The concept of energy, the premier concept of physics and indeed of all science, is here investigated from the standpoint of its early historical origin and the philosophical implications thereof. The fundamental assumption is made that the root of the concept is the notion of invariance or constancy in the midst of change. Salient points in the development of this idea are presented from ancient times up to the publication of Lagrange'sMécanique Analytique (1788).

Misconceptions about energy conservation abound due to the gap between physics and secondary school chemistry. This paper surveys this difference and its relevance to the 1690s–2010s Leibnizian argument that mind-body interaction is impossible due to conservation laws. Justifications for energy conservation are partly empirical, such as Joule’s paddle wheel experiment, and partly theoretical, such as Lagrange’s statement in 1811 that energy is conserved if the potential energy does not depend on time. In 1918 Noether generalized results like Lagrange’s and proved (...) a converse: symmetries imply conservation laws and vice versa. Conservation holds if and only if nature is uniform. The rise of field physics during the 1860s–1920s implied that energy is located in particular places and conservation is primordially local: energy cannot disappear in Cambridge and reappear in Lincoln instantaneously or later; neither can it simply disappear in Cambridge or simply appear in Lincoln. A global conservation law can be inferred in some circumstances. Einstein’s General Relativity, which stimulated Noether’s work, is another source of difficulty for conservation laws. As is too rarely realized, the theory admits conserved quantities due to symmetries of the Lagrangian, like other theories. Indeed General Relativity has more symmetries and hence more conserved energies. An argument akin to Leibniz’s finally gets some force. While the mathematics is too advanced for secondary school, the ideas that conservation is tied to uniformities of nature and that energy is in particular places, are accessible. Improved science teaching would serve the truth and enhance the social credibility of science. (shrink)

Since Leibniz's time, Cartesian mental causation has been criticized for violating the conservation of energy and momentum. Many dualist responses clearly fail. But conservation laws have important neglected features generally undermining the objection. Conservation is _local_, holding first not for the universe, but for everywhere separately. The energy in any volume changes only due to what flows through the boundaries. Constant total energy holds if the global summing-up of local conservation laws converges; it probably doesn't in reality. Energy conservation holds (...) if there is symmetry, the sameness of the laws over time. Thus, if there are time-places where symmetries fail due to nonphysical influence, conservation laws fail there and then, while holding elsewhere, such as refrigerators and stars. Noether's converse first theorem shows that conservation laws imply symmetries. Thus conservation trivially nearly entails the causal closure of the physical. But expecting conservation to hold in the brain simply assumes the falsehood of Cartesianism. Hence Leibniz's objection begs the question. Empirical neuroscience is another matter. So is Einstein's General Relativity: far from providing a loophole, General Relativity makes mental causation _harder_. (shrink)

This paper examines Du Châtelet’s and Kant’s responses to the famous vis viva controversy – Du Châtelet in her Institutions Physiques (1742) and Kant in his debut, the Thoughts on the True Estimation of Living Forces (1746–49). The Institutions was not only a highly influential contribution to the vis viva controversy, but also a pioneering attempt to integrate Leibnizian metaphysics and Newtonian physics. The young Kant’s evident knowledge of this work has led some to speculate about his indebtedness to her (...) philosophy. My study corrects such speculations as well as misunderstandings of the Living Forces. This corrective result has implications for how to investigate Kant’s relation to the ever-evolving landscape of Leibniz exegeses. (shrink)

It is often claimed (most recently by Michael Friedman) that Kant intended to justify Newton’s most fundamental claims expressed in the Principia, such as his laws of motion and the law of universal gravitation. In this article, I argue that the differences between Newton’s laws of motion and Kant’s laws of mechanics are not superficial or merely apparent. Rather, they reflect fundamental differences in their respective projects. This point can be seen especially clearly by considering the nature of the various (...) projects undertaken in Germany prior to Kant that discuss the laws of motion. Wolff and his followers qua metaphysicians were especially interested in providing nonempirical justifications of their laws of motion as well as an intelligible account of the fundamental properties of bodies in terms of substance, accident, and force. Maupertuis and Euler, despite often being seen as Newtonians, both drew on traditions other than Newton’s. Physics textbooks (by figures such as Erxleben, Karsten, ‘s Gravesande, and Musschenbroek) vary considerably in their aims, but in none of these cases is Newton’s main argument of the Principia presented. In light of the fact that these projects are distinct in significant ways from Newton’s project, the differences between Newton’s laws of motion and Kant’s laws of mechanics are most likely not merely apparent but reflect the fact that Kant, too, was pursuing a project fundamentally distinct from Newton’s. (shrink)

This article discusses the quest for the mechanical advantage of the wedge in the eighteenth century. As a case study, the wedge enlightens our understanding of eighteenth-century mechanics in general and the controversy over “force” or vis viva in particular. In this article, I show that the two different approaches to mechanics, the one that favoured force in terms of velocities and the one that primarily used displacements—known as the ‘Newtonian’ and ‘Leibnizian’ methods, respectively—were not at all on par in (...) their ability to solve the problem of the wedge. In general, only those who used the Leibnizian concept of force or some related notion were able to get to the conventional results. This article thus rebuts the received view that the vis viva controversy was merely a semantic one. Instead, it shows that different understandings of “force” led to real and pragmatic differences in eighteenth-century mechanics. (shrink)

It has been suggested in the literature that, although Willem Jacob ‘s Gravesande occasionally treated Newton's doctrines in a selective manner, he was nevertheless an unremitting follower of Newton's methodology. As part of a reassessment of ‘s Gravesande's Newtonianism, I argue that, although ‘s Gravesande took over key terms of Newton's methodological canon, his methodological ideas are upon close scrutiny quite different from and occasionally even incongruent with Newton's views on the matter.

By the time of the Leibniz-Clarke correspondence of 1716 the Newtonian and Leibnizian systems of natural philosophy had reached maturity. Each system consisted of different physical as well as metaphysical principles which, taken together, formed a world view. At the time of their famous debates, Leibniz at 70 and Newton at 74, the founders of two highly developed scientific philosophies, were struggling to establish and defend the ontological and mechanical bases of differing bodies of organized knowledge.

I explain Kant’s critique of Leibniz’s rejection of real opposition in the Amphiboly in the context of Kant’s pre-Critical writings on vis viva and negative magnitudes and his Metaphysical Foundations of Natural Science. Properly contextualized in terms of the vis viva controversy, I argue, Kant’s arguments against Leibniz succeed, even though they are laden with theoretical inconsistencies and operate under false physical premises.

Euler’s ‘On the force of percussion and its true measure’, published in 1746, shows that not only had the issue of vis viva not been settled, but that the concepts of inertia and even force were still very much up for grabs. This paper details Euler’s treatment of the vis viva problem. Within those details we find differences between his physics and that of Newton, in particular the rejection of empty space and reduction of all forces to the operation of (...) inertia through contact. One can further see how Euler’s philosophy of science embraced explanation through mechanisms and equilibrium conditions.Keywords: Leonhard Euler; Vis viva; Equlibrium; Mechanics; Eighteenth century. (shrink)

Leibniz’s mature philosophical understanding of the laws of nature emerges rather suddenly in the late 1670’s to early 1680’s and is signaled by his embrace of three central theses.1 The first, what I’ll call the thesis of Contingency, suggests that the laws of nature are not only contingent, but, in some sense, paradigmatically contingent; they are supposed to provide insight into the very nature of contingency as Leibniz comes to understand it. The second, what I’ll call the thesis of Providence, (...) suggests that the laws of nature provide a basis for a new argument from design by showing how reflection on God’s ends can be positively useful in the practice of natural philosophy. The third, what I’ll call thesis of .. (shrink)