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    In paraconsistent logics like Priest's LP, contradictions... — Carmelics
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    Supports→Fitch's knowability argument does not straightforwardly apply to paraconsistent logics

    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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    Reasons For

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    • 1.Classical logic's explosion principle (ex falso quodlibet) is a stipulated rule, not a logical law, so rejecting it preserves rational discourse.
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    • 2.Self-knowledge paradoxes like K(p ∧ ¬Kp) arise from classical assumptions; paraconsistent logic dissolves them without abandoning the propositions involved.
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    • 3.Semantic gluts (true and false simultaneously) occur in natural language and belief revision; paraconsistent systems model this phenomenon directly.
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    Reasons Against

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    • 1.If K(p ∧ ¬Kp) is truly both assertible and deniable, speakers cannot coordinate on its truth-value, undermining the communicative function of language.
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    • 2.Paraconsistent logics preserve ¬(p ∧ ¬p) as valid in most systems (weak explosion); they don't genuinely tolerate true contradictions, only shift the problem.
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    • 3.Accepting genuine contradictions at the object level requires explaining why we should believe any negation, risking incoherent rational belief systems.
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    Truth & Knowledge1 linkedModality & Possibility1 linked

    Related

    Accepting genuine contradictions at the object level requires explaining why we ...Classical logic's explosion principle (ex falso quodlibet) is a stipulated rule,...Fitch's knowability argument does not straightforwardly apply to paraconsistent ...If K(p ∧ ¬Kp) is truly both assertible and deniable, speakers cannot coordinate ...
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    Paraconsistent logics preserve ¬(p ∧ ¬p) as valid in most systems (weak explosio...Self-knowledge paradoxes like K(p ∧ ¬Kp) arise from classical assumptions; parac...Semantic gluts (true and false simultaneously) occur in natural language and bel...

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