The baker's transformation is one of the earliest and simplest examples of a bijective mixing transformation. By determining its cycle structure, we show that this transformation is not embeddable in any flow, i.e., one-parameter semigroup, on the nonnegative rationals and,a fortiori, not emdeddable in any flow on the reals.

Recently, P. D. Finch and R. Groblicki determined all bivariate probability densities with specified margins. We point out that their result follows immediately from the complete solution to the problem of determining all n-dimensional cumulative probability distribution functions with specified one-dimensional margins, which was solved by one of us in 1959.

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)

In this book, Lawrence Sklar demonstrates the interdependence of science and philosophy by examining a number of crucial problems on the nature of space and ...

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)

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)

Skeptics have cast doubt on the idea that scientific theories give us a true picture of an objective world. Lawrence Sklar examines three kinds of skeptical arguments about scientific truth, and explores the important role they play within foundational science itself. Sklar demonstrates that these kinds of philosophical critique are employed within science, and reveals the clear difference between how they operate in a scientific context and more abstract philosophical contexts. The underlying theme of Theory and Truth is that science (...) and philosophy are essential to one another. Sklar advances the claim that one cannot understand the methods of science without a comprehension of philosophy, and one cannot fruitfully pursue philosophy of science without understanding fundamental science as well. (shrink)

Twelve essays explore the philosophy of science in general and the physical sciences in particular A common theme unites all twelve essays: In discussing the ...

It has been argued, most trenchantly by Nancy Cartwright, that the diversity of the concepts and regularities we actually use to describe nature and predict and explain its behavior leaves us with no reason to believe that our foundational physical theories actually "apply" outside of delicately contrived systems within the laboratory. This paper argues that, diversity of method notwithstanding, there is indeed good reason to think that the foundational laws of physics are universal in their scope.

Although now replaced by more modern theories, classical mechanics remains a core foundational element of physical theory. From its inception, the theory of dynamics has been riddled with conceptual issues and differing philosophical interpretations and throughout its long historical development, it has shown subtle conceptual refinement. The interpretive program for the theory has also shown deep evolutionary change over time. Lawrence Sklar discusses crucial issues in the central theory from which contemporary foundational theories are derived and shows how some core (...) issues have nevertheless remained deep puzzles despite the increasingly sophisticated understanding of the theory which has been acquired over time. His book will be of great interest to philosophers of science, philosophers in general and physicists concerned with foundational interpretive issues in their field. (shrink)

The study of the physical world had its origins in philosophy, and, two-and-one-half millennia later, the scientific advances of the twentieth century are bringing the two fields closer together again. So argues Lawrence Sklar in this brilliant new text on the philosophy of physics.Aimed at students of both disciplines, Philosophy of Physics is a broad overview of the problems of contemporary philosophy of physics that readers of all levels of sophistication should find accessible and engaging. Professor Sklar’s talent for clarity (...) and accuracy is on display throughout as he guides students through the key problems: the nature of space and time, the problems of probability and irreversibility in statistical mechanics, and, of course, the many notorious problems raised by quantum mechanics.Integrated by the theme of the interconnectedness of philosophy and science, and linked by many references to the history of both disciplines, Philosophy of Physics is always clear, while remaining faithful to the complexity and integrity of the issues. It will take its place as a classic text in a field of fundamental intellectual importance. (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)

Naturalists tell us to rely on what science tells about the world and to eschew aprioristic philosophy. But foundational physics relies internally on modes of thinking that can only be called philosophical, and philosophical arguments rely upon what can only be called scientific inference. So what, then, could the naturalistic thesis really amount to?

Explaining Chaos provides both a succinct and accurate introduction to the physics and mathematics of chaotic dynamical systems along with a number of pertinent philosophical commentaries on the scientific results. The book provides the clearest and most sensible treatment of chaos theory from a philosophical perspective available in the literature.

Perceptual conscious experiences result from non-conscious processes that precede them. We document a new characteristic of the cognitive system: the speed with which visual meaningful stimuli are prioritized to consciousness over competing noise in visual masking paradigms. In ten experiments (N = 399) we find that an individual's non-conscious visual prioritization speed (NVPS) is ubiquitous across a wide variety of stimuli, and generalizes across visual masks, suppression tasks, and time. We also find that variation in NVPS is unique, in that (...) it cannot be explained by variation in general speed, perceptual decision thresholds, short-term visual memory, or three networks of attention (alerting, orienting and executive). Finally, we find that NVPS is correlated with subjective measures of sensitivity, as they are measured by the Highly Sensitive Person scale. We conclude by discussing the implications of variance in NVPS for understanding individual variance in behavior and the neural substrates of consciousness. (shrink)

About the Series Contemporary philosophy of science combines a general study from a philosophical perspective of the methods of science, with an inquiry, again from the philosophical point of view, into foundational issues that arise in the various special sciences. Methodological philosophy of science has deep connections with issues at the center of pure philosophy. It makes use of important results, for example, in traditional epistemology, metaphysics and the philosophy of language. It also connects in various ways with other disciplines (...) such as the history and sociology of the sciences, with pure logic, and with such branches of mathematics as probability theory. These volumes are, for the most part, devoted to readings in the methodological aspects of the philosophy of science. One volume, however, takes up the philosophical issues in the foundations of a particularly important special science, that is the issues in the foundations of theories of contemporary physics. The methodological volumes cover a number of crucial general problem areas. The first volume takes up issues in the nature of scientific explanation, and the related issues of the nature of scientific law and of the casual relation among events. The second volume explores issues in the nature and structure of scientific theories. The third volume collects inquiries into the nature of scientific change, as one theory is replaced by another. Volume four is devoted to readings concerning the nature of probability and the nature and justification of inductive reasoning in science. The following volume continues the exploration of the issue of confirming and rejecting theories with a series of readings devoted to Bayesian methodologies in science and to the exploration of non-inductive strategies for rationalizing belief. Finally, volume six explores three major problem areas in the foundation of physics: the nature and rationale for physical theories of space and time; the interpretive problems arising out of the quantum theory; and some puzzles arising out of statistical mechanical theories of physics. The readings are selected and arranged to provide the user with systematic access to the most important contemporary themes in methodological philosophy of science and in philosophy of physics. The selections include many recent contributions to the field, as well as papers and extracts from books and journals otherwise not easily available. (shrink)

This is the text of a talk given at the Robert and Sarah Boote Conference in Reductionism and Anti-Reductionism in Physics, 22-23 April, 2006, Center for Philosophy of Science University of Pittsburgh.

Salmon, following Reichenbach and others, maintained that distant simultaneity was conventional in a special relativistic world in a way in which this was not so in prerelativistic spacetime. This paper surveys and criticizes a number of proposals to unpack this claim. It goes on to argue that if the claim has validity, it rests upon differing facts about epistemic accessibility of temporal relations in the different spacetimes, and not directly upon any facts about differing causal structures in these worlds.

Tipler has previously argued that the nature of the universe is a matter of contingency rather than necessity. Now he argues that the existence of the universe can also be demonstrated to be a matter of necessity. I argue that both arguments are fatally flawed, and that neither supports the conclusion it is intended to establish.

In this paper, I want to focus attention on ways in which the role of idealization in science has been rather neglected by standard methodology, and suggest that this distinct role for idealization is the truly important role it plays in science. Further, I suggest that there are a number of important cases in theoretical science where the issue of idealization is not the issue of misrepresentation in some sense. Rather, the question is which of several alternative idealizations correctly represents (...) the fundamental causalstructure of the world, and which idealizations, consequently, are appropriate for the scientific account of the world that is correct in its basic notion of what is an appropriate explanatory format for dealing with the physical phenomena in question. My argument is that the issues of idealization are important for methodology not primarily for the reasons that have so far exercised most philosophers of science who have worried about idealization in science. (shrink)

Explaining Chaos provides both a succinct and accurate introduction to the physics and mathematics of chaotic dynamical systems along with a number of pertinent philosophical commentaries on the scientific results. The book provides the clearest and most sensible treatment of chaos theory from a philosophical perspective available in the literature.

The claim that some assertion is true “as a matter of convention” is likely to arise only in the circumstance that the assertion is allowed to be true, though an account of its believability as being warranted by its conformity to observable facts is taken to be inadequate.

Some of what is true about the world is thought, by some, to be true of necessity. Other truths about the world are merely contingently true, it is said. Next we get a familiar distinguishing of necessity into its various kinds. Anything whose contrary would contradict the laws of logic is logically necessary. Anything compatible with these laws is logically contingent. There are, of course, grave problems in finding a principled way of discriminating the logical truths from all the others. (...) Some propositions are not logically necessary but are metaphysically necessary. For Kant, I suppose, the alleged facts that every event had a cause, and that in any change a substance remained unchanged would be such facts. So, I suppose, would be the necessary but synthetic truths of geometry and arithmetic. For more contemporary philosophers genuine identity statements, either singular or general, might have such a status. (shrink)

In this article I address how one might develop states of freedom in analysis and in the analyst from the tangles of unconsciousness that exist in one’s unconscious mind, within the society that trained one, and from the unspoken depths of our European culture. How can one think about trauma in the individual without thinking of it in generational terms? In a similar way the cultural heritage that formed the backdrop to the development of psychoanalysis from within the Austro-Hungarian Empire (...) and its aftermath has its own value transmitting unconscious imprints on analytic societies. What are the interfaces between personal and historical trauma, and in particular the interface with unconscious processes? What we can grasp of the innermost life of the patient and of the world he or she lives in, and by which he or she is so profoundly affected, is also a part of a broader history and specific culture. Totalitarian regimes in the twentieth century have, of course, had a massive impact on Europe, including analytic societies, which I will argue is ongoing. How can the mind take a measure of history, when history will submit neither to the reason of the world nor to the mind that confronts it? (shrink)

Given the central role played by space and time both in our ordinary experience and in our attempts to understand the world by means of scientific theory, it is no surprise that attempts to understand space and time form a central locus of the interaction of philosophy and the physical sciences.

Trust is a natural mechanism by which an autonomous party, an agent, can deal with the inherent uncertainty regarding the behaviours of other parties and the uncertainty in the information it shares with those parties. Trust is thus crucial in any decentralised system. This paper builds on recent efforts to use argumentation to reason about trust. Specifically, a set of schemes is provided, and abstract patterns of reasoning that apply in multiple situations geared towards trust. Schemes are described in which (...) one agent, A, can establish arguments for trusting another agent, B, directly, as well as schemes that A can use to construct arguments for trusting C, where C is trusted by B. For both sets of schemes, a set of critical questions is offered that identify the situations in which these schemes can fail. (shrink)

Motorcycle helmet laws are perceived to infringe upon individual rights even though they reduce mortality and health care costs. We describe proposed helmet legislation that protects individual rights and provides incentives for helmet use through a differential motorcycle registration fee that requires higher fees for those who wish to ride without a helmet.

Paul Valéry1 Valéry’s “Variation sur Descartes” excellently evokes the vanishing act that has haunted philosophy ever since Darwin overturned the Cartesian tradition. If my body is composed of nothing but a team of a few trillion robotic cells, mindlessly interacting to produce all the large-scale patterns that tradition would attribute to the nonmechanical workings of my mind, there seems to be nothing left over to be me. Lurking in Darwin’s shadow there is a bugbear: the incredible Disappearing Self.2 One of (...) Darwin’s earliest critics saw what was coming and could scarcely contain his outrage. (shrink)

This thoughtful and carefully crafted book is a plea for "pluralism" in science. This pluralism includes a tolerance of a wide variety of conceptual classificatory schemes and of a variety of methods for the sciences as well, the varying schemes and methods determined by the specific needs of the specific sciences.

In an important study, Lawrence Sklar has defended a doctrine of methodological conservatism (very roughly, the principle that a proposition derives some sort of epistemic warrant from being believed). I argue that Sklar's careful formulation of methodological conservatism remains too strong, and that a yet weaker version of the doctrine cannot be successfully defended. I also criticize Sklar's argument that the rejection of methodological conservatism would result in total skepticism. Finally, I turn to a closely related issue, and try to (...) show why different people with the same evidence should be justified in believing the same things. (shrink)

Julian Barbour's approach to dynamics is reviewed. With a particular focus on questions of explanation and confirmation, the approach is contrasted with standard formulations of dynamics. This paper expands upon my commentary on Lawrence Sklar's paper at the Philosophy of Time Society meeting at the APA's Central Division meeting in Chicago, April 2004. Although a commentary, the current paper is comprehensible without reference to Sklar's paper.