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anonym comments on The Least Convenient Possible World - Less Wrong
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"Would you say that axioms in math are meaningless?"
They distinguish one hypothetical world from another. Furthermore, some of them can be empirically tested. At present, Euclidean geometry seems to be false and Riemannian to be true, and the only difference is a single axiom.
They distinguish one hypothetical world from another.
It's a subtle distinction, but I think it's more accurate and useful to say that the axioms define a mathematical universe, and that a mathematical universe cannot be true or false but only a better or poorer model of the physical universe.