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    Nieuwentijdt's nilsquare condition can be reinterpreted a... — Carmelics
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    Challenges→To do full justice to both Leibniz's and Nieuwentijdt's conceptions of infinitesimals, two distinct sorts of infinitesimals are required.

    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.

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    Key Terms

    Fictional calculus(as a mathematical framework)
    A mathematical system that works internally consistent rules but may not claim to describe reality—think of it as a useful tool or game with its own logic rather than a true description of the world.
    Nieuwentijdt (or Nieuwentijdt's nilsquare condition)(as a mathematical principle being reinterpreted philosophically)
    A rule from early calculus history (named after mathematician Bernard Nieuwentijdt) that says infinitesimally small quantities squared become so tiny they can be ignored in calculations.
    Ontology/Ontological(in metaphysics)
    The philosophical study of what actually exists or is real, as opposed to what merely seems to exist or what we can know about things.
    Order of approximation(as a concept in mathematical precision)
    How close a mathematical estimate or simplified version gets to the true answer—like how rounding 3.14159 to 3.14 is a 'second-order' approximation because it's pretty accurate.

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    ontological dualism(Source physicalists may be ontological dualists)
    A view compatible with source physicalism, holding that mental entities are distinct in nature from physical entities but still causally dependent on them.

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    Truth & Knowledge1 linkedPhilosophy of Language1 linked

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    To do full justice to both Leibniz's and Nieuwentijdt's conceptions of infinites...

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