(2005). Wonder in the face of scientific revolutions: Adam Smith on Newton's ‘Proof’ of Copernicanism. British Journal for the History of Philosophy: Vol. 13, No. 4, pp. 697-732. doi: 10.1080/09608780500293042.

Craig Callender, Jonathan Cohen and Markus Schrenk have recently argued for an amended version of the best system account of laws – the better best system account (BBSA). This account of lawhood is supposed to account for laws in the special sciences, among other desiderata. Unlike David Lewis's original best system account of laws, the BBSA does not rely on a privileged class of natural predicates, in terms of which the best system is formulated. According to the BBSA, a contingently (...) true generalization is a law of a special science S iff the generalization is an axiom (or a theorem) of the best system relative to the set of predicates used by special science S. We argue that the BBSA is, at best, an incomplete theory of special science laws, as it does not account for typical features of special science laws, such as attached ceteris paribus conditions and the idealized character of law statements in these disciplines. (shrink)

The aim of this paper is twofold: (1) to show the principal aspects of the way in which Newton conceived his mathematical concepts and methods and applied them to rational mechanics in his Principia; (2) to explain how the editors of the Geneva Edition interpreted, clarified, and made accessible to a broader public Newton’s perfect but often elliptic proofs. Following this line of inquiry, we will explain the successes of Newton’s mechanics, but also the problematic aspects of his perfect geometrical (...) methods, more elegant, but less malleable than analytical procedures, of which Newton himself was one of the inventors. Furthermore, we will also consider the way in which Newtonianism was spread before in England and afterwards on continental Europe. In this respect the Geneva Edition plays a fundamental role because of its complete apparatus of notes, and because it appeared only thirteen years after the publication of the third edition of the Principia (1726). Finally, we will also confront some problems connected to the metaphysics of calculus. Therefore, the case of Newton is one of those in which, starting from mathematics applied to physics, it is possible to connect an impressive series of fundamental arguments such as the role of mathematics in science; the comparison between Newton’s geometrical methods and analytical methods; the way in which Newtonianism was spread as well as the philosophical implications of Newton’s mathematical concepts. (shrink)

This article casts light on the intimate relationship between metaphysics and science in Adam Smith’s thought. Understanding this relationship can help in resolving an enduring dispute or misreading concerning the status and role of natural theology and the ‘invisible hand’ doctrine. In Smith’s scientific realism, ontological issues are necessary prerequisites for scientific inquiry, and metaphysical ideas thus play an organizing and regulatory role. Smith also recognized the importance of scientifically informed metaphysics in science’s historical development. In this sense, for Smith, (...) the metaphysico-scientific link, was a basic criterion of scientific validation by Inference to the Best Explanation. Furthermore, Smith’s comments implicitly suggest that in scientific progress there is a dialectic between metaphysics and science. These themes are illustrated primarily through his writings on the history of astronomy. (shrink)

In this paper an analysis of Newton’s argument for universal gravitation is provided. In the past, the complexity of the argument has not been fully appreciated. Recent authors like George E. Smith and William L. Harper have done a far better job. Nevertheless, a thorough account of the argument is still lacking. Both authors seem to stress the importance of only one methodological component. Smith stresses the procedure of approximative deductions backed-up by the laws of motion. Harper stresses “systematic dependencies” (...) between theoretical parameters and phenomena. I will argue that Newton used a variety of different inferential strategies: causal parsimony considerations, deductions, demonstrative inductions, abductions and thought-experiments. Each of these strategies is part of Newton’s famous argument. (shrink)

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)

This article argues that early modern philosophy should be seen as an integrated enterprise of moral and natural philosophy. Consequently, early modern moral and natural philosophy should be taught as intellectual enterprises that developed hand in hand. Further, the article argues that the unity of these two fields can be best introduced through methodological ideas. It illustrates these theses through a case study on Scottish Newtonianism, starting with visions concerning the unity of philosophy and then turning to a discussion of (...) how methodological ideas figure in those visions. Finally, the article argues that methodological considerations can serve as good starting points to introduce and discuss central topics and canonical figures of the early modern period. (shrink)

Ursula Klein has argued that Geoffroy’s table of chemical affinities, published in 1718, marked the emergence of the concepts of chemical compound and chemical combination central to chemistry. In this paper her position is summarised and then modified to render it immune to criticism that has been levelled against it. The essentials of Geoffroy’s chemistry are clarified and adapted to Klein’s picture by way of a detailed comparison of it with Boyle’s corpuscular chemistry that proceeded Geoffroy’s by over half a (...) century. The idea that Geoffroy’s notion of chemical combination marked a significant turning point in the emergence of modern chemistry is defended against the charge that it is Whiggish. (shrink)

Reid was a Newtonian and a Theist, but did he found his Theism on Newton’s physics? In opposition to commonplace assumptions about the role of Theism in Reid’s philosophy, my answer is no. Reid prefers to found his Theism on a priori reasons, rather than on physics. Reid’s understanding of physics as an empirical science stops it from contributing in any clear and efficient way to issues of natural theology. In addition, Reid is highly sceptical of our ability to discover (...) the efficient and final causes of natural phenomena, knowledge of which is essential for natural theology. To bring out Reid’s differences with classical Newtonian Theists Richard Bentley and William Whiston, I examine their use of the law and force of general gravitation, and reconstruct what would be Reidian objections.Keywords: Thomas Reid; William Whiston; Richard Bentley; Physics; Theism; Isaac Newton. (shrink)

In contrast with some recent theories of infinitesimals as non-Archimedean entities, Leibniz’s mature interpretation was fully in accord with the Archimedean Axiom: infinitesimals are fictions, whose treatment as entities incomparably smaller than finite quantities is justifiable wholly in terms of variable finite quantities that can be taken as small as desired, i.e. syncategorematically. In this paper I explain this syncategorematic interpretation, and how Leibniz used it to justify the calculus. I then compare it with the approach of Smooth Infinitesimal Analysis, (...) as propounded by John Bell. I find some salient differences, especially with regard to higher-order infinitesimals. I illustrate these differences by a consideration of how each approach might be applied to propositions of Newton’s Principia concerning the derivation of force laws for bodies orbiting in a circle and an ellipse. “If the Leibnizian calculus needs a rehabilitation because of too severe treatment by historians in the past half century, as Robinson suggests (1966, 250), I feel that the legitimate grounds for such a rehabilitation are to be found in the Leibnizian theory itself.”—(Bos 1974–1975, 82–83). (shrink)

Isaac Newton is best known as a mathematician and physicist. He invented the calculus, discovered universal gravitation and made significant advances in theoretical and experimental optics. His master-work on gravitation, the Principia, is often hailed as the crowning achievement of the scientific revolution. His significance for philosophers, however, extends beyond the philosophical implications of his scientific discoveries. Newton was an able and subtle philosopher, working at a time when science was not yet recognized as an activity distinct from philosophy. He (...) engaged with the work of Rene Descartes and G.W. Leibniz, and showed sensitivity to the work of John Locke, Francis Bacon, Pierre Gassendi and Henry More, to name just a few. In his time, Newton was not perceived as a scientific outsider, but as an active and knowledgeable participant in philosophical debates.... (shrink)

We argue that a conflict between two conceptions of “quantity of matter” employed in a corollary to proposition 6 of Book III of the Principia illustrates a deeper conflict between Newton’s view of the nature of extended bodies and the concept of mass appropriate for the theoretical framework of the Principia. We trace Newton’s failure to recognize the conflict to the fact that he allowed for the justification of natural philosophical claims by two types of a posteriori, empiricist methodologies. Newton's (...) thoughts on these methodologies demonstrate that his natural philosophy continued to develop after the publication of the first edition of Principia and that De Grav should be understood as an early, and not necessarily representative, text. (shrink)