In this systematic study, Professor Achinstein analyzes such concepts as definitions, theories, and models, and contrasts his view with currently held positions that he finds inadequate.

Metaphysicians speak of laws of nature in terms of necessity and universality; scientists, in terms of symmetry and invariance. In this book van Fraassen argues that no metaphysical account of laws can succeed. He analyzes and rejects the arguments that there are laws of nature, or that we must believe there are, and argues that we should disregard the idea of law as an adequate clue to science. After exploring what this means for general epistemology, the author develops the empiricist (...) view of science as a construction of models to represent the phenomena. (shrink)

This book is well known for its proof that many mathematical systems - including lattice theory and closure algebras - are undecidable. It consists of three treatises from one of the greatest logicians of all time: "A General Method in Proofs of Undecidability," "Undecidability and Essential Undecidability in Mathematics," and "Undecidability of the Elementary Theory of Groups.".

Introduction: Science and Common Sense Long before the beginnings of modern civilization, men ac- quired vast funds of information about their environment. ...

8.3 The consistency proof -- 8.4 Applications of the consistency proof -- 8.5 Second-order arithmetic -- Problems -- Chapter 9: Set Theory -- 9.1 Axioms for sets -- 9.2 Development of set theory -- 9.3 Ordinals -- 9.4 Cardinals -- 9.5 Interpretations of set theory -- 9.6 Constructible sets -- 9.7 The axiom of constructibility -- 9.8 Forcing -- 9.9 The independence proofs -- 9.10 Large cardinals -- Problems -- Appendix The Word Problem -- Index.

New edition (previously 1971) of an anthology for an undergraduate course. Comprises four parts: theories, explanation and causality, confirmation of scientific hypotheses, selected problems of particular sciences. Annotation copyrighted by Book News, Inc., Portland, OR.

In this book van Fraassen develops an alternative to scientific realism by constructing and evaluating three mutually reinforcing theories.

Traditionally a scientific theory is viewed as based on universal laws of nature that serve as axioms for logical deduction. In analyzing the logical structure of evolutionary biology, Elisabeth Lloyd argues that the semantic account is more appropriate and powerful. This book will be of interest to biologists and philosophers alike.

Call a bit of scientific discourse a description of a missing system when (i) it has the surface appearance of an accurate description of an actual, concrete system (or kind of system) from the domain of inquiry, but (ii) there are no actual, concrete systems in the world around us fitting the description it contains, and (iii) that fact is recognised from the outset by competent practitioners of the scientific discipline in question. Scientific textbooks, classroom lectures, and journal articles abound (...) with such passages; and there is a widespread practice of talking and thinking as though there are systems which fit the descriptions they contain perfectly, despite the recognition that no actual, concrete systems do so—call this the face value practice. There are, furthermore, many instances in which philosophers engage in the face value practice whilst offering answers to epistemological and methodological questions about the sciences. Three questions, then: (1) How should we interpret descriptions of missing systems? (2) How should we make sense of the face value practice? (3) Is there a set of plausible answers to (1) and (2) which legitimates reliance on the face value practice in our philosophical work, and can support the weight of the accounts which are entangled with that practice? In this paper I address these questions by considering three answers to the first: that descriptions of missing systems are straightforward descriptions of abstract objects, that they are indirect descriptions of “property-containing” abstracta, and that they are (in a different way) indirect descriptions of mathematical structures. All three proposals are present in the literature, but I find them wanting. The result is to highlight the importance of developing a satisfactory understanding of descriptions of missing systems and the face value practice, to put pressure on philosophical accounts which rely on the practice, and to help us assess the viability of certain approaches to thinking about models, theory structure, and scientific representation. (shrink)

Suppe, F. The search for philosophic understanding of scientific theories (p. [1]-241)--Proceedings of the symposium.--Bibliography, compiled by Rew A. Godow, Jr. (p. [615]-646).

Van Fraassen defines constructive empiricism as the view that science aims to produce empirically adequate theories. But this account has been misunderstood. Constructive empiricism in not, as it seems, a description of the intentional features of scientific practice, nor is it a normative prescription for their revision. It is rather a fiction about the practice of science that van Fraassen displays in the interests of a broader empiricism. The paper concludes with a series of arguments designed to show that constructive (...) empiricism so understood is self-undermining. (shrink)

Cases where analogy has played a significant role in the formation of a new scientific concept are well-documented. Yet, how is it that genuinely new representations can be constructed from existing representations? It is argued that the process of ‘generic modeling’ enables abstraction of features common to both the domain of the source of the analogy and of the target phenomena. The analysis focuses on James Clerk Maxwell's construction of the electromagnetic field concept. The mathematical representation Maxwell constructed turned out (...) to be a system of abstract laws that when applied to electromagnetic systems yield laws of a dynamical system that will not map back onto the mechanicals domains used in their construction. (shrink)

Cases where analogy has played a significant role in the formation of a new scientific concept are well-documented. Yet, how is it that genuinely new representations can be constructed from existing representations? It is argued that the process of ‘generic modeling’ enables abstraction of features common to both the domain of the source of the analogy and of the target phenomena. The analysis focuses on James Clerk Maxwell's construction of the electromagnetic field concept. The mathematical representation Maxwell constructed turned out (...) to be a system of abstract laws that when applied to electromagnetic systems yield laws of a dynamical system that will not map back onto the mechanicals domains used in their construction. (shrink)

This classic work in the philosophy of physical science is an incisive and readable account of the scientific method. Pierre Duhem was one of the great figures in French science, a devoted teacher, and a distinguished scholar of the history and philosophy of science. This book represents his most mature thought on a wide range of topics.

Modal logic is the study of modalities - expressions that qualify assertions about the truth of statements - like the ordinary language phrases necessarily, possibly, it is known/believed/ought to be, etc., and computationally or mathematically motivated expressions like provably, at the next state, or after the computation terminates. The study of modalities dates from antiquity, but has been most actively pursued in the last three decades, since the introduction of the methods of Kripke semantics, and now impacts on a wide (...) range of disciplines, including the philosophy of language and linguistics ('possible words' semantics for natural language), constructive mathematics (intuitionistic logic), theoretical computer science (dynamic logic, temporal and other logics for concurrency), and category theory (sheaf semantics). This volume collects together a number of the author's papers on modal logic, beginning with his work on the duality between algebraic and set-theoretic modals, and including two new articles, one on infinitary rules of inference, and the other about recent results on the relationship between modal logic and first-order logic. Another paper on the 'Henkin method' in completeness proofs has been substantially extended to give new applications. Additional articles are concerned with quantum logic, provability logic, the temporal logic of relativistic spacetime, modalities in topos theory, and the logic of programs. (shrink)

Frederick Suppe has come to enjoy a position of undisputed leadership in the post-positivistic philosophy of science.

Abraham Pais's Subtle Is the Lord was a publishing phenomenon: a mathematically sophisticated exposition of the science and the life of Albert Einstein that reached a huge audience and won an American Book Award. Reviewers hailed the book as "a monument to sound scholarship and graceful style", "an extraordinary biography of an extraordinary man", and "a fine book". In this groundbreaking new volume, Pais undertakes a history of the physics of matter and of physical forces since the discovery of x-rays. (...) The book attempts to relate not only what has happened over the last hundred years but why it happened the way it did, what it was like for those scientists involved, and how what at the time may have seemed a series of bizarre or unrelated events, now with hindsight emerges as a logical sequence of events. Pais, a noted physicist, was personally involved in many of the developments he describes, and thus Inward Bound, like his earlier book, is filled with unique insights into the world of big and small physics. Between 1895 and 1983, the period he covers, the smallest distances explored have shrunk a hundred millionfold, Pais notes. Along this incompletely traveled "road inward," scientists have established markers that later generations will rank among the principal monuments of the twentieth century. In alternating technical and nontechnical sections, this magisterial survey richly conveys what has been discovered about the constituents of matter, the laws to which they are subject, and the forces that act on them. But the advances have certainly not come smoothly. The book shows that these have been times of progress and stagnation, of order and chaos, of clarity and confusion, of belief and incredulity, of the conventional and the bizarre; also of revolutionaries and conservatives, of science by individuals and by consortia, of little gadgets and big machines, and of modest funds and big money. About the Author: Abraham Pais is Detlev W. Bronk Professor of Physics at the Rockefeller University. The author of the prizewinning biography of Einstein now undertakes a history of modern physics. (shrink)

Mathias Frisch provides the first sustained philosophical discussion of conceptual problems in classical particle-field theories. Part of the book focuses on the problem of a satisfactory equation of motion for charged particles interacting with electromagnetic fields. As Frisch shows, the standard equation of motion results in a mathematically inconsistent theory, yet there is no fully consistent and conceptually unproblematic alternative theory. Frisch describes in detail how the search for a fundamental equation of motion is partly driven by pragmatic considerations (like (...) simplicity and mathematical tractability) that can override the aim for full consistency. The book also offers a comprehensive review and criticism of both the physical and philosophical literature on the temporal asymmetry exhibited by electromagnetic radiation fields, including Einstein's discussion of the asymmetry and Wheeler and Feynman's influential absorber theory of radiation. Frisch argues that attempts to derive the asymmetry from thermodynamic or cosmological considerations fail and proposes that we should understand the asymmetry as due to a fundamental causal constraint. The book's overarching philosophical thesis is that standard philosophical accounts that strictly identify scientific theories with a mathematical formalism and a mapping function specifying the theory's ontology are inadequate, since they permit neither inconsistent yet genuinely successful theories nor thick causal notions to be part of fundamental physics. (shrink)

In this dissertation I address the general question, "What is the role of mathematical models in the way in which scientific theories represent the world?" The specific questions I address are these: What is the relation between the laws of a theory and its models? Do scientific theories give us coherent accounts of physical possibility? Must a theory represent a phenomenon truthfully in order to explain it? ;In the first chapter I distinguish and examine some central uses to which the (...) term "model" has been put in philosophical discussions of scientific theories. According to the current "semantic view," theories are to be understood as consisting of families of models. I argue that standard presentations of the semantic view are guilty of confounding two distinct notions of model: that of a structure which represents the world and that of a structure which satisfies a set of sentences. ;In the second chapter I examine the relation between the general principles or "laws" of a theory and the mathematical models that scientists use to represent individual phenomena within the theory's purview. According to an intuitively plausible view, individual models satisfy the laws of the theory and can, at least in principle, be integrated into coherent 'global' representations of the phenomena in the domain of the theory. Scientific theories, according to this view, delineate coherent physical possibilities. Against this, I show in a detailed case study of classical electrodynamics that there are no possible worlds of which all the basic equations of the theory are simultaneously true under their standard interpretation. Instead of presenting us with a conceptually coherent picture of a range of possibilities, classical electrodynamics allows for the construction of a variety of models which locally represent different phenomena, but which cannot be integrated into a single unified and coherent account. ;In the third and fourth chapters, I take up the question of whether a theory must represent the phenomena within its purview truthfully in order to explain them. Classical electrodynamics could not possibly be a true theory, yet, perhaps surprisingly, physicists take the theory to provide adequate explanations. After surveying many of the major current accounts of explanation, most of which hold that truth is a necessary condition of explanatory adequacy, I propose an account of scientific explanation that does two things: it tries to do justice to the intuition embodied in these accounts that there is a close connection between explanation and truth, but at the same time it allows good scientific explanations to be at least partially untrue. To explain a phenomenon, I argue, is to exhibit it as part of a systematic pattern of alternative possibilities. I elaborate this idea and show how it can be made precise by proposing a technical framework which appeals to Tarski's notion of a relational system. I argue that we use three criteria to evaluate putative explanations: degrees of truth, richness of explanatory pattern, and simplicity; and I claim that something like the weighted average of the three criteria determines the goodness of an explanation. I show how my proposal can account for the structure of paradigmatic instances of scientific explanations, and I defend the proposal from challenges posed by causal theories of explanation. (shrink)