I argue that Norton & Earman's hole argument, despite its historical association with General Relativity, turns upon very general features of any linguistic system that can represent substances by names. After exploring various means by which mathematical objects can be interpreted as representing physical possibilities, I suggest that a form of essentialism can solve the hole dilemma without abandoning either determinism or substantivalism. Finally, I identify the basic tenets of such an essentialism in Newton's writings and consider how they can (...) be updated to apply to the case provided by General Relativity. (shrink)

I argue that the Hole Argument is based on a misleading use of the mathematical formalism of general relativity. If one is attentive to mathematical practice, I will argue, the Hole Argument is blocked.

I argue that a criterion of theoretical equivalence due to Glymour :227–251, 1977) does not capture an important sense in which two theories may be equivalent. I then motivate and state an alternative criterion that does capture the sense of equivalence I have in mind. The principal claim of the paper is that relative to this second criterion, the answer to the question posed in the title is “yes”, at least on one natural understanding of Newtonian gravitation.

It is widely accepted that the notion of an inertial frame is central to Newtonian mechanics and that the correct space-time structure underlying Newton’s methods in Principia is neo-Newtonian or Galilean space-time. I argue to the contrary that inertial frames are not needed in Newton’s theory of motion, and that the right space-time structure for Newton’s Principia requires the notion of parallelism of spatial directions at different times and nothing more. Only relative motions are definable in this framework, never absolute (...) ones. (shrink)

David Lewis holds that a single possible world can provide more than one way things could be. But what are possible worlds good for if they come apart from ways things could be? We can make sense of this if we go in for a metaphysical understanding of what the world is. The world does not include everything that is the case—only the genuine facts. Understood this way, Lewis's “cheap haecceitism” amounts to a kind of metaphysical anti-haecceitism: it says there (...) aren't any genuine facts about individuals over and above their qualitative roles. (shrink)

I describe a problem about the relations among symmetries, laws and measurable quantities. I explain why several ways of trying to solve it will not work, and I sketch a solution that might work. I discuss this problem in the context of Newtonian theories, but it also arises for many other physical theories. The problem is that there are two ways of defining the space-time symmetries of a physical theory: as its dynamical symmetries or as its empirical symmetries. The two (...) definitions are not equivalent, yet they pick out the same extension. This coincidence cries out for explanation, and it is not clear what the explanation could be. The Puzzle: Symmetries, Measurability and Invariance 1.1 The symmetries and the measurable quantities of Newtonian mechanics 1.2 The puzzle Two Easy Answers Another Unsuccessful Solution: Appeal to Geometrical Symmetries Locating the Puzzle The Relation between Laws and Measurability A Possible Solution CiteULike Connotea Del.icio.us What's this? (shrink)

According to the indispensability argument, the fact that we quantify over numbers, sets and functions in our best scientific theories gives us reason for believing that such objects exist. I examine a strategy to dispense with such quantification by simply replacing any given platonistic theory by the set of sentences in the nominalist vocabulary it logically entails. I argue that, as a strategy, this response fails: for there is no guarantee that the nominalist world that go beyond the set of (...) sentences in the nominalist language such theories entail. However, I argue that what such theories show is that mathematics can enable us to express possibilities about the concrete world that may not be expressible in nominalistically acceptable language. While I grant that this may make quantification over abstracta indispensable, I deny that such indispensability is a reason for accepting them into our ontology. I urge that the nominalist should be allowed to quantify over abstracta whilst denying their existence and I explain how this apparently contradictory practice (a practice I call 'weaseling') is in fact coherent, unproblematic and rational. Finally, I examine the view that platonistic theories are simpler or more attractive than their nominalistic reformulations, and thus that abstract ought to be accepted into our ontology for the same sorts of reasons as other theoretical objects. I argue that, at least in the case of numbers, functions and sets, such arguments misunderstand the kind of simplicity and attractiveness we seek. (shrink)

(1) The average Mum has 2.4 children. (2) The number of Argle’s fingers equals the number of Bargle’s toes. (3) There are two possible ways in which Joe could win this chess game. In the right contexts, and outside the philosophy room, all the above sentences may be completely uncontroversial. For instance, if we know that Joe could win either by exchanging queens and entering an endgame, or by initiating a kingside attack then, if ignorant of Quine’s work on ontology, (...) we would take (3) to be uncontroversially true. (shrink)

This paper sketches a taxonomy of forms of substantivalism and relationism concerning space and time, and of the traditional arguments for these positions. Several natural sorts of relationism are able to account for Newton's bucket experiment. Conversely, appropriately constructed substantivalism can survive Leibniz's critique, a fact which has been obscured by the conflation of two of Leibniz's arguments. The form of relationism appropriate to the Special Theory of Relativity is also able to evade the problems raised by Field. I survey (...) the effect of the General Theory of Relativity and of plenism on these considerations. (shrink)

I argue that the best spacetime setting for Newtonian gravitation (NG) is the curved spacetime setting associated with geometrized Newtonian gravitation (GNG). Appreciation of the ‘Newtonian equivalence principle’ leads us to conclude that the gravitational field in NG itself is a gauge quantity, and that the freely falling frames are naturally identified with inertial frames. In this context, the spacetime structure of NG is represented not by the flat neo-Newtonian connection usually made explicit in formulations, but by the sum of (...) the flat connection and the gravitational field. 1 Introduction2 Newtonian Gravity: The Orthodox Approach3 Newtonian Gravity: Additional Symmetries4 Cosmological Considerations5 A Newtonian Equivalence Principle: Inertial Frames in Newtonian Gravitation6 Theory Equivalence?7 Conclusion. (shrink)

Quantum mechanics predicted the Aharonov-Bohm effect and violations of Bell inequalities before either phenomenon was experimentally verified. It is now commonly taken to explain both phenomena. Maudlin has pointed out significant disanalogies between these phenomena. But he has failed to appreciate the striking analogy that emerges when one examines the structure of their quantum mechanical explanations. The fact that each may be explained quantum mechanically in terms of a locally-acting, but nonseparable process suggests that the lesson of quantum nonlocality may (...) be that while there is no action at a distance, the world is nonseparable. (shrink)

According to the semantic view of scientific theories, theories are classes of models. I show that this view -- if taken seriously as a formal explication -- leads to absurdities. In particular, this view equates theories that are truly distinct, and it distinguishes theories that are truly equivalent. Furthermore, the semantic view lacks the resources to explicate interesting theoretical relations, such as embeddability of one theory into another. The untenability of the semantic view -- as currently formulated -- threatens to (...) undermine scientific structuralism. (shrink)

Symmetries in physics are a guide to reality. That much is well known. But what is less well known is why symmetry is a guide to reality. What justifies inferences that draw conclusions about reality from premises about symmetries? I argue that answering this question reveals that symmetry is an epistemic notion twice over. First, these inferences must proceed via epistemic lemmas: premises about symmetries in the first instance justify epistemic lemmas about our powers of detection, and only from those (...) epistemic lemmas can we draw conclusions about reality. Second, in order to justify those epistemic lemmas, the notion of symmetry must be defined partly in epistemic terms. 1 Symmetry-to-Reality Reasoning1.1 A rough introduction to symmetry1.2 The symmetry-to-reality inference1.3 Two questions1.4 Two answers1.5 Preliminary clarifications2 Against Redundancy2.1 Redundancy2.2 Is absolute velocity redundant?2.3 Some redundancies3 Against Objectivity4 From Symmetry to Detection4.1 The epistemic approach4.2 The Occamist norm4.3 From symmetry to detection5 The Meaning of ‘Symmetry’5.1 A framework5.2 Formal definitions5.3 Ontic definitions6 Epistemic Definitions6.1 Taking observation seriously6.2 How things look6.3 Observation sentences6.4 Observational equivalence7 Symmetry as an Epistemic Notion 7.1 Observational equivalence and metaphysics7.2 The Occamist norm revisted7.3 Consequences8 Conclusion. (shrink)

Hartry Field has shown us a way to be nominalists: we must purge our scientific theories of quantification over abstracta and we must prove the appropriate conservativeness results. This is not a path for the faint hearted. Indeed, the substantial technical difficulties facing Field's project have led some to explore other, easier options. Recently, Jody Azzouni, Joseph Melia, and Stephen Yablo have argued that it is a mistake to read our ontological commitments simply from what the quantifiers of our best (...) scientific theories range over. In this paper, I argue that all three arguments fail and they fail for much the same reason; would-be nominalists are thus left facing Field's hard road. (shrink)

As Pooley (2001) explains, the challenge of giving a relational account of orientability (and topology more generally) is not an easy one. This paper criticizes Pooley's and other proposals, raises a range of problems for the project, and then proposes a novel way for the relationist to understand not only topology, but also the geometry of space. This proposal is the `regularity account' since it claims that geometry and topology supervene on the regular ways in which relations evolve.

In the first part of this paper a relational account of incongruent counterparts is defended against an argument due to Kant. I then consider a more recent attack on such an account, due to John Earman, which alleges that the relationalist cannot account for the lawlike left--right asymmetry manifested in parity-violating phenomena. I review Hoefer's, Huggett's and Saunders' responses to Earman's argument and argue that, while a relationalist account of parity-violating laws is possible, it comes at the cost of non-locality.

This paper is concerned with the relation between two notions: that of two solutions or models of a theory being related by a symmetry of the theory and that of solutions or models being physically equivalent. A number of authors have recently discussed this relation, some taking an optimistic view, on which there is a suitable concept of the symmetry of a theory relative to which these two notions coincide, others taking a pessimistic view, on which there is no such (...) concept. The present paper arrives at a cautiously pessimistic conclusion. (shrink)