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    It is not the case that Leibniz's argument that Δx² = 0 depends crucially on the assumption that the portion of the curve between abscissae 0 and Δx is straight.

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.Leibniz's method of infinitesimals operates within a formal calculus where Δx² vanishes by the law of homogeneity, not by geometric straightness assumptions.
      ?

      Think about whether this reason is strong or weak

    • 2.Henk Bos's historical analysis shows Leibniz grounded the omission of higher-order infinitesimals in algebraic order relations, not local linearity of curves.
      ?

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    • 3.The straightness assumption conflates Newton's method of first and last ratios with Leibniz's distinct algebraic framework for differential calculus.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.Robinson's non-standard analysis vindicates Leibniz's infinitesimal reasoning by showing Δx² = 0 relative to Δx follows from rigorous hyperreal arithmetic, not geometric assumptions.
      ?

      Think about whether this reason is strong or weak

    • 2.If Δx is a non-zero infinitesimal, then Δx² is infinitesimal of higher order, making Δx²/Δx standard-part zero without presupposing any straightness of the curve.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.If the portion of the curve between abscissae 0 and Δx is not assumed to be straight, it does not follow that Δx² = 0.
      ?

      Think about whether this reason is strong or weak

    • 2.Denying the straightness assumption undermines the derivation of Δx² = 0.
      ?

      Think about whether this reason is strong or weak

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