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 Leibniz himself denied that infinitesimals had any fixed ontological status, treating them as useful fictions governed by the law of continuity rather than as genuine magnitudes of a specific kind.

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Leibniz's monadic metaphysics suggests he may have endorsed infinitesimals as real features of his actual infinite metaphysical structure.
      ?

      Think about whether this reason is strong or weak

    • 2.His private correspondence reveals commitments to infinitesimal reality that contradict the 'useful fiction' interpretation of published work.
      ?

      Think about whether this reason is strong or weak

    • 3.If infinitesimals are mere fictions, the law of continuity cannot explain why they yield empirically accurate physical predictions reliably.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Leibniz's extensive use of infinitesimals in calculus while denying their reality suggests he viewed them pragmatically as computational tools.
      ?

      Think about whether this reason is strong or weak

    • 2.The law of continuity allows infinitesimals to produce correct results without requiring commitment to their actual existence as magnitudes.
      ?

      Think about whether this reason is strong or weak

    • 3.Treating infinitesimals as fictions avoids metaphysical problems about infinite divisibility that plagued contemporary mathematics.
      ?

      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.