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  1. 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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  2. 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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  3. 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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  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. 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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  6. 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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  7. Gordon Belot & John Earman (1999). From Metaphysics to Physics. In Jeremy Butterfield & Constantine Pagonis (eds.), From Physics to Philosophy. Cambridge University Press. 166--86.
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  8. 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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  9. Jeremy Butterfield (1989). The Hole Truth. British Journal for the Philosophy of Science 40 (1):1-28.
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  10. Jeremy Butterfield (1987). Substantivalism and Determinism. International Studies in the Philosophy of Science 2 (1):10 – 32.
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  11. Jeremy Butterfield & Constantine Pagonis (eds.) (1999). From Physics to Philosophy. Cambridge University Press.
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  12. 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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  13. John Earman (1989). World Enough and Spacetime. MIT press.
  14. 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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  15. 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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  16. Amit Hagar (2013). Review of Tim Maudlin's Philosophy of Physics: Space & Time. [REVIEW] Physics in Perspective (x).
  17. Carl Hoefer (1996). The Metaphysics of Space-Time Substantivalism. Journal of Philosophy 93 (1):5-27.
  18. 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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  19. 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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  20. Alan Macdonald, Einstein's Hole Argument.
    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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  21. 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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  22. 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.
  23. 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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  24. 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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  25. 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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  26. 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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  27. 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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  28. 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 (now) 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 (...)
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  29. 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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  30. 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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  31. 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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  32. 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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  33. 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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  34. 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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  35. Robert Rynasiewicz (1996). Is There a Syntactic Solution to the Hole Problem? Philosophy of Science 63 (3):62.
    After some background setting in which it is shown how Maudlin's (1989, 1990) response to the hole argument of Earman and Norton (1987) is related to that of Rynasiewicz (1994), it is argued that the syntactic proposals of Mundy (1992) and of Leeds (1995), which claim to dismiss the hole argument as an uninteresting blunder, are inadequate. This leads to a discussion of how the responses of Maudlin and Rynasiewicz relate to issues about gauge freedom and relativity principles.
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  36. Robert Rynasiewicz (1994). The Lessons of the Hole Argument. British Journal for the Philosophy of Science 45 (2):407-436.
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  37. Simon Saunders (2002). Indiscernibles, General Covariance, and Other Symmetries. In Abhay Ashtekar, Jürgen Renn, Don Howard, Abner Shimony & S. Sarkar (eds.), Revisiting the Foundations of Relativistic Physics. Festschrift in Honour of John Stachel. Kluwer.
    What is the meaning of general covariance? We learn something about it from the hole argument, due originally to Einstein. In his search for a theory of gravity, he noted that if the equations of motion are covariant under arbitrary coordinate transformations, then particle coordinates at a given time can be varied arbitrarily - they are underdetermined - even if their values at all earlier times are held fixed. It is the same for the values of fields. The argument can (...)
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  38. Paul Teller (2001). The Ins and Outs of Counterfactual Switching. Noûs 35 (3):365–393.
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  39. Paul Teller (1987). Space-Time as a Physical Quantity. In P. Achinstein & R. Kagon (eds.), Kelvin's Baltimore Lectures and Modern Theoretical Physics. Mit Press. 425--448.
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