One can (for the most part) formulate a model of a classical system in either the Lagrangian or the Hamiltonian framework. Though it is often thought that those two formulations are equivalent in all important ways, this is not true: the underlying geometrical structures one uses to formulate each theory are not isomorphic. This raises the question whether one of the two is a more natural framework for the representation of classical systems. In the event, the answer is yes: I state and sketch proofs of two technical results, inspired by simple physical arguments about the generic properties of classical systems, to the effect that, in a precise sense, classical systems evince exactly the geometric structure Lagrangian mechanics provides for the representation of systems, and none that Hamiltonian mechanics does. The argument not only clarifies the conceptual structure of the two systems of mechanics, their relations to each other, and their respective mechanisms for representing physical systems. It also shows why naively structural approaches to the representational content of physical theories cannot work.

I argue that, contrary to the recent claims of physicists and philosophers of physics, general relativity requires no interpretation in any substantive sense of the term. I canvass the common reasons given in favor of the alleged need for an interpretation, including the difficulty in coming to grips with the physical significance of diffeomorphism invariance and of singular structure, and the problems faced in the search for a theory of quantum gravity. I find that none of them shows any defect in our comprehension of general relativity as a physical theory. I conclude by comparing general relativity with quantum mechanics, a theory that manifestly does stand in need of an interpretation in an important sense. Although many aspects of the conceptual structure of general relativity remain poorly understood, it suffers no incoherence in its formulation as a physical theory that only an “interpretation” could resolve.

A review of the state of the art concerning philosophical investigation of issues pertaining to singular structure and black holes in relativistic spacetimes. Issues treated include: the definition of singular structure; the type of existence, if any, one can ascribe to singular structure; the laws of black hole mechanics; some attempts in programs in quantum gravity to derive the mechanical black hole laws.

In 1672, Isaac Newton published in the “Transactions of the Royal Society” his theory of the structure of light rays. It was not understood by even his most brilliant contemporaries, scientific luminaries such as Robert Hooke and Christian Huygens. The primary obstacle hindering their understanding was their conception of proper scientific methodology, the hypethetico-deductive method as applied solely in the theater of the mechanical philosophy. Neither Newton's account of the derivation of his theory nor the theory itself conformed to this conception of science, much to the discredit of that conception. In the 1990s, quantum gravity came into its own as an accepted, even a sexy field of research in theoretical physics. Except for adherence to the mechanical philosophy, all the major research programs in quantum gravity today do conform to the conception of science championed by Newton's contemporaries, much to the discredit of quantum gravity. In this paper I make the case for this claim, and discuss a few of its unfortunate corollaries. I also examine the scientific standing of various programs in quantum gravity as reported by proponents of those programs in order to criticize what I see as their immodesty–unwarranted in light of my arguments in the first part of the paper–which at times seems to cross the border into disingenuity. It is no mere Pauline gripe I have against this immodesty; I think it does real damage to science on many levels. I conclude with a few reflections on this matter and on the role, if any, that philosophers of science ought to play in the maintenance of working science's integrity.

All accounts of causality that presuppose the propagation or transfer of some physical stuff to be an essential part of the causal relation rely for the force of their causal claims on a principle of conservation for that stuff. General Relativity does not permit the rigorous formulation of appropriate conservation principles. Consequently, in so far as General Relativity is considered a fundamental physical theory, such accounts of causality cannot themselves be considered fundamental. The continued use of such accounts of causality perhaps ought not be proscribed, but justification is due from those who would use them..

Much controversy surrounds the question of what ought to be the proper definition of “singularity” in general relativity, and the question of whether the prediction of such entities leads to a crisis for the theory. I argue that there is no single canonical definition of such a things, and that none is required–various definitions present themselves, respectively suitable for different sorts of investigations. In particular, I argue that a definition in terms of curve incompleteness is adequate for most purposes, though the idea that singularities correspond to “missing points” has insurmountable problems. I conclude that singularities per se pose no serious problem for the theory, but their analysis does bring into focus several problems of interpretation at the foundation of the theory often ignored in the philosophical literature.

I neither attack nor defend Jarrett's (1984) conclusions concerning adequacy constraints appropriate to (models of) physical theories mooted in discussions of Bell's Theorem. Rather I attempt to clarify what sorts of arguments can and cannot coherently be made when Jarrett-type premises are accepted (or are accepted at least for the sake of argument). In particular I show that certain recent construals of Jarrett's 1984 argument that focus on the notion of causality not only are beside the point of Jarrett's argument but, more important, obfuscate what salutary can be gleaned from his argument. Martin Jones and Rob Clifton among recent commentators on Jarrett not only are notable for their clarity, precision and thoroughness of argument, but they also are typical in what, I suspect, is the main culprit behind confused arguments that are concerned with issues of causality, viz., a careless deployment of the notion of “causality” itself. For this reason I have chosen them as a foil, precisely because theirs seems to me the clearest, best case for what I take to be at bottom a confused way both of thinking of Jarrett's argument in particular, and of deploying causal arguments in general.

I argue that an adequate semantics for physical theories must be grounded on an account of the way that a theory provides formal and conceptual resources appropriate for—that have propriety in—the construction of representations of the physical systems the theory purports to treat. I sketch a precise, rigorous definition of the required forms of propriety, and argue that semantic content accrues to scientific representations of physical systems primarily in virtue of the propriety of its resources. In particular, neither the adequacy (soundness, accuracy, truth, ...) of those representations nor any referential relations their terms may enter into play any fundamental role in the determination of the representation's semantic content. One consequence is that anything like traditional Tarskian semantics is inadequate for the task.

The dispute over the viability of various theories of relativistic, dissipative fluids is analyzed. The focus of the dispute is identified as the question of determining what it means for a theory to be applicable to a given type of physical system under given conditions. The idea of a physical theory's regime of propriety is introduced, in an attempt to clarify the issue, along with the construction of a formal model trying to make the idea precise. This construction involves a novel generalization of the idea of a field on spacetime, as well as a novel method of approximating the solutions to partial-differential equations on relativistic spacetimes in a way that tries to account for the peculiar needs of the interface between the exact structures of mathematical physics and the inexact data of experimental physics in a relativistically invariant way. It is argued, on the basis of these constructions, that the idea of a regime of propriety plays a central role in attempts to understand the semantical relations between theoretical and experimental knowledge of the physical world in general, and in particular in attempts to explain what it may mean to claim that a physical theory models or represents a kind of physical system. This discussion necessitates an examination of the initial-value formulation of the partial-differential equations of mathematical physics, which suggests a natural set of conditions–by no means meant to be canonical or exhaustive–one may require a mathematical structure, in conjunction with a set of physical postulates, satisfy in order to count as a physical theory. Based on the novel approximating methods developed for solving partial-differential equations on a relativistic spacetime by finite-difference methods, a technical result concerning a peculiar form of theoretical under-determination is proved, along with a technical result purporting to demonstrate a necessary condition for the self-consistency of a physical theory.

I examine an extraordinary circumstance of the work as a whole, a circumstance that has gone largely, and oddly, unremarked in the secondary literature. At the conclusion of both Socrates's antepenultimate (IV.445ab) and penultimate (IX.580bc) answers to the brothers' challenges, he asks Glaukon to render judgement on the worth and intrinsic goodness of justice and the just man's life. Glaukon without hesitation declares justice to be good in and of itself, and the just life to be the best and the happiest of lives. In both places, to drive the point home, Socrates makes sure to mention one of the primary terms of the challenges: that justice and the just life have this character whether the just man is known to be just or not (IV.445a), in either the eyes of god or men (IX.580c), which Glaukon readily grants. And yet, for the entirety of his construction of the just city, his account of justice itself, and most of all his characterization of the just man, the just man both has seemed and has been known by all to be just. Socrates has flagrantly flouted the most fundamental term of the challenge, and not only this term but all the rest as well, for the just man, in Socrates's recounting of his life, has had accrue to him all the appurtenances, pleasures, rewards and good repute that Glaukon and Adeimantos demanded be stripped from him, so they could with surety conclude that justice is good in and of itself rather than on account only of its repute and rewards. Are Glaukon and Adeimantos simpletons, dupes, that they would readily accept as an answer to their challenges one that is, prima facie, an answer to no question they had asked? I do not think Plato wanted us to draw this conclusion. What else, then, can be the resolution of this puzzle? I attempt in this series of three papers to sketch one: Socrates has, in fact, answered each of their challenges to the letter. In working out the answers, Socrates and the sons of Ariston have discovered that the nature of true justice demands that the just man live a life that will accrue to itself many (though by no means all) of the concomitants and the rewards and much of the repute given, according to common belief, to the just man (or, at least, the seemingly just man) on account of his (seeming) justice, not, however, as consequences of justice, but rather as necessary constituents, in some way or other, of justice itself. It follows that justice is, by its nature, a virtue that demands that its agent inhabit a definite sort of place in a richly appointed and textured society---it is essentially a social virtue, without real substance or sense in isolation from the social roles the just man plays and the acts he performs. In this first paper of the three, I explicate the brothers' challenges to demonstrate how, on the face of it, Socrates does not answer them.

General remarks on what it is to learn philosophy---the reading and the writing of it, and the production of philosophical arguments---with emphasis on the relation between teacher and student, the roles and responsibilities of each. Reference is made to two essays by Mark Twain, Fenimore Cooper's Literary Offences and Fenimore Cooper's Further Literary Offences: Cooper's Prose Style.

Based on an analysis of what it may mean for one tensor to depend in the proper way on another, I prove that, under certain natural conditions, there can be no tensor whose interpretation could be that it represents gravitational stress-energy in general relativity. It follows that gravitational energy, such as it is in general relativity, is necessarily non-local. Along the way, I prove a result of some interest in own right about the structure of the associated jet bundles of the bundle of Lorentz metrics over spacetime.

I give a novel construction and presentation of the intrinsic geometry of a generic tangent bundle, in the terms of which the Euler-Lagrange Equation can be formulated in a geometric, illuminating way. I conclude by proving a result that shows that, in a strong sense, not only must Lagrangian Mechanics be formulated on tangent bundles (as opposed to Hamiltonian Mechanics, which can be formulated on any symplectic manifold, whether diffeomorphic to a cotangent bundle or not), but moreover the intrinsic geometry of the Euler-Lagrange Equation itself allows one to completely reconstruct the space on which one formulates it as a tangent bundle over a particular base space.