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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
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    Perspectives
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    Home/Original/inverse
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    Inverse View

    It is not the case that To do full justice to both Leibniz's and Nieuwentijdt's conceptions of infinitesimals, two distinct sorts of infinitesimals are required.

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.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.
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      Think about whether this reason is strong or weak

    • 2.If Leibnizian differentials are fictions rather than objects, the contrast with Nieuwentijdt's nilsquare infinitesimals is a difference in formal role, not a difference in kind requiring two distinct sorts of entity.
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      Think about whether this reason is strong or weak

    • 3.Nieuwentijdt's nilsquare condition can be reinterpreted as a constraint on the order of approximation within a single fictional calculus, dissolving the purported need for ontological dualism.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
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    • 1.Abraham Robinson's non-standard analysis provides a single coherent framework in which both Leibnizian differentials and nilsquare-like infinitesimals are expressible as distinct elements within one number system.
      ?

      Think about whether this reason is strong or weak

    • 2.If a unified formal system can accommodate both conceptions without positing ontologically distinct kinds, the claim that two *sorts* of infinitesimals are required overstates the metaphysical need.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Leibniz's conception requires differentials that obey the same algebraic laws as finite quantities.
      ?

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    • 2.Nieuwentijdt's conception requires nilsquare infinitesimals that measure the lengths of the sides of infinilateral polygons.
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      Think about whether this reason is strong or weak

    • 3.Nilsquare infinitesimals are necessarily smaller than Leibnizian differentials.
      ?

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