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    Fitch's knowability argument does not straightforwardly a... — Carmelics
    Home/Modality & Possibility
    HistoryEditSee Inverse

    Fitch's knowability argument does not straightforwardly apply to paraconsistent logics

    Modality & Possibility
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    2 reasons for
    1 reason against

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 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 for 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.
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    • 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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    Reasons Against

    1 perspective
    Reason against
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    • 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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    Topics

    Modality & PossibilityTruth & Knowledge

    Related

    Fitch's proof requires explosion (ex contradictione quodlibet) to derive that om...Fitch's reasoning relies on reductio ad absurdum to establish that K(p ∧ ¬Kp) is...Fitch's reasoning relies on the inference from necessary falsehood to impossibil...If possible worlds can be inconsistent, as in Priest's impossible worlds semanti...
    +5 moreShow less
    In paraconsistent logics like Priest's LP, contradictions can be true without tr...Paraconsistentists may reject reductio ad absurdumParaconsistentists may reject the inference from □¬p to ¬◇pRoutley and Meyer's relevant logic tradition denies that □¬p entails ¬◇p when mo...Without explosion, the knowability paradox's reductio cannot establish that K(p ...

    Similar

    Therefore, □¬p does not entail ¬◇p in paraconsistent logic, and counte...83%The inference from □¬K(p ∧ ¬Kp) to ¬◇K(p ∧ ¬Kp) may not be valid in pa...83%E-knowability denies the assumption that if p is known in situation s,...81%E-knowability commits us to possible knowledge that p ∧ ¬Kp is actuall...80%

    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