We address the problem of observables in generally invariant spacetime theories such as Einstein’s general relativity. Using the refined notion of an event as a “point-coincidence” between scalar fields that completely characterise a spacetime model, we propose a generalisation of the relational local observables that does not require the existence of four everywhere invertible scalar fields. The collection of all point-coincidences forms in generic situations a four-dimensional manifold, that is naturally identified with the physical spacetime.

I have argued that even if time travel is metaphysically possible, there are some things a time traveler would not be able to do. I reply here to critics who have argued that my account entails fatalism about the past or entails that the time traveler is unfree or that she is bound by “strange shackles.” My argument does not entail any sort of fatalism. The time traveler is able to do many of the things that everyone else can do (...) and is as free as any non-time-traveler. The time traveler is constrained only as we all are by the laws of nature. My argument shows only how strangely those constraints must operate if those laws permit time travel. (shrink)

We show a sense in which the spacetime property of effective completeness—a type of “local hole-freeness” or “local inextendibility”—is not stable.

The paper discusses major implications of high energy physics for the scientific realism debate. The first part analyses the ways in which aspects of the empirically well-confirmed standard model of particle physics are relevant for a reassessment of entity realism, ontological realism and structural realism. The second part looks at the implications of more far-reaching concepts like string theory. While those theories have not found empirical confirmation, if they turned out viable, their implications for the realism debate would be more (...) substantial than those of the standard model. (shrink)

In this article, I examine whether or not the Hamiltonian and Lagrangian formulations of classical mechanics are equivalent theories. I do so by applying a standard for equivalence that was recently introduced into philosophy of science by Halvorson and Weatherall. This case study yields three general philosophical payoffs. The first concerns what a theory is, while the second and third concern how we should interpret what our physical theories say about the world. 1Introduction 2When Are Two Theories Equivalent? 3Preliminaries on (...) Classical Mechanics 3.1Hamiltonian mechanics 3.2Lagrangian mechanics 4Are Hamiltonian and Lagrangian Mechanics Equivalent Theories? 4.1Tangent bundle versus cotangent bundle 4.2Tangent bundle versus symplectic manifold 4.3Lagrangian vector field versus Hamiltonian vector field 5Conclusion Appendix. (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)

Bayesian Coherence Theory of Justification or, for short, Bayesian Coherentism, is characterized by two theses, viz. (i) that our degree of confidence in the content of a set of propositions is positively affected by the coherence of the set, and (ii) that coherence can be characterized in probabilistic terms. There has been a longstanding question of how to construct a measure of coherence. We will show that Bayesian Coherentism cannot rest on a single measure of coherence, but requires a vector (...) whose components exhaustively characterize the coherence properties of the set. Our degree of confidence in the content of the information set is a function of the reliability of the sources and the components of the coherence vector. The components of this coherence vector are weakly but not strongly separable, which blocks the construction of a single coherence measure. (shrink)

In this paper, we examine the relationship between general relativity and the theory of Einstein algebras. We show that according to a formal criterion for theoretical equivalence recently proposed by Halvorson and Weatherall, the two are equivalent theories.

I address a question recently raised by Simon Saunders concerning the relationship between the space-time structure of Newton-Cartan theory and that of what I will call “Maxwell-Huygens space-time.” This discussion will also clarify a connection between Saunders’s work and a recent paper by Eleanor Knox.

An outstanding problem in so-called modal interpretations of quantum mechanics has been the specification of a dynamics for the properties introduced in such interpretations. We develop a general framework (in the context of the theory of stochastic processes) for specifying a dynamics for interpretations in this class, focusing on the modal interpretation by Vermaas and Dieks. This framework admits many empirically equivalent dynamics. We give some examples, and discuss some of the properties of one of them. This approach is applicable (...) to a wider class of theories, in particular, those using (discrete) strict effective—as in decoherence theory—superselection rules. (shrink)

Celem artykułu jest pokazanie, skąd się biorą nasze trudności z wyjaśnieniem, na czym polega upływ czasu, oraz przedstawienie pewnej propozycji rozwiązania tego problemu, opartej na koncepcji dynamicznego istnienia rzeczy, a rozwijającej ideę absolutnego stawania się. Rozważania oparte są na założeniu, że nasze podstawowe teorie metafizyczne – podobnie jak te stosowane w naukach przyrodniczych – powinny spełniać warunek spójności, prostoty oraz bogatej zawartości.

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.

This survey article is divided into two parts. In the first (section 2), I give a brief account of the structure of classical relativity theory. In the second (section 3), I discuss three special topics: (i) the status of the relative simultaneity relation in the context of Minkowski spacetime; (ii) the ``geometrized" version of Newtonian gravitation theory (also known as Newton-Cartan theory); and (iii) the possibility of recovering the global geometric structure of spacetime from its ``causal structure".

The causal set programme towards a quantum theory of gravity is situated vis-à-vis the long-standing debate between eternalism (block theory) and past-presentism or possibilism (growing block theory) in the philosophy of time. It is argued that despite 'appearances' and declarations to the contrary, the programme does not side with growing block theorists when it comes to harboring a robust notion of Becoming - at least, not more than familiar relativistic theories on continuous spacetime manifolds. The problem stems mainly from the (...) postulate of discrete general covariance - a requirement imposed upon the only fully worked out kind of dynamics for causal sets to date, a dynamics of a classical stochastic process. (shrink)

The paper is an overview of the connections between scientific psychology and religion. The thesis that scientific psychology, which deals with empirical research of all manifestations of spirituality and religiousness within the different principles and contexts of culture, cannot refer to the doctrine of religion, but it should take into account in its research the cultural aspects of the religion without valuing them at the individual human level and their influence on the "fate" of the world, is being discussed. Conclusion: (...) Against the background of the twentieth-century Anglo-Saxon psychology, based on the positivist paradigm, there is no place on the basis of valid methodological canons for building a direct relationship between scientific psychology and religion. (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)

The difficult issues related to the interpretation of quantum mechanics and, in particular, the “measurement problem” are revisited using as motivation the process of generation of structure from quantum fluctuations in inflationary cosmology. The unessential mathematical complexity of the particular problem is bypassed, facilitating the discussion of the conceptual issues, by considering, within the paradigm set up by the cosmological problem, another problem where symmetry serves as a focal point: a simplified version of Mott’s problem.

Under the normal assumptions of quantum field theory, Haag’s theorem states that any field unitarily equivalent to a free field must itself be a free field. Unfortunately, the derivation of the Dyson series perturbation expansion relies on the use of the interaction picture, in which the interacting field is unitarily equivalent to the free field but must still account for interactions. Thus, the traditional perturbative derivation of the scattering matrix in quantum field theory is mathematically ill defined. Nevertheless, perturbative quantum (...) field theory is currently the only practical approach for addressing scattering for realistic interactions, and it has been spectacularly successful in making empirical predictions. This paper explains this success by showing that Haag’s Theorem can be avoided when quantum field theory is formulated using an invariant, fifth path parameter in addition to the usual four position parameters, such that the Dyson perturbation expansion for the scattering matrix can still be reproduced. As a result, the parameterized formalism provides a consistent foundation for the interpretation of quantum field theory as used in practice and, perhaps, for better dealing with other mathematical issues. (shrink)

I address the problem of indefiniteness in quantum mechanics: the problem that the theory, without changes to its formalism, seems to predict that macroscopic quantities have no definite values. The Everett interpretation is often criticised along these lines, and I shall argue that much of this criticism rests on a false dichotomy: that the macroworld must either be written directly into the formalism or be regarded as somehow illusory. By means of analogy with other areas of physics, I develop the (...) view that the macroworld is instead to be understood in terms of certain structures and patterns which emerge from quantum theory (given appropriate dynamics, in particular decoherence). I extend this view to the observer, and in doing so make contact with functionalist theories of mind. (shrink)

A critical re-examination of the history of the concepts of space (including spacetime of general relativity and relativistic quantum field theory) reveals a basic ontological elusiveness of spatial extension, while, at the same time, highlighting the fact that its epistemic primacy seems to be unavoidably imposed on us (as stated by A.Einstein “giving up the extensional continuum … is like to breathe in airless space”). On the other hand, Planck’s discovery of the atomization of action leads to the fundamental recognition (...) of an ontology of non-spatial, abstract entities (Quine) for the quantum level of reality (QT), as distinguished from the necessarily spatio-temporal, experimental revelations (measurements). The elementary quantum act (measured by Planck’s constant) has neither duration nor extension, and any genuinely quantum process literally does not belong in the Raum and time of our experience. As Heisenberg stresses: “Während also die klassische Physik ein objectives Geschehen in Raum and Zeit zum Gegenstand hat, für dessen Existenz seine Beobachtung völlig irrelevant war, behandelt die Quantentheorie Vorgänge, die sozusagen nur in den Momenten der Beobachtung als raumzeitliche Phänomene aufleuchten, und über die in der zwischenzeit anschaulische physikalische Aussagen sinloss sind”. An admittedly speculative, hazardous conjecture is then advanced concerning the relation of such quantum ontology with the role of the pre-phenomenal continuum (Husserl) in the perception of macroscopically distinguishable objects in the Raum and time of our experience. Although rather venturesome, it brings together important philosophical issues. Coherently with recent general results in works on the foundations of QT, it is assumed that the linearity of quantum dynamical evolution does not apply to the central nervous system of living beings at a certain level of the evolutionary ramification and at the pre-conscious stage of subjectivity. Accordingly, corresponding to the onset of a non-linear dynamic evolution, a ‘primary spatial’ reduction is ‘continually’ taking place, thereby constituting the neural precondition for the experience of distinguishable macroscopic objects in the continuous spatial extension. While preventing the theoretically possible quantum superpositions of macroscopic objects from being perceivable by living beings, the ‘primary reduction’ has no effect on the standard processes concerning quantum level entities involved in laboratory man-made experiments. In this connection, an experimental check which might falsify the conjecture is briefly discussed. The approach suggested here, if sound, leads to a naturalization of that part of Kant’s Transcendental Aesthetics than can survive the Euclidean catastrophe. According to such naturalized transcendentalism, “space can well be transcendental without the axioms being so”, in agreement with a well-known statement by Boltzman. Finally, as far as QT is concerned, the conjecture entails that a scheme for quantum measurement of the von Neumann type cannot even ‘leave the ground’, vindicating Bohr’s viewpoint. A quantum theory of measurement, in a proper sense, turns out to be unnecessary and in fact impossible. (shrink)

I present a very general and simple argument—based on the no-signalling theorem—showing that within the framework of the unitary Schrödinger equation it is impossible to reproduce the phenomenological description of quantum mechanical measurements (in particular the collapse of the state of the measured system) by assuming a suitable mixed initial state of the apparatus. The thrust of the argument is thus similar to that of the ‘insolubility theorems’ for the measurement problem of quantum mechanics (which, however, focus on the impossibility (...) of reproducing the macroscopic measurement results). Although I believe this form of the argument is new, I argue it is essentially a variant of Einstein’s reasoning in the context of the EPR paradox—which is thereby illuminated from a new angle. (shrink)

String Theory is the result of the conjunction of three conceptually independent elements: the metaphysical idea of a nomological unity of the forces, the model-theoretical paradigm of Quantum Field Theory, and the conflict resulting from classical gravity in a quantum world - the motivational starting point of the search for a theory of Quantum Gravity. String Theory is sometimes assumed to solve this conflict: by means of an application of the model-theoretical apparatus of Quantum Field Theory, interpreting gravity as the (...) result of an exchange of gravitons, taken here to be dynamical states of the string. But, String Theory does not really solve the conflict. Rather it exemplifies the inadequacy of the apparatus of Quantum Field Theory in the context of Quantum Gravity: After several decades of development it still exists only in an essentially perturbative formulation. And, due to its quantum field theoretical heritage, it is conceptually incompatible with central implications of General Relativity, especially those resulting from the general relativistic relation between gravity and spacetime. All known formulations of String Theory are background-dependent. And no physical motivation is given for this conceptual incompatibility. On the other hand, although String Theory identifies all gauge bosons as string states, it was not even possible to reproduce the Standard Model. Instead, String Theory led to a multitude of internal problems - and to the plethora of low-energy scenarios with different nomologies and symmetries, known as the String Landscape. All attempts to find a dynamically motivated selection principle remained without success, leaving String Theory without any predictive power. The nomological unification of the fundamental forces, including gravity, is only achieved in a purely formal way within the model-theoretical paradigm of Quantum Field Theory - by means of physically unmotivated epicycles like higher dimensionality, Calabi-Yau spaces, branes, etc. Finally, the possibility remains that some of the central assumptions of String Theory are physically wrong. On the one hand, the idea of a nomological unity of the forces could be simply wrong. On the other hand, even if a nomological unity of all fundamental forces should be realized in nature, the possibility remains that gravity is not a fundamental force, but a residual, emergent and possibly intrinsically classical phenomenon, resulting from a quantum substrate without any gravitational degrees of freedom. (shrink)

This paper addresses the problem that Bayesian statistical inference cannot accommodate theory change, and proposes a framework for dealing with such changes. It first presents a scheme for generating predictions from observations by means of hypotheses. An example shows how the hypotheses represent the theoretical structure underlying the scheme. This is followed by an example of a change of hypotheses. The paper then presents a general framework for hypotheses change, and proposes the minimization of the distance between hypotheses as a (...) rationality criterion. Finally the paper discusses the import of this for Bayesian statistical inference. (shrink)

I criticise the view that the relativity and equivalence principles are consequences of the small-scale structure of the metric in general relativity, by arguing that these principles also apply to systems with non-trivial self-gravitation and hence non-trivial spacetime curvature (such as black holes). I provide an alternative account, incorporating aspects of the criticised view, which allows both principles to apply to systems with self-gravity.

Philosophies of nature over the past three centuries have gone through three distinct phases, beginning with classical views and now evolving into a process view at the dawn of the 21st century. These phases derive from a complex weaving of two frameworks of physics since Newton's time [classical, modern] with two principal metaphysical frameworks[substance, event]. Problematic fin de sicle claims at the end of both the 19th and 20th centuries appear to have a common root in substance metaphysics and part/whole (...) reductionism. Going beyond such simplistic forms of modernism requires a more integrated, ecological worldview, or process view of nature. (shrink)

This review of Julian Barbour's The End of Time ([1999]) discusses his Machian theories of dynamics, and his proposal that a Machian perspective enables one to solve the problem of time in quantum geometrodynamics, viz. by saying that there is no time! 1 Introduction 2 Machian themes in classical physics 2.1 The status quo 2.2 Machianism 2.2.1 The temporal metric as emergent 2.2.2 Machian theories 2.2.3 Assessing intrinsic dynamics 3 The end of time? 3.1 Time unreal? The classical case 3.1.1 (...) Spontaneity 3.1.2 Barbour's vision: time capsules 3.2 Evidence from quantum physics? 3.2.1 Mott scattering as a model for time capsules 3.2.2 Solving the problem of time? (shrink)

Richard Jeffrey developed the formula for probability kinematics with the intent that it would show that strong foundations are epistemologically unnecessary. But the reasons that support strong foundationalism are considerations of dynamics rather than kinematics. The strong foundationalist is concerned with the origin of epistemic force; showing how epistemic force is propagated therefore cannot undermine his position. The weakness of personalism is evident in the difficulty the personalist has in giving a principled answer to the question of when the conditions (...) for the application of the kinematic formula—the rigidity of the posteriors—are fulfilled, a problem made intractable by the personalist commitment to treating changes in intermediate probability as unexplained surds. Because the strong foundationalist admits changes in the intermediate probability of propositions only when there is some change in the foundations, he can avail himself of ananswer to the problem of the rigidity of the posteriors which the personalist cannot regard as complete. While probability kinematics does not make certain foundations unnecessary, the possession of certain foundations also does not make the probability kinematics formula superfluous. The formula allowsus to model the indirect routes by which the foundations influence various non-foundational propositions in the probability distribution. (shrink)

Kant claims that we cannot cognize the mutual interaction of substances without their being in space; he also claims that we cannot cognize a ‘spatial community’ among substances without their being in mutual interaction. I situate these theses in their historical context and consider Kant’s reasons for accepting them. I argue that they rest on commitments regarding the metaphysical grounding of, first, the possibility of mutual interaction among substances-as-appearances and, second, the actuality of specific distance-relations among such substances. By illuminating (...) these commitments, I shed light on Kant’s metaphysics of space and its relation to Newton and Leibniz’s views. (shrink)

The traditional Bayesian qualitative account of evidential support (TB) takes assertions of the form 'E evidentially supports H' to affirm the existence of a two-place relation of evidential support between E and H. The analysans given for this relation is $C(H,E) =_{def} Pr(H\arrowvertE) \models Pr(H)$ . Now it is well known that when a hypothesis H entails evidence E, not only is it the case that C(H,E), but it is also the case that C(H&X,E) for any arbitrary X. There is (...) a widespread feeling that this is a problematic result for TB. Indeed, there are a number of cases in which many feel it is false to assert 'E evidentially supports H&X', despite H entailing E. This is known, by those who share that feeling, as the 'tacking problem' for Bayesian confirmation theory. After outlining a generalization of the problem, I argue that the Bayesian response has so far been unsatisfactory. I then argue the following: (i) There exists, either instead of, or in addition to, a two-place relation of confirmation, a three-place, 'contrastive' relation of confirmation, holding between an item of evidence E and two competing hypotheses H₁ and H₂. (ii) The correct analysans of the relation is a particular probabilistic inequality, abbreviated C(H₁, H₂, E). (iii) Those who take the putative counterexamples to TB discussed to indeed be counterexamples are interpreting the relevant utterances as implicitly contrastive, contrasting the relevant hypothesis H₁ with a particular competitor H₂. (iv) The probabilistic structure of these cases is such that ∼C(H₁, H₂, E). This solves my generalization of the tacking problem. I then conclude with some thoughts about the relationship between the traditional Bayesian account of evidential support and my proposed account of the three-place relation of confirmation. (shrink)

It appears that light may be thrown on the nature of moral principles if they are construed as moral laws analogous to ceteris-paribus laws of nature. Luke Robinson objects that the analogy either cannot explain how moral principles are necessary or cannot explain how obligations can be pro-tanto; and that a dispositional account of moral obligation has explanatory superiority over one in terms of moral laws. I explain the analogy, construing laws of nature as necessary relationships after the fashion of (...) William Kneale and Karl Popper. I then show that Robinson’s objections are mistaken and that if the difference between a dispositional account and a law account is not merely verbal, then it is the law account that is superior. I also dispel the common confusion between the necessity of laws and the existence of forces. (shrink)

In 1916, a 41 year old woman with little formal scientific education became the secretary of the New York Aquarium. In becoming the Aquarium’s first female officer, Ida M. Mellen realized her lifelong dream of successfully pursuing a career in the biological sciences and broke with the limitations and low expectations surrounding her sex and class backgrounds. By 1930, Mellen left the NYA and pursued a career in popular hobbyist writing, becoming the foremost expert on aquarium fishes and domesticated cats (...) in the United States. Margaret Rossiter and other historians of science have illuminated women’s common career paths in the sciences, but little work has been done on individuals whose gender and class impacted their career. Building on Rossiter’s framework, this case study suggests that class, as much as gender, structured the scientific career of women. Through the narrative of the outsider scientific practitioner, we can more fully illuminate the social structure of scientific work. Examining the struggles of Mellen to enter and maintain a scientific career sheds light, not just on her own career path, but those alternately closed to her. If we wish to understand science in the early twentieth century, especially questions of inclusion and exclusion in the scientific process, we must examine those individuals who operated on the periphery of the “traditional” scientific path. (shrink)

To systematically answer the generalized Kretschmann objection, I propose a mean to make operational a criterion widely recognized as allowing one to decide whether the gauge symmetry of a theory is artificial or substantial. My proposition is based on the dressing field method of gauge symmetry reduction, a new simple tool from mathematical physics. This general scheme allows one in particular to straightforwardly argue that the notion of spontaneous symmetry breaking is superfluous to the empirical success of the electroweak theory. (...) Important questions regarding the context of justification of the theory then arise. (shrink)

I have so far ignored Earman's Section IV in which spatiotemporal coincidence is discussed. The answer will be clear from the preceding: the exact definitions and principles of the exact theories we have displayed are to be discussed with reference to the special and not the general theory of relativity. But moreover, Earman's transition from (C) to (1) assumes what we do not grant: that events are causally connectible exactly if the points in the mathematical space-time at which they are (...) located are linked by a causal curve.This captures in a nutshell my own conclusions. The first is that the causal theory, after its success vis-à-vis the STR, must now provide a detailed analysis of spatiotemporal concepts in the GTR. The second is that the points raised by Earman do not provide substantive reasons for doubting the adequacy of the causal theory to this task, because Earman insists in his extrapolations on a much closer relation between the empirical structure of events and the mathematical structures that model it than ought to be assumed. (shrink)

The notion of a severe test has played an important methodological role in the history of science. But it has not until recently been analyzed in any detail. We develop a generally Bayesian analysis of the notion, compare it with Deborah Mayo’s error-statistical approach by way of sample diagnostic tests in the medical sciences, and consider various objections to both. At the core of our analysis is a distinction between evidence and confirmation or belief. These notions must be kept separate (...) if mistakes are to be avoided; combined in the right way, they provide an adequate understanding of severity. Those who think that the weight of the evidence always enables you to choose between hypotheses “ignore one of the factors (the prior probability) altogether, and treat the other (the likelihood) as though it ...meant something other than it actually does. This is the same mistake as is made by someone who has scruples about measuring the arms of a balance (having only a tape measure at his disposal ...), but is willing to assert that the heavier load will always tilt the balance (thereby implicitly assuming, although without admitting it, that the arms are of equal length!). (Bruno de Finetti, Theory of Probability)2. (shrink)

We introduce an epistemic theory of truth according to which the same rational degree of belief is assigned to Tr(. It is shown that if epistemic probability measures are only demanded to be finitely additive (but not necessarily σ-additive), then such a theory is consistent even for object languages that contain their own truth predicate. As the proof of this result indicates, the theory can also be interpreted as deriving from a quantitative version of the Revision Theory of Truth.

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)

Much controversy surrounds the question of what ought to be the proper definition of 'singularity' in general relativity, and the question of whether the prediction of such entities leads to a crisis for the theory. I argue that a definition in terms of curve incompleteness is adequate, and in particular that the idea that singularities correspond to 'missing points' has insurmountable problems. I conclude that singularities per se pose no serious problem for the theory, but their analysis does bring into (...) focus several problems of interpretation at the foundation of the theory often ignored in the philosophical literature. (shrink)

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.

Here we provide a proof that there exist closed timelike curves in Gödel spacetime with total acceleration less than 2π(9 + 6√3)^1/2. This answers a question posed by David Malament.

In the four papers available on our web site (of which this is the first), we propose to develop an inductive logic. By “inductive logic” we mean a set of principles that distinguish between successful and unsuccessful strategies for scientific inquiry. Our logic will have a technical character, since it is built from the concepts and terminology of (elementary) model theory. The reader may therefore wish to know something about the kind of results on offer before investing time in definitions (...) and notation. Providing such an informal overview is the purpose of the present essay. We begin with discussion of the central concept under investigation, namely, theory acceptance. (shrink)

Sklar ([1974]) claimed that relationalism about ontology-the doctrine that space and time do not exist-is compatible with Newtonian mechanics. To defend this claim he sketched a relationalist interpretation of Newtonian mechanics. In his interpretation, absolute acceleration is a fundamental, intrinsic property of material bodies; that a body undergoes absolute acceleration does not entail that space and time exist. But Sklar left his proposal as just a sketch; his defense of relationalism succeeds only if the sketch can be filled in. I (...) argue that this cannot be done. There can be no (relationalist) dynamical laws of motion based on Sklar's proposal that capture the content of Newton's theory. So relationalists must look elsewhere for a relationalist interpretation of Newtonian mechanics. (shrink)