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 If curves are infinilateral polygons, then the lengths of the sides of those polygons must be nilsquare infinitesimals.

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.Robinson's non-standard analysis rigorously formalizes infinitesimals without nilsquare conditions, using hyperreals where e²≠0 for any nonzero e.
      ?

      Think about whether this reason is strong or weak

    • 2.If a consistent alternative infinitesimal framework assigns nonzero squares to infinitesimals, then nilsquareness is not a necessary condition for infinilateral polygon sides.
      ?

      Think about whether this reason is strong or weak

    • 3.The Leibnizian geometric intuition of infinitesimal curve segments can be preserved under hyperreal arithmetic without invoking nilsquare constraints.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.Berkeley's critique in 'The Analyst' established that infinitesimals treated as nonzero when convenient and zero when convenient commit a logical fallacy of inconsistent supposition.
      ?

      Think about whether this reason is strong or weak

    • 2.The derivation of e²=0 from e≠0 in the supporting argument relies on the same equivocation Berkeley identified: e is nonzero to generate a segment, then its square is annihilated.
      ?

      Think about whether this reason is strong or weak

    • 3.A quantity derived through inconsistent suppositional reasoning cannot serve as a well-defined mathematical object, undermining nilsquare infinitesimals as legitimate curve-side lengths.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Leibniz grants that there is an infinitesimal straight stretch of the curve (a side of an infinilateral polygon coinciding with the curve) between abscissae 0 and e, which does not reduce to a single point.
      ?

      Think about whether this reason is strong or weak

    • 2.If such a stretch exists, then e cannot be equated to 0.
      ?

      Think about whether this reason is strong or weak

    • 3.The argument shows that e² = 0 given the assumption of an infinitesimal straight stretch.
      ?

      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.