The ZFC Axiom of Choice

Is there traditional mathematics? That's an open question. I think it's partly a philosophical question because it's a matter of what is mathematics, right? It comes back to that basic question. The ZFC axioms which were developed a bit over a hundred years ago are ones which we kind of generally agree that these are true or these are properties that set should have but they're not complete. We tend to believe that ZFC is consistent because we haven't discovered any contradictions. If you believe that, then by Goertals and completeness theorem, ZFC is not going to be able to prove that it's consistent.