Substantivalism is the view that space exists in addition to any material bodies situated within it. Relationalism is the opposing view that there is no such thing as space; there are just material bodies, spatially related to one another. This paper assesses this issue in the context of classical physics. It starts by describing the bucket argument for substantivalism. It then turns to anti-substantivalist arguments, including Leibniz's classic arguments and their contemporary reincarnation under the guise of ‘symmetry’. It argues that (...) these anti-substantivalist arguments are stronger than is often acknowledged. (shrink)

This paper investigates Newton’s ontology of space in order to determine its commitment, if any, to both Cambridge neo-Platonism, which posits an incorporeal basis for space, and substantivalism, which regards space as a form of substance or entity. A non-substantivalist interpretation of Newton’s theory has been famously championed by Howard Stein and Robert DiSalle, among others, while both Stein and the early work of J. E. McGuire have downplayed the influence of Cambridge neo-Platonism on various aspects of Newton’s own spatial (...) hypotheses. Both of these assertions will be shown to be problematic on various grounds, with special emphasis placed on Stein’s influential case for a non-substantivalist reading. Our analysis will strive, nonetheless, to reveal the unique or forward-looking aspects of Newton’s approach, most notably, his critical assessment of substance ontologies, that help to distinguish his theory of space from his neo-Platonic contemporaries and predecessors. (shrink)

Desde hace algunas décadas es un lugar común en la Industria Newton mencionar una y otra vez la creencia de Isaac Newton en una sabiduría perdida. Sin embargo, el trabajo de crítica e interpretación al respecto se ha limitado a enunciar esta creencia sin ensayar una interpretación. Quienes más han trabajado el problema se han limitado a mostrar cómo esta creencia era plausible en el contexto intelectual de la época señalando a predecesores y seguidores de Newton que compartían esta creencia. (...) En contraste con lo anterior, este artículo indaga cómo, desde puntos de vista epistemológicos y filosóficos, la sabiduría de los antiguos era para Newton una fuente legítima de información sobre el mundo y sus designios, proponiendo una distinción entre tiempo y temporalidad como niveles complementarios pero diferentes de indagación sobre lo creado. (shrink)

The author argues that Newton’s distinction between absolute and relative motion, i.e. the refusal to define motion in relation to sensible things, in “Scholium on time, space, place and motion” from _Mathematical Principles of Natural Philosophy_, stems in great part from his critical stance towards Descartes’s philosophy of nature. This is apparent from the comparison of “Scholium”, in which Descartes is not mentioned at all, with Newton’s criticism of him in his manuscript _De gravitatione_. The positive results of Newton’s encounter (...) with Descartes’s theory of motion is almost completely identical to those of the “Scholium”: the definition of motion must concern the whole body and not just its surface; instead of “mutual translation”, it must include the force that is the cause of the physical motion; the motion of the bodies is uniform and straightforward, which can only be achieved within absolute space. As far as the theory of motion is concerned, Newton’s philosophical challenge was always Descartes. (shrink)

Scholars have long recognized that Newton regarded Descartes as his principal philosophical interlocutor when composing the first edition of Philosophiae Naturalis Principia Mathematica in 1687. The arguments in the Scholium on space and time, for instance, can profitably be interpreted as focusing on the conception of space and motion in part two of Descartes's Principles of Philosophy (1644). What is less well known, however, is that this Cartesian conception, along with Descartes's attempt to avoid Galileo's fate in 1633, serves as (...) an essential background to understanding Newton's own (poorly understood) view of the theological implications of his theory of space and motion. In particular, after withdrawing Le Monde from publication in 1633 because of its Copernican leanings, Descartes later introduced what some regard as a “fudge factor” into the theory of motion in the Principles: from an ordinary perspective the earth does move; but from a philosophical one, it does not. This background indicates the novelty and originality of Newton's own attempt to explicate how scriptural passages concerning the motions of the heavenly bodies can be reconciled with the philosophical views he developed during the 1680s. New evidence from archival sources and correspondence supports this argument, shedding light on the Scholium and on Newton's conception of philosophy's relation to theology. (shrink)

Newton's Principia begins with eight formal definitions and a scholium, the so-called scholium on space and time. Despite a history of misinterpretation, scholars now largely agree that the purpose of the scholium is to establish and defend the de fi nitions of key concepts. There is no consensus, however, on how those definitions differ in kind from the Principia's formal definitions and why they are set-off in a scholium. The purpose of the present essay is to shed light on the (...) scholium by focusing on Newton's notion and use of de fi nition. The resulting view is developmental. I argue that when Newton first wrote the Principia, he viewed the scholium's definitions as items of “natural philosophy.” By the time of the third edition, however, he came to view their methodological status differently; he viewed them as belonging to the more qualified “manner of geometers.” I explicate the two methods of natural inquiry and draw out their implications for Newton's account of space. (shrink)

One of the issues dividing "absolutists" and "relationists" is the question whether all motion is relative motion or, in the words of Earman, spacetime has "structures that support absolute quantities of motion." This paper argues that, despite the enormous literature bearing on the topic, it is problematic to formulate a general criterion for when a quantity counts as absolute in contrast to merely relative in a way that is not hopelessly parasitic on other, presumably distinct, senses of "absolute." Furthermore, I (...) suggest that the vicissitudes of the evolution of the concept of absolute motion have contributed to this difficulty. (shrink)

Einstein regarded as one of the triumphs of his 1915 theory of gravity - the general theory of relativity - that it vindicated the action-reaction principle, while Newtonian mechanics as well as his 1905 special theory of relativity supposedly violated it. In this paper we examine why Einstein came to emphasise this position several years after the development of general relativity. Several key considerations are relevant to the story: the connection Einstein originally saw between Mach's analysis of inertia and both (...) the equivalence principle and the principle of general covariance, the waning of Mach's influence owing to de Sitter's 1917 results, and Einstein's detailed correspondence with Moritz Schlick in 1920. (shrink)

In the Scholium to the Definitions at the beginning of the {\em Principia\/} Newton distinguishes absolute time, space, place and motion from their relative counterparts and attempts to justify they are indeed ontologically distinct in that the absolute quantity cannot be reduced to some particular category of the relative, as Descartes had attempted by defining absolute motion to be relative motion with respect to immediately ambient bodies. Newton's bucket experiment, rather than attempting to show that absolute motion exists, is one (...) of five arguments from the properties, causes and effects of motion that attempts to show that no such program can succeed, and thus that true motion can be adequately analyzed only by invoking immovable places, i.e., the parts of absolute space. (shrink)

This paper has two goals. (i) I explore the limits of the mathematical theory of spacetime (more generally, differential geometry) as an analytical tool for interpreting early modern thought. While it dramatically clarifies some issues, it can also lead to misunderstandings of some figures, and is a very poor tool indeed for others - Leibniz in particular. (ii) I will show how to blunt a very influential argument against a relational conception of spacetime - the view that the properties and (...) relations of bodies exhaust the spatiotemporal. (shrink)