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

    It is not the case that NFSI is consistent

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.By Gödel's second incompleteness theorem, any consistency proof of NFSI conducted within a system of comparable strength is epistemically circular.
      ?

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    • 2.The metatheory used to verify the finite/cofinite structure is a model must itself be stronger than NFSI, making the consistency claim relative rather than absolute.
      ?

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    • 3.Holmes's 2024 claimed proof of NF's consistency, on which NFSI consistency claims partly depend, remained under peer scrutiny and is not yet universally accepted.
      ?

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    Reason for 2 of 2
    ?
    • 1.The finite/cofinite structure satisfies only a fragment of NFSI, and full NFSI includes stratified comprehension axioms not modeled by that structure.
      ?

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    • 2.A consistency proof relative to a restricted model does not establish consistency of the full theory unless the model is demonstrably a model of all axioms.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.A structure exists in which the sets are exactly the finite and cofinite collections and this structure satisfies NFSI
      ?

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    • 2.A theory is consistent if a model of it exists
      ?

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