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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    It is provably the case that the full description of our ... — Carmelics
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Skepticism
    HistoryEditSee Inverse

    It is provably the case that the full description of our knowledge includes both K(k) and ¬K(k).

    Skepticism
    ?Rate how convincing each reason is below to see the overall strength.
    2 reasons for
    1 reason against

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.Fitch's paradox demonstrates that classical epistemic logic generates genuine contradictions when self-referential knowledge claims are admitted.
      ?

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    • 2.Priest's dialetheism holds that some contradictions are true and that paraconsistent logic can model real features of epistemic reality.
      ?

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    • 3.A paraconsistent epistemic framework licenses K(k) and ¬K(k) as jointly assertable without trivializing the system via explosion.
      ?

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    Reason for 2 of 2
    ?
    • 1.Kripke's fixed-point semantics for self-referential sentences assigns stable truth values to sentences that predicate properties of themselves.
      ?

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    • 2.The sentence k, asserting its own unknownness, occupies a fixed point where both knowing and not-knowing it are forced by the semantic closure conditions.
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    • 3.Fixed-point constructions formally validate the co-provability of K(k) and ¬K(k) as a structural feature of the semantic model, not a mere paradox.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.It is known that k is unknown, which means k is known (since k asserts its own unknownness).
      ?

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    • 2.If k is known, then k is both known and unknown (established by the first argument).
      ?

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    • 3.Therefore K(k) and ¬K(k) are both provable.
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    Topics

    SkepticismTruth & Knowledge

    Key Terms

    knowledge(Distinguished from mere true belief, which may be the product of indoctrination and need not exercise deliberative capacities.)
    Justified true belief — true belief that has been arrived at through the exercise of deliberative capacities, including comparison of and deliberation among alternatives.

    Related

    A paraconsistent epistemic framework licenses K(k) and ¬K(k) as jointly assertab...Fitch's paradox demonstrates that classical epistemic logic generates genuine co...Fixed-point constructions formally validate the co-provability of K(k) and ¬K(k)...If k is known, then k is both known and unknown (established by the first argume...
    +5 moreShow less
    It is known that k is unknown, which means k is known (since k asserts its own u...Kripke's fixed-point semantics for self-referential sentences assigns stable tru...Priest's dialetheism holds that some contradictions are true and that paraconsis...The sentence k, asserting its own unknownness, occupies a fixed point where both...Therefore K(k) and ¬K(k) are both provable.

    Similar

    Knowledge is what it is in relation to what it is knowledge of (P4).81%Therefore K(k) and ¬K(k) are both provable.79%Safety is understood only in terms of knowledge.79%Wisdom includes not only knowledge but also action78%

    Source

    AI-extracted1/3 agreementValid
    SEP: fitch-paradox
    View source passageHide passage
    Assume for the sake of argument that \(k\) is known. Then, presuming that knowledge entails truth, \(k\) is true. But \(k\) says that \(k\) is unknown. So \(k\) is unknown. Consequently, \(k\) is both known and unknown. But then our assumption (i.e., that \(k\) is known) is false, and provably so. And, granting that a proven falsehood is known to be false, it follows that it is known that \(k\) is unknown. That is to say, it is known that \(k\). But we have already shown that if it is known that
    Extraction notes

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

    Details

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