Varieties of Class-Theoretic Potentialism

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Review of Symbolic Logic 17 (1):272-304 (2024)
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Abstract

We explain and explore class-theoretic potentialism—the view that one can always individuate more classes over a set-theoretic universe. We examine some motivations for class-theoretic potentialism, before proving some results concerning the relevant potentialist systems (in particular exhibiting failures of the $\mathsf {.2}$ and $\mathsf {.3}$ axioms). We then discuss the significance of these results for the different kinds of class-theoretic potentialists.

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10.1017/s1755020323000126

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Neil Barton
University of Oslo

Citations of this work

28 Reflection in Apophatic Mathematics and Theology.Neil Barton - 2024 - In Mirosław Szatkowski (ed.), Ontology of Divinity. De Gruyter. pp. 583-612.

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References found in this work

Parts of Classes.David K. Lewis - 1991 - Mind 100 (3):394-397.
Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2001 - Studia Logica 76 (1):142-148.
The potential hierarchy of sets.Øystein Linnebo - 2013 - Review of Symbolic Logic 6 (2):205-228.
The set-theoretic multiverse.Joel David Hamkins - 2012 - Review of Symbolic Logic 5 (3):416-449.

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