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    The ex falso quodlibet — (A ∧ ¬A) → B — is not logically ... — Carmelics
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    The ex falso quodlibet — (A ∧ ¬A) → B — is not logically valid in relevant logic

    Modality & Possibility
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    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 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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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 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 against 2 of 2
    ?
    • 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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    Topics

    Philosophy of LanguageModality & Possibility

    Related

    Classical logic's ex falso is not merely a formal artifact but tracks the metaph...Graham Priest's dialetheism, which accepts true contradictions, undermines the r...If no contradictions can obtain, conditionals with contradictory antecedents hav...In (A ∧ ¬A) → B, the antecedent A ∧ ¬A and the consequent B need not share any s...
    +5 moreShow less
    Relevant logic's rejection of ex falso is therefore justified on either dialethe...Relevant logic's variable-sharing condition (VSP) conflates syntactic topic-over...The supporting argument's appeal to VSP thus misidentifies the real logical work...Therefore the connection requirement is not satisfiedVSP requires that antecedent and consequent share a sentential variable for a co...

    Similar

    Fitch's reasoning relies on reductio ad absurdum to establish that K(p...79%K(p ∧ ¬Kp) is necessarily false (□¬K(p ∧ ¬Kp))77%Knowledge that p ∧ ¬Kp is actually the case cannot itself be actual76%K(p ∧ ¬Kp) is false76%

    Source

    AI-extracted1/3 agreementValid
    SEP: hyperintensionality
    View source passageHide passage
    In this program, an agreed upon necessary (though, in general, not sufficient) condition for a conditional to be logically valid is that there be some connection between antecedent and consequent. Historically, this has often been phrased via a requirement called the Variable Sharing Property (VSP): \(A \rightarrow B\) is valid only when \(A\) and \(B\) share some sentential variable or parameter (cf. Anderson & Belnap 1975: 32–3). VSP delivers hyperintensional distinctions: conditionals wit
    Extraction notes

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

    Details

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