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 Quine's original NF and Jensen's NFU differ in that NFU's urelements create asymmetry: V and ℘₁(V) can have different cardinalities, making the bijection's non-existence a cardinality fact, not merely a stratification fact.

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Stratification constraints in NFU still govern what bijections are *definable*, so cardinality differences may remain formal rather than deep.
      ?

      Think about whether this reason is strong or weak

    • 2.Urelements' non-membership in any set doesn't obviously make cardinality gaps ontologically significant versus NF's elegant type-theoretic closure.
      ?

      Think about whether this reason is strong or weak

    • 3.Both theories preserve bijection-non-existence; calling one 'cardinality fact' and the other 'stratification fact' may be terminological, not substantive.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Urelements in NFU break the self-applicability that forces NF's cardinality constraints, allowing genuine set-theoretic distinctions absent in NF.
      ?

      Think about whether this reason is strong or weak

    • 2.If V and ℘₁(V) have different cardinalities in NFU, this reflects fundamental ontological asymmetry rather than mere syntactic stratification artifacts.
      ?

      Think about whether this reason is strong or weak

    • 3.NFU's consistency relative to ZFC suggests its cardinality facts track genuine mathematical reality, not arbitrary formal restrictions.
      ?

      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.