This seems a little glib wrt the meaning of something being "true". We have undecidability results: the Axiom of Choice and its negation are both consistent with the Zermelo-Frankel axioms. The continuum hypothesis and its negation are both consistent with the ZFC axioms. The Parallel Postulate and its negation are both consistent with the other Euclidean axioms.
Are we justified in saying that for each of these, one must be true and the other false? Of course not. To resolve them one way or the other, you need additional axioms; none of those six propositions is true platonically. What you choose depends on the problem you're trying to describe.
Are we justified in saying that for each of these, one must be true and the other false? Of course not. To resolve them one way or the other, you need additional axioms; none of those six propositions is true platonically. What you choose depends on the problem you're trying to describe.