  One lightweight form of object realism is the “full-blooded platonism” of Balaguer 1998. This view is characterized by a plenitude principle to the effect that any mathematical objects that could exist actually do exist. For instance, since the Continuum Hypothesis is independent of the standard axiomatization of set theory, there is a universe of sets in which the hypothesis is true and another in which it is false. And neither universe is metaphysically privileged. By contrast, traditional platonism asserts that there is a unique universe of sets in which the Continuum Hypothesis is either determinately true or determinately false.[15]