The debate concerning the ontological status of spacetime is standardly construed as a dilemma between substantivalism and relationalism. I argue that a trilemma is more appropriate, emergent spacetime theories being the third category. Traditional philosophical arguments do not distinguish between emergent spacetime and substantivalism. It is arguments from physics that suggest giving up substantivalism in favour of emergent spacetime theories. The remaining new dilemma is between emergent spacetime and relationalism. I provide a list of questions, (...) which one should consider when discussing emergent spacetime theories, and apply them to a quantum superfluid toy model of emergent spacetime. (shrink)

This book argues that our current best theories of fundamental physics are best interpreted as positing spacetime as non-fundamental. It is written in accessible language and largely avoids mathematical technicalities by instead focusing on the key metaphysical and foundational lessons for the fundamentality of spacetime. -/- According to orthodoxy, spacetime and spatiotemporal properties are regarded as fundamental structures of our world. Spacetime fundamentalism, however, faces challenges from speculative theories of quantum gravity – roughly speaking, the project (...) of applying the lessons of quantum mechanics to gravitation and spacetime. This book demonstrates that the non-fundamentality of spacetime does not rely on speculative physics alone. Rather, one can give an interpretation of general relativity that supports some form of spacetime non-fundamentalism. The author makes the case for spacetime non-fundamentalism in three steps. First, he confronts the standard geometrical interpretation of general relativity with Brown and Pooley’s dynamical approach to relativity theory. Second, he considers an alternative derivation of the Einstein field equations, namely the classical spin-2 approach, and argues that it paves the way for a refined dynamical approach to general relativity. Finally, he argues that particle physics can serve as a continuity condition for the metaphysics of spacetime. -/- The Non-Fundamentality of Spacetime will be of interest to scholars and advanced students working in philosophy of physics, philosophy of science, and metaphysics. (shrink)

I give a new and more general argument against presentism within relativistic spacetimes. This argument is untouched by different recent proposals designed to save presentism in a relativistic setting.

Consider the following pair of theses: all fundamental physical objects are spatiotemporal and all non-fundamental physical objects are ultimately composed of fundamental objects. Work on the physics of quantum gravity suggests that spacetime is a non-fundamental, emergent phenomenon and thus that thesis is false. The fundamentals are non-spatiotemporal in nature. This paper will argue against on the grounds that non-fundamental spatiotemporal objects cannot be composed of fundamental non-spatiotemporal objects. So, assuming that spacetime is emergent, new metaphysical resources are (...) needed to explain the relationship between the fundamental objects posited by quantum gravity and spacetime. (shrink)

I propose a theory of space with infinitesimal regions called smooth infinitesimal geometry based on certain algebraic objects, which regiments a mode of reasoning heuristically used by geometricists and physicists. I argue that SIG has the following utilities. It provides a simple metaphysics of vector fields and tangent space that are otherwise perplexing. A tangent space can be considered an infinitesimal region of space. It generalizes a standard implementation of spacetime algebraicism called Einstein algebras. It solves the long-standing (...) problem of interpreting smooth infinitesimal analysis realistically, an alternative foundation of spacetime theories to real analysis, 277–392, 1980). SIA is formulated in intuitionistic logic and is thought to have no classical reformulations. Against this, I argue that SIG is such a reformulation. But SIG has an unorthodox mereology, in which the principle of supplementation fails. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Emergent Spacetime, the Megastructure Problem, and the Metaphysics of the SelfSusan Schneider (bio)The aim of this article is to introduce new thoughts on some pressing topics relating to my book, Artificial You, ranging from the fundamental nature of reality to quantum theory and emergence in large language models (LLM) like GPT-4. Since Artificial You was published, the innovations in the domain of AI chatbots like GPT-4 have (...) been rapid-fire, and at times dizzying. The thoughtful discussion in this symposium offers an important opportunity for cross-cultural engagement on these issues and more. I am grateful for the opportunity to learn from the insights of these authors and editors. [End Page 314]The order of my comments will be as follows: in the context of considering Christian Coseru's intriguing response (section 1), I begin by discussing the nature of the self, which I use as a springboard into larger, vexing issues about the nature of fundamental reality, given work on emergent spacetime (ES) (section 2). I offer a "Prototime Interpretation" of quantum mechanics in which spacetime emerges from a prototemporal arena, and use this idea to explore the nature of the self and mind.Using the assumption of ES, I devise an approach to metaphysically fundamental objects (which I call "quantum objects") based on quantum entanglement and the bundle theory of substance. I illustrate how the self or mind, insofar as it is a substance that supervenes on quantum objects, could be partly or fully determined by the properties of the quantum objects on which it supervenes. Intriguingly, this would mean that the self or mind is not located in any singular point in space at a given time. I also explain how the Prototime Interpretation of quantum mechanics is compatible with change and causation at the fundamental level.In section 3 I turn to Inês Hipólito's interesting article, discussing the import of not underestimating AI autonomy in light of the increasingly sophisticated large-language models (LLMs).1 I raise the "AI Megastructure Problem," a new problem of AI control arising in the context of the incipient AGI systems that are now populating the AI ecosystem. The problem, which arose from a collaboration with Kyle Kilian, considers the possibility of emergent properties from the interaction of the LLMs and other AI's in the AI ecosystem (Schneider and Kilian 2023). Then, turning to Noam Cook's intriguing discussion of Japanese philosophy, I consider the pressing issue of testing for machine consciousness, devising a modified version of my AI consciousness test (ACT), originally developed with astrophysicist Edwin Turner. I add an "interpretability component" to the ACT to deal with the case of LLMs (section 4).I. Patternism and the Biological Process ViewChristian Coseru's intriguing piece focuses on the chapters on personal identity in Artificial You, proposing that when it comes to the nature of the self, one should adopt "a biologically informed process-ontology perspective on personal identity," which "means recognizing that organic identity is different in kind: it is an identity of form rather than of matter."His position is akin to the patternist views that I argue against in Artificial You in the sense that it embraces the idea that form, rather than the particular matter that comprises one's brain and body, is key to one's survival over time. But there are important differences as well. For transhumanists tend to believe that the self can survive radical changes in one's substrate, transitioning from thinking with a biological brain to computing with a network of microchips, for instance. Coseru departs from this, writing: [End Page 315]As organisms, persons endure by undergoing constant change on a fundamentally cellular level, including the change in the neural pathways that realize the cognitive processes of thinking and expressing these very thoughts right now.Furthermore:[I]f persons are processes rather than things, then they cannot be cognitively enhanced by augmenting, replacing or transferring their functioning parts (e.g., brain cells).I will call this position the "Biological Process View" (BPV). I have several questions about it. First, how does this position solve one of the key problems I raised for... (shrink)

Recent decades have seen a revived interest in super-substantivalism, the idea that spacetime is the only fundamental substance and matter some kind of aspect, property or consequence of spacetime structure. However, the metaphysical debate so far has misidentified a particular variant of super-substantivalism with the position per se. I distinguish between a super-substantival core commitment and different ways of fleshing it out. I then investigate how general relativity and alternative spacetime theories square with the different variants of (...) super-substantivalism. (shrink)

I focus on the stochastic gravity program, a program that conceptualizes spacetime as the hydrodynamic limit of the correlation hierarchy of an underlying quantum theory, that is, a theory of the microscopic theory of gravity. This approach is relatively obscure, and so I begin by outlining the stochastic gravity program in enough detail to make clear the basic sense in which, on this approach, spacetime emerges from more fundamental physical structures. The theory, insofar as it is a univocal (...) theory, is quite clear in its basic features, and so issues of philosophical interpretation can be readily isolated.The most obvious reason to investigate the theory as a model for the emergence of spacetime structure is how close it is to the stage at which the behavior that we recognize as spacetime actually emerges from the micro gravitational system. Approaches that begin with fully quantum gravity treat a system that is conceptually quite far removed from the stage at which emergence is relevant. The stochastic approach however begins by identifying the point at which spacetime emerges as a phenomena of interest.I begin with an analysis of the emergence question generally and ask how best we should understand it, especially from the point of view of thinking of spacetime as emergent. A nice feature of the stochastic program is how clear the question of emergence is on this approach. In part this is because of its similarity by design to the kinetic theory of gases and solid state physics. And so many of the analyses of the emergence of macroscopic variables in the thermodynamic limit can be repurposed to understand how an apparently continuous metrical space emerges from the behavior of a non-spatial system.A serious interpretive problem looms however. The problem is that there is no clear connection between features of the kinetic theory of gravity, as a quantum theory, and any final theory of gravity. In the third part of the paper I will argue that as far as questions of emergence are concerned, we need not begin with a final, underlying theory, and I attempt to identify general issues connected to the emergence of spacetime that can be addressed in isolation from our certainty about that final theory. I will argue that this is a common way in which we treat our other, after all, provisional theories. We begin with the theories we have and ask about their implications without assuming that they are final theories, and yet also without explicitly downplaying the significance of the results we derive. Moreover I will attempt to show that, whatever character a final theory of micro gravity has, spacetime as an emergent structure in that theory is likely to be similar in important respects to the way it manifests in the stochastic gravity program. Briefly this is precisely because of the metaphysical neutrality of the kinetic theory. I will expand, in this section, on the nature of the emergence of the spacetime structure in the context of the stochastic gravity program and explain how the emergence is tied not to the particular model of interactions appealed to, but rather to the generic features of quantum fields with correlated fluctuations at all orders. (shrink)

This book provides an up-to-date overview of the foundations of spacetime physics. It features original essays written by world-class experts in the physics and philosophy of spacetime. The foundational questions regarding the origin and nature of spacetime are branching into new and exciting directions. These questions are not restricted to the quantum gravity program but also arise in the context of a well-established theory like general relativity. Against the background of these quick and diverse developments, this volume (...) features a broad range of perspectives on spacetime. Part I focuses on the nature of spacetime in non-quantum theories, such as Newtonian mechanics and relativity. Part II explores some intriguing conceptual implications of developing a quantum theory of spacetime. The Foundations of Spacetime Physics is an essential resource for scholars and advanced students working in philosophy of physics, philosophy of science, and scientific metaphysics. (shrink)

Newton and Einstein each in his way showed us the following: an epistemologically responsible physicist adopts the most measured understanding possible of spacetime structure. The proper way to infer a doctrine of spacetime is by a kind of measuring inference -- a deduction from phenomena. Thus it was (I argue) by an out-and-out deduction from the phenomena of inertiality (as colligated by the three laws of motion) that Newton delineated the conceptual presuppositions concerning spacetime structure that are (...) needed before we can actually think coherently about these phenomena. And Einstein (I argue) very much recapitulated this argument pattern, twice over in fact, recolligating the phenomena first so as to add something from the laws of electromagnetism, and then so as to add everything about gravitation, into what he understood by inertiality. Notably, to deduce one’s theoretical conclusions from phenomena is both more cautious and more cogent than to "infer to the best explanation". And in the context of the development of a doctrine of spacetime, deductions from phenomena lay before us formal rather than causal understanding. Deductions from phenomena tell us, in this context, not what things or what causes there are, but rather what our concepts should be like. The more measured the inference is, however, the more definitively it tells us this. For these reasons the most measured understanding of spacetime lies on a line between conventionalism and realism, between relationalism and absolutism, and indeed (as I demonstrate) between empiricism and rationalism. Spacetime is understood as neither merely immanent in material goings-on, nor truly transcendent of them either. In order to explain this understanding as adequately as I can and in order to remark its excellences most fully, I consider some respects in which the tertium quid between metaphysical realism and strict empiricism about spacetime is wise in the sense of practical wisdom. The wisest understanding of spacetime illustrates, I argue, an original and fundamental connection that epistemology has with ethics. (shrink)

How does the modern scientific conception of time constrain the project of assigning the mind its proper place in nature? On the scientific conception, it makes no sense to speak of the duration of a pain, or the simultaneity of sensations occurring in different parts of the brain. Such considerations led Henri Poincaré, one of the founders of the modern conception, to conclude that consciousness does not exist in spacetime, but serves as the basic material out of which we (...) must create the physical world. The central claim of Sensorama is that Poincaré was substantially correct. The best way to reconcile the scientific conception of time with the evidence of introspection is through a phenomenalist metaphysic according to which consciousness exists in neither time nor space, but serves as a basis for the logical construction of spacetime and its contents. (shrink)

The main research programs in quantum gravity tend to suggest in one way or another that most spacetime structures are not fundamental. At the same time, work in quantum foundations highlights fundamental features that are in tension with any straightforward space- time understanding. This paper aims to explore the little investigated but potentially fruitful links between these two fields.

Work in quantum gravity suggests that spacetime is not fundamental. Rather, spacetime emerges from an underlying, non-spatiotemporal reality. After clarifying the type of emergence at issue, I argue that standard conceptions of emergence available in metaphysics won’t work for the emergence of spacetime. I go on to consider spacetime functionalism as a way to make sense of spacetime emergence. I argue that a functionalist approach to spacetime modelled on mental state functionalism is not (...) a viable alternative to the standard conception of emergence in metaphysics. I go on to consider an alternative: ‘partial’ functionalism, whereby certain aspects of spacetime are functionalised, rather than spacetime as a whole. (shrink)

Leibnizian metaphysics underpins the universally held view that spacetime must be inextendible – that it must be “as large as it can be” in a sense. But here we demonstrate a surprising fact within the context of general relativity: the property of inextendibility turns out to be unstable when attention is restricted to certain collections of “physically reasonable”spacetimes.

The paper presents a metaphysical characterization of spatiotemporal backgrounds from a realist perspective. The conceptual analysis is based on a heuristic sketch that encompasses the common formal traits of the major spacetime theories, such as Newtonian mechanics and general relativity. It is shown how this framework can be interpreted in a fully realist fashion, and what is the role of background structures in such a picture. In the end it is argued that, although backgrounds are a source of metaphysical (...) discomfort, still they make a spacetime theory easy to interpret. It is also suggested that this conclusion partially explains why the notion of background independence carries a lot of conceptual difficulties. (shrink)

This paper argues against the proposal to draw from current research into a physical theory of quantum gravity the ontological conclusion that spacetime or spatiotemporal relations are not fundamental. As things stand, the status of this proposal is like the one of all the other claims about radical changes in ontology that were made during the development of quantum mechanics and quantum field theory. However, none of these claims held up to scrutiny as a consequence of the physics once (...) the theory was established and a serious discussion about its ontology had begun. Furthermore, the paper argues that if spacetime is to be recovered through a functionalist procedure in a theory that admits no fundamental spacetime, standard functionalism cannot serve as a model: all the known functional definitions are definitions in terms of a causal role for the motion of physical objects and hence presuppose spatiotemporal relations. (shrink)

ABSTRACT: Special Relativity is not a branch of electromagnetism: it does not depend on light’s having a constant, limiting speed. If the theory is true, it depends on no matter theory. Rather, very general and familiar symmetries of space and time impose the form of the Lorentz transformation on every matter theory, independently of any that obeys it. I explore this and its metaphysical consequences.

Questions about the metaphysics of causation may be usefully divided as follows. First, there are questions about the nature of the causal relata, including (1.1) whether they are in spacetime immanence), (1.2) how fine grained they are individuation), and (1.3) how many there are adicity). Second, there are questions about the metaphysics of the causal relation, including (2.1) what is the difference between causally related and causally unrelated sequences connection), (2.2) what is the difference between sequences related (...) as cause to effect, and those related as effect to cause or as joint effects of a common cause direction), and (2.3) what is the difference between sequences involving the cause, and those involving mere conditions selection). (shrink)

Metaphysics of Quantum Gravity The metaphysics of quantum gravity explores metaphysical issues related to research programs in theoretical physics clustered under the term quantum gravity. These research programs aim at the formulation of a theory that reconciles the theory of general relativity with quantum theory. The goal is not necessarily to come up with a … Continue reading Metaphysics of Quantum Gravity →.

We consider to what extent the fundamental question of spacetime singularities is relevant for the philosophical debate about the nature of spacetime. After reviewing some basic aspects of the spacetime singularities within general relativity, we argue that the well known difficulty to localize them in a meaningful way may challenge the received metaphysical view of spacetime as a set of points possessing some intrinsic properties together with some spatiotemporal relations. Considering the algebraic formulation of general relativity, (...) we argue that the spacetime singularities highlight the philosophically misleading dependence on the standard geometric representation of spacetime. †To contact the author, please write to: Department of Philosophy, University of Lausanne, CH-1015 Lausanne, Switzerland; e-mail: [email protected]. (shrink)

The debate between substantivalists and relationists about spacetime was given a new lease of life approximately twenty years ago, when John Earman and John Norton published an argument for the conclusion that, in the light of general relativity, substantivalism is untenable. Responses to Earman and Norton’s argument generated a proliferation of ‘substantivalisms’, and a debate between them that was, to the ears of at least some, distinctively metaphysical in character.

There are two metaphysical pictures of spacetime: The evolutionary picture and the all-at-once picture. According to the evolutionary picture, spacetime is nothing but the evolution of space over time. In contrast, the all-at-once picture considers spacetime as ‘a global, four-dimensional boundary value problem’ that can be solved only in an all-at-once manner, i.e. as a whole which is fundamentally four-dimensional and non-decomposable into spatial and temporal parts. The two most-known formulations of general theory of relativity, i.e. the (...) Hamiltonian (or the canonical) and the Lagrangian (or the standard) formulations, enjoy the evolutionary and all-at-once pictures of spacetime respectively. Here, we have argued that (1) the all-at-once picture is more aligned with the philosophy of relativity theory, i.e. uniting space and time into spacetime, (2) the evolutionary picture is not as general as the all-at-once, since only in special cases, such as globally hyperbolic spacetimes, is it possible to deal with spacetime as the evolution of a spatial slice over time, and (3) the all-at-once picture paves the way to better understanding _four-dimensional_ physical entities, like event horizons, which cannot be explained within an evolutionary picture without raising a paradox. Therefore, the evolutionary picture is neither the _fundamentally-true_ nor the _naturally-chosen_ picture of spacetime. Rather, we choose the evolutionary picture for practical and computational reasons. While the all-at-once picture seems a more appropriate description of the quantum and cosmological reality, the evolutionary picture can be applied occasionally and locally, or quasi-locally, and is not the proper metaphysical picture of spacetime at the fundamental level of reality. (shrink)

This paper aims to discuss two realist conceptions about causation in the light of the general theory of relativity. I first consider the conserved quantity of causation, which explicitly relies on the energy conservation principle. Such principle is however problematic within GTR, mainly because of the dynamical nature of the spacetime structure itself. I then turn to the causal theory of properties, according to which properties are such that insofar as they are certain qualities, they are powers to produce (...) certain effects. In order to be compatible with GTR, such theory has to assume non-trivial global conditions on the spacetime structure; such assumptions seem to deprive the „singularist‟ non-Humean feature of this theory of causation. The question of the possible causal nature of spacetime properties is addressed in the conclusion. (shrink)

The procedures of canonical quantization of the gravitational field apparently lead to entities for which any interpretation in terms of spatio-temporal localization or spatio-temporal extension seems difficult. This fact is the main ground for the suggestion that can often be found in the physics literature on canonical quantum gravity according to which spacetime may not be fundamental in some sense. This paper aims to investigate this radical suggestion from an ontologically serious point of view in the cases of two (...) standard forms of canonical quantum gravity, quantum geometrodynamics and loop quantum gravity. We start by discussing the physical features of the quantum wave functional of quantum geometrodynamics and of the spin networks of loop quantum gravity that motivate the view according to which spacetime is not fundamental. We then point out that, by contrast, for any known ontologically serious understanding of quantum entanglement, the commitment to spacetime seems indispensable. Against this background, we then critically discuss the idea that spacetime may emerge from more fundamental entities. As a consequence, we finally suggest that the emergence of classical spacetime in canonical quantum gravity faces a dilemma: either spacetime ontologically emerges from more fundamental non-spatio-temporal entities or it already belongs to the fundamental quantum gravitational level and the emergence of the classical picture is merely a matter of levels of description. On the first horn of the dilemma, it is unclear how to make sense of concrete physical entities that are not in spacetime and of the notion of ontological emergence that is involved. The second horn runs into the difficulties raised by the physics of canonical quantum gravity. (shrink)

Dispositionalism is the view that causal powers are among the irreducible properties of nature. It has long been among the core competing positions in the metaphysics of laws, but its potential implications for other key debates within metaphysics and the philosophy of science have remained under-explored. Travis Dumsday fills this major gap in the literature by establishing new connections between dispositionalism and such topics as substance ontology, ontic structural realism, material composition, emergentism, natural-kind essentialism, perdurantism, time travel, and (...) spacetime substantivalism. He also puts forward a novel view concerning the precise relationship between causal powers and the fundamental laws of nature. His rich and accessible study will appeal to readers interested in contemporary analytic metaphysics and philosophy of science. (shrink)

Supersymmetry (SUSY) is a proposed symmetry between bosons and fermions. The structure of the space of SUSY generators is such that the distinction between internal and spacetime symmetries is blurred. As a result, there are two viable candidates for the correct spacetime setting for a flat supersymmetric field theory---Minkowski spacetime and superspace. an extension of four- dimensional Minkowski spacetime to include (at least) four new dimensions, coordinatised by mathematical objects known as supernumbers. These objects are, in (...) one significant way, quite different from real or complex number---some of them have the property that their order of multiplication makes a difference; in mathematical terms, they are said to have nontrivial commutation properties. This paper argues for two theses: first, that one standard set of arguments, related to universality of symmetry behaviour, that motivate a particular choice of spacetime structure in familiar spacetime theories motivates the choice of superspace as the appropriate spacetime for SUSY field theories. And second, that the metaphysical utility of the concept of spacetime requires more than just the satisfaction of this universality condition; in supersymmetric theories, the spacetime concept is not as useful as in special relativity. (shrink)

This essay demonstrates the inadequacy of contemporary substantivalist and relationist interpretations of quantum gravity hypotheses via an historical investigation of the debate on the underlying ontology of space in the seventeenth century. Viewed in the proper context, there are crucial similarities between seventeenth century theories of space and contemporary work on the ontological foundations of spacetime theories, and these similarities challenge the utility of the substantival/relational dichotomy by revealing a host of underlying conceptual issues that do not naturally align (...) with that distinction. (shrink)

This volume explores the inadequacies of the two standard conceptions of space or spacetime, substantivalism and relationism, and in the process, proposes a new historical interpretation of these physical theories. This book also examines and develops alternative ontological conceptions of space, such as the property theory of space and emergent spacetime hypotheses, and explores additional historical elements of seventeenth century theories and other metaphysical themes. Readers will learn about specific problems with the substantivalism versus relationism dichotomy. First, Newton (...) and Leibniz are often upheld as the retrospective forerunners of, respectively, substantivalism and relationism, but their work often contradicts the central tenets of these views. Second, these theories have proven problematic when transferred to a modern setting, especially with regards to general relativity and the recent quantum gravity hypotheses. In order to address these problems, the author develops a new classificational system that provides a more accurate taxonomy for the elements of all spatial ontologies, both in the seventeenth century and for contemporary theories of physics. This classification obtains successful analogies between Newton, Leibniz, and other natural philosophers with contemporary physical theories, and it also admits a role for the current brand of emergent spacetime hypotheses and the property theory of space. (shrink)

We present a new metaphysical framework for physics that is conceptually clear, ontologically parsimonious, and empirically adequate. This framework relies on the notion of self-subsisting structure, that is, a set of fundamental physical elements whose individuation and behavior are described in purely relational terms, without any need for a background spacetime. Although the specification of the fundamental elements of the ontology depends on the particular physical domain considered---and is thus susceptible to scientific progress---, the empirically successful structural features of (...) the framework are preserved through theory change. The kinematics and dynamics of these self-subsisting structures are technically implemented using the theoretical framework of Pure Shape Dynamics, which provides a completely relational physical description of a system in terms of the intrinsic geometry of a suitably defined space called shape space. (shrink)

This paper has a twofold objective. First, it engages with the interrelation of time, space, and matter in Kant, Heidegger, and Derrida and questions whether and how this interrelation effects the possibility of self-relation. In Kant and the Problem of Metaphysics Heidegger suggests that the very structure of subjectivity is constituted by what he calls the ‘pure self-affection’ of time and thus the possibility of self-relation is intimately bound up with the temporalizing of time. In his 1964–65 seminar, Heidegger: (...) the Question of Being and History, Derrida translates this pure affection of time into the more generic term ‘auto-affection,’ which will remain a pivotal reference point for his deconstruction of the metaphysical privileging of time as presence. Derrida shows how the (im)possibility of auto-affection is bound up not only with time but also with space, or rather with the ‘spacing of time’ that he also refers to as ‘the trace.’ Second, the paper moves across the frontiers of philosophy and physics posing anew the question concerning the interrelations of temporality, spatiality, and materiality. With reference to what in general relativity is called ‘the curvature of spacetime,’ the efficacy of materiality in the movement of auto-affection is called into question. (shrink)

This essay develops a interpretation of Leibniz’ theory of motion that strives to integrate his metaphysics of force with his doctrine of the equivalence of hypotheses, but which also supports a realist, as opposed to a fully idealist, interpretation of his natural philosophy. Overall, the modern approaches to Leibniz’ physics that rely on a fixed spacetime backdrop, classical mechanical constructions, or absolute speed, will be revealed as deficient, whereas a more adequate interpretation will be advanced that draws inspiration (...) from an invariantist conception of reality and recent non-classical theories of physics. (shrink)

The goal of this essay is twofold. First, it provides a quick look at the foundations of modern relational mechanics by tracing its development from Julian Barbour and Bruno Bertotti's original ideas until present-day's pure shape dynamics. Secondly, it discusses the most appropriate metaphysics for pure shape dynamics, showing that relationalism is more of a nuanced thesis rather than an elusive one. The chapter ends with a brief assessment of the prospects of pure shape dynamics in light of quantum (...) physics. (shrink)

Realism about general relativity (GR) seems to imply realism about spacetime curvature. The existence of the teleparallel equivalent of general relativity (TEGR) calls this into question, for (a) TEGR is set in a torsionful but flat spacetime, and (b) TEGR is empirically equivalent to GR. Knox (Stud Hist Philos Sci Part B Stud Hist Philos Mod Phys 42(4):264–275, 2011) claims that there is no genuine underdetermination between GR and TEGR; we call this verdict into question by isolating and (...) addressing her individual arguments. In addition, we anticipate and evaluate two further worries for realism about the torsionful spacetimes of TEGR, which we call the ‘problem of operationalisability’ and the ‘problem of visualisability’. (shrink)

Eleanor Knox has argued that our concept of spacetime applies to whichever structure plays a certain functional role in the laws (the role of determining local inertial structure). I raise two complications for this approach. First, our spacetime concept seems to have the structure of a cluster concept, which means that Knox's inertial criteria for spacetime cannot succeed with complete generality. Second, the notion of metaphysical fundamentality may feature in the spacetime concept, in which case (...) class='Hi'>spacetime functionalism may be uninformative in the absence of answers to fundamental metaphysical questions like the substantivalist/relationist debate. (shrink)

The hole argument purports to show that all spacetime theories of a certain form are indeterministic, including the General Theory of Relativity. The argument has given rise to an industry of searching for a metaphysics of spacetime that delivers the right modal implications to rescue determinism. In this paper, I first argue that certain prominent extant replies to the hole argument—namely, those that appeal to an essentialist doctrine about spacetime—fail to deliver the requisite modal implications. As (...) part of my argument, I show that threats to determinism of the sort brought out by the hole argument are more general than has heretofore been recognized. I then use these results to propose a novel essentialist doctrine about spacetime that successfully rescues determinism, what I call sufficiency metric essentialism. However, I go on to argue that once we realize what an essentialist doctrine about spacetime must look like in order to address the hole argument, we should reject all such doctrines, because they can't fulfill their ambition of improving on standard modal replies to the argument. I close by suggesting some lessons for future work on spacetime and the metaphysics of physics more broadly, and also drawing some general morals for contemporary metaphysics, in particular about (i) whether essence can be used to articulate a precise structuralist doctrine, and (ii) the relationship between essence and modality. (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)

The mathematical structure of realist quantum theories has given rise to a debate about how our ordinary 3-dimensional space is related to the 3N-dimensional configuration space on which the wave function is defined. Which of the two spaces is our (more) fundamental physical space? I review the debate between 3N-Fundamentalists and 3D-Fundamentalists and evaluate it based on three criteria. I argue that when we consider which view leads to a deeper understanding of the physical world, especially given the deeper topological (...) explanation from the unordered configurations to the Symmetrization Postulate, we have strong reasons in favor of 3D-Fundamentalism. I conclude that our evidence favors the view that our fundamental physical space in a quantum world is 3-dimensional rather than 3N-dimensional. I outline lines of future research where the evidential balance can be restored or reversed. Finally, I draw lessons from this case study to the debate about theoretical equivalence. (shrink)

Graham Nerlich is one of the most distinguished of contemporary philosophers of space and time. Eleven of his essays are here brought together in a carefully structured volume, which deal with ontology and methodology in relativity, variable curvature and general relativity, and time and causation. The author has provided a new general introduction and also introductions to each part to bring the discussion more up to date and draw out the general themes. The book will be welcomed by all philosophers (...) of physics, and of science in general. (shrink)

This paper challenges the traditional metaphysical assumption that properties can be located in spacetime and examines the ontological implications of categorizing spacetime itself. By introducing a two-category ontology, we argue that attempts to locate properties in spacetime represent a category mistake, as this notion fails to address the fundamental categorization of spacetime. We propose that the notion of instantiation should be conceptually separated from spatiotemporal location, thereby allowing for properties that are Platonic yet immanent. Furthermore, we (...) reevaluate the debate between Platonism and Aristotelianism, advocating that Platonic properties can possess a form of immanence previously thought to be exclusive to Aristotelian frameworks. This reformation not only underscores the need for categorizing spacetime but also reshapes our understanding of the instantiation and immanence of properties within ontological dependence frameworks. (shrink)

A number of approaches to quantum gravity (QG) seem to imply that spacetime does not exist. Philosophers are quick to point out, however, that the loss of spacetime should not be regarded as total. Rather, we should interpret these approaches as ones that threaten the fundamentality but not the existence of spacetime. In this paper, I argue for two claims. First, I argue that spacetime realism is not forced by QG; spacetime eliminativism remains an option. (...) Second, I argue that eliminativism provides a useful framework for developing two existing approaches to the metaphysics of QG, involving functionalism and mereology respectively. (shrink)

There are famously two main metaphysics of persistence, namely three and four-dimensionalism. Both yield a particular solution to the so called puzzle of change. I argue that typical three-dimensionalist solutions to the puzzle face insurmountable difficulties even in the simplest relativistic setting, that of Minkowski spacetime.

Eleanor Knox has argued that our concept of spacetime applies to whichever structure plays a certain functional role in the laws. I raise two objections to this inertial functionalism. First, it depends on a prior assumption about which coordinate systems defined in a theory are reference frames, and hence on assumptions about which geometric structures are spatiotemporal. This makes Knox’s account circular. Second, her account is vulnerable to several counterexamples, giving the wrong result when applied to topological quantum field (...) theories and parity- and time-asymmetric theories. I advance an alternative account on which our spacetime concept is a cluster concept. On this view, the notion of metaphysical fundamentality may feature in the cluster, in which case spacetime functionalism may be uninformative in the absence of answers to fundamental metaphysical questions like the substantivalist/relationist debate. (shrink)

This paper examines how science and metaphysics interact in our theories about space and time. It is argued that scientific development affects philosophical thoughts about space and time. We first review the traditional arguments of substantivalists and relationists about space and time, especially those contained in the correspondence between Leibniz and Clarke. Then we show the mutual influence of science and metaphysics in the modern scientific era: for example, in neo-Newtonian structure, field theory, and special and general theories (...) of relativity. In the end, we claim that the substantivalist's position seems more defensible considering new scientific theories, such as Einstein's theory of general relativity. (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)

A collection of previously published papers with short new introductions, the volume supplements Nerlich's argument for realism about spacetime in The Shape of Space which appeared in its second edition together with the present book. The first group of essays in the collection discusses how properly to put questions about ontological commitments to theories of spacetime and how to answer them. Do not just ask the Quinean question, Nerlich suggests, "Which objects does the theory quantify over?" The proper (...) question rather is: "What 'ontic structures' does the theory specify; i.e., in what relations do the objects of the theory stand to each other?". This methodological strategy prepares the ground for Nerlich's own view on spacetime: It is a geometric structure, a way of relating objects which exists independently of the objects, a "physical particular" but not a material substance. Nerlich is a "realist about geometric structure," hence opposed to relationalist views of spacetime, but nevertheless he is not a substantivalist. (shrink)

This paper is an investigation of metaphysical nihilism: the view that there could have been no contingent or concrete objects. I begin by showing the connections of the nihilistic theses to other philosophical doctrines. I then go on to look at the arguments for and against metaphysical nihilism in the literature and find both to be flawed. In doing so I will look at the nature of abstract objects, the nature of spacetime and mereological simples, the existence of the (...) empty set, the dependence of universals on particulars, and other general questions of ontology. (shrink)

One of the most intuitive views about the metaphysics of laws of nature is Tim Maudlin's idea of a Fundamental Law of Temporal Evolution. So-called FLOTEs are primitive elements of the universe that produce later states from earlier states. While FLOTEs are at home in traditional Newtonian and non-relativistic quantum mechanical theories (not to mention our pre-theoretic conception of the world), I consider here whether they can be made to work with relativity. In particular, shifting to relativistic spacetimes poses (...) two threats to FLOTEs. First, the lack of a privileged spacelike hypersurface in relativistic spacetime makes it unclear how to understand what produces what. A survey of several conceptions of the nomic production relation compatible with relativity reveals all of them to be lacking. Second, relativity motivates a four-dimensional block universe conception of time, according to which all events that will ever occur already exist. On such a view, it's unclear what work there is to be done by FLOTEs. I consider how a proponent of FLOTEs might respond, but conclude that these combined threats seriously undermine the prospects of a productive conception of laws. In short, if spacetime is relativistic, laws are not productive. (shrink)