Do Newton’s rules of reasoning guarantee truth … must they?

Newton’s Principia introduces four rules of reasoning for natural philosophy. Although useful, there is a concern about whether Newton’s rules guarantee truth. After redirecting the discussion from truth to validity, I show that these rules are valid insofar as they fulfill Goodman’s criteria for inductive rules and Newton’s own methodological program of experimental philosophy; provided that cross-checks are used prior to applications of rule 4 and immediately after applications of rule 2 the following activities are pursued: (1) research addressing observations that systematically deviate from theoretical idealizations and (2) applications of theory that safeguard ongoing research from proceeding down a garden path.     

The third law in Newton’s Waste book (or, the road less taken to the second law)

On the basis of evidence drawn from the Waste book, Westfall and Nicholas have argued that Newton arrived at his second law of motion by reflecting on the implications of the first law. I analyze another argument in the Waste book which reveals that Newton also arrived at the second law by another very different route. On this route, it is the consideration of the third law and the principle of conservation of motion—and not the first law—that prompts Newton to formulate the second law. The existence of these two routes is significant because each employs a distinct kind of reasoning about forces. Whereas the Nicholas-Westfall route via the principle of inertia bears the mark of Descartes’s influence, the alternative route proceeds from the action-reaction principle, which is widely regarded as an original Newtonian contribution to mechanics. In the course of exploring this alternate route to the second law, the origins and justification of the third law are examined.     

Making sense of Day 1 of the Two New Sciences: Galileo’s Aristotelian-inspired agenda and his Jesuit readers

This study proposes an explanation for the choice of topics Galileo addressed in Day 1 of his 1638 Two New Sciences, a section of the work which has long puzzled historians of science. I argue that Galileo’s agenda in Day 1, that is the topics he discusses and the questions he poses, was shaped by contemporary teaching commentaries on Books 3 through 8 of Aristotle’s Physics. Building on the insights and approach of theorists of reader reception, I confirm this interpretation by examining the response of professors of natural philosophy at the Jesuit Collegio Romano to Galileo’s text.