While many take Newton's argument for absolute space to be an inference to the best explanation, some argue that Newton is primarily concerned with the proper definition of true motion, rather than with independent existence of spatial points. To an extent the latter interpretation is correct. However, all prior interpretations are mistaken in thinking that 'absolute motion' is defined as motion with respect to absolute space. Newton is also using this notion to refer to the quantity of motion (momentum). This (...) reading reveals a misunderstood argument for absolute space, according to which absolute space is necessary for a workable definition of momentum. (shrink)

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)

In this paper I offer a fresh interpretation of Leibniz’s theory of space, in which I explain the connection of his relational theory to both his mathematical theory of analysis situs and his theory of substance. I argue that the elements of his mature theory are not bare bodies (as on a standard relationalist view) nor bare points (as on an absolutist view), but situations. Regarded as an accident of an individual body, a situation is the complex of its angles (...) and distances to other co-existing bodies, founded in the representation or state of the substance or substances contained in the body. The complex of all such mutually compatible situations of co-existing bodies constitutes an order of situations, or instantaneous space. Because these relations of situation change from one instant to another, space is an accidental whole that is continuously changing and becoming something different, and therefore a phenomenon. As Leibniz explains to Clarke, it can be represented mathematically by supposing some set of existents hypothetically (and counterfactually) to remain in a fixed mutual relation of situation, and gauging all subsequent situations in terms of transformations with respect to this initial set. Space conceived in terms of such allowable transformations is the subject of Analysis Situs. Finally, insofar as space is conceived in abstraction from any bodies that might individuate the situations, it encompasses all possible relations of situation. This abstract space, the order of all possible situations, is an abstract entity, and therefore ideal. (shrink)

The selections contained in these volumes from the papers and letters of Leibniz are intended to serve the student in two ways: first, by providing a more adequate and balanced conception of the full range and penetration of Leibniz's creative intellectual powers; second, by inviting a fresher approach to his intellectual growth and a clearer perception of the internal strains in his thinking, through a chronological arrangement. Much confusion has arisen in the past through a neglect of the develop ment (...) of Leibniz's ideas, and Couturat's impressive plea, in his edition of the Opuscu/es et fragments (p. xii), for such an arrangement is valid even for incomplete editions. The beginning student will do well, however, to read the maturer writings of Parts II, III, and IV first, leaving Part I, from a period too largely neglected by Leibniz criticism, for a later study of the still obscure sources and motives of his thought. The Introduction aims primarily to provide cultural orientation and an exposition of the structure and the underlying assumptions of the philosophical system rather than a critical evaluation. I hope that together with the notes and the Index, it will provide those aids to the understanding which the originality of Leibniz's scientific, ethical, and metaphysical efforts deserve. (shrink)

The correspondence between Leibniz and Samuel Clarke was probably the most famous and influential philosophical exchange of the eighteenth century. It focused on the clash between the Newtonian and Leibnizian world systems, involving disputes in physics, theology, and metaphysics. Vailati's book provides a comprehensive overview and commentary on this important body of letters. He not only identifies and evaluates the various arguments, but situates the views advanced by the correspondence in the context of their principal writings.

My talk today will be about Newton’s avowed methodology, and specifically the place of experiment in his conception of science, and how his ideas changed significantly over the course of his career. I also want to look at his actual scientific practice and see how this influenced his views on the nature of the experimental sciences.

As I have read the scholium, it divides into three main parts, not including the introductory paragraph. The first consists of paragraphs one to four in which Newton sets out his characterizations of absolute and relative time, space, place, and motion. Although some justificatory material is included here, notably in paragraph three, the second part is reserved for the business of justifying the characterizations he has presented. The main object is to adduce grounds for believing that the absolute quantities are (...) indeed distinct from their relative measures and are not reducible to them. Paragraph five takes this up for the case of time. Paragraphs eight to twelve endeavor to do this for rest and motion by appealing to their properties, causes and effects. In arguing that absolute motion is not reducible to any particular form of the relative motion of bodies with respect to one another, and thus, as is directly argued in the third argument, must be understood in terms of motionless places, Newton thereby constructs an indirect case that absolute space is indeed something distinct from any relative space. Paragraph thirteen functions as conclusion to this line of inquiry and comments on how, in the light of this, the names of these quantities are to be interpreted in the scriptures. The third and final part consists of paragraph fourteen alone, and addresses the question: given that true motion is motion with respect to absolute space, but the parts of the latter are not perceivable, is it possible for us to know the true motions of individual bodies? Newton illustrates how this may be done from the evidence provided by their apparent motions and the forces which are the causes and effects of true motion. This forms a bridge to the body of the work insofar as the purpose of the Principia, according to Newton, is to show how this, and the converse problem, of inferring true and apparent motions from the forces, can be dealt with.Part II of this paper will appear in the next issue of Studies in History and Philosophy of Science. (shrink)

In Section 21 of his fifth letter to Clarke Leibniz attempts to derive the Identity of Indiscernibles from an application of the Principle of Sufficient Reason to God´s act of creation, namely that God has a reason to create the world he creates. In this paper I argue that this argument fails, not just because the Identity of Indiscernibles is false, but because there is a counterexample to one of the premises that Leibniz cannot satisfactorily rule out.

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)

Department of History and Philosophy of Science. University of Cambridge, Free School Lane, Cambridge CB2 3RH This paper is concerned with the question of whether atomic particles of the same species, i. e. with the same intrinsic state-independent properties of mass, spin, electric charge, etc, violate the Leibnizian Principle of the Identity of Indiscernibles, in the sense that, while there is more than one of them, their state-dependent properties may also all be the same. The answer depends on what exactly (...) the state-dependent properties of atomic particles are taken to be. On the plausible interpretation that these should comprise all monadic and relational properties that can be expressed in terms of physical magnitudes associated with self-adjoint operators that can be defined for the individual particles, then the weakest form of the Principle is shown to be violated for bosons, fermions and higher-order paraparticles, treated in first quantization *Some of the arguments inn this paper appeared in a thesis submited by one of us (S.F.) In partial fulfilment of the requirements for the PhD degree of the University of London, in 1984. entitled 'Identity and ‘Individuality in Classical and Quantum Physics’. (shrink)

Some recent work in the philosophy of quantum mechanics has suggested that quantum systems can be thought of as non-separable and therefore non-individual, in some sense, in Bell and E.P.R. type situations. This suggestion is set in the context of previous work regarding the individuality of quantal particles and it is argued that such entities can be considered as individuals if their non-classical statistical correlations are understood in terms of non-supervenient relations holding between them. We conclude that such relations are (...) strongly non-supervenient in Cleland's sense and note a possible connection between this idea and the realist quantum logic programme. (shrink)

Volumes I and II provided a completely new translation of the philosophical works of Descartes, based on the best available Latin and French texts. Volume III contains 207 of Descartes' letters, over half of which have previously not been translated into English. It incorporates, in its entirety, Anthony Kenny's celebrated translation of selected philosophical letters, first published in 1970. In conjunction with Volumes I and II it is designed to meet the widespread demand for a comprehensive, authoritative and accurate edition (...) of Descartes' philosophical writings in clear and readable modern English. (shrink)

Tout au long de sa vie Leibniz remettra sur le metier le projet d'un calcul geometrique qui exprime directement, et non par le biais des equations de l'analyse, les relations purement geometriques et leur degre zero, la situation ou situs. Dans cet echantillon de caracteristique universelle il n'est guere difficile d'identifier les premisses de la topologie moderne. Nous trouvons ici un apercu quasi complet (et en grande partie inedit) de la premiere phase des travaux leibniziens, dont l'objectif initial est a (...) lui seul une gageure, la reforme de l'axiomatique euclidienne. (shrink)

`Mr Russell's very brilliant criticism of Leibniz ... is a piece of controversial philosophy as well as a contribution to history.' - Bernard Bosanquet.

Presents Newton's unifying idea of gravitation and explains how he converted physics from a science of explanation into a general mathematical system.