In this lecture I review an ensemble of historical and especially philosophical issues that attended the development of classical mechanics from Isaac Newton's innovations in the late 17th century to a massive rise during the 18th century. Three traditions developed then, of which Newtonian mechanics was only one. Of the philosophical questions discussed, some are epistemological, including claims of reduction; others are methodological. The place of mathematical theories in physical theories is also addressed in this context, since all three traditions profoundly influenced classical mathematical physics as it rose in its various branches in the 19th century; mechanics itself expanded still further in some notable ways.
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