Chapter 19 - Formalization: mass and force

Summary

The realization that a branch of knowledge could be presented in a form in which the entire contents of the field of investigation could be expressed by positing a small number of basic truths and by claiming that all the other truths of the discipline followed from these basic posits by pure deductive reasoning alone predated any serious development of dynamics or of other branches of physical science. The axiomatization of geometry has its origin at such an early date, in fact, that we have no good record of when or how the very idea of presenting geometry as a deductive formal discipline arose.

This early discovery of a branch of mathematics as a formal science had many consequences for the history of science and the history of philosophy of science. The entire history of the rationalist approach to knowledge in philosophy is founded on the early discovery that geometry could be structured as a set of consequences logically deducible from apparently “self-evident” first principles. Closer to our concerns, it is clear that Newton's Principia is itself structured to resemble as closely as possible the standard presentation of geometry. But there is, of course, no pretence on Newton's part that his first principles could themselves be established without reference to empirical experiment. (It was left to Kant to fall into the trap of trying to establish Newtonian dynamics as a fully a-priori science!)