In this paper I challenge the usual interpretations of Newton's and Leibniz's views on the nature of space and the relativity of motion. Newton's ‘relative space’ is not a reference frame; and Leibniz did not regard space as defined with respect to actual enduring bodies. Newton did not subscribe to the relativity of intertial motions; whereas Leibniz believed no body to be at rest, and Newton's absolute motion to be a useful fiction. A more accurate rendering of the opposition between (...) them, I argue, leads to a wholly different understanding of Leibniz's theory of space, one which is not susceptible to the objections Newton had raised against Descartes regarding the representation of motion. This in turn suggests a new approach for contemporary theory of space, one which neither hypostatizes space nor tries to reduce it to relations among actual things. * This work was generously supported by the National Endowment for the Humanities, with a Fellowship for College Teachers and Independent Scholars (FB-26897-89), and also by a sabbatical leave from my institution, Middlebury College. Iam very grateful to various members of faculty of York University for their appreciative reception of an earlier one-week-old version of this paper. ‘Relative Space in Newton and Leibniz’, read to the Department of Philosophy there in January 1990, and to Robert Rynasiewicz for criticisms of an extract read at the 1991 History of Science meeting. (shrink)

This paper explores various metaphysical aspects of Leibniz’s concepts of space, motion, and matter, with the intention of demonstrating how the distinctive role of force in Leibnizian physics can be used to develop a theory of relational motion using privileged reference frames. Although numerous problems will remain for a consistent Leibnizian relationist account, the version developed within our investigation will advance the work of previous commentators by more accurately reflecting the specific details of Leibniz’s own natural philosophy, especially his handling (...) of the dynamical interactions of plenum bodies. (shrink)

I elaborate and defend an interpretation of Leibniz on which he is committed to a stronger space-time structure than so-called Leibnizian space-time, with absolute speeds grounded in his concept of force rather than in substantival space and time. I argue that this interpretation is well-motivated by Leibniz's mature writings, that it renders his views on space, time, motion, and force consistent with his metaphysics, and that it makes better sense of his replies to Clarke than does the standard interpretation. Further, (...) it illuminates the way in which Leibniz took his physics to be grounded in his metaphysics. (shrink)

Leibniz has been widely praised for maintaining against the Newtonians of his day the view that space and time are relative. At the same time, he has been roundly criticized for allowing that we can distinguish absolute from merely relative motion. This distribution of applause and criticism, I will argue, is in a measure unjustified. For on the one hand, those arguments, found in his correspondence with Clarke, by which Leibniz seeks to reject the view that space and time are (...) “something absolute” are for the most part unsatisfactory, and on the other hand, Leibniz was not so naive as his critics have supposed in allowing absolute motions. Sections I ‐ V of this essay will be concerned with the former issue; Leibniz's views on motion will be taken up in Section VI. The chief interest in all of this for present‐day philosophers may lie, not so much in the historical issues concerning Leibniz and the Newtonians, but in a meta‐philosophical question which inevitably arises from the historical issues, namely, the question whether developments in science can undermine the soundness of philosophical arguments which appeal to ordinary usage. (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)

Leibniz vertrat auf der einen Seite die Überzeugung, es gebe Relationen weder als abstrakte Universalien noch als konkrete Akzidenzen. Auf der anderen Seite war er überzeugt, daß es relationale Eigenschaften von physischen Gegenständen, die nicht auf nicht-relationale Eigenschaften dieser Objekte reduziert werden können, gebe. Die wirklichen Einzeldinge haben jedoch keine nicht-formalen relationalen Eigenschaften. Sie stehen zwar in Beziehung oder sind miteinander verknüpft, aber nur durch Perzeptionen, so daß der Begriff Beziehung hier ein Begriff der zweiten Ordnung ist. Die physische Welt (...) mit ihren relationalen Eigenschaften ist fundiert in den Monaden. Die Fundierung ist eine Reduktion, aber es ist ein Mißverständnis, wenn man diese Reduktion so beschreibt, als impliziere sie eine Reduktion von relationalen Eigenschaften physischer Gegenstände; denn ihre nicht relationalen Eigenschaften werden in gleicher Weise reduziert. (shrink)