Skip to content
Carmelics
TopicsThinkersChangesContributorsLoading account…

    Carmelics

    A reasoning platform. Break down any belief into clear reasons, explore both sides, and weigh the evidence honestly.

    Navigate

    • Topics
    • Search
    • Recent Changes
    • Contribute
    • How It Works
    • Glossary
    • Thinkers
    • Contributors
    • About
    • Statistics
    • Terms
    • Privacy

    Database

    Statements
    —
    Perspectives
    —
    Topics
    —

    Press ? for keyboard shortcuts

    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 Among the unsolvable decision problems of recursively enumerable sets, there is a highest degree of unsolvability.

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.Post's problem (1944) demonstrated that intermediate degrees exist between decidable and complete r.e. sets, undermining claims of a single highest degree.
      ?

      Think about whether this reason is strong or weak

    • 2.Friedberg and Muchnik (1956) independently proved incomparable r.e. degrees exist, showing the r.e. degrees form a non-linearly-ordered structure.
      ?

      Think about whether this reason is strong or weak

    • 3.A non-linear partial order with incomparable elements cannot possess a unique maximal element in any straightforward sense without further qualification.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.The halting problem is Turing-complete for r.e. sets, but 'highest degree' conflates m-reducibility and Turing reducibility, which diverge extensionally.
      ?

      Think about whether this reason is strong or weak

    • 2.Lachlan and Yates showed the r.e. degrees lack a definable well-ordering, making 'highest' a structurally ambiguous predicate absent a fixed reducibility notion.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.The theory of recursively enumerable sets admits a primary problem of determining degrees of unsolvability of their unsolvable decision problems.
      ?

      Think about whether this reason is strong or weak

    • 2.The structure of reducibility among these problems yields at least one problem to which all others are reducible.
      ?

      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.