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    A motion is governed purely by centripetal forces if and ... — Carmelics
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    Home/Causation
    HistoryEditSee Inverse

    A motion is governed purely by centripetal forces if and only if equal areas are swept out in equal times

    Causation
    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 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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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 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 against 2 of 2
    ?
    • 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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    Related

    A frame-relative biconditional cannot serve as a foundational criterion for cent...An approximate equivalence cannot ground a strict biconditional claim without ad...If the limiting passage from discrete impulsive forces to continuous centripetal...If the reference frame presupposed by the biconditional cannot be non-circularly...
    +4 moreShow less
    Newton's Propositions 1 and 2 assume an inertial reference frame, but no such fr...Proposition 1 establishes that equal areas swept in equal times implies purely c...Proposition 2 establishes that purely centripetal force governance implies equal...Proposition 2's converse proof relies on the limit argument that infinitesimal i...

    Similar

    A motion is quam proxime governed purely by centripetal forces if and ...90%Proposition 1 establishes that equal areas swept in equal times implie...88%Proposition 2 establishes that purely centripetal force governance imp...86%Propositions 1 and 2 establish the exact biconditional between centrip...80%

    Source

    AI-extracted1/3 agreementValid
    SEP: newton-principia
    View source passageHide passage
    This is not the only place in Book 1 where Newton takes the trouble to derive an “If…quam proxime, then…quam proxime” version of an exact “If…, then…” proposition. Propositions 1 and 2 establish that a motion is governed purely by centripetal forces if and only if equal areas are swept out in equal times. The second and third corollaries of Proposition 3 then yield the conclusion that a motion is quam proxime governed purely by centripetal forces if and only if equal areas are quam proxime swept
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit