The fundamental problem of Christology is the apparent contradiction of Christ as recorded at Chalcedon. Christ is human and Christ is divine. Being divine entails being immutable. Being human entails being mutable. Were Christ two different persons there’d be no apparent contradiction. But Chalcedon rules as much out. Were Christ only partly human or only partly divine there’d be no apparent contradiction. But Chalcedon rules as much out. Were the very meaning of ‘mutable’ and/or ‘immutable’ other than what they are, (...) there’d be no apparent contradiction. But the meaning is what it is, and changing the meaning of our terms to avoid the apparent contradiction of Christ is an apparent flight from reality. What, in the end, is the explanation of the apparent contradiction of Christ? Theologians and philosophers have long advanced many consistency-seeking answers, all of which increase the metaphysical or semantical complexity of the otherwise strikingly simple but radical core of Christianity’s GodMan. In this paper, I put the simplest explanation on the theological table: namely, Christ appears to be contradictory because Christ is contradictory. This explanation may sound complicated to the many who are steeped in the mainstream account of logic according to which logic precludes the possibility of true contradictions. But the mainstream account of logic can and should be rejected. Ridding theology of the dogma of mainstream logic illuminates the simple though striking explanation of the apparent contradiction of Christ — namely, that Christ is a contradictory being. Just as the simplest explanation to the apparent roundness of the earth has earned due acceptance, so too should the simplest explanation of the apparent contradiction of Christ. (shrink)

This is a corrected version of the final proofs. I've fixed a number of typos, and corrected a blunder in chapter 4. In chapter 4 I say that 'this is this' is analytic, and 'this is not this' is antonymous. This is inconsistent with what I say in chapter 5, and not what I actually think. Rather, 'this is this' is taugologous, and 'this is not this' is contradictory. Analyticity and autnonmy are sense properties while tautologousness and contradictoriness are formal (...) logical properties. Heading, ToC and Index updated accordingly. (Oxford will make these corrections in their online version and in future print runs.). (shrink)

Consequence is at the heart of logic; an account of consequence, of what follows from what, offers a vital tool in the evaluation of arguments. Since philosophy itself proceeds by way of argument and inference, a clear view of what logical consequence amounts to is of central importance to the whole discipline. In this book JC Beall and Greg Restall present and defend what thay call logical pluralism, the view that there is more than one genuine deductive consequence relation, a (...) position which has profound implications for many linguists as well as for philosophers. We should not search for one true logic, since there are many. (shrink)

A number of philosophers endorse, without argument, the view that there’s something it’s like consciously to think that p, which is distinct from what it’s like consciously to think that q. This thesis, if true, would have important consequences for philosophy of mind and cognitive science. In this paper I offer an argument for it, and attempt to induce examples of it in the reader. The argument claims it would be impossible introspectively to distinguish conscious thoughts with respect to their (...) content if there weren’t something it’s like to think them. This argument is defended against several objections. Then I use what I call “minimal pair” experiences—sentences read without and with understanding—to induce in the reader an experience of the kind I claim exists. Further objections are considered and rebutted. (shrink)

Consequence is at the heart of logic; an account of consequence, of what follows from what, offers a vital tool in the evaluation of arguments. Since philosophy itself proceeds by way of argument and inference, a clear view of what logical consequence amounts to is of central importance to the whole discipline. In this book JC Beall and Greg Restall present and defend what thay call logical pluralism, the view that there is more than one genuine deductive consequence relation, a (...) position which has profound implications for many linguists as well as for philosophers. We should not search for one true logic, since there are many. (shrink)

In this paper, we distinguish two versions of Curry's paradox: c-Curry, the standard conditional-Curry paradox, and v-Curry, a validity-involving version of Curry's paradox that isn’t automatically solved by solving c-curry. A unified treatment of curry paradox thus calls for a unified treatment of both c-Curry and v-Curry. If, as is often thought, c-Curry paradox is to be solved via non-classical logic, then v-Curry may require a lesson about the structure—indeed, the substructure—of the validity relation itself.

1. In both Benedetto Croce's and Hegel's own terminology, dialectics can be understood as dottrina degli opposti (the doctrine of the opposites – Lehre der Gegensätze).1 In the dialectical process,...

According to the Feigl–Reichenbach–Salmon–Schurz pragmatic justification of induction, no predictive method is guaranteed or even likely to work for predicting the future; but if anything will work, induction will work—at least when induction is employed at the meta-level of predictive methods in light of their track records. One entertains a priori all manner of esoteric prediction methods, and is said to arrive a posteriori at the conclusion, based on the actual past, that object-level induction is optimal. Schurz’s refinements largely solve (...) the notorious short-run problem. A difficulty is noted, however, related to short-run worries but based on localized disagreement about the past, a feature characteristic of real debates (especially early modern) involving induction in intellectual history. Given the evidence about past events, _unfiltered by induction_, meta-induction might support a partly non-inductive method—especially as judged by proponents of esoteric prediction methods, who presumably believe that their methods have worked. Thus induction is justified meta-inductively in contexts where it was uncontroversial, while not obviously justified in key contexts where it has been disputed. This objection, momentarily sensed by Reichenbach regarding clairvoyance, is borne out by the Stoics’ use of meta-induction to justify both science and divination and by ancient Hebrew examples of meta-induction. Schurz’s recently introduced criteria for acceptance of testimony play a crucial role in arriving at object-level induction using meta-induction, but one might question them. Given the need for judgment in accepting testimony, it is unclear that the subjectivity of Howson’s Bayesian answer to Hume’s problem is overcome. (shrink)

The notion of a "mental representation" is, arguably, in the first instance a theoretical construct of cognitive science. As such, it is a basic concept of the Computational Theory of Mind, according to which cognitive states and processes are constituted by the occurrence, transformation and storage (in the mind/brain) of information-bearing structures (representations) of one kind or another.

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)

In the past few years, a number of philosophers ; Horgan and Tienson 2002; Pitt 2004) have maintained the following three theses: there is a distinctive sort of phenomenology characteristic of conscious thought, as opposed to other sorts of conscious mental states; different conscious thoughts have different phenomenologies; and thoughts with the same phenomenology have the same intentional content. The last of these three claims is open to at least two different interpretations. It might mean that the phenomenology of (...) a thought expresses its intentional content, where intentional content is understood as propositional, and propositions are understood as mind-and language-independent abstract entities. And it might mean that the phenomenology of a thought is its intentional content—that is, that the phenomenology of a thought, like the phenomenology of a sensation, constitutes its content. The second sort of view is a kind of psychologism. Psychologistic views hold that one or another sort of thing—numbers, sentences, propositions, etc.—that we can think or know about is in fact a kind of mental thing. Since Frege, psychologism has been in bad repute among analytic philosophers. It is widely held that Frege showed that such views are untenable, since, among other things, they subjectivize what is in fact objective, and, hence, relativize such things as consistency and truth to the peculiarities of human psychology. The purpose of this paper is to explore the consequences of the thesis that intentional mental content is phenomenological and to try to reach a conclusion about whether it yields a tenable view of mind, thought and meaning. I believe the thesis is not so obviously wrong as it will strike many philosophers of mind and language. In fact, it can be defended against the standard objections to psychologism, and it can provide the basis for a novel and interesting account of mentality. (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)

This paper offers a new and very simple alternative to Bochvar's well known nonsense -- or meaninglessness -- interpretation of Weak Kleene logic. To help orient discussion I begin by reviewing the familiar Strong Kleene logic and its standard interpretation; I then review Weak Kleene logic and the standard interpretation. While I note a common worry about the Bochvar interpretation my aim is only to give an alternative -- and I think very elegant -- interpretation, not necessarily a replacement.

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)

Drawing from Frantz Fanon’s writings on racialized alienation and psychopathology, this paper argues that Fanon’s engagement with phenomenology shaped his framing of the sociogenic origins of racialized perceptions of criminality in French psychiatry and that such a novel etiology reflects a commitment to political transformation. First, I trace Fanon’s notion of sociogeny as it develops both in his early writings, and in secondary scholarship on Fanon that highlights the phenomenological dimensions of sociogeny. In the second section, I turn specifically to (...) racialized conceptions of criminality within French colonial medicine and Fanon’s writings on psychiatry to trace some complicated aspects of his critique of colonization and its relationship to medical institutions, including the forced confinement of psychiatric patients. I then conclude by briefly returning to how Fanon’s conception of sociogeny functions in a phenomenological register, and I propose that Fanon’s interests in Merleau-Ponty are based on important shared political and sociological commitments across their respective writings. However, I propose that Fanon’s interventions in phenomenology during the mid-twentieth century contain core critical insights, not shared by his predecessor, that remain relevant for critical phenomenologists today. (shrink)

Some analytic philosophers have recently been defending the thesis that there’s “something it’s like” to consciously think a particular thought, which is qualitatively different from what it’s like to be in any other kind of conscious mental state and from what it’s like to think any other thought, and which constitutes the thought’s intentional content. (I call this the “intentional phenomenology thesis”). One objection to this thesis concerns the introspective availability of such content: If it is true that intentional phenomenology (...) is constitutive of intentional content, and that conscious phenomenology is always introspectively available, then it ought to be true that the content of any concept consciously entertained is always introspectively available. But it is not. For example, one can know introspectively that one is thinking that one knows that p without knowing introspectively what the content of the concept of knowledge is. Hence, it cannot be that intentional content is constituted by cognitive phenomenology. -/- I explore three responses to this objection. First, it is not clear that all of the contents of consciousness must be equally available to introspection. The capacities for conscious experience and introspective attention to it are distinct. It is not implausible that the resolving power of the latter might be insufficient to discern all of the fine-grained details of the former, or that its scope might be limited. Second, it is possible that in cases of incomplete accessibility one is entertaining only part of the concept the relevant term expresses in one’s language. In the knowledge case, for example, perhaps one is thinking only that one has justified true belief that p (one’s self-attribution of a thought about knowledge is in fact false). Finally, in such cases one might be consciously entertaining only part of the relevant concept, the rest remaining unconscious, and so unavailable to conscious introspection. I conclude that the objection is not decisive against the intentional phenomenology thesis. (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)

Reductive representationalism is the view that the qualitative properties associated with conscious experience are properties of the objects of the experience, and not of the experience itself. A prima facie problem for this view arises from dreams and hallucinations, in which qualitative properties are experienced but not instantiated in external objects of perception. I argue that representationalist attempts to solve it by appeal to actually uninstantiated properties are guilty of an absurdity akin to that which Ryle accused Descartes of in (...) the latter’s doctrine of immaterial substance. (shrink)

The general aim of this paper is to provide insight into the relevance of critical phenomenology for the study of the patient-provider relationship in health care systems in U.S. jails, prisons, and detention facilities. In particular, I utilize tools from the work of scholars studying phenomenological approaches to health care and structural forms of oppression to analyze several harms that arise from the provision of medical care under the punitive constraints of carceral facilities.

This paper applies what I call the shrieking method (a refined version of an idea with roots in Priest's work) to one of – if not the – issues confronting glut-theoretic approaches to paradox (viz., the problem of ‘just true’ or, what comes to the same, ‘just false’). The paper serves as a challenge to formulate a problem of ‘just true’ that isn't solved by shrieking (as advanced in this paper), if such a problem be thought to exist.

Been working on this approach for years. Hope to get around to publishing it sometime soon!

This paper is a sequel to Beall (2011), in which I both give and discuss the philosophical import of a result for the propositional (multiple-conclusion) logic LP+. Feedback on such ideas prompted a spelling out of the first-order case. My aim in this paper is to do just that: namely, explicitly record the first-order result(s), including the collapse results for K3+ and FDE+.

The Law of Non-Contradiction - that no contradiction can be true - has been a seemingly unassailable dogma since the work of Aristotle, in Book G of the Metaphysics. It is an assumption challenged from a variety of angles in this collection of original papers. Twenty-three of the world's leading experts investigate the 'law', considering arguments for and against it and discussing methodological issues that arise whenever we question the legitimacy of logical principles. The result is a balanced inquiry into (...) a venerable principle of logic, one that raises questions at the very centre of logic itself. The aim of this volume is to present a comprehensive debate about the Law of Non-Contradiction, from discussions as to how the law is to be understood, to reasons for accepting or re-thinking the law, and to issues that raise challenges to the law, such as the Liar Paradox, and a 'dialetheic' resolution of that paradox. The editors contribute an introduction which surveys the issues and serves to frame the debate, and a useful bibliography offering a guide to further reading. This volume will be of interest to anyone working on philosophical logic, and to anyone who has ever wondered about the status of logical laws and about how one might proceed to mount arguments for or against them. (shrink)

The first sentence in this essay is a lie. There is something odd about saying so, as has been known since ancient times. To see why, remember that all lies are untrue. Is the first sentence true? If it is, then it is a lie, and so it is not true. Conversely, suppose that it is not true. As we (viz., the authors) have said it, presumably with the intention of you believing it when it is not true, it is (...) a lie. But then it is true! (shrink)

I believe that, for reasons elaborated elsewhere (Beall, 2009; Priest, 2006a, 2006b), the logic LP (Asenjo, 1966; Asenjo & Tamburino, 1975; Priest, 1979) is roughly right as far as logic goes.1 But logic cannot go everywhere; we need to provide nonlogical axioms to specify our (axiomatic) theories. This is uncontroversial, but it has also been the source of discomfort for LP-based theorists, particularly with respect to true mathematical theories which we take to be consistent. My example, throughout, is arithmetic; but (...) the more general case is also considered. (shrink)

The Assumption of Agency Theory revisits the Turing Test and€examines what Turing's assessor knew. It asks important questions about how machines vis à vis humans have been characterized since Turing, and seeks to reverse the trend of looking closely at the machine by asking what humans know in interaction and how they know it.€This book€characterizes a non-human agent that shows itself in interaction but is distinct from human agency: an agent acting with us in our ongoing reproduction and transformation of (...) structure. Turing predicted that at the end of the twentieth century, w. (shrink)

A thematic priority of the European Union’s Framework V research and development programme was the creation of a user-friendly information society which met the needs of citizens and enterprises. In practice, though, for example in the case of on-line digital music, the needs of citizens and enterprises may be in conflict. This paper proposes to leverage the appearance of ‘intelligence’ in the platform layer of a layered communications architecture to avoid such conflicts in similar applications in the future. The key (...) idea is that if the intelligence is encapsulated in an agent, then the agents should be organized as a society, and then the rules of the society can be used to ensure ‘responsible’ behaviour. We discuss how an agent society can be used to regulate behaviour in future information trading scenarios, and conclude that this approach offers a ‘third way’ which can satisfy the (reasonable) needs of both citizens and enterprises in the user-friendly information society. (shrink)

_Logic: The Basics_ is an accessible introduction to several core areas of logic. The first part of the book features a self-contained introduction to the standard topics in classical logic, such as: · mathematical preliminaries · propositional logic · quantified logic · English and standard ‘symbolic translations’ · tableau procedures. Alongside comprehensive coverage of the standard topics, this thoroughly revised second edition also introduces several philosophically important nonclassical logics, free logics, and modal logics, and gives the reader an idea of (...) how they can take their knowledge further. With its wealth of exercises, _Logic: The Basics _is a useful textbook for courses ranging from the introductory level to the early graduate level, and also as a reference for students and researchers in philosophical logic. (shrink)

In this paper I advance and defend a very simple position according to which logic is subclassical but is weaker than the leading subclassical-logic views have it.

Traditional monotheism appears to many to involve contradiction in basic 'omni' properties (e.g. omnipotence and too-heavy stones, etc.). A glut-theoretic account of such problems treats them as gluts (dual to familiar truth-value gaps): 'omnipotence' is both true of and false of God. Many philosophers, glut theorists and otherwise, acknowledge that such a glut-theoretic account of at least some traditional omni-god problems is natural, at least in the abstract. But what about the problem of evil? The unanimous view even among glut (...) theorists (including myself until now) has long been clear: gluts have nothing to offer in response to the problem of evil even if they are involved in true theology elsewhere. This paper refutes said view by advancing a simple glut-theoretic response to the target problem of evil on the assumption that gluts are involved in the theology elsewhere (notably, at 'omnipotent' or 'omniscient' or both). (shrink)

Since the publication of Carl Hempel and Paul Oppenheim's ground-breaking work "Studies in the Logic of Explanation," the theory of explanation has remained a major topic in the philosophy of science. This valuable collection provides readers with the opportunity to study some of the classic essays on the theory of explanation along with the best examples of the most recent work being done on the topic. In addition to the original Hempel and Oppenheim paper, the volume includes Scriven's critical reaction (...) to it, Wilfrid Sellars's discussion of the problem of theoretical explanation, and pieces by Salmon, Railton, van Fraassen, Friedman, Kitcher, and Achinstein in which they demonstrate the vitality of the subject by extending the scope of the inquiry. (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)

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Since Leibniz's time, Cartesian mental causation has been criticized for violating the conservation of energy and momentum. Many dualist responses clearly fail. But conservation laws have important neglected features generally undermining the objection. Conservation is _local_, holding first not for the universe, but for everywhere separately. The energy in any volume changes only due to what flows through the boundaries. Constant total energy holds if the global summing-up of local conservation laws converges; it probably doesn't in reality. Energy conservation holds (...) if there is symmetry, the sameness of the laws over time. Thus, if there are time-places where symmetries fail due to nonphysical influence, conservation laws fail there and then, while holding elsewhere, such as refrigerators and stars. Noether's converse first theorem shows that conservation laws imply symmetries. Thus conservation trivially nearly entails the causal closure of the physical. But expecting conservation to hold in the brain simply assumes the falsehood of Cartesianism. Hence Leibniz's objection begs the question. Empirical neuroscience is another matter. So is Einstein's General Relativity: far from providing a loophole, General Relativity makes mental causation _harder_. (shrink)