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    Home/Original/inverse
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    Inverse View

    It is not the case that VSP yields hyperintensional distinctions among conditionals with impossible antecedents

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    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Nuel Belnap and J. Michael Dunn's relevance logic tradition requires that valid inference preserve truth in virtue of meaning-connections, not mere syntactic overlap between variables.
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    • 2.VSP's variable-sharing condition is necessary but not sufficient for relevance in the sense demanded by the Anderson-Belnap program, so VSP distinctions among impossible-antecedent conditionals may be too coarse-grained to capture the intended hyperintensional differences.
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    • 3.A criterion that admits 'p ∧ ¬p → q ∨ ¬q' as valid on variable-sharing grounds conflates tautological entailment with genuinely content-sensitive implication, undermining the claim that VSP yields philosophically significant distinctions.
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    Reason for 2 of 2
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    • 1.Variable-sharing is a syntactic criterion that fails to track genuine relevance, as logically equivalent formulations of the same proposition may share or lack variables arbitrarily.
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    • 2.If the validity of a conditional with an impossible antecedent can shift merely by rewriting premises in logically equivalent form, VSP distinctions reflect notational accident rather than metaphysically robust hyperintensional structure.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Under classical logic, all conditionals with impossible antecedents are trivially valid
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    • 2.Under VSP, only those conditionals where antecedent and consequent share a variable are valid
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    • 3.Therefore some conditionals with impossible antecedents are valid and others are not, producing distinctions classical logic cannot draw
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