Reductionism is often understood to include two theses: (1) every singular occurrence that the special sciences can explain also can be explained by physics; (2) every law in a higher-level science can be explained by physics. These claims are widely supposed to have been refuted by the multiple realizability argument, formulated by Putnam (1967, 1975) and Fodor (1968, 1975). The present paper criticizes the argument and identifies a reductionistic thesis that follows from one of the argument's premises.

This paper analyses the anti-reductionist argument from renormalisation group explanations of universality, and shows how it can be rebutted if one assumes that the explanation in question is captured by the counterfactual dependence account of explanation.

I analyze the extent to which classical phase transitions, both first order and continuous, pose a challenge for intertheoretic reduction. My contention is that phase transitions are compatible with a notion of reduction that combines Nagelian reduction and what Thomas Nickles called Reduction2. I also argue that, even if the same approach to reduction applies to both types of phase transitions, there is a crucial difference in their physical treatment: in addition to the thermodynamic limit, in continuous phase transitions there (...) is a second infinite limit involved, which marks an important difference in the reduction of first-order and continuous phase transitions. (shrink)

It is proposed that we use the term “approximation” for inexact description of a target system and “idealization” for another system whose properties also provide an inexact description of the target system. Since systems generated by a limiting process can often have quite unexpected, even inconsistent properties, familiar limit systems used in statistical physics can fail to provide idealizations, but are merely approximations. A dominance argument suggests that the limiting idealizations of statistical physics should be demoted to approximations.

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)

Despite the close connection between the central limit theorem and renormalization group (RG) methods, the latter should be considered fundamentally distinct from the kind of probabilistic framework associated with statistical mechanics, especially the notion of averaging. The mathematics of RG is grounded in dynamical systems theory rather than probability, which raises important issues with respect to the way RG generates explanations of physical phenomena. I explore these differences and show why RG methods should be considered not just calculational tools but (...) the basis for a physical understanding of complex systems in terms of structural properties and relations. (shrink)

It is commonly claimed that the universality of critical phenomena is explained through particular applications of the renormalization group. This article has three aims: to clarify the structure of the explanation of universality, to discuss the physics of such RG explanations, and to examine the extent to which universality is thus explained. The derivation of critical exponents proceeds via a real-space or a field-theoretic approach to the RG. Building on work by Mainwood, this article argues that these approaches ought to (...) be distinguished: while the field-theoretic approach explains universality, the real-space approach fails to provide an adequate explanation. (shrink)

This paper investigates the consequences for our understanding of physical theories as a result of the development of the renormalization group. Kadanoff's assessment of these consequences is discussed. What he called the ``extended singularity theorem'' poses serious difficulties for philosophical interpretation of theories. Several responses are discussed. The resolution demands a philosophical rethinking of the role of mathematics in physical theorizing.

This paper concerns what Jerry Fodor calls a 'metaphysical mystery': How can there by macroregularities that are realized by wildly heterogeneous lower level mechanisms? But the answer to this question is not as mysterious as many, including Jaegwon Kim, Ned Block, and Jerry Fodor might think. The multiple realizability of the properties of the special sciences such as psychology is best understood as a kind of universality, where 'universality' is used in the technical sense one finds in the physics literature. (...) It is argued that the same explanatory strategy used by physicists to provide understanding of universal behavior in physics can be used to explain how special science properties can be heterogeneously multiply realized. (shrink)

This paper looks at emergence in physical theories and argues that an appropriate way to understand socalled “emergent protectorates” is via the explanatory apparatus of the renormalization group. It is argued that mathematical singularities play a crucial role in our understanding of at least some well-defined emergent features of the world.

This paper aims to draw attention to an explanatory problem posed by the existence of multiply realized or universal behavior exhibited by certain physical systems. The problem is to explain how it is possible that systems radically distinct at lower-scales can nevertheless exhibit identical or nearly identical behavior at upper-scales. Theoretically this is reflected by the fact that continuum theories such as fluid mechanics are spectacularly successful at predicting, describing, and explaining fluid behaviors despite the fact that they do not (...) recognize the discrete nature of fluids. A standard attempt to reduce one theory to another, is shown to fail to answer the appropriate question about autonomy. (shrink)

Phase transitions are an important instance of putatively emergent behavior. Unlike many things claimed emergent by philosophers, the alleged emergence of phase transitions stems from both philosophical and scientific arguments. Here we focus on the case for emergence built from physics, in particular, arguments based upon the infinite idealization invoked in the statistical mechanical treatment of phase transitions. After teasing apart several challenges, we defend the idea that phase transitions are best thought of as conceptually novel, but not ontologically or (...) explanatorily irreducible to finite physics; indeed, by looking at ongoing work on “smooth phase transitions” we even suggest that they’re not even conceptually novel. In the case of renormalization group theory, consideration of infinite systems and their singular behavior provides a central theoretical tool, but this is compatible with an explanatory reduction. Phase transitions may be “emergent” in some sense of this protean term, but not in a sense that is incompatible with the reductionist project broadly construed. (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)

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)

In this paper, I analyze the extent to which classical phase transitions, especially continuous phase transitions, impose a challenge for reduction- ism. My main contention is that classical phase transitions are compatible with reduction, at least with the notion of limiting reduction, which re- lates the behavior of physical quantities in different theories under certain limiting conditions. I argue that this conclusion follows even after rec- ognizing the existence of two infinite limits involved in the treatment of continuous phase transitions.