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    Logical validity requires that premises be relevant to th... — Carmelics
    Home/Philosophy of Language
    HistoryEditSee Inverse

    Logical validity requires that premises be relevant to the conclusion they support

    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.If X and A together entail B, then X must be relevant to A
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    • 2.Premise combination should be restricted so that adding irrelevant material Y does not preserve a valid deduction
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
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    • 1.Classical logic's material conditional 'A → B' is truth-functional and has proven indispensable in mathematics and science without relevance constraints.
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    • 2.Restricting entailment to relevant premises would invalidate ex falso quodlibet, undermining the consistency proofs that ground formal systems like Peano Arithmetic.
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    • 3.The theoretical cost of abandoning monotonicity—which relevance logic requires—exceeds any gain, since paraconsistency can be achieved by less revisionary means.
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    Reason against 2 of 2
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    • 1.Lewis and Langford's strict implication shows that necessary truths are entailed by any proposition, making irrelevance in modal contexts not a defect but a feature of necessity.
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    • 2.If relevance is a pragmatic constraint on assertion rather than a semantic condition on validity, then Grice's maxims already handle apparent irrelevance without revising logic itself.
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    Topics

    Philosophy of LanguageModality & Possibility

    Related

    Classical logic's material conditional 'A → B' is truth-functional and has prove...If X and A together entail B, then X must be relevant to AIf relevance is a pragmatic constraint on assertion rather than a semantic condi...Lewis and Langford's strict implication shows that necessary truths are entailed...
    +3 moreShow less
    Premise combination should be restricted so that adding irrelevant material Y do...Restricting entailment to relevant premises would invalidate ex falso quodlibet,...The theoretical cost of abandoning monotonicity—which relevance logic requires—e...

    Similar

    Logical validity requires that if all premises of an argument are true...90%Justifying a conclusion requires that the conclusion follows from the ...86%Cogency requires that premises be acceptable, relevant, and sufficient...86%Justifying a conclusion requires premises that are acceptable85%

    Source

    AI-extracted1/3 agreementValid
    SEP: logic-substructural
    View source passageHide passage
    Many people have wanted to give an account of logical validity which pays some attention to conditions of relevance. If \(X,A \vdash B\) holds, then \(X\) must somehow be relevant to \(A\). Premise combination is restricted in the following way. We may have \(X \vdash A\) without also having \(X,Y \vdash A\) . The new material \(Y\) might not be relevant to the deduction. In the 1950s, Moh (1950), Church (1951) and Ackermann (1956) all gave accounts of what a ‘relevant’ logic could be. The idea
    Extraction notes

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

    Details

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