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 Classical non-standard analysis already permits neglecting higher-order infinitesimals via the standard part function without logical inconsistency.

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.The standard part function itself requires appeal to classical completeness axioms, making NSA dependent on classical logic rather than independent.
      ?

      Think about whether this reason is strong or weak

    • 2.Neglecting higher-order infinitesimals via the standard part assumes a hidden ordering principle that lacks explicit justification within NSA's axioms.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.The standard part function provides a rigorous mapping from hyperreals to reals, formally justifying infinitesimal neglect without contradiction.
      ?

      Think about whether this reason is strong or weak

    • 2.Keisler's elementary calculus demonstrates that NSA computations yield identical results to classical analysis, validating the infinitesimal approach.
      ?

      Think about whether this reason is strong or weak

    • 3.Higher-order infinitesimals (ε², ε³, etc.) are logically subordinate to first-order ones; their omission reflects a principled hierarchy, not inconsistency.
      ?

      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.