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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Original/inverse
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    Inverse View

    It is not the case that The proposition 'Always, if every A is B, then every C is D' implies 'Never, if every A is B, then not every C is D'

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    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Ibn Sina's conditional propositions admit of 'descriptional' readings where the antecedent restricts the time of predication, not logical necessity.
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    • 2.Under a descriptional reading, 'Always, if every A is B, then every C is D' can be true in all actual cases while 'not every C is D' holds in unrealized possible antecedent-scenarios.
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    • 3.If the conditional's truth is indexed to actual co-obtaining states rather than all possible worlds, the negation of the consequent in counterfactual antecedent-conditions does not contradict the original proposition.
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    Reason for 2 of 2
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    • 1.Łukasiewicz and later paraconsistent logicians demonstrated that classical contradiction-based inference patterns fail in systems tolerating truth-value gaps or gluts.
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    • 2.The supporting argument's step from 'sometimes not-Q' to 'not always Q' relies on the classical duality of quantified modals, which Ibn Sina's own modal square does not straightforwardly vindicate for conditional propositions.
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    • 3.If Ibn Sina's 'always' and 'never' operators on conditionals do not form a standard contradictory pair—as Wilfrid Hodges's formal reconstruction of Avicennan logic suggests—the reductio in the supporting argument fails to close.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.Assuming 'Always, if every A is B, then every C is D' holds, if 'Never, if every A is B, then not every C is D' did not hold, then 'Sometimes, if every A is B, then not every C is D' would be true
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    • 2.If 'Sometimes, if every A is B, then not every C is D' is true, then 'Not always, if every A is B, then every C is D' follows
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    • 3.This contradicts the initial assumption, so the implication must hold
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