'The arrow of time' refers to the curious asymmetry that distinguishes the future from the past. Reversing the Arrow of Time argues that there is an intimate link between the symmetries of 'time itself' and time reversal symmetry in physical theories, which has wide-ranging implications for both physics and its philosophy. This link helps to clarify how we can learn about the symmetries of our world, how to understand the relationship between symmetries and what is real, and how to overcome (...) pervasive illusions about the direction of time. Roberts explains the significance of time reversal in a way that intertwines physics and philosophy, to establish what the arrow of time means and how we can come to know it. This book is both mathematically and philosophically rigorous yet remains accessible to advanced undergraduates in physics and the philosophy of physics. This title is also available as Open Access on Cambridge Core. (shrink)

Is the world internally connected by a web of necessary connections or is everything loose and independent? Followers of David Hume accept the latter by upholding Hume’s Dictum, according to which there are no necessary connections between distinct existences. Roughly put, anything can coexist with anything else, and anything can fail to coexist with anything else. Hume put it like this: “There is no object which implies the existence of any other if we consider these objects in themselves.” Since Hume’s (...) day, Hume’s Dictum has played a major role in philosophy, especially in contemporary metaphysics. In ruling out necessary connections, Hume’s Dictum implies that causal relations and the laws of nature are contingent. It makes other demands on our metaphysics of science as well; for example, it places restrictions on our metaphysics of counterfactuals, dispositions, and explanation. The principle has applications in other areas too. Hume’s Dictum places constraints on our theories of abstract objects and moral properties. For example, Hume’s Dictum rules out the view that moral properties are distinct from, but necessarily connected to, non-moral properties. While Hume’s Dictum is a prominent principle in metaphysics, few Humeans have defended the principle at length. It is assumed more often than it is argued for. As a result, Hume’s Dictum no longer enjoys the reputation it once did. It’s common to hear complaints about the lack of arguments in support of Hume’s Dictum. Moreover, philosophers are increasingly willing to defend views that are at odds with Hume’s Dictum. A striking example of this is the recent explosion of interest in views that take causal relations and the laws of nature to be necessary. Humeans can no longer afford to be complacent. An extended defense of Hume’s Dictum is called for, and that’s what this dissertation aims to offer. This dissertation has three parts. In the first part, I lay out some preliminaries and offer a precise formulation of Hume’s Dictum. In the second part, I develop three arguments in favor of Hume’s Dictum. In the final part, I defend Hume’s Dictum against objections. (shrink)

The consensus among spacetime substantivalists is to respond to Leibniz's classic shift arguments, and their contemporary incarnation in the form of the hole argument, by pruning the allegedly problematic metaphysical possibilities that generate these arguments. Some substantivalists do so by directly appealing to a modal doctrine akin to anti-haecceitism. Other substantivalists do so by appealing to an underlying hyperintensional doctrine that implies some such modal doctrine. My first aim in this paper is to pose a challenge for all extant forms (...) of this consensus position. My second aim is to show what form substantivalism must take in order to uphold the consensus while addressing this challenge. The result is a novel "plenitudinous" substantivalist view, which predicts that certain modal facts about spacetime are vague or indeterminate. I then argue against this view on independent grounds, concluding that substantivalists should reject the consensus position. The paper also discusses the way forward for substantivalists in light of this conclusion. (shrink)

I explore two views about the relationship between spatial experience and spatial reality: spatial functionalism and spatial presentationalism. Roughly, spatial functionalism claims that the instantiated spatial properties are those playing a certain causal role in producing spatial experience while spatial presentationalism claims that the instantiated spatial properties include those presented in spatial experience. I argue that each view, in its own way, leads to an ontologically inflationary form of primitivism: whereas spatial functionalism leads to primitivism about phenomenal representation, spatial presentationalism (...) leads to primitivism about spatial properties. I conclude by discussing how to adjudicate between spatial functionalism and spatial presentationalism. (shrink)

I critically examine the assumption that the theoretical structure that varies under theoretical symmetries is redundant and should be eliminated from a metaphysical picture of the universe, following a ‘symmetry to reality’ inference. I do so by analysing the status of coordinate change symmetries taking a pragmatic approach. I argue that coordinate systems function as indexical devices, and play an important pragmatic role for representing concrete physical systems. I examine the implications of considering this pragmatic role seriously, taking what I (...) call a perspectivist stance. My conclusion is that under a perspectivist stance, all symmetries (including local gauge symmetries) potentially have a direct empirical status: they point to dynamical aspects that are invariant under changes of operationalisation, and they constitute a guide not to reality, but to nomology and kinship. (shrink)

There exists a common view that for theories related by a ‘duality’, dual models typically may be taken ab initio to represent the same physical state of affairs, i.e. to correspond to the same possible world. We question this view, by drawing a parallel with the distinction between ‘interpretational’ and ‘motivational’ approaches to symmetries.

Ontic structural realism is at its core the view that “structure is ontologically fundamental.” Informed from its inception by the scientific revolutions that punctuated the 20th century, its advocates often present the position as the perspective on ontology best befitting of modern physics. But the idea that structure is fundamental has proved difficult to articulate adequately, and what OSR's claimed naturalistic credentials consist in is hard to precisify as well. Nor is it clear that the position is actually supported by (...) our most fundamental physical theories. What is clear, however, is that structuralists have revealed a seam of material at the core of modern physics that is replete with implications for metaphysics. This article will survey some positions subsumed under the rubric of OSR, considering both their warrant and the interconnections that exist between them. It will be argued that the fundamental kind properties pose a challenge to ontic structuralism, because it seems that these properties do not supervene upon the relevant structures. But it will also be argued that the development of structuralist metaphysics will require both an engagement with the details of modern physical theories and the deployment of tools more typically developed in a priori metaphysics. As such, it seems armchair metaphysicians have not just a stake in whether OSR's claims may ultimately be shown to stand up, but a crucial role to play in getting them to the point where they can be subjected to scrutiny in the first place. (shrink)

In the recent philosophical debate about the relationship between symmetries and physical equivalence, two approaches have been distinguished: motivationalism and interpretationalism. In this paper, I point out that there are variants of interpretationalism that have not been taken into account by the proponents of motivationalism. I also argue that some of these overlooked variants of interpretationalism are not prone to the motivationalists’ criticism and overall are the most attractive positions available.

In the recent philosophical literature, several counterexamples to the interpretative principle that symmetry-related models are physically equivalent have been suggested The Oxford handbook of philosophy of physics, Oxford University Press, Oxford, 2013, Noûs 52:946–981, 2018; Fletcher in Found Phys 50:228–249, 2020). Arguments based on these counterexamples can be understood as arguments from scientific practice of roughly the following form: because in scientific practice such-and-such symmetry-related models are treated as representing distinct physical situations, these models indeed represent distinct physical situations. In (...) this paper, a strategy for analysing arguments of this type is presented and applied to the examples that can be found in the literature. I argue that if we are exclusively interested in models understood as representing entire possible worlds, arguments from scientific practice should involve some additional assumptions to guarantee they are relevant for models understood in this way. However, none of the examples presented in the literature satisfy all these additional assumptions, which leads to the conclusion that arguments from scientific practice based on these examples do not undermine the interpretative principle that different symmetry-related models represent the same possible world. (shrink)

Symmetry-based inferences have permeated many discussions in philosophy of physics and metaphysics of science. It is claimed that symmetries in our physical theories would allow us to draw metaphysical conclusions about the world, a view that I call ‘symmetry inferentialism’. This paper is critical to this view. I claim that (a) it assumes a philosophically questionable characterization of the relevant validity domain of physical symmetries, and (b) it overlooks a distinction between two opposing ways through which relevant physical symmetries become (...) established. My conclusion is that symmetry inferentialism loses persuasive force when these two points are taken into consideration. (shrink)

In this article I shall defend, against the conventional understanding of the matter, that two coherent and tenable approaches to time reversal can be suitably introduced in standard quantum mechanics: an “orthodox” approach that demands time reversal to be represented in terms of an anti-unitary and anti-linear time-reversal operator, and a “heterodox” approach that represents time reversal in terms of a unitary, linear time-reversal operator. The rationale shall be that the orthodox approach in quantum theories assumes a relationalist metaphysics of (...) time, according to which time reversal is nothing but motion reversal. But, when one shifts gears and turn to a substantivalist metaphysics of time the heterodox approach to time reversal in quantum mechanics comes up in a more natural way. (shrink)

In this article I shall defend, against the conventional understanding of the matter, that two coherent and tenable approaches to time reversal can be suitably introduced in standard quantum mechanics: an “orthodox” approach that demands time reversal to be represented in terms of an anti-unitary and anti-linear time-reversal operator, and a “heterodox” approach that represents time reversal in terms of a unitary, linear time-reversal operator. The rationale shall be that the orthodox approach in quantum theories assumes a relationalist metaphysics of (...) time, according to which time reversal is nothing but motion reversal. But, when one shifts gears and turn to a substantivalist metaphysics of time the heterodox approach to time reversal in quantum mechanics comes up in a more natural way. (shrink)

The notion of time reversal has caused some recent controversy in philosophy of physics. The debate has mainly put the focus on how the concept of time reversal should be formally implemented across different physical theories and models, as if time reversal were a single, unified concept that physical theories should capture. In this paper, I shift the focus of the debate and defend that the concept of time reversal involves at least three facets, where each of them gives rise (...) to opposing views. In particular, I submit that any account of time reversal presupposes (explicitly or implicitly) modal, metaphysical, and heuristic facets. The comprehension of this multi-faceted nature of time reversal, I conclude, shows that time reversal can be coherently said in many ways, suggesting a disunified concept. (shrink)

Symmetry fundamentalism claims that symmetries should be taken metaphysically seriously as part of the fundamental ontology. The main aim of this paper is to bring some novel objections against this view. I make two points. The first places symmetry fundamentalism within a broader network of philosophical commitments. I claim that symmetry fundamentalism entails idealization realism which, in turn, entails the reification of further theoretical structures. This might lead to an overloaded ontology as well as open the way to criticisms from (...) metaphysical frameworks that reject such reifications. The second point contrasts symmetry fundamentalism with the now common view that regards symmetries as stipulations guiding empirical research and theory construction. I claim that both views clash each other and cannot be held together. I finish the paper with a more positive prospect that will be developed in future work—symmetry deflationism. (shrink)

Scientists often think of the world as a dynamical system, a stochastic process, or a generalization of such a system. Prominent examples of systems are the system of planets orbiting the sun or any other classical mechanical system, a hydrogen atom or any other quantum–mechanical system, and the earth’s atmosphere or any other statistical mechanical system. We introduce a general and unified framework for describing such systems and show how it can be used to examine some familiar philosophical questions, including (...) the following: how can we define nomological possibility, necessity, determinism, and indeterminism; what are symmetries and laws; what regularities must a system display to make scientific inference possible; how might principles of parsimony such as Occam’s Razor help when we make such inferences; what is the role of space and time in a system; and might they be emergent features? Our framework is intended to serve as a toolbox for the formal analysis of systems that is applicable in several areas of philosophy. (shrink)

Fragmentalism was first introduced by Kit Fine in his ‘Tense and Reality’. According to fragmentalism, reality is an inherently perspectival place that exhibits a fragmented structure. The current paper defends the fragmentalist interpretation of the special theory of relativity, which Fine briefly considers in his paper. The fragmentalist interpretation makes room for genuine facts regarding absolute simultaneity, duration and length. One might worry that positing such variant properties is a turn for the worse in terms of theoretical virtues because such (...) properties are not involved in physical explanations and hence theoretically redundant. It will be argued that this is not right: if variant properties are indeed instantiated, they will also be involved in straightforward physical explanations and hence not explanatorily redundant. Hofweber and Lange, in their ‘Fine’s Fragmentalist Interpretation of Special Relativity’, object that the fragmentalist interpretation is in tension with the right explanation of the Lorentz transformations. It will be argued that their objection targets an inessential aspect of the fragmentalist framework and fails to raise any serious problem for the fragmentalist interpretation of special relativity. (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)

It is now standard to interpret symmetry-related models of physical theories as representing the same state of affairs. Recently, a debate has sprung up around the question when this interpretational move is warranted. In particular, Møller-Nielsen :1253–1264, 2017) has argued that one is only allowed to interpret symmetry-related models as physically equivalent when one has a characterisation of their common content. I disambiguate two versions of this claim. On the first, a perspicuous interpretation is required: an account of the models’ (...) common ontology. On the second, stricter, version of this claim, a perspicuous formalism is required in addition: one whose mathematical structures ‘intrinsically’ represent the physical world, in the sense of Field. Using Dewar’s :485–521, 2019) distinction between internal and external sophistication as a case study, I argue that the second requirement is decisive. This clarifies the conditions under which it is warranted to interpret symmetry-related models as physically equivalent. (shrink)

ABSTRACT In this journal, Middleton and Murgueitio Ramírez argue that absolute velocity is measurable, contrary to the received wisdom. Specifically, they claim that ‘there exists at least one reasonable analysis of measurement according to which the speedometer in [a world called “the Basic World”] measures the absolute velocity of the car.’ In this note, I critically respond to that claim: the analysis of measurement that Middleton and Murgueitio Ramírez propose is not reasonable; nor does it entail that absolute velocities are (...) measurable. (shrink)

It is often claimed that one can avoid the kind of underdetermination that is a typical consequence of symmetries in physics by stipulating that symmetry-related models represent the same state of affairs (Leibniz Equivalence). But recent commentators (Dasgupta 2011; Pooley 2021; Pooley and Read 2021; Teitel 2021a) have responded that claims about the representational capacities of models are irrelevant to the issue of underdetermination, which concerns possible worlds themselves. In this paper I distinguish two versions of this objection: (1) that (...) a theory’s formalism does not (fully) determine the space of physical possibilities, and (2) that the relevant notion of possibility is not physical possibility. I offer a refutation of each. (shrink)

Two approaches to elevating certain laws of nature over others have come to prominence recently. On the one hand, according to the meta-laws approach, there are meta-laws, laws which relate to laws as those laws relate to particular facts. On the other hand, according to the modal, or non-absolutist, approach, some laws are necessary in a stricter sense than others. Both approaches play an important role in current research, questioning the ‘orthodoxy’ represented by the leading philosophical theories of natural laws—Humeanism, (...) the DTA view, dispositional essentialism and primitivism. This paper clarifies the relations between these two emerging approaches, as well as their applicability to physical laws and the status of the challenges they pose for standard theories of laws of nature. We first argue that, despite some significant similarities between the two approaches (especially in the context of Lange’s counterfactual account of laws), they are in general distinct and largely independent of each other. Then, we argue that the support for meta-laws from physical theory and practice is more questionable than usually presented. (shrink)

This essay revisits some classic problems in the philosophy of space and time concerning the counting of possibilities. I argue that we should think that two Newtonian worlds can differ only as to when or where things happen and that general relativistic worlds can differ in something like the same way—the first of these theses being quaintly heterodox, the second baldly heretical, according to the mores of contemporary philosophy of physics.

In this paper I elicit a prediction from structural realism and compare it, not to a historical case, but to a contemporary scientific theory. If structural realism is correct, then we should expect physics to develop theories that fail to provide an ontology of the sort sought by traditional realists. If structure alone is responsible for instrumental success, we should expect surplus ontology to be eliminated. Quantum field theory (QFT) provides the framework for some of the best confirmed theories in (...) science, but debates over its ontology are vexed. Rather than taking a stand on these matters, the structural realist can embrace QFT as an example of just the kind of theory SR should lead us to expect. Yet, it is not clear that QFT meets the structuralist's positive expectation by providing a structure for the world. In particular, the problem of unitarily inequivalent representations threatens to undermine the possibility of QFT providing a unique structure for the world. In response to this problem, I suggest that the structuralist should endorse pluralism about structure. (shrink)

Philosophy and Phenomenological Research, EarlyView.

Recent work on the hole argument in general relativity by Weatherall has drawn attention to the neglected concept of models’ representational capacities. I argue for several theses about the structure of these capacities, including that they should be understood not as many-to-one relations from models to the world, but in general as many-to-many relations constrained by the models’ isomorphisms. I then compare these ideas with a recent argument by Belot for the claim that some isometries “generate new possibilities” in general (...) relativity. Philosophical orthodoxy, by contrast, denies this. Properly understanding the role of representational capacities, I argue, reveals how Belot’s rejection of orthodoxy does not go far enough, and makes better sense of our practices in theorizing about spacetime. (shrink)

Much recent philosophy of physics has investigated the process of symmetry breaking. Here, I critically assess the alleged symmetry restoration at the fundamental scale. I draw attention to the contingency that gauge symmetries exhibit, that is, the fact that they have been chosen from an infinite space of possibilities. I appeal to this feature of group theory to argue that any metaphysical account of fundamental laws that expects symmetry restoration up to the fundamental level is not fully satisfactory. This is (...) a symmetry argument in line with Curie’s first principle. Further, I argue that this same feature of group theory helps to explain the ‘unreasonable’ effectiveness of mathematics in physics, and that it reduces the philosophical significance that has been attributed to the objectivity of gauge symmetries. (shrink)

In this paper, we put forward an alternative interpretation of time-reversal symmetry in philosophy of physics: Humean time-reversal symmetry. According to it, time-reversal symmetry is understood as a heuristic, epistemic virtue of the best system, not as a property of the Humean mosaic. One of the consequences of this view is that one of the main arguments against a primitive direction of time is rendered harmless, which paves the way for primitivism about the direction of time.

Suppose that one thinks that certain symmetries of a theory reveal “surplus structure”. What would a formalism without that surplus structure look like? The conventional answer is that it would be a reduced theory: a theory which traffics only in structures invariant under the relevant symmetry. In this paper, I argue that there is a neglected alternative: one can work with a sophisticated version of the theory, in which the symmetries act as isomorphisms.

This article gives an explicit presentation of Newtonian gravitation on the backdrop of Maxwell space-time, giving a sense in which acceleration is relative in gravitational theory. However, caution is needed: assessing whether this is a robust or interesting sense of the relativity of acceleration depends on some subtle technical issues and on substantive philosophical questions over how to identify the space-time structure of a theory.

This paper argues that much of the literature on interpreting scientific theories presupposes a certain picture of what interpretation involves: a picture according to which interpreting a theory is like translating from one language to another. In place of this “external” approach to interpretation, this paper proposes an “internal” approach, according to which interpretation is more concerned with delineating a theory’s internal semantic architecture.

Scientific properties come in degrees: elephants are more massive than mice. Are facts like these fundamental or can they be explained in other terms? This article argues that the structure of physical quantities like mass reduces to facts about the role that mass plays in the laws of nature. On this view elephants are more massive than mice partly in virtue of the fact that elephants are harder to throw around.

Substantivalism is the view that space exists in addition to any material bodies situated within it. Relationalism is the opposing view that there is no such thing as space; there are just material bodies, spatially related to one another. This paper assesses this issue in the context of classical physics. It starts by describing the bucket argument for substantivalism. It then turns to anti-substantivalist arguments, including Leibniz's classic arguments and their contemporary reincarnation under the guise of ‘symmetry’. It argues that (...) these anti-substantivalist arguments are stronger than is often acknowledged. (shrink)

Symmetries in physics are a guide to reality. That much is well known. But what is less well known is why symmetry is a guide to reality. What justifies inferences that draw conclusions about reality from premises about symmetries? I argue that answering this question reveals that symmetry is an epistemic notion twice over. First, these inferences must proceed via epistemic lemmas: premises about symmetries in the first instance justify epistemic lemmas about our powers of detection, and only from those (...) epistemic lemmas can we draw conclusions about reality. Second, in order to justify those epistemic lemmas, the notion of symmetry must be defined partly in epistemic terms. 1 Symmetry-to-Reality Reasoning1.1 A rough introduction to symmetry1.2 The symmetry-to-reality inference1.3 Two questions1.4 Two answers1.5 Preliminary clarifications2 Against Redundancy2.1 Redundancy2.2 Is absolute velocity redundant?2.3 Some redundancies3 Against Objectivity4 From Symmetry to Detection4.1 The epistemic approach4.2 The Occamist norm4.3 From symmetry to detection5 The Meaning of ‘Symmetry’5.1 A framework5.2 Formal definitions5.3 Ontic definitions6 Epistemic Definitions6.1 Taking observation seriously6.2 How things look6.3 Observation sentences6.4 Observational equivalence7 Symmetry as an Epistemic Notion 7.1 Observational equivalence and metaphysics7.2 The Occamist norm revisted7.3 Consequences8 Conclusion. (shrink)

Do properties have intrinsic properties of their own? If so, which second-order properties are intrinsic? This paper introduces two competing views about second-order intrinsicality: generalism, according to which the intrinsic–extrinsic distinction cuts across all orders of properties and applies to the properties of properties as well as the properties of objects, and objectualism, according to which intrinsicality is a feature exclusive to the properties of objects. The case for generalism is then surveyed along with some proposals for distinguishing intrinsic second-order (...) properties from extrinsic ones. After addressing these broad questions about the nature of second-order intrinsicality, the Problem of Accidental Intrinsic Properties of Properties is introduced and put to work as a case study for the significance of second-order intrinsicality. The connection between this problem and the metaphysics of quantitative properties is then examined. (shrink)

This paper aims to characterise properly entanglement as an external relation obtaining between multiple quantum degrees of freedom. In particular, we argue that the entanglement relation is a unique relation fully characterised by mutual information, i.e. a quantity standardly used as a measure of entanglement. This analysis leads us to propose a new metaphysical account of entanglement, which we call Relational Entanglement Tesseract. Such an account characterises entanglement for both bipartite and multipartite cases, and, at the same time, it satisfies (...) what we argue are three important desiderata of any metaphysical account of entanglement. (shrink)

Mathematicians, physicists, and philosophers of physics often look to the symmetries of an object for insight into the structure and constitution of the object. My aim in this paper is to explain why this practice is successful. In order to do so, I present a collection of results that are closely related to (and in a sense, generalizations of) Beth’s and Svenonius’ theorems.

Imagine that we are on a train playing with some mechanical systems. Why can’t we detect any differences in their behavior when the train is parked versus when it is moving uniformly? The standard answer is that boosts are symmetries of Newtonian systems. In this paper, I use the case of a spring to argue that this answer is problematic because symmetries are neither sufficient nor necessary for preserving its behavior. I also develop a new answer according to which boosts (...) preserve the relational properties on which the behavior of a system depends, even when they are not symmetries. (shrink)

A new argument is given for the thesis that only symmetry-invariant physical quantities are real. Non-invariant quantities are dynamically epiphenomenal in that they have no effect on the evolution of invariant quantities, and it is a significant theoretical vice to posit epiphenomenal quantities.

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.

Pettit (2006) argues that deferring to majority testimony is not generally rational: it may lead to inconsistent beliefs. He suggests that “another ... approach will do better”: deferring to supermajority testimony. But this approach may also lead to inconsistencies. In this paper, I describe conditions under which deference to supermajority testimony ensures consistency, and conditions under which it does not. I also introduce the concept of “consistency of degree k”, which is weaker than full consistency by ruling out only “blatant” (...) inconsistencies in an agent’s beliefs while permitting less blatant ones, and show that, while super-majoritarian deference often fails to ensure full consistency, it is a route to consistency in this weaker sense. (shrink)

This paper is concerned with the relation between two notions: that of two solutions or models of a theory being related by a symmetry of the theory and that of solutions or models being physically equivalent. A number of authors have recently discussed this relation, some taking an optimistic view, on which there is a suitable concept of the symmetry of a theory relative to which these two notions coincide, others taking a pessimistic view, on which there is no such (...) concept. The present paper arrives at a cautiously pessimistic conclusion. (shrink)