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    Carmelics

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    Made withinDC&Austin
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    Home/Original/inverse
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    Inverse View

    It is not the case that A conditional is logically valid only if the antecedent and consequent share at least one sentential variable or parameter

    ?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 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 for 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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    Reasons Against

    1 perspective
    Reason against
    ?
    • 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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