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    The inference from □¬K(p ∧ ¬Kp) to ¬◇K(p ∧ ¬Kp) may not b... — Carmelics
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    Home/Modality & Possibility
    HistoryEditSee Inverse

    The inference from □¬K(p ∧ ¬Kp) to ¬◇K(p ∧ ¬Kp) may not be valid in paraconsistent logic

    Modality & Possibility
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    2 reasons for
    1 reason against

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.In Priest's LP (Logic of Paradox), the De Morgan duality between □ and ◇ breaks down when truth-value gluts are permitted at accessible worlds.
      ?

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    • 2.If ¬◇p is defined as □¬p holding without p holding at any accessible world, then paraconsistent models can satisfy □¬p while some accessible world contains p in its extension.
      ?

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    • 3.Therefore, the S5-valid inference from □¬K(p ∧ ¬Kp) to ¬◇K(p ∧ ¬Kp) presupposes classical modal duality that paraconsistent semantics explicitly rejects.
      ?

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    Reason for 2 of 2
    ?
    • 1.Berto and Priest's paraconsistent modal frameworks allow worlds where both Kφ and ¬Kφ hold, meaning knowledge attributions can be glutty without trivializing the logic.
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    • 2.If the knowability proof's contradiction K(p ∧ ¬Kp) produces a glut rather than absolute falsehood, then ¬◇K(p ∧ ¬Kp) does not follow, since the world realizing the glut remains accessible.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.In paraconsistent logic, a necessarily false statement may be both false and true at some world
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    • 2.If a statement is both necessarily false and true at some world, it is both necessarily false and possible
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    • 3.Therefore, □¬p does not entail ¬◇p in paraconsistent logic, and counterexamples to this inference exist
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    Modality & PossibilityTruth & Knowledge

    Related

    Berto and Priest's paraconsistent modal frameworks allow worlds where both Kφ an...If a statement is both necessarily false and true at some world, it is both nece...If the knowability proof's contradiction K(p ∧ ¬Kp) produces a glut rather than ...If ¬◇p is defined as □¬p holding without p holding at any accessible world, then...
    +4 moreShow less
    In Priest's LP (Logic of Paradox), the De Morgan duality between □ and ◇ breaks ...In paraconsistent logic, a necessarily false statement may be both false and tru...Therefore, the S5-valid inference from □¬K(p ∧ ¬Kp) to ¬◇K(p ∧ ¬Kp) presupposes ...Therefore, □¬p does not entail ¬◇p in paraconsistent logic, and counterexamples ...

    Similar

    Therefore, □¬p does not entail ¬◇p in paraconsistent logic, and counte...87%Fitch's knowability argument does not straightforwardly apply to parac...83%In paraconsistent logic, a necessarily false statement may be both fal...81%K(p ∧ ¬Kp) is false79%

    Source

    AI-extracted1/3 agreementValid
    SEP: fitch-paradox
    View source passageHide passage
    Notice that our presentation of Fitch’s reasoning makes no explicit mention of the assumption that \(Kp \wedge \neg Kp\) is impossible. So here we attempt to pinpoint exactly where Fitch’s reasoning goes wrong on the above account. It is claimed at line 9 (in the first section of this entry) that \(K(p \wedge \neg Kp)\) is impossible. Of course \(K(p \wedge \neg Kp)\) entails the contradiction \(Kp \wedge \neg Kp\). And so, if the reasoning is that \(K(p \wedge \neg Kp)\) is impossible because c
    Extraction notes

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

    Details

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