In this monograph, a historically detailed and philosophical-systematic study will be undertaken of Newton''s scientific methodology. It will be shown that the hypothesis that Newton was a bad or confused methodologist is beset with many difficulties and that Newton was not a simplistic inductivist nor did he believe that causes can be derived unconditionally from phenomena. Special attention will be given to Newton'¬"s Principia-style methodology. With respect to Newton'¬"s Principia-style methodology, it will be shown that Newton carefully distinguished between the (physico-)mathematical treatment of force and the physical treatment of force and that the former should always precede the latter in order to uncover the forces present in rerum natura more safely. In the (physico-)mathematical treatment of force, Newton explicated the physico-mathematical conditions under which, given the laws of motion, certain motions would occur exactly or quam proxime. Of course, Newton clearly focused on those motions which would be relevant in the study of the systema mundi, i.e. Keplerian motions.
It will be shown that the models of Book I are not purely mathematical, but physico-mathematical instead: the idealized motions and forces of the models of Book I are iso-nomological to real-world bodies and forces and they are analyzable by the same technical concepts, i.e. Definitions I-VIII. Given these features, Newton could bridge the gap between mathematics and physics: the physico-mathematical conditions, which are structurally similar to what would become their referents in the context of Book III, are predicated under the same laws that hold in the empirical world and, given the Definitions, one could relate certain technical terms to their quasi-physical measures. What sets Newton'¬"s Principia-style approach apart from a hypothetico-deductive approach is the fact that he derived the physico-mathematical models presented in Book I from the laws of motion. This shows that Newton was clearly aware of the need to introduce certain theoretical assumptions. However, Newton carefully restricted these theoretical principles to those principles that have empirical support and that have already shown their potential in the study of force and motion, on the one hand, and to those principles that remain neutral with respect to the cause of gravity, on the other. This process of theoretical prioritization served as a tool to reduce arbitrary speculation.
A central purpose of Book I was to bi-conditionally relate certain physico-mathematical conditions to certain mathematical regularities, given the laws of motion. By means of the exact causal inference tickets Newton explicated, given the laws of motion, the necessary and sufficient physico-mathematical conditions which hold exactly under which bodies describe motions according to a mathematical regularity that holds exactly. By means of the quam proxime causal inference-tickets, Newton anticipated the problem that the mathematical regularities as stipulated in the exact causal inference-tickets will not hold exactly in the empirical world, but only as most closely as possible. Newton sought to overcome this difficulty by showing, by a deduction from the laws of motion, that an overall centripetal force directed to a centre of force quam proxime is a necessary and sufficient condition for quam proxime time-area proportionality. In this way, he was able to infer that, given the laws of motion, a body as most closely as possible describing equal areas in equal times is urged by a centripetal force tending as most closely as possible toward a centre of force. The dynamics that drives Book I is furthermore inter-theoretical: it is predicated under a logic that the demonstration of the more complex models requires the demonstration of the more basic models. Once Newton established that Keplerian motion occurs in the empirical world in Phenomena I-VI, he was no longer dealing with abstract quasi-physical measures but with concrete measurements. Correspondingly, in Book I Newton'¬"s physico-mathematical models turned into natural-philosophical models.
On the basis of the exact of quam proxime causal inference-tickets established in Book I and on the basis of Phenomena I-VI, Newton inferred instances of inverse-square centripetal forces. Because of the bi-conditional relations he had derived from the laws of motion, Newton could present his inferences of inverse-square centripetal forces as deduction, or as deductions from phenomena. Typically, did not stop at that point. Given the systematic discrepancies he had established in Book I, Newton moved on to the search for residual forces. In other words, in Newton'¬"s methodology the attention shifts to a continuous exploration of residual forces and the establishment of their potential explanation. Correspondingly, in the Principia Newton made the study of deviations from exact mathematical regularities a focal point of natural-philosophical investigation. From the perspective of the laws of motion, each deviation from a relevant mathematical regularity is seen as evidence that an additional force, not tracked in our initial approximation, is affecting the situation under consideration. Accordingly, Newton approached empirical questions in a sequence of successive approximations.
In the context of confirmation, Newton demanded more than empirical confirmation of deduced consequences, since he insisted on accurate measurement of parameters and on convergence of independently measured parameters. Once Newton had inferred instances of inverse-square centripetal forces, he moved on to a series of gradual and increasingly wider inductive generalizations which would ultimately result in the law of universal gravitation. In order to back-up these generalizations, Newton introduced a series of regulae philosophandi. Based on new manuscript findings, the meaning and methodological significance of Newton'¬"s regulae philosophandi will be provided. In short, it will be shown that the '¬SNewtonian Revolution'¬ was not restricted to the empirical and theoretical dimensions of science, but equally applied to the methodological dimension of science as well. Based on a thorough survey of Newton'¬"s manuscripts, it will be clarified in what sense Newton conceived of natural-philosophical knowledge as causal knowledge. Additionally, attention will be given to Newton'¬"s attempt to methodize optics. With respect to Newton'¬"s optical work it will be shown that Newton was unable to methodize optics according to his Principia-style methodology.
Finally, a new account will be provided of the complex interaction between Newton'¬"s physics and his theology. For a description of the content of each chapter I refer to the introduction of my book.