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Summary General Relativity is our best large-scale physical theory. One often investigates which philosophical consequences follow from the theory. 
Key works Sklar 1974 is an early text. Earman 1995 is the definitive modern survey of philosophical topics. Malament 2012 is a self-contained primer to the mathematical and logical foundations. 
Introductions Glymour 1972, Malament 1984, Earman & Norton 1987, Earman et al 2009, Manchak 2009
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  1. Diederik Aerts (1996). Relativity Theory: What is Reality? [REVIEW] Foundations of Physics 26 (12):1627-1644.
    In classical Newtonian physics there was a clear understanding of “what reality is.≓ Indeed in this classical view, reality at a certain time is the collection of all what is actual at this time, and this is contained in “the present.≓ Often it is stated that three-dimensional space and one-dimensional time hare been substituted by four-dimensional space-time in relativity theory, and as a consequence the classical concept of reality, as that which is “present,≓ cannot be retained. Is reality then the (...)
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  2. Y. Aharonov & G. Carmi (1973). Quantum Aspects of the Equivalence Principle. Foundations of Physics 3 (4):493-498.
    Two thought experiments are discussed which suggest, first, a geometric interpretation of the concept of a (say, vector) potential (i.e., as a kinematic quantity associated with a transformation between moving frames of reference suitably related to the problem) and, second, that, in a quantum treatment one should extend the notion of the equivalence principle to include not only the equivalence of inertial forces with suitable “real” forces, but also the equivalence of potentials of such inertial forces and the potentials of (...)
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  3. R. Ainscough (1922). Some Remarks on Relativity. Mind 31 (124):489-495.
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  4. Marcus Alfred, Petero Kwizera, James V. Lindesay & H. Pierre Noyes (2004). A Nonperturbative, Finite Particle Number Approach to Relativistic Scattering Theory. Foundations of Physics 34 (4):581-616.
    We present integral equations for the scattering amplitudes of three scalar particles, using the Faddeev channel decomposition, which can be readily extended to any finite number of particles of any helicity. The solution of these equations, which have been demonstrated to be calculable, provide a nonperturbative way of obtaining relativistic scattering amplitudes for any finite number of particles that are Lorentz invariant, unitary, cluster decomposable and reduce unambiguously in the nonrelativistic limit to the nonrelativistic Faddeev equations. The aim of this (...)
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  5. Marcus Alfred & James Lindesay (2003). A Test of the Calculability of a Three-Body Relativistic, Cluster Decomposable, Unitary, Covariant Scattering Theory. Foundations of Physics 33 (8):1253-1264.
    In this work a calculation of the cluster decomposable formalism for relativistic scattering as developed by Lindesay, Markevich, Noyes, and Pastrana (LMNP) is made for an ultra-light quantum model. After highlighting areas of the theory vital for calculation, a description is made of the process to go from the general theory to an eigen-integral equation for bound state problems, and calculability is demonstrated. An ultra-light quantum exchange model is then developed to examine calculability.
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  6. Ben Almassi (2009). Trust in Expert Testimony: Eddington's 1919 Eclipse Expedition and the British Response to General Relativity. Studies in History and Philosophy of Science Part B 40 (1):57-67.
  7. C. Marcio do Amaral (1969). Flat-Space Metric in the Quaternion Formulation of General Relativity. Rio De Janeiro, Centro Brasileiro De Pesquisas Físicas.
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  8. Jeeva Anandan & Harvey R. Brown (1995). On the Reality of Space-Time Geometry and the Wavefunction. Foundations of Physics 25 (2):349--60.
    The action-reaction principle (AR) is examined in three contexts: (1) the inertial-gravitational interaction between a particle and space-time geometry, (2) protective observation of an extended wave function of a single particle, and (3) the causal-stochastic or Bohm interpretation of quantum mechanics. A new criterion of reality is formulated using the AR principle. This criterion implies that the wave function of a single particle is real and justifies in the Bohm interpretation the dual ontology of the particle and its associated wave (...)
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  9. James L. Anderson (1971). Covariance, Invariance, and Equivalence: A Viewpoint. General Relativity and Gravitation 2:161--72.
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  10. Hajnal Andréka, Judit X. Madarász, István Németi & Gergely Székely, A Logic Road From Special to General Relativity.
    We present a streamlined axiom system of special relativity in firs-order logic. From this axiom system we ``derive'' an axiom system of general relativity in two natural steps. We will also see how the axioms of special relativity transform into those of general relativity. This way we hope to make general relativity more accessible for the non-specialist.
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  11. Hajnal Andréka, Judit X. Madarász, István Németi & Gergely Székely (2012). A Logic Road From Special Relativity to General Relativity. Synthese 186 (3):633 - 649.
    We present a streamlined axiom system of special relativity in first-order logic. From this axiom system we "derive" an axiom system of general relativity in two natural steps. We will also see how the axioms of special relativity transform into those of general relativity. This way we hope to make general relativity more accessible for the non-specialist.
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  12. G. S. Asanov (1983). Gravitational Field Equations Based on Finsler Geometry. Foundations of Physics 13 (5):501-527.
    The analysis of a previous paper (see Ref. 1), in which the possibility of a Finslerian generalization of the equations of motion of gravitational field sources was demonstrated, is extended by developing the Finslerian generalization of the gravitational field equations on the basis of the complete contractionK = K lj lj of the Finslerian curvature tensorK l j hk (x, y). The relevant Lagrangian is constructed by the replacement of the directional variabley i inK by a vector fieldy i (x), (...)
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  13. G. S. Asanov (1981). A Finslerian Extension of General Relativity. Foundations of Physics 11 (1-2):137-154.
    A Finslerian extension of general relativity is examined with particular emphasis on the Finslerian generalization of the equation of motion in a gravitational field. The construction of a gravitational Lagrangian density by substituting the osculating Riemannian metric tensor in the Einstein density is studied. Attention is drawn to an interesting possibility for developing the theory of test bodies against the Finslerian background.
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  14. William K. Atkins (1983). A Fundamental Quadratic Variational Principle Underlying General Relativity. Foundations of Physics 13 (5):545-552.
    The fundamental result of Lanczos is used in a new type of quadratic variational principle whose field equations are the Einstein field equations together with the Yang-Mills type equations for the Riemann curvature. Additionally, a spin-2 theory of gravity for the special case of the Einstein vacuum is discussed.
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  15. Jonathan Bain (2004). Theories of Newtonian Gravity and Empirical Indistinguishability. Studies in History and Philosophy of Modern Physics 35 (3):345--76.
    In this essay, I examine the curved spacetime formulation of Newtonian gravity known as Newton–Cartan gravity and compare it with flat spacetime formulations. Two versions of Newton–Cartan gravity can be identified in the physics literature—a ‘‘weak’’ version and a ‘‘strong’’ version. The strong version has a constrained Hamiltonian formulation and consequently a well-defined gauge structure, whereas the weak version does not (with some qualifications). Moreover, the strong version is best compared with the structure of what Earman (World enough and spacetime. (...)
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  16. Jonathan Bain (1998). Whitehead's Theory of Gravity. Studies in History and Philosophy of Modern Physics 29 (4):547-574.
    In 1922 in The Principle of Relativity, Whitehead presented an alternative theory of gravitation in response to Einstein’s general relativity. To the latter, he objected on philosophical grounds—specifically, that Einstein’s notion of a variable spacetime geometry contingent on the presence of matter (a) confounds theories of measurement, and, more generally, (b) is unacceptable within the bounds of a reasonable epistemology. Whitehead offered instead a theory based within a comprehensive philosophy of nature. The formulal Whitehead adopted for the gravitational field has (...)
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  17. Julian B. Barbour (1995). General Relativity as a Perfectly Machian Theory. In Julian B. Barbour & H. Pfister (eds.), Mach's Principle: From Newton's Bucket to Quantum Gravity. Birkhäuser. 214--36.
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  18. C. Barceló, L. J. Garay & G. Jannes (2011). Quantum Non-Gravity and Stellar Collapse. Foundations of Physics 41 (9):1532-1541.
    Observational indications combined with analyses of analogue and emergent gravity in condensed matter systems support the possibility that there might be two distinct energy scales related to quantum gravity: the scale that sets the onset of quantum gravitational effects $E_{\rm B}$ (related to the Planck scale) and the much higher scale $E_{\rm L}$ signalling the breaking of Lorentz symmetry. We suggest a natural interpretation for these two scales: $E_{\rm L}$ is the energy scale below which a special relativistic spacetime emerges, (...)
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  19. Carlos Barceló & Gil Jannes (2008). A Real Lorentz-FitzGerald Contraction. Foundations of Physics 38 (2):191-199.
    Many condensed matter systems are such that their collective excitations at low energies can be described by fields satisfying equations of motion formally indistinguishable from those of relativistic field theory. The finite speed of propagation of the disturbances in the effective fields (in the simplest models, the speed of sound) plays here the role of the speed of light in fundamental physics. However, these apparently relativistic fields are immersed in an external Newtonian world (the condensed matter system itself and the (...)
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  20. Thomas Bartelborth (1993). Hierarchy Versus Holism: A Structuralist View on General Relativity. [REVIEW] Erkenntnis 39 (3):383 - 412.
    The philosophical debate whether the epistemological and conceptual structure of science is better characterized as hierarchical or as holistic cannot be decideda priori. A case study on general relativity should help to clarify our representation of this section of physics. For this purpose Sneed's model-theoretic approach is used to reconstruct the structure of relativity. The proposed axiomatization of general relativity takes into account approximations and utilizes local models for a realistic view on the functioning of the theory. A central objective (...)
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  21. A. O. Barut (1988). Combining Relativity and Quantum Mechanics: Schrödinger's Interpretation of Ψ. [REVIEW] Foundations of Physics 18 (1):95-105.
    The incongruence between quantum theory and relativity theory is traced to the probability interpretation of the former. The classical continium interpretation of ψ removes the difficulty. How quantum properties of matter and light, and in particular the radiative problems, like spontaneous emission and Lamb shift, may be accounted in a first quantized Maxwell-Dirac system is discussed.
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  22. R. G. Beil (2003). Finsler Geometry and Relativistic Field Theory. Foundations of Physics 33 (7):1107-1127.
    Finsler geometry on the tangent bundle appears to be applicable to relativistic field theory, particularly, unified field theories. The physical motivation for Finsler structure is conveniently developed by the use of “gauge” transformations on the tangent space. In this context a remarkable correspondence of metrics, connections, and curvatures to, respectively, gauge potentials, fields, and energy-momentum emerges. Specific relativistic electromagnetic metrics such as Randers, Beil, and Weyl can be compared.
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  23. Jacob D. Bekenstein & Asaf Oron (2001). Extended Kelvin Theorem in Relativistic Magnetohydrodynamics. Foundations of Physics 31 (6):895-907.
    We prove the existence of a generalization of Kelvin's circulation theorem in general relativity which is applicable to perfect isentropic magnetohydrodynamic flow. The argument is based on a new version of the Lagrangian for perfect magnetohydrodynamics. We illustrate the new conserved circulation with the example of a relativistic magnetohydrodynamic flow possessing three symmetries.
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  24. A. B. Bell & D. M. Bell (1975). A Highly Ordered Universe. Foundations of Physics 5 (3):455-480.
    A highly ordered universe is described in terms of neutrino and electrino alone as basic particles, and length and time alone as dimensional units. New theories are obtained of particles, nuclides, atomic spectra, general relativity, and gravitation.
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  25. Gordon Belot, Background-Independence.
    Intuitively, a classical field theory is background-independent if the structure required to make sense of its equations is itself subject to dynamical evolution, rather than being imposed ab initio. The aim of this paper is to provide an explication of this intuitive notion. background-independence is not a not formal property of theories: the question whether a theory is background-independent depends upon how the theory is interpreted. Under the approach proposed here, a theory is fully backgroundindependent relative to an interpretation if (...)
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  26. Gordon Belot (1996). Why General Relativity Does Need an Interpretation. Philosophy of Science 63 (3):88.
    There is a widespread impression that General Relativity, unlike Quantum Mechanics, is in no need of an interpretation. I present two reasons for thinking that this is a mistake. The first is the familiar hole argument. I argue that certain skeptical responses to this argument are too hasty in dismissing it as being irrelevant to the interpretative enterprise. My second reason is that interpretative questions about General Relativity are central to the search for a quantum theory of gravity. I illustrate (...)
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  27. Thomas Benda (2013). An Axiomatic Foundation of Relativistic Spacetime. Synthese:1-16.
    An ab-initio foundation for relativistic spacetime is given, which is a conservative extension of Zermelo’s set theory with urelemente. Primitive entities are worldlines rather than spacetime points. Spacetime points are sets of intersecting worldlines. By the proper axioms, they form a manifold. Entities known in differential geometry, up to a metric, are defined and have the usual properties. A set-realistic point of view is adopted. The intended ontology is a set-theoretical hierarchy with a broad base of the empty set and (...)
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  28. Peter Gabriel Bergmann (1969). The Riddle of Gravitation. London, J. Murray.
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  29. Peter Gabriel Bergmann (1942). Introduction to the Theory of Relativity. New York, Prentice-Hall, Inc..
    Comprehensive coverage of the special theory (frames of reference, Lorentz transformation, relativistic mechanics of mass points, more), the general theory ...
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  30. Frank Blume (2006). A Nontemporal Probabilistic Approach to Special and General Relativity. Foundations of Physics 36 (9):1404-1440.
    We introduce a discrete probabilistic model of motion in special and general relativity that is shown to be compatible with the standard model in the statistical limit.
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  31. Hermann Bondi (1970). General Relativity as an Open Theory. In Hermann Bondi, Wolfgang Yourgrau & Allen duPont Breck (eds.), Physics, Logic, and History. New York,Plenum Press. 265--276.
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  32. Hermann Bondi (1964). Relativity and Common Sense. Garden City, N.Y.,Anchor Books.
    Radically reoriented presentation of Einstein's Special Theory and one of most valuable popular accounts available derives relativity from Newtonian ideas, ...
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  33. Giovanni Boniolo & Fernando de Felice (2000). On the Philosophical Foundations of Measurements in General Relativity. Foundations of Physics 30 (10):1629-1641.
    In this paper, first, the question of what a measurement is in General Relativity is tackled; then, some foundational problems it involves are analysed. In particular, by recalling what a measurement is in general, we will try to precisely define what it is in General Relativity. Then, we will analyse, by means of a suitable example, some foundational problems it involves. It will be stressed that such foundational problems do not arise owing to the gauge invariance or the correlation among (...)
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  34. W. B. Bonnor (1969). Status of General Relativity. Guernsey, C.I.]F. Hodgson.
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  35. Ramiro Délio Borges de Meneses (2012). Special Relativity Einstein's Lost Frame: From Metric to Philosophy. Filosofia Oggi 35 (3-4):385-404.
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  36. H. -H. V. Borzeszkowski & H. -J. Treder (1982). Quantum Theory and Einstein's General Relativity. Foundations of Physics 12 (11):1113-1129.
    We discuss the meaning and prove the accordance of general relativity, wave mechanics, and the quantization of Einstein's gravitation equations themselves. Firstly, we have the problem of the influence of gravitational fields on the de Broglie waves, which influence is in accordance with Eeinstein's weak principle of equivalence and the limitation of measurements given by Heisenberg's uncertainty relations. Secondly, the quantization of the gravitational fields is a “quantization of geometry.” However, classical and quantum gravitation have the same physical meaning according (...)
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  37. H. -H. V. Borzeszkowski & H. -J. Treder (1982). Remarks on the Relation Between General Relativity and Quantum Theory. Foundations of Physics 12 (4):413-418.
    A discussion of the diffraction and scattering of particles by a grating shows that the experiment discussed by H. Hönl and by L. Rosenfeld in 1965 and again in 1981 does not reveal any contradiction between general relativity and quantum theory. Moreover, these theories, in principle, cannot refute one another because the (weak) principle of equivalence, underlying general relativity theory, entails that gravitation does not alter the laws of microphysics.
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  38. Alessandro Braccesi (2008). Al di Là Dell'intuizione: Per Una Storia Della Fisica Del Ventesimo Secolo: Relatività E Quantistica. Bononia University Press.
    Proseguendo nella rilettura della fisica iniziata con il volume Una storia della fisica classica, l'autore tenta di tracciare una storia delle teorie della relatività e di quelle quantistiche. -/- Il taglio è quello del precedente volume: cercare di riscoprire le cose così come apparvero all'atto della loro scoperta e presentarle cercando di essere il più fedele possibile ai lavori originali, utilizzando ampie citazioni tratte da questi e mettendone in evidenza le motivazioni e i limiti. -/- Questa via, una via più (...)
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  39. C. D. Broad (1921). The Philosophical Aspect of the Theory of Relativity. Philosophical Review 30:125.
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  40. Harvey R. Brown (1997). On the Role of Special Relativity in General Relativity. International Studies in the Philosophy of Science 11 (1):67 – 81.
    The existence of a definite tangent space structure (metric with Lorentzian signature) in the general theory of relativity is the consequence of a fundamental assumption concerning the local validity of special relativity. There is then at the heart of Einstein's theory of gravity an absolute element which depends essentially on a common feature of all the non-gravitational interactions in the world, and which has nothing to do with space-time curvature. Tentative implications of this point for the significance of the vacuum (...)
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  41. Harvey R. Brown & Oliver Pooley (2001). The Origins of the Spacetime Metric: Bell's Lorentzian Pedagogy and its Significance in General Relativity. In Craig Callender & Nick Huggett (eds.), Physics Meets Philosophy at the Plank Scale. Cambridge University Press. 256--72.
    The purpose of this paper is to evaluate the `Lorentzian Pedagogy' defended by J.S. Bell in his essay ``How to teach special relativity'', and to explore its consistency with Einstein's thinking from 1905 to 1952. Some remarks are also made in this context on Weyl's philosophy of relativity and his 1918 gauge theory. Finally, it is argued that the Lorentzian pedagogy---which stresses the important connection between kinematics and dynamics---clarifies the role of rods and clocks in general relativity.
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  42. Harvey Brown & D. E. Rowe, The Role of Rods and Clocks in General Relativity and the Meaning of the Metric Field.
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  43. Todd A. Brun & Mark M. Wilde (2012). Perfect State Distinguishability and Computational Speedups with Postselected Closed Timelike Curves. Foundations of Physics 42 (3):341-361.
    Bennett and Schumacher’s postselected quantum teleportation is a model of closed timelike curves (CTCs) that leads to results physically different from Deutsch’s model. We show that even a single qubit passing through a postselected CTC (P-CTC) is sufficient to do any postselected quantum measurement with certainty, and we discuss an important difference between “Deutschian” CTCs (D-CTCs) and P-CTCs in which the future existence of a P-CTC might affect the present outcome of an experiment. Then, based on a suggestion of Bennett (...)
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  44. Tim Budden (1997). Galileo's Ship and Spacetime Symmetry. British Journal for the Philosophy of Science 48 (4):483-516.
    The empirical content of the modern definition of relativity given in the Andersonian approach to spacetime theory has been overestimated. It does not imply the empirical relativity Galileo illustrated in his famous ship thought experiment. I offer a number of arguments—some of which are in essential agreement with a recent analysis of Brown and Sypel [1995]—which make this plausible. Then I go on to present example spacetime theories which are modern relativistic but violate Galileo's relativity. I end by briefly discussing (...)
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  45. Tim Budden (1992). The Relativity Principle and the Isotropy of Boosts. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1992:528 - 541.
    A class of theories which satisfy the Relativity Principle has been overlooked. The kinematics for these theories is derived by relaxing the 'boost isotropy' symmetry normally invoked, and the role the dynamical fields play in determining the inertial coordinate systems is emphasised, leading to a criticism of Friedman's (1983) practice of identifying them via the absolute objects of a spacetime theory alone. Some theories complete with 'boost anisotropic' dynamics are given.
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  46. Mario Bunge (1979). Relativity and Philosophy. In Jan Bärmark (ed.), Perspectives in Metascience. Kungl. Vetenskaps- Och Vitterhets-Samhället. 2--75.
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  47. Jeremy Butterfield & John Earman (eds.) (2007). Philosophy of Physics. Elsevier.
    The ambition of this volume is twofold: to provide a comprehensive overview of the field and to serve as an indispensable reference work for anyone who wants to work in it. For example, any philosopher who hopes to make a contribution to the topic of the classical-quantum correspondence will have to begin by consulting Klaas Landsman’s chapter. The organization of this volume, as well as the choice of topics, is based on the conviction that the important problems in the philosophy (...)
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  48. Tim Button (2009). SAD Computers and Two Versions of the Church–Turing Thesis. British Journal for the Philosophy of Science 60 (4):765-792.
    Recent work on hypercomputation has raised new objections against the Church–Turing Thesis. In this paper, I focus on the challenge posed by a particular kind of hypercomputer, namely, SAD computers. I first consider deterministic and probabilistic barriers to the physical possibility of SAD computation. These suggest several ways to defend a Physical version of the Church–Turing Thesis. I then argue against Hogarth's analogy between non-Turing computability and non-Euclidean geometry, showing that it is a non-sequitur. I conclude that the Effective version (...)
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  49. John M. Cage (1937). The Relativity of the Availability of Energy. [Los Angeles.
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  50. Favio Ernesto Cala Vitery (2008). Sobre la Dinámica Relacional Del Espaciotiempo y la Conservación de la Energía En la Teoría General de la Relatividad. Theoria 23 (2):175-193.
    RESUMEN: En este artículo pretendo desmantelar la opinión generalizada según la cual una interpretación relacional del espaciotiempo no es posible. Centro mi atención en el hecho de que las variables dinámicas usualmente están asociadas a objetos materiales en las teorías físicas. El tensor métrico de la Teoría General de la Relatividad (TGR) es un objeto dinámico así que —sostengo— este debe ser mejor entendido como un campo material en toda regla. Este argumento me lleva a vincular la naturaleza relacional del (...)
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