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)

Available for the first time in 20 years, here are two important works from the 1920s by the best-known representative of the Vienna Circle.

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 that is novel. Here, my aim is again to reconcile reduction and emergence, for a case which is apparently more problematic than those I treated before: renormalization. My main point is that renormalizability being a generic feature 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. (shrink)

This is a companion to another paper. Together they rebut two widespread philosophical doctrines about emergence. The first, and main, doctrine is that emergence is incompatible with reduction. The second is that emergence is supervenience; or more exactly, supervenience without reduction.In the other paper, I develop these rebuttals in general terms, emphasising the second rebuttal. Here I discuss the situation in physics, emphasising the first rebuttal. I focus on limiting relations between theories and illustrate my claims with four examples, each (...) of them a model or a framework for modelling, from well-established mathematics or physics.I take emergence as behaviour that is novel and robust relative to some comparison class. I take reduction as, essentially, deduction. The main idea of my first rebuttal will be to perform the deduction after taking a limit of some parameter. Thus my first main claim will be that in my four examples (and many others), we can deduce a novel and robust behaviour, by taking the limit N→∞ of a parameter N.But on the other hand, this does not show that the N=∞ limit is “physically real”, as some authors have alleged. For my second main claim is that in these same examples, there is a weaker, yet still vivid, novel and robust behaviour that occurs before we get to the limit, i.e. for finite N. And it is this weaker behaviour which is physically real.My examples are: the method of arbitrary functions (in probability theory); fractals (in geometry); superselection for infinite systems (in quantum theory); and phase transitions for infinite systems (in statistical mechanics). (shrink)

This is one of two papers about emergence, reduction and supervenience. It expounds these notions and analyses the general relations between them. The companion paper analyses the situation in physics, especially limiting relations between physical theories. I shall take emergence as behaviour that is novel and robust relative to some comparison class. I shall take reduction as deduction using appropriate auxiliary definitions. And I shall take supervenience as a weakening of reduction, viz. to allow infinitely long definitions. The overall claim (...) of this paper will be that emergence is logically independent both of reduction and of supervenience. In particular, one can have emergence with reduction, as well as without it; and emergence without supervenience, as well as with it. Of the subsidiary claims, the four main ones are: : I defend the traditional Nagelian conception of reduction ; : I deny that the multiple realizability argument causes trouble for reductions, or ``reductionism'' ; : I stress the collapse of supervenience into deduction via Beth's theorem ; : I adapt some examples already in the literature to show supervenience without emergence and vice versa. (shrink)

We examine cases of emergent behavior in physics, and argue for an account of emergence based on features of the phase space portraits of certain dynamical systems. On our account, the phase space portraits of systems displaying emergent behavior are topologically inequivalent to those of the systems from which they ‘emerge’. This account gives us an objective sense in which emergent phenomena are qualitatively novel, without involving the difficulties associated with downward causation and the like. We also argue that the (...) role of complexity in emergence has been overstated: emergent behavior can occur in very simple systems, and even when it occurs in complex systems it is the qualitative novelty of that behavior, rather that the complexity of the system, that matters for emergence. (shrink)

Research in quantum gravity strongly suggests that our world in not fundamentally spatiotemporal, but that spacetime may only emerge in some sense from a non-spatiotemporal structure, as this paper illustrates in the case of causal set theory and loop quantum gravity. This would raise philosophical concerns regarding the empirical coherence and general adequacy of theories in quantum gravity. If it can be established, however, that spacetime emerges in the appropriate circumstances and how all its relevant aspects are explained in fundamental (...) non-spatiotemporal terms, then the challenge is fully met. It is argued that a form of spacetime functionalism offers the most promising template for this project. (shrink)

Among the very architects of the recent re-emergence of emergentism in the physical sciences, Robert B. Laughlin certainly occupies a prominent place. Through a series of works beginning as early as his Nobel lecture in 1998, a lecture given after having been awarded, together with Störmer and Tsui, the Nobel prize in physics for its contribution in the elucidation of the fractional quantum Hall effect, Laughlin openly and relentlessly advocated a strongly anti-reductionistic view of physics – and, more particularly, of (...) the interface between condensed matter and particles physics – which culminated in what can be considered his emergentist manifesto: A Different Universe. Reinventing Physics from the Bottom Down (2005). In spite of this prominent role in the vindication of emergentism, rare are the philosophers, among whom even those sympathetic to the idea of emergence, who have paid serious attention to Laughlin’s insights. The subtleties of his view – it is true, often concealed in many technicalities – have accordingly, and somewhat unfortunately, mainly passed unnoticed. (shrink)

Emergence develops a novel account of diachronic ontological emergence called transformational emergence and locates it in an established historical framework. The author shows how many problems affecting ontological emergence result from a dominant but inappropriate metaphysical tradition and provides a comprehensive assessment of current theories of emergence.

This book discusses the notion that quantum gravity may represent the "breakdown" of spacetime at extremely high energy scales. If spacetime does not exist at the fundamental level, then it has to be considered "emergent", in other words an effective structure, valid at low energy scales. The author develops a conception of emergence appropriate to effective theories in physics, and shows how it applies (or could apply) in various approaches to quantum gravity, including condensed matter approaches, discrete approaches, and loop (...) quantum gravity. (shrink)

The traditional way of thinking about science goes back to the corpuscular philosophy with its micro-reductive mechanism and metaphor of reading God's Book of Nature. This "story-1" with its rhetoric of exact truths contrasts with "story-2" which describes science as a continuation of the always imperfect powers of representation given to us by evolution. On story-2 reduction is one among other knowledge fashioning strategies and shares the imperfections of all human knowledge. When we appreciate that human knowledge always admits of (...) refinement, what appear as "emergent properties" no long seems mysterious. (shrink)

The intimate relationship between X and Y consists in the existence of (metaphysically) necessary truths correlating their occurrences/existences/instantiations. E would be in some sense “overdetermined” if caused by both X and Y.2 Some philosophers say this would be bad, that this cannot or does not happen, that we should construct theories ruling it out, at least in certain cases.3 But why? Given the necessary truths correlating objects and their parts, objects and events concerning those objects, physical and supervenient mental properties, (...) and so on, X and Y do both seem to be causes of E. Should we say that a baseball.. (shrink)

This paper looks at the nature of idealizations and representational structures appealed to in the context of the fractional quantum Hall effect, specifically, with respect to the emergence of anyons and fractional statistics. Drawing on an analogy with the Aharonov–Bohm effect, it is suggested that the standard approach to the effects— the topological approach to fractional statistics—relies essentially on problematic idealizations that need to be revised in order for the theory to be explanatory. An alternative geometric approach is outlined and (...) endorsed. Roles for idealizations in science, as well as consequences for the debate revolving around so-called essential idealizations, are discussed. (shrink)

Various claims regarding intertheoretic reduction, weak and strong notions of emergence, and explanatory fictions have been made in the context of first-order thermodynamic phase transitions. By appealing to John Norton’s recent distinction between approximation and idealization, I argue that the case study of anyons and fractional statistics, which has received little attention in the philosophy of science literature, is more hospitable to such claims. In doing so, I also identify three novel roles that explanatory fictions fulfill in science. Furthermore, I (...) scrutinize the claim that anyons, as they are ostensibly manifested in the fractional quantum Hall effect, are emergent entities and urge caution. Consequently, it is suggested that a particular notion of strong emergence signals the need for the development of novel physical–mathematical research programs. (shrink)

This paper explicates two notions of emergencewhich are based on two ways of distinguishinglevels of properties for dynamical systems.Once the levels are defined, the strategies ofcharacterizing the relation of higher level to lower levelproperties as diachronic and synchronic emergenceare the same. In each case, the higher level properties aresaid to be emergent if they are novel or irreducible with respect to the lower level properties. Novelty andirreducibility are given precise meanings in terms of the effectsthat the change of a bifurcation (...) or perturbation parameterin the system has. (The same strategy can be applied to otherways of separating levels of properties, like themicro/macro distinction.)The notions of emergence developed here are notions of emergencein a weak sense: the higher level emergent properties wecapture are always structural properties (or are realized insuch properties), that is, they are defined in terms of the lowerlevel properties and their relations. Diachronic and synchronicemergent properties are distinctions within thecategory of structural properties. (shrink)

In the philosophy of the analytical tradition, set theory and formal logic are familiar formal tools. I think there is no deep reason why the philosopher’s tool kit should be restricted to just these theories. It might well be the case—to generalize a dictum of Suppes concerning philosophy of science—that the appropriate formal device for doing philosophy is mathematics in general; it may be set theory, algebra, topology, or any other realm of mathematics. In this paper I want to employ (...) elementary topological considerations to shed new light on the intricate problem of the relation of qualities and similarity. Thereby I want to make plausible the general thesis that topology might be a useful device for matters epistemological. (shrink)

Scientists and philosophers frequently speak about levels of description, levels of explanation, and ontological levels. In this paper, I propose a unified framework for modelling levels. I give a general definition of a system of levels and show that it can accommodate descriptive, explanatory, and ontological notions of levels. I further illustrate the usefulness of this framework by applying it to some salient philosophical questions: (1) Is there a linear hierarchy of levels, with a fundamental level at the bottom? And (...) what does the answer to this question imply for physicalism, the thesis that everything supervenes on the physical? (2) Are there emergent properties? (3) Are higher-level descriptions reducible to lower-level ones? (4) Can the relationship between normative and non-normative domains be viewed as one involving levels? Although I use the terminology of “levels”, the proposed framework can also represent “scales”, “domains”, or “subject matters”, where these are not linearly but only partially ordered by relations of supervenience or inclusion. (shrink)

A similarity relation is a reflexive and symmetric binary relation between objects. Similarity is relative: it depends on the set of properties of objects used in determining their similarity or dissimilarity. A multi-modal logical language for reasoning about relative similarities is presented. The modalities correspond semantically to the upper and lower approximations of a set of objects by similarity relations corresponding to all subsets of a given set of properties of objects. A complete deduction system for the language is presented.

I discuss here a number of different kinds of diachronic emergence, noting that they differ in important ways from synchronic conceptions. I argue that Bedau’s weak emergence has an essentially historical aspect, in that there can be two indistinguishable states, one of which is weakly emergent, the other of which is not. As a consequence, weak emergence is about tokens, not types, of states. I conclude by examining the question of whether the concept of weak emergence is too weak and (...) note that there is at present no unifying account of diachronic and synchronic concepts of emergence. (shrink)

A framework for representing a specific kind of emergent property instance is given. A solution to a generalized version of the exclusion argument is then provided and it is shown that upwards and downwards causation is unproblematical for that kind of emergence. One real example of this kind of emergence is briefly described and the suggestion made that emergence may be more common than current opinions allow.

This paper examines two cosmological models of quantum gravity to investigate the foundational and conceptual issues arising from quantum treatments of the big bang. While the classical singularity is erased, the quantum evolution that replaces it may not correspond to classical spacetime: it may instead be a non-spatiotemporal region, which somehow transitions to a spatiotemporal state. The different kinds of transition involved are partially characterized, the concept of a physical transition without time is investigated, and the problem of empirical incoherence (...) for regions without spacetime is discussed. (shrink)

In this paper, we put forward a new account of emergence called “transformational emergence”. Such an account captures a variety of emergence that can be considered as being diachronic and weakly ontological. The fact that transformational emergence actually constitutes a genuine form of emergence is motivated. Besides, the account is free of traditional problems surrounding more usual, synchronic versions of emergence, and it can find a strong empirical support in a specific physical phenomenon, the fractional quantum Hall effect, which has (...) long been touted as a paradigmatic case of emergence. (shrink)

Emergence develops a novel account of diachronic ontological emergence called transformational emergence and locates it in an established historical framework. The author shows how many problems affecting ontological emergence result from a dominant but inappropriate metaphysical tradition and provides a comprehensive assessment of current theories of emergence.

The concept of emergence is commonly invoked in modern physics but rarely defined. Building on recent influential work by Jeremy Butterfield, I provide precise definitions of emergence concepts as they pertain to properties represented in models, applying them to some basic examples from space-time and thermostatistical physics. The chief formal innovation I employ, similarity structure, consists in a structured set of similarity relations among those models under analysis—and their properties—and is a generalization of topological structure. Although motivated from physics, this (...) similarity-structure-based account of emergence applies to any science that represents its possibilia with models. (shrink)

Since it was first published, Quantum Field Theory in a Nutshell has quickly established itself as the most accessible and comprehensive introduction to this profound and deeply fascinating area of theoretical physics. Now in this fully revised and expanded edition, A. Zee covers the latest advances while providing a solid conceptual foundation for students to build on, making this the most up-to-date and modern textbook on quantum field theory available. -/- This expanded edition features several additional chapters, as well as (...) an entirely new section describing recent developments in quantum field theory such as gravitational waves, the helicity spinor formalism, on-shell gluon scattering, recursion relations for amplitudes with complex momenta, and the hidden connection between Yang-Mills theory and Einstein gravity. Zee also provides added exercises, explanations, and examples, as well as detailed appendices, solutions to selected exercises, and suggestions for further reading. (shrink)

The notion of fundamentality, as it is used in metaphysics, aims to capture the idea that there is something basic or primitive in the world. This metaphysical notion is related to the vernacular use of “fundamental”, but philosophers have also put forward various technical definitions of the notion. Among the most influential of these is the definition of absolute fundamentality in terms of ontological independence or ungroundedness. Accordingly, the notion of fundamentality is often associated with these two other technical notions.

There are a wide variety of theories of causation available in the philosophical literature. For the philosopher working in philosophy of mind, who makes use of causal concepts, what is to be made of this embarrassment of riches? By considering a variety of theoretical perspectives, she can discover which principles or assumptions about causation are robust, and which hold only within particular frameworks. In particular, she should be suspicious when the different premises in an argument can only be made true (...) by shifting between different theories of causation. I illustrate these themes using the causal exclusion argument. (shrink)