keithb wrote:Not only this, but I think that the whole idea of the hierarchy of infinite sets with different cardinalities also seems to pose problems to this notion, as I noted in one of my earliest posts on this forum.
Suppose that a god exists with some sort of knowledge set that is infinite in scope. What I argued in my post (and what I believe can be easily shown) is that there exists a super set that can be constructed from this original set (assuming the axiom of choice) that has a higher cardinality than the original set (and thus can not be mapped onto the original set with a one-to-one correspondence).
I am sure that Tarski could probably talk in more depth about these types of theoretical mathematical topics than I could, but the very idea of an omniscient god existing is for me problematic on a philosophical and mathematical level.
That was a cool thread by the way, I forget if this was answered, but couldn't one define God's knowledge as the set of all sets?