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    Carmelics

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    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that L is a proper subset of PSPACE

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.The Space Hierarchy Theorem establishes proper containment between complexity classes only within a formal axiomatic system, not as a mind-independent metaphysical fact.
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      Think about whether this reason is strong or weak

    • 2.Gödel's incompleteness results show that sufficiently expressive formal systems cannot prove all true statements about their own syntactic objects, including complexity class relationships.
      ?

      Think about whether this reason is strong or weak

    • 3.The modal claim that L is *necessarily* a proper subset of PSPACE may be unprovable within the formal systems we use to reason about computation, making 'proper subset' a claim about provability, not possibility.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.The Space Hierarchy Theorem presupposes that space-constructible functions are well-defined, but constructibility itself is a notion relative to a model of computation with no canonical metaphysical grounding.
      ?

      Think about whether this reason is strong or weak

    • 2.Relativization results (Baker-Gill-Solovay 1975) demonstrate that there exist oracles relative to which standard separation arguments fail, meaning the hierarchy theorems establish class separation only in unrelativized models.
      ?

      Think about whether this reason is strong or weak

    • 3.A claim of proper subset that holds only within specific, oracle-free computational models does not establish the unrestricted modal claim that L is necessarily a proper subset of PSPACE across all possible computational frameworks.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    3 perspectives
    Reason against 1 of 3
    ?
    • 1.The Space Hierarchy Theorem holds for space constructible functions
      ?

      Think about whether this reason is strong or weak

    • 2.log(n) and n^k satisfy the conditions of the Space Hierarchy Theorem
      ?

      Think about whether this reason is strong or weak

    Reason against 2 of 3
    ?
    • 1.By the Space Hierarchy Theorem, if s1(n)/s2(n) → 0 then SPACE(s1(n)) is a proper subset of SPACE(s2(n))
      ?

      Think about whether this reason is strong or weak

    • 2.log(n) grows strictly slower than any polynomial in n
      ?

      Think about whether this reason is strong or weak

    Reason against 3 of 3
    ?
    • The Time Hierarchy Theorem part iii) implies proper containment between L and PSPACE
      ?

      Think about whether this reason is strong or weak

    Next step

    Based on where you are in your exploration

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