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    Made withinDC&Austin
    It is known that k is unknown. — Carmelics
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    It is known that k is unknown.

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.The assumption that k is known leads to a contradiction (k is both known and unknown).
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    • 2.That assumption is therefore false.
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    • 3.A proven falsehood is known to be false.
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.The inference from 'the assumption K(k) leads to contradiction' to 'K(¬K(k))' illicitly conflates object-level refutation with epistemic closure.
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    • 2.Knowing that a proposition is false requires more than deriving a contradiction from it within a formal system — it requires an epistemic agent with access to the proof.
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    • 3.On a factive, agent-relative epistemology (as in Williamson's knowledge-first framework), no actual knower need possess the proof, so 'it is known' remains unwarranted.
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    Reason against 2 of 2
    ?
    • 1.Fitch's proof operates within a classical modal-epistemic logic, but if the logic governing knowledge is paraconsistent, contradictions derived from K(k) do not force ¬K(k).
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    • 2.Graham Priest and other dialetheists argue that some propositions can be both known and unknown without trivializing the system, blocking the reductio at P2.
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    Connections

    1 linked claim

    Therefore k is unknown.

    Related

    A proven falsehood is known to be false.Fitch's proof operates within a classical modal-epistemic logic, but if the logi...Graham Priest and other dialetheists argue that some propositions can be both kn...Knowing that a proposition is false requires more than deriving a contradiction ...
    +6 moreShow less
    On a factive, agent-relative epistemology (as in Williamson's knowledge-first fr...That assumption is therefore false.The assumption that k is known leads to a contradiction (k is both known and unk...The inference from 'the assumption K(k) leads to contradiction' to 'K(¬K(k))' il...Therefore it is known that the assumption 'k is known' is false, i.e., it is kno...Therefore k is unknown.

    Similar

    Therefore k is unknown.97%But k was assumed to be known, so k is both known and unknown.92%It is known that k is unknown, which means k is known (since k asserts...92%Assume k is known.91%

    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 (1 for, 2 against)
    Edits
    1 edit