Energy Conservation in GTR

The topics of gravitational field energy and energy-momentum conservation in General Relativity theory have been unjustly neglected by philosophers. If the gravitational field in space free of ordinary matter, as represented by the metric g_ab itself, can be said to carry genuine energy and momentum, this is a powerful argument for adopting the substantivalist view of spacetime.This paper explores the standard textbook account of gravitational field energy and argues that (a) so-called stress-energy of the gravitational field is well-defined neither locally nor globally; and (b) there is no general principle of energy-momentum conservation to be found in General Relativity. I discuss the nature and justification of the zero-divergence law for ordinary stress-energy, and its possible connection with the failure of General Relativity to realise Mach's principle.     

On geometric objects,the non-existence of a gravitational stress-energy tensor,and the uniqueness of the Einstein field equation

The question of the existence of gravitational stress-energy in general relativity has exercised investigators in the field since the inception of the theory. Folklore has it that no adequate definition of a localized gravitational stress-energetic quantity can be given. Most arguments to that effect invoke one version or another of the Principle of Equivalence. I argue that not only are such arguments of necessity vague and hand-waving but, worse, are beside the point and do not address the heart of the issue. Based on a novel analysis of what it may mean for one tensor to depend in the proper way on another, which, en passant, provides a precise characterization of the idea of a “geometric object”, I prove that, under certain natural conditions, there can be no tensor whose interpretation could be that it represents gravitational stress-energy in general relativity. It follows that gravitational energy, such as it is in general relativity, is necessarily non-local. Along the way, I prove a result of some interest in own right about the structure of the associated jet bundles of the bundle of Lorentz metrics over spacetime. I conclude by showing that my results also imply that, under a few natural conditions, the Einstein field equation is the unique equation relating gravitational phenomena to spatiotemporal structure, and discuss how this relates to the non-localizability of gravitational stress-energy. The main theorem proven underlying all the arguments is considerably stronger than the standard result in the literature used for the same purposes (Lovelock's theorem of 1972): it holds in all dimensions (not only in four); it does not require an assumption about the differential order of the desired concomitant of the metric; and it has a more natural physical interpretation.     

The Curie's Lab and its Women (1906–1934) Le laboratoire Curie et ses Femmes (1906–1934)

When Bouvet discovered the relationship between the binary arithmetic of Leibniz and the hexagrams of the I ching—in reality only a purely formal correspondence—he sent to Leibniz a woodcut diagram of the Fu-Hsi arrangement, which provides the key to the analogy. This diagram, in a re-drawn version, was first published by Gorai Kinzō in a study of Leibniz's interpretation of the I ching and Confucianism which has been influential in providing, indirectly, the principal source for the accounts of Wilhelm and Needham. Yet this pioneering study of Leibniz's interpretation of the hexagrams is virtually unknown. Even the account of Needham, who saved it from complete obscurity, contains one or two inaccuracies about it and these are repeated by Zacher in his otherwise excellent monograph on Leibniz's binary arithmetic.     

Kant and the scope of analogy in the life sciences

In the present paper I investigate the role that analogy plays in eighteenth-century biology and in Kant's philosophy of biology. I will argue that according to Kant, biology, as it was practiced in the eighteenth century, is fundamentally based on analogical reflection. However, precisely because biology is based on analogical reflection, biology cannot be a proper science. I provide two arguments for this interpretation. First, I argue that although analogical reflection is, according to Kant, necessary to comprehend the nature of organisms, it is also necessarily insufficient to fully comprehend the nature of organisms. The upshot of this argument is that for Kant our understanding of organisms is necessarily limited. Second, I argue that Kant did not take biology to be a proper science because biology was based on analogical arguments. I show that Kant stemmed from a philosophical tradition that did not assign analogical arguments an important justificatory role in natural science. Analogy, according to this conception, does not provide us with apodictically certain cognition. Hence, sciences based on analogical arguments cannot constitute proper sciences.     

Dissolving the measurement problem is not an option for the realist

This paper critically assesses the proposal that scientific realists do not need to search for a solution of the measurement problem in quantum mechanics, but should instead dismiss the problem as ill-posed. James Ladyman and Don Ross have sought to support this proposal with arguments drawn from their naturalized metaphysics and from a Bohr-inspired approach to quantum mechanics. I show that the first class of arguments is unsuccessful, because formulating the measurement problem does not depend on the metaphysical commitments which are undermined by ontic structural realism, rainforest realism, or naturalism in general. The second class of arguments is problematic due to its refusal to provide an analysis of the term “measurement”. It turns out that the proposed dissolution of the measurement problem is in conflict not only with traditional forms of scientific realism but even with the rather minimal realism that Ladyman and Ross themselves defend. The paper concludes with a brief discussion of two related proposals: Healey's pragmatist approach and Bub's information-theoretic interpretation.     

Cosmology and convention

I argue that some important elements of the current cosmological model are 'conventionalist’ in the sense defined by Karl Popper. These elements include dark matter and dark energy; both are auxiliary hypotheses that were invoked in response to observations that falsified the standard model as it existed at the time. The use of conventionalist stratagems in response to unexpected observations implies that the field of cosmology is in a state of 'degenerating problemshift’ in the language of Imre Lakatos. I show that the 'concordance’ argument, often put forward by cosmologists in support of the current paradigm, is weaker than the convergence arguments that were made in the past in support of the atomic theory of matter or the quantization of energy.     

Fantastic Beasts and where (not) to find them: Local gravitational energy and energy conservation in general relativity

This paper critically examines energy-momentum conservation and local (differential) notions of gravitational energy in General Relativity (GR). On the one hand, I argue that energy-momentum of matter is indeed locally (differentially) conserved: Physical matter energy-momentum 4-currents possess no genuine sinks/sources. On the other hand, global (integral) energy-momentum conservation is contingent on spacetime symmetries. Local gravitational energy-momentum is found to be a supererogatory notion. Various explicit proposals for local gravitational energy-momentum are investigated and found wanting. Besides pseudotensors, the proposals considered include those of Lorentz and Levi-Civita, Pitts and Baker. It is concluded that the ontological commitment we ought to have towards gravitational energy in GR mimics the natural anti-realism/eliminativism towards apparent forces in Newtonian Mechanics.     

Epistemology of a believing historian: Making sense of Duhem's anti-atomism

Pierre Duhem's (1861–1916) lifelong opposition to 19th century atomic theories of matter has been traditionally attributed to his conventionalist and/or positivist philosophy of science. Relatively recently, this traditional view position has been challenged by the claim that Duhem's opposition to atomism was due to the precarious state of atomic theories during the beginning of the 20th century. In this paper I present some of the difficulties with both the traditional and the new interpretation of Duhem's opposition to atomism and provide a new framework in which to understand his rejection of atomic hypotheses. I argue that although not positivist, instrumentalist, or conventionalist, Duhem's philosophy of physics was not compatible with belief in unobservable atoms and molecules. The key for understanding Duhem's resistance to atomism during the final phase of his career is the historicist arguments he presented in support of his ideal of physics.     

Evidence and explanation in Cicero's On Divination

In this paper, I examine Cicero's oft-neglected De Divinatione, a dialogue investigating the legitimacy of the practice of divination. First, I offer a novel analysis of the main arguments for divination given by Quintus, highlighting the fact that he employs two logically distinct argument forms. Next, I turn to the first of the main arguments against divination given by Marcus. Here I show, with the help of modern probabilistic tools, that Marcus' skeptical response is far from the decisive, proto-naturalistic assault on superstition that it is sometimes portrayed to be. Then, I offer an extended analysis of the second of the main arguments against divination given by Marcus. Inspired by Marcus' second main argument, I formulate, explicate, and defend a substantive principle of scientific methodology that I call the “Ciceronian Causal-Nomological Requirement” (CCR). Roughly, this principle states that causal knowledge is essential for relying on correlations in predictive inference. Although I go on to argue that Marcus' application of the CCR in his debate with Quintus is dialectically inadequate, I conclude that De Divinatione deserves its place in Cicero's philosophical corpus, and that ultimately, its significance for the history and philosophy of science ought to be recognized.     

Un-conventional wisdom: theory-specificity in Reichenbach's geometric conventionalism

The standard account portrays Hans Reichenbach's argument for geometric conventionalism as based upon general epistemological concerns of verifiability. As such, his version of conventionalism ought to be equally well applicable to all theories that posit a geometric structure to space–time. But when Reichenbach's writings from the period between the publication of Relativitätstheorie und Erkenntnis Apriori and Axiomatik der Raum-Zeit-Lehre, i.e., between 1920 and 1924, are examined, a very different picture emerges. The argument for the conventionality of geometry that appears in these writings is tied to discussions of the theory of general relativity and Reichenbach explicitly argues that geometry in Minkowski space–time is not conventional once the definition of simultaneity is put in place. In light of this, the received interpretation of Reichenbach's position needs to be replaced with a theory-specific picture of geometric conventionalism. This change has interesting consequences for both the standard arguments against Reichenbach's view and for questions in Reichenbach scholarship.     

A history of entanglement: Decoherence and the interpretation problem

This paper examines the interweaving of the history of quantum decoherence and the interpretation problem in quantum mechanics through the work of two physicists—H. Dieter Zeh and Wojciech Zurek. In the early 1970s Zeh anticipated many of the important concepts of decoherence, framing it within an Everett-type interpretation. Zeh has since remained committed to this view; however, Zurek, whose papers in the 1980s were crucial in the treatment of the preferred basis problem and the subsequent development of density matrix formalism, has argued that decoherence leads to what he terms the ‘existential interpretation’, compatible with certain aspects of both Everett's relative-state formulation and the Bohr's ‘Copenhagen interpretation’. I argue that these different interpretations can be traced back to the different early approaches to the study of environment-induced decoherence in quantum systems, evident in the early work of Zeh and Zurek. I also show how Zurek's work has contributed to the tendency to see decoherence as contributing to a ‘new orthodoxy’ or a reconstruction of the original Copenhagen interpretation.     

Proving the principle: Taking geodesic dynamics too seriously in Einstein's theory

In this paper I critically review attempts to formulate and derive the geodesic principle, which claims that free massive bodies follow geodesic paths in general relativity theory. I argue that if the principle is (canonically) interpreted as a law of motion describing the actual evolution of gravitating bodies, then it is impossible to generically apply the law to massive bodies in a way that is coherent with Einstein's field equations. Rejecting the canonical interpretation, I propose an alternative interpretation of the geodesic principle as a type of universality thesis analogous to the universality behavior exhibited in thermal systems during phase transitions.     

Scrutinizing thing knowledge

In his book Thing Knowledge Davis Baird argues that our accustomed understanding of knowledge as justified true beliefs is not enough to understand progress in science and technology. To be more accurate he argues that scientific instruments are to be seen as a form of “objective knowledge” in the sense of Karl Popper.I want to examine if this idea is plausible. In a first step I want to show that this proposal implies that nearly all man-made artifacts are materialized objective knowledge. I argue that this radical change in our concept of knowledge demands strong reasons and that Baird does not give them. I take a look at the strongest strand of arguments of Baird's book—the arguments from cognitive autonomy—and conclude that they do not suffice to make Baird's view of scientific instruments tenable.     

The problem of grounding natural modality in Kant's account of empirical laws of nature

One of the central problems of Kant's account of the empirical laws of nature is: What grounds their necessity? In this article I discuss the three most important lines of interpretation and suggest a novel version of one of them. While the first interpretation takes the transcendental principles as the only sources of the empirical laws' necessity, the second interpretation takes the systematicity of the laws to guarantee their necessity. It is shown that both views involve serious problems. The third interpretation, the “causal powers interpretation”, locates the source of the laws' necessity in the properties of natural objects. Although the second and third interpretations seem incompatible, I analyse why Kant held both views and I argue that they can be reconciled, because the metaphysical grounding project of the laws' necessity is accounted for by Kant's causal powers account, while his best system account explains our epistemic access to the empirical laws. If, however, causal powers are supposed to fulfil the grounding function for the laws' natural modality, then I suggest that a novel reading of the causal powers interpretation should be formulated along the lines of a genuine dispositionalist conception of the laws of nature.     

The roots of the silver tree: Boyle,alchemy, and teleology

Though Robert Boyle called final causes one of the most important subjects for a natural philosopher to study, his own treatise on the subject, the Disquisition about Final Causes, has received comparatively little scholarly attention. In this paper, I explicate Boyle's complex argument against the use of teleological explanations for inanimate bodies, such as metals. The central object of this argument is a mysterious allusion to a silver plant. I claim that the silver plant is best understood as a reference to alchemical product: the Arbor Dianae, an offshoot of George Starkey's recipe for the Philosophers' Stone. Then, I show how the context of alchemy not only clarifies Boyle's argument but also places it within a wider dialectic about matter and teleology. I then contrast the parallel arguments of Boyle and John Ray on the question of whether metals have divine purposes and show that the difference is explained by Boyle's belief in the transmutation of metals.     

Computation, individuation, and the received view on representation

The ‘received view’ about computation is that all computations must involve representational content. Egan and Piccinini argue against the received view. In this paper, I focus on Egan’s arguments, claiming that they fall short of establishing that computations do not involve representational content. I provide positive arguments explaining why computation has to involve representational content, and how that representational content may be of any type (distal, broad, etc.). I also argue (contra Egan and Fodor) that there is no need for computational psychology to be individualistic. Finally, I draw out a number of consequences for computational individuation, proposing necessary conditions on computational identity and necessary and sufficient conditions on computational I/O equivalence of physical systems.     

I ain’t afraid of no ghost

This paper criticizes the traditional philosophical account of the quantization of gauge theories and offers an alternative. On the received view, gauge theories resist quantization because they feature distinct mathematical representatives of the same physical state of affairs. This resistance is overcome by a sequence of ad hoc modifications, justified in part by reference to semiclassical electrodynamics. Among other things, these modifications introduce ”ghosts”: particles with unphysical properties which do not appear in asymptotic states and which are said to be purely a notational convenience. I argue that this sequence of modifications is unjustified and inadequate, making it a poor basis for the interpretation of ghosts. I then argue that gauge theories can be quantized by the same method as any other theory. On this account, ghosts are not purely notation: they are coordinates on the classical configuration space of the theory—specifically, on its gauge structure. This interpretation does not fall prey to the standard philosophical arguments against the significance of ghosts, due to Weingard. Weingard’s argumentative strategy, properly applied, in fact tells in favor of ghosts’ physical significance.     

Inference to the best explanation and Norton's material theory of induction

I argue that we should consider Norton's material theory of induction as consisting of two largely independent claims. First, there is the claim that material facts license inductions - a claim which I interpret as a type of contextualism about induction. Second, there is the claim that there are no universal rules of induction. While a good case can be made for the first claim, I believe that Norton's arguments for the second claim are lacking. In particular, I spell out Norton's argument against the claim that all induction may be reduced to inference to the best explanation, and argue that it is not persuasive. Rejecting this part of Norton's theory does not however require us to abandon the first claim that material facts license inductions. In this way, I distinguish the parts of the material theory of induction we should happily accept from the parts about which we should be more skeptical.     

Coincidence and reproducibility in the EHT black hole experiment

This paper discusses some philosophical aspects related to the recent publication of the experimental results of the 2017 black hole experiment, namely the first image of the supermassive black hole at the center of galaxy M87. In this paper I present a philosophical analysis of the 2017 Event Horizon Telescope (EHT) black hole experiment. I first present Hacking's philosophy of experimentation. Hacking gives his taxonomy of elements of laboratory science and distinguishes a list of elements. I show that the EHT experiment conforms to major elements from Hacking's list. I then describe with the help of Galison's Philosophy of the Shadow how the EHT Collaboration created the famous black hole image. Galison outlines three stages for the reconstruction of the black hole image: Socio-Epistemology, Mechanical Objectivity, after which there is an additional Socio-Epistemology stage. I subsequently present my own interpretation of the reconstruction of the black hole image and I discuss model fitting to data. I suggest that the main method used by the EHT Collaboration to assure trust in the results of the EHT experiment is what philosophers call the Argument from Coincidence. I show that using this method for the above purpose is problematic. I present two versions of the Argument from Coincidence: Hacking's Coincidence and Cartwright's Reproducibility by which I analyse the EHT experiment. The same estimation of the mass of the black hole is reproduced in four different procedures. The EHT Collaboration concludes: the value we have converged upon is robust. I analyse the mass measurements of the black hole with the help of Cartwright's notion of robustness. I show that the EHT Collaboration construe Coincidence/Reproducibility as Technological Agnosticism and I contrast this interpretation with van Fraassen's scientific agnosticism.     

The material theory of induction and the epistemology of thought experiments

John D. Norton is responsible for a number of influential views in contemporary philosophy of science. This paper will discuss two of them. The material theory of induction claims that inductive arguments are ultimately justified by their material features, not their formal features. Thus, while a deductive argument can be valid irrespective of the content of the propositions that make up the argument, an inductive argument about, say, apples, will be justified (or not) depending on facts about apples. The argument view of thought experiments claims that thought experiments are arguments, and that they function epistemically however arguments do. These two views have generated a great deal of discussion, although there hasn't been much written about their combination. I argue that despite some interesting harmonies, there is a serious tension between them. I consider several options for easing this tension, before suggesting a set of changes to the argument view that I take to be consistent with Norton's fundamental philosophical commitments, and which retain what seems intuitively correct about the argument view. These changes require that we move away from a unitary epistemology of thought experiments and towards a more pluralist position.