Metaphysical Multiversism: from Armchair to Practice
Sabina Dominguez Parrado

Abstract:
This thesis assesses whether the ontological commitments of an emerging position within the philosophy of set theory – metaphysical multiversism – are justified. Metaphysical multiversism can be characterised as the conjunction of two theses. First, that there is not one unique ultimate set-theoretic universe, but rather a plurality of universes (the ‘multiverse’). Second, metaphysical multiversism qualifies as a form of mathematical realism, since it takes these universes to exist ‘platonistically’. The present thesis constitutes the first systematic attempt to explore, clarify and evaluate the realist ontology posited by metaphysical multiversism.
I begin by introducing a novel taxonomy: I distinguish between conservative and radical metaphysical multiversism. According to the former, universes are models of consistent set-theoretic theories; according to the latter, universes are models of consistent, or non-trivial inconsistent set-theoretic theories. Next, in the central chapters of the thesis, I explore two strategies to justify the ontological commitments of both varieties of metaphysical multiversism. The first strategy relies on what I call the epistemic argument, which claims that metaphysical multiversism is the only version of mathematical realism rising to the Benacerraf-Field Challenge, and also on the well-known indispensability argument. The second strategy attempts to justify the realist commitments of metaphysical multiversism on the basis of a practice-based argument. This strategy is inspired and informed by Penelope Maddy’s Second Philosophy.
My conclusion will be the following: while both strategies can justify the ontology posited by conservative metaphysical multiversism, they do not as straightforwardly justify the ontological commitments of radical metaphysical multiversism. Therefore, only conservative metaphysical multiversism can legitimately justify its realist ontological commitments.