Varieties of Class-Theoretic Potentialism

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

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.

Similar books and articles

Multiverse Conceptions in Set Theory.Carolin Antos, Sy-David Friedman, Radek Honzik & Claudio Ternullo - 2018 - In Carolin Antos, Sy-David Friedman, Radek Honzik & Claudio Ternullo (eds.), The Hyperuniverse Project and Maximality. Basel, Switzerland: Birkhäuser. pp. 47-73.
Modern Class Forcing.Carolin Antos & Victoria Gitman - forthcoming - In D. Gabbay M. Fitting (ed.), Research Trends in Contemporary Logic. College Publications.
Sets and Probability.Leon Horsten & Hazel Brickhill - forthcoming - Erkenntnis:1-26.
Proof-theoretic analysis by iterated reflection.Lev D. Beklemishev - 2003 - Archive for Mathematical Logic 42 (6):515-552.
Potentialism and S5.Jonas Werner - 2022 - Canadian Journal of Philosophy 52 (6):622-635.

Analytics

Added to PP
2021-08-03

Downloads
486 (#41,252)

6 months
176 (#18,906)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

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.

Add more citations

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.

View all 32 references / Add more references