Another answer is that the axioms jibe with our actual, though limited, experience of space and that we are justified in extrapolating from the small to the universal. But, although much inductive evidence can be adduced to support this claim, our best proof would be logically incomplete. For even if all the observed facts are in agreement with the axioms, the possibility is open that a hitherto unobserved fact may contradict them and so destroy their title to universality. Inductive considerations can show no more than that the axioms are plausible or probably true.
Imagine what would happen if we built a whole universe based on certain axioms which are taken at face value as true, and centuries later derive two contradicting theorems.
