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    Carmelics

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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 Q extended with the necessitist principle N_Q collapses into SQML

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    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.The equivalence of N_Q and □N holds only under classical quantification rules that free logicians like Nolt explicitly reject.
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    • 2.Free logic permits non-denoting terms and empty domains, making N_Q weaker than □N without the presupposition that all singular terms refer.
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    • 3.If the background quantification theory is free rather than classical, Q + N_Q remains strictly weaker than SQML and does not collapse into it.
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    Reason for 2 of 2
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    • 1.Williamson's necessitism, while endorsing □∀x□∃y(y=x), grounds this in a metaphysics of necessary beings that is not captured by purely syntactic collapse of proof systems.
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    • 2.The claim that Q + N_Q collapses into SQML conflates provability-theoretic equivalence with semantic equivalence over intended models of modal reality.
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    • 3.Actualist models satisfying N_Q can systematically differ from SQML's Kripkean constant-domain semantics in how they interpret the inner domain, preserving a real distinction Linsky and Zalta have defended.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.N_Q and the necessitist principle □N are equivalent in Q
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    • 2.For any formula φ of L_□, φ is a theorem of SQML if and only if φ is a theorem of Q + N_Q
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    • 3.φ is a theorem of Q + N_Q if and only if ∀xSx → φ is a theorem of Q
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