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VARIETIES OF CLASS-THEORETIC POTENTIALISM

Part of: General and miscellaneous specific topics Set theory Philosophical aspects of logic and foundations

Published online by Cambridge University Press:  22 May 2023

NEIL BARTON Open the ORCID record for NEIL BARTON [Opens in a new window]  and
KAMERYN J. WILLIAMS
NEIL BARTON
Affiliation:
IFIKK, UNIVERSITETET I OSLO POSTBOKS 1020, BLINDERN 0315 OSLO, NORWAY E-mail: [email protected] URL: https://neilbarton.net/
KAMERYN J. WILLIAMS*
Affiliation:
BARD COLLEGE AT SIMON’S ROCK DIVISION OF SCIENCE, MATHEMATICS, AND COMPUTING 84 ALFORD ROAD GREAT BARRINGTON, MA 01230, USA URL: https://kamerynjw.net
*
E-mail: [email protected]
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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.

Keywords

class theorypotentialismtruth predicates

MSC classification

Primary: 00A30: Philosophy of mathematics 03A05: Philosophical and critical 03E70: Nonclassical and second-order set theories
Type
Research Article
Information
The Review of Symbolic Logic , Volume 17 , Issue 1 , March 2024 , pp. 272 - 304
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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References

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