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    Made withinDC&Austin
    In classical theories of entailment, the relevant possibi... — Carmelics
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    Home/Philosophy of Language
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    In classical theories of entailment, the relevant possibilities are those where all necessities in X are true

    Modality & PossibilityPhilosophy of Language
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    1 reason for
    2 reasons against

    Reasons For

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

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    Reason against 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 against 2 of 2
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    • 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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    Philosophy of LanguageModality & Possibility

    Related

    A theory that validates explosion cannot be tracking the right space of possibil...Classical entailment restricts the space of relevant possibilities to those sati...Classical modal semantics permits irrelevant entailments like 'A∧¬A ⊢ B', which ...If the relevant possibilities exclude worlds falsifying necessities, hyperintens...
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    Impossible worlds semantics (Priest, Berto) demonstrates that some entailment re...Relevant logic (Anderson & Belnap) requires that premises and conclusions share ...

    Similar

    According to modern logical entailment, every necessary proposition en...82%Under an entailment criterion, a theory is committed to universals if ...81%Classical entailment restricts the space of relevant possibilities to ...80%Under an entailment account, a theory T is ontologically committed to ...79%

    Source

    AI-extracted1/3 agreementValid
    SEP: logic-substructural
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    This counterexample can also be understood in terms of behaviour of premise combination. Here when we say \(X,A \vdash B\) is true, we are not just saying that \(B\) holds in any circumstance in which \(X\) and \(A\) both hold. If we are after a genuine entailment A \(\rightarrow\) B, then we want \(B\) to be true in any (related) circumstance in which \(A\) is true. So, \(X,A \vdash B\) says that in any possibility in which \(A\) is true, so is \(B\). These possibilities might not satisfy all
    Extraction notes

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

    Details

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