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)

Weak emergence is the view that a system’s macro properties can be explained by its micro properties but only in an especially complicated way. This paper explains a version of weak emergence based on the notion of explanatory incompressibility and “crawling the causal web.” Then it examines three reasons why weak emergence might be thought to be just in the mind. The first reason is based on contrasting mere epistemological emergence with a form of ontological emergence that involves irreducible downward (...) causation. The second reason is based on the idea that attributions of emergence are always a reflection of our ignorance of non-emergent explanations. The third reason is based on the charge that complex explanations are anthropocentric. Rather than being just in the mind, weak emergence is seen to involve a distinctive kind of complex, macro-pattern in the mind-independent objective micro-causal structure that exists in nature. The paper ends by addressing two further questions. One concerns whether weak emergence applies only or mainly to computer simulations and computational systems. The other concerns the respect in which weak emergence is dynamic rather than static. (shrink)

Condensed matter approaches to quantum gravity suggest that spacetime emerges in the low-energy sector of a fundamental condensate. This essay investigates what could be meant by this claim. In particular, I offer an account of low-energy emergence that is appropriate to effective field theories in general, and consider the extent to which it underwrites claims about the emergence of spacetime in effective field theories of condensed matter systems of the type that are relevant to quantum gravity.

This essay considers the extent to which a concept of emergence can be associated with Effective Field Theories (EFTs). I suggest that such a concept can be characterized by microphysicalism and novelty underwritten by the elimination of degrees of freedom from a high-energy theory, and argue that this makes emergence in EFTs distinct from other concepts of emergence in physics that have appeared in the recent philosophical literature.

Introduction: Science and Common Sense Long before the beginnings of modern civilization, men ac- quired vast funds of information about their environment. ...

We survey and clarify some recent appearances of the term ‘emergence’. We distinguish epistemological emergence, which is merely a limitation of descriptive apparatus, from ontological emergence, which should involve causal features of a whole system not reducible to the properties of its parts, thus implying the failure of part/whole reductionism and of mereological supervenience for that system. Are there actually any plausible cases of the latter among the numerous and various mentions of ‘emergence’ in the recent literature? Quantum mechanics seems (...) to offer one, in the Bell properties of entangled particles, but other apparently promising candidates, such as non‐linear dynamical systems investigated by complexity studies and chaos theory, seem on careful analysis to display only epistemological emergence. We examine the consequences for physicalism of admitting ontological emergence in the micro‐physical. (shrink)

Despite all the criticism showered on Nagel’s classic account of reduction, it meets a fundamental desideratum in an analysis of reduction that is difficult to question, namely of providing for a proper identification of the reducing theory. This is not clearly accommodated in radically different accounts. However, the same feature leads me to question Nagel’s claim that the reducing theory can be separated from the putative bridge laws, and thus to question his notion of heterogeneous reduction. A further corollary to (...) the requirement that all the necessary conditions be incorporated in an adequate formulation of the putative reducing theory is that the standard example of gas temperature is not reducible to average molecular kinetic energy. As originally conceived, Nagel’s conception of reduction takes no account of approximate reasoning and this failure has certainly restricted its applicability, perhaps to the point of making it unrealistic as a model of reduction in science. I suggest approximation can be accommodated by weakening the original requirement of deduction without jeopardizing the fundamental desideratum. Finally, I turn to briefly consider the idea sometimes raised of the ontological reducibility of chemistry. (shrink)

This article examines ontological/dynamical aspects of emergence, specifically the micro-macro relation in cases of universal behavior. I discuss superconductivity as an emergent phenomenon, showing why microphysical features such as Cooper pairing are not necessary for deriving characteristic properties such as infinite conductivity. I claim that the difficulties surrounding the thermodynamic limit in explaining phase transitions can be countered by showing how renormalization group techniques facilitate an understanding of the physics behind the mathematics, enabling us to clarify epistemic and ontological aspects (...) of emergence. I close with a discussion of the impact of these issues for questions concerning natural kinds. (shrink)

In Mind in a Physical World (1998), Jaegwon Kim has recently extended his ongoing critique of `non-reductive materialist' positions in philosophy of mind by arguing that Nagel's model of reduction is the wrong paradigm in terms of which to contest the issue of psychophysical reduction, and that an altogether different model of scientific reduction – a functional model of reduction – is needed. In this paper I argue, first, that Kim's conception of the Nagelian model is substantially impoverished and potentially (...) misleading; second, that his own functional model is problematic in several respects; and, third, that the basic idea underlying his functional model can well be accommodated within a properly reinterpreted Nagelian model. I conclude with some reflections on the issue of psychophysical reduction. (shrink)

Unlike the overall framework of Ernest Nagel's work on reduction, his theory of intertheoretic connection still has life in it. It handles aptly cases where reduction requires complex representation of a target domain. Abandoning his formulation as too liberal was a mistake. Arguments that it is too liberal at best touch only Nagel's deductivist theory of explanation, not his condition of connectability. Taking this condition seriously gives a powerful view of reduction, but one which requires us to index explanatory power (...) to sciences as they are formulated at particular times. While we may thereby reduce more than philosophers have supposed, we must abandon hope (as Nagel did) of saying anything useful about reductionism. (shrink)

I critically evaluate the influential new wave account of theory reduction in science developed by Paul Churchland and Clifford Hooker. First, I cast doubt on claims that the new wave account enjoys a number of theoretical virtues over its competitors, such as the ability to represent how false theories are reduced by true theories. Second, I argue that the genuinely novel claim that a corrected theory must be specified entirely by terms from the basic reducing theory is in fact too (...) restrictive for scientific practice and should be rejected. Basic theories co-evolve with nonbasic theories in a mutually interactive way, and thus the basic theories incorporate the concepts and concerns of nonbasic theories. Third, I show that once its ontological consequences are duly noted, the reductive part the new wave account collapses into the classical theory developed within the logical empiricist tradition. As such, it still falls prey to standard anti-reductionist argument based upon multiple realizability and the cross-classification of special science and physical science terms. (shrink)

Weak emergence has been offered as an explication of the ubiquitous notion of emergence used m complexity science After outlining the problem of emergence and comparing weak emergence with the two other weak objectivist approaches to emergence, the paper explains a version of weak emergence and illustrates at with cellular automata Then it explains the sort of downward causation and explanatory autonomy involved m weak emergence.

We survey some philosophical aspects of the search for a quantum theory of gravity, emphasising how quantum gravity throws into doubt the treatment of spacetime common to the two `ingredient theories' (quantum theory and general relativity), as a 4-dimensional manifold equipped with a Lorentzian metric. After an introduction (Section 1), we briefly review the conceptual problems of the ingredient theories (Section 2) and introduce the enterprise of quantum gravity (Section 3). We then describe how three main research programmes in quantum (...) gravity treat four topics of particular importance: the scope of standard quantum theory; the nature of spacetime; spacetime diffeomorphisms, and the so-called `problem of time' (Section 4). These programmes are the old particle-physics approach, superstring theory, and canonical quantum gravity. By and large, these programmes accept most of the ingredient theories' treatment of spacetime, albeit with a metric with some type of quantum nature; but they also suggest that the treatment has fundamental limitations. This prompts the idea of going further: either by quantizing structures other than the metric, such as the topology; or by regarding such structures as phenomenological. We discuss this in Section 5. (shrink)

This thesis gives a philosophical assessment of a contemporary movement, influential amongst physicists, about the status of microscopic and macroscopic properties. The fountainhead for the movement was a short 1972 paper `More is Different', written by the condensed-matter physicist, Philip Anderson. Each of the chapters is concerned with themes mentioned in that paper, or subsequently expounded by Anderson and his followers. In Chapter 1, I aim to locate Anderson's existence claims for `emergent properties' within the metaphysical, epistemological and methodological doctrines (...) that identify themselves as `emergentist'. I argue, against the commentators' consensus, that the New Emergentists make claims about the metaphysical status of physical properties, and should not be read as concerned only with matters of research methodology for physics. In Chapter 2, I look at the physical examples that the New Emergentists appeal to, and propose a way of formulating their main claims within modern analytic metaphysics. I argue that it is possible to view their thesis as an updated version of `British Emergentism' a movement popular in the early years of the twentieth century. I support this contention by comparing examples of emergent properties put forward by the British and the New Emergentists. Chapter 3 is a discussion of the significance of renormalisation techniques. I attack a set of claims by Robert Batterman, who presents renormalisation as an explanatory strategy unrecognised by the philosophy of science. I separate several different methods of renormalisation analysis, and argue that he has conflated them. In Chapter 4, I discuss the theoretical representation of phase transitions in condensed matter physics; in particular, their appeal to the limit of an infinite system. I examine and refute various claims to the effect that the ineliminability of this limit in modelling phase transitions is of great metaphysical significance. I suggest a definition of phase transitions for finite systems that dissolves this illusion, and gives us reason to trust the results of the theories that only apply in the infinite limit. %I then comment on the significance of these results for a suggestion of Laura Ruetsche, that quantum statistical mechanics should be used as a guide to the interpretation of quantum field theory. Chapter 5 revisits the doctrines of the New Emergentists in order to place their views within some wider philosophical debates. I look at how their doctrines bear on issues in the interpretation of quantum mechanics, in the philosophy of mind and the philosophy of science. I close by returning to the context within physics, in which the New Emergentists originally made their presence felt: the controversy over whether elementary particle physics should enjoy greater status than other areas. (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)