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 Inconsistent non-standard analysis has computational advantages over classical non-standard analysis in the theory of differentiation

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.Classical non-standard analysis already permits neglecting higher-order infinitesimals via the standard part function without logical inconsistency.
      ?

      Think about whether this reason is strong or weak

    • 2.A computational advantage gained by tolerating contradiction is undermined if the same results are derivable in a consistent framework by equivalent means.
      ?

      Think about whether this reason is strong or weak

    • 3.Robinson's transfer principle provides a rigorous and conservative method for discarding infinitesimal remainders, rendering the inconsistent approach redundant rather than advantageous.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.Priest's dialetheist frameworks permitting true contradictions require paraconsistent logic, which weakens the inferential power needed to derive reliable computational results.
      ?

      Think about whether this reason is strong or weak

    • 2.In paraconsistent arithmetic, the loss of ex contradictione quodlibet comes at the cost of blocking valid classical inferences that underpin standard differentiation techniques.
      ?

      Think about whether this reason is strong or weak

    • 3.A system offering computational shortcuts through inconsistency trades formal reliability for convenience, violating the mathematician's minimal criterion of trustworthy proof.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Robinson's non-standard analysis is based on infinitesimals and their reciprocals, the infinite numbers
      ?

      Think about whether this reason is strong or weak

    • 2.An inconsistent version of non-standard analysis permits discarding higher-order infinitesimals
      ?

      Think about whether this reason is strong or weak

    • 3.The ability to discard higher-order infinitesimals yields computational advantages in the theory of differentiation
      ?

      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.