 (2) Similar claims can be made for mathematical conjectures. Different set theorists have different views on controversial subjects such as non-well-founded sets, the  Continuum Hypothesis,  the Axiom of Choice, the set/(proper-)class distinction, etc. If one embraces the Platonic view (subscribed to, at least implicitly, by many set theorists) that there is One True Universe of sets, then at most one of the alternative set theories can be correct: the others are wrong, and necessarily so. But people can work under the hypothesis that a necessarily false basic mathematical principle holds, and reason coherently from this: