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    N_Q and the necessitist principle □N are equivalent in Q — Carmelics
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    Supports→Q extended with the necessitist principle N_Q collapses into SQML

    N_Q and the necessitist principle □N are equivalent in Q

    Modality & Possibility
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    For any formula φ of L_□, φ is a theorem of SQML if and only if φ is a theorem o...Q extended with the necessitist principle N_Q collapses into SQMLφ is a theorem of Q + N_Q if and only if ∀xSx → φ is a theorem of Q

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    Q extended with the necessitist principle N_Q collapses into SQML87%The full necessitism principle (Box-N) is invalid in KQML87%The Barcan Formula (BF) and Converse Barcan Formula (CBF) are unproble...81%Q is SQML minus its necessitism80%

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    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

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