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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 Fagin's theorem and Immerman-Vardi establish co-extensionality of classes, not identity of properties, so the biconditional is weaker than it appears.

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

    Reasons For

    1 perspective
    Reason for
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    • 1.In logic, a true biconditional between formal definitions is precisely what identity of logical properties means; extensionality is identity here.
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    • 2.The distinction between co-extensionality and property-identity presumes an unexplained gap between syntax and semantics in formal systems.
      ?

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    • 3.If FO+LFP and SO express identical computable classes, distinguishing their 'properties' lacks clear meaning without external metaphysical commitment.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Co-extensionality (same truth conditions) differs from identity (same intrinsic nature); biconditionals only guarantee the former.
      ?

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    • 2.FO+LFP and SO capture identical problem sets extensionally, but may involve fundamentally different computational properties or mechanisms.
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    • 3.Properties concern how something works; classes concern what gets classified. The theorems address only classification equivalence.
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