Newton and Leibniz had profound disagreements concerning metaphysics and the relationship of mathematics to natural philosophy, as well as deeply opposed attitudes towards analysis. Nevertheless, or so I shall argue, despite these deeply held and distracting differences in their background assumptions and metaphysical views, there was a considerable consilience in their positions on the status of infinitesimals. In this paper I compare the foundation Newton provides in his Method Of First and Ultimate Ratios (sketched at some time between 1671 and (...) 1684, and published in the Principia of 1687) with that provided independently by Leibniz in his unpublished manuscript De quadratura arithmetica (1675-6) as well as in later writings. I argue that both appeal to a version of the Archimedean Axiom to underwrite their use of infinitesimal techniques, which must be interpreted as a shorthand for rigorously finitist methods. (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)

The insights described by Nevin & Grace may be summarized without reference to the Newtonian concepts they suggest. The metaphor to Newtonian mechanics seems dubious in three ways: (1) extensions seem to lead to paradoxes; (2) many well-known phenomena are ignored; (3) the Newtonian concepts seem difficult to reconcile with the larger framework of evolutionary theory.

This paper reexamines the historical debate between Leibniz and Newton on the nature of space. According to the traditional reading, Leibniz (in his correspondence with Clarke) produced metaphysical arguments (relying on the Principle of Sufficient Reason and the Principle of Identity of Indiscernibles) in favor of a relational account of space. Newton, according to the traditional account, refuted the metaphysical arguments with the help of an empirical argument based on the bucket experiment. The paper claims that Leibniz’s and Newton’s arguments (...) cannot be understood apart from the distinct dialectics of their respective positions vis-à-vis Descartes’ theory of space and physics. Against the traditional reading, the paper argues that Leibniz and Newton are operating within a different metaphysics and different conceptions of “place,” and that their respective arguments can largely remain intact without undermining the other philosopher’s conception of space. The paper also takes up the task of clarifying the distinction between true and absolute motion, and of explaining the relativity of motion implied by Leibniz’s account. The paper finally argues that the two philosophers have different conceptions of the relation between metaphysics and science, and that Leibniz’s attempt to base physical theory on an underlying metaphysical account of forces renders his account of physics unstable. (shrink)

In this paper we argue that the primary issue in Descartes’ Principles of Philosophy, Part II, articles 1-40, is the problem of individuating bodies. We demonstrate that Descartes departs from the traditional quest for a principle of individuation, moving to a different strategy with the more modest aim of constructing bodies adequate to the needs of his cosmology. In doing this he meets with a series of difficulties, and this is precisely the challenge that Newton took up. We show that (...) Descartes’ questions and his strategy influenced not only Newton’s account of physical bodies, but also the structure of his mechanics. (shrink)

European philosophy from the late seventeenth century through most of the eighteenth is broadly conceived as the "Enlightenment," a period of empricist reaction to the great seventeeth century Rationalists. This volume begins with Herbert of Cherbury and the Cambridge Platonists and with Newton and the early English Enlightenment. Locke is a key figure, as a result of his importance both in the development of British and Irish philosophy and because of his seminal influence in the Enlightenment as a whole. British (...) Philosophy and the Age of the Enlightenment includes discussion of the Scott Enlightenment and its influence on the German Aufklaring , and consequently on Kant. The French Enlightenment, which in turn affected the late radical Enlightenment, especially Bentham, is also considered here. This survey brings together clear, authorative chapters from leading experts and provides a scholarly introduction to this period in the history of philosophy. It includes a glossary of technical terms and a chronological table of important political, philosophical, scientific and other cultural events. (shrink)

My object is to question a recurrent claim made to the point that Thomas Reid (1710–1796) was hostile to ether theories and that this hostility had its source in his distinctive interpretation of the first of Newton's regulæ philosophandi. Against this view I will argue that Reid did not have any quarrel at all with unobservable or theoretical entities as such, and that his objections against actual theories concerning ether were scientific rather than philosophical, even when based on Newton's first (...) rule. I argue further that Reid's insistence on Newton's rule concerns, not direct observation, but rather the notion of explanation itself. (shrink)

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)

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 book presents extracts from Leibniz's letters to Newtonian scientist Samuel Clarke.

In this volume a team of distinguished contributors examine all the main aspects of Newton s thought, including not only his approach to space, time, mechanics, ...

I argue that, while Hume’s approach to Newton is sometimes critical and sometimes not, Hume’s position with regard to newtonian method is coherent overall. Rather than speaking of two Humes (one a newtonian, the other not), from an humean perspective we should rather speak of two Newtons: the positivist and the theologian.

It is common wisdom in intellectual history that eighteenth-century science of man evolved under the aegis of Newton. It is also frequently suggested that David Hume, one of the most influential practitioners of this kind of inquiry, aspired to be the Newton of the moral sciences. Usually this goes hand in hand with a more or less explicit reading of Hume’s theory of human nature as written in an idiom of particulate inert matter and active forces acting on it, i.e. (...) essentially that of Newton’s Principia. Hume’s outlook on the mental world is thus frequently described in terms of conceptual atoms whose association is compared to interparticulate attractions analogous with Newtonian forces in general, and gravity in particular. In the present paper I argue that Hume’s theory can indeed be understood in Newton’s wake, but not in the context of the Principa’s reception but that of the Opticks, which exerted a more significant influence on natural inquiry in eighteenth-century Scotland. I intend to show that Hume speaks a language and represents an outlook on human matters convergent with “philosophical chemistry” in Scotland at that time, and particularly to his later friend and physician William Cullen. (shrink)

Current philosophical reflections on science have departed from mainstream history of science with respect to both methodology and conclusions. The article investigates how different approaches to reconstructing commitments can explain these differences and facilitate a mutual understanding and communication of these two perspectives on science. Translating the differences into problems pertaining to principles of charity, the paper offers a platform for clarification and resolution of the differences between the two perspectives. The outlined contextual approach occupies a middle ground between mainstream (...) history and sociology of science, bracketing questions of rationality, and individual coherence-maximizing, rationality-centered approaches. It can satisfy those, who believe that science is an epistemically privileged endeavor, and its epistemic content should not be neglected when reconstructing the scientists’ positions. It can also satisfy those who hold that it is naive to believe that the immediate context, e.g. the challenges to a theory, the expectations of the author about his audience, etc., does not affect the position a scientist takes. Its theoretical considerations are exemplified with a close study of the debate following the 1672 publication of Newton's theory of light and colours, also offering a novel reading of the development of his methodological views concerning the demonstrativity of the famous crucial experiment. Although we only show the capacity of the framework to analyze a direct controversy, given that it is hard to think about any scientific text as detached from an argumentative context, this approach has the potential to be a general guide for interpretation. (shrink)

Presenting the history of space-time physics, from Newton to Einstein, as a philosophical development DiSalle reflects our increasing understanding of the connections between ideas of space and time and our physical knowledge. He suggests that philosophy's greatest impact on physics has come about, less by the influence of philosophical hypotheses, than by the philosophical analysis of concepts of space, time, and motion and the roles they play in our assumptions about physical objects and physical measurements. This way of thinking leads (...) to new interpretations of the work of Newton and Einstein and the connections between them. It also offers new ways of looking at old questions about a priori knowledge, the physical interpretation of mathematics, and the nature of conceptual change. Understanding Space-Time will interest readers in philosophy, history and philosophy of science, and physics, as well as readers interested in the relations between physics and philosophy. (shrink)

Abstract Einstein intended the general theory of relativity to be a generalization of the relativity of motion and, therefore, a radical departure from previous spacetime theories. It has since become clear, however, that this intention was not fulfilled. I try to explain Einstein's misunderstanding on this point as a misunderstanding of the role that spacetime plays in physics. According to Einstein, earlier spacetime theories introduced spacetime as the unobservable cause of observable relative motions and, in particular, as the cause of (...) inertial effects of ?absolute? motion. I use a comparative analysis of Einstein and Newton to show that spacetime is not introduced as an explanation of observable effects, but rather is defined through those effects in arguments like Newton's ?water bucket? argument and Einstein's argument for special relativity. I then argue that to claim that a spacetime theory is true, or to claim that a spacetime structure is ?real?, is not to claim that a theoretical object explains the observable. Rather, it is to claim that the fundamental definitions that link spacetime structure to physical phenomena are empirically sound, i.e. that they can be successfully applied empirically. This leads to a new and clearer view of the empirical content of spacetime theories and of the meaning of ?realism? about spacetime. (shrink)

Commentators attempting to understand the empirical method that Isaac Newton applies in his Mathematical Principles of Natural Philosophy (1687) are forced to grapple with the thorny issue of how to reconcile Newton's rejection of hypotheses with his appeal to absolute space. On the one hand, Newton claims that his experimental philosophy does not rely on claims that are assumed without empirical evidence, and on the other hand, Newton appeals to an absolute space that, by his own characterization, does not make (...) any impressions on our senses. Howard Stein (1967, 2002) has offered an insightful strategy for reconciling this apparent contradiction and suggested a way to enhance our understanding of Newton's 'empiricism' such that absolute space can be preserved as a legitimate part of Newton's experimental project. Recently, Andrew Janiak (2008) has posed a worthy challenge to Stein's empirical reading of Newton and directed our attention to the metaphysical commitments that underlie the experimental philosophy of Newton's Principia . Although Stein and Janiak disagree on the degree to which Newton's empiricism influences his natural philosophy, both agree and clearly show that an adequate treatment of Newton's empiricism cannot be divorced from consideration of Newton's views on God and God's relationship to nature. (shrink)

In the Preface to the Principia (1687) Newton famously states that “geometry is founded on mechanical practice”. Several commentators have taken this and similar remarks as an indication that Newton was firmly situated in the constructivist tradition of geometry that was prevalent in the seventeenth century. By drawing on a selection of Newton’s unpublished texts, I hope to show the faults of such an interpretation. In these texts, Newton not only rejects the constructivism that took its birth in Descartes’ Géométrie (...) (1637); he also presents the science of geometry as being more powerful than his Principia remarks may lead us to believe. (shrink)

Mathematical and philosophical Newton Content Type Journal Article Pages 1-10 DOI 10.1007/s11016-010-9520-2 Authors Steffen Ducheyne, Centre for Logic and Philosophy of Science, Ghent University, Blandijnberg 2, 9000 Ghent, Belgium Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796.

In this essay, I attempt to assess Henk de Regt and Dennis Dieks recent pragmatic and contextual account of scientific understanding on the basis of an important historical case-study: understanding in Newton’s theory of universal gravitation and Huygens’ reception of universal gravitation. It will be shown that de Regt and Dieks’ Criterion for the Intelligibility of a Theory (CIT), which stipulates that the appropriate combination of scientists’ skills and intelligibility-enhancing theoretical virtues is a condition for scientific understanding, is too strong. (...) On the basis of this case-study, it will be shown that scientists can understand each others’ positions qualitatively and quantitatively, despite their endorsement of different worldviews and despite their convictions as what counts as a proper explanation. (shrink)

Here, I shall argue that Van Helmont needs to be added to the list of sources on which Newton drew when formulating his doctrine of absolute time. This by no means implies that Van Helmont is the factual source of Newton's views on absolute time (I have found no clear-cut evidence in support of this claim). It is by no means my aim to debunk the importance of the other sources, but rather to broaden them. Different authors help to explain (...) different aspects of Newton's conception of absolute time. (shrink)

The Reeh-Schlieder theorem asserts the vacuum and certain other states to be spacelike superentangled relative to local fields. This motivates an inquiry into the physical status of various concepts of localization. It is argued that a covariant generalization of Newton-Wigner localization is a physically illuminating concept. When analyzed in terms of nonlocally covariant quantum fields, creating and annihilating quanta in Newton-Wigner localized states, the vacuum is seen to not possess the spacelike superentanglement that the Reeh-Schlieder theorem displays relative to local (...) fields, and to be locally empty as well as globally empty. Newton-Wigner localization is then shown to be physically interpretable in terms of a covariant generalization of the center of energy, the two localizations being identical if the system has no internal angular momentum. Finally, some of the counterintuitive features of Newton-Wigner localization are shown to have close analogues in classical special relativity. (shrink)

In this paper I will attempt to show how incommensurability between theories is usually manifested, framing this notion in a sense similar to the Kuhnian one in certain aspects, though very different in others. Further, I will show that it is possible, and desirable, to rid Kuhn’s thesis of the idea that in many important theories a certain part of the theoretical nucleus partially contains in a more or less vague sense, synthetic a priori or even analytic statements. Alternatively, I (...) present a motive for the change of meaning in the basic terms of a theory wherein fundamental laws maintain their synthetic a posteriori character. Incommensurability in this case has to do with the change of lexicon for internal properties, independently of whether or not there is a change in the meaning of the primitive terms of the theory. (shrink)

Cartesian method both organizes and impoverishes the domains to which Descartes applies it. It adjusts geometry so that it can be better integrated with algebra, and yet deflects a full-scale investigation of curves. It provides a comprehensive conceptual framework for physics, and yet interferes with the exploitation of its dynamical and temporal aspects. Most significantly, it bars a fuller unification of mathematics and physics, despite Descartes' claims to quantify nature. The work of his contemporaries Galileo and Torricelli, and of his (...) successor Newton, illustrates conceptual possibilities Descartes left aside, due to his attachment to method. (shrink)

The traditional absolutist-relationist debate is still clearly formulable in the context of General Relativity Theory (GTR), despite the important differences between Einstein's theory and the earlier context of Newtonian physics. This paper answers recent arguments by Robert Rynasiewicz against the significance of the debate in the GTR context. In his (1996) (‘Absolute vs. Relational Spacetime: An Outmoded Debate?’), Rynasiewicz argues that already in the late nineteenth century, and even more so in the context of General Relativity theory, the terms of (...) the original Descartes–Newton–Leibniz dispute about space are not to be found. Nineteenth-century ether theories of electromagnetism, and the metric field of GTR, he claims, do not lend themselves to being interpreted clearly as either absolute space à la Newton, or relational structures à la either Descartes or Leibniz. I argue that, while in some imaginable theories Rynasiewicz's claim that the classical debate dissolves would be correct, in fact in the most important historical theories he discusses, this is not the case. In particular, I argue that in both Lorentz's ether theory and General relativity theory, there is a clear and compelling way to establish connections to the classical absolutist-relationist disputes, and that in both these theories it is the absolutist position that is prima facie victorious. To support my arguments and give a clear overview of the whole debate, I end by offering definitional sketches of relationism and absolutism (substantivalism) about spacetime in the context of contemporary physics. The sketches show the clear connections between these views today and their ancestors in Newton and Leibniz. But at the same time, they indicate how both views are not just claims about existing physical theories, but rather also bets about how future physics will clarify the ontological picture. (shrink)

Where should we begin our story? Many books start with Newton, but Newton was responding to both Galileo1 and especially (for our purposes) Descartes. But Galileo and Descartes themselves were writing in the context of late Aristotelianism, and so were trained in and critical of that rich school of thought, so if we want to fully understand their work we would need to understand scholastic views on space and motion (see Grant, 1974, Murdoch and Sylla, 1978 and Ariew and Gabbey, (...) 1998). But late scholasticism itself is the result of a long history tracing from Plato and Aristotle through Jewish, Arabic, Islamic and European thought. And of course Plato and Aristotle are explicitly reacting to their predecessors and contemporaries. In other words, we could start the story as early in recorded thought as we like. (shrink)