Hierarchy of set theoretical multiverse
Ahmet Çevik
This work presents a novel version of the multiverse theory of sets called hierarchical pluralism by introducing the desideretum of ‘degrees of intentionality’ of theories. The presented view is articulated for the purpose of reconciling, in the philosophy of set theory, 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.