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    Carmelics

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

    It is not the case that Scott's theorem shows measurability implies V≠L, but this is an external judgment requiring a richer metatheory, not a failure of L's internal recognition.

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.If V≠L is true, L's claim to capture all sets is objectively false, regardless of whether L 'recognizes' this internally.
      ?

      Think about whether this reason is strong or weak

    • 2.The distinction between 'internal recognition' and 'external judgment' dissolves if both operate within the same mathematical reality.
      ?

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    • 3.Requiring a richer metatheory to expose L's inadequacy suggests L itself is inadequate—the metatheory isn't external but foundational.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.L's internal logic is consistent; external theorems about L don't contradict L's self-conception, only our external knowledge.
      ?

      Think about whether this reason is strong or weak

    • 2.Metatheory can access facts about models that the model itself cannot recognize without additional axioms beyond its own theory.
      ?

      Think about whether this reason is strong or weak

    • 3.Scott's theorem uses strong assumptions (measurable cardinals) absent from L; the gap reflects mathematical expressiveness, not L's failure.
      ?

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