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    A criterion that admits 'p ∧ ¬p → q ∨ ¬q' as valid on var... — Carmelics
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    Challenges→VSP yields hyperintensional distinctions among conditionals with impossible antecedents

    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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    Key Terms

    Implication(as what the arrow symbol (→) represents)
    A logical connection between two statements where if the first is true, the second must also be true; written as 'p → q' meaning 'if p then q.'
    content-sensitive(in philosophical logic)
    Depending on or responsive to the actual meaning and subject matter of what's being discussed, rather than just abstract form.
    criterion(as used in philosophy to describe a test for whether an idea works)
    A standard or rule used to decide whether something counts as true or valid.
    entailment(Conceptualist framework)
    Understood in terms of truth at a world
    p ∧ ¬p → q ∨ ¬q(in formal logic)

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    A symbolic formula meaning 'if (p AND not-p) then (q OR not-q)' — it expresses a logical relationship using symbols instead of words.
    philosophically significant distinctions(in philosophy generally)
    Meaningful differences that matter for understanding real philosophical problems and questions, not just technical tricks.
    tautological entailment(System E of relevance logic)
    Anderson and Belnap's notion of entailment requiring shared propositional variables between premises and conclusion
    valid(Contrasted with the proof-theoretic notion of deducibility)
    A model-theoretic notion indicating that a conclusion is true in every model in which the premises are true
    variable-sharing grounds(in modern logic theory)
    A reason based on whether different parts of a logical statement share the same basic elements or topics; VSP stands for 'variable-sharing principle.'

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    Modality & Possibility1 linkedPhilosophy of Language1 linked

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    VSP yields hyperintensional distinctions among conditionals with impossible ante...

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