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 The infinitesimal concept should be retained in the foundations of the calculus

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.Weierstrass, Cauchy, and Dedekind successfully rebuilt calculus on rigorous epsilon-delta foundations without invoking infinitesimals.
      ?

      Think about whether this reason is strong or weak

    • 2.A foundational concept that can be eliminated without expressive or inferential loss fails the criterion of theoretical indispensability.
      ?

      Think about whether this reason is strong or weak

    • 3.The standard real analysis framework achieves greater ontological parsimony by grounding limits in quantified inequalities over real numbers alone.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.Berkeley's critique in 'The Analyst' demonstrated that 17th-century infinitesimals involved contradictory reasoning: treated as nonzero in division, then discarded as zero.
      ?

      Think about whether this reason is strong or weak

    • 2.Non-standard analysis (Robinson, 1966) rescues infinitesimals only by embedding them in a hyperreal system requiring the ultrafilter lemma, a strong set-theoretic axiom.
      ?

      Think about whether this reason is strong or weak

    • 3.Introducing ontologically exotic entities requiring powerful axioms to avoid contradiction imposes a foundational cost that outweighs alleged gains in geometric intuition.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Infinitesimal methods are more efficient than alternative approaches
      ?

      Think about whether this reason is strong or weak

    • 2.Infinitesimals serve as the 'glue' that causes points on a continuous line to lose their individual identity, which is essential to a proper conception of continuity
      ?

      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.