The aim of this paper is to analyze Leibniz and Newton’s conception of space, and to point out where their agreements and disagreements lie with respect to its mode of existence. I shall offer a definite characterization of Leibniz and Newton’s conceptions of space. I will show that, according to their own concepts of substance, both Newtonian and Leibnizian spaces are not substantiva!. The reason of that consists in the fact that space is not capable of action. Moreover, there is (...) a sense in which space is relational, because their parts are individuated only by means of their mutual relations. (shrink)

This is the chapter on general relativity for the Cambridge Companion to Einstein which I am co-editing with Christoph Lehner.

In the first part of this paper a relational account of incongruent counterparts is defended against an argument due to Kant. I then consider a more recent attack on such an account, due to John Earman, which alleges that the relationalist cannot account for the lawlike left--right asymmetry manifested in parity-violating phenomena. I review Hoefer's, Huggett's and Saunders' responses to Earman's argument and argue that, while a relationalist account of parity-violating laws is possible, it comes at the cost of non-locality.

This paper will serve as the editorial note on Einstein's 1916 review article on general relativity in a planned volume with all of Einstein's papers in Annalen der Physik. It summarizes much of my other work on history of general relativity and draws heavily on the annotation of Einstein's writings and correspondence on general relativity for Vols. 4, 7, and 8 of the Einstein edition.

Relative motion of particles is examined in the context of relational space-time. It is shown that de Broglie waves may be derived as a representation of the coordinate maps between the rest-frames of these particles. Energy and momentum are not absolute characteristics of these particles, they are understood as parameters of the coordinate maps between their rest-frames. It is also demonstrated the position of a particle is not an absolute, it is contingent on the frame of reference used to observe (...) the particle. (shrink)

I argue that notions of relative fundamentality need to be invoked if there is to be something substantive at stake in the debate between proponents of Harvey Brown's dynamical approach to relativity and defenders of a more traditional interpretation of spacetime. I will review some problems that stand in the way of the advocate of the dynamical approach making good on their claim that dynamical symmetries are more fundamental than spacetime symmetries.

Urban void sometimes amplifies alienation within urban space, and thus leads the way to the human craving for authenticity. Juxtaposing urban void with the conventional notion of urban objects, furthermore, conforms to Nietzsche's distinction between Dionysian and Apollonian deportment. The Apollonian is at the founding of the Platonic myth of the Ideal City and its modern descendant, the myth of the Rational City. Modern urban planning has been object-directed and, consistent with the historical trend since the Renaissance, has become a (...) constituent of a Neo-Platonic mythology that insists on forging a city as an urban technological artifact. Most existing urban parks and squares, as well as suburban gardens, within this approach, only augment the subordinate standing of urban voids. Yet the significance of urban void, as the unplanned place that represents the pre-rational, the genuine and the unadulterated, ought to lead to its re-introduction into city-form as a conduit for self-reflection and authenticity. Recognizing urban void for its significance may reintroduce an important Dionysian feature into city-form, leading to deliberate carving of authentic urban spaces. (shrink)

A relationist will account for the use of ‘left’ and ‘right’ in terms of relative orientations, and other properties and relations invariant under mirroring. This analysis will apply whenever mirroring is a symmetry, so it certainly applies to classical mechanics; we argue it applies to any physical theory formulated on a manifold: it is in this sense an a priori symmetry. It should apply in particular to parity violating theories in quantum mechanics; mirror symmetry is only broken in such theories (...) as a special symmetry. (shrink)

Discussions concerning belief revision, theorydevelopment, and ``creativity'' in philosophy andAI, reveal a growing interest in Peirce'sconcept of abduction. Peirce introducedabduction in an attempt to providetheoretical dignity and clarification to thedifficult problem of knowledge generation. Hewrote that ``An Abduction is Originary inrespect to being the only kind of argumentwhich starts a new idea'' (Peirce, CP 2.26).These discussions, however, led to considerabledebates about the precise way in which Peirce'sabduction can be used to explain knowledgegeneration (cf. Magnani, 1999; Hoffmann, 1999).The crucial question is (...) that of understandinghow we can get the new elements capableof enlarging our theories. Under thesecircumstances, it might be helpful to step outof the entanglement and reconsider the basis ofthe problem that originally triggered Peirce'sinterest in abduction. This will lead us toanother Peircean concept, that of ``diagrammaticreasoning,'' which I discuss here in the contextof his ``pragmatism.'' In this way, I hope toreach a better understanding of thecontribution of ``abduction'' to the knowledgegeneration process. (shrink)

We should see the debate over the existence of spacetime as a debate about the fundamentality of spatiotemporal structure to the physical world. This is a non-traditional conception of the debate, which captures the spirit of the traditional one. At the same time, it clarifies the point of contention between opposing views and offsets worries that the dispute is stagnant or non-substantive. It also unearths a novel argument for substantivalism, given current physics. Even so, that conclusion can be overridden by (...) future physics. I conclude that this debate is a substantive one, which the substantivalist is currently winning. (shrink)

When distinguishing absolute, true, and mathematical time from relative, apparent, and common time, Newton wrote: “absolute, true, and mathematical time, in and of itself and of its own nature, without reference to anything external, flows uniformly” [Newton 2004b: 64]. Newton thought that the temporal metric is intrinsic. Many philosophers have argued—for empiricist reasons or otherwise—that Newton was wrong about the nature of time. They think that the flow of time does involve “reference to something external.” They think that the temporal (...) metric is extrinsic. Among others, Mach, Poincaré, and Grünbaum seem to accept this view.1 And these are not the only two views available. Perhaps both Newton and his opponents are wrong and there is no temporal metric at all. (shrink)

This paper considers the implications for the relational-substantival debate of observations of parity nonconservation in weak interactions, a much neglected topic. It is argued that 'geometric proofs' of absolute space, first proposed by Kant (1768), fail, but that parity violating laws allow 'mechanical proofs', like Newton's laws. Parity violating laws are explained and arguments analogous to those of Newton's Scholium are constructed to show that they require absolute spacetime structure--namely, an orientation--as Newtonian mechanics requires affine structure. Finally, it is considered (...) how standard relationist responses to Newton's argument might respond to the new challenge of parity nonconservation. (shrink)

Absolutism about mass claims that mass ratios obtain in virtue of absolute masses. Comparativism denies this. Dasgupta, Oxford studies in metaphysics, Oxford University Press, Oxford, 2013) argues for comparativism about mass, in the context of Newtonian Gravity. Such an argument requires proving that comparativism is empirically adequate. Dasgupta equates this to showing that absolute masses are undetectable, and attempts to do so. This paper develops an argument by Baker to the contrary: absolute masses are in fact empirically meaningful, that is (...) detectable. Additionally, it is argued that the requirement of empirical adequacy should not be cashed out in terms of undetectability in the first place. The paper closes by sketching the possible strategies that remain for the comparativist. Along the way a framework is developed that is useful for thinking about these issues: Ozma games—how could one explain to an alien civilisation what an absolute mass is? (shrink)