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    Carmelics

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    Made withinDC&Austin
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    Home/Original/inverse
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    Inverse View

    It is not the case that In classical theories of entailment, the relevant possibilities are those where all necessities in X are true

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    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Relevant logic (Anderson & Belnap) requires that premises and conclusions share topic-content, not merely modal closure over necessities.
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    • 2.Classical modal semantics permits irrelevant entailments like 'A∧¬A ⊢ B', which violates the relevance constraint on genuine implication.
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    • 3.A theory that validates explosion cannot be tracking the right space of possibilities for real inferential connection between X and its consequences.
      ?

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    Reason for 2 of 2
    ?
    • 1.Impossible worlds semantics (Priest, Berto) demonstrates that some entailment relations require ranging over worlds where necessities fail.
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    • 2.If the relevant possibilities exclude worlds falsifying necessities, hyperintensional distinctions—e.g., between '2+2=4' and 'Fermat's Last Theorem'—cannot be drawn.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • Classical entailment restricts the space of relevant possibilities to those satisfying what is taken as necessary in X
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