That's not how it works, though. We can study any set of axioms we want. Mathematics often study "multiple incompatible worlds". For example, euclidean space where parallel lines never meet, and projective space, where parallel lines do meet at infinity. This is a general theme of math; we can study different sets of "beliefs" when we don't know which one is the "correct belief".

Thus, we come out on top, since we know what happens in all possible worlds.