Higher-Order Platonism and Multiversism
Claudio Ternullo

TL;DR
This paper explores higher-order Platonism within the multiverse view of set theory, using Zalta and Linsky's Object Theory to formalize and address philosophical criticisms of multiversism.
Contribution
It formalizes higher-order Platonism in the context of Hamkins' multiversism using Object Theory, aiding in addressing key philosophical criticisms.
Findings
Object Theory faithfully expresses Hamkins' multiverse conception
Embedding clarifies the articulation and skeptical issues of multiversism
Supports the relationship between multiversism and set-theoretic practice
Abstract
Joel Hamkins has described his multiverse position as being one of `higher-order realism -- Platonism about universes', whereby one takes models of set theory to be actually existing objects (vis-\`a-vis `first-order realism', which takes only sets to be actually existing objects). My goal in this paper is to make sense of the view in the very context of Hamkins' own multiversism. To this end, I will explain what may be considered the central features of higher-order platonism, and then will focus on Zalta and Linsky's Object Theory, which, I will argue, is able to faithfully express Hamkins' conception. I will then show how the embedding of higher-order platonism into Object Theory may help the Hamkinsian multiversist to respond to salient criticisms of the multiverse conception, especially those relating to its articulation, skeptical attitude, and relationship with set-theoretic…
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Taxonomy
TopicsPhilosophy and Theoretical Science · Philosophy and History of Science · Philosophy, Science, and History
