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    VSP yields hyperintensional distinctions among conditiona... — Carmelics
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    Home/Philosophy of Language
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    VSP yields hyperintensional distinctions among conditionals with impossible antecedents

    Modality & Possibility
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    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
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    • 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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    Reasons Against

    2 perspectives
    Reason against 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 against 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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    Philosophy of LanguageModality & Possibility

    Related

    A criterion that admits 'p ∧ ¬p → q ∨ ¬q' as valid on variable-sharing grounds c...If the validity of a conditional with an impossible antecedent can shift merely ...Nuel Belnap and J. Michael Dunn's relevance logic tradition requires that valid ...Therefore some conditionals with impossible antecedents are valid and others are...
    +4 moreShow less
    Under VSP, only those conditionals where antecedent and consequent share a varia...Under classical logic, all conditionals with impossible antecedents are triviall...VSP's variable-sharing condition is necessary but not sufficient for relevance i...Variable-sharing is a syntactic criterion that fails to track genuine relevance,...

    Similar

    Therefore some conditionals with impossible antecedents are valid and ...82%Under classical logic, all conditionals with impossible antecedents ar...78%If sentences were about understandings, the antecedent of that conditi...74%If a criterion of classification yields contradictory or arbitrary ass...72%

    Source

    AI-extracted1/3 agreementValid
    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