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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 The translation function Trans presupposes a fixed domain across modal contexts, smuggling in a Barcan-style assumption that S4 itself does not require.

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Standard S4 semantics typically employ constant domains in Kripke models; Trans simply reflects the dominant metalogical convention, not a hidden assumption.
      ?

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    • 2.Any effective translation between modal and first-order logic requires *some* domain specification; calling this 'smuggling in' conflates necessary with problematic presuppositions.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.S4 modal logic is axiomatically neutral on domain variation; it permits but doesn't mandate fixed domains across possible worlds.
      ?

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    • 2.Translation functions that map modal formulas to first-order logic must make domain assumptions explicit; hidden assumptions violate logical transparency.
      ?

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    • 3.The Barcan formula's validity depends on constant domains, yet S4 remains consistent with variable domain semantics, showing they're independent commitments.
      ?

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