The main aim of this paper is to make a remark about the relation between dualities between theories, as `duality' is understood in physics and 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: which is illustrated here with several examples, from both elementary physics and string theory. Thus I argue that in some examples, including in string theory, two dual theories disagree in their claims about the world. I also spell out how this remark implies a limitation of proposals to understand theoretical equivalence as either logical equivalence or a weakening of it. (shrink)

We have two aims. The main one is to expound the idea of renormalization in quantum field theory, with no technical prerequisites. 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. 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 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” 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. (shrink)

We discuss from a philosophical perspective the way in which the normal concept of time might be said to `emerge' in a quantum theory of gravity. After an introduction, we briefly discuss the notion of emergence, without regard to time. We then introduce the search for a quantum theory of gravity ; and review some general interpretative issues about space, time and matter. We then discuss the emergence of time in simple quantum geometrodynamics, and in the Euclidean approach. Section 6 (...) concludes. (shrink)

In another paper, one of us argued that emergence and reduction are compatible, and presented four examples illustrating both. The main purpose of this paper is to develop this position for the example of phase transitions. We take it that emergence involves behaviour that is novel compared with what is expected: often, what is expected from a theory of the system's microscopic constituents. We take reduction as deduction, aided by appropriate definitions. Then the main idea of our reconciliation of emergence (...) and reduction is that one makes the deduction after taking a limit of an appropriate parameter $N$. Thus our first main claim will be that in some situations, one can deduce a novel behaviour, by taking a limit $N\to\infty$. Our main illustration of this will be Lee-Yang theory. But on the other hand, this does not show that the $N=\infty$ limit is physically real. For our second main claim will be that in such situations, there is a logically weaker, yet still vivid, novel behaviour that occurs before the limit, i.e. for finite $N$. And it is this weaker behaviour which is physically real. Our main illustration of this will be the renormalization group description of cross-over phenomena. (shrink)

Life and works of Ācārya Madhva, chief proponent of the Dvaita school of Vedanta.

This paper expounds the relations between continuous symmetries and conserved quantities, i.e. Noether's ``first theorem'', in both the Lagrangian and Hamiltonian frameworks for classical mechanics. This illustrates one of mechanics' grand themes: exploiting a symmetry so as to reduce the number of variables needed to treat a problem. I emphasise that, for both frameworks, the theorem is underpinned by the idea of cyclic coordinates; and that the Hamiltonian theorem is more powerful. The Lagrangian theorem's main ``ingredient'', apart from cyclic coordinates, (...) is the rectification of vector fields afforded by the local existence and uniqueness of solutions to ordinary differential equations. For the Hamiltonian theorem, the main extra ingredients are the asymmetry of the Poisson bracket, and the fact that a vector field generates canonical transformations iff it is Hamiltonian. (shrink)

I have two main aims. The first is general, and more philosophical. The second is specific, and more closely related to physics. 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, emphasizing 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. (shrink)

I extract some philosophical morals from some aspects of Lagrangian mechanics. One main moral concerns methodology: Lagrangian mechanics provides a level of description of phenomena which has been largely ignored by philosophers, since it falls between their accustomed levels---``laws of nature'' and ``models''. Another main moral concerns ontology: the ontology of Lagrangian mechanics is both more subtle and more problematic than philosophers often realize. The treatment of Lagrangian mechanics provides an introduction to the subject for philosophers, and is technically elementary. (...) In particular, it is confined to systems with a finite number of degrees of freedom, and for the most part eschews modern geometry. (shrink)

Abstract: This paper assesses the Everettian approach to the measurement problem, especially the version of that approach advocated by Simon Saunders and David Wallace. I emphasise conceptual, indeed metaphysical, aspects rather than technical ones; but I include an introductory exposition of decoherence. In particular, I discuss whether---as these authors maintain---it is acceptable to have no precise definition of 'branch' (in the Everettian kind of sense). (A version of this paper will appear in a CTNS/Vatican Observatory volume on Quantum Theory and (...) Divine Action, ed. Robert Russell et al.). (shrink)

This paper expounds the modern theory of symplectic reduction in finite-dimensional Hamiltonian mechanics. This theory generalizes the well-known connection between continuous symmetries and conserved quantities, i.e. Noether's theorem. It also illustrates one of mechanics' grand themes: exploiting a symmetry so as to reduce the number of variables needed to treat a problem. The exposition emphasises how the theory provides insights about the rotation group and the rigid body. The theory's device of quotienting a state space also casts light on philosophical (...) issues about whether two apparently distinct but utterly indiscernible possibilities should be ruled to be one and the same. These issues are illustrated using ``relationist'' mechanics. (shrink)

This paper forms part of a wider campaign: to deny 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. Elsewhere, I argued against pointillisme about chrono-geometry, and about velocity in classical mechanics. In both cases, attention focussed on temporal extrinsicality: (...) i.e. on what an ascription of a property implies about other times. Therefore, I also discussed the metaphysical debate whether persistence should be understood as endurance or perdurance. In this paper, I focus instead on spatial extrinsicality: i.e. on what an ascription of a property implies about other places. The main idea will be that the classical mechanics of continuous media involves a good deal of spatial extrinsicality---which seems not to have been noticed by philosophers, even those who have no inclination to pointillisme. I begin by describing my wider campaign. Then I present some elementary aspects of stress, strain and elasticity---emphasising the kinds of spatial extrinsicality they each involve. I conduct the discussion entirely in the context of `Newtonian' ideas about space and time. But my arguments carry over to relativistic physics. (shrink)

This paper discusses some of the modal involvements of analytical mechanics. I first review the elementary aspects of the Lagrangian, Hamiltonian and Hamilton-Jacobi approaches. I then discuss two modal involvements; both are related to David Lewis' work on modality, especially on counterfactuals. The first is the way Hamilton-Jacobi theory uses ensembles, i.e. sets of possible initial conditions. The structure of this set of ensembles remains to be explored by philosophers. The second is the way the Lagrangian and Hamiltonian approaches' variational (...) principles state the law of motion by mentioning contralegal dynamical evolutions. This threatens to contravene the principle that any actual truth, in particular an actual law, is made true by actual facts. Though this threat can be avoided, at least for simple mechanical systems, it repays scrutiny; not least because it leads to some open questions. (shrink)

From lectures over the BBC by a Cambridge professor on answers to our problems on the meaning of life.

I show that locality, as it occurs in EPR arguments for the incompleteness of quantum mechanics, can be construed as causal independence understood in terms of Lewis' counterfactual analysis of causation. This construal has two benefits. It supplements recent analyses, which have not treated locality in detail. And it clarifies the relation between two EPR arguments that have recently been distinguished. It shows that the simpler of the two is more complex than has been thought; and that the other argument (...) does not need 'counterfactual definiteness'. (shrink)

Some recent philosophical debate about persistence has focussed on an argument against perdurantism that discusses rotating perfectly homogeneous discs. The argument has been mostly discussed by metaphysicians, though it appeals to ideas from classical mechanics, especially about rotation. In contrast, I assess the RDA from the perspective of the philosophy of physics. After introducing the argument and emphasizing the relevance of physics, I review some metaphysicians' replies to the argument, especially those by Callender, Lewis, Robinson and Sider. Thereafter, I argue (...) for three main conclusions. They all arise from the fact, emphasized in Section 2, that classical mechanics is both more subtle, and more problematic, than philosophers generally realize. 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 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 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: can do the jobs within the endurantism- perdurantism debate that the perdurantist wants temporal parts to do; and are supported by both classical and quantum mechanics. (shrink)

We explain two ways of revising a tense logic like kripke's (1963) modal logic by adding predicate modifiers. first we show that modifiers allow us to render valid some mixing formulas--conditionals reversing the order of a quantifier and an operator--within a complete bivalent system. then we show how modifiers enable a tense logic to give analyses close to the surface form for sentences with temporal qualifications of singular terms, e.g., 'toby was fatter then than william is today'.

Work on Nyaya philosophy; includes Siddhāntamuktāvalī autocommentary and Dinakarī of Dinakarabhaṭṭa, 18th cent.

Study on creation in R̥gveda and Vedic literature and philosophy.

This is the editors' introduction to a new anthology of commissioned articles covering the various branches of philosophy of physics. We introduce the articles in terms of the three pillars of modern physics: relativity theory, quantum theory and thermal physics. We end by discussing the present state, and future prospects, of fundamental physics.

This volume gathers together ground-breaking work on the foundations and philosophy of quantum physics, by one of the most brilliant and productive researchers in the field. Rob Clifton died tragically in 2002 at the age of 38; two of his colleagues, themselves leading philosophers of physics, present fourteen of his finest papers here, all of which combine exciting philosophical discussion with rigorous mathematical results. Quantum Entanglements offers inspiration and substantial reward to anyone working on the foundations of quantum theory, with (...) backgrounds in philosophy, physics, or mathematics. (shrink)

This is a discussion of some themes in Max Tegmark’s recent book, Our Mathematical Universe. It was written as a review for Plus Magazine, the online magazine of the UK’s national mathematics education and outreach project, the Mathematics Millennium Project. Since some of the discussion---about symmetry breaking, and Pythagoreanism in the philosophy of mathematics---went beyond reviewing Tegmark’s book, the material was divided into three online articles. This version combines those three articles, and adds some other material, in particular a brief (...) defence of quidditism about properties. It also adds some references, to other Plus articles as well as academic articles. But it retains the informal style of Plus. (shrink)

I present aspects of causal set theory (a research programme in quantum gravity) as being en route to achieving a reduction of Lorentzian geometry to causal sets. I take reduction in philosophers' sense; and I argue that the prospects are good for there being a reduction of the type envisaged by Nagel. (I also discuss the prospects for the stronger functionalist variant of Nagelian reduction, that was formulated by Lewis.) One main theme will be causal set theory's use of a (...) physical scale (viz. the Planck scale) to formulate how it recovers a Lorentzian manifold. This use illustrates various philosophical topics relevant to reduction, such as limiting relations between theories, and the role of analogy. I also emphasise causal set theory's probabilistic method, viz. Poisson sprinkling: which is used both for formulating the reduction and for exploring its prospects. (shrink)

This paper gives a technically elementary treatment of some aspects of Hamilton -Jacobi theory, especially in relation to the calculus of variations. The second half of the paper describes the application to geometric optics, the optico-mechanical analogy and the transition to quantum mechanics. Finally, I report recent work of Holland providing a Hamiltonian formulation of the pilot-wave theory.

Can there be `peaceful coexistence' between quantum theory and special relativity? Thirty years ago, Shimony hoped that isolating the culprit 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. Then I analyse Outcome Independence in Kent's realist (...) one-world Lorentz-invariant interpretation of quantum theory. 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. 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. (shrink)

This article reviews 1 decade of research on cheating in academic institutions. This research demonstrates that cheating is prevalent and that some forms of cheating have increased dramatically in the last 30 years. This research also suggests that although both individual and contextual factors influence cheating, contextual factors, such as students' perceptions of peers' behavior, are the most powerful influence. In addition, an institution's academic integrity programs and policies, such as honor codes, can have a significant influence on students' behavior. (...) Finally, we offer suggestions for managing cheating from students' and faculty members' perspectives. (shrink)

Two works, with commentaries, on Jaina ethics.

In this paper we present a schema for describing dualities between physical theories, and illustrate it in detail with the example of bosonization: a boson-fermion duality in two-dimensional quantum field theory. The schema develops proposals in De Haro : 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:--- 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 {\it exactly}. This exactness can be exhibited explicitly. The bosonization example illustrates both the cases of isomorphic and {\it non-isomorphic} models: which we believe the literature on dualities has not so far discussed. (shrink)

I discuss three connections between Dummett's writings about time and philosophical aspects of physics. The first connection arises from remarks of Dummett's about the different relations of observation to time and to space. The main point is uncontroversial and applies equally to classical and quantum physics. It concerns the fact that perceptual processing is so rapid, compared with the typical time-scale on which macroscopic objects change their observable properties, that it engenders the idea of a `common now', spread across space. (...) The other two connections are specific to quantum theory, as interpreted along the lines of Everett. So for these two connections, the physics side is controversial, just as the philosophical side is. In Section 3, I connect the subjective uncertainty before an Everettian `splitting' of the multiverse to Dummett's suggestion, inspired by McTaggart, that a complete, i.e. indexical-free description of a temporal reality is impossible. And in Section 4, I connect Barbour's denial that time is real---a denial along the lines of Everett, rather than McTaggart---to Dummett's suggestion that statements about the past are not determinately true or false, because they are not effectively decidable. (shrink)

I reject Norton and Earman's hole argument that spacetime substantivalism is incompatible with determinism. I reconcile these both technically and philosophically. There is a technical definition of determinism that is not violated by pairs of models of the kind used in the hole argument. And technicalities aside, the basic idea of determinism is not violated if we claim that at most one of the two models represents a possible world. This claim can be justified either by metrical essentialism, or by (...) denying transworld identity for points: I prefer the latter. (shrink)

Compendium of Advaita school in Hindu philosophy; includes Naiṣkarmyasiddhicandrikā commentary by Jñānottama Miśra.

Study of the concept of verbal testimony in Nyaya system in Hindu philosophy.

These two books, both by distinguished authors, are excellent. Though they are written by and for physicists, they are an invaluable resource for philosophers interested in the grand theme of how classical physical phenomena emerge from the quantum realm. Both individually and taken together, they are fine representatives of the present state of knowledge about this theme, and about many more specific topics falling under it. They are also pedagogic, though aimed at an advanced level—graduate students and beyond, in physics (...) and mathematics. Thus, they are packed with sophisticated expositions of such topics as quantum Brownian motion, and decoherence in quantum field theory, the rigorous definition of macroscopic observables and of their evolution laws in quantum statistical physics, and the rigorous treatment of open quantum systems. So overall, they provide an invaluable overview of a large and lively research area of physics. But the books are also different in several ways. The first book, by Joos et al., has six authors, all theoretical physicists based in Germany and part of the ‘Heidelberg school’ of decoherence physics, which has grown up in the last twenty-five years under the tutelage of Heinz- Dieter Zeh. The second book is a monograph: Sewell is a British mathematical physicist, most of whose work has been in the algebraic approach to quantum statistical mechanics. Other, less obvious, differences follow on from these. By and large, the material in Decoherence is both more familiar and more accessible to philosophers of physics. And for reviewing the books for philosophers of physics, it will be a convenient strategy to spell out the three reasons for this contrast. But as we shall see, Quantum Mechanics being more difficult need not mean it is less valuable. First, decoherence processes of the kinds that Joos, et al., mostly discuss are now well-known to philosophers of quantum theory, not least through the work of the Heidelberg school itself and of the ‘Los Alamos school’ of Zurek and coauthors. Indeed, Joos’ own Chapter 3, “Decoherence through Interaction with the... (shrink)