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  1. P. Achinstein & R. Kagon (eds.) (1987). Kelvin's Baltimore Lectures and Modern Theoretical Physics. MIT Press.
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  2. Abhay Ashtekar, Jürgen Renn, Don Howard, Abner Shimony & S. Sarkar (eds.) (2002). Revisiting the Foundations of Relativistic Physics. Festschrift in Honour of John Stachel. Kluwer.
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  3. Jonathan Bain, Algebraic Substantivalism and the Hole Argument.
    Algebraic substantivalism, as an interpretation of general relativity formulated in the Einstein algebra formalism, avoids the hole argument against manifold substantivalism. In this essay, I argue that this claim is well-founded. I first identify the hole argument as an argument against a specific form of semantic realism with respect to spacetime. I then consider algebraic substantivalism as an alternative form of semantic realism. In between, I justify this alternative form by reviewing the Einstein algebra formalism and indicating the extent to (...)
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  4. Jonathan Bain (2003). Einstein Algebras and the Hole Argument. Philosophy of Science 70 (5):1073-1085.
    Einstein algebras have been suggested (Earman 1989) and rejected (Rynasiewicz 1992) as a way to avoid the hole argument against spacetime substantivalism. In this article, I debate their merits and faults. In particular, I suggest that a gauge‐invariant interpretation of Einstein algebras that avoids the hole argument can be associated with one approach to quantizing gravity, and, for this reason, is at least as well motivated as sophisticated substantivalist and relationalist interpretations of the standard tensor formalism.
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  5. Jonathan Bain (2003). Einstein Algebras and the Hole Argument. Philosophy of Science 70 (5):1073-1085.
    Einstein algebras have been suggested (Earman 1989) and rejected (Rynasiewicz 1992) as a way to avoid the hole argument against spacetime substantivalism. In this article, I debate their merits and faults. In particular, I suggest that a gauge-invariant interpretation of Einstein algebras that avoids the hole argument can be associated with one approach to quantizing gravity, and, for this reason, is at least as well motivated as sophisticated substantivalist and relationalist interpretations of the standard tensor formalism.
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  6. Jonathan Stanley Bain (1998). Representations of Spacetime: Formalism and Ontological Commitment. Dissertation, University of Pittsburgh
    This dissertation consists of two parts. The first is on the relation between formalism and ontological commitment in the context of theories of spacetime, and the second is on scientific realism. The first part begins with a look at how the substantivalist/relationist debate over the ontological status of spacetime has been influenced by a particular mathematical formalism, that of tensor analysis on differential manifolds . This formalism has motivated the substantivalist position known as manifold substantivalism. Chapter 1 focuses on the (...)
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  7. Andreas Bartels (1996). Modern Essentialism and the Problem of Individuation of Spacetime Points. Erkenntnis 45 (1):25--43.
    In this paper Modern Essentialism is used to solve a problem of individuation of spacetime points in General Relativity that has been raised by a New Leibnizian Argument against spacetime substantivalism, elaborated by Earman and Norton. An earlier essentialistic solution, proposed by Maudlin, is criticized as being against both the spirit of metrical essentialism and the fundamental principles of General Relativity. I argue for a modified essentialistic account of spacetime points that avoids those obstacles.
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  8. Gordon Belot (2000). Geometry and Motion. British Journal for the Philosophy of Science 51 (4):561--95.
    I will discuss only one of the several entwined strands of the philosophy of space and time, the question of the relation between the nature of motion and the geometrical structure of the world.1 This topic has many of the virtues of the best philosophy of science. It is of long-standing philosophical interest and has a rich history of connections to problems of physics. It has loomed large in discussions of space and time among contemporary philosophers of science. Furthermore, there (...)
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  9. Gordon Belot (1995). New Work for Counterpart Theorists: Determinism. British Journal for the Philosophy of Science 46 (2):185-195.
    Recently Carolyn Brighouse and Jeremy Butterfield have argued that David Lewis's counterpart theory makes it possible both to believe in the reality of spacetime points and to consider general relativity to be a deterministic theory, thus avoiding the ‘hole argument’ of John Earman and John Norton. Butterfield's argument relies on Lewis's own counterpart-theoretic analysis of determinism. In this paper, I argue that this analysis is inadequate. This leaves a gap in the Butterfield–Brighouse defence against the hole argument.
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  10. Gordon Belot (1995). Determinism and Ontology. International Studies in the Philosophy of Science 9 (1):85 – 101.
    Abstract In the philosophical literature, there are two common criteria for a physical theory to be deterministic. The older one is due to the logical empiricists, and is a purely formal criterion. The newer one can be found in the work of John Earman and David Lewis and depends on the intended interpretation of the theory. In this paper I argue that the former must be rejected, and something like the latter adopted. I then discuss the relevance of these points (...)
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  11. Gordon Scott Belot (1996). Whatever is Never and Nowhere is Not: Space, Time, and Ontology in Classical and Quantum Gravity. Dissertation, University of Pittsburgh
    Substantivalists claim that spacetime enjoys an existence analogous to that of material bodies, while relationalists seek to reduce spacetime to sets of possible spatiotemporal relations. The resulting debate has been central to the philosophy of space and time since the Scientific Revolution. Recently, many philosophers of physics have turned away from the debate, claiming that it is no longer of any relevance to physics. At the same time, there has been renewed interest in the debate among physicists working on quantum (...)
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  12. Gordon Belot & John Earman (1999). From Metaphysics to Physics. In Jeremy Butterfield & Constantine Pagonis (eds.), From Physics to Philosophy. Cambridge University Press 166--86.
    We discuss the relationship between the interpretative problems of quantum gravity and those of general relativity. We argue that classical and quantum theories of gravity resuscitate venerable philosophical questions about the nature of space, time, and change; and that the resolution of some of the difficulties facing physicists working on quantum theories of gravity would appear to require philosophical as well as scientific creativity.
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  13. Carolyn Brighouse (1997). Determinism and Modality. British Journal for the Philosophy of Science 48 (4):465-481.
    The hole argument contends that a substantivalist has to view General Relativity as an indeterministic theory. A recent form of substantivalist reply to the hole argument has urged the substantivalist to identify qualitatively isomorphic possible worlds. Gordon Belot has argued that this form of substantivalism is unable to capture other genuine violations of determinism. This paper argues that Belot's alleged examples of indeterminism should not be seen as a violation of a form of determinism that physicists are interested in. What (...)
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  14. Carolyn Jane Brighouse (1996). The Case for Substantivalism. Dissertation, University of Southern California
    My dissertation is a discussion of the ontological commitment of spacetime theories. I am concerned about whether we should be realists about spacetime. I outline a version of substantivalism that I show is attractive on general grounds in that it treats spacetime in just the same way that a realist ought to treat entities she is a realist about. I then show that this version of substantivalism is immune to the hole argument and other recent criticisms of substantivalism. I also (...)
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  15. Jeremy Butterfield (1989). The Hole Truth. British Journal for the Philosophy of Science 40 (1):1-28.
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  16. Jeremy Butterfield (1988). Albert Einstein Meets David Lewis. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1988:65-81.
    I reject Norton and Earman's hole argument that spacetime substantivalism is incompatible with determinism. I reconcile these both technically and philosophically. There is a technical definition of determinism that is not violated by pairs of models of the kind used in the hole argument. And technicalities aside, the basic idea of determinism is not violated if we claim that at most one of the two models represents a possible world. This claim can be justified either by metrical essentialism, or by (...)
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  17. Jeremy Butterfield (1987). Substantivalism and Determinism. International Studies in the Philosophy of Science 2 (1):10 – 32.
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  18. Jeremy Butterfield & Constantine Pagonis (eds.) (1999). From Physics to Philosophy. Cambridge University Press.
    This collection of essays by leading philosophers of physics was first published in 2000, and offers philosophical perspectives on two of the central elements of modern physics, quantum theory and relativity. The topics examined include the notorious 'measurement problem' of quantum theory and the attempts to solve it by attributing extra values to physical quantities, the mysterious non-locality of quantum theory, the curious properties of spatial localization in relativistic quantum theories, and the problem of time in the search for a (...)
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  19. Erik Curiel, On the Existence of Spacetime Structure.
    I examine the debate between substantivalists and relationalists about the ontological character of spacetime and conclude it is not well posed. I argue that the so-called Hole Argument does not bear on the debate, because it provides no clear criterion to distinguish the positions. I propose two such precise criteria and construct separate arguments based on each to yield contrary conclusions, one supportive of something like relationalism and the other of something like substantivalism. The lesson is that one must fix (...)
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  20. John Earman (2002). Thoroughly Modern Mctaggart: Or, What Mctaggart Would Have Said If He Had Read the General Theory of Relativity. Philosophers' Imprint 2 (3):1-28.
    The philosophical literature on time and change is fixated on the issue of whether the B-series account of change is adequate or whether real change requires Becoming of either the property-based variety of McTaggart's A-series or the non-property-based form embodied in C. D. Broad's idea of the piling up of successive layers of existence. For present purposes it is assumed that the B-series suffices to ground real change. But then it is noted that modern science in the guise of Einstein's (...)
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  21. John Earman (1989). World Enough and Spacetime. MIT Press.
  22. John Earman & John Norton (1987). What Price Spacetime Substantivalism? The Hole Story. British Journal for the Philosophy of Science 38 (4):515-525.
    Spacetime substantivalism leads to a radical form of indeterminism within a very broad class of spacetime theories which include our best spacetime theory, general relativity. Extending an argument from Einstein, we show that spacetime substantivalists are committed to very many more distinct physical states than these theories' equations can determine, even with the most extensive boundary conditions.
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  23. Shan Gao, Derivation of the Schrödinger Equation.
    It is shown that the heuristic "derivation" of the Schrödinger equation in quantum mechanics textbooks can be turned into a real derivation by resorting to spacetime translation invariance and relativistic invariance.
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  24. Marco Giovanelli (2013). Leibniz-Äquivalenz vs. Einstein-Äquivalenz. Was man von der Logisch-Empiristischen Interpretation des Punkt-Koinzidenz-Arguments lernen kann. Philosophia Naturalis 50 (1):115-164.
    The discovery that Einstein's celebrated argument for general covariance, the 'point-coincidence argument ', was actually a response to the ' hole argument ' has generated an intense philosophical debate in the last thirty years. Even if the philosophical consequences of Einstein's argument turned out to be highly controversial, the protagonists of such a debate seem to agree on considering Einstein's argument as an expression of 'Leibniz equivalence', a modern version of Leibniz's celebrated indiscernibility arguments against Newton's absolute space. The paper (...)
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  25. Marco Giovanelli, Leibniz Equivalence. On Leibniz's Influence on the Logical Empiricist Interpretation of General Relativity.
    Einstein’s “point-coincidence argument'” as a response to the “hole argument” is usually considered as an expression of “Leibniz equivalence,” a restatement of indiscernibility in the sense of Leibniz. Through a historical-critical analysis of Logical Empiricists' interpretation of General Relativity, the paper attempts to show that this labeling is misleading. Logical Empiricists tried explicitly to understand the point-coincidence argument as an indiscernibility argument of the Leibnizian kind, such as those formulated in the 19th century debate about geometry, by authors such as (...)
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  26. Hanns Hagen Goetzke, Einstein's Hole Argument and its Legacy.
    In 1915 not being able to find field equations for a generally covariant theory of gravitation Einstein came up with a fundamental argument against general covariance – the hole argument. This essay discusses the hole argument and focusses on its consequences for substantivalism and determinism. Two different definitions of determinism are introduced and their compatibility with general covariance from a substantivalist's point of view is discussed.
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  27. Amit Hagar (2013). Review of Tim Maudlin's Philosophy of Physics: Space & Time. [REVIEW] Physics in Perspective (x).
  28. Carl Hoefer (1996). The Metaphysics of Space-Time Substantivalism. Journal of Philosophy 93 (1):5-27.
  29. Keiko Ichiye (1996). The Hole Argument of the Substantivalism-Relationism Debate. Dissertation, Indiana University
    Since the time of antiquity, philosophers and scientists have debated the independent nature of space and, more recently, of spacetime. Substantivalists, on the one hand, argue that spacetime exists independently of material objects and provides an objective framework for spatiotemporal relations. Relationists, on the other hand, deny the independent existence of spacetime and hold that spacetime is simply a system of spatiotemporal relations between objects. ;John Earman and John Norton present their criticism of substantivalism: the "hole argument." General relativity yields (...)
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  30. Chuang Liu (1996). Gauge Invariance, Cauchy Problem, Indeterminism, and Symmetry Breaking. Philosophy of Science 63 (3):79.
    The concepts in the title refer to properties of physical theories and this paper investigates their nature and relations. The first three concepts, especially gauge invariance and indeterminism, have been widely discussed in connection to spacetime theories and the hole argument. Since the gauge invariance principle is at the crux of the issue, this paper aims at clarifying the nature of gauge invariance. I first explore the following chain of relations: gauge invariance $\Rightarrow $ the conservation laws $\Rightarrow $ the (...)
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  31. Luca Lusanna & Massimo Pauri (2006). Explaining Leibniz Equivalence as Difference of Non-Inertial Appearances: Dis-Solution of the Hole Argument and Physical Individuation of Point-Events. Studies in History and Philosophy of Science Part B 37 (4):692-725.
    ”The last remnant of physical objectivity of space-time” is disclosed in the case of a continuous family of spatially non-compact models of general relativity (GR). The physical individuation of point-events is furnished by the autonomous degrees of freedom of the gravitational field, (viz, the Dirac observables) which represent -as it were -the ontic part of the metric field. The physical role of the epistemic part (viz. the gauge variables) is likewise clarified as embodying the unavoidable non-inertial aspects of GR. At (...)
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  32. Luca Lusanna & Massimo Pauri, General Covariance and the Objectivity of Space-Time Point-Events: The Physical Role of Gravitational and Gauge Degrees of Freedom - DRAFT.
    This paper deals with a number of technical achievements that are instrumental for a dis-solution of the so-called "Hole Argument" in general relativity. Such achievements include: 1) the analysis of the "Hole" phenomenology in strict connection with the Hamiltonian treatment of the initial value problem. The work is carried through in metric gravity for the class of Christoudoulou-Klainermann space-times, in which the temporal evolution is ruled by the "weak" ADM energy; 2) a re-interpretation of "active" diffeomorphisms as "passive and metric-dependent" (...)
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  33. Alan Macdonald (2001). Einstein's Hole Argument. American Journal of Physics 69:223-225.
    In general relativity, a spacetime and a gravitational field form an indivisible unit: no field, no spacetime. This is a lesson of Einstein's hole argument. We use a simple transformation in a Schwartzschild pacetime to illustrate this.
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  34. Tim Maudlin (2002). Thoroughly Muddled Mctaggart: Or, How to Abuse Gauge Freedom to Create Metaphysical Monostrosities. Philosophers' Imprint 2 (4):1-23.
    It has long been a commonplace that there is a problem understanding the role of time when one tries to quantize the General Theory of Relativity (GTR). In his "Thoroughly Modern McTaggart" (Philosophers' Imprint Vol 2, No. 3), John Earman presents several arguments to the conclusion that there is a problem understanding change and the passage of time in the unadorned GTR, quite apart from quantization. His Young McTaggart argues that according to the GTR, no physical magnitude ever changes. A (...)
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  35. Tim Maudlin (1990). Substances and Space-Time: What Aristotle Would Have Said to Einstein. Studies in History and Philosophy of Science 21 (4):531--61.
  36. Tim Maudlin (1988). The Essence of Space-Time. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1988:82 - 91.
    I argue that Norton & Earman's hole argument, despite its historical association with General Relativity, turns upon very general features of any linguistic system that can represent substances by names. After exploring various means by which mathematical objects can be interpreted as representing physical possibilities, I suggest that a form of essentialism can solve the hole dilemma without abandoning either determinism or substantivalism. Finally, I identify the basic tenets of such an essentialism in Newton's writings and consider how they can (...)
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  37. J. Melia (1999). Holes, Haecceitism and Two Conceptions of Determinism. British Journal for the Philosophy of Science 50 (4):639--64.
    In this paper I claim that Earman and Norton 's hole argument against substantivalist interpretations of General Relativity assumes that the substantivalist must adopt a conception of determinism which I argue is unsatisfactory. Butterfield and others have responded to the hole argument by finding a conception of determinism open to the substantivalist that is not prone to the hole argument. But, unfortunately for the substantivalist, I argue this conception also turns out to be unsatisfactory. Accordingly, I search for a conception (...)
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  38. Brent Mundy (1992). Space-Time and Isomorphism. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1992:515-527.
    Earman and Norton argue that manifold realism leads to inequivalence of Leibniz-shifted space-time models, with undesirable consequences such as indeterminism. I respond that intrinsic axiomatization of space-time geometry shows the variant models to be isomorphic with respect to the physically meaningful geometric predicates, and therefore certainly physically equivalent because no theory can characterize its models more closely than this. The contrary philosophical arguments involve confusions about identity and representation of space-time points, fostered by extrinsic coordinate formulations and irrelevant modal metaphysics. (...)
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  39. John Norton, A Conjecture on Einstein, the Independent Reality of Spacetime Coordinate Systems and the Disaster of 1913.
    Two fundamental errors led Einstein to reject generally covariant gravitational field equations for over two years as he was developing his general theory of relativity. The first is well known in the literature. It was the presumption that weak, static gravitational fields must be spatially flat and a corresponding assumption about his weak field equations. I conjecture that a second hitherto unrecognized error also defeated Einstein's efforts. The same error, months later, allowed the hole argument to convince Einstein that all (...)
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  40. John Norton (1988). The Hole Argument. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1988:56 - 64.
    I give an informal outline of the hole argument which shows that spacetime substantivalism leads to an undesirable indeterminism in a broad class of spacetime theories. This form of the argument depends on the selection of differentiable manifolds within a spacetime theory as representing spacetime. I consider the conditions under which the argument can be extended to address versions of spacetime substantivalism which select these differentiable manifolds plus some further structure to represent spacetime. Finally, I respond to the criticisms of (...)
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  41. Glenn Gerard Parsons (2001). The Bundle Theory, Substance and Spacetime. Dissertation, University of Alberta (Canada)
    The past thirty years has witnessed a resurgence of interest in 'realist ontologies': views that treat properties and relations realistically. Such views necessitate a metaphysical account of the structure of concrete particulars. One such account is the Substratum theory of concrete particulars, on which concrete particulars are composed of their properties together with a substratum that individuates them and bears these properties. A traditional objection to this account is that the substratum would be unknowable. Recently, several philosophers supporting a realist (...)
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  42. Glenn Parsons & Patrick McGivern (2001). Can the Bundle Theory Save Substantivalism From the Hole Argument? Proceedings of the Philosophy of Science Association 2001 (3):S358-.
    One of the most serious theoretical obstacles to contemporary spacetime substantivalism is Earman and Norton's hole argument. We argue that applying the bundle theory of substance to spacetime points allows spacetime substantivalists to escape the conclusion of this argument. Some philosophers have claimed that the bundle theory cannot be applied to substantival spacetime in this way due to problems in individuating spacetime points in symmetrical spacetimes. We demonstrate that it is possible to overcome these difficulties if spatiotemporal properties are viewed (...)
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  43. Oliver Pooley (2013). Substantivalist and Relationalist Approaches to Spacetime. In Robert Batterman (ed.), The Oxford Handbook of Philosophy of Physics. Oxford University Press
    Substantivalists believe that spacetime and its parts are fundamental constituents of reality. Relationalists deny this, claiming that spacetime enjoys only a derivative existence. I begin by describing how the Galilean symmetries of Newtonian physics tell against both Newton's brand of substantivalism and the most obvious relationalist alternative. I then review the obvious substantivalist response to the problem, which is to ditch substantival space for substantival spacetime. The resulting position has many affinities with what are arguably the most natural interpretations of (...)
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  44. Oliver Pooley (2006). A Hole Revolution, or Are We Back Where We Started? Studies in History and Philosophy of Science Part B 37 (2):372-380.
    Doubts are raised concerning Rickles' claim that ``an exact analog of the hole argument can be constructed in the loop representation of quantum gravity'' (Rickles, `A new spin on the hole argument', Studies in History and Philosophy of Modern Physics 36 (2005) 415–434).
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  45. Oliver Pooley (2006). Points, Particles and Structural Realism. In Dean Rickles, Steven French & Juha Saatsi (eds.), The Structural Foundations of Quantum Gravity. Oxford University Press 83--120.
    In his paper ``What is Structural Realism?'' James Ladyman drew a distinction between epistemological structural realism and metaphysical (or ontic) structural realism. He also drew a suggestive analogy between the perennial debate between substantivalist and relationalist interpretations of spacetime on the one hand, and the debate about whether quantum mechanics treats identical particles as individuals or as `non-individuals' on the other. In both cases, Ladyman's suggestion is that an ontic structural realist interpretation of the physics might be just what is (...)
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  46. Tim Räz, Gone Till November: A Disagreement in Einstein Scholarship.
    The present paper examines an episode from the historiography of the genesis of general relativity. Einstein rejected a certain theory in the so-called “Zurich notebook” in 1912-13, but he reinstated the same theory for a short period of time in the November of 1915. Why did Einstein reject the theory at first, and why did he change his mind later? The group of Einstein scholars who reconstructed Einstein’s reasoning in the Zurich notebook disagree on how to answer these questions. According (...)
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  47. Dean Rickles (2006). Bringing the Hole Argument Back in the Loop: A Response to Pooley. Studies in History and Philosophy of Science Part B 37 (2):381-387.
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  48. Dean Rickles (2005). A New Spin on the Hole Argument. Studies in History and Philosophy of Science Part B 36 (3):415-434.
    This brief paper shows how an exact analogue of Einstein's original hole argument can be constructed in the loop representation of quantum gravity. The new argument is based on the embedding of spin-networks in a manifold and the action of the diffeomorphism constraint on them. The implications of this result are then discussed. I argue that the conclusions of many physicists working on loop quantum gravity---Rovelli and Smolin in particular---that the loop representation uniquely supports relationalism are unfounded.
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  49. Dean Rickles, What Price Determinism? The Hole Story!
    In their modern classic ``What Price Substantivalism? The Hole Story'' Earman and Norton argued that substantivalism about spacetime points implies that general relativity is indeterministic and, for that reason, must be rejected as a candidate ontology for the theory. More recently, Earman has cottoned on to a related argument (in fact, related to a \emph{response} to the hole argument) that arises in the context of canonical general relativity, according to which the enforcing of determinism along standard lines---using the machinery of (...)
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  50. Dean Rickles, Steven French & Juha Saatsi (eds.) (2006). The Structural Foundations of Quantum Gravity. Oxford University Press.
    This volume closes that gap, with essays written by some of the leading researchers in the field.
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