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Publication Detail
LEVEL THEORY, PART 2: AXIOMATIZING THE BARE IDEA OF A POTENTIAL HIERARCHY
  • Publication Type:
    Journal article
  • Authors:
    BUTTON TIM
  • Publisher:
    Cambridge University Press (CUP)
  • Publication date:
    12/2021
  • Pagination:
    461, 484
  • Journal:
    The Bulletin of Symbolic Logic
  • Volume:
    27
  • Issue:
    4
  • Status:
    Published
  • Print ISSN:
    1079-8986
  • Language:
    en
Abstract
AbstractPotentialists 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.
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