  In this paper, I develop a novel version of the multiverse theory of sets
called hierarchical pluralism by introducing the notion of `degrees of
intentionality' of theories. The presented view is articulated for the purpose
of reconciling epistemological realism and the multiverse theory of sets so as
to preserve a considerable amount of epistemic objectivity when working with
the multiverse theory. I give some arguments in favour of a hierarchical
picture of the multiverse in which theories or models are thought to be ordered
with respect to their plausibility, as a manifestation of endorsing the idea
that some set theories are more plausible than others. The proposed multiverse
account settles the pluralist's dilemma, the dichotomy that there is a
trade-off between the richness of mathematical ontology and the objectivity of
mathematical truth. The view also extends and serves as an alternative position
to Balaguer's intention-based Platonism from which he claims that a certain
version of mathematical pluralism follows.
