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    A conditional is logically valid only if the antecedent a... — Carmelics
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    Home/Philosophy of Language
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    A conditional is logically valid only if the antecedent and consequent share at least one sentential variable or parameter

    Modality & PossibilityPhilosophy of Language
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    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
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    • 1.A necessary condition for a conditional to be logically valid is that there be some connection between antecedent and consequent
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    • 2.The Variable Sharing Property (VSP) formalizes this connection requirement by demanding shared sentential variables
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
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    • 1.Classical logic validates (A ∧ ¬A) → B for any B, yet this explosion schema is not merely tolerated but foundational to classical consequence.
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    • 2.If logical validity requires variable sharing, then classical logic's most central structural rules—including ex falso quodlibet—are rendered invalid, contradicting centuries of logical practice endorsed by Frege, Russell, and Hilbert.
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    • 3.A revisionary criterion that invalidates the core of classical logic bears a burden of proof that mere 'relevance intuitions' cannot discharge without abandoning the classical framework wholesale.
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    Reason against 2 of 2
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    • 1.Anderson and Belnap's relevance logic, which enforces VSP, requires rejection of the disjunctive syllogism (A ∨ B, ¬A ⊢ B), a inference form Lewis and others argue is indispensable to ordinary reasoning.
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    • 2.C.I. Lewis demonstrated that any system preserving strict implication's modal character licenses variable-free validities like ¬◇(A ∧ ¬A) → B without logical incoherence.
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    • 3.VSP thus purchases intuitive 'relevance' at the cost of severing modal logic from its Lewisian foundations, trading one philosophical desideratum for a more consequential theoretical loss.
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    Philosophy of LanguageModality & Possibility

    Related

    A necessary condition for a conditional to be logically valid is that there be s...A revisionary criterion that invalidates the core of classical logic bears a bur...Anderson and Belnap's relevance logic, which enforces VSP, requires rejection of...C.I. Lewis demonstrated that any system preserving strict implication's modal ch...
    +4 moreShow less
    Classical logic validates (A ∧ ¬A) → B for any B, yet this explosion schema is n...If logical validity requires variable sharing, then classical logic's most centr...The Variable Sharing Property (VSP) formalizes this connection requirement by de...VSP thus purchases intuitive 'relevance' at the cost of severing modal logic fro...

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    Source

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    SEP: hyperintensionality
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    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