This book presents the concept of “complementary science” which contributes to scientific knowledge through historical and philosophical investigations. It emphasizes the fact that many simple items of knowledge that we take for granted were actually spectacular achievements obtained only after a great deal of innovative thinking, painstaking experiments, bold conjectures, and serious controversies. Each chapter in the book consists of two parts: a narrative part that states the philosophical puzzle and gives a problem-centred narrative on the historical attempts to solve (...) the puzzle; and the analysis part which provides in-depth analyses of certain scientific, historical, and philosophical aspects of the story. (shrink)

In this important new study Ian Hacking continues the enquiry into the origins and development of certain characteristic modes of contemporary thought undertaken in such previous works as his best selling Emergence of Probability. Professor Hacking shows how by the late nineteenth century it became possible to think of statistical patterns as explanatory in themselves, and to regard the world as not necessarily deterministic in character. Combining detailed scientific historical research with characteristic philosophic breath and verve, The Taming of Chance (...) brings out the relations among philosophy, the physical sciences, mathematics and the development of social institutions, and provides a unique and authoritative analysis of the "probabilization" of the Western world. (shrink)

Historical records show that there was no real concept of probability in Europe before the mid-seventeenth century, although the use of dice and other randomizing objects was commonplace. Ian Hacking presents a philosophical critique of early ideas about probability, induction, and statistical inference and the growth of this new family of ideas in the fifteenth, sixteenth, and seventeenth centuries. Hacking invokes a wide intellectual framework involving the growth of science, economics, and the theology of the period. He argues that the (...) transformations that made it possible for probability concepts to emerge have constrained all subsequent development of probability theory and determine the space within which philosophical debate on the subject is still conducted. First published in 1975, this edition includes an introduction that contextualizes his book in light of developing philosophical trends. Ian Hacking is the winner of the Holberg International Memorial Prize 2009. (shrink)

The basic theme of Popper's philosophy--that something can come from nothing--is related to the present situation in physical theory. Popper carries his investigation right to the center of current debate in quantum physics. He proposes an interpretation of physics--and indeed an entire cosmology--which is realist, conjectural, deductivist and objectivist, anti-positivist, and anti-instrumentalist. He stresses understanding, reminding us that our ignorance grows faster than our conjectural knowledge.

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)

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)

This paper discusses the mistake of understanding the laws and concepts of thermodynamics too literally in the foundations of statistical mechanics. Arguing that this error is still made in subtle ways, the article explores its occurrence in three examples: the Second Law, the concept of equilibrium and the definition of phase transitions.

The aim of this article is to analyse the relation between the second law of thermodynamics and the so-called arrow of time. For this purpose, a number of different aspects in this arrow of time are distinguished, in particular those of time-reversal (non-)invariance and of (ir)reversibility. Next I review versions of the second law in the work of Carnot, Clausius, Kelvin, Planck, Gibbs, Caratheodory and Lieb and Yngvason, and investigate their connection with these aspects of the arrow of time. It (...) is shown that this connection varies a great deal along with these formulations of the second law. According to the famous formulation by Planck, the second law expresses the irreversibility of natural processes. But in many other formulations irreversibility or even time-reversal non-invariance plays no role. I therefore argue for the view that the second law has nothing to do with the arrow of time. (shrink)

Thermodynamics and Statistical Mechanics are related to one another through the so-called "thermodynamic limit'' in which, roughly speaking the number of particles becomes infinite. At critical points (places of physical discontinuity) this limit fails to be regular. As a result, the "reduction'' of Thermodynamics to Statistical Mechanics fails to hold at such critical phases. This fact is key to understanding an argument due to Craig Callender to the effect that the thermodynamic limit leads to mistakes in Statistical Mechanics. I discuss (...) this argument and argue that the conclusion is misguided. In addition, I discuss an analogous example where a genuine physical discontinuity---the breaking of drops---requires the use of infinite idealizations. (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.

In the last quarter of the nineteenth century, Ludwig Boltzmann explained how irreversible macroscopic laws, in particular the second law of thermodynamics, originate in the time-reversible laws of microscopic physics. Boltzmann’s analysis, the essence of which I shall review here, is basically correct. The most famous criticisms of Boltzmann’s later work on the subject have little merit. Most twentieth century innovations – such as the identification of the state of a physical system with a probability distribution on its phase space, (...) of its thermodynamic entropy with the Gibbs entropy of , and the invocation of the notions of ergodicity and mixing for the justification of the foundations of statistical mechanics – are thoroughly misguided. (shrink)

A popular and plausible response against Laudan's “pessimistic induction” has been what I call “preservative realism,” which argues that there have actually been enough elements of scientific knowledge preserved through major theory‐change processes, and that those elements can be accepted realistically. This paper argues against preservative realism, in particular through a critical review of Psillos's argument concerning the case of the caloric theory of heat. Contrary to his argument, the historical record of the caloric theory reveals that beliefs about the (...) properties of material caloric, rejected by subsequent theories, were indeed central to the successes of the caloric theory. Therefore caloric remains a favorable case for Laudan. Further, I argue that even confirmed cases of preservation do not warrant an inference to truth. (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 is rejected. Prospects for a 'Theory of Everything' are considered, and the related question of how to assess scientific progress is carefully examined. (shrink)

This paper investigates what the source of time-asymmetry is in thermodynamics, and comments on the question whether a time-symmetric formulation of the Second Law is possible.

For the generalizations of thermodynamics to obtain, it appears that a very ‘special’ initial condition of the universe is required. Is this initial condition itself in need of explanation? I argue that it is not. In so doing, I offer a framework in which to think about ‘special’ initial conditions in all areas of science, though I concentrate on the case of thermodynamics. I urge the view that it is not always a serious mark against a theory that it must (...) posit an ‘improbable’ initial condition. (shrink)

We argue that, contrary to some analyses in the philosophy of science literature, ergodic theory falls short in explaining the success of classical equilibrium statistical mechanics. Our claim is based on the observations that dynamical systems for which statistical mechanics works are most likely not ergodic, and that ergodicity is both too strong and too weak a condition for the required explanation: one needs only ergodic-like behaviour for the finite set of observables that matter, but the behaviour must ensure that (...) the approach to equilibrium for these observables is on the appropriate time-scale. (shrink)

Why does classical equilibrium statistical mechanics work? Malament and Zabell (1980) noticed that, for ergodic dynamical systems, the unique absolutely continuous invariant probability measure is the microcanonical. Earman and Rédei (1996) replied that systems of interest are very probably not ergodic, so that absolutely continuous invariant probability measures very distant from the microcanonical exist. In response I define the generalized properties of epsilon-ergodicity and epsilon-continuity, I review computational evidence indicating that systems of interest are epsilon-ergodic, I adapt Malament and Zabell’s (...) defense of absolute continuity to support epsilon-continuity, and I prove that, for epsilon-ergodic systems, every epsilon-continuous invariant probability measure is very close to the microcanonical. (shrink)

Landauer’s principle is the loosely formulated notion that the erasure of n bits of information must always incur a cost of k ln n in thermodynamic entropy. It can be formulated as a precise result in statistical mechanics, but for a restricted class of erasure processes that use a thermodynamically irreversible phase space expansion, which is the real origin of the law’s entropy cost and whose necessity has not been demonstrated. General arguments that purport to establish the unconditional validity of (...) the law fail. They turn out to depend on the illicit formation of a canonical ensemble from memory devices holding random data. To exorcise Maxwell’s demon one must show that all candidate devices—the ordinary and the extraordinary—must fail to reverse the second law of thermodynamics. The theorizing surrounding Landauer’s principle is too fragile and too tied to a few specific examples to support such general exorcism. Charles Bennett’s recent extension of Landauer’s principle to the merging of computational paths fails for the same reasons as trouble the original principle. (shrink)

Landauer's principle, often regarded as the basic principle of the thermodynamics of information processing, holds that any logically irreversible manipulation of information, such as the erasure of a bit or the merging of two computation paths, must be accompanied by a corresponding entropy increase in non-information-bearing degrees of freedom of the information-processing apparatus or its environment. Conversely, it is generally accepted that any logically reversible transformation of information can in principle be accomplished by an appropriate physical mechanism operating in a (...) thermodynamically reversible fashion. These notions have sometimes been criticized either as being false, or as being trivial and obvious, and therefore unhelpful for purposes such as explaining why Maxwell's Demon cannot violate the second law of thermodynamics. Here I attempt to refute some of the arguments against Landauer's principle, while arguing that although in a sense it is indeed a straightforward consequence or restatement of the Second Law, it still has considerable pedagogic and explanatory power, especially in the context of other influential ideas in nineteenth and twentieth century physics. Similar arguments have been given by Jeffrey Bub. (shrink)

We propose an "explanation scheme" for why the Gibbs phase average technique in classical equilibrium statistical mechanics works. Our account emphasizes the importance of the Khinchin-Lanford dispersion theorems. We suggest that ergodicity does play a role, but not the one usually assigned to it.

This book is devoted to a thorough analysis of the role that models play in the practise of physical theory. The authors, a mathematical physicist and a philosopher of science, appeal to the logicians’ notion of model theory as well as to the concepts of physicists.

The concept of classical indistinguishability is analyzed and defended against a number of well-known criticisms, with particular attention to the Gibbs’paradox. Granted that it is as much at home in classical as in quantum statistical mechanics, the question arises as to why indistinguishability, in quantum mechanics but not in classical mechanics, forces a change in statistics. The answer, illustrated with simple examples, is that the equilibrium measure on classical phase space is continuous, whilst on Hilbert space it is discrete. The (...) relevance of names, or equivalently, properties stable in time that can be used as names, is also discussed. (shrink)

Some philosphers of science of an empiricist and pragmatist bent have proposed models of statistical explanation, but have then become sceptical of the adequacy of these models. It is argued that general considerations concerning the purpose of function of explanation in science which are usually appealed to by such philosophers show that their scepticism is not well taken; for such considerations provide much the same rationale for the search for statistical explanations, as these philosophers have characterized them, as they do (...) for lawlike explanations. But, it is further argued, a significant piece of what is frequently offered as an explanation of well known phenomena in statistical mechanics, fails to meet this general "pragmatic rationale" for statistical, or indeed any kind of, explanation. The question then arises whether the physicists have misconstrued the value of this piece of physical theorizing, ergodic theory, taking it to be explanatory when it is actually not; or whether, instead, the philosopher's account of just what is genuinely explanatory is too narrow. (shrink)

Phase transitions are well-understood phenomena in thermodynamics (TD), but it turns out that they are mathematically impossible in finite SM systems. Hence, phase transitions are truly emergent properties. They appear again at the thermodynamic limit (TL), i.e., in infinite systems. However, most, if not all, systems in which they occur are finite, so whence comes the justification for taking TL? The problem is then traced back to the TD characterization of phase transitions, and it turns out that the characterization is (...) the result of serious idealizations which under suitable circumstances approximate actual conditions. (shrink)

We introduce a simple model for so-called spin-echo experiments. We show that the model is a mincing system. On the basis of this model we study fine-grained entropy and coarse-grained entropy descriptions of these experiments. The coarse-grained description is shown to be unable to provide an explanation of the echo signals, as a result of the way in which it ignores dynamically generated correlations. This conclusion is extended to the general debate on the foundations of statistical mechanics. We emphasize the (...) need for an appropriate mechanism to explain the gradual suppression over time of the correlations in a thermodynamic system. We argue that such a mechanism can only be provided by the interventionist approach, in which the interaction of the system with its environment is taken into account. Irreversible behavior is then seen to arise not as a result of limited measurement accuracy , but as a result of the fact that thermodynamic systems are limited systems which interact with their environment. A detailed discussion is given of recent objections to the interventionist approach in the literature. (shrink)

Not limited to merely mathematics, probability has a rich and controversial philosophical aspect. _A Philosophical Introduction to Probability_ showcases lesser-known philosophical notions of probability and explores the debate over their interpretations. Galavotti traces the history of probability and its mathematical properties and then discusses various philosophical positions on probability, from the Pierre Simon de Laplace's “classical” interpretation of probability to the logical interpretation proposed by John Maynard Keynes. This book is a valuable resource for students in philosophy and mathematics and (...) all readers interested in notions of probability. (shrink)

The principle of maximum entropy is a general method to assign values to probability distributions on the basis of partial information. This principle, introduced by Jaynes in 1957, forms an extension of the classical principle of insufficient reason. It has been further generalized, both in mathematical formulation and in intended scope, into the principle of maximum relative entropy or of minimum information. It has been claimed that these principles are singled out as unique methods of statistical inference that agree with (...) certain compelling consistency requirements. This paper reviews these consistency arguments and the surrounding controversy. It is shown that the uniqueness proofs are flawed, or rest on unreasonably strong assumptions. A more general class of inference rules, maximizing the so-called Re[acute ]nyi entropies, is exhibited which also fulfill the reasonable part of the consistency assumptions. (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)

The principle of maximum entropy is a method for assigning values to probability distributions on the basis of partial information. In usual formulations of this and related methods of inference one assumes that this partial information takes the form of a constraint on allowed probability distributions. In practical applications, however, the information consists of empirical data. A constraint rule is then employed to construct constraints on probability distributions out of these data. Usually one adopts the rule that equates the expectation (...) values of certain functions with their empirical averages. There are, however, various other ways in which one can construct constraints from empirical data, which makes the maximum entropy principle lead to very different probability assignments. This paper shows that an argument by Jaynes to justify the usual constraint rule is unsatisfactory and investigates several alternative choices. The choice of a constraint rule is also shown to be of crucial importance to the debate on the question whether there is a conflict between the methods of inference based on maximum entropy and Bayesian conditionalization. (shrink)

On an influential account, chaos is explained in terms of random behaviour; and random behaviour in turn is explained in terms of having positive Kolmogorov-Sinai entropy (KSE). Though intuitively plausible, the association of the KSE with random behaviour needs justification since the definition of the KSE does not make reference to any notion that is connected to randomness. I provide this justification for the case of Hamiltonian systems by proving that the KSE is equivalent to a generalized version of Shannon's (...) communication-theoretic entropy under certain plausible assumptions. I then discuss consequences of this equivalence for randomness in chaotic dynamical systems. Introduction Elements of dynamical systems theory Entropy in communication theory Entropy in dynamical systems theory Comparison with other accounts Product versus process randomness. (shrink)

Classic work on probability which contains the study of the famous paradox of Bertrand. Extensive preface deals with laws of chance.