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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
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    Perspectives
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    42
    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that PH is expected to lack complete problems, unlike PSPACE

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.Epistemic consensus about complexity separations lacks the deductive warrant required to ground modal claims about mathematical structure.
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    • 2.The belief that PH ≠ PSPACE is itself unproven, making any inference from it to claims about completeness epistemically circular.
      ?

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    • 3.Unproven conjectures in mathematics cannot serve as premises in arguments about what structures 'lack' properties without begging the question.
      ?

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    Reason for 2 of 2
    ?
    • 1.Hilbert's formalist tradition warns that mathematical existence claims require constructive proof, not inference from expected separations.
      ?

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    • 2.The argument conflates the absence of known complete problems with the principled impossibility of such problems existing for PH.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.If PH = PSPACE, then PH would have a complete problem (TWO PLAYER SAT)
      ?

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    • 2.PH is widely believed to differ from PSPACE
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    • 3.The existence of a complete problem for PH would imply PH collapses, which is contrary to expectation
      ?

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