In this paper I discuss Newton's first optical paper. My aim is to examine the type of argument which Newton uses in order to convince his readers of the truth of his theory of colors. My claim is that this argument is an induction by elimination, and that the Newtonian method of justification is a kind of “generative justification”, a term due to T. Nickles. To achieve my aim I analyze in some detail the arguments in Newton's first optical paper, (...) relating the paper with Newton's other writings in optics, and especially his early correspondence in defence of his theory of colors. (shrink)

The first proposition of the Principia records two fundamental properties of an orbital motion: the Fixed Plane Property (that the orbit lies in a fixed plane) and the Area Property (that the radius sweeps out equal areas in equal times). Taking at the start the traditional view, that by an orbital motion Newton means a centripetal motion – this is a motion ``continually deflected from the tangent toward a fixed center'' – we describe two serious flaws in the Principia's argument (...) for Proposition 1, an argument based on a polygonal impulse approximation. First, the persuasiveness of the argument depends crucially on the validity of the Impulse Assumption: that every centripetal motion can be represented as a limit of polygonal impulse motions. Yet Newton tacitly takes the Impulse Assumption for granted. The resulting gap in the argument for Proposition 1 is serious, for only a nontrivial analysis, involving the careful estimation of accumulating local errors, verifies the Impulse Assumption. Second, Newton's polygonal approximation scheme has an inherent and ultimately fatal disability: it does not establish nor can it be adapted to establish the Fixed Plane Property. Taking then a different view of what Newton means by an orbital motion – namely that an orbital motion is by definition a limit of polygonal impulse motions – we show in this case that polygonal approximation can be used to establish both the fixed plane and area properties without too much trouble, but that Newton's own argument still has flaws. Moreover, a crucial question, haunted by error accumulation and planarity problems, now arises: How plentiful are these differently defined orbital motions? Returning to the traditional view, that Newton's orbital motions are by definition centripetal motions, we go on to give three proofs of the Area Property which Newton ``could have given'' – two using polygonal approximation and a third using curvature – as well as a proof of the Fixed Plane Property which he ``almost could have given.''. (shrink)

I am grateful to Peter Achinstein, Don Howard, and the other participants at the conference, 'The Role of Experiments in Scientific Changer', Virginia Polytechnic Institute and State University, 30 March to 1 April, 1990, for helpful discussion, and especially to Ron Laymon for his discussion comments presented at the conference on an earlier version of this paper.

I take Newton’s arguments to inverse square centripetal forces from Kepler’s harmonic and areal laws to be classic deductions from phenomena. I argue that the theorems backing up these inferences establish systematic dependencies that make the phenomena carry the objective information that the propositions inferred from them hold. A review of the data supporting Kepler’s laws indicates that these phenomena are Whewellian colligations—generalizations corresponding to the selection of a best fitting curve for an open-ended body of data. I argue that (...) the information theoretic features of Newton’s corrections of the Keplerian phenomena to account for perturbations introduced by universal gravitation show that these corrections do not undercut the inferences from the Keplerian phenomena. Finally, I suggest that all of Newton’s impressive applications of Universal gravitation to account for motion phenomena show an attempt to deliver explanations that share these salient features of his classic deductions from phenomena. (shrink)

The Description for this book, Theory and Evidence, will be forthcoming.

In this essay I argue against I. Bernard Cohen's influential account of Newton's methodology in the Principia: the 'Newtonian Style'. The crux of Cohen's account is the successive adaptation of 'mental constructs' through comparisons with nature. In Cohen's view there is a direct dynamic between the mental constructs and physical systems. I argue that his account is essentially hypothetical-deductive, which is at odds with Newton's rejection of the hypothetical-deductive method. An adequate account of Newton's methodology needs to show how Newton's (...) method proceeds differently from the hypothetical-deductive method. In the constructive part I argue for my own account, which is model based: it focuses on how Newton constructed his models in Book I of the Principia. I will show that Newton understood Book I as an exercise in determining the mathematical consequences of certain force functions. The growing complexity of Newton's models is a result of exploring increasingly complex force functions (intra-theoretical dynamics) rather than a successive comparison with nature (extra-theoretical dynamics). Nature did not enter the scene here. This intra-theoretical dynamics is related to the 'autonomy of the models'. (shrink)

n this paper I deal with a neglected topic with respect to unification in Newton’s Principia. I will clarify Newton’s notion and practice of unification . In order to do so, I will use the recent theories on unification as tools of analysis . I will argue, after showing that neither Kitcher’s nor Schurz’s account aptly capture Newton’s notion and practice of unification, that Salmon’s later work is a good starting point for analysing this notion and its practice in the (...) Principia. Finally, I will supplement Salmon’s account in order to answer the question at stake.Keywords: Explanation; Isaac Newton; Principia; Unification. (shrink)

I examine Popper’s claims about Newton’s use of induction in Principia with the actual contents of Principia and draw two conclusions. Firstly, in common with most other philosophers of his generation, it appears that Popper had very little acquaintance with the contents and methodological complexities of Principia beyond what was in the famous General Scholium. Secondly Popper’s ideas about induction were less sophisticated than those of Newton, who recognised that it did not provide logical proofs of the results obtained using (...) it, because of the possibilities of later, contrary evidence. I also trace the historical background to commonplace misconceptions about Newton’s method.Author Keywords: Newton; Popper; Induction; Principia; Kepler’s laws. (shrink)

In this volume a team of distinguished contributors examine all the main aspects of Newton s thought, including not only his approach to space, time, mechanics, ...

I take Newton's arguments to inverse square centripetal forces from Kepler's harmonic and areal laws to be classic deductions from phenomena. I argue that the theorems backing up these inferences establish systematic dependencies that make the phenomena carry the objective information that the propositions inferred from them hold. A review of the data supporting Kepler's laws indicates that these phenomena are Whewellian colligations-generalizations corresponding to the selection of a best fitting curve for an open-ended body of data. I argue that (...) the information theoretic features of Newton's corrections of the Keplerian phenomena to account for perturbations introduced by universal gravitation show that these corrections do not undercut the inferences from the Keplerian phenomena. Finally, I suggest that all of Newton's impressive applications of Universal gravitation to account for motion phenomena show an attempt to deliver explanations that share these salient features of his classic deductions from phenomena. (shrink)