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    The proposition 'Always, if every A is B, then every C is... — Carmelics
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    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'

    Philosophy of LanguageTruth & Knowledge
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    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 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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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 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 against 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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    Related

    Assuming 'Always, if every A is B, then every C is D' holds, if 'Never, if every...Ibn Sina's conditional propositions admit of 'descriptional' readings where the ...If 'Sometimes, if every A is B, then not every C is D' is true, then 'Not always...If Ibn Sina's 'always' and 'never' operators on conditionals do not form a stand...
    +5 moreShow less
    If the conditional's truth is indexed to actual co-obtaining states rather than ...The supporting argument's step from 'sometimes not-Q' to 'not always Q' relies o...This contradicts the initial assumption, so the implication must holdUnder a descriptional reading, 'Always, if every A is B, then every C is D' can ...Łukasiewicz and later paraconsistent logicians demonstrated that classical contr...

    Similar

    If 'Sometimes, if every A is B, then not every C is D' is true, then '...93%Assuming 'Always, if every A is B, then every C is D' holds, if 'Never...92%If the (a-C)aa proposition ('Always, if every A is B, then every C is ...87%It allows distinguishing the trivial proposition 'Hesperus is Hesperus...81%

    Source

    AI-extracted1/3 agreementValid
    SEP: ibn-sina-logic
    View source passageHide passage
    In Qiyās VII.1, Avicenna considers a basic set of quantified conditional statements with quantified antecedents and consequents. Assuming the four basic forms of quantified conditional statements (a-\(\mathbb{C}\)), (e-\(\mathbb{C}\)), (i-\(\mathbb{C}\)), and (o-\(\mathbb{C}\)) and all permutations of a-, e-, i-, o-propositions as antecedents and consequents, Avicenna generates four groups of sixteen conditional propositions (see Appendix B) and argues that any of those forms is logically equi
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit