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    Proposition 2's converse proof relies on the limit argume... — Carmelics
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    Challenges→A motion is governed purely by centripetal forces if and only if equal areas are swept out in equal times

    Proposition 2's converse proof relies on the limit argument that infinitesimal impulses approximate continuous centripetal force, a step Berkeleys critiques of the calculus in 'The Analyst' show is logically unrigorous.

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    Key Terms

    Berkeley(as the author being discussed)
    George Berkeley was an Irish philosopher from the 1600s-1700s who argued that physical objects don't exist independently of being perceived—they only exist because someone is thinking about or observing them.
    Calculus(as used in mathematics and logic)
    In this context, a mathematical system or set of rules for solving problems (not just the calculus taught in high school).
    Converse(referring to some claim being discussed)
    The flipped version of a statement; if the original says 'A implies B,' the converse says 'B implies A.'
    Limit argument(calculus)
    A mathematical technique where you show what happens to something as it gets closer and closer to a certain point or value.
    Logically unrigorous

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    (philosophy and mathematics)
    Reasoning or arguments that don't follow strict logical rules and contain gaps or weak points in their justification.
    The Analyst(as the specific work being referenced)
    A famous philosophical essay Berkeley wrote in 1734 that criticized the mathematical methods of calculus, arguing they contained logical inconsistencies.
    centripetal force(Book 1, Propositions 1 and 2)
    A force directed toward a fixed center that governs orbital motion; Newton's framework requires purely centripetal forces to produce the equal-areas property
    impulses(in ethics and philosophy of action)
    Sudden desires, urges, or inclinations to act a certain way that arise in the moment.
    infinitesimal(Nonstandard analysis)
    A hyperreal a whose absolute value |a| is less than 1/(n+1) for every natural number n
    proof(Frege's formal system; the definition still used by logicians today)
    Any finite sequence of statements such that each statement is either an axiom of the formal system or follows from previous members of the sequence by a valid rule of inference.
    proposition(Used in the context of a semantic theory sensitive to differences in subject matter.)
    The content expressed by a sentence, individuated at least in part by the subject matter of the sentence and the contents of its subsentential expressions.

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    Truth & Knowledge1 linkedCausation1 linked

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    A motion is governed purely by centripetal forces if and only if equal areas are...

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