Citations of:
Geometry and motion
British Journal for the Philosophy of Science 51 (4):56195 (2000)
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This essay explores the possibility of constructing a structural realist interpretation of spacetime theories that can resolve the ontological debate between substantivalists and relationists. Drawing on various structuralist approaches in the philosophy of mathematics, as well as on the theoretical complexities of general relativity, our investigation will reveal that a structuralist approach can be beneficial to the spacetime theorist as a means of deflating some of the ontological disputes regarding similarly structured spacetimes. 

This essay explores the use of platonist and nominalist concepts, derived from the philosophy of mathematics and metaphysics, as a means of elucidating the debate on spacetime ontology and the spatial structures endorsed by scientific realists. Although the disputes associated with platonism and nominalism often mirror the complexities involved with substantivalism and relationism, it will be argued that a more refined threepart distinction among platonist/nominalist categories can nonetheless provide unique insights into the core assumptions that underlie spatial ontologies, but it (...) 

Absolutism about mass within Newtonian gravity claims that mass ratios obtain in virtue of absolute masses. Comparativism denies this. Defenders of comparativism promise to recover all the empirical and theoretical virtues of absolutism, but at a lower ‘metaphysical cost’. This article develops a Machian form of comparativism about mass in Newtonian gravity, obtained by replacing Newton’s constant in the law of universal gravitation by another constant divided by the sum over all masses. Although this form of comparativism is indeed empirically (...) 

I discuss the debate between dynamical versus geometrical approaches to spacetime theories, in the context of both special and general relativity, arguing that the debate takes a substantially different form in the two cases; different versions of the geometrical approach—only some of which are viable—should be distinguished; in general relativity, there is no difference between the most viable version of the geometrical approach and the dynamical approach. In addition, I demonstrate that what have previously been dubbed two ‘miracles’ of general (...) 

This review of Julian Barbour's The End of Time ([1999]) discusses his Machian theories of dynamics, and his proposal that a Machian perspective enables one to solve the problem of time in quantum geometrodynamics, viz. by saying that there is no time! 1 Introduction 2 Machian themes in classical physics 2.1 The status quo 2.2 Machianism 2.2.1 The temporal metric as emergent 2.2.2 Machian theories 2.2.3 Assessing intrinsic dynamics 3 The end of time? 3.1 Time unreal? The classical case 3.1.1 (...) 

It is argued that Minkowski spacetime cannot serve as the deep structure within a ``constructive'' version of the special theory of relativity, contrary to widespread opinion in the philosophical community. 

This essay aims to provide a selfcontained introduction to time in relativistic cosmology that clarifies both how questions about the nature of time should be posed in this setting and the extent to which they have been or can be answered empirically. The first section below recounts the loss of Newtonian absolute time with the advent of special and general relativity, and the partial recovery of absolute time in the form of cosmic time in some cosmological models. Section II considers (...) 

This paper elaborates on relationalism about space and time as motivated by a minimalist ontology of the physical world: there are only matter points that are individuated by the distance relations among them, with these relations changing. We assess two strategies to combine this ontology with physics, using classical mechanics as example: the Humean strategy adopts the standard, nonrelationalist physical theories as they stand and interprets their formal apparatus as the means of bookkeeping of the change of the distance relations (...) 

Two symmetry arguments are discussed, each purporting to show that there is no more room for a preferred division of spacetime into instants of time in general relativistic cosmology than in Minkowski spacetime. The first argument is due to Gödel, and concerns the symmetries of his famous rotating cosmologies. The second turns upon the symmetries of a certain space of relativistic possibilities. Both arguments are found wanting. 

The implications for the substantivalist–relationalist controversy of Barbour and Bertotti's successful implementation of a Machian approach to dynamics are investigated. It is argued that in the context of Newtonian mechanics, the Machian framework provides a genuinely relational interpretation of dynamics and that it is more explanatory than the conventional, substantival interpretation. In a companion paper (Pooley [2002a]), the viability of the Machian framework as an interpretation of relativistic physics is explored. 1 Introduction 2 Newton versus Leibniz 3 Absolute space versus (...) 

In a companion paper (Pooley & Brown 2001) it is argued that Julian Barbour's Machian approach to dynamics provides a genuinely relational interpretation of Newtonian dynamics and that it is more explanatory than the conventional, substantival interpretation. In this paper the extension of the approach to relativistic physics is considered. General relativity, it turns out, can be reinterpreted as a perfectly Machian theory. However, there are difficulties with viewing the Machian interpretation as more fundamental than the conventional, spacetime interpretation. Moreover, (...) 

Symplectic reduction is a formal process through which degeneracy within the mathematical representations of physical systems displaying gauge symmetry can be controlled via the construction of a reduced phase space. Typically such reduced spaces provide us with a formalism for representing both instantaneous states and evolution uniquely and for this reason can be justifiably afforded the status of fun damental dynamical arena  the otiose structure having been eliminated from the original phase space. Essential to the application of symplectic reduction (...) 

In this paper I examine the connection between symmetry and modality from the perspective of `reduction' methods in geometric mechanics. I begin by setting the problem up as a choice between two opposing views: reduction and nonreduction. I then discern four views on the matter in the literature; they are distinguished by their advocation of distinct geometric spaces as representing `reality'. I come down in favour of nonreductive methods. 

Einstein considered general covariance to characterize the novelty of his General Theory of Relativity (GTR), but Kretschmann thought it merely a formal feature that any theory could have. The claim that GTR is ``already parametrized'' suggests analyzing substantive general covariance as formal general covariance achieved without hiding preferred coordinates as scalar ``clock fields,'' much as Einstein construed general covariance as the lack of preferred coordinates. Physicists often install gauge symmetries artificially with additional fields, as in the transition from Proca's to (...) 

I present an argument against a relational theory of spacetime that regards spacetime as a ‘structural quality of the field’. The argument takes the form of a trilemma. To make the argument, I focus on relativistic worlds in which there exist just two fields, an electromagnetic field and a gravitational field. Then there are three options: either spacetime is a structural quality of each field separately, both fields together, or one field but not the other. I argue that the first (...) 

The paper provides a critical discussion of the SuperHumean view of spacetime and the “minimalist ontology” in terms of Leibnizian relations and primitive matter points, recently developed by Esfeld et al. It investigates, in particular, the empirical adequacy of the proposed metaphysics, arguing that SuperHumeanism cannot provide a plausible account of space and time without committing to bona fide geometric structure in the fundamental relations. Against this backdrop, I propose a moderate version of SuperHumeanism and discuss its possible application to (...) 

It is widely believed that shapes are intrinsic properties. But this claim is hard to defend. I survey all known theories of shape properties, and argue that each theory is either incompatible with the claim that shapes are intrinsic, or can be shown to be false. 

This essay demonstrates the inadequacy of contemporary substantivalist and relationist interpretations of quantum gravity hypotheses via an historical investigation of the debate on the underlying ontology of space in the seventeenth century. Viewed in the proper context, there are crucial similarities between seventeenth century theories of space and contemporary work on the ontological foundations of spacetime theories, and these similarities challenge the utility of the substantival/relational dichotomy by revealing a host of underlying conceptual issues that do not naturally align with (...) 

I discuss several issues related to "classical" spacetime structure. I review Galilean, Newtonian, and Leibnizian spacetimes, and briefly describe more recent developments. The target audience is undergraduates and early graduate students in philosophy; the presentation avoids mathematical formalism as much as possible. 

In this paper I wish to make some headway on understanding what \emph{kind} of problem the ``problem of time'' is, and offer a possible resolutionor, rather, a new way of understanding an old resolution. The response I give is a variation on a theme of Rovelli's \emph{evolving constants of motion} strategy. I argue that by giving correlation strategies a \emph{structuralist} basis, a number of objections to the standard account can be blunted. Moreover, I show that the account I offer provides (...) 

The analysis of the temporal structure of canonical general relativity and the connected interpretational questions with regard to the role of time within the theory both rest upon the need to respect the fundamentally dual role of the Hamiltonian constraints found within the formalism. Any consistent philosophical approach towards the theory must pay dues to the role of these constraints in both generating dynamics, in the context of phase space, and generating unphysical symmetry transformations, in the context of a hypersurface (...) 

This thesis concerns the metaphysics of scale. It investigates the implications of a physical determinable being dimensionful. In particular, it considers the case study of mass, as it features within Newtonian Gravity. Nevertheless, most of the terminology, methodology and arguments developed should be relatively straightforwardly applicable to other determinables and theories. / Weak Absolutism about mass holds that mass ratios obtain in virtue of absolute masses. Weak Comparativism denies this. In the first five chapters I argue in favour of Weak (...) 

Julian Barbour's approach to dynamics is reviewed. With a particular focus on questions of explanation and confirmation, the approach is contrasted with standard formulations of dynamics. This paper expands upon my commentary on Lawrence Sklar's paper at the Philosophy of Time Society meeting at the APA's Central Division meeting in Chicago, April 2004. Although a commentary, the current paper is comprehensible without reference to Sklar's paper. 

