Simple models have played an important role in the discussion of foundational issues in statistical mechanics. Among them the spin-echo system is of particular interest since it can be realized experimentally. This has led to inferences being drawn about approaches to the foundations of statistical mechanics, particularly with respect to the use of coarse-graining. We examine these claims with the help of computer simulations.

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)

We offer a new argument for the claim that there can be non-degenerate objective chance (“true randomness”) in a deterministic world. Using a formal model of the relationship between different levels of description of a system, we show how objective chance at a higher level can coexist with its absence at a lower level. Unlike previous arguments for the level-specificity of chance, our argument shows, in a precise sense, that higher-level chance does not collapse into epistemic probability, despite higher-level properties (...) supervening on lower-level ones. We show that the distinction between objective chance and epistemic probability can be drawn, and operationalized, at every level of description. There is, therefore, not a single distinction between objective and epistemic probability, but a family of such distinctions. (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.

Philosophers of science increasingly recognize the importance of idealization: the intentional introduction of distortion into scientific theories. Yet this recognition has not yielded consensus about the nature of idealization. e literature of the past thirty years contains disparate characterizations and justifications, but little evidence of convergence towards a common position.

Emergence is a notorious philosophical term of art. A variety of theorists have appropriated it for their purposes ever since George Henry Lewes gave it a philosophical sense in his 1875 Problems of Life and Mind. We might roughly characterize the shared meaning thus: emergent entities (properties or substances) ‘arise’ out of more fundamental entities and yet are ‘novel’ or ‘irreducible’ with respect to them. (For example, it is sometimes said that consciousness is an emergent property of the brain.) Each (...) of the quoted terms is slippery in its own right, and their specifications yield the varied notions of emergence that we discuss below. There has been renewed interest in emergence within discussions of the behavior of complex systems and debates over the reconcilability of mental causation, intentionality, or consciousness with physicalism. (shrink)

I attempt to get as clear as possible on the chain of reasoning by which irreversible macrodynamics is derivable from time-reversible microphysics, and in particular to clarify just what kinds of assumptions about the initial state of the universe, and about the nature of the microdynamics, are needed in these derivations. I conclude that while a “Past Hypothesis” about the early Universe does seem necessary to carry out such derivations, that Hypothesis is not correctly understood as a constraint on the (...) early Universe’s entropy. (shrink)

The physics of time asymmetry has never been a single well-defined subject, but more a collection of consistency problems which arise in almost all branches ...

Approaches to explanation -- Causal and explanatory relevance -- The kairetic account of /D making -- The kairetic account of explanation -- Extending the kairetic account -- Event explanation and causal claims -- Regularity explanation -- Abstraction in regularity explanation -- Approaches to probabilistic explanation -- Kairetic explanation of frequencies -- Kairetic explanation of single outcomes -- Looking outward -- Looking inward.

The final work of a distinguished physicist, this remarkable volume examines the emotive significance of time, the time order of mechanics, the time direction of thermodynamics and microstatistics, the time direction of macrostatistics, and the time of quantum physics. Coherent discussions include accounts of analytic methods of scientific philosophy in the investigation of probability, quantum mechanics, the theory of relativity, and causality. "[Reichenbach’s] best by a good deal."—Physics Today. 1971 ed.

Suppose that God or a demon informs you of the following future fact: despite recent cosmological evidence, the universe is indeed closed and it will have a ‘final’ instant of time; moreover, at that final moment, all 49 of the world’s Imperial Faberge eggs will be in your bedroom bureau’s sock drawer. You’re absolutely certain that this information is true. All of your other dealings with supernatural powers have demonstrated that they are a trustworthy lot.

Some claim that Non- reductive Physicalism is an unstable position, on grounds that NRP either collapses into reductive physicalism, or expands into emergentism of a robust or ‘strong’ variety. I argue that this claim is unfounded, by attention to the notion of a degree of freedom—roughly, an independent parameter needed to characterize an entity as being in a state functionally relevant to its law-governed properties and behavior. I start by distinguishing three relations that may hold between the degrees of freedom (...) needed to characterize certain special science entities, and those needed to characterize their composing physical entities; these correspond to what I call ‘reductions’, ‘restrictions’, and ‘eliminations’ in degrees of freedom. I then argue that eliminations in degrees of freedom, in particular—when strictly fewer degrees of freedom are required to characterize certain special science entities than are required to characterize their composing physical entities—provide a basis for making sense of how certain special science entities can be both physically acceptable and ontologically irreducible to physical entities. (shrink)

Models are of central importance in many scientific contexts. The centrality of models such as inflationary models in cosmology, general-circulation models of the global climate, the double-helix model of DNA, evolutionary models in biology, agent-based models in the social sciences, and general-equilibrium models of markets in their respective domains is a case in point (the Other Internet Resources section at the end of this entry contains links to online resources that discuss these models). Scientists spend significant amounts of time building, (...) testing, comparing, and revising models, and much journal space is dedicated to interpreting and discussing the implications of models. In short, models are one of the principal instruments of modern science. (shrink)

This is an extensive review of recent work on the foundations of statistical mechanics.

This paper examines contemporary attempts to explicate the explanatory role of mathematics in the physical sciences. Most such approaches involve developing so-called mapping accounts of the relationships between the physical world and mathematical structures. The paper argues that the use of idealizations in physical theorizing poses serious difficulties for such mapping accounts. A new approach to the applicability of mathematics is proposed.

The term ‘emergence’ often causes confusion in science and philosophy, as it is used to express at least two quite different concepts. We can label these concepts _strong_ _emergence_ and _weak emergence_. Both of these concepts are important, but it is vital to keep them separate.

Are there really beliefs? Or are we learning (from neuroscience and psychology, presumably) that, strictly speaking, beliefs are figments of our imagination, items in a superceded ontology? Philosophers generally regard such ontological questions as admitting just two possible answers: either beliefs exist or they don't. There is no such state as quasi-existence; there are no stable doctrines of semi-realism. Beliefs must either be vindicated along with the viruses or banished along with the banshees. A bracing conviction prevails, then, to the (...) effect that when it comes to beliefs (and other mental items) one must be either a realist or an eliminative materialist. (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)

Philosophers of physics are very familiar with foundational problems in quantum mechanics and in the theory of relativity. In both fields, the puzzles, if not solved, are at least reasonably well formulated and possess well-characterized solution strategies. Sklar’s book Physics and Chance focuses on a pair of theories, thermodynamics and statistical mechanics, for which puzzles and foundational paradoxes abound, but where there is very little agreement upon the means with which they may best be approached. As he notes in the (...) introduction. (shrink)

Several modern accounts of explanation acknowledge the importance of abstraction and idealization for our explanatory practice. However, once we allow a role for abstraction, questions remain. I ask whether the relation between explanations at different theoretical levels should be thought of wholly in terms of abstraction, and argue that changes of the quantities in terms of which we describe a system can lead to novel explanations that are not merely abstractions of some more detailed picture. I use the example of (...) phase transitions as described by statistical mechanics and thermodynamics to illustrate this, and to demonstrate some details of the relationship between abstraction, idealization, and novel explanation. (shrink)

It is often supposed that the spectacular successes of our modern mathematical sciences support a lofty vision of a world completely ordered by one single elegant theory. In this book Nancy Cartwright argues to the contrary. When we draw our image of the world from the way modern science works - as empiricism teaches us we should - we end up with a world where some features are precisely ordered, others are given to rough regularity and still others behave in (...) their own diverse ways. This patchwork makes sense when we realise that laws are very special productions of nature, requiring very special arrangements for their generation. Combining classic and newly written essays on physics and economics, The Dappled World carries important philosophical consequences and offers serious lessons for both the natural and the social sciences. (shrink)

This article argues that most of the approaches to the foundations of statistical mechanics have severed their link with the original foundational project, the project of demonstrating how real mechanical systems can behave thermodynamically.

Scientists and philosophers frequently speak about levels of description, levels of explanation, and ontological levels. This paper presents a framework for studying levels. I give a general definition of a system of levels and discuss several applications, some of which refer to descriptive or explanatory levels while others refer to ontological levels. I illustrate the usefulness of this framework by bringing it to bear on some familiar philosophical questions. Is there a 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? Are there emergent higher-level properties? Are higher-level descriptions reducible to lower-level ones? Can the relationship between normative and non-normative domains be viewed as one involving levels? And might a levelled framework shed light on the relationship between third-personal and first-personal phenomena? (shrink)

Statistical mechanics is one of the crucial fundamental theories of physics, and in his new book Lawrence Sklar, one of the pre-eminent philosophers of physics, offers a comprehensive, non-technical introduction to that theory and to attempts to understand its foundational elements. Among the topics treated in detail are: probability and statistical explanation, the basic issues in both equilibrium and non-equilibrium statistical mechanics, the role of cosmology, the reduction of thermodynamics to statistical mechanics, and the alleged foundation of the very notion (...) of time asymmetry in the entropic asymmetry of systems in time. The book emphasises the interaction of scientific and philosophical modes of reasoning, and in this way will interest all philosophers of science as well as those in physics and chemistry concerned with philosophical questions. The book could also be read by an informed general reader interested in the foundations of modern science. (shrink)

Woodward's long awaited book is an attempt to construct a comprehensive account of causation explanation that applies to a wide variety of causal and explanatory claims in different areas of science and everyday life. The book engages some of the relevant literature from other disciplines, as Woodward weaves together examples, counterexamples, criticisms, defences, objections, and replies into a convincing defence of the core of his theory, which is that we can analyse causation by appeal to the notion of manipulation.

This chapter contains sections titled: Introduction: The Problem of Emergence and Reduction The Varieties of Reductionism: Ontological and Epistemological The Reduction and Emergence Debate Today: Specific Cases Seeming to Warrant the Label of Ontological or Epistemological Emergence Questions for Future Research.

It has become something of a dogma in the philosophy of science that modern cosmology has completed Boltzmann's program for explaining the statistical validity of the Second Law of thermodynamics by providing the low entropy initial state needed to ground the asymmetry in entropic behavior that underwrites our inference about the past. This dogma is challenged on several grounds. In particular, it is argued that it is likely that the Boltzmann entropy of the initial state of the universe is an (...) ill-defined or severely hobbled concept. It is also argued that even if the entropy of the initial state of the universe had a well-defined, low value, this would not suffice to explain why thermodynamics works as well as it does for the kinds of systems we care about. Because the role of Boltzmann entropy in our inferences to the past has been vastly overrated, the failure of the Boltzmann program does not pose a serious problem for our knowledge of the past. But it does call a different explanation of why thermodynamics works as well as it does. A suggestion is offered for a different approach. (shrink)

The book is drawn from the Tarner lectures, delivered in Cambridge in 1993. It is concerned with the ultimate nature of reality, and how this is revealed by modern physical theories such as relativity and quantum theory. The objectivity and rationality of science are defended against the views of relativists and social constructionists. It is claimed that modern physics gives us a tentative and fallible, but nevertheless rational, approach to the nature of physical reality. The role of subjectivity in science (...) is examined in the fields of relativity theory, statistical mechanics and quantum theory, and recent claims of an essential role for human consciousness in physics are rejected. Prospects for a 'Theory of Everything' are considered, and the related question of how to assess scientific progress is carefully examined. (shrink)

Many have suggested that the transformation standardly referred to as `time reversal' in quantum theory is not deserving of the name. I argue on the contrary that the standard definition is perfectly appropriate, and is indeed forced by basic considerations about the nature of time in the quantum formalism.

In this paper I first argue that the objection which is most commonly levelled against the coarse-graining approach-viz. that it introduces an element of subjectivity into what ought to be a purely objective formalism-is ultimately unfounded. I then proceed to argue that two different objections to the coarse-graining approach indicate that it is an inadequate approach to statistical mechanics. The first objection is based on the fact that the appeal to appearances by the coarse-graining approach fails to justify the coarse-graining (...) strategy of ignoring the physical differences between so-called quasi-equilibrium distributions and equilibrium distributions. The second objection is centred on the notion of a coarse-grained entropy. I will argue that the required increase in the coarse-grained entropy is obtained by disregarding the dynamical constraints on the system. This undermines the very task statistical mechanics has set out to accomplish, viz. to provide a microdynamical underpinning of thermodynamics. (shrink)

Every process studied in any science other than physics defines an arrow of time – to say nothing for the directedness of the processes of causation, inference, memory, control, and counterfactual dependence that occur in everyday life. The discussion in this chapter is confined to the arrow of time as it occurs in physics. The chapter briefly discusses those features of microscopic physics, which seem to conflict with time asymmetry. It explains just how this conflict plays out in the important (...) context of thermodynamics and statistical mechanics. The chapter then reviews the main strategies available for resolving the conflict between reversible microdynamics and irreversible macrodynamics, working within the context of the quantitative, time‐irreversible evolution laws that seem to apply to large‐scale phenomena. Finally, it offers a broad the discussion covering other arrows of time within physics. (shrink)

Statistical mechanics is one of the crucial fundamental theories of physics, and in his new book Lawrence Sklar, one of the pre-eminent philosophers of physics, offers a comprehensive, non-technical introduction to that theory and to attempts to understand its foundational elements. Among the topics treated in detail are: probability and statistical explanation, the basic issues in both equilibrium and non-equilibrium statistical mechanics, the role of cosmology, the reduction of thermodynamics to statistical mechanics, and the alleged foundation of the very notion (...) of time asymmetry in the entropic asymmetry of systems in time. The book emphasises the interaction of scientific and philosophical modes of reasoning, and in this way will interest all philosophers of science as well as those in physics and chemistry concerned with philosophical questions. The book could also be read by an informed general reader interested in the foundations of modern science. (shrink)