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  1. Derivation of the Schrödinger equation.Shan Gao - manuscript
    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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  2. Counterparts, Determinism, and the Hole Argument.Franciszek Cudek - forthcoming - British Journal for the Philosophy of Science.
    The hole argument concludes that substantivalism about spacetime entails the radical indeterminism of the general theory of relativity (GR). In this paper, I amend and defend a response to the hole argument first proposed by Butterfield (1989) that relies on the idea of counterpart substantivalism. My amendment clarifies and develops the metaphysical presuppositions of counterpart substantivalism and its relation to various definitions of determinism. My defence consists of two claims. First, contra Weatherall (2018) and others: the hole argument is not (...)
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  3. Closing the Hole Argument.Hans Halvorson & John Byron Manchak - forthcoming - British Journal for the Philosophy of Science.
    The hole argument purportedly shows that spacetime substantivalism implies a pernicious form of indeterminism. We show that the argument is seductive only because it mistakes a trivial claim (viz. there are isomorphic models) for a significant claim (viz. there are hole isomorphisms). We prove that the latter claim is false -- thereby closing the debate about whether substantivalism implies indeterminism.
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  4. On the Mathematics and Metaphysics of the Hole Argument.Oliver Pooley & James Read - forthcoming - The British Journal for the Philosophy of Science.
    We make some remarks on the mathematics and metaphysics of the hole argument, in response to a recent article in this journal by Weatherall ([2018]). Broadly speaking, we defend the mainstream philosophical literature from the claim that correct usage of the mathematics of general relativity `blocks' the argument.
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  5. Eight Arguments for First‐Person Realism.David Builes - 2024 - Philosophy Compass 19 (1):e12959.
    According to First-Person Realism, one's own first-person perspective on the world is metaphysically privileged in some way. After clarifying First-Person Realism by reference to parallel debates in the metaphysics of modality and time, I survey eight different arguments in favor of First-Person Realism.
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  6. Some Neglected Possibilities: A Reply to Teitel.Caspar Jacobs - 2024 - Journal of Philosophy 121 (2):108-120.
    The infamous Hole Argument has led philosophers to develop various versions of substantivalism, of which metric essentialism and sophisticated substantivalism are the most popular. In this journal, Trevor Teitel has recently advanced novel arguments against both positions. However, Teitel does not discuss the position of Jeremy Butterfield, which appeals to Lewisian counterpart theory in order to avoid the Hole Argument. In this note I show that the Lewis-Butterfield view is immune to Teitel’s challenges.
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  7. The Hole Argument without the notion of isomorphism.Joanna Luc - 2024 - Synthese 203 (3).
    In this paper, I argue that the Hole Argument can be formulated without using the notion of isomorphism, and for this reason it is not threatened by the criticism of Halvorson and Manchak (Br J Philos Sci, 2022. https://doi.org/10.1086/719193). Following Earman and Norton (Br J Philos Sci 38, pp. 515–525, 1987), I divide the Hole Argument into two steps: the proof of the Gauge Theorem and the transition from the Gauge Theorem to the conclusion of radical indeterminism. In the analaysis (...)
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  8. Reopening the Hole Argument.Klaas Landsman - 2023 - Philosophy of Physics 1 (1).
    This expository paper relates the Hole Argument in general relativity (GR) to the well-known theorem of Choquet-Bruhat and Geroch (1969) on the existence and uniqueness of globally hyperbolic solutions to the Einstein field equations. Like the Earman–Norton (1987) version of the Hole Argument (which is originally due to Einstein), this theorem exposes the tension between determinism and some version of spacetime substantivalism. But it seems less vulnerable to the campaign by Weatherall (2018) and followers to close the Hole Argument on (...)
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  9. Some Remarks on Recent Formalist Responses to the Hole Argument.Tushar Menon & James Read - 2023 - Foundations of Physics 54 (1):1-20.
    In a recent article, Halvorson and Manchak (Br J Philos Sci, Forthcoming) claim that there is no basis for the Hole Argument, because (in a certain sense) hole isometries are unique. This raises two important questions: (a) does their argument succeed?; (b) how does this formalist response to the Hole Argument relate to other recent responses to the Hole Argument in the same tradition—in particular, that of Weatherall (Br J Philos Sci 69(2):329–350, 2018)? In this article, _ad_ (a), we argue (...)
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  10. Mathematical Responses to the Hole Argument: Then and Now.Clara Bradley & James Owen Weatherall - 2022 - Philosophy of Science 89 (5):1223-1232.
    We argue that several apparently distinct responses to the hole argument, all invoking formal or mathematical considerations, should be viewed as a unified “mathematical response.” We then consider and rebut two prominent critiques of the mathematical response before reflecting on what is ultimately at issue in this literature.
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  11. How to Be a Spacetime Substantivalist.Trevor Teitel - 2022 - Journal of Philosophy 119 (5):233-278.
    The consensus among spacetime substantivalists is to respond to Leibniz's classic shift arguments, and their contemporary incarnation in the form of the hole argument, by pruning the allegedly problematic metaphysical possibilities that generate these arguments. Some substantivalists do so by directly appealing to a modal doctrine akin to anti-haecceitism. Other substantivalists do so by appealing to an underlying hyperintensional doctrine that implies some such modal doctrine. My first aim in this paper is to pose a challenge for all extant forms (...)
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  12. The Hole Argument, Manifold Substantivalism, and Ontic Structural Realism.Saeed Masoumi - 2021 - Journal of Philosophical Investigations 15 (35):379-401.
    The hole argument has become one of the main issues in the philosophy of space-time after the article by Earman and Norton (1987), according to which a certain version of substantivalism (manifold substantivalism) cannot be defended because it brings about to a radical indeterminism. In this article, we try to show that, first, the naming of manifold substantivalism is not appropriate since as some philosophers have said, manifold points cannot be considered to have an independent identity. Second, with a commitment (...)
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  13. The Hole Argument.Oliver Pooley - 2021 - In Eleanor Knox & Alastair Wilson (eds.), The Routledge Companion to the Philosophy of Physics. Routledge. pp. 145-158.
    This paper reviews the hole argument as an argument against spacetime substantivalism. After a careful presentation of the argument itself, I critically review possible responses.
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  14. The Hole Argument, take n.John Dougherty - 2020 - Foundations of Physics 50 (4):330-347.
    I apply homotopy type theory to the hole argument as formulated by Earman and Norton. I argue that HoTT gives a precise sense in which diffeomorphism-related Lorentzian manifolds represent the same spacetime, undermining Earman and Norton’s verificationist dilemma and common formulations of the hole argument. However, adopting this account does not alleviate worries about determinism: general relativity formulated on Lorentzian manifolds is indeterministic using this standard of sameness and the natural formalization of determinism in HoTT. Fixing this indeterminism results in (...)
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  15. Holes in Spacetime: Some Neglected Essentials.Trevor Teitel - 2019 - Journal of Philosophy 116 (7):353-389.
    The hole argument purports to show that all spacetime theories of a certain form are indeterministic, including the General Theory of Relativity. The argument has given rise to an industry of searching for a metaphysics of spacetime that delivers the right modal implications to rescue determinism. In this paper, I first argue that certain prominent extant replies to the hole argument—namely, those that appeal to an essentialist doctrine about spacetime—fail to deliver the requisite modal implications. As part of my argument, (...)
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  16. Fifty Million Elvis Fans Can’t be Wrong.Gordon Belot - 2018 - Noûs:946-981.
    This essay revisits some classic problems in the philosophy of space and time concerning the counting of possibilities. I argue that we should think that two Newtonian worlds can differ only as to when or where things happen and that general relativistic worlds can differ in something like the same way—the first of these theses being quaintly heterodox, the second baldly heretical, according to the mores of contemporary philosophy of physics.
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  17. Space, Time, and (how they) Matter: a Discussion about some Metaphysical Insights Provided by our Best Fundamental Physical Theories.Valia Allori - 2016 - In G. C. Ghirardi & S. Wuppuluri (eds.), Space, Time, and The Limits of Human Understanding. Springer. pp. 95-107.
    This paper is a brief (and hopelessly incomplete) non-standard introduction to the philosophy of space and time. It is an introduction because I plan to give an overview of what I consider some of the main questions about space and time: Is space a substance over and above matter? How many dimensions does it have? Is space-time fundamental or emergent? Does time have a direction? Does time even exist? Nonetheless, this introduction is not standard because I conclude the discussion by (...)
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  18. Gone Till November: A Disagreement in Einstein Scholarship.Tim Räz - 2016 - In Raphael Scholl & Tilman Sauer (eds.), The Philosophy of Historical Case Studies. Springer Verlag.
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  19. Regarding the ‘Hole Argument’.James Owen Weatherall - 2016 - British Journal for the Philosophy of Science:axw012.
    I argue that the Hole Argument is based on a misleading use of the mathematical formalism of general relativity. If one is attentive to mathematical practice, I will argue, the Hole Argument is blocked.
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  20. On the Existence of Spacetime Structure.Erik Curiel - 2014 - British Journal for the Philosophy of Science:axw014.
    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 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 an (...)
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  21. Leibniz-Äquivalenz vs. Einstein-Äquivalenz. Was man von der Logisch-Empiristischen (Fehl-)Interpretation des Punkt-Koinzidenz-Arguments lernen kann.Marco Giovanelli - 2013 - 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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  22. Review of Tim Maudlin's Philosophy of Physics: Space & Time. [REVIEW]Amit Hagar - 2013 - Physics in Perspective (x).
  23. Substantivalist and Relationalist Approaches to Spacetime.Oliver Pooley - 2013 - 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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  24. Return of Logos: Ontological Memory → Information → Time.Vladimir Rogozhin - 2013 - FQXi Contest 2013:00-08.
    Total ontological unification of matter at all levels of reality as a whole, its “grasp” of its dialectical structure, space dimensionality and structure of the language of nature – “house of Being” [1], gives the opportunity to see the “place” and to understand the nature of information as a phenomenon of Ontological (structural) Memory (OntoMemory), the measure of being of the whole, “the soul of matter”, qualitative quantity of the absolute forms of existence of matter (absolute states). “Information” and “time” (...)
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  25. Explaining Leibniz equivalence as difference of non-inertial appearances: Dis-solution of the Hole Argument and physical individuation of point-events.Luca Lusanna & Massimo Pauri - 2006 - Studies in History and Philosophy of Modern Physics 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. The physical individuation of point-events is furnished by the autonomous degrees of freedom of the gravitational field, which represent -as it were -the ontic part of the metric field. The physical role of the epistemic part is likewise clarified as embodying the unavoidable non-inertial aspects of GR. At the end the philosophical import of the Hole Argument (...)
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  26. A hole revolution, or are we back where we started?Oliver Pooley - 2006 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 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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  27. Bringing the hole argument back in the loop: A response to Pooley.Dean Rickles - 2006 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 37 (2):381-387.
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  28. A Conjecture on Einstein, the Independent Reality of Spacetime Coordinate Systems and the Disaster of 1913.John D. Norton - 2005 - In .
    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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  29. Points, particles, and structural realism.Oliver Pooley - 2005 - In Dean Rickles, Steven French & Juha T. Saatsi (eds.), The Structural Foundations of Quantum Gravity. Oxford University Press. pp. 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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  30. A new spin on the hole argument.Dean Rickles - 2004 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 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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  31. Einstein algebras and the hole argument.Jonathan Bain - 2003 - 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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  32. Revisiting the Foundations of Relativistic Physics. Festschrift in Honour of John Stachel.Abhay Ashtekar, Jürgen Renn, Don Howard, Abner Shimony & S. Sarkar (eds.) - 2002 - Kluwer Academic Publishers.
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  33. Thoroughly modern Mctaggart: Or, what Mctaggart would have said if he had read the general theory of relativity.John Earman - 2002 - Philosophers' Imprint 2:1-28.
    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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  34. Thoroughly muddled Mctaggart: Or, how to abuse gauge freedom to create metaphysical monostrosities.Tim Maudlin - 2002 - Philosophers' Imprint 2:1-23.
    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. The relations between things' versus 'the things between relations': The deeper meaning of the hole argument.John Stachel - 2002 - In David B. Malament (ed.), Reading Natural Philosophy: Essays in the History and Philosophy of Science and Mathematics. Open Court. pp. 231--66.
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  36. Einstein's hole argument.Alan Macdonald - 2001 - 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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  37. The Bundle Theory, Substance and Spacetime.Glenn Gerard Parsons - 2001 - 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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  38. Can the Bundle Theory Save Substantivalism from the Hole Argument?Glenn Parsons & Patrick McGivern - 2001 - Philosophy of Science 68 (S3):S358-S370.
    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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  39. Indiscernibles, general covariance, and other symmetries.Simon Saunders - 2001 - 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 Academic Publishers.
    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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  40. The ins and outs of counterfactual switching.Paul Teller - 2001 - Noûs 35 (3):365–393.
  41. Geometry and motion.Gordon Belot - 2000 - 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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  42. From metaphysics to physics.Gordon Belot & John Earman - 1999 - In Jeremy Butterfield & Constantine Pagonis (eds.), From Physics to Philosophy. Cambridge University Press. pp. 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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  43. From Physics to Philosophy.Jeremy Butterfield & Constantine Pagonis (eds.) - 1999 - 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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  44. Holes, haecceitism and two conceptions of determinism.Joseph Melia - 1999 - 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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  45. Representations of Spacetime: Formalism and Ontological Commitment.Jonathan Stanley Bain - 1998 - 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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  46. Determinism and modality.Carolyn Brighouse - 1997 - 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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  47. Modern essentialism and the problem of individuation of spacetime points.Andreas Bartels - 1996 - 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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  48. Whatever is Never and Nowhere is Not: Space, Time, and Ontology in Classical and Quantum Gravity.Gordon Scott Belot - 1996 - 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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  49. The Case for Substantivalism.Carolyn Jane Brighouse - 1996 - 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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  50. The metaphysics of space‐time substantivalism.Carl Hoefer - 1996 - Journal of Philosophy 93 (1):5-27.
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