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)

It is widely accepted that the notion of an inertial frame is central to Newtonian mechanics and that the correct space-time structure underlying Newton’s methods in Principia is neo-Newtonian or Galilean space-time. I argue to the contrary that inertial frames are not needed in Newton’s theory of motion, and that the right space-time structure for Newton’s Principia requires the notion of parallelism of spatial directions at different times and nothing more. Only relative motions are definable in this framework, never absolute (...) ones. (shrink)

Hume notoriously maintains that contiguity, succession, and constant conjunction are individually necessary and jointly sufficient conditions of causation. While his arguments for the necessity of constant conjunction have been thoroughly dissected, his arguments for contiguity and succession have generally been either ignored or misstated. I hope both to correct this unfortunate state of affairs and to show some fatal defects in Hume's account.The pertinent passages in Hume's writings acknowledge three conceivable ways in which the temporal relation between causes and effects (...) might be construed: as separated by some interval; as perfectly contiguous, so that the effect succeeds the cause in the very next moment; as perfectly contemporaneous, existing at the same moment. Hume defends the correctness of and denies the tenability of both and. (shrink)

I defend a how-possibly argument for Kantian (or Kant*-ian) transcendental idealism, drawing on concepts from David Chalmers, Nick Bostrom, and the cyberpunk subgenre of science fiction. If we are artificial intelligences living in a virtual reality instantiated on a giant computer, then the fundamental structure of reality might be very different than we suppose. Indeed, since computation does not require spatial properties, spatiality might not be a feature of things as they are in themselves but instead only the way that (...) things necessarily appear to us. It might seem unlikely that we are living in a virtual reality instantiated on a non-spatial computer. However, understanding this possibility can help us appreciate the merits of transcendental idealism in general, as well as transcendental idealism’s underappreciated skeptical consequences. (shrink)

I examine here if Kant can explain our knowledge of duration by showing that time has metric structure. To do so, I spell out two possible solutions: time’s metric could be intrinsic or extrinsic. I argue that Kant’s resources are too weak to secure an intrinsic, transcendentally-based temporal metrics; but he can supply an extrinsic metric, based in a metaphysical fact about matter. I conclude that Transcendental Idealism is incomplete: it cannot account for the durative aspects of experience—or it can (...) do so only with help from a non-trivial metaphysics of material substance. (shrink)

In a recent article in this journal, Barbara Lariviere offers a very useful distinction between two ways of understanding the claims that Leibniz, or relational theorists in general, might wish to make about the nature of motion and the structure of space and time; viz., There is no real inertial structure to space-time.and There is a real inertial structure to space-time, but it is dynamical rather than absolute.Citing the authority of Weyl, the author argues that L1 is untenable; indeed, the (...) argument purports to show that if L1 were true, then there would be no coherent basis for a theory of motion, not even a relational theory. My main goal in this note is to point out why this argument is mistaken while at the same time sketching the real reason why the relational conception of motion is untenable. In addition I will offer a few remarks about the relevance of L2 to the absolute-relational controvery. (shrink)

This paper distinguishes between 3 meanings of reversal, all of which are mathematically equivalent in classical mechanics: velocity reversal, retrodiction, and time reversal. It then concludes that in order to have well defined velocities a primitive arrow of time must be included in every time slice. The paper briefly mentions that this arrow cannot come from the Second Law of thermodynamics, but this point is developed in more details elsewhere.

What is the meaning of general covariance? We learn something about it from the hole argument, due originally to Einstein. In his search for a theory of gravity, he noted that if the equations of motion are covariant under arbitrary coordinate transformations, then particle coordinates at a given time can be varied arbitrarily - they are underdetermined - even if their values at all earlier times are held fixed. It is the same for the values of fields. The argument can (...) also be made out in terms of transformations acting on the points of the manifold, rather than on the coordinates assigned to the points. So the equations of motion do not fix the particle positions, or the values of fields at manifold points, or particle coordinates, or fields as functions of the coordinates, even when they are specified at all earlier times. It is surely the business of physics to predict these sorts of quantities, given their values at earlier times. The principle of general covariance therefore seems untenable. (shrink)

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

In this paper I examine the connection between symmetry and modality from the perspective of `reduction' methods in geometric mechanics. I begin by setting the problem up as a choice between two opposing views: reduction and non-reduction. I then discern four views on the matter in the literature; they are distinguished by their advocation of distinct geometric spaces as representing `reality'. I come down in favour of non-reductive methods.

Lexical evidence reveals that ordinary notions of space underwent a dramatic change from the late seventeenth century into the first decades of the nineteenth century: the word’s core meaning metamorphosed from INTERVAL to DIMENSION, revolutionizing relations between ordinary conceptions of time and space. Analyzing instances of the word in French over the years 1330–1835 indicates this conceptual change of SPACE was concurrent with growing interest in metaphysics and natural philosophy and echoed debates—provoked by Newton’s Principia (1687)—over the precise nature of (...) space. Employing both quantitative and qualitative methodologies, I show how changes in philosophical and scientific theory reshaped the general lexicon. I argue that ordinary lexical mechanisms largely determine the manner of science’s dissemination into culture and propose a model accounting for such changes. (shrink)

Can one deny the intelligibility of “extramental nonbeing” in pure ontology while affirming its intelligibility in physics? When one sweeps the heavens clean of matter does one also necessarily affirm the existence of absolute nonbeing in those “clean” spaces? Does talking about space necessarily mean talking about nonbeing? How could there possibly be “space” which is not absolute nothingness? How, if at all, can statements about space be reconciled with such self-contradictory statements as “What is not, is“?The purpose of this (...) brief paper is not to argue, within the context of the physical sciences, about whether or not there exist voids or absolutely empty spaces in the universe. Neither is it to discuss the existence or nonexistence of the aether. And although I shall be using texts taken from several famous historical figures, my purpose is not primarily historical. (shrink)