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 L's 'thinness' is relative to a background universe; from within L, all cardinals satisfy L's own definability conditions.

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.If L's thinness is merely relative, this threatens absolutism about mathematical truth; some claim L's structure should be intrinsically objective.
      ?

      Think about whether this reason is strong or weak

    • 2.The claim conflates two distinct facts: L being definable relative to V, versus cardinal properties being relative; the latter seems to confuse internal and external perspectives.
      ?

      Think about whether this reason is strong or weak

    • 3.From within L, the claim that 'all cardinals satisfy L's conditions' is trivially true but uninformative; it obscures that fewer sets exist in L than V.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.L is definable within ZFC but not absolutely definable; its thinness depends on comparing it against V, which is background-relative.
      ?

      Think about whether this reason is strong or weak

    • 2.Within L's own internal logic, all ordinals and cardinals satisfy L's constructibility conditions by definition—no external comparison needed.
      ?

      Think about whether this reason is strong or weak

    • 3.Different models of set theory contain different versions of L with different cardinalities, confirming L's properties are relative to ambient universe.
      ?

      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