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    Carmelics

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    Made withinDC&Austin
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    Home/Original/inverse
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    Inverse View

    It is not the case that Berkeley's critique in 'The Analyst' established that infinitesimals treated as nonzero when convenient and zero when convenient commit a logical fallacy of inconsistent supposition.

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

    Reasons For

    1 perspective
    Reason for
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    • 1.Infinitesimals need not be real numbers; modern nonstandard analysis treats them rigorously as elements of hyperreal fields with consistent logical status.
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    • 2.Berkeley conflated informal heuristic procedures with formal logical claims; useful computational methods need not satisfy strict philosophical rigor simultaneously.
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    • 3.The infinitesimal's varying role reflects context-dependent reasoning (algebraic vs. limiting), not inconsistency—similar to how 'open' differs in topology and everyday language.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.A quantity cannot logically be both zero and nonzero simultaneously in the same derivation without violating the law of non-contradiction.
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    • 2.Early calculus texts explicitly treated infinitesimals as nonzero for division, then discarded them as zero for final answers, lacking rigorous justification.
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    • 3.Berkeley's critique forced mathematicians to develop rigorous limits theory, ultimately vindicating his demand for logical consistency in foundations.
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