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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that At least one of the inclusions among L, P, NP, PSPACE, and EXP must be proper

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.The inference from known endpoint separations (L⊊PSPACE, P⊊EXP) to an intermediate proper inclusion commits the fallacy of assuming transitivity of witness.
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    • 2.Knowing that a chain A⊆B⊆C satisfies A⊊C does not logically entail which intermediate link is proper without independent diagonalization or oracle separation for that link.
      ?

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    • 3.The supporting argument thus smuggles in a distributional assumption about where separation occurs that the mathematics does not yet license.
      ?

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    Reason for 2 of 2
    ?
    • 1.Epistemic humility in formal ontology, as urged by Penelope Maddy's naturalism, requires distinguishing what is proven from what is structurally suggested by incomplete evidence.
      ?

      Think about whether this reason is strong or weak

    • 2.The claim 'at least one inclusion is proper' is presented as established fact, yet it rests on no single proof that directly witnesses a proper inclusion within the chain L⊆P⊆NP⊆PSPACE.
      ?

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    • 3.Conflating the modal claim 'some inclusion must be proper' with the epistemically stronger 'we know which one' obscures that the claim's truth-value is currently grounded in inference, not demonstration.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.L is a proper subset of PSPACE and P is a proper subset of EXP
      ?

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    • 2.The chain L ⊆ P ⊆ NP ⊆ PSPACE ⊆ EXP must include at least one proper inclusion to account for the known separations at its ends
      ?

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    Strongest counterpoint
    Explore the most compelling reason on the other side.