Abstract
Is there a universal set? There are different theories which give different answers to this question. There is Zermelo-Fraenkel (ZF) in which there is no universal set. There is the theory propounded by Quine in 'New Foundations' (NF) in which there is a universal set. The question is puzzling. For if each theory is consistent, how can one fault either answer? The dogmatist and the skeptic agree that there is an objective truth about the matter. They disagree about whether this truth is knowable, with the dogmatist saying the human mind can reach it and the skeptic denying that this is possible. In contrast, a relativist says there is no objective truth to be known. We distinguish two versions of this general idea. Both versions agree that the NF assertion that there is a universal set and the ZF denial are each correct as long as the two theories are internally consistent. We defend the second of these two versions and show that, on this second version, relativism is a reasonable alternative to both realism and nominalism with respect to ontological questions.
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