Earlier today, I pondered whether this infinite set atheism thing is something Eliezer merely claims to believe as some sort of test of basic rationality. It's a belief that, as far as I can tell, makes no prediction.

But here's what I predict that I would say if I had Eliezer's opinions and my mathematical knowledge: I'm a fan of thinking of ZFC as being its countably infinite model, in which the class of all sets is enumerable, and every set has a finite representation. Of course, things like the axiom of infinity and Cantor's diagonal argument still apply; it's just that "uncountably infinite set" simply means "set whose bijection with the natural numbers is not contained in the model".

(Yes, ZFC has a countable model, assuming it's consistent. I would call this weird, but I hate admitting that any aspect of math is counterintuitive.)