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    Carmelics

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

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

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    1 perspective
    Reason for
    ?
    • 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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    Reasons Against

    2 perspectives
    Reason against 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.
      ?

      Think about whether this reason is strong or weak

    • 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.
      ?

      Think about whether this reason is strong or weak

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

      Think about whether this reason is strong or weak

    Reason against 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.
      ?

      Think about whether this reason is strong or weak

    • 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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    Strongest counterpoint
    Explore the most compelling reason on the other side.