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    BF and CBF are theorems of SQML — Carmelics
    Home/Modality & Possibility
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    Supports→The Barcan Formula (BF) and Converse Barcan Formula (CBF) are unproblematic theorems under necessitism

    BF and CBF are theorems of SQML

    Modality & Possibility
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    Necessitism entails N_QQ + N_Q collapses into SQMLThe Barcan Formula (BF) and Converse Barcan Formula (CBF) are unproblematic theo...

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    φ is a theorem of Q + N_Q if and only if ∀xSx → φ is a theorem of Q

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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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