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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    PH is expected to lack complete problems, unlike PSPACE — Carmelics
    Home/Skepticism
    HistoryEditSee Inverse

    PH is expected to lack complete problems, unlike PSPACE

    Modality & PossibilitySkepticism
    ?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.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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    Reasons Against

    2 perspectives
    Reason against 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 against 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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    Topics

    SkepticismModality & Possibility

    Connections

    2 topics

    Truth & Knowledge2 linkedProof of definition segments1 linked

    Related

    Epistemic consensus about complexity separations lacks the deductive warrant req...Hilbert's formalist tradition warns that mathematical existence claims require c...If PH = PSPACE, then PH would have a complete problem (TWO PLAYER SAT)PH is widely believed to differ from PSPACE
    +4 moreShow less
    The argument conflates the absence of known complete problems with the principle...The belief that PH ≠ PSPACE is itself unproven, making any inference from it to ...The existence of a complete problem for PH would imply PH collapses, which is co...Unproven conjectures in mathematics cannot serve as premises in arguments about ...

    Similar

    If P ⊊ NP, then NP-complete problems are not in P.86%If PH = PSPACE, PH would have complete problems (since PSPACE has comp...85%PSPACE is likely properly contained in EXP but still contains many app...84%NP-complete problems are the most difficult problems in NP (assuming P...80%

    Source

    AI-extracted1/3 agreementValid
    SEP: computational-complexity
    View source passageHide passage
    Consider, for instance the following variation on the standard rules of Go: (i) the game is played on an \(n \times n\) board; (ii) the winner of the game is the player with the most stones at the end of \(n^2\) rounds. e. the player who moves first)? [30] What these games have in common is that the definition of a winning strategy for the player who moves first involves the alternation of existential and universal quantifiers in a manner which mimics the definition of the classes \(\Sigma^P_n\)
    Extraction notes

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

    Details

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