> In general case given a system it is impossible to prove it is not self-contradictory. If you're asserting it, by merely asserting axioms, then (in the gener

> In general case given a system it is impossible to prove it is not self-contradictory. If you're asserting it, by merely asserting axioms, then (in the general case,) yes. If you're constructing it, and showing that the axioms are satisfied, then no: there are several ways to construct a model that nobody has ever found a contradiction in, and you can construct spherical geometry this way.