This article develops an analogy proposed by Stachel between general relativity (GR) and quantum mechanics (QM) as regards permutation invariance. Our main idea is to overcome Pooley's criticism of the analogy by appeal to paraparticles. In GR, the equations are (the solution space is) invariant under diffeomorphisms permuting spacetime points. Similarly, in QM the equations are invariant under particle permutations. Stachel argued that this feature—a theory's ‘not caring which point, or particle, is which’—supported a structuralist ontology. Pooley criticizes this analogy: (...) in QM the (anti-)symmetrization of fermions and bosons implies that each individual state (solution) is fixed by each permutation, while in GR a diffeomorphism yields in general a distinct, albeit isomorphic, solution. We define various versions of structuralism, and go on to formulate Stachel's and Pooley's positions, admittedly in our own terms. We then reply to Pooley. Though he is right about fermions and bosons, QM equally allows more general types of particle symmetry, in which states (vectors, rays, or density operators) are not fixed by all permutations (called ‘paraparticle states’). Thus Stachel's analogy is revived. (shrink)

Using the Hilbert-Bernays account as a spring-board, we first define four ways in which two objects can be discerned from one another, using the non-logical vocabulary of the language concerned. Because of our use of the Hilbert-Bernays account, these definitions are in terms of the syntax of the language. But we also relate our definitions to the idea of permutations on the domain of quantification, and their being symmetries. These relations turn out to be subtle---some natural conjectures about them are (...) false. We will see in particular that the idea of symmetry meshes with a species of indiscernibility that we will call `absolute indiscernibility'. We then report all the logical implications between our four kinds of discernibility. We use these four kinds as a resource for stating four metaphysical theses about identity. Three of these theses articulate two traditional philosophical themes: viz. the principle of the identity of indiscernibles, and haecceitism. The fourth is recent. Its most notable feature is that it makes diversity weaker than what we will call individuality : two objects can be distinct but not individuals. For this reason, it has been advocated both for quantum particles and for spacetime points. Finally, we locate this fourth metaphysical thesis in a broader position, which we call structuralism. We conclude with a discussion of the semantics suitable for a structuralist, with particular reference to physical theories as well as elementary model theory. (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. _1._ Introduction _2._ A Warmup Exercise _3._ The Hole Argument _4._ An Argument from Classical Spacetime Theory _5._ The Hole Argument Revisited.

The concept of classical indistinguishability is analyzed and defended against a number of well-known criticisms, with particular attention to the Gibbs’paradox. Granted that it is as much at home in classical as in quantum statistical mechanics, the question arises as to why indistinguishability, in quantum mechanics but not in classical mechanics, forces a change in statistics. The answer, illustrated with simple examples, is that the equilibrium measure on classical phase space is continuous, whilst on Hilbert space it is discrete. The (...) relevance of names, or equivalently, properties stable in time that can be used as names, is also discussed. (shrink)

A relationist will account for the use of ‘left’ and ‘right’ in terms of relative orientations, and other properties and relations invariant under mirroring. This analysis will apply whenever mirroring is a symmetry, so it certainly applies to classical mechanics; we argue it applies to any physical theory formulated on a manifold: it is in this sense an a priori symmetry. It should apply in particular to parity violating theories in quantum mechanics; mirror symmetry is only broken in such theories (...) as a special symmetry. (shrink)

There exists a common view that for theories related by a ‘duality’, dual models typically may be taken ab initio to represent the same physical state of affairs, i.e. to correspond to the same possible world. We question this view, by drawing a parallel with the distinction between ‘interpretational’ and ‘motivational’ approaches to symmetries.

I begin by criticizing an elaboration of an argument in this journal due to Hawley , who argued that, where Leibniz’s Principle of the Identity of Indiscernibles faces counterexamples, invoking relations to save PII fails. I argue that insufficient attention has been paid to a particular distinction. I proceed by demonstrating that in most putative counterexamples to PII , the so-called Discerning Defence trumps the Summing Defence of PII. The general kind of objects that do the discerning in all cases (...) form a category that has received little if any attention in metaphysics. This category of objects lies between indiscernibles and individuals and is called relationals: objects that can be discerned by means of relations only and not by properties. Remarkably, relationals turn out to populate the universe. (shrink)

The presence of symmetries in physical theories implies a pernicious form of underdetermination. In order to avoid this theoretical vice, philosophers often espouse a principle called Leibniz Equivalence, which states that symmetry-related models represent the same state of affairs. Moreover, philosophers have claimed that the existence of non-trivial symmetries motivates us to accept the Invariance Principle, which states that quantities that vary under a theory’s symmetries aren’t physically real. Leibniz Equivalence and the Invariance Principle are often seen as part of (...) the same package. I argue that this is a mistake: Leibniz Equivalence and the Invariance Principle are orthogonal to each other. This means that it is possible to hold that symmetry-related models represent the same state of affairs whilst having a realist attitude towards variant quantities. Various arguments have been presented in favour of the Invariance Principle: a rejection of the Invariance Principle is inter alia supposed to cause indeterminism, undetectability or failure of reference. I respond that these arguments at best support Leibniz Equivalence. (shrink)

The indistinguishability of bosons and fermions has been an essential part of our ideas of quantum mechanics since the 1920s. But what is the mathematical basis for this indistinguishability? An answer was provided in the group representation theory that developed alongside quantum theory and quickly became a major part of its mathematical structure. In the 1930s such a complex and seemingly abstract theory came to be rejected by physicists as the standard functional analysis picture presented by John von Neumann took (...) hold. The purpose of the present account is to show how indistinguishability is explained within representation theory. (shrink)

In this paper, I consider the role of exact symmetries in theories of physics, working throughout with the example of gravitation set in Newtonian spacetime. First, I spend some time setting up a means of thinking about symmetries in this context; second, I consider arguments from the seeming undetectability of absolute velocities to an anti-realism about velocities; and finally, I claim that the structure of the theory licences us to interpret models which differ only with regards to the absolute velocities (...) of objects as depicting the same physical state of affairs. In defending this last claim, I consider how ideas and resources from the philosophy of language may usefully be brought to bear on this topic. (shrink)

This paper argues that much of the literature on interpreting scientific theories presupposes a certain picture of what interpretation involves: a picture according to which interpreting a theory is like translating from one language to another. In place of this “external” approach to interpretation, this paper proposes an “internal” approach, according to which interpretation is more concerned with delineating a theory’s internal semantic architecture.

This is the chapter on general relativity for the Cambridge Companion to Einstein which I am co-editing with Christoph Lehner.