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    The proposition k is both known and unknown, which is a c... — Carmelics
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Skepticism
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    The proposition k is both known and unknown, which is a contradiction.

    SkepticismTruth & Knowledge
    ?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.Self-referential propositions about their own epistemic status generate genuine paradox, as Kaplan and Montague showed for modalized self-reference.
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    • 2.No revision of classical logic dissolves this contradiction without either abandoning knowledge-factivity or prohibiting legitimate epistemic propositions.
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    • 3.Williamson's knowledge-first epistemology confirms factivity as non-negotiable, so the contradiction cannot be escaped by weakening the knowledge operator.
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    Reason for 2 of 2
    ?
    • 1.Fitch's 1963 proof demonstrates that the conjunction K(p & ~Kp) distributes to Kp & K~Kp via the factivity and distribution of knowledge.
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    • 2.K~Kp entails ~Kp by factivity, so Kp & ~Kp follows necessarily, making the contradiction a formal theorem, not a mere assumption.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Assume k is known.
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    • 2.Knowledge entails truth, so if k is known, k is true.
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    • 3.k asserts that k is unknown.
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    SkepticismTruth & Knowledge

    Related

    Assume k is known.But k was assumed to be known, so k is both known and unknown.Fitch's 1963 proof demonstrates that the conjunction K(p & ~Kp) distributes to K...Knowledge entails truth, so if k is known, k is true.
    +6 moreShow less
    K~Kp entails ~Kp by factivity, so Kp & ~Kp follows necessarily, making the contr...No revision of classical logic dissolves this contradiction without either aband...Self-referential propositions about their own epistemic status generate genuine ...Therefore k is unknown.Williamson's knowledge-first epistemology confirms factivity as non-negotiable, ...k asserts that k is unknown.

    Similar

    The assumption that k is known leads to a contradiction (k is both kno...93%If k is known, then k is both known and unknown (established by the fi...89%It is known that k is unknown, which means k is known (since k asserts...87%Therefore it is known that the assumption 'k is known' is false, i.e.,...86%

    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