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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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.