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
    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that There exists a single universal list of all possible positions in well-ordered sets, called the ordinal numbers.

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.The totality of all ordinal numbers cannot itself form a set, as shown by the Burali-Forti paradox of 1897.
      ?

      Think about whether this reason is strong or weak

    • 2.Any purported 'universal list' of ordinals would itself occupy an ordinal position, generating a strictly larger ordinal beyond the list.
      ?

      Think about whether this reason is strong or weak

    • 3.A collection that cannot be a completed set cannot serve as a well-defined universal enumeration of positions.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.In predicativist foundations (Weyl, Feferman), only those ordinals definable from prior stages without impredicative totalities are mathematically legitimate.
      ?

      Think about whether this reason is strong or weak

    • 2.A 'single universal list' of all ordinals presupposes the completed infinite totality of transfinite positions, which predicativism rejects as circular self-constitution.
      ?

      Think about whether this reason is strong or weak

    • 3.Without an independent justification for impredicative set formation, the claim oversteps what constructively grounded mathematics can sanction.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.All positions of one well-ordering must correspond to initial positions in any other well-ordering.
      ?

      Think about whether this reason is strong or weak

    • 2.The correspondence of positions across all well-ordered sets is total and consistent.
      ?

      Think about whether this reason is strong or weak

    • 3.A single sequence beginning with first, second, third, and so on, can enumerate all such positions.
      ?

      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.
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42