a set of all contingent facts, but there is no such set. I wonder how this could be answered…
[Edit: obviously, that the maximally specific true proposition is contingent, and requires an explanation].