Lawrence Sklar

In theoretical physics the physical states of systems are represented by components of mathematical structures. This paper explores three ways in which the representation of states by mathematics can give rise to foundational problems, sometimes on the side of the mathematics and sometimes on the side of understanding what the physical states are that the mathematics represents, that is on the side of interpreting the theory. Examples are given from classical mechanics, quantum mechanics and statistical mechanics

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.

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.

Mathematical physics works by representing the contents of the world and the world’s dynamical changes by the components of some mathematical structure and the transformations one can impose on these components. Quite rightly, philosophers of science have concentrated much attention on trying to understand how physicists arrive at the appropriate transformational rules to represent dynamical evolution in the world, that is, on how they find the correct laws of nature. But the preliminary problem, how to choose the appropriate mathematical representatives for the things of the world and their states of being, has received, perhaps, less attention than it deserves.

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.

Those who think of some aspects of the world as "physically necessary" usually think of this kind of necessity as being confined to the general law of nature, initial conditions being "contingent." Tachyon theory and general relativity provide independent but related reasons for thinking that some initial states are, however, "impossible." And statistical mechanics seems to lead us to conclude that some initial conditions are, if not impossible, "highly improbable." We are then, led from these aspects of physics to wonder if initial conditions are always "freely specifiable" and in the domain of physical contingency.

Despite over one-hundred years of effort, the origin of temporal asymmetry in the physical world still eludes us. While much has been learned about the role played by fundamental instabilities in microdynamics, by the imperfect isolation of systems and by cosmological facts in the origin of the behavior described by kinetic theory and thermodynamics, important puzzles still remain which continue to make the origins of asymmetric thermal behavior out of dynamically time symmetric underlying laws mysterious to us.

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.