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)

This paper develops and defends three related forms of relationism about spacetime against attacks by contemporary substantivalists. It clarifies Newton's globes argument to show that it does not bear on relations that fail to determine geodesic motions, since the inertial effects on which Newton relies are not simply correlated with affine structure, but must be understood in dynamical terms. It develops remarks by Sklar and van Fraassen into relational versions of Newtonian mechanics, and argues that Earman does not show them (...) to trivialize the debate. (shrink)

This paper considers the implications for the relational-substantival debate of observations of parity nonconservation in weak interactions, a much neglected topic. It is argued that 'geometric proofs' of absolute space, first proposed by Kant (1768), fail, but that parity violating laws allow 'mechanical proofs', like Newton's laws. Parity violating laws are explained and arguments analogous to those of Newton's Scholium are constructed to show that they require absolute spacetime structure--namely, an orientation--as Newtonian mechanics requires affine structure. Finally, it is considered (...) how standard relationist responses to Newton's argument might respond to the new challenge of parity nonconservation. (shrink)

Immanuel Kant's Metaphysical Foundations of Natural Science (1786) provides metaphysical foundations for the application of mathematics to empirically given nature. The application that Kant primarily has in mind is that achieved in Isaac Newton's Principia (1687). Thus, Kant's first chapter, the Phoronomy, concerns the mathematization of speed or velocity, and his fourth chapter, the Phenomenology, concerns the empirical application of the Newtonian notions of true or absolute space, time, and motion. This paper concentrates on Kant's second and third chapters—the Dynamics (...) and the Mechanics, respectively—and argues that they are best read as providing a transcendental explanation of the conditions for the possibility of applying the (mathematical) concept of quantity of matter to experience. Kant again has in mind the empirical measures of this quantity that Newton fashions in the Principia, and he aims to make clear, in particular, how Newton achieves a universal measure for all bodies whatsoever by projecting the static quantity of terrestrial weight into the heavens by means of the theory of universal gravitation. Kant is not attempting to prove a priori what Newton has established empirically but, rather, to clarify the character of Newton's mathematization by building Newton's empirical measures into the very concept of matter that is articulated in the Metaphysical Foundations. (shrink)

The paper investigates possible readings of the later Heisenberg's remarks on the nature of quantum states. It discusses, in particular, whether Heisenberg should be seen as a proponent of the epistemic conception of states – the view that quantum states are not descriptions of quantum systems but rather reflect the state assigning observers' epistemic relations to these systems. On the one hand, it seems plausible that Heisenberg subscribes to that view, given how he defends the notorious "collapse of the wave (...) function" by relating it to a sudden change in the epistemic situation of the observer registering a measured result. On the other hand, his remarks on quantum probabilities as "potentia" or "objective tendencies" are difficult to reconcile with such a reading. The accounts that are attributed to Heisenberg by the different possible readings considered are subjected to closer scrutiny; at the same time, their respective virtues and problems are discussed. _German_ Diese Arbeit untersucht mögliche Lesarten von Heisenbergs späten Bemerkungen über die Natur von Quantenzuständen. Insbesondere wird die Frage diskutiert, ob Heisenberg als Vertreter der epistemischen Auffassung von Quantenzuständen gelten kann – der Idee, dass Quantenzustände nicht Beschreibungen der objektiven Eigenschaften von Quantensystemen sind sondern die epistemischen Beziehungen von Beobachtern zu diesen Systemen widerspiegeln. Einerseits erscheint es plausibel, dass Heisenberg dieser Sichtweise zustimmt, wenn man sich ansieht, wie er den berüchtigten,,Kollaps der Wellenfunktion" verteidigt, indem er ihn mit einer plötzlichen Änderung in der Kenntnis des ein Messergebnis registrierenden Beobachters in Zusammenhang bringt. Andererseits sind seine Bemerkungen über quantenmechanische Wahrscheinlichkeiten als,,Potentia" oder,,objektive Tendenzen" mit einer solchen Lesart nur schwer in Einklang zu bringen. Die Positionen, die Heisenberg den verschiedenen möglichen Lesarten zufolge vertritt, werden eingehenden Untersuchungen unterzogen; gleichzeitig werden ihre jeweiligen Vorzüge und Probleme diskutiert. (shrink)

Utilizing Einstein’s comparison of General Relativity and Descartes’ physics, this investigation explores the alleged conventionalism that pervades the ontology of substantival and relationist conceptions of spacetime. Although previously discussed, namely by Rynasiewicz and Hoefer, it will be argued that the close similarities between General Relativity and Cartesian physics have not been adequately treated in the literature—and that the disclosure of these similarities bolsters the case for a conventionalist interpretation of spacetime ontology.

Newton characterizes the reasoning of Principia Mathematica as geometrical. He emulates classical geometry by displaying, in diagrams, the objects of his reasoning and comparisons between them. Examination of Newton’s unpublished texts shows that Newton conceives geometry as the science of measurement. On this view, all measurement ultimately involves the literal juxtaposition—the putting-together in space—of the item to be measured with a measure, whose dimensions serve as the standard of reference, so that all quantity is ultimately related to spatial extension. I (...) use this conception of Newton’s project to explain the organization and proofs of the first theorems of mechanics to appear in the Principia. The placementof Kepler’s rule of areas as the first proposition, and the manner in which Newton proves it, appear natural on the supposition that Newton seeks a measure, in the sense of a moveable spatial quantity, of time. I argue that Newton proceeds in this way so that his reasoning can have the ostensive certainty of geometry. (shrink)

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)

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)

Discussions of the metaphysical status of spacetime assume that a spacetime theory offers a causal explanation of phenomena of relative motion, and that the fundamental philosophical question is whether the inference to that explanation is warranted. I argue that those assumptions are mistaken, because they ignore the essential character of spacetime theory as a kind of physical geometry. As such, a spacetime theory does notcausally explain phenomena of motion, but uses them to construct physicaldefinitions of basic geometrical structures by coordinating (...) them with dynamical laws. I suggest that this view of spacetime theories leads to a clearer view of the philosophical foundations of general relativity and its place in the historical evolution of spacetime theory. I also argue that this view provides a much clearer and more defensible account of what is entailed by realism concerning spacetime. (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)

I argue that there is natural relationist interpretation of Newtonian and relativistic non-quantum physics. Although relationist, this interpretation does not fall prey to the traditional objections based on the existence of inertial effects.

Textbooks present classical particle and field physics as theories of physical systems situated in Newtonian absolute space. This absolute space has an influence on the evolution of physical processes, and can therefore be seen as a physical system itself; it is substantival. It turns out to be possible, however, to interpret the classical theories in another way. According to this rival interpretation, spatiotemporal position is a property of physical systems, and there is no substantival spacetime. The traditional objection that such (...) a relationist view could not cope with the existence of inertial effects and other manifestations of the causal efficacy of spacetime can be answered successfully. According to the new point of view, the spacetime manifold of classical physics is a purely representational device. It represents possible locations of physical objects or events; but these locations are physical properties inherent in the physical objects or events themselves and having no existence independently of them. In relativistic quantum field theory the physical meaning of the spacetime manifold becomes even less tangible. Not only does the manifold lose its status as a substantival container, but also its function as a representation of spacetime properties possessed by physical systems becomes problematic. 'Space and time' become ordering parameters in the web of properties of physical systems. They seem to regain their traditional meaning only in the non-relativistic limit in which the classical particle concept becomes approximately applicable. (shrink)

This paper concerns the rational reconstruction of physical theories initially advanced by F. P. Ramsey and later elaborated by Rudolf Carnap. The Carnap–Ramsey reconstruction of theoretical knowledge is a natural development of classical empiricist ideas, one that is informed by Russell's philosophical logic and his theories of propositional understanding and knowledge of matter ; as such, it is not merely a schematic representation of the notion of an empirical theory, but the backbone of a general account of our knowledge of (...) the physical world. Carnap–Ramsey is an illuminating approach to epistemological problems that remain with us, one whose difficulties are shared by accounts that have sought to replace it. 1 Introduction 2 Russell's theory of propositional understanding 3 Ramsey's primary and secondary systems 4 Carnap's reconstruction of the language of science and an observation of Newman 5 Extension of the foregoing to constructive empiricism 6 Putnam's model-theoretic argument and the semantic view of theories 7 The problem clarified and resolved. (shrink)

The analysis of theory-confirmation generally takes the deductive form: show that a theory in conjunction with physical data and auxiliary hypotheses yield a prediction about phenomena; verify the prediction; provide a quantitative measure of the degree of theory-confirmation this yields. The issue of confirmation for an entire framework either does not arise, or is dismissed in so far as frameworks are thought not to be the kind of thing that admits scientific confirmation. I argue that there is another form of (...) scientific reasoning that has not received philosophical attention, what I call Newtonian abduction, that does provide confirmation for frameworks as a whole, and does so in two novel ways. I further argue that Newtonian abduction is at least as important a form of reasoning in science as standard deductive and inductive forms. The form is beautifully summed up by Maxwell : “The true method of physical reasoning is to begin with the phenomena and to deduce the forces from them by a direct application of the equations of motion.”. (shrink)

The analysis of theory-confirmation generally takes the deductive form: show that a theory in conjunction with physical data and auxiliary hypotheses yield a prediction about phenomena; verify the prediction; provide a quantitative measure of the degree of theory-confirmation this yields. The issue of confirmation for an entire framework (e.g., Newtonian mechanics en bloc, as opposed, say, to Newton’s theory of gravitation) either does not arise, or is dismissed in so far as frameworks are thought not to be the kind of (...) thing that admits scientific confirmation. I argue that there is another form of scientific reasoning that has not received philosophical attention, what I call Newtonian abduction, that does provide confirmation for frameworks as a whole, and does so in two novel ways. (In particular, Newtonian abduction is not inference to the best explanation, but rather is closer to Peirce’s original idea of abduction.) I further argue that Newtonian abduction is at least as important a form of reasoning in science as standard deductive and inductive forms. The form is beautifully summed up by Maxwell (Proc Camb Philos Soc II:292–294, 1876): “The true method of physical reasoning is to begin with the phenomena and to deduce the forces from them by a direct application of the equations of motion.”. (shrink)

Making a history of the principle of inertia, as of any other principle or concept, is a complex but still possible operation. In this work it has been chosen to make a back story which seemed the most natural way for a reconstruction. On the way back, it has been decided to stop at the 6th century CE with the contribution of Ioannes Philoponus. The principle he stated, although very different from the modern one, is certainly associated with it. Going (...) back in time it is still possible and of course one could proceed to the origins of the homo sapiens who perhaps posed the problem of why a club thrown with his hand could go so far from him. But the similarities that one can find with the modern principle are very vague, too perhaps. Without going so far one could see an embryonic idea of the principle of inertia in the atomistic theory of Democritus in the 5th century BCE. The motion of atoms whirling with no apparent reason can suggest the idea that a body can also move with no reason. But the transition from the atom, a metaphysical being, to the body, an empirical being, is far from immediate. (shrink)

We address a recent proposal concerning ‘surplus structure’ due to Nguyen et al.. We argue that the sense of ‘surplus structure’ captured by their formal criterion is importantly different from—and in a sense, opposite to—another sense of ‘surplus structure’ used by philosophers. We argue that minimizing structure in one sense is generally incompatible with minimizing structure in the other sense. We then show how these distinctions bear on Nguyen et al.’s arguments about Yang-Mills theory and on the hole argument.

I argue that Isaac Newton's De Gravitatione should not be considered an authoritative expression of his thought about the metaphysics of space and its relation to physical inquiry. I establish the following narrative: In De Gravitatione (circa 1668–84), Newton claimed he had direct experimental evidence for the work's central thesis: that space had "its own manner of existing" as an affection or emanative effect. In the 1710s, however, through the prodding of Roger Cotes and G. W. Leibniz, he came to (...) see that this evidence relied on assumptions that his own Principia rendered unjustifiable. Consequently, he (i) revised the conclusions he explicitly drew from the experimental evidence, (ii) rejected the idea that his spatial metaphysics was grounded in experimental evidence, and (iii) reassessed the epistemic status of key concepts in his metaphysics and natural philosophy. The narrative I explore shows not only that De Gravitatione did not constitute the metaphysical backdrop of the Principia as Newton ultimately understood it, but that it was the Principia itself that ultimately lead to the demise of key elements of De Gravitatione. I explore the implications of this narrative for Andrew Janiak's and Howards Stein's interpretations of Newton's metaphysics. (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)

This is a short, nontechnical introduction to features of time in classical and relativistic physics and their representation in the four-dimensional geometry of spacetime. Topics discussed include: the relativity of simultaneity in special and general relativity; the ‘twin paradox’ and differential aging effects in special and general relativity; and time travel in general relativity.

I will discuss only one of the several entwined strands of the philosophy of space and time, the question of the relation between the nature of motion and the geometrical structure of the world.1 This topic has many of the virtues of the best philosophy of science. It is of long-standing philosophical interest and has a rich history of connections to problems of physics. It has loomed large in discussions of space and time among contemporary philosophers of science. Furthermore, there (...) is, I think, widespread agreement that recent insights here have lead to a genuine deepening of our understanding. (shrink)

One major motivation for nominalism, at least according to Hartry Field, is the desirability of intrinsic explanations: explanations that don’t invoke objects that are causally irrelevant to the phenomena being explained. There is something right about the search for such explanations. But that search must be carefully implemented. Nothing is gained if, to avoid a certain class of objects, one only introduces other objects and relations that are just as nominalistically questionable. We will argue that this is the case for (...) two alleged nominalist views: Field’s fictionalism, and Frank Arntzenius and Cian Dorr’s geometricalism. Central to our competing approach to nominalism is a distinction between terms that refer to objects and ones that instead code empirical phenomena while being referentially empty. We next contrast our approach to nominalism, which uses this term-grained distinction between coding and referring, with approaches that instead attempt to make a sentence-grained distinction between mathematical and non-mathematical content. We show the latter approach fails to be responsive to objections raised by van Fraassen. In the end, only one last approach to nominalism is left standing. 1 Introduction2 Troubles for Mathematical Fictionalism2.1 A distinction2.2 Field’s programme2.3 Parts of nominalistically acceptable entities are nominalistically acceptable2.4 Structural assumptions: How far can these be pushed?2.5 Cases of indispensable theories where the mathematical posits are known not to be real2.6 How does science distinguish between the indispensable structural presuppositions taken to be real and those that aren’t?2.7 Do physicists distinguish between mathematical posits and non-mathematical posits?2.8 Mathematical coding versus genuine metaphysics. Case study: Fields2.9 The upshot3 Troubles for Topologism4 Contrasts: Kitcher, Maddy, Sober, and van Fraassen4.1 Sober’s approach4.2 Maddy’s approach4.3 Kitcher’s approach4.4 Where do we go from here?4.5 Van Fraassen’s objection to Maddy’s approach to ontological commitment5 Conclusion. (shrink)

In this contribution, I comment on Raffaella Campaner’s defense of explanatory pluralism in psychiatry (in this volume). In her paper, Campaner focuses primarily on explanatory pluralism in contrast to explanatory reductionism. Furthermore, she distinguishes between pluralists who consider pluralism to be a temporary state on the one hand and pluralists who consider it to be a persisting state on the other hand. I suggest that it would be helpful to distinguish more than those two versions of pluralism – different understandings (...) of explanatory pluralism both within philosophy of science and psychiatry – namely moderate/temporary pluralism, anything goes pluralism, isolationist pluralism, integrative pluralism and interactive pluralism. Next, I discuss the pros and cons of these different understandings of explanatory pluralism. Finally, I raise the question of how to implement or operationalize explanatory pluralism in scientific practice; how to structure the “genuine dialogue” or shape “the pluralistic attitude” Campaner is referring to. As tentative answers, I explore a question-based framework for explanatory pluralism as well as social-epistemological procedures for interaction among competing approaches and explanations. (shrink)

The word “effective” has become the standard label attached to scientific theories these days. An effective theory allows us to make accurate predictions about a physical system at a certain (energy, length) scale while being largely ignorant of the details at more fundamental levels. One does not need to know anything about the deeper, quantum structure of water molecules to describe the macroscopic behaviour of waves or water in a glass. Although effective descriptions so broadly construed have been part of (...) research in physics since the earliest stages of modern science, it is particle physics that has most clearly relied on and brought to the fore some of the most interesting and admittedly puzzling aspects of this way of looking at theories. Indeed, the effective field theory (EFT) program in QFT has established itself as the most natural way to understand renormalisation and dissipate initial reservations about the status of these techniques by treating higher-order processes as contributions suppressed at lower energy scales. QFT is thus treated as the “effective” framework par excellence with the decoupling of scales constituting its permeating tenet. The goal of this project is to attempt a philosophical appraisal of EFTs as currently used in high energy physics as well as assess the possibility that the whole program eventually breaks down, i.e. fails to apply when certain preconditions do not hold. Accordingly, the dissertation is logically divided into two parts with the first two chapters dedicated to discussion of the relation between EFTs and traditional questions in the philosophy of science concerning the structure of scientific theories, the formulation and defence of scientific realism as well as its connection to possible ontological readings of EFTs. The second part constitutes an analysis of two well-known problems that have been accorded the status of crises in the physics literature: the hierarchy problem and the cosmological constant problem. Our main focus will be to uncover those assumptions responsible for undermining the validity of the EFT techniques in their respective context. In light of this analysis, we will ultimately lean towards a more cautionary or “reserved” approach to EFTs. (shrink)

I argue that Immanuel Kant's critical philosophy—in particular the doctrine of transcendental idealism which grounds it—is best understood as an `epistemic' or `metaphilosophical' doctrine. As such it aims to show how one may engage in the natural sciences and in metaphysics under the restriction that certain conditions are imposed on our cognition of objects. Underlying Kant's doctrine, however, is an ontological posit, of a sort, regarding the fundamental nature of our cognition. This posit, sometimes called the `discursivity thesis', while considered (...) to be completely obvious and uncontroversial by some, has nevertheless been denied by thinkers both before and after Kant. One such thinker is Jakob Friedrich Fries, an early neo-Kantian thinker who, despite his rejection of discursivity, also advocated for a metaphilosophical understanding of critical philosophy. As I will explain, a consequence for Fries of the denial of discursivity is a radical reconceptualisation of the method of critical philosophy; whereas this method is a priori for Kant, for Fries it is in general empirical. I discuss these issues in the context of quantum theory, and I focus in particular on the views of the physicist Niels Bohr and the Neo-Friesian philosopher Grete Hermann. I argue that Bohr's understanding of quantum mechanics can be seen as a natural extension of an orthodox Kantian viewpoint in the face of the challenges posed by quantum theory, and I compare this with the extension of Friesian philosophy that is represented by Hermann's view. -/- A shorter version of this paper, focusing specifically on the views of Grete Hermann, has been published as: Cuffaro, Michael (2023). Grete Hermann, Quantum Mechanics, and the Evolution of Kantian Philosophy. In Jeanne Peijnenburg & Sander Verhaegh (eds.), Women in the History of Analytic Philosophy. Cham: Springer. pp. 114-145. (shrink)

Graham Solomon, to whom this collection is dedicated, went into hospital for antibiotic treatment of pneumonia in Oc- ber, 2001. Three days later, on Nov. 1, he died of a massive stroke, at the age of 44. Solomon was well liked by those who got the chance to know him—it was a revelation to?nd out, when helping to sort out his a?airs after his death, how many “friends” he had whom he had actually never met, as his email included correspondence (...) with philosophers around the world running sometimes to hundreds of messages. He was well respected in the philosophical community more broadly. He was for several years a member of the editorial board for the Western Ontario Series in Philosophy of Science. While he was employed at Wilfrid Laurier University in Waterloo, Ontario, several of us at the University of Wat- loo always regarded our own department as a sort of second academic home for him. We therefore decided that it would be appropriate to hold a memorial conference in his honour. Thanks to the generous?nancial support of the Humphrey Conference Fund, we were able to do so in May 2003. Many of the papers in this volume were presented at that conf- ence. (shrink)

This paper proposes a parallel in the forms of Aristotle’s and Einstein’s physics. It’s an exercise on conceptual analysis rather than history. The possible similarity between Aristotle’s world and the form (global geometry) of Einstein’s universe is discussed. The correlation between kinematics, dynamics and gravity in their respective theories is also studied. Finally, Aristotle’s ontology of space is compared to the relativistic ontology spacetime.

Substantivalists believe that spacetime and its parts are fundamental constituents of reality. Relationalists deny this, claiming that spacetime enjoys only a derivative existence. I begin by describing how the Galilean symmetries of Newtonian physics tell against both Newton's brand of substantivalism and the most obvious relationalist alternative. I then review the obvious substantivalist response to the problem, which is to ditch substantival space for substantival spacetime. The resulting position has many affinities with what are arguably the most natural interpretations of (...) special and general relativity. I move on to consider and reject two recent antisubstantivalist lines of thought. The interim conclusion is that the best argument for relationalism is an appeal to Ockham's razor. However, for this to be successful there must be genuine relationalist theories that share the theoretical virtues of their substantivalist rivals but without the additional ontological commitment. The bulk of the paper is therefore an investigation of various concrete relationalist proposals. I distinguish three options for the relationalist in the face of the success of Galilean invariant physics and trace how these generalise to relativistic physics. One of the options is particularly promising but, since its basic objects end up being spacetime points, this does not help the prospects of relationalism as traditionally conceived. I end with some reflections on the fate of substantivalism in the aftermath of the Hole Argument, concluding that we have as yet to be given good reasons to abandon the natural, substantivalist interpretation of current physics. (shrink)

We should see the debate over the existence of spacetime as a debate about the fundamentality of spatiotemporal structure to the physical world. This is a non-traditional conception of the debate, which captures the spirit of the traditional one. At the same time, it clarifies the point of contention between opposing views and offsets worries that the dispute is stagnant or non-substantive. It also unearths a novel argument for substantivalism, given current physics. Even so, that conclusion can be overridden by (...) future physics. I conclude that this debate is a substantive one, which the substantivalist is currently winning. (shrink)

When Newton articulated the concept of absolute time in his treatise, Philosophae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), along with its correlate, absolute space, he did not present it as anything controversial. Whereas his references to attraction are accompanied by the self- protective caveats that typically signal an expectation of censure, the Scholium following Principia’s definitions is free of such remarks, instead elaborating his ideas as clarifications of concepts that, in some manner, we already possess. This is not (...) surprising. The germ of the concept emerged naturally from astronomers’ findings, and variants of it had already been formulated by other seventeenth century thinkers. Thus the novelty of Newton’s absolute time lay mainly in the use to which he put it. (shrink)

Newton’s Regulae philosophandi—the rules for reasoning in natural philosophy—are maxims of causal reasoning and induction. This essay reviews their significance for Newton’s method of inquiry, as well as their application to particular propositions within the Principia. Two main claims emerge. First, the rules are not only interrelated, they defend various facets of the same core idea: that nature is simple and orderly by divine decree, and that, consequently, human beings can be justified in inferring universal causes from limited phenomena, if (...) only fallibly. Second, the rules make substantive ontological assumptions on which Newton’s argument in the Principia relies. (shrink)

I review some recent work on applications of category theory to questions concerning theoretical structure and theoretical equivalence of classical field theories, including Newtonian gravitation, general relativity, and Yang-Mills theories.

I state and prove, in the context of a space having only the metrical structure imposed by the geometrized version of Newtonian gravitational theory, a theorem analagous to that of Weyl's in a Lorentzian space. The theorem, loosely speaking, says that a projective structure and a suitably defined compatible conformal structure on such a space jointly suffice for fixing the metrical structure of a Newtonian spacetime model up to constant factors. It allows one to give a natural, physically compelling interpretation (...) of the spatiotemporal geometry of a geometrized Newtonian gravity spacetime manifold, in close analogy with the way Weyl's Theorem allows one to do in general relativity. (shrink)

Non-relativistic quantum mechanics is grounded on ‘classical’ space and time. The mathematical description of these con- cepts entails that any two spatially separated objects are necessarily dif- ferent, which implies that they are discernible — we say that the space is T2, or "Hausdorff". But quantum systems, in the most interesting cases, some- times need to be taken as indiscernible, so that there is no way to tell which system is which, and this holds even in the case of fermions. (...) But in the NST setting, it seems that we can always give an identity to them, which seems to be contra the physical situation. In this paper we discuss this topic for a case study and con- clude that, taking into account the quantum case, that is, when physics enter the discussion, even NST cannot be used to say that the systems do have identity. (shrink)

Einstein’s “point-coincidence argument'” as a response to the “hole argument” is usually considered as an expression of “Leibniz equivalence,” a restatement of indiscernibility in the sense of Leibniz. Through a historical-critical analysis of Logical Empiricists' interpretation of General Relativity, the paper attempts to show that this labeling is misleading. Logical Empiricists tried explicitly to understand the point-coincidence argument as an indiscernibility argument of the Leibnizian kind, such as those formulated in the 19th century debate about geometry, by authors such as (...) Poincaré, Helmholtz or Hausdorff. However, they clearly failed to give a plausible account of General Relativity. Thus the point-coincidence/hole argument cannot be interpreted as Leibnizian indiscernibility argument, but must be considered as an indiscernibility argument of a new kind. Weyl's analysis of Leibniz's and Einstein's indiscernibility arguments is used to support this claim. (shrink)