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    If a unified formal system can accommodate both conceptio... — 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.

    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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    Key Terms

    Ontologically distinct(as what Aristotle argues perception and reason are NOT)
    Completely separate in what they actually *are* as things—not just different functions, but fundamentally different kinds of existence.
    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.
    infinitesimals(Peirce's philosophy of mathematics and foundations of calculus)
    Quantities that constitute the 'glue' causing points on a continuous line to lose their individual identity, thereby grounding the concept of a true continuum
    metaphysical need(in philosophy)
    A requirement that something must actually exist or be real in order for a theory or explanation to work.
    unified formal system

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    (in mathematics and logic)
    A single set of mathematical or logical rules that can describe and explain different things without needing separate rule-sets for each.

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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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