Newton’s Quest for a Mathematical-Demonstrative Optics

In this paper, I take up and develop the suggestion made by the late I. Bernard Cohen, Casper Hakfoort and Alan E. Shapiro that Newton's methodological ideal of "deducing causes from phenomena" was not equally attainable in the study of optical phenomena. If this suggestion is correct, then in the apex of Newton's optical researches, The Opticks, which in fact contained a set of interrelated theories on optical phenomena, Newton failed to rigidly deduce these theories in the sense he had done in the Principia. By contrasting Newton's methodology in the Principia with the way in which theoretical conclusions are established in The Opticks, I shall be able to explain why Newton was less successful to accommodate optical phenomena according to his own methodological desiderata of deducing causes from phenomena. After having commented briefly upon Newton's methodology in the Principia, I will review the kinds of trouble that Newton ran into when trying to methodize optics in a Principia Style fashion. My focal point will be Newton's arguments for the thesis that white light consists of rays differently 'refrangible'. Special attention will be paid to Newton's presumed application of Rule II of the regulae philosophandi in establishing that part of his optical theory. It is shown that Rule II licenses the identification of instances of causes of the same kind which have been shown to be true and sufficient to explain their phenomena. Thus, on the basis of Rule II we identify two instances of causal parameters of the same kind, which have separately been derived from phenomena. The disanalogy involved is thus that in the experimentum crucis (and its related sections in The Opticks) we use an argument for uniformity to establish a single causal claim, while Rule II licences the identification of similar causal parameters which were independently established and were deduced from phenomena by systematic dependencies. In the Principia there are systematic dependencies, derived from the laws of motion, between causes and effects. Given the absence of systematic dependencies, Newton could offer only sufficient causes in The Opticks. Moreover, by means of what I call 'macro-micro inference tickets' (i.e. Props. LXX-LVI, Book I), Newton was able to license conclusions about the inverse-square centripetal forces of each of the individual micro-particles that constitute a macroscopic body from the overall inverse-square centripetal force exerted by that body (in this way, Newton was thus able to back up transductive inferences about the particles constituting a macroscopic body). In The Opticks none of the above was at hand. Newton clearly wanted to do more than to simply establish the phenomenological laws regulating optical phenomena: he also wanted to provide a solid physical account of optical phenomena. However, given the empirical and methodological problems Newton later encountered when methodizing optics in a Principia-style, it turned out that establishing non-hypothetical physical interpretations of optical phenomena was quite a difficult matter. It is the aim of this talk to pinpoint the dynamics between method and 'phenomena' in Newton's optical research.