The celu of the philosophical literature on the hole argument is the 1987 paper by Earman \& Norton ["What Price Space-time Substantivalism? The Hole Story" Br. J. Phil. Sci.]. This paper has a well-known back-story, concerning work by Stachel and Norton on Einstein's thinking in the years 1913-15. Less well-known is a connection between the hole argument and Earman's work on Leibniz in the 1970s and 1980s, which in turn can be traced to an argument first presented in 1975 by (...) Howard Stein. Remarkably, this thread originates with a misattribution: the argument Earman attributes to Stein, which ultimately morphs into the hole argument, was not the argument Stein gave. The present paper explores this episode and presents some reflections on how it bears on the subsequent literature. (shrink)

Formal criteria of theoretical equivalence are mathematical mappings between specific sorts of mathematical objects, notably including those objects used in mathematical physics. Proponents of formal criteria claim that results involving these criteria have implications that extend beyond pure mathematics. For instance, they claim that formal criteria bear on the project of using our best mathematical physics as a guide to what the world is like, and also have deflationary implications for various debates in the metaphysics of physics. In this paper, (...) I investigate whether there is a defensible view according to which formal criteria have significant non-mathematical implications, of these sorts or any other, reaching a chiefly negative verdict. Along the way, I discuss various foundational issues concerning how we use mathematical objects to describe the world when doing physics, and how this practice should inform metaphysics. I diagnose the prominence of formal criteria as stemming from contentious views on these foundational issues, and endeavor to motivate some alternative views in their stead. (shrink)

I argue that Hume’s philosophy of time is relationist in the following two senses. 1) Standard definition of relationism. Time is a succession of indivisible moments. Hence there is no time independent of change. Time is a relational, not substantial feature of the world. 2) Rigid relationism. There is no evidence of uniform natural standard for synchronization of clocks. No absolute temporal metric is available. There are countless times, and no time is privileged. Combining 1) and 2) shows that Hume’s (...) ontology of time is thoroughly relationist. (shrink)

En este artículo examinamos los aspectos más relevantes de la concepción del espacio de Leibniz. A través de un enfoque genético, nuestro propósito es mostrar que, en su desarrollo evolutivo, dicha concepción sufre dos transiciones destacables, las que separan y distinguen tres versiones teóricas. En su juventud, Leibniz defiende una concepción substancialista del espacio. Sin embargo, debido a la adopción del nominalismo, dicha concepción sufre un primer giro que decanta en un monismo substancialoide, el que se consolida en el período (...) medio de la filosofía de Leibniz. Ya en el período tardío, Leibniz reformula, en una segunda transición, su concepción del espacio, la que adopta la forma definitiva de -lo que llamamos- un relacionismo substancialoide. (shrink)

In a number of publications, John Earman has advocated a tertium quid to the usual dichotomy between substantivalism and relationism concerning the nature of spacetime. The idea is that the structure common to the members of an equivalence class of substantival models is captured by a Leibniz algebra which can then be taken to directly characterize the intrinsic reality only indirectly represented by the substantival models. An alleged virtue of this is that, while a substantival interpretation of spacetime theories falls (...) prey to radical local indeterminism, the Leibniz algebras do not. I argue that the program of Leibniz algebras is subject to radical local indeterminism to the same extent as substantivalism. In fact, for the category of topological spaces of interest in spacetime physics, the program is equivalent to the original spacetime approach. Moreover, the motivation for the program--that isomorphic substantival models should be regarded as representing the same physical situation--is misguided. (shrink)

In this paper, we examine the relationship between general relativity and the theory of Einstein algebras. We show that according to a formal criterion for theoretical equivalence recently proposed by Halvorson and Weatherall, the two are equivalent theories.

In this article, I examine whether or not the Hamiltonian and Lagrangian formulations of classical mechanics are equivalent theories. I do so by applying a standard for equivalence that was recently introduced into philosophy of science by Halvorson and Weatherall. This case study yields three general philosophical payoffs. The first concerns what a theory is, while the second and third concern how we should interpret what our physical theories say about the world. 1Introduction 2When Are Two Theories Equivalent? 3Preliminaries on (...) Classical Mechanics 3.1Hamiltonian mechanics 3.2Lagrangian mechanics 4Are Hamiltonian and Lagrangian Mechanics Equivalent Theories? 4.1Tangent bundle versus cotangent bundle 4.2Tangent bundle versus symplectic manifold 4.3Lagrangian vector field versus Hamiltonian vector field 5Conclusion Appendix. (shrink)

For the past two decades, Einstein's Hole Argument (which deals with the apparent indeterminateness of general relativity due to the general covariance of the field equations) and its resolution in terms of "Leibniz equivalence" (the statement that pseudo-Riemannian geometries related by active diffeomorphisms represent the same physical solution) have been the starting point for a lively philosophical debate on the objectivity of the point-events of space-time. It seems that Leibniz equivalence makes it impossible to consider the points of the space-time (...) manifold as physically individuated without recourse to dynamical individuating fields. Various authors have posited that the metric field itself can be used in this way , but nobody so far has considered the problem of explicitly distilling the "metrical fingerprint" of point-events from the gauge-dependent elements of the metric field. Working in the Hamiltonian formulation of general relativity, and building on the results of Lusanna and Pauri (2002), we show how Bergmann and Komar's "intrinsic pseudo-coordinates" (based on the value of curvature invariants) can be used to provide a physical individuation of point-events in terms of the true degrees of freedom (the "Dirac observables") of the gravitational field, and we suggest how this conceptual individuation could in principle be implemented with a well-defined empirical procedure. We argue from these results that point-events retain a significant kind of physical objectivity. (shrink)

I review some recent work on applications of category theory to questions concerning theoretical structure and theoretical equivalence of classical field theories, including Newtonian gravitation, general relativity, and Yang-Mills theories.