The implications for the substantivalist–relationalist controversy of Barbour and Bertotti's successful implementation of a Machian approach to dynamics are investigated. It is argued that in the context of Newtonian mechanics, the Machian framework provides a genuinely relational interpretation of dynamics and that it is more explanatory than the conventional, substantival interpretation. In a companion paper (Pooley [2002a]), the viability of the Machian framework as an interpretation of relativistic physics is explored. 1 Introduction 2 Newton versus Leibniz 3 Absolute space versus (...) an affine connection 4 Anti-relationalist arguments 5 Rehabilitating relationalism 6 Dynamics on the relative configuration space 7 Intrinsic particle dynamics 8 Conclusion. (shrink)

This dissertation is divided into two parts. In the first part I defend substantivalism. I do this by offering, in chapter 1, a counterpart-theoretic defense of substantivalism from Leibniz’ shift arguments. Then, in chapter 2, I defend substantivalism from the hole argument and argue, against the consensus, that the question of haecceitism is irrelevant to substantivalism in the context of general relativity. In the second part of the dissertation I defend supersubstantivalism. I do this by offering, in chapter 3, an (...) argument against dualistic substantivalism. The argument appeals to plausible principles of modal plenitude to show that the dualist is committed to a range of problematic possibilities. Then, in chapter 4, I consider a range of supersubstantivalist positions. I conclude by arguing for a version of supersubstantivalism I call compresence supersubstantivalism. (shrink)

I argue that the Hole Argument is based on a misleading use of the mathematical formalism of general relativity. If one is attentive to mathematical practice, I will argue, the Hole Argument is blocked.

I argue that the hole argument is based on a misleading use of the mathematical formalism of general relativity. If one is attentive to mathematical practice, I will argue, the hole argument is blocked. _1._ Introduction _2._ A Warmup Exercise _3._ The Hole Argument _4._ An Argument from Classical Spacetime Theory _5._ The Hole Argument Revisited.

After some background setting in which it is shown how Maudlin's (1989, 1990) response to the hole argument of Earman and Norton (1987) is related to that of Rynasiewicz (1994), it is argued that the syntactic proposals of Mundy (1992) and of Leeds (1995), which claim to dismiss the hole argument as an uninteresting blunder, are inadequate. This leads to a discussion of how the responses of Maudlin and Rynasiewicz relate to issues about gauge freedom and relativity principles.

In a number of publications, John Earman has advocated a tertium quid to the usual dichotomy between substantivalism and relationism concerning the nature of spacetime. The idea is that the structure common to the members of an equivalence class of substantival models is captured by a Leibniz algebra which can then be taken to directly characterize the intrinsic reality only indirectly represented by the substantival models. An alleged virtue of this is that, while a substantival interpretation of spacetime theories falls (...) prey to radical local indeterminism, the Leibniz algebras do not. I argue that the program of Leibniz algebras is subject to radical local indeterminism to the same extent as substantivalism. In fact, for the category of topological spaces of interest in spacetime physics, the program is equivalent to the original spacetime approach. Moreover, the motivation for the program--that isomorphic substantival models should be regarded as representing the same physical situation--is misguided. (shrink)

This special issue of Foundations of Physics collects together articles representing some recent new perspectives on the hole argument in the history and philosophy of physics. Our task here is to introduce those new perspectives.

According to substantivalism, spacetime points and regions are real entities whose existence is not dependent on matter. In this paper, I motivate and defend a version of substantivalism which takes the totality of spacetime as fundamental, and show how this position avoids certain problem cases, in particular the objection from static Leibniz shifts, and better conforms to how we think about space in physics. I argue that, even though the static Leibniz shifts do not show ordinary substantivalism is committed to (...) in-principle undetectable physical structure ), they do indicate something problematic about the modal profile of space-time and its constituents. While the problem is modal, the solution cannot be solely a matter of revising the substantivalist's modal claims. Rather, I argue, the substantivalist must revise her background ontology of space-time. I show how this can be done by developing substantivalist theory that rejects this picture in favor of an alternative ontology of space-time in the spirit of priority monism. (shrink)

This article deals with empty spacetime and the question of its physical reality. By “empty spacetime” we mean a collection of bare spacetime points, the remains of ridding spacetime of all matter and fields. We ask whether these geometric objects—themselves intrinsic to the concept of field—might be observable through some physical test. By taking quantum-mechanical notions into account, we challenge the negative conclusion drawn from the diffeomorphism invariance postulate of general relativity, and we propose new foundational ideas regarding the possible (...) observation—as well as conceptual overthrow—of this geometric ether. (shrink)

”The last remnant of physical objectivity of space-time” is disclosed in the case of a continuous family of spatially non-compact models of general relativity. The physical individuation of point-events is furnished by the autonomous degrees of freedom of the gravitational field, which represent -as it were -the ontic part of the metric field. The physical role of the epistemic part is likewise clarified as embodying the unavoidable non-inertial aspects of GR. At the end the philosophical import of the Hole Argument (...) is substantially weakened and in fact the Argument itself dis-solved, while a specific four-dimensional holistic and structuralist view of space-time emerges, including elements common to the tradition of both substantivalism and relationism. The observables of our models undergo real temporal change: this gives new evidence to the fact that statements like the frozen-time character of evolution, as other ontological claims about GR, are model dependent. (shrink)

The concepts in the title refer to properties of physical theories and this paper investigates their nature and relations. The first three concepts, especially gauge invariance and indeterminism, have been widely discussed in connection to spacetime theories and the hole argument. Since the gauge invariance principle is at the crux of the issue, this paper aims at clarifying the nature of gauge invariance. I first explore the following chain of relations: gauge invariance $\Rightarrow $ the conservation laws $\Rightarrow $ the (...) Cauchy problem $\Rightarrow $ indeterminism. Then I discuss gauge invariance in light of our understanding of the above relations and the possibility of spontaneous symmetry breaking. (shrink)

The presence of symmetries in physical theories implies a pernicious form of underdetermination. In order to avoid this theoretical vice, philosophers often espouse a principle called Leibniz Equivalence, which states that symmetry-related models represent the same state of affairs. Moreover, philosophers have claimed that the existence of non-trivial symmetries motivates us to accept the Invariance Principle, which states that quantities that vary under a theory’s symmetries aren’t physically real. Leibniz Equivalence and the Invariance Principle are often seen as part of (...) the same package. I argue that this is a mistake: Leibniz Equivalence and the Invariance Principle are orthogonal to each other. This means that it is possible to hold that symmetry-related models represent the same state of affairs whilst having a realist attitude towards variant quantities. Various arguments have been presented in favour of the Invariance Principle: a rejection of the Invariance Principle is inter alia supposed to cause indeterminism, undetectability or failure of reference. I respond that these arguments at best support Leibniz Equivalence. (shrink)

The paper tries to develop Bartels’s modern essentialism as a structural-role theory of identity for spacetime points. I adopt Hoefer’s idea of denying primitive identity for this theory and apply it to GTR and prerelativistic physics to find different versions of essentialism and different definitions of determinism which are coherent with them. I also try to argue that modified essentialism helps us to refute objections raised against essentialism and offers us the best understanding of prerelativistic and relativistic theories.

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)

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)

I examine the debate between substantivalists and relationalists about the ontological character of spacetime and conclude it is not well posed. I argue that the hole argument does not bear on the debate, because it provides no clear criterion to distinguish the positions. I propose two such precise criteria and construct separate arguments based on each to yield contrary conclusions, one supportive of something like relationalism and the other of something like substantivalism. The lesson is that one must fix an (...) investigative context in order to make such criteria precise, but different investigative contexts yield inconsistent results. I examine questions of existence about spacetime structures other than the spacetime manifold itself to argue that it is more fruitful to focus on pragmatic issues of physicality, a notion that lends itself to several different explications, all of philosophical interest, none privileged a priori over any of the others. I conclude by suggesting an extension of the lessons of my arguments to the broader debate between realists and instrumentalists. 1 Introduction2 The Hole Argument3 Limits of Spacetimes4 Pointless Constructions5 The Debate between Substantivalists and Relationalists6 Existence and Physicality: An Embarassment of Spacetime Structures7 Valedictory Remarks on Realism and Instrumentalism, and the Structure of Our Knowledge of Physics. (shrink)

The symmetries of a physical theory are often associated with two things: conservation laws and representational redundancies. But how can a physical theory's symmetries give rise to interesting conservation laws, if symmetries are transformations that correspond to no genuine physical difference? In this article, I argue for a disambiguation in the notion of symmetry. The central distinction is between what I call "analytic" and "synthetic" symmetries, so called because of an analogy with analytic and synthetic propositions. "Analytic" symmetries are the (...) turning of idle wheels in a theory's formalism, and correspond to no physical change; "synthetic" symmetries cover all the rest. I argue that analytic symmetries are distinguished because they act as fixed points or constraints in any interpretation of a theory, and as such are akin to Poincaré's conventions or Reichenbach's 'axioms of co-ordination', or 'relativized constitutive a priori principles'. (shrink)

This article develops an analogy proposed by Stachel between general relativity (GR) and quantum mechanics (QM) as regards permutation invariance. Our main idea is to overcome Pooley's criticism of the analogy by appeal to paraparticles. In GR, the equations are (the solution space is) invariant under diffeomorphisms permuting spacetime points. Similarly, in QM the equations are invariant under particle permutations. Stachel argued that this feature—a theory's ‘not caring which point, or particle, is which’—supported a structuralist ontology. Pooley criticizes this analogy: (...) in QM the (anti-)symmetrization of fermions and bosons implies that each individual state (solution) is fixed by each permutation, while in GR a diffeomorphism yields in general a distinct, albeit isomorphic, solution. We define various versions of structuralism, and go on to formulate Stachel's and Pooley's positions, admittedly in our own terms. We then reply to Pooley. Though he is right about fermions and bosons, QM equally allows more general types of particle symmetry, in which states (vectors, rays, or density operators) are not fixed by all permutations (called ‘paraparticle states’). Thus Stachel's analogy is revived. (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.

There is a widespread impression that General Relativity, unlike Quantum Mechanics, is in no need of an interpretation. I present two reasons for thinking that this is a mistake. The first is the familiar hole argument. I argue that certain skeptical responses to this argument are too hasty in dismissing it as being irrelevant to the interpretative enterprise. My second reason is that interpretative questions about General Relativity are central to the search for a quantum theory of gravity. I illustrate (...) this claim by examining the interpretative consequences of a particular technical move in canonical quantum gravity. (shrink)

The determination of inertia by matter is looked at in general relativity, where inertia can be represented by affine or projective structure. The matter tensor T seems to underdetermine affine structure by ten degrees of freedom, eight of which can be eliminated by gauge choices, leaving two. Their physical meaning---which is bound up with that of gravitational waves and the pseudotensor t, and with the conservation of energy-momentum---is considered, along with the dependence of reality on invariance and of causal explanation (...) on conservation. (shrink)

In his paper ``What is Structural Realism?'' James Ladyman drew a distinction between epistemological structural realism and metaphysical (or ontic) structural realism. He also drew a suggestive analogy between the perennial debate between substantivalist and relationalist interpretations of spacetime on the one hand, and the debate about whether quantum mechanics treats identical particles as individuals or as `non-individuals' on the other. In both cases, Ladyman's suggestion is that an ontic structural realist interpretation of the physics might be just what is (...) needed to overcome the stalemate. The main thesis of this paper is that, whatever the interpretative difficulties of generally covariant spacetime physics are, they do not support or suggest structural realism. In particular, I hope to show that there is in fact no analogy that supports a similar interpretation of the metaphysics of spacetime points and of quantum particles. (shrink)

We make some remarks on the mathematics and metaphysics of the hole argument, in response to a recent article in this journal by Weatherall ([2018]). Broadly speaking, we defend the mainstream philosophical literature from the claim that correct usage of the mathematics of general relativity `blocks' the argument.

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)

One of Julian Barbour’s main aims is to solve the problem of time that appears in quantum geometrodynamics (QG). QG involves the application of canonical quantization procedure to the Hamiltonian formulation of General Relativity. The problem of time arises because the quantization of the Hamiltonian constraint results in an equation that has no explicit time parameter. Thus, it appears that the resulting equation, as apparently timeless, cannot describe evolution of quantum states. Barbour attempts to resolve the problem by allegedly eliminating (...) time from his interpretation of QG. In order to evaluate the efficacy of his solution, it is necessary to ascertain in what sense time has been eliminated from his theory. I proceed to do so by developing a form of conceptual analysis that is applicable to the concept of time in physical theories and applying this analysis to Barbour’s account. (shrink)

The main aim of this paper is to make a remark about the relation between dualities between theories, as `duality' is understood in physics and equivalence of theories, as `equivalence' is understood in logic and philosophy. The remark is that in physics, two theories can be dual, and accordingly get called `the same theory', though we interpret them as disagreeing---so that they are certainly not equivalent, as `equivalent' is normally understood. So the remark is simple: but, I shall argue, worth (...) stressing---since often neglected. My argument for this is based on the account of duality developed by De Haro: which is illustrated here with several examples, from both elementary physics and string theory. Thus I argue that in some examples, including in string theory, two dual theories disagree in their claims about the world. I also spell out how this remark implies a limitation of proposals to understand theoretical equivalence as either logical equivalence or a weakening of it. (shrink)

For the past two decades, Einstein's Hole Argument (which deals with the apparent indeterminateness of general relativity due to the general covariance of the field equations) and its resolution in terms of "Leibniz equivalence" (the statement that pseudo-Riemannian geometries related by active diffeomorphisms represent the same physical solution) have been the starting point for a lively philosophical debate on the objectivity of the point-events of space-time. It seems that Leibniz equivalence makes it impossible to consider the points of the space-time (...) manifold as physically individuated without recourse to dynamical individuating fields. Various authors have posited that the metric field itself can be used in this way , but nobody so far has considered the problem of explicitly distilling the "metrical fingerprint" of point-events from the gauge-dependent elements of the metric field. Working in the Hamiltonian formulation of general relativity, and building on the results of Lusanna and Pauri (2002), we show how Bergmann and Komar's "intrinsic pseudo-coordinates" (based on the value of curvature invariants) can be used to provide a physical individuation of point-events in terms of the true degrees of freedom (the "Dirac observables") of the gravitational field, and we suggest how this conceptual individuation could in principle be implemented with a well-defined empirical procedure. We argue from these results that point-events retain a significant kind of physical objectivity. (shrink)

In the first part of this paper a relational account of incongruent counterparts is defended against an argument due to Kant. I then consider a more recent attack on such an account, due to John Earman, which alleges that the relationalist cannot account for the lawlike left--right asymmetry manifested in parity-violating phenomena. I review Hoefer's, Huggett's and Saunders' responses to Earman's argument and argue that, while a relationalist account of parity-violating laws is possible, it comes at the cost of non-locality.

This thesis analyses the ontological nature of quantum particles. In it I argue that quantum particles, despite their indistinguishability, are objects in much the same way as classical particles. This similarity provides an important point of continuity between classical and quantum physics. I consider two notions of indistinguishability, that of indiscernibility and permutation symmetry. I argue that neither sort of indistinguishability undermines the identity of quantum particles. I further argue that, when we understand in distinguishability in terms of permutation symmetry, (...) classical particles are just as indistinguishable as quantum particles; for classical physics also possesses permutation symmetry. (shrink)

In their modern classic ``What Price Substantivalism? The Hole Story'' Earman and Norton argued that substantivalism about spacetime points implies that general relativity is indeterministic and, for that reason, must be rejected as a candidate ontology for the theory. More recently, Earman has cottoned on to a related argument (in fact, related to a \emph{response} to the hole argument) that arises in the context of canonical general relativity, according to which the enforcing of determinism along standard lines---using the machinery of (...) gauge theory---leads to a `frozen universe' picture (grounded in an absence of changes in values of general relativity's observables). \emph{Prima facie} this would seem to land the anti-substantivalist in waters at least as deep as those that Earman and Norton argued troubled substantivalism. In this paper I introduce the argument in what I think are clearer terms than Earman's, and assess his treatment of the problem. For the most part I agree with Earman about the nature of the problem, but I find aspects of his discussion wanting, especially as regards his proposed ontology. I argue that ontological sense can be made of the changelessness if a structuralist stance is adopted with respect to a natural class of observables. (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)