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 Cantor's transfinite arithmetic demonstrates that completed infinities obey consistent, non-contradictory formal laws, satisfying the existence criterion Hilbert called 'consistency entails existence'.

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Consistency alone cannot guarantee existence; Euclidean geometry was consistent yet describes a non-actual spatial structure.
      ?

      Think about whether this reason is strong or weak

    • 2.Hilbert never endorsed the equation 'consistency entails existence' as a general metaphysical principle, only as a methodological tool.
      ?

      Think about whether this reason is strong or weak

    • 3.Transfinite infinities may be useful fictions without corresponding to mind-independent mathematical reality or completed totalities.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Cantor's set theory generates consistent formal systems with no known contradictions after rigorous examination by mathematicians.
      ?

      Think about whether this reason is strong or weak

    • 2.Transfinite arithmetic enables successful predictions and applications in topology, analysis, and logic, demonstrating practical utility.
      ?

      Think about whether this reason is strong or weak

    • 3.Formal consistency is the minimal criterion for mathematical existence; without it, no abstract objects warrant ontological commitment.
      ?

      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.