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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that A motion is governed purely by centripetal forces if and only if equal areas are swept out in equal times

    ?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.Newton's Propositions 1 and 2 assume an inertial reference frame, but no such frame is strictly identifiable without circular appeal to the very laws being established.
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    • 2.If the reference frame presupposed by the biconditional cannot be non-circularly fixed, the 'if and only if' relation is frame-relative, not an absolute physical equivalence.
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    • 3.A frame-relative biconditional cannot serve as a foundational criterion for centripetal force governance without smuggling in empirical assumptions Newton treats as a priori.
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    Reason for 2 of 2
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    • 1.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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    • 2.If the limiting passage from discrete impulsive forces to continuous centripetal force is not rigorously justified, the reverse implication—area law entails purely centripetal force—is not deductively established but only approximated.
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    • 3.An approximate equivalence cannot ground a strict biconditional claim without additional stipulation of idealization conditions Newton leaves tacit.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Proposition 1 establishes that equal areas swept in equal times implies purely centripetal force governance
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    • 2.Proposition 2 establishes that purely centripetal force governance implies equal areas swept in equal times
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