Structural realist interpretations of generally relativistic spacetimes have recently come to enjoy a remarkable degree of popularity among philosophers. I present a challenge to these structuralist interpretations that arises from considering cosmological models in general relativity. As a consequence of their high degree of spacetime symmetry, these models resist a structuralist interpretation. I then evaluate the various strategies available to the structuralist to react to this challenge. †To contact the author, please write to: Department of Philosophy, 9500 Gilman Drive, 0119, (...) University of California, San Diego, La Jolla, CA 92093‐0119; e‐mail: [email protected]. (shrink)

This paper presents two interpretations of the fiber bundle fonnalism that is applicable to all gauge field theories. The constructionist interpretation yields a substantival spacetime. The analytic interpretation yields a structural spacetime, a third option besides the familiar substantivalism and relationalism. That the same mathematical fonnalism can be derived in two different ways leading to two different ontological interpretations reveals the inadequacy of pure fonnal arguments.

This essay explores the possibility of constructing a structural realist interpretation of spacetime theories that can resolve the ontological debate between substantivalists and relationists. Drawing on various structuralist approaches in the philosophy of mathematics, as well as on the theoretical complexities of general relativity, our investigation will reveal that a structuralist approach can be beneficial to the spacetime theorist as a means of deflating some of the ontological disputes regarding similarly structured spacetimes.

This paper investigates the question of, and the degree to which, Newton’s theory of space constitutes a third-way between the traditional substantivalist and relationist ontologies, i.e., that Newton judged that space is neither a type of substance/entity nor purely a relation among such substances. A non-substantivalist reading of Newton has been famously defended by Howard Stein, among others; but, as will be demonstrated, these claims are problematic on various grounds, especially as regards Newton’s alleged rejection of the traditional substance/accident dichotomy (...) concerning space. Nevertheless, our analysis of the metaphysical foundations of Newton’s spatial theory will strive to uncover its unique and innovative characteristics, most notably, the distinctive role that Newton’s “immaterialist” spatial ontology plays in his dynamics. (shrink)

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)

Paragraph 6 of Newtons Scholium argues that the parts of space cannot move. A premise of the argument – that parts have individuality only through an order of position – has drawn distinguished modern support yet little agreement among interpretations of the paragraph. I argue that the paragraph offers an a priori, metaphysical argument for absolute motion, an argument which is invalid. That order of position is powerless to distinguish one part of Euclidean space from any other has gone virtually (...) unremarked. It remains uncertain what the import of the paragraph is but it is not close to apparently similar arguments of Leibniz. (shrink)

Paragraph 6 of Newton's Scholium argues that the parts of space cannot move. A premise of the argument -- that parts have individuality only through an "order of position" -- has drawn distinguished modern support yet little agreement among interpretations of the paragraph. I argue that the paragraph offers an a priori, metaphysical argument for absolute motion, an argument which is invalid. That "order of position" is powerless to distinguish one part of Euclidean space from any other has gone virtually (...) unremarked. It remains uncertain what the import of the paragraph is but it is not close to apparently similar arguments of Leibniz. (shrink)

Manuscript Add. 3965, section 13, folios 541r–542r and 545r–546r is in the Portsmouth Collection of manuscripts and housed in the University Library, Cambridge. These drafts contain a careful account, in Newton's hand, of his views on place, time, and God. They are part of a large number of drafts relating to the three official editions of the Principia published in Newton's lifetime.

Newton's arguments for the immobility of the parts of absolute space have been claimed to licence several proposals concerning his metaphysics. This paper clarifies Newton, first distinguishing two distinct arguments. Then, it demonstrates, contrary to Nerlich ([2005]), that Newton does not appeal to the identity of indiscernibles, but rather to a view about de re representation. Additionally, DiSalle ([1994]) claims that one argument shows Newton to be an anti-substantivalist. I agree that its premises imply a denial of a kind of (...) substantivalism, but I show that they are inconsistent with Newton's core doctrine that not all motion is the relative motions of bodies, and so conclude that they are not part of his considered views on space. The Arguments The Identity Argument 2.1 Identity of indiscernibles for individuals 2.2 Identity of indiscernibles for worlds and states 2.3 Representation de re Kinematic Relationism Conclusion CiteULike Connotea Del.icio.us What's this? (shrink)

Spacetime substantivalism leads to a radical form of indeterminism within a very broad class of spacetime theories which include our best spacetime theory, general relativity. Extending an argument from Einstein, we show that spacetime substantivalists are committed to very many more distinct physical states than these theories' equations can determine, even with the most extensive boundary conditions.

Debates about the ontological implications of the general theory of relativity have long oscillated between spacetime substantivalism and relationism. I evaluate such debates by claiming that we need a third option, which I refer to as “structural spacetime realism.” Such a tertium quid sides with the relationists in defending the relational nature of the spacetime structure, but joins the substantivalists in arguing that spacetime exists, at least in part, independently of particular physical objects and events, the degree of “independence” being (...) given by the extent to which geometrical laws exist “over and above” physical events exemplifying them. By showing that structural spacetime realism is the natural outcome of a semantic, model-theoretic approach to the nature of scientific theories, I conclude by arguing that the notion of partial isomorphic representation is the most plausible candidate to connect spacetime models with reality. (shrink)

Quantum field theory (QFT) combines quantum mechanics with Einstein's special theory of relativity and underlies elementary particle physics. This book presents a philosophical analysis of QFT. It is the first treatise in which the philosophies of space-time, quantum phenomena, and particle interactions are encompassed in a unified framework. Describing the physics in nontechnical terms, and schematically illustrating complex ideas, the book also serves as an introduction to fundamental physical theories. The philosophical interpretation both upholds the reality of the quantum world (...) and acknowledges the irreducible cognitive elements in its representation. The interpretation is based on an analysis of our ways of thinking as the are embedded in the logical structure of QFT. The author argues that philosophical categories are significant only if they play active and essential roles in our knowledge and hence constitute part of the theories in actual use. Thus she regards physical theories as primary, extracts their categorical structure, and uses it to rethink key philosophical questions. Among the questions this book tries to answer are: What are the quantum properties independent of measurements? How do we refer to individual things in a continuous field? How do theories relate to objects? What are the general conditions of the world and of our ways of thinking that make possible our knowledge of the microscopic realm, which is so intangible and counterintuitive? As a penetrating analysis of vital themes in contemporary science, the book will engage the interest of students and professionals in physics and philosophy alike. (shrink)

This paper presents two interpretations of the fiber bundle formalism that is applicable to all gauge field theories. The constructionist interpretation yields a substantival spacetime. The analytic interpretation yields a structural spacetime, a third option besides the familiar substantivalism and relationalism. That the same mathematical formalism can be derived in two different ways leading to two different ontological interpretations reveals the inadequacy of pure formal arguments.

Sir Isaac Newton (1642-1727) left a voluminous legacy of writings. Despite his influence on the early modern period, his correspondence, manuscripts, and publications in natural philosophy remain scattered throughout many disparate editions. In this volume, Newton's principal philosophical writings are for the first time collected in a single place. They include excerpts from the Principia and the Opticks, his famous correspondence with Boyle and with Bentley, and his equally significant correspondence with Leibniz, which is often ignored in favor of Leibniz's (...) later debate with Samuel Clarke. Newton's exchanges with Leibniz place their different understandings of natural philosophy in sharp relief. The volume also includes 'De Gravitatione', offered here in a corrected translation, which is crucial for understanding Newton's relation to his great predecessor Descartes. In a historical and philosophical introduction, Andrew Janiak examines Newton's philosophical positions and his relations to canonical figures in early modern philosophy. (shrink)

A magisterial study of the philosophy of physics that both introduces the subject to the non-specialist and contains many original and important contributions for professionals in the area. Modern physics was born as a part of philosophy and has retained to this day a properly philosophical concern for the clarity and coherence of ideas. Any introduction to the philosophy of physics must therefore focus on the conceptual development of physics itself. This book pursues that development from Galileo and Newton through (...) Maxwell and Boltzmann to Einstein and the founders of quantum mechanics. There is also discussion of important philosophers of physics in the eighteenth and nineteenth centuries and of twentieth-century debates. In the interest of appealing to the broadest possible readership the author avoids technicalities and explains both the physics and philosophical terms. (shrink)

Science Without Numbers caused a stir in 1980, with its bold nominalist approach to the philosophy of mathematics and science. It has been unavailable for twenty years and is now reissued in a revised edition with a substantial new preface presenting the author's current views and responses to the issues raised in subsequent debate.

Thomas Holden presents a fascinating study of theories of matter in the seventeenth and eighteenth centuries. These theories were plagued by a complex of interrelated problems concerning matter's divisibility, composition, and internal architecture. Is any material body infinitely divisible? Must we posit atoms or elemental minima from which bodies are ultimately composed? Are the parts of material bodies themselves material concreta? Or are they merely potentialities or possible existents? Questions such as these -- and the press of subtler questions hidden (...) in their amibiguities -- deeply unsettled philosophers of the early modern period. They seemed to expose serious paradoxes in the new world view pioneered by Galileo, Descartes, and Newton. The new science's account of a fundamentally geometrical Creation, mathematicizable and intelligible to the human inquirer, seemed to be under threat. This was a great scandal, and the philosophers of the period accordingly made various attempts to disarm the paradoxes. All the great figures address the issue: most famously Leibniz and Kant, but also Galileo, Hobbes, Newton, Hume, and Reid, in addition to a crowd of lesser figures. Thomas Holden offers a brilliant synthesis of these discussions and presents his own overarching interpretation of the controversy, locating the underlying problem in the tension between the early moderns' account of material parts on the one hand and the program of the geometrization of nature on the other. (shrink)

The primary objective of this study is to provide a description of the major ideas about void space within and beyond the world that were formulated between the fourteenth and early eighteenth centuries. The second part of the book - on infinite, extracosmic void space - is of special significance. The significance of Professor Grant's account is twofold: it provides the first comprehensive and detailed description of the scholastic Aristotelian arguments for and against the existence of void space; and it (...) presents (again for the first time) an analysis of the possible influence of scholastic ideas and arguments on the interpretations of space proposed by the nonscholastic authors who made the Scientific Revolution possible. The concluding chapter of the book is unique in not only describing the conceptualizations of space proposed by the makers of the Scientific Revolution, but in assessing the role of readily available scholastic ideas on the conception of space adopted for the Newtonian world. (shrink)

I argue that Norton & Earman's hole argument, despite its historical association with General Relativity, turns upon very general features of any linguistic system that can represent substances by names. After exploring various means by which mathematical objects can be interpreted as representing physical possibilities, I suggest that a form of essentialism can solve the hole dilemma without abandoning either determinism or substantivalism. Finally, I identify the basic tenets of such an essentialism in Newton's writings and consider how they can (...) be updated to apply to the case provided by General Relativity. (shrink)