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    Q extended with the necessitist principle N_Q collapses i... — Carmelics
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    Home/Modality & Possibility
    HistoryEditSee Inverse

    Q extended with the necessitist principle N_Q collapses into SQML

    Modality & Possibility
    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 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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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 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 against 2 of 2
    ?
    • 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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    Modality & Possibility

    Related

    Actualist models satisfying N_Q can systematically differ from SQML's Kripkean c...For any formula φ of L_□, φ is a theorem of SQML if and only if φ is a theorem o...Free logic permits non-denoting terms and empty domains, making N_Q weaker than ...If the background quantification theory is free rather than classical, Q + N_Q r...
    +5 moreShow less
    N_Q and the necessitist principle □N are equivalent in QThe claim that Q + N_Q collapses into SQML conflates provability-theoretic equiv...The equivalence of N_Q and □N holds only under classical quantification rules th...Williamson's necessitism, while endorsing □∀x□∃y(y=x), grounds this in a metaphy...φ is a theorem of Q + N_Q if and only if ∀xSx → φ is a theorem of Q

    Similar

    N_Q and the necessitist principle □N are equivalent in Q87%The full necessitism principle (Box-N) is invalid in KQML84%Leibniz's doctrine of complete concepts risks collapsing into Spinozis...77%Q is SQML minus its necessitism77%

    Source

    AI-extracted1/3 agreementValid
    SEP: possibilism-actualism
    View source passageHide passage
    Q simply collapses into SQML.[81] (The reader can quickly verify that \(\textbf{N}_{Q}\) and the necessitist principle \(\Box\textbf{N},\) are equivalent in Q.) More exactly put: for any formula \(\varphi\) of \(\scrL_\Box,\) \(\varphi\) is a theorem of SQML if and only if it is a theorem of \(Q+ \textbf{N}_{Q}\) and hence if and only if \(\forall \sfx\rS\sfx \to \varphi\) is a theorem of Q. In particular, both BF and CBF fall out as entirely unproblematic theorems under the assumption of nece
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit