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This three-part paper comprises: (i) a critique by Halvorson of Bell's (1973) paper "Subject and Object"; (ii) a comment by Butterfield; (iii) a reply by Halvorson. An Appendix gives the passage from Bell that is the focus of Halvorson's critique.

We develop some ideas about gauge symmetry in the context of Maxwell's theory of electromagnetism in the Hamiltonian formalism. One great benefit of this formalism is that it pairs momentum and configurational degrees of freedom, so that a decomposition of one side into subsets can be translated into a decomposition of the other. In the case of electromagnetism, this enables us to pair degrees of freedom of the electric field with degrees of freedom of the vector potential. Another benefit is that the formalism algorithmically identifies subsets of the equations of motion that represent time-dependent symmetries. For electromagnetism, these two benefits allow us to define gauge-fixing in parallel to special decompositions of the electric field. More specifically, we apply the Helmholtz decomposition theorem to split the electric field into its Coulombic and radiative parts, and show how this gives a special role to the Coulomb gauge (i.e. div$({\bf A}) = 0$). We relate this argument to Maudlin's (2018) discussion, which advocated the Coulomb gauge., 29 pages

The main aim of this paper is to make a remark about the relation between (i) dualities between theories, as ‘duality’ is understood in physics and (ii) equivalence of theories, as ‘equivalence’ is understood in logic and philosophy. The remark is that in physics, two theories can be dual, and accordingly get called ‘the same theory’, though we interpret them as disagreeing—so that they are certainly not equivalent, as ‘equivalent’ is normally understood. So the remark is simple, but, I shall argue, worth stressing, since often neglected. My argument for this is based on the account of duality developed by De Haro. I also spell out how this remark implies a limitation of proposals (both traditional and recent) to understand theoretical equivalence as either logical equivalence or a weakening of it.

In this contribution in honour of Paul Busch, we criticise the claims of many expositions that the time-energy uncertainty principle allows both a violation of energy conservation, and particle creation, provided that this happens for a sufficiently short time. But we agree that there are grains of truth in these claims: which we make precise and justify using perturbation theory., Forthcoming in Journal of Physics: Conference Proceedings, Mathematical Foundations of Quantum Mechanics in Memoriam Paul Busch

This is one of a pair of papers that give a historical-\emph{cum}-philosophical analysis of the endeavour to understand black hole entropy as a statistical mechanical entropy obtained by counting string-theoretic microstates. Both papers focus on Andrew Strominger and Cumrun Vafa's ground-breaking 1996 calculation, which analysed the black hole in terms of D-branes. The first paper gives a conceptual analysis of the Strominger-Vafa argument, and of several research efforts that it engendered. In this paper, we assess whether the black hole should be considered as emergent from the D-brane system, particularly in light of the role that duality plays in the argument. We further identify uses of the quantum-to-classical correspondence principle in string theory discussions of black holes, and compare these to the heuristics of earlier efforts in theory construction, in particular those of the old quantum theory., 40 pages

Can there be ‘peaceful coexistence’ between quantum theory and special relativity? Thirty years ago, Shimony hoped that isolating the culprit (i.e. the false assumption) in proofs of Bell inequalities as Outcome Independence would secure such peaceful coexistence: or, if not secure it, at least show a way—maybe the best or only way—to secure it. In this paper, I begin by being sceptical of Shimony’s approach, urging that we need a relativistic solution to the quantum measurement problem (Sect. 2). Then I analyse Outcome Independence in Kent’s realist one-world Lorentz-invariant interpretation of quantum theory (Sects. 3 and 4). Then I consider Shimony’s other condition, Parameter Independence, both in Kent’s proposal and more generally, in the light of recent remarkable theorems by Colbeck, Renner and Leegwater (Sect. 5). For both Outcome Independence and Parameter Independence, there is a striking analogy with the situation in pilot-wave theory. Finally, I will suggest that these recent theorems make some kind of peaceful coexistence mandatory for someone who, like Shimony, endorses Parameter Independence.

We make two points about dualities in string theory. The first point is that the conception of duality, which we will discuss, meshes with two dual theories being ‘gauge related’ in the general philosophical sense of being physically equivalent. The second point is a result about gauge/gravity duality that shows its relation to gauge symmetries to be subtler than one might expect: each of a certain class of gauge symmetries in the gravity theory, that is, diffeomorphisms, is related to a position-dependent symmetry of the gauge theory.

We give an introductory review of gauge/gravity duality, and associated ideas of holography, emphasising the conceptual aspects. The opening Sections gather the ingredients, viz. anti-de Sitter spacetime, conformal field theory and string theory, that we need for presenting, in Section 5, the central and original example: Maldacena's AdS/CFT correspondence. Sections 6 and 7 develop the ideas of this example, also in applications to condensed matter systems, QCD, and hydrodynamics. Sections 8 and 9 discuss the possible extensions of holographic ideas to de Sitter spacetime and to black holes. Section 10 discusses the bearing of gauge/gravity duality on two philosophical topics: the equivalence of physical theories, and the idea that spacetime, or some features of it, are emergent., 49 pages, invited review for Foundations of Physics

We report Adrian Kent's proposed framework for a realist, one-world, Lorentz-invariant formulation of quantum theory. The idea is to postulate a final boundary condition: in effect, a late-time distribution of mass-energy recording how photons scattered off macroscopic objects. Nature selects this final boundary condition with the orthodox late-time Born probability; and this defines the probability space of events, to give a realist quantum theory. We emphasize two topics. First, we consider this formulation's verdicts about traditional locality conditions, such as Outcome Independence and Parameter Independence. Second, we discuss a possible amendment to Kent's proposal that, roughly speaking, allows for the emergence of a quasiclassical history even when mass-energy is shielded or delayed from appearing in the final boundary condition., Comment: 14 pages, 7 figures, submitted to Journal of Physics: Conference Series

The microscopic state counting of the extremal Reissner-Nordstr\"om black hole performed by Andrew Strominger and Cumrun Vafa in 1996 has proven to be a central result in string theory. Here, with a philosophical readership in mind, the argument is presented in its contemporary context and its rather complex conceptual structure is analysed. In particular, we will identify the various inter-theoretic relations, such as duality and linkage relations, on which it depends. We further aim to make clear why the argument was immediately recognised as a successful accounting for the entropy of this black hole and how it engendered subsequent work that intended to strengthen the string theoretic analysis of black holes. Its relation to the formulation of the AdS/CFT conjecture will be briefly discussed, and the familiar reinterpretation of the entropy calculation in the context of the AdS/CFT correspondence is given. Finally, we discuss the heuristic role that Strominger and Vafa's microscopic account of black hole entropy played for the black hole information paradox. A companion paper analyses the ontology of the Strominger-Vafa black hole states, the question of emergence of the black hole from a collection of D-branes, and the role of the correspondence principle in the context of string theory black holes., Comment: 70 pages

In this paper we present a schema for describing dualities between physical theories (Sects. 2 and 3), and illustrate it in detail with the example of bosonization: a boson-fermion duality in two-dimensional quantum field theory (Sects. 4 and 5). The schema develops proposals in De Haro (Space and Time after Quantum Gravity, 2016 [15]; Duality and Physical Equivalence, 2016a [16]): these proposals include construals of notions related to duality, like representation, model, symmetry and interpretation. The aim of the schema is to give a more precise criterion for duality than has so far been considered. The bosonization example, or boson-fermion duality, has the feature of being simple yet rich enough to illustrate the most relevant aspects of our schema, which also apply to more sophisticated dualities. The richness of the example consists, mainly, in its concern with two non-trivial quantum field theories: including massive Thirring-sine-Gordon duality, and non-abelian bosonization. This prompts two comparisons with the recent philosophical literature on dualities. (a) Unlike the standard cases of duality in quantum field theory and string theory, where only specific simplifying limits of the theories are explicitly known, the boson-fermion duality is known to hold exactly. This exactness can be exhibited explicitly. (b) The bosonization example illustrates both the cases of isomorphic and non-isomorphic models: which we believe the literature on dualities has not so far discussed.

We discuss scientific realism from the perspective of modern cosmology, especially primordial cosmology: i.e. the cosmological investigation of the very early universe. We first (Section 2) state our allegiance to scientific realism, and discuss what insights about it cosmology might yield, as against "just" supplying scientific claims that philosophers can then evaluate. In particular, we discuss: the idea of laws of cosmology, and limitations on ascertaining the global structure of spacetime. Then we review some of what is now known about the early universe (Section 3): meaning, roughly, from a thousandth of a second after the Big Bang onwards(!). The rest of the paper takes up two issues about primordial cosmology, i.e. the very early universe, where "very early" means, roughly, much earlier (logarithmically) than one second after the Big Bang: say, less than 10^{-11} seconds. Both issues illustrate that familiar philosophical threat to scientific realism, the under-determination of theory by data---on a cosmic scale. The first issue (Section 4) concerns the difficulty of observationally probing the very early universe. More specifically, the difficulty is to ascertain details of the putative inflationary epoch. The second issue (Section 5) concerns difficulties about confirming a cosmological theory that postulates a multiverse, i.e. a set of domains (universes) each of whose inhabitants (if any) cannot directly observe, or otherwise causally interact with, other domains. This again concerns inflation, since many inflationary models postulate a multiverse. For all these issues, it will be clear that much remains unsettled, as regards both physics and philosophy. But we will maintain that these remaining controversies do not threaten scientific realism.

The aim of this paper is to contribute to a better conceptual understanding of gauge quantum field theories, such as quantum chromodynamics, by discussing a famous physical limit, the 't Hooft limit, in which the theory concerned often simplifies. The idea of the limit is that the number $N$ of colours (or charges) goes to infinity. The simplifications that can happen in this limit, and that we will consider, are: (i) the theory's Feynman diagrams can be drawn on a plane without lines intersecting (called `planarity'); and (ii) the theory, or a sector of it, becomes integrable, and indeed corresponds to a well-studied system, viz. a spin chain. Planarity is important because it shows how a quantum field theory can exhibit extended, in particular string-like, structures; in some cases, this gives a connection with string theory, and thus with gravity. Previous philosophical literature about how one theory (or a sector, or regime, of a theory) might be emergent from, and-or reduced to, another one has tended to emphasize cases, such as occur in statistical mechanics, where the system before the limit has finitely many degrees of freedom. But here, our quantum field theories, including those on the way to the 't Hooft limit, will have infinitely many degrees of freedom. Nevertheless, we will show how a recent schema by Butterfield and taxonomy by Norton apply to the quantum field theories we consider; and we will classify three physical properties of our theories in these terms. These properties are planarity and integrability, as in (i) and (ii) above; and the behaviour of the beta-function reflecting, for example, asymptotic freedom. Our discussion of these properties, especially the beta-function, will also relate to recent philosophical debate about the propriety of assessing quantum field theories, whose rigorous existence is not yet proven., Comment: 44 pp. arXiv admin note: text overlap with arXiv:1012.3983, arXiv:hep-ph/9802419, arXiv:1012.3997 by other authors

The twentieth century saw two fundamental revolutions in physics -- relativity and quantum. Daily use of these theories can numb the sense of wonder at their immense empirical success. Does their instrumental effectiveness stand on the rock of secure concepts or the sand of unresolved fundamentals? Does measuring a quantum system probe, or even create, reality, or merely change belief? Must relativity and quantum theory just co-exist or might we find a new theory which unifies the two? To bring such questions into sharper focus, we convened a conference on Quantum Physics and the Nature of Reality. Some issues remain as controversial as ever, but some are being nudged by theory's secret weapon of experiment., Comment: 8 pages

I discuss how modern cosmology illustrates underdetermination of theoretical hypotheses by data, in ways that are different from most philosophical discussions. I confine the discussion to the history of the observable universe from about one second after the Big Bang, as described by the mainstream cosmological model: in effect, what cosmologists in the early 1970s dubbed the ‘standard model’, as elaborated since then. Or rather, the discussion is confined to a (very!) few aspects of that history. I emphasize that despite the underdetermination, a scientific realist can, and should, endorse this description.

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. (These definitions are based on definitions made by Quine and Saunders.) 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 (which will come in two versions), and haecceitism. The fourth is recent. Its most notable feature is that it makes diversity (i.e. non-identity) weaker than what we will call individuality (being an individual): 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., 55 pages, 21 figures. Forthcoming, after an Appendectomy, in the British Journal for the Philosophy of Science

We discuss some aspects of the relation between dualities and gauge symmetries. Both of these ideas are of course multi-faceted, and we confine ourselves to making two points. Both points are about dualities in string theory, and both have the 'flavour' that two dual theories are 'closer in content' than you might think. For both points, we adopt a simple conception of a duality as an 'isomorphism' between theories: more precisely, as appropriate bijections between the two theories' sets of states and sets of quantities. The first point (Section 3) is that this conception of duality meshes with two dual theories being 'gauge related' in the general philosophical sense of being physically equivalent. For a string duality, such as T-duality and gauge/gravity duality, this means taking such features as the radius of a compact dimension, and the dimensionality of spacetime, to be 'gauge'. The second point (Sections 4, 5 and 6) is much more specific. We give a result about gauge/gravity duality that shows its relation to gauge symmetries (in the physical sense of symmetry transformations that are spacetime-dependent) to be subtler than you might expect. For gauge theories, you might expect that the duality bijections relate only gauge-invariant quantities and states, in the sense that gauge symmetries in one theory will be unrelated to any symmetries in the other theory. This may be so in general; and indeed, it is suggested by discussions of Polchinski and Horowitz. But we show that in gauge/gravity duality, each of a certain class of gauge symmetries in the gravity/bulk theory, viz. diffeomorphisms, is related by the duality to a position-dependent symmetry of the gauge/boundary theory., Comment: 33 pages. Forthcoming in: Studies in History and Philosophy of Modern Physics. This is an expanded version of the paper, "On the Relation between Dualities and Gauge Symmetries", which is forthcoming in Philosophy of Science (PSA2014 Proceedings)

We have two aims. The main one is to expound the idea of renormalization in quantum field theory, with no technical prerequisites (Sections 2 and 3). Our motivation is that renormalization is undoubtedly one of the great ideas—and great successes--of twentieth-century physics. Also it has strongly influenced in diverse ways, how physicists conceive of physical theories. So it is of considerable philosophical interest. Second, we will briefly relate renormalization to Ernest Nagel's account of inter-theoretic relations, especially reduction (Section 4). One theme will be a contrast between two approaches to renormalization. The old approach, which prevailed from ca. 1945 to 1970, treated renormalizability as a necessary condition for being an acceptable quantum field theory. On this approach, it is a piece of great good fortune that high energy physicists can formulate renormalizable quantum field theories that are so empirically successful. But the new approach to renormalization (from 1970 onwards) explains why the phenomena we see, at the energies we can access in our particle accelerators, are described by a renormalizable quantum field theory. For whatever non-renormalizable interactions may occur at yet higher energies, they are insignificant at accessible energies. Thus the new approach explains why our best fundamental theories have a feature, viz. renormalizability, which the old approach treated as a selection principle for theories. That is worth saying since philosophers tend to think of scientific explanation as only explaining an individual event, or perhaps a single law, or at most deducing one theory as a special case of another. Here we see a framework in which there is a space of theories. And this framework is powerful enough to deduce that what seemed “manna from heaven” (that some renormalizable theories are empirically successful) is to be expected: the good fortune is generic. We also maintain that universality, a concept stressed in renormalization theory, is essentially the familiar philosophical idea of multiple realizability; and that it causes no problems for reductions of a Nagelian kind.

I discuss various formulations of stochastic Einstein locality (SEL), which is a version of the idea of relativistic causality, i.e. the idea that influences propagate at most as fast as light. SEL is similar to Reichenbach's Principle of the Common Cause (PCC), and Bell's Local Causality. My main aim is to discuss formulations of SEL for a fixed background spacetime. I previously argued that SEL is violated by the outcome dependence shown by Bell correlations, both in quantum mechanics and in quantum field theory. Here I re-assess those verdicts in the light of some recent literature which argues that outcome dependence does not violate the PCC. I argue that the verdicts about SEL still stand. Finally, I briefly discuss how to formulate relativistic causality if there is no fixed background spacetime., Comment: 59 pages latex, 3 figures. Forthcoming in The British Journal for the Philosophy of Science

This paper forms part of a wider campaign: to deny em pointillisme. That is the doctrine that a physical theory's fundamental quantities are defined at points of space or of spacetime, and represent intrinsic properties of such points or point-sized objects located there; so that properties of spatial or spatiotemporal regions and their material contents are determined by the point-by-point facts. More specifically, this paper argues against pointillisme about the concept of velocity in classical mechanics; especially against proposals by Tooley, Robinson and Lewis. A companion paper argues against pointillisme about (chrono)-geometry, as proposed by Bricker. To avoid technicalities, I conduct the argument almost entirely in the context of ``Newtonian'' ideas about space and time, and the classical mechanics of point-particles, i.e. extensionless particles moving in a void. But both the debate and my arguments carry over to relativistic physics.

The rotating discs argument (RDA) against perdurantism has been mostly discussed by metaphysicians, though the argument of course appeals to ideas from classical mechanics, especially about rotation. In contrast, I assess the RDA from the perspective of the philosophy of physics. I argue for three main conclusions. The first conclusion is that the RDA can be formulated more strongly than is usually recognized: it is not necessary to imagine away the dynamical effects of rotation. The second is that in general relativity, the RDA fails because of frame-dragging. The third conclusion is that even setting aside general relativity, the strong formulation of the RDA can after all be defeated. Namely, by the perdurantist taking objects in classical mechanics (whether point-particles or continuous bodies) to have only temporally extended, i.e. non-instantaneous, temporal parts: which immediately blocks the RDA. Admittedly, this version of perdurantism defines persistence in a weaker sense of `definition' than pointilliste versions that aim to define persistence assuming only instantaneous temporal parts. But I argue that temporally extended temporal parts: (i) can do the jobs within the endurantism-perdurantism debate that the perdurantist wants temporal parts to do; and (ii) are supported by both classical and quantum mechanics. This is an extract from a much longer paper, which is available at: http://philsci-archive.pitt.edu/archive/00001760. The main differences are that the longer paper: (i) gives much more detail about the form and scope of the RDA, the interpretative subtleties of classical mechanics, and the physics of rotation; and (ii) reports and assesses several other replies to the RDA, especially those by Callender, Lewis, Robinson and Sider.

I commemorate David Lewis by discussing an aspect of modality within analytical mechanics, which is closely related to his work on counterfactuals. This concerns the way Hamilton-Jacobi theory uses ensembles, i.e. sets of possible initial conditions. (A companion paper discusses other aspects of modality in analytical mechanics that are equally related to Lewis's work.)

We extend the topos-theoretic treatment given in previous papers of assigning values to quantities in quantum theory. In those papers, the main idea was to assign a sieve as a partial and contextual truth-value to a proposition that the value of a quantity lies in a certain set D of real numbers. Here we relate such sieve-valued valuations to valuations that assign to quantities subsets, rather than single elements, of their spectrum (we call these interval valuations). There are two main results. First, there is a natural correspondence between these two kinds of valuation, which uses the notion of a state's support for a quantity (Section 3). Second, if one starts with a more general notion of interval valuation, one sees that our interval valuations based on the notion of support (and correspondingly, our sieve-valued valuations) are a simple way to secure certain natural properties of valuations, such as monotonicity (Section 4).

I discuss how modern cosmology illustrates under-determination of theoretical hypotheses by data, in ways that are different from most philosophical discussions. I emphasize cosmology's concern with what data could in principle be collected by a single observer (Section 2); and I give a broadly sceptical discussion of cosmology's appeal to the cosmological principle as a way of breaking the under-determination (Section 3). I confine most of the discussion to the history of the observable universe from about one second after the Big Bang, as described by the mainstream cosmological model: in effect, what cosmologists in the early 1970s dubbed the `standard model', as elaborated since then. But in the closing Section 4, I broach some questions about times earlier than one second., 31 pages, no figures

First, I briefly review the different conceptions of time held by three rival interpretations of quantum theory: the collapse of the wave-packet, the pilot-wave interpretation, and the Everett interpretation (Section 2). Then I turn to a much less controversial task: to expound the recent understanding of the time-energy uncertainty principle, and indeed of uncertainty principles in general, that has been established by such authors as Busch, Hilgevoord and Uffink. Although this may at first seem a narrow topic, I point out connections to other conceptual topics about time in quantum theory: for example, the question under what circumstances there is a time operator (Section 4.3)., 26 pages; no figures

I have two main aims. The first is general, and more philosophical (Section 2). The second is specific, and more closely related to physics (Sections 3 and 4). The first aim is to state my general views about laws and causation at different 'levels'. The main task is to understand how the higher levels sustain notions of law and causation that 'ride free' of reductions to the lower level or levels. I endeavour to relate my views to those of other symposiasts. The second aim is to give a framework for describing dynamics at different levels, emphasising how the various levels' dynamics can mesh or fail to mesh. This framework is essentially that of elementary dynamical systems theory. The main idea will be, for simplicity, to work with just two levels, dubbed 'micro' and 'macro' which are related by coarse-graining. I use this framework to describe, in part, the first four of Ellis' five types of top-down causation., 29 pages, 3 figures

In previous work, I described several examples combining reduction and emergence: where reduction is understood a la Ernest Nagel, and emergence is understood as behaviour or properties that are novel (by some salient standard). Here, my aim is again to reconcile reduction and emergence, for a case which is apparently more problematic than those I treated before: renormalization. Renormalization is a vast subject. So I confine myself to emphasizing how the modern approach to renormalization (initiated by Wilson and others between 1965 and 1975), when applied to quantum field theories, illustrates both Nagelian reduction and emergence. My main point is that the modern understanding of how renormalizability is a generic feature of quantum field theories at accessible energies gives us a conceptually unified family of Nagelian reductions. That is worth saying since philosophers tend to think of scientific explanation as only explaining an individual event, or perhaps a single law, or at most deducing one theory as a special case of another. Here we see a framework in which there is a space of theories endowed with enough structure that it provides a family of reductions., 43 pages, no figures

We extend the topos-theoretic treatment given in previous papers of assigningvalues to quantities in quantum theory, and of related issues such as theKochen–Specker theorem. This extension has two main parts: the use of vonNeumann algebras as a base category and the relation of our generalized valuationsto (i) the assignment to quantities of intervals of real numbers and (ii) the ideaof a subobject of the coarse-graining presheaf.

We discuss some ways in which topos theory (a branch of category theory) can be applied to interpretative problems in quantum theory and quantum gravity. In Section 1, we introduce these problems. In Section 2, we introduce topos theory, especially the idea of a topos of presheaves. In Section 3, we discuss several possible applications of topos theory to the problems in Section 1. In Section 4, we draw some conclusions.

In a previous paper, we proposed assigning asthe value of a physical quantity in quantum theory acertain kind of set (a sieve) of quantities that arefunctions of the given quantity. The motivation was in part physical — such a valuationilluminates the Kochen–Specker theorem — andin part mathematical — the valuation arisesnaturally in the topos theory of presheaves. This paperdiscusses the conceptual aspects of this proposal. We also undertake two othertasks. First, we explain how the proposed valuationscould arise much more generally than just in quantumphysics; in particular, they arise as naturally in classical physics. Second, we give anothermotivation for such valuations (that applies equally toclassical and quantum physics). This arises fromapplying to propositions about the values of physical quantities some general axioms governingpartial truth for any kind of proposition.

Any attempt to construct a realistinterpretation of quantum theory founders on theKochen–Specker theorem, which asserts theimpossibility of assigning values to quantum quantitiesin a way that preserves functional relations between them. We constructa new type of valuation which is defined on alloperators, and which respects an appropriate version ofthe functional composition principle. The truth-values assigned to propositions are (i) contextual and(ii) multivalued, where the space of contexts and themultivalued logic for each context come naturally fromthe topos theory of presheaves. The first step in our theory is to demonstrate that theKochen–Specker theorem is equivalent to thestatement that a certain presheaf defined on thecategory of self-adjoint operators has no globalelements. We then show how the use of ideas drawn from the theory ofpresheaves leads to the definition of a generalizedvaluation in quantum theory whose values are sieves ofoperators. In particular, we show how each quantum state leads to such a generalized valuation. Akey ingredient throughout is the idea that, in asituation where no normal truth-value can be given to aproposition asserting that the value of a physical quantity A lies in a subset \(\Delta \subseteq \mathbb{R}\), it is nevertheless possible toascribe a partial truth-value which is determined by theset of all coarse-grained propositions that assert thatsome function f(A) lies in f(Δ), and that are true in a normalsense. The set of all such coarse-grainings forms asieve on the category of self-adjoint operators, and ishence fundamentally related to the theory ofpresheaves.

This paper gives a philosophical assessment of the Montevideo interpretation of quantum theory, advocated by Gambini, Pullin and co-authors. This interpretation has the merit of linking its proposal about how to solve the measurement problem to the search for quantum gravity: namely by suggesting that quantum gravity makes for fundamental limitations on the accuracy of clocks, which imply a type of decoherence that "collapses the wave-packet". I begin (Section 2) by sketching the topics of decoherence, and quantum clocks, on which the interpretation depends. Then I expound the interpretation, from a philosopher's perspective (Sections 3, 4 and 5). Finally, in Section 6, I argue that the interpretation, at least as developed so far, is best seen as a form of the Everett interpretation: namely with an effective or approximate branching, that is induced by environmental decoherence of the familiar kind, and by the Montevideans' "temporal decoherence"., Comment: 28 pages, no figures, Studies in the History and Philosophy of Modern Physics (online) May 2014