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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
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    42
    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that Under AFA, ℘* and ℘* are distinct

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Under ZFC with the Foundation Axiom, V=WF, so ℘* and ℘* collapse into the same object, making their distinctness a feature of AFA alone.
      ?

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    • 2.A claim about distinctness that holds only relative to a chosen axiomatic system cannot be treated as an absolute ontological fact about sets.
      ?

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    • 3.Benacerraf's structuralist insight entails that multiple incompatible set-theoretic universes can equally well serve as foundations, undermining privileging AFA's verdict.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.Boolos and others in the iterative conception tradition argue that the cumulative hierarchy exhausts the genuinely coherent notion of set, making WF=V non-negotiable.
      ?

      Think about whether this reason is strong or weak

    • 2.If WF=V is conceptually mandatory, then ℘* and ℘* are necessarily co-extensional, and their alleged distinctness under AFA reflects notational inflation rather than real mathematical difference.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.AFA (Anti-Foundation Axiom) permits non-wellfounded sets
      ?

      Think about whether this reason is strong or weak

    • 2.Under AFA, ℘* equals WF (well-founded sets only) while ℘* equals V (the full universe including non-wellfounded sets)
      ?

      Think about whether this reason is strong or weak

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