In this paper, I discuss one form of the idea that spacetime and gravity might ‘emerge’ from quantum theory, i.e. via a holographic duality, and in particular via AdS/CFT duality. I begin by giving a survey of the general notion of duality, as well as its connection to emergence. I then review the AdS/CFT duality and proceed to discuss emergence in this context. We will see that it is difficult to find compelling arguments for the emergence of full quantum gravity (...) from gauge theory via AdS/CFT, i.e. for the boundary theory's being metaphysically more fundamental than the bulk theory. (shrink)

This article investigates and resolves the question whether gauge symmetry can display analogs of the famous Galileo’s ship scenario. In doing so, it builds on and clarifies the work of Greaves and Wallace on this subject.

As a prolegomenon to understanding the sense in which dualities are theoretical equivalences, we investigate the intuitive `equivalence' of hyper-regular Lagrangian and Hamiltonian classical mechanics. We show that the symplectification of these theories provides a sense in which they are isomorphic, and mutually and canonically definable through an analog of `common definitional extension'.

This article uncovers a foundational relationship between the ‘gauge symmetry’ of a Newton-Cartan theory and the celebrated Trautman Recovery Theorem and explores its implications for recent philosophical work on Newton-Cartan gravitation.

Philosophers of physics and physicists have long been intrigued by the analogies and disanalogies between gravitational theories and gauge theories. Indeed, repeated attempts to collapse these disanalogies have made us acutely aware that there are fairly general obstacles to doing so. Nonetheless, there is a special case space-time dimensions) in which gravity is often claimed to be identical to a gauge theory. I subject this claim to philosophical scrutiny in this article. In particular, I analyse how the standard disanalogies can (...) be overcome in dimensions, and consider whether really licenses the interpretation of gravity as a gauge theory. Our conceptual analysis reveals more subtle disanalogies between gravity and gauge, and connects these to interpretive issues in classical and quantum gravity. 1 Introduction1.1 Motivation1.2 Prospectus2 Disanalogies3 Three-dimensional gravity and gauge3.1 gravity3.2 Chern–Simons3.2.1 Cartan geometry3.2.2 Overcoming obst-gauge via Cartan connections3.3 Disanalogies collapsed4 Two More Disanalogies4.1 What about the symmetries?4.2 The phase spaces of the two theories5 Summary and Conclusion. (shrink)

It is part of information theory folklore that, while quantum theory prohibits the generic cloning of states, such cloning is allowed by classical information theory. Indeed, many take the phenomenon of no-cloning to be one of the features that distinguishes quantum mechanics from classical mechanics. In this paper, we use symplectic geometry to argue that pace conventional wisdom, in the case where one does not include a machine system, there is an analog of the no-cloning theorem for classical systems. However, (...) upon adjoining a non-trivial machine system one finds that, pace the quantum case, the obstruction to cloning disappears for pure states. We then discuss the difference between this result and the quantum case, and show that it can be explained in terms of the rigidity of the theories' respective geometries. Finally, we discuss the relationship between this result and classical no-cloning arguments in the context of symmetric monoidal categories and statistical classical mechanics. (shrink)

Foundations of Relational Realism: A Topological Approach to Quantum Mechanics and the Philosophy of Nature by Michael Epperson and Elias Zafiris sets out to achieve three goals: to develop a version of Whiteheadian metaphysics that the authors call “relational realism”; to formalize relational realism in terms of category theory, in particular sheaf theory; and to use relational realism to solve the interpretative problems of quantum mechanics. These goals are ambitious, to say the least, and all this is leaving aside those (...) sections of FRR which argue that relational realism yields the key to understanding quantum gravity!The text is 388 pages long and comprises two parts. Part I, by Epperson, introduces relational realism and its application to quantum mechanics. Part II, by Zafiris, develops the sheaf theory formalism for relational realism. As the authors say, their exposition is “nonlinear”, and this feature of FRR, alon .. (shrink)

Rovelli’s “Why Gauge?” offers a parable to show that gauge-dependent quantities have a modal and relational physical significance. We subject the morals of this parable to philosophical scrutiny and argue that, while Rovelli’s main point stands, there are important disanalogies between his parable and Yang-Mills type gauge theory.

The idea that gauge theory has `surplus' structure poses a puzzle: in one much discussed sense, this structure is redundant; but on the other hand, it is also widely held to play an essential role in the theory. In this paper, we employ category-theoretic tools to illuminate an aspect of this puzzle. We precisify what is meant by `surplus' structure by means of functorial comparisons with equivalence classes of gauge fields, and then show that such structure is essential for any (...) theory that represents a rich collection of physically relevant fields which are `local' in nature. (shrink)

The equivalence principle has constituted one of the cornerstones of discussions in the foundations of spacetime theories over the past century. However, up to this point the principle has been considered overwhelmingly only within the context of relativistic physics. In this article, we demonstrate that the principle has much broader, super-theoretic significance: to do so, we present a unified framework for understanding the principle in its various guises, applicable to both relativistic and Newtonian contexts. We thereby deepen significantly our understanding (...) of the role played by the equivalence principle in a broad class of spacetime theories. (shrink)

It is now well-known that Newton–Cartan theory is the correct geometrical setting for modelling the quantum Hall effect. In addition, in recent years edge modes for the Newton–Cartan quantum Hall effect have been derived. However, the existence of these edge modes has, as of yet, been derived using only orthodox methodologies involving the breaking of gauge-invariance; it would be preferable to derive the existence of such edge modes in a gauge-invariant manner. In this article, we employ recent work by Donnelly (...) and Freidel in order to accomplish exactly this task. Our results agree with known physics, but afford greater conceptual insight into the existence of these edge modes: in particular, they connect them to subtle aspects of Newton–Cartan geometry and pave the way for further applications of Newton–Cartan theory in condensed matter physics. (shrink)

Postmodernism and poststructuralism challenge fundamental positions in social theory. This book sets out some of the components of a postmodern social theory of health and healing, deriving from theorists including Derrida, Deleuze and Guattari, Foucault, Cixous and Kristeva. Nicholas J. Fox observes that the knowledge of the medical profession about the body, illness and health supplies the basis for medical dominance. The body of the patient is inscribed by discourses of professional `care,' an interaction which subjectifies the patient. Fox (...) explores the character of this power - and how it may be, and is, resisted. The book illustrates with detailed examples how the organization of health care and the caring relationship itself are sites for this contestation of power. Elements of feminist theory, and Derridean concepts of diffrance and intertextuality, supply the framework for the politics and ethics of the postmodern position on health. Deleuze and Guattari's radical challenge to psychoanalysis and familial repetitions within the healer/patient contact allows a re-reading of central ideas in medical sociology. While focusing upon the possibilities of postmodern social theory, the book demands a reappraisal of issues of structure, identity and knowledge in modernist medical sociology. Modernist sociology, Fox suggests, has been complicit in the creation of `the patient,' and of 'health' and 'illness.' Written with an emphasis on accessibility, this book explores the practical consequences of postmodern theory as well as familiarizing the reader with the concepts of postmodernism. (shrink)

In VAGUENESS AND DEGREES OF TRUTH, Nicholas Smith develops a new theory of vagueness: fuzzy plurivaluationism. -/- A predicate is said to be VAGUE if there is no sharply defined boundary between the things to which it applies and the things to which it does not apply. For example, 'heavy' is vague in a way that 'weighs over 20 kilograms' is not. A great many predicates -- both in everyday talk, and in a wide array of theoretical vocabularies, from (...) law to psychology to engineering -- are vague. -/- Smith argues, based on a detailed account of the defining features of vagueness, that an accurate theory of vagueness must involve the idea that truth comes in degrees. The core idea of degrees of truth is that while some sentences are true and some are false, others possess intermediate truth values: they are truer than the false sentences, but not as true as the true ones. Degree-theoretic treatments of vagueness have been proposed in the past, but all have encountered significant objections. In light of these, Smith develops a new type of degree theory. Its innovations include a definition of logical consequence that allows the derivation of a classical consequence relation from the degree-theoretic semantics, a unified account of degrees of belief and their relationships with degrees of truth and subjective probabilities, and the incorporation of semantic indeterminacy -- the view that vague statements need not have unique meanings -- into the degree-theoretic framework. -/- As well as being essential reading for those working on vagueness, Smith's book provides an excellent entry-point for newcomers to the area -- both from elsewhere in philosophy, and from computer science, logic and engineering. It contains a thorough introduction to existing theories of vagueness and to the requisite logical background. (shrink)

I have argued for a picture of decision theory centred on the principle of Rationally Negligible Probabilities. Isaacs argues against this picture on the grounds that it has an untenable implication. I first examine whether my view really has this implication; this involves a discussion of the legitimacy or otherwise of infinite decisions. I then examine whether the implication is really undesirable and conclude that it is not.

From Fine and Kamp in the 70’s—through Osherson and Smith in the 80’s, Williamson, Kamp and Partee in the 90’s and Keefe in the 00’s—up to Sauerland in the present decade, the objection continues to be run that fuzzy logic based theories of vagueness are incompatible with ordinary usage of compound propositions in the presence of borderline cases. These arguments against fuzzy theories have been rebutted several times but evidently not put to rest. I attempt to do so in this (...) paper. (shrink)

In his celebrated article on the contrary-to-fact conditional Roderick Chisholm makes the following astute observation.

Logic is essential to correct reasoning and also has important theoretical applications in philosophy, computer science, linguistics, and mathematics. This book provides an exceptionally clear introduction to classical logic, with a unique approach that emphasizes both the hows and whys of logic. Here Nicholas Smith thoroughly covers the formal tools and techniques of logic while also imparting a deeper understanding of their underlying rationales and broader philosophical significance. In addition, this is the only introduction to logic available today that (...) presents all the major forms of proof--trees, natural deduction in all its major variants, axiomatic proofs, and sequent calculus. The book also features numerous exercises, with solutions available on an accompanying website. -/- Logic is the ideal textbook for undergraduates and graduate students seeking a comprehensive and accessible introduction to the subject. -/- Provides an essential introduction to classical logic Emphasizes the how and why of logic Covers both formal and philosophical issues Presents all the major forms of proof--from trees to sequent calculus Features numerous exercises, with solutions available online The ideal textbook for undergraduates and graduate students . (shrink)

This paper defends the idea that there might be vagueness or indeterminacy in the world itself--as opposed to merely in our representations of the world--against the charges of incoherence and unintelligibility. First we consider the idea that the world might contain vague properties and relations ; we show that this idea is already implied by certain well-understood views concerning the semantics of vague predicates (most notably the fuzzy view). Next we consider the idea that the world might contain vague objects (...) ; we argue that an object is indeterminate in a certain respect (colour, size, etc.) just in case it is a borderline case of a maximally specific colour (size, etc.) property. Finally we consider the idea that the world as a whole might be indeterminate; we argue that the world is indeterminate just in case it lacks a determinate division into determinate objects. (shrink)

This paper presents a new solution to the problems for orthodox decision theory posed by the Pasadena game and its relatives. I argue that a key question raised by consideration of these gambles is whether evaluative compositionality (as I term it) is a requirement of rationality: is the value that an ideally rational agent places on a gamble determined by the values that she places on its possible outcomes, together with their mode of composition into the gamble (i.e. the probabilities (...) assigned to them)? The paper first outlines a certain simple response to the Pasadena game and identifies two problems with this response, the second of which is that it leads to a wholesale violation of evaluative compositionality. I then argue that rationality does not require decision makers to factor in outcomes of arbitrarily low probability. A method for making decisions which flows from this basic idea is then developed, and it is shown that this decision method (Truncation) leads to a limited — as opposed to wholesale — violation of evaluative compositionality. The paper then argues that the truncation method yields solutions to the problems posed by the Pasadena game and its relatives that are both attractive in themselves and superior to those yielded by alternative proposals in the literature. (shrink)

This paper argues that the most famous objection to backward time travel can carry no weight. In its classic form, the objection is that backward time travel entails the occurrence of impossible things, such as auto-infanticide—and hence is itself impossible. David Lewis has rebutted the classic version of the objection: auto-infanticide is prevented by coincidences, such as time travellers slipping on banana peels as they attempt to murder their younger selves. I focus on Paul Horwich‘s more recent version of the (...) objection, according to which backward time travel entails not impossible things, but improbable ones—such as the string of slips on banana peels that would be required to stop a determined auto-infanticidal maniac from murdering her younger self—and hence is itself highly improbable. I argue that backward time travel does not entail unusual numbers of coincidences; and that, even if it did, that would not render its occurrence unlikely. (shrink)

This paper defends the idea that there might be vagueness or indeterminacy in the world itself---as opposed to merely in our representations of the world---against the charges of incoherence and unintelligibility. First we consider the idea that the world might contain vague *properties and relations*; we show that this idea is already implied by certain well-understood views concerning the semantics of vague predicates (most notably the fuzzy view). Next we consider the idea that the world might contain vague *objects*; we (...) argue that an object is indeterminate in a certain respect (colour, size, etc.) just in case it is a borderline case of a maximally specific colour (size, etc.) property. Finally we consider the idea that the *world as a whole* might be indeterminate; we argue that the world is indeterminate just in case it lacks a determinate division into determinate objects. (shrink)

This paper presents a new argument against A-theories of time. A-theorists hold that there is an objective now (present moment) and an objective flow of time, the latter constituted by the movement of the objective now through time. A-theorists therefore want to draw different pictures of reality—showing the objective now in different positions—depending upon the time at which the picture is drawn. In this paper it is argued that the times at which the different pictures are drawn may be taken (...) to be normal times or hypertimes. If they are normal times then the A-theory is inconsistent, or else collapses to the B-theory—and appealing to primitive tense operators will not help A-theorists avoid this conclusion. If the times are hypertimes then the A-theory is consistent, but deeply problematic none the less. (shrink)

Contains exercises and solutions to accompany Logic: The Laws of Truth by Nicholas J. J. Smith (Princeton University Press, 2012).

A requirement on any theory of vagueness is that it solve the sorites paradox. It is generally agreed that there are two aspects to such a solution: one task is to locate the error in the sorites argument; the second task is to explain why the sorites reasoning is a paradox rather than a simple mistake. I argue for a further constraint on approaches to the second task: they should conform to the standard modus operandi in formal semantics, in which (...) the semantic theory one develops is taken to be implicit in the ordinary usage of competent speakers. Thus it should not turn out that one's explanation of why ordinary speakers react to the sorites reasoning in the way they do depends on speakers not thinking that the semantics of vague language is governed by the theory one is advocating. I then argue that, out of the current main contenders for a theory of vagueness, only theories that posit degrees of truth can meet this further constraint. (shrink)

This paper defends the idea that there might be vagueness or indeterminacy in the world itself---as opposed to merely in our representations of the world---against the charges of incoherence and unintelligibility. First we consider the idea that the world might contain vague *properties and relations*; we show that this idea is already implied by certain well-understood views concerning the semantics of vague predicates (most notably the fuzzy view). Next we consider the idea that the world might contain vague *objects*; we (...) argue that an object is indeterminate in a certain respect (colour, size, etc.) just in case it is a borderline case of a maximally specific colour (size, etc.) property. Finally we consider the idea that the *world as a whole* might be indeterminate; we argue that the world is indeterminate just in case it lacks a determinate division into determinate objects. (shrink)

Orthodoxy has it that mereological composition can never be a vague matter, for if it were, then existence would sometimes be a vague matter too, and that's impossible. I accept that vague composition implies vague existence, but deny that either is impossible. In this paper I develop degree-theoretic versions of quantified modal logic and of mereology, and combine them in a framework that allows us to make clear sense of vague composition and vague existence, and the relationships between them.

There is an extensive literature on time travel in both philosophy and physics. Part of the great interest of the topic stems from the fact that reasons have been given both for thinking that time travel is physically possible—and for thinking that it is logically impossible! This entry deals primarily with philosophical issues; issues related to the physics of time travel are covered in the separate entries on time travel and modern physics and time machines. We begin with the definitional (...) question: what is time travel? We then turn to the major objection to the possibility of backwards time travel: the Grandfather paradox. Next, issues concerning causation are discussed—and then, issues in the metaphysics of time and change. We end with a discussion of the question why, if backwards time travel will ever occur, we have not been visited by time travellers from the future. (shrink)

Fox writes about the nomadic project for people with bodies wherever they live, in what turned out not quite to be the planned sequel to his Postmodernism, Sociology, and Health (1993), but a treatment of the very practical issue of embodiment. Aspiring to transcend the conceptualization of embodiment by modern medicine, the caring professions, and other institutions, he suggests that it is possible to have a non-essentialist yet becoming body, not a being-body, not to be trammelled by notions of health (...) and illness. Distributed in the US by ISBS. Annotation copyrighted by Book News, Inc., Portland, OR. (shrink)

One of the most striking differences between Frege's Begriffsschrift (logical system) and standard contemporary systems of logic is the inclusion in the former of the judgement stroke: a symbol which marks those propositions which are being asserted , that is, which are being used to express judgements . There has been considerable controversy regarding both the exact purpose of the judgement stroke, and whether a system of logic should include such a symbol. This paper explains the intended role of the (...) judgement stroke in a way that renders it readily comprehensible why Frege insisted that this symbol was an essential part of his logical system. The key point here is that Frege viewed logic as the study of inference relations amongst acts of judgement , rather than – as in the typical contemporary view – of consequence relations amongst certain objects (propositions or well-formed formulae). The paper also explains why Frege's use of the judgement stroke is not in conflict with his avowed anti-psychologism, and why Wittgenstein's criticism of the judgement stroke as 'logically quite meaningless' is unfounded. The key point here is that while the judgement stroke has no content , its use in logic and mathematics is subject to a very stringent norm of assertion. (shrink)

In a warm and enjoyable dialogue the meaning of health, in its fullest sense, becomes a philosophical issue as much as a biological. For isn't the essence of health a general sense of well-being? Health can be seen as reflecting satisfaction with our quality of life; but how do we achieve that? Here, a character who is heading off for a job teaching health has an extended conversation with a trusted mentor, and they test various definitions, various visions, and some (...) of the infinite possibilities of the idea of health, in the process coming to a deeper and more invigorating understanding of life itself. They arrive at the notion of symbiosis - a living together to the advantage of each. And isn't a good conversation a sort of living together to the advantage of each? In such dialogue, we engage with our hearts and minds. When are we more alive than that? What is the peak of health if not this life, this engagement? The two friends want to know what health is. But they want more: They want to be healthy. They see three basic types of health - bodily, mental, and societal. These three types affect one another. How they affect one another matters in a critical way. But there is more. A friendly conversation allows special access to what is critical. Our guard is down in such a conversation. We are less likely to be defensive. We are more likely to keep our minds open and clear. We are likely to feel the confidence it takes to learn. (shrink)

A philosophical treatment of the idea of authority, this book is a dialogue between three characters. "Director," a philosopher, challenges the others to think through their ideas of authority, how it is established, how it works, and how it can be either subtle or bold.

"Rule" adopts the tradition of political philosophy begun by Socrates, refined by Xenophon and Plato. The book concentrates on something the characters call life-without-rule. What would that be? Is it a sort of utopia? How does it differ from anarchy? What makes it so appealing and what are the trade-offs?

This paper presents and defends a definition of vagueness, compares it favourably with alternative definitions, and draws out some consequences of accepting this definition for the project of offering a substantive theory of vagueness. The definition is roughly this: a predicate 'F' is vague just in case for any objects a and b, if a and b are very close in respects relevant to the possession of F, then 'Fa' and 'Fb' are very close in respect of truth. The definition (...) is extended to cover vagueness of many-place predicates, of properties and relations, and of objects. Some of the most important advantages of the definition are that it captures the intuitions which motivate the thought that vague predicates are tolerant, without leading to contradiction, and that it yields a clear understanding of the relationships between higher-order vagueness, sorites susceptibility, blurred boundaries, and borderline cases. The most notable consequence of the definition is that the correct theory of vagueness must countenance degrees of truth. (shrink)

A number of authors have noted that vagueness engenders degrees of belief, but that these degrees of belief do not behave like subjective probabilities. So should we countenance two different kinds of degree of belief: the kind arising from vagueness, and the familiar kind arising from uncertainty, which obey the laws of probability? I argue that we cannot coherently countenance two different kinds of degree of belief. Instead, I present a framework in which there is a single notion of degree (...) of belief, which in certain circumstances behaves like a subjective probability assignment and in other circumstances does not. The core idea is that one’s degree of belief in a proposition P is one’s expectation of P’s degree of truth. (shrink)

Graham Priest (1994) has argued that the following paradoxes all have the same structure: Russell’s Paradox, Burali-Forti’s Paradox, Mirimanoff’s Paradox, König’s Paradox, Berry’s Paradox, Richard’s Paradox, the Liar and Liar Chain Paradoxes, the Knower and Knower Chain Paradoxes, and the Heterological Paradox. Their common structure is given by Russell’s Schema: there is a property φ and function δ such that..

One of Tarski’s stated aims was to give an explication of the classical conception of truth—truth as ‘saying it how it is’. Many subsequent commentators have felt that he achieved this aim. Tarski’s core idea of defining truth via satisfaction has now found its way into standard logic textbooks. This paper looks at such textbook definitions of truth in a model for standard first-order languages and argues that they fail from the point of view of explication of the classical notion (...) of truth. The paper furthermore argues that a subtly different definition—also to be found in classic textbooks but much less prevalent than the kind of definition that proceeds via satisfaction—succeeds from this point of view. (shrink)