> Is the axiom of choice "true"? Does it make sense to say that it has a truth value? Is such a truth value amenable to human discovery? I imagine PG would say

> Is the axiom of choice "true"? Does it make sense to say that it has a truth value? Is such a truth value amenable to human discovery? I imagine PG would say that these are not purely mathematical questions, but rather metamathematical questions. Theorems remain theorems regardless of whether the axiom of choice is "true", although one may contend that theorems assuming that the AOC is false (or true) are vacuous. Aliens would surely agree with us on statements of the form "working in first-order logic (or whatever) formalized in XXX way, assuming axioms YYY and ZZZ, we may prove that...".