When something is neither obvious (like, say, the axioms of planar geometry) nor subject to geometric or mathematical proof (like, say, the infinitude of primes

When something is neither obvious (like, say, the axioms of planar geometry) nor subject to geometric or mathematical proof (like, say, the infinitude of primes) or experimentation (the atomic theory of matter), it's interesting at a philosophical level to discuss why we should believe P or not-P (or neither or both, I suppose) Personally, since it appears that there's no feasible physical scenario which would point to the "truth" of ZFC over ZF+~C, I have trouble understanding how it's useful to debate the point. I can tell you what happens in the thought experiment with the infinite number of prisoners: according to GR, since they are infinitely massive they collapse into a black hole no matter the average density of the sphere enclosing all the prisoners. Thus, the axiom of choice is disproven :-P