This article defends the principle of sufficient reason (PSR) from a simple and direct valid argument according to which PSR implies that there is a truth that explains every truth, namely an omni-explainer. Many proponents of PSR may be willing to bite the bullet and maintain that, if PSR is true, then there is an omni-explainer. I object to this strategy by defending the principle that explanation is irreflexive. Then I argue that proponents of PSR can resist the conclusion that (...) there is an omni-explainer by denying that explanation distributes over conjunction. In the final section, I consider a plausible revision of this assumption. I argue there that, given the revised assumption, PSR seems to yield a striking picture of the explanatory structure of the universe. I explain why the resulting model does not appear utterly implausible to me. (shrink)

The dynamic nature of physics cannot be captured through an exclusive focus on the static mathematical formulations of physical theories. Instead, we can more fruitfully think of physics as a set of distinctively social, cognitive, and theoretical/methodological practices. An emphasis on practice has been one of the most notable aspects of the recent “naturalistic turn” in general philosophy of science, in no small part due to the arguments of many feminist philosophers of science. A major project of feminist philosophy of (...) physics has been to shine a critical light on the social and cognitive practices in physics, and how those ultimately influence other aspects of the science. Here we argue that traditional philosophy of physics has focused exclusively on the theoretical/methodological practices of physics, and that feminist philosophy of physics seeks to broaden the focus to include the social and cognitive practices as well. (shrink)

Black holes are extremely relativistic objects. Physical processes around them occur in a regime where the gravitational field is extremely intense. Under such conditions, our representations of space, time, gravity, and thermodynamics are pushed to their limits. In such a situation philosophical issues naturally arise. In this chapter I review some philosophical questions related to black holes. In particular, the relevance of black holes for the metaphysical dispute between presentists and eternalists, the origin of the second law of thermadynamics and (...) its relation to black holes, the problem of information, black holes and hypercomputing, the nature of determinsim, and the breakdown of predictability in black hole space-times. I maintain that black hole physics can be used to illuminate some important problems in the border between science and philosophy, either epistemology and ontology. (shrink)

An energy condition, in the context of a wide class of spacetime theories, is, crudely speaking, a relation one demands the stress-energy tensor of matter satisfy in order to try to capture the idea that "energy should be positive". The remarkable fact I will discuss in this paper is that such simple, general, almost trivial seeming propositions have profound and far-reaching import for our understanding of the structure of relativistic spacetimes. It is therefore especially surprising when one also learns that (...) we have no clear understanding of the nature of these conditions, what theoretical status they have with respect to fundamental physics, what epistemic status they may have, when we should and should not expect them to be satisfied, and even in many cases how they and their consequences should be interpreted physically. Or so I shall argue, by a detailed analysis of the technical and conceptual character of all the standard conditions used in physics today, including examination of their consequences and the circumstances in which they are believed to be violated. (shrink)

In this dissertation, I argue that understanding possesses unique epistemic value. I propose and defend a novel account of understanding that I call the management account of understanding, which is the view that an agent A understands a subject matter S just in case A has the ability to extract the relevant information and exploit it with the relevant cognitive capacities to answer questions in S. Since inquiry is the process of raising and answering questions, I argue that without understanding, (...) it would be impossible to engage in successful inquiry. I argue that understanding is indispensable for effective cognition and that it is irreducible to other epistemic categories, such as knowledge, justification, or rationality. Understanding is an irreducible component of epistemic excellence. In arguing for this account, I focus on the nature and requirements of cognition and pay less attention to intuitions about hypothetical cases, in contrast to previous approaches to understanding. I draw upon psychology and cognitive science, especially work on the frame problem, to demonstrate the importance (and difficulty) of finding relevant information and exploiting it in relevant ways to answer questions. One’s cognitive system must be organized in such a way that one has the ability to think the relevant thoughts in the relevant ways to answer the relevant questions. This reveals well-defined directions in which future research on understanding should move. In addition to proposing and defending the management account of understanding, I explore several features of understanding, including some interesting consequences of the management account. I argue that the management account and commonly used methods of measuring degrees of understanding imply that understanding can be based on false beliefs. I argue that the management account (and any account of understanding that implies understanding is an ability) implies that understanding can be acquired by luck. I also argue that understanding is ontologically prior to explanation: a good explanation is essentially an act that produces understanding in the relevant cognitive background. (shrink)

One usually identifies a particular collection of geometric objects with the models of general relativity. But within this standard collection lurk ‘physically unreasonable’ models of spacetime. If such models are ruled out, attention can be restricted to some sub-collection of ‘physically reasonable’ models which can be considered a variant theory of general relativity. Since we have yet to identify a privileged sub-collection of ‘physically reasonable’ models, it is helpful to think of ‘general relativity’ in a pluralistic way; we can study (...) a collection of such ‘physically reasonable’ collections of models. (shrink)

This article deals with the question of what time reversal means. It begins with a presentation of the standard account of time reversal, with plenty of examples, followed by a popular non-standard account. I argue that, in spite of recent commentary to the contrary, the standard approach to the meaning of time reversal is the only one that is philosophically and physically viable. The article concludes with a few open research problems about time reversal.

I investigate the principle *anything goes* within the context of general relativity. After a few preliminaries, I show a sense in which the universe is unknowable from within this context; I suggest that we 'keep our options open' with respect to competing models of it. Given the state of affairs, proceeding counter-inductively seems to be especially appropriate; I use this method to blur some of the usual lines between 'reasonable' and 'unreasonable' models of the universe. Along the way, one is (...) led to a useful collection of variant theories of general relativity -- each theory incompatible with the standard formulation. One may contrast one variant theory with another in order to understand foundational questions within 'general relativity' in a more nuanced way. I close by sketching some of the work ahead if we are to embrace such a pluralistic methodology. (shrink)

Malament-Hogarth spacetimes are the sort of models within general relativity that seem to allow for the possibility of supertasks. There are various ways in which these spacetimes might be considered physically problematic. Here, we examine these criticisms and investigate the prospect of escaping them.

The beauty of electricity, or of any other force, is not that the power is mysterious and unexpected, touching every sense at unawares in turn, but that it is under law... Michael Faraday, Wheatstone's Electric Telegraph's Relation to Science (being an argument in favour of the full recognition of Science as a branch of Education), 1854.

Here we briefly review the concept of "prediction" within the context of classical relativity theory. We prove a theorem asserting that one may predict one's own future only in a closed universe. We then question whether prediction is possible at all (even in closed universes). We note that interest in prediction has stemmed from considering the epistemological predicament of the observer. We argue that the definitions of prediction found thus far in the literature do not fully appreciate this predicament. We (...) propose a more adequate alternative and show that, under this definition, prediction is essentially impossible in general relativity. (shrink)

This paper is a sequel to my 'Theological Misinterpretations of Current Physical Cosmology' (Foundations of Physics [1996], 26 (4); revised in Philo [1998], 1 (1)). There I argued that the Big Bang models of (classical) general relativity theory, as well as the original 1948 versions of the steady state cosmology, are each logically incompatible with the time-honored theological doctrine that perpetual divine creation ('creatio continuans') is required in each of these two theorized worlds. Furthermore, I challenged the perennial theological doctrine (...) that there must be a divine creative cause (as distinct from a transformative one) for the very existence of the world, a ratio essendi. This doctrine is the theistic reply to the question: 'Why is there something, rather than just nothing?' I begin my present paper by arguing against the response by the contemporary Oxford theist Richard Swinburne and by Leibniz to what is, in effect, my counter-question: 'But why should there be just nothing, rather than something?' Their response takes the form of claiming that the a priori probability of there being just nothing, vis-à-vis the existence of alternative states, is maximal, because the non-existence of the world is conceptually the simplest. On the basis of an analysis of the role of simplicity in scientific explanations, I show that this response is multiply flawed, and thus provides no basis for their three contentions that (i) if there is a world at all, then its 'normal', natural, spontaneous state is one of utter nothingness or total non-existence, so that (ii) the very existence of matter, energy and living beings constitutes a deviation from the allegedly 'normal', spontaneous state of 'nothingness', and (iii) that deviation must thus have a suitably potent (external) divine cause. Related defects turn out to vitiate the medieval Kalam Argument for the existence of God, as espoused by William Craig. Next I argue against the contention by such theists as Richard Swinburne and Philip L. Quinn that (i) the specific content of the scientifically most fundamental laws of nature, including the constants they contain, requires supra-scientific explanation, and (ii) a satisfactory explanation is provided by the hypothesis that the God of theism willed them to be exactly what they are. Furthermore, I contend that the theistic teleological gloss on the 'Anthropic Principle' is incoherent and explanatorily unavailing. Finally, I offer an array of considerations against Swinburne's attempt to show, via Bayes's theorem, that the existence of God is more probable than not. (shrink)

On the orthodox interpretation of bounce cosmologies, a preceding universe was compressed to a small size before “bouncing” to form the present expanding universe. William Lane Craig and James Sinclair have argued that the orthodox interpretation is incorrect if the entropy reaches a minimum at the bounce. In their view, the interface between universes represents the birth of two expanding universes, i.e., a “double bang” instead of a “big bounce”. Here, I reply to Craig and Sinclair in defense of the (...) orthodox interpretation. Contrary to their interpretation, features of one universe explain features of the other universe and so must precede the other universe in time. Moreover, contrary to a crucial part of Craig and Sinclair’s interpretation, there are bounce cosmologies in which the thermodynamic arrow of time is continuous through the bounce even though the entropy is “reset” at the bounce. (shrink)

The singularities from the general relativity resulting by solving Einstein's equations were and still are the subject of many scientific debates: Are there singularities in spacetime, or not? Big Bang was an initial singularity? If singularities exist, what is their ontology? Is the general theory of relativity a theory that has shown its limits in this case? In this essay I argue that there are singularities, and the general theory of relativity, as any other scientific theory at present, is not (...) valid for singularities. But that does not mean, as some scientists think, that it must be regarded as being obsolete. After a brief presentation of the specific aspects of Newtonian classical theory and the special theory of relativity, and a brief presentation of the general theory of relativity, the chapter Ontology of General Relativity presents the ontological aspects of general relativity. The next chapter, Singularities, is dedicated to the presentation of the singularities resulting in general relativity, the specific aspects of the black holes and the event horizon, including the Big Bang debate as original singularity, and arguments for the existence of the singularities. In Singularity Ontology, I am talking about the possibilities of ontological framing of singularities in general and black holes in particular, about the hole argument highlighted by Einstein, and the arguments presented by scientists that there are no singularities and therefore that the general theory of relativity is in deadlock. In Conclusions I outline and summarize briefly the arguments that support my above views. -/- DOI: 10.58679/TW62329. (shrink)

There exists a growing literature on the so-called physical Church-Turing thesis in a relativistic spacetime setting. The physical Church-Turing thesis is the conjecture that no computing device that is physically realizable can exceed the computational barriers of a Turing machine. By suggesting a concrete implementation of a beyond-Turing computer in a spacetime setting, Istvan Nemeti and Gyula David have shown how an appreciation of the physical Church-Turing thesis necessitates the confluence of mathematical, computational, physical, and indeed cosmological ideas. In this (...) essay, I will honour Istvan's seventieth birthday, as well as his longstanding interest in, and his seminal contributions to, this field going back to as early as 1987 by modestly proposing how the concrete implementation in Nemeti and D\'avid might be complemented by a quantum-information-theoretic communication protocol between the computing device and the logician who sets the beyond-Turing computer a task such as determining the consistency of Zermelo-Fraenkel set theory. This suggests that even the foundations of quantum theory and, ultimately, quantum gravity may play an important role in determining the validity of the physical Church-Turing thesis. (shrink)

We address the question of whether it is possible to operate a time machine by manipulating matter and energy so as to manufacture closed timelike curves. This question has received a great deal of attention in the physics literature, with attempts to prove no- go theorems based on classical general relativity and various hybrid theories serving as steps along the way towards quantum gravity. Despite the effort put into these no-go theorems, there is no widely accepted definition of a time (...) machine. We explain the conundrum that must be faced in providing a satisfactory definition and propose a resolution. Roughly, we require that all extensions of the time machine region contain closed timelike curves; the actions of the time machine operator are then sufficiently "potent" to guarantee that closed timelike curves appear. We then review no-go theorems based on classical general relativity, semi-classical quantum gravity, quantum field theory on curved spacetime, and Euclidean quantum gravity. Our verdict on the question of our title is that no result of sufficient generality to underwrite a confident "yes" has been proven. Our review of the no-go results does, however, highlight several foundational problems at the intersection of general relativity and quantum physics that lend substance to the search for an answer. (shrink)

I discuss singular space-times in the context of the geometrized formulation of Newtonian gravitation. I argue first that geodesic incompleteness is a natural criterion for when a model of geometrized Newtonian gravitation is singular, and then I show that singularities in this sense arise naturally in classical physics by stating and proving a classical version of the Raychaudhuri-Komar singularity theorem.

I argue that the best interpretation of the general theory of relativity has need of a causal entity, and causal structure that is not reducible to light cone structure. I suggest that this causal interpretation of GTR helps defeat a key premise in one of the most popular arguments for causal reductionism, viz., the argument from physics.

I argue that the Carroll-Chen cosmogonic model does not provide a plausible scientific explanation of the past hypothesis (the thesis that our universe began in an extremely low-entropy state). I suggest that this counts as a welcomed result for those who adopt a Mill-Ramsey-Lewis best systems account of laws and maintain that the past hypothesis is a brute fact that is a non-dynamical law.

I articulate and discuss a geometrical interpretation of Yang–Mills theory. Analogies and disanalogies between Yang–Mills theory and general relativity are also considered.

Every process studied in any science other than physics defines an arrow of time – to say nothing for the directedness of the processes of causation, inference, memory, control, and counterfactual dependence that occur in everyday life. The discussion in this chapter is confined to the arrow of time as it occurs in physics. The chapter briefly discusses those features of microscopic physics, which seem to conflict with time asymmetry. It explains just how this conflict plays out in the important (...) context of thermodynamics and statistical mechanics. The chapter then reviews the main strategies available for resolving the conflict between reversible microdynamics and irreversible macrodynamics, working within the context of the quantitative, time‐irreversible evolution laws that seem to apply to large‐scale phenomena. Finally, it offers a broad the discussion covering other arrows of time within physics. (shrink)

If time travel is possible, presumably so is my shooting my younger self ; then apparently I can kill him – I can commit retrosuicide. But if I were to kill him I would not exist to shoot him, so how can I kill him? The standard solution to this paradox understands ability as compossibility with the relevant facts and points to an equivocation about which facts are relevant: my killing YS is compossible with his proximity but not with his (...) survival, so I can kill him if facts like his survival are irrelevant but I cannot if they are relevant. I identify a lacuna in this solution, namely its reliance without argument on the hidden assumption that my killing YS is possible: if it is impossible, it is not compossible with anything. I argue that this lacuna is important, and I sketch a different solution to the paradox. (shrink)

We explore aspects of an experimental approach to mathematical proof, most notably number crunching, or the verification of subsequent particular cases of universal propositions. Since the rise of the computer age, this technique has indeed conquered practice, although it implies the abandonment of the ideal of absolute certainty. It seems that also in mathematical research, the qualitative criterion of effectiveness, i.e. to reach one’s goals, gets increasingly balanced against the quantitative one of efficiency, i.e. to minimize one’s means/ends ratio. Our (...) story will lead to the consideration of some limit cases, opening up the possibility of proofs of infinite length being surveyed in a finite time. By means of example, this should show that mathematical practice in vital aspects depends upon what the actual world is like. (shrink)

I consider the problem of extending Reichenbach's principle of the common cause to more than two events, vis-a-vis an example posed by Bernstein. It is argued that the only reasonable extension of Reichenbach's principle stands in conflict with a recent proposal due to Horwich. I also discuss prospects of the principle of the common cause in the light of these and other difficulties known in the literature and argue that a more viable version of the principle is the one provided (...) by Penrose and Percival (1962). (shrink)

Book Review of The Future of Spacetime, by Stephen Hawking et al.

In a recent publication in the European Journal for Philosophy of Science, Romero and Pérez claim to reveal new trouble for the already difficult life of presentism in relativistic spacetimes. Their argument purports to demonstrate the impossibility of postulating a viable present in the presence of black holes, in particular the Schwarzschild geometries. I argue that their argument is flawed, and that the Schwarzschild geometries they consider offer no novel threats to presentism. However, if we consider more general black holes, (...) different and more potent threats may be lurking in the dark. I discuss these threats and sketch how a presentist may respond, thus painting a more balanced picture of the way the existence of black holes might impact presentist metaphysics. At present there is no decisive verdict from black holes, but it turns out a close scrutiny of the developments in the relevant physics will be needed to see whether their import will remain so inconclusive. (shrink)

I wish to discuss a supposed implication of one sort of time travel. The sort of time travel is time travel into one’s past along a closed timelike curve. The implication is that in spacetimes with CTCs there can be no temporal passage or “flow” of time. I will argue that the implication does not hold.

I argue that there are no physical singularities in space–time. Singular space–time models do not belong to the ontology of the world, because of a simple reason: they are concepts, defective solutions of Einstein’s field equations. I discuss the actual implication of the so-called singularity theorems. In remarking the confusion and fog that emerge from the reification of singularities I hope to contribute to a better understanding of the possibilities and limits of the theory of general relativity.

H. G. Wells’ Time Traveller inhabits uniform Newtonian time. Where relativistic/quantum travelers into the past follow spacetime curvatures, past-bound Wellsians must reverse their direction of travel relative to absolute time. William Grey and Robin Le Poidevin claim reversing Wellsians must overlap with themselves or fade away piecemeal like the Cheshire Cat. Self-overlap is physically impossible but ‘Cheshire Cat’ fades destroy Wellsians’ causal continuity and breed bizarre fusions of traveler-stages with opposed time-directions. However, Wellsians who rotate in higher-dimensional space can reverse (...) temporal direction without self-overlap, Cheshire Cats or mereological monstrosities. Alas, hyper-rotation in Newtonian space poses dynamic and biological problems,. Controllable and survivable Wellsian travel needs topologically-variable spaces. Newtonian space, not Newtonian time, is Wellsians’ real enemy. (shrink)

Special relativity has been understood by many as vindicating a tenseless conception of time, denying the existence of tensed facts and a fortiori objective temporal passage. The reason for this is straightforward: both passage and the obtaining of tensed facts require a universal knife-edge present moment—yet this structure is not easily reconcilable with the relativity of simultaneity. The above being said, the prospects for tense and passage are sometimes claimed to be improved on moving to cosmological solutions of general relativity. (...) In this paper, we evaluate in detail these arguments, finding that there remain several open questions to be addressed if the introduction of tensed facts into the relativistic context is to be compelling. Moreover, we argue that, even setting aside these issues, objective tense stands and falls in relativity for exactly the same reasons that it does in classical philosophical discussions on the matter. (shrink)

The paper describes two approaches to determinism: one focuses on the features of global objects, such as possible worlds or models of a theory, whereas the other’s concern is the possible behaviour of individual objects. It then gives an outline of an individuals-based analysis of the determinism of theories. Finally, a general relativistic spacetime with non-isometric extensions is described and used to illustrate a conflict between the two approaches: this spacetime is indeterministic by the first approach but deterministic by the (...) second approach. (shrink)

The cosmic singularity provides negligible evidence for creation in the finite past, and hence theism. A physical theory might have no metric or multiple metrics, so a ‘beginning’ must involve a first moment, not just finite age. Whether one dismisses singularities or takes them seriously, physics licenses no first moment. The analogy between the Big Bang and stellar gravitational collapse indicates that a Creator is required in the first case only if a Destroyer is needed in the second. The need (...) for and progress in quantum gravity and the underdetermination of theories by data make it difficult to take singularities seriously. The singularity exemplifies the sort of gap that is likely to be closed by scientific progress, obviating special divine action. The apparent irrelevance of cardinality to practices of counting infinite sets in classical field theory and Fourier analysis is noted. Introduction The Doctrine of Creation and Its Warrant Cardinality and Sizes of Infinity Modern Cosmology and Creation Tolerance or Intolerance toward Singularities? Leibniz against Incompetent Watchmaker? Induction from Earlier Theories' Breakdown? Stellar Collapse Implies Theistic Destroyer Stacking the Deck for GTR Quantum Gravity Tends to Resolve Singularities Vicious God-of-the-Gaps Character Fluctuating or Inaccessible Warrant Big Bang Cosmology Not Especially Congenial to Faith CiteULike Connotea Del.icio.us What's this? (shrink)

Ulrich Meyer's book The Nature of Time uses tense logic to argue for a `modal' view of time, which replaces substantial times with `ersatz times' constructed using conceptually basic tense operators. He also argues against Bertrand Russell's relationist theory, in which times are classes of events, and against the idea that relativity compels the integration of time and space. I find fault with each of these negative arguments, as well as with Meyer's purported reconstruction of empty spacetime from tense operators (...) and substantial spatial points. I suggest that Meyer's positive project is best conceived as an elimination of time in the mode of Julian Barbour's The End of Time. (shrink)

This paper provides a taxonomy of cosmological arguments and givesgeneral reasons for thinking that arguments that belong to a given category do not succeed.

This chapter contains sections titled: Highlights of Past Literature Current Work Future Work.

Recent work in the physics literature demonstrates that, in particular classes of rotating spacetimes, physical light rays in general do not traverse null geodesics. Having presented this result, we discuss its philosophical significance, both for the clock hypothesis, and for the operational meaning of the metric field.

In a world awash in statistical patterns, should we conclude that the universe’s evolution or genesis is somehow subject to chance? I draw attention to alternatives that must be acknowledged if we are to have an adequate assessment of what chance the universe might have had.

Several authors have claimed that prediction is essentially impossible in the general theory of relativity, the case being particularly strong, it is said, when one fully considers the epistemic predicament of the observer. Each of these claims rests on the support of an underdetermination argument and a particular interpretation of the concept of prediction. I argue that these underdetermination arguments fail and depend on an implausible explication of prediction in the theory. The technical results adduced in these arguments can be (...) related to certain epistemic issues, but can only be misleadingly or mistakenly characterized as related to prediction. (shrink)

The claim of inflationary cosmology to explain certain observable facts, which the Friedmann-Roberston-Walker models of `Big-Bang' cosmology were forced to assume, has already been the subject of significant philosophical analysis. However, the principal empirical claim of inflationary cosmology, that it can predict the scale-invariant power spectrum of density perturbations, as detected in measurements of the cosmic microwave background radiation, has hitherto been taken at face value by philosophers. The purpose of this paper is to expound the theory of density perturbations (...) used by inflationary cosmology, to assess whether inflation really does predict a scale-invariant spectrum, and to identify the assumptions necessary for such a derivation. The first section of the paper explains what a scale invariant power-spectrum is, and the requirements placed on a cosmological theory of such density perturbations. The second section explains and analyses the concept of the Hubble horizon, and its behaviour within an inflationary space-time. The third section expounds the inflationary derivation of scale-invariance, and scrutinises the assumptions within that derivation. The fourth section analyses the explanatory role of `horizon-crossing' within the inflationary scenario. (shrink)

I present a recent historical case from cosmology—the story of inflationary cosmology—and on its basis argue that solving explanatory problems is a reliable method for making progress in science. In particular, I claim that the success of inflationary theory at solving its predecessor’s explanatory problems justified the theory epistemically, even in advance of the development of novel predictions from the theory and the later confirmation of those predictions.

Cosmological inflation is widely considered an integral and empirically successful component of contemporary cosmology. It was originally motivated by its solution of certain so-called fine-tuning problems of the hot big bang model, particularly what are known as the horizon problem and the flatness problem. Although the physics behind these problems is clear enough, the nature of the problems depends on the sense in which the hot big bang model is fine-tuned and how the alleged fine-tuning is problematic. Without clear explications (...) of these, it remains unclear precisely what problems inflationary theory is meant to be solving and whether it does in fact solve them. I analyze the structure of these problems and consider various interpretations that may substantiate the alleged fine-tuning. On the basis of this analysis I argue that at present there is no unproblematic interpretation available for which it can be said that inflation solves the big bang model’s alleged fine-tuning problems. (shrink)

Cosmologists often use certain global properties to exclude "physically unreasonable" cosmological models from serious consideration. But, on what grounds should these properties be regarded as "physically unreasonable" if we cannot rule out, even with a robust type of inductive reasoning, the possibility of the properties obtaining in our own universe?

We discuss some recent work by Tim Maudlin concerning Black Hole Information Loss. We argue, contra Maudlin, that there is a paradox, in the straightforward sense that there are propositions that appear true, but which are incompatible with one another. We discuss the significance of the paradox and Maudlin's response to it.

Here, we clarify the relationship among three space-time conditions of interest: geodesic completeness, hole-freeness, and inextendibility. In addition, we introduce a related fourth condition: effective completeness.

It has been argued that spacetime must be inextendible – that it must be “as large as it can be” in some sense. Here, we register some skepticism with respect to this position.

This article shows a clear sense in which general relativity allows for a type of ‘machine’ that can bring about a spacetime structure suitable for the implementation of ‘supertasks’. 1Introduction2Preliminaries3Malament–Hogarth Spacetimes4Machines5Malament–Hogarth Machines6Conclusion.

In this note, we cast doubt on the requirement of spacetime inextendibility; it is not at all clear that our universe is “as large as it can be.”.