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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Home/Original/inverse
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    Inverse View

    It is not the case that Fitch's knowability argument does not straightforwardly apply to paraconsistent logics

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Fitch's reasoning relies on reductio ad absurdum to establish that K(p ∧ ¬Kp) is false
      ?

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    • 2.Fitch's reasoning relies on the inference from necessary falsehood to impossibility (□¬p → ¬◇p)
      ?

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    • 3.Paraconsistentists may reject reductio ad absurdum
      ?

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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.In paraconsistent logics like Priest's LP, contradictions can be true without trivializing the system, so K(p ∧ ¬Kp) being both assertible and deniable need not yield absurdity.
      ?

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    • 2.Fitch's proof requires explosion (ex contradictione quodlibet) to derive that omniscience follows from knowability, but LP explicitly blocks explosion as a valid inference.
      ?

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    • 3.Without explosion, the knowability paradox's reductio cannot establish that K(p ∧ ¬Kp) is necessarily unknowable, leaving the anti-realist's knowability principle intact.
      ?

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    Reason against 2 of 2
    ?
    • 1.Routley and Meyer's relevant logic tradition denies that □¬p entails ¬◇p when modal operators are interpreted through world-relative inconsistency-tolerant accessibility relations.
      ?

      Think about whether this reason is strong or weak

    • 2.If possible worlds can be inconsistent, as in Priest's impossible worlds semantics, then a world where K(p ∧ ¬Kp) holds need not be ruled out by modal logic's standard duality axioms.
      ?

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