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 Goldbach's Conjecture (GC) is not a mathematical proposition

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.A meaningful mathematical proposition requires a known method of algorithmic decision
      ?

      Think about whether this reason is strong or weak

    • 2.We do not know how to decide GC algorithmically
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.For Wittgenstein, mathematical meaning is constituted by proof techniques, not by the mere syntactic form of a proposition.
      ?

      Think about whether this reason is strong or weak

    • 2.GC has no proof technique: no known method determines its truth, making it semantically idle rather than genuinely mathematical.
      ?

      Think about whether this reason is strong or weak

    • 3.A string of symbols that plays no role in mathematical practice—yielding no calculations, proofs, or decisions—lacks the use that constitutes meaning.
      ?

      Think about whether this reason is strong or weak

    Reason against 2 of 2
    ?
    • 1.Hilbert's formalist program implicitly concedes that undecidable statements require new axioms or methods before they can be treated as genuine mathematical claims.
      ?

      Think about whether this reason is strong or weak

    • 2.Gödel's incompleteness results show that statements like GC may be undecidable within any consistent formal system, meaning their 'truth' is system-relative rather than intrinsic.
      ?

      Think about whether this reason is strong or weak

    • 3.A claim whose truth-value is permanently inaccessible within any specifiable formal system cannot function as a proposition in the normative sense mathematics requires.
      ?

      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.