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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
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    42
    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that The ex falso quodlibet — (A ∧ ¬A) → B — is not logically valid in relevant logic

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Classical logic's ex falso is not merely a formal artifact but tracks the metaphysical principle that contradictions are impossible worlds, making any proposition vacuously true there.
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    • 2.If no contradictions can obtain, conditionals with contradictory antecedents have empty domains of evaluation, and vacuous truth is the correct semantic verdict regardless of variable sharing.
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    • 3.Relevant logic's variable-sharing condition (VSP) conflates syntactic topic-overlap with semantic relevance, rejecting valid inferences on purely formal grounds that have no metaphysical basis.
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    Reason for 2 of 2
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    • 1.Graham Priest's dialetheism, which accepts true contradictions, undermines the relevantist motivation: if some contradictions are true, ex falso fails for different reasons than VSP supplies.
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    • 2.Relevant logic's rejection of ex falso is therefore justified on either dialetheist or paraconsistent grounds, but VSP as the stated mechanism is neither necessary nor sufficient for either justification.
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    • 3.The supporting argument's appeal to VSP thus misidentifies the real logical work, leaving the claim without an adequately grounded rationale even if the conclusion is correct.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.VSP requires that antecedent and consequent share a sentential variable for a conditional to be valid
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    • 2.In (A ∧ ¬A) → B, the antecedent A ∧ ¬A and the consequent B need not share any sentential variable
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    • 3.Therefore the connection requirement is not satisfied
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