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LEVEL THEORY, PART 2: AXIOMATIZING THE BARE IDEA OF A POTENTIAL HIERARCHY

Part of: Philosophical aspects of logic and foundations Set theory

Published online by Cambridge University Press:  29 April 2021

TIM BUTTON
TIM BUTTON*
Affiliation:
DEPARTMENT OF PHILOSOPHY UNIVERSITY COLLEGE LONDON GOWER STREET, LONDON, WC1E 6BT, UKE-mail: [email protected]: http://www.nottub.com
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Abstract

Potentialists think that the concept of set is importantly modal. Using tensed language as a heuristic, the following bare-bones story introduces the idea of a potential hierarchy of sets: ‘Always: for any sets that existed, there is a set whose members are exactly those sets; there are no other sets’. Surprisingly, this story already guarantees well-foundedness and persistence. Moreover, if we assume that time is linear, the ensuing modal set theory is almost definitionally equivalent with non-modal set theories; specifically, with Level Theory, as developed in Part 1.

Keywords

set theorylevel theoryrankpotentialismactualism

MSC classification

Primary: 03A05: Philosophical and critical
Secondary: 03E30: Axiomatics of classical set theory and its fragments
Type
Articles
Information
Bulletin of Symbolic Logic , Volume 27 , Issue 4 , December 2021 , pp. 461 - 484
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Copyright
The Author(s), 2021. Published by Cambridge University Press on behalf of Association for Symbolic Logic

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