Paralleling the formal derivation of general relativity as a flat spacetime theory, we introduce in addition a preferred temporal foliation. The physical interpretation of the formalism is considered in the context of 5-dimensional “parametrized” and 4-dimensional preferred frame contexts. In the former case, we suggest that our earlier proposal of unconcatenated parametrized physics requires that the dependence on τ be rather slow. In the 4-dimensional case, we consider and tentatively reject several areas of physics that might require a preferred foliation, (...) but find a need for one in the process (“flowing”) theory of time. We then suggest why such a foliation might reasonably be unobservable. (shrink)

Change and local spatial variation are missing in canonical General Relativity's observables as usually defined, an aspect of the problem of time. Definitions can be tested using equivalent formulations of a theory, non-gauge and gauge, because they must have equivalent observables and everything is observable in the non-gauge formulation. Taking an observable from the non-gauge formulation and finding the equivalent in the gauge formulation, one requires that the equivalent be an observable, thus constraining definitions. For massive photons, the de Broglie-Proca (...) non-gauge formulation observable A_{\mu} is equivalent to the Stueckelberg-Utiyama gauge formulation quantity A_{\mu} + \partial_{\mu} \phi, which must therefore be an observable. To achieve that result, observables must have 0 Poisson bracket not with each first-class constraint, but with the Rosenfeld-Anderson-Bergmann-Castellani gauge generator G, a tuned sum of first-class constraints, in accord with the Pons-Salisbury-Sundermeyer definition of observables. The definition for external gauge symmetries can be tested using massive gravity, where one can install gauge freedom by parametrization with clock fields X^A. The non-gauge observable g^{\mu\nu} has the gauge equivalent X^A,_{\mu} g^{\mu\nu} X^B,_{\nu}. The Poisson bracket of X^A,_{\mu} g^{\mu\nu} X^B,_{\nu} with G turns out to be not 0 but a Lie derivative. This non-zero Poisson bracket refines and systematizes Kuchař's proposal to relax the 0 Poisson bracket condition with the Hamiltonian constraint. Thus observables need covariance, not invariance, in relation to external gauge symmetries. The Lagrangian and Hamiltonian for massive gravity are those of General Relativity + \Lambda + 4 scalars, so the same definition of observables applies to General Relativity. Local fields such as g_{\mu\nu} are observables. Thus observables change. Requiring equivalent observables for equivalent theories also recovers Hamiltonian-Lagrangian equivalence. (shrink)

In General Relativity in Hamiltonian form, change has seemed to be missing, defined only asymptotically, or otherwise obscured at best, because the Hamiltonian is a sum of first-class constraints and a boundary term and thus supposedly generates gauge transformations. Attention to the gauge generator G of Rosenfeld, Anderson, Bergmann, Castellani et al., a specially _tuned sum_ of first-class constraints, facilitates seeing that a solitary first-class constraint in fact generates not a gauge transformation, but a bad physical change in electromagnetism or (...) General Relativity. The change spoils the Lagrangian constraints, Gauss's law or the Gauss-Codazzi relations describing embedding of space into space-time, in terms of the physically relevant velocities rather than auxiliary canonical momenta. But the resemblance between the gauge generator G and the Hamiltonian H leaves still unclear where objective change is in GR. Insistence on Hamiltonian-Lagrangian equivalence, a theme emphasized by Castellani, Sugano, Pons, Salisbury, Shepley and Sundermeyer among others, holds the key. Taking objective change to be ineliminable time dependence, one recalls that there is change in vacuum GR just in case there is no time-like vector field xi^a satisfying Killing's equation L_xi g_mn=0, because then there exists no coordinate system such that everything is independent of time. Throwing away the spatial dependence of GR for convenience, one finds explicitly that the time evolution from Hamilton's equations is real change just when there is no time-like Killing vector. The inclusion of a massive scalar field is simple. No obstruction is expected in including spatial dependence and coupling more general matter fields. Hence change is real and local even in the Hamiltonian formalism. The considerations here resolve the Earman-Maudlin standoff over change in Hamiltonian General Relativity: the Hamiltonian formalism is helpful, and, suitably reformed, it does not have absurd consequences for change and observables. Hence the classical problem of time is resolved. The Lagrangian-equivalent Hamiltonian analysis of change in General Relativity is compared to Belot and Earman's treatment. The more serious quantum problem of time, however, is not automatically resolved due to issues of quantum constraint imposition. (shrink)

Recent work on the history of General Relativity by Renn, Sauer, Janssen et al. shows that Einstein found his field equations partly by a physical strategy including the Newtonian limit, the electromagnetic analogy, and energy conservation. Such themes are similar to those later used by particle physicists. How do Einstein's physical strategy and the particle physics derivations compare? What energy-momentum complex did he use and why? Did Einstein tie conservation to symmetries, and if so, to which? How did his work (...) relate to emerging knowledge of the canonical energy-momentum tensor and its translation-induced conservation? After initially using energy-momentum tensors hand-crafted from the gravitational field equations, Einstein used an identity from his assumed linear coordinate covariance x'=Mx to relate it to the canonical tensor. Usually he avoided using matter Euler-Lagrange equations and so was not well positioned to use or reinvent the Herglotz-Mie-Born understanding that the canonical tensor was conserved due to translation symmetries, a result with roots in Lagrange, Hamilton and Jacobi. Whereas Mie and Born were concerned about the canonical tensor's asymmetry, Einstein did not need to worry because his Entwurf Lagrangian is modeled not so much on Maxwell's theory as on a scalar theory. Einstein's theory thus has a symmetric canonical energy-momentum tensor. But as a result, it also has 3 negative-energy field degrees of freedom. Thus the Entwurf theory fails a 1920s-30s a priori particle physics stability test with antecedents in Lagrange's and Dirichlet's stability work; one might anticipate possible gravitational instability. This critique of the Entwurf theory can be compared with Einstein's 1915 critique of his Entwurf theory for not admitting rotating coordinates and not getting Mercury's perihelion right. One can live with absolute rotation but cannot live with instability. Particle physics also can be useful in the historiography of gravity and space-time, both in assessing the growth of objective knowledge and in suggesting novel lines of inquiry to see whether and how Einstein faced the substantially mathematical issues later encountered in particle physics. This topic can be a useful case study in the history of science on recently reconsidered questions of presentism, whiggism and the like. Future work will show how the history of General Relativity, especially Noether's work, sheds light on particle physics. (shrink)

The A-theory of time has intuitive and metaphysical appeal, but suffers from tension, if not inconsistency, with the special and general theories of relativity (STR and GTR). The A-theory requires a notion of global simultaneity invariant under the symmetries of the world's laws, those ostensible transformations of the state of the world that in fact leave the world as it was before. Relativistic physics, if read in a realistic sense, denies that there exists any notion of global simultaneity that is (...) invariant under the symmetries of the world's laws. If physics is at least a decent guide to metaphysics--as sympathies for scientific realism would suggest--then relativistic physics supports the B-theory. If there were a physically natural way to modify the symmetries of the physical laws so as to remove those that are repugnant to the A-theory, while retaining empirical adequacy, then such an altered physics might be attractive to the A-theorist and would weaken the support given by relativity to the B-theory. I exhibit a way to do so here, displaying a Lagrangian density explicitly containing distant simultaneity, yet implying Einstein's field equations. The modification involves a change in the nature of the lapse function and makes use of the Dirac-Bergmann formalism of constrained dynamics, which recently has been discussed much by John Earman. Here this formalism is adapted slightly to permit both local and global generalized coordinates. A classification of senses in which time might be absolute or not is made along the way. Some suggestions for extending the work by finding a first principles motivation are made. An appendix outlines an argument why many local presents are insufficient and a global present is attractive, while two more appendices review the Dirac-Bergmann apparatus for GTR and then apply it to the theory at hand. (shrink)

What if gravity satisfied the Klein-Gordon equation? Both particle physics from the 1920s-30s and the 1890s Neumann-Seeliger modification of Newtonian gravity with exponential decay suggest considering a "graviton mass term" for gravity, which is _algebraic_ in the potential. Unlike Nordström's "massless" theory, massive scalar gravity is strictly special relativistic in the sense of being invariant under the Poincaré group but not the 15-parameter Bateman-Cunningham conformal group. It therefore exhibits the whole of Minkowski space-time structure, albeit only indirectly concerning volumes. Massive (...) scalar gravity is plausible in terms of relativistic field theory, while violating most interesting versions of Einstein's principles of general covariance, general relativity, equivalence, and Mach. Geometry is a poor guide to understanding massive scalar gravity: matter sees a conformally flat metric due to universal coupling, but gravity also sees the rest of the flat metric in the mass term. What is the 'true' geometry, one might wonder, in line with Poincaré's modal conventionality argument? Infinitely many theories exhibit this bimetric 'geometry,' all with the total stress-energy's trace as source; thus geometry does not explain the field equations. The irrelevance of the Ehlers-Pirani-Schild construction to a critique of conventionalism becomes evident when multi-geometry theories are contemplated. Much as Seeliger envisaged, the smooth massless limit indicates underdetermination of theories by data between massless and massive scalar gravities---indeed an unconceived alternative. At least one version easily could have been developed before General Relativity; it then would have motivated thinking of Einstein's equations along the lines of Einstein's newly re-appreciated "physical strategy" and particle physics and would have suggested a rivalry from massive spin 2 variants of General Relativity. The Putnam-Grünbaum debate on conventionality is revisited with an emphasis on the broad modal scope of conventionalist views. Massive scalar gravity thus contributes to a historically plausible rational reconstruction of much of 20th-21st century space-time philosophy in the light of particle physics. An appendix reconsiders the Malament-Weatherall-Manchak conformal restriction of conventionality and constructs the 'universal force' influencing the causal structure. Subsequent works will discuss how massive gravity could have provided a template for a more Kant-friendly space-time theory that would have blocked Moritz Schlick's supposed refutation of synthetic _a priori_ knowledge, and how Einstein's false analogy between the Neumann-Seeliger-Einstein modification of Newtonian gravity and the cosmological constant \Lambda generated lasting confusion that obscured massive gravity as a conceptual possibility. (shrink)

James L. Anderson analyzed the novelty of Einstein's theory of gravity as its lack of "absolute objects." Michael Friedman's related work has been criticized by Roger Jones and Robert Geroch for implausibly admitting as absolute the timelike 4-velocity field of dust in cosmological models in Einstein's theory. Using the Rosen-Sorkin Lagrange multiplier trick, I complete Anna Maidens's argument that the problem is not solved by prohibiting variation of absolute objects in an action principle. Recalling Anderson's proscription of "irrelevant" variables, I (...) generalize that proscription to locally irrelevant variables that do no work in some places in some models. This move vindicates Friedman's intuitions and removes the Jones-Geroch counterexample: some regions of some models of gravity with dust are dust-free and so naturally lack a timelike 4-velocity, so diffeomorphic equivalence to is spoiled. Torretti's example involving constant curvature spaces is shown to have an absolute object on Anderson's analysis, viz., the conformal spatial metric density. The previously neglected threat of an absolute object from an orthonormal tetrad used for coupling spinors to gravity appears resolvable by eliminating irrelevant fields. However, given Anderson's definition, GTR itself has an absolute object : a change of variables to a conformal metric density and a scalar density shows that the latter is absolute. (shrink)

An overlap between the general relativist and particle physicist views of Einstein gravity is uncovered. Noether's 1918 paper developed Hilbert's and Klein's reflections on the conservation laws. Energy-momentum is just a term proportional to the field equations and a "curl" term with identically zero divergence. Noether proved a \emph{converse} "Hilbertian assertion": such "improper" conservation laws imply a generally covariant action. Later and independently, particle physicists derived the nonlinear Einstein equations assuming the absence of negative-energy degrees of freedom for stability, along (...) with universal coupling: all energy-momentum including gravity's serves as a source for gravity. Those assumptions imply that the energy-momentum is only a term proportional to the field equations and a symmetric curl, which implies the coalescence of the flat background geometry and the gravitational potential into an effective curved geometry. The flat metric, though useful in Rosenfeld's stress-energy definition, disappears from the field equations. Thus the particle physics derivation uses a reinvented Noetherian converse Hilbertian assertion in Rosenfeld-tinged form. The Rosenfeld stress-energy is identically the canonical stress-energy plus a Belinfante curl and terms proportional to the field equations, so the flat metric is only a convenient mathematical trick without ontological commitment. Neither generalized relativity of motion, nor the identity of gravity and inertia, nor substantive general covariance is assumed. The more compelling criterion of lacking ghosts yields substantive general covariance as an output. Hence the particle physics derivation, though logically impressive, is neither as novel nor as ontologically laden as it has seemed. (shrink)

It is a commonplace in the philosophy of physics that any local physical theory can be represented using arbitrary coordinates, simply by using tensor calculus. On the other hand, the physics literature often claims that spinors \emph{as such} cannot be represented in coordinates in a curved space-time. These commonplaces are inconsistent. What general covariance means for theories with fermions, such as electrons, is thus unclear. In fact both commonplaces are wrong. Though it is not widely known, Ogievetsky and Polubarinov constructed (...) spinors in coordinates in 1965, enhancing the unity of physics and helping to spawn particle physicists' concept of nonlinear group representations. Roughly and locally, these spinors resemble the orthonormal basis or "tetrad" formalism in the symmetric gauge, but they are conceptually self-sufficient and more economical. The typical tetrad formalism is de-Ockhamized, with six extra field components and six compensating gauge symmetries to cancel them out. The Ogievetsky-Polubarinov formalism, by contrast, is Ockhamized, with most of the fluff removed. As developed nonperturbatively by Bilyalov, it admits any coordinates at a point, but "time" must be listed first. Here "time" is defined in terms of an eigenvalue problem involving the metric components and the matrix $diag$, the product of which must have no negative eigenvalues in order to yield a real symmetric square root that is a function of the metric. Thus even formal general covariance requires reconsideration; the atlas of admissible coordinate charts should be sensitive to the types and \emph{values} of the fields involved. Apart from coordinate order and the usual spinorial two-valuedness, Ogievetsky-Polubarinov spinors form, with the metric, a nonlinear geometric object, for which important results on Lie and covariant differentiation are recalled. Such spinors avoid a spurious absolute object in the Anderson-Friedman analysis of substantive general covariance. They also permit the gauge-invariant localization of the infinite-component gravitational energy in General Relativity. Density-weighted spinors exploit the conformal invariance of the massless Dirac equation to show that the volume element is absent. Thus instead of an arbitrary nonsingular matrix with 16 components, 6 of which are gauged away by a new local $O$ gauge group and one of which is irrelevant due to conformal covariance, one can, and presumably should, use density-weighted Ogievetsky-Polubarinov spinors coupled to the 9-component symmetric square root of the part of the metric that fixes null cones. Thus $\frac{7}{16}$ of the orthonormal basis is eliminated as surplus structure. Greater unity between spinors and tensors and the like is achieved, such as regarding conservation laws. Regarding the conventionality of simultaneity, an unusually wide range of $\epsilon$ values is admissible, but some extreme values are inadmissible. Standard simultaneity uniquely makes the spinor transformation law linear and independent of the metric, because transformations among the standard Cartesian coordinate systems fall within the conformal group, for which the spinor transformation law is linear. The surprising mildness of the restrictions on coordinate order as applied to the Schwarzschild solution is exhibited. (shrink)

Already in 1835 Lobachevski entertained the possibility of multiple geometries of the same type playing a role. This idea of rival geometries has reappeared from time to time but had yet to become a key idea in space-time philosophy prior to Brown's _Physical Relativity_. Such ideas are emphasized towards the end of Brown's book, which I suggest as the interpretive key. A crucial difference between Brown's constructivist approach to space-time theory and orthodox "space-time realism" pertains to modal scope. Constructivism takes (...) a broad modal scope in applying to all local classical field theories---modal cosmopolitanism, one might say, including theories with multiple geometries. By contrast the orthodox view is modally provincial in assuming that there exists a _unique_ geometry, as the familiar theories have. These theories serve as the "canon" for the orthodox view. Their historical roles also suggest a Whiggish story of inevitable progress. Physics literature after c. 1920 is relevant to orthodoxy primarily as commentary on the canon, which closed in the 1910s. The orthodox view explains the spatio-temporal behavior of matter in terms of the manifestation of the real geometry of space-time, an explanation works fairly well within the canon. The orthodox view, Whiggish history, and the canon have a symbiotic relationship. If one happens to philosophize about a theory outside the canon, space-time realism sheds little light on the spatio-temporal behavior of matter. Worse, it gives the _wrong_ answer when applied to an example arguably _within_ the canon, a sector of Special Relativity, namely, _massive_ scalar gravity with universal coupling. Which is the true geometry---the flat metric from the Poincare' symmetry group, the conformally flat metric exhibited by material rods and clocks, or both---or is the question faulty? How does space-time realism explain the fact that all matter fields see the same curved geometry, when so many ways to mix and match exist? Constructivist attention to dynamical details is vindicated; geometrical shortcuts can disappoint. The more exhaustive exploration of relativistic field theories in particle physics, especially massive theories, is a largely untapped resource for space-time philosophy. (shrink)

Theory. Moral knowledge and moral principles -- Victorian Matters. First principles and common-sense morality in Sidgwick's ethics ; Moral problems and moral philosophy in the Victorian Period -- On the historiography of moral philosophy. Moral crisis and the history of ethics ; Modern moral philosophy : from beginning to end? : No discipline, no history : the case of moral philosophy ; Teaching the history of moral philosophy -- Seventeenth- and eighteenth-century moral philosophy. The divine corporation and the history of (...) ethics ; Natural law ; The misfortunes of virtue ; Voluntarism and the foundations of ethics ; Hume and the religious significance of moral rationalism -- On Kant. Why study Kant's Groundwork ; Autonomy, obligation, and virtue : an overview of Kant's moral philosophy ; Kant and Stoic ethics ; Toward enlightenment : Kant and the sources of darkness ; Kantian unsocial sociability : good out of evil -- Moral psychology. The active powers -- Afterword. Sixty years of philosophy in a life. (shrink)

This is the fourth volume of the Clarendon edition of Robert Burton's Anatomy of Melancholy and the first of three volumes of Commentary. It contains commentary on the text up to p. 327 of volume one - i.e. The Argument of the Frontispeice, Democritus to the Reader, and Partition 1 as far as the end of Section 2, Member 3, Subsection 15: 'Misery of Schollers'. In his study of morbid psychology as it was understood in his day, Burton cites many (...) other writers. No previous edition of the Anatomy has identified all of these or verified all his quotations. In addition to explanatory notes and translations of all the passages in Latin, this edition attempts to locate all Burton's sources in the actual books he himself owned or to which he probably had access. The last of the three volumes of commentary will contain a Biobibliography listing over 1,500 authorities referred to by Burton, many very obscure, and will give not only bibliographical details but information about the writers. (shrink)

This is the fourth volume of the Clarendon edition of Robert Burton's Anatomy of Melancholy and the first of three volumes of Commentary. It contains commentary on the text up to p. 327 of volume one - i.e. The Argument of the Frontispeice, Democritus to the Reader, and Partition 1 as far as the end of Section 2, Member 3, Subsection 15: 'Misery of Schollers'. In his study of morbid psychology as it was understood in his day, Burton cites many (...) other writers. No previous edition of the Anatomy has identified all of these or verified all his quotations. In addition to explanatory notes and translations of all the passages in Latin, this edition attempts to locate all Burton's sources in the actual books he himself owned or to which he probably had access. The last of the three volumes of commentary will contain a Biobibliography listing over 1,500 authorities referred to by Burton, many very obscure, and will give not only bibliographical details but information about the writers. (shrink)

Background: We aimed to determine the smallest changes in health-related quality of life (HRQoL) scores in the European Organisation for Research and Treatment of Cancer Quality of Life Questionnaire core 30 and the Brain Cancer Module (QLQ-BN20), which could be considered as clinically meaningful in brain cancer patients. Materials and methods: World Health Organisation performance status (PS) and mini-mental state examination (MMSE) were used as clinical anchors appropriate to related subscales to determine the minimal clinically important differences (MCIDs) in HRQoL (...) change scores (range 0-100) in the QLQ-C30 and QLQ-BN20. A threshold of 0.2 standard deviation (SD) (small effect) was used to exclude anchor-based MCID estimates considered too small to inform interpretation. Results: Based on PS, our findings support the following integer estimates of the MCID for improvement and deterioration, respectively: physical (6, 9), role (14, 12), and cognitive functioning (8, 8); global health status (7, 4(star)), fatigue (12, 9), and motor dysfunction (4(star), 5). Anchoring with MMSE, cognitive functioning MCID estimates for improvement and deterioration were (11, 2(star)) and for communication deficit were (9, 7). Estimates with asterisks were <0.2 SD and were excluded from our MCID range of 5-14. Conclusion: These estimates can help clinicians evaluate changes in HRQoL over time, assess the value of a health care intervention and can be useful in determining sample sizes in designing future clinical trials. (shrink)

Influential cases have been provided that seem to suggest that one can fail to have knowledge because of the social environment. If not a distinct kind of social defeater, is there a uniquely social phenomenon that defeats knowledge? My aim in this paper is to explore these questions. I shall argue that despite initial appearances to the contrary, we have no reason to accept a special class of social defeater, nor any essentially social defeat phenomenon. We can explain putative cases (...) of social defeat with our existing epistemological apparatus. (shrink)

One thing nearly all epistemologists agree upon is that Gettier cases are decisive counterexamples to the tripartite analysis of knowledge; whatever else is true of knowledge, it is not merely belief that is both justified and true. They now agree that knowledge is not justified true belief because this is consistent with there being too much luck present in the cases, and that knowledge excludes such luck. This is to endorse what has become known as the 'anti-luck platitude'. <br /><br (...) />But what if generations of philosophers have been mistaken about this, blinded at least partially by a deeply entrenched professional bias? There has been another, albeit minority, response to Gettier: to deny that the cases are counterexamples at all. <br /><br />Stephen Hetherington, a principal and vocal proponent of this view, advances what he calls the 'Knowing Luckily Proposal'. If Hetherington is correct, this would call for a major re-evaluation and re-orientation of post-Gettier analytic epistemology, since much of it assumes the anti-luck platitude both in elucidating the concept of knowledge, and in the application of such accounts to central philosophical problems. It is therefore imperative that the Knowing Luckily Proposal be considered and evaluated in detail. <br /><br />In this paper I critically assess the Knowing Luckily Proposal. I argue that while it draws our attention to certain important features of knowledge, ultimately it fails, and the anti-luck platitude emerges unscathed. Whatever else is true of knowledge, therefore, it is non-lucky true belief. For a proposition to count as knowledge, we cannot arrive at its truth accidentally or for the wrong reason. (shrink)

A clear accurate translation of one of Plato's most facinating dialogues, with an extensive philosophical commentary.

Prior thinks that Edwards' argument depends on a metaphysical turn of phrase. Edwards, he says, subsumes "all happenings, or anyhow... all changes, under the idea of the 'beginning to be' either of concrete objects or of abstract ones". We are not to say, "My head began to ache," we are to say, "My headache began to exist." The shift may seem trivial, but actually it is "of the very first importance": Edwards' argument "depends on it." The reason is the following. (...) Edwards says that objects or substances cannot begin to be without a cause; that if they could, it would be prima facie implausible to hold that substances of only one kind, of all the millions of kinds of substance, should causelessly come to be; and that the implausibility cannot be removed by appealing to the nature of what thus comes to be, because until it actually exists there is nothing there to explain anything. Prior agrees with all that. But he holds that it is not impossible that some already existing substances should have a special kind of property which would make it possible for them to change or act causelessly. Of course, if we have to say that a change or an act is just another kind of coming to be of a substance, this too is impossible. Hence Prior thinks that by showing that changes and acts need not be construed as Edwards construes them, he will have made room for the possibility of limited indeterminism. (shrink)

Now it is tempting to try to generalize the view that means-ends considerations play a part in determining what is the right theory. It is tempting, that is, to try to use a similar view to give an account of the nature of truth or knowledge quite generally. For can we not say that truth is simply what we ought to believe, and that knowledge is what we are justified in believing? After all, terms like "true," "false," "probable," "doubtful," "known," (...) "believed," and so on, are not merely descriptive terms. They are used to evaluate the degree to which a belief or proposition is one which we ought to accept. And if in the case of so important an area of human knowledge as scientific theory what we ought to accept is determined in large part by means-ends considerations, may it not be true that in other areas of human knowledge means-ends considerations have a similar function? Perhaps it would even be possible to define truth, or knowledge, in terms of what serves some end or purpose. (shrink)