These are the proceedings of the Workshop on Quantum Logic held in Erice (Sicily), December 2 - 9, 1979, at the Ettore Hajorana Centre for Scientific Culture. A conference of this sort was originally proposed by Giuliano Toraldo di Francia, who suggested the idea to Antonino Zichichi, and thus laid the foundation for the Workshop. To both of them we express our appreciation and thanks, also on behalf of the other participants, for having made this conference possible. There were approximately fifty participants; their names and institutions are listed in the text. Quantum logic, which has now a history of some forty or more years, has seen remarkable growth during the sixties and seventies. The papers in the present volume presuppose, by and large, some acquaintance with the elements of the subject. These may be found in the well-known books by J.H. Jauch (Foundations of Quantum Hechanics; Reading, 1968), V.S. Varadarajan (Geometry of Quantum Theory: Princeton, 1968), and C. Piron (Foundations of Quantum Theory; New York, 1976). The initial program for the conference listed about twenty-five invited papers. But in the context of a very active and qualified attendance, other contributions were offered. This volume contains all of them. The program listed six main topics: I. Classification or different areas of quantum logic, and open problems. II. Comparison and unification of different approaches to quantum theories; problems of interpretation. III. Formal quantum logic; axiomatics. IV. Hodal interpretations of quantum logic. v vi FOREWORD V. Quantum set theory.

Bas C. van Fraassen presents an original exploration of how we represent the world. Science represents natural phenomena by means of theories, as well as in many concrete ways by such means as pictures, graphs, table-top models, and computer simulations. Scientific Representation begins with an inquiry into the nature of representation in general, drawing on such diverse sources as Plato's dialogues, the development of perspectival drawing in the Renaissance, and the geometric styles of modelling in modern physics. Starting with Mach's and Poincare's analyses of measurement and the 'problem of coordination', van Fraassen then presents a view of measurement outcomes as representations. With respect to the theories of contemporary science he defends an empiricist structuralist version of the 'picture theory' of science, through an inquiry into the paradoxes that came to light in twentieth-century philosophies of science. Van Fraassen concludes with an analysis of the complex relationship between appearance and reality in the scientific world-picture.

After introducing the empiricist point of view in philosophy of science, and the concepts and methods of the semantic approach to scientific theories, Professor van Fraassen discusses quantum theory in three stages. He first examines the question of whether and how empirical phenomena require a non-classical theory, and what sort of theory they require. He then discusses the mathematical foundations of quantum theory with special reference to developments in the modelling of interaction, composite systems, and measurement. Finally, the author broaches the main questions of interpretation. After offering a critique of earlier interpretations, he develops a new one - the modal interpretation - which attempts to stay close to the original Copenhagen ideas without implying a radical incompleteness in quantum theory. He again gives special attention to the character of composite, many-body systems and especially to the peculiar character of assemblies of indentical particles in quantum statistics.;The work is aimed at philosophers of science, scientists and mathematicians interested in the philosophy of mathematics and science.

Extensively classroom-tested, this text provides an accessible and carefully structured introduction to modal and many-valued logic. The authors cover the basic formal frameworks, as well as considering a variety of philosophical issues surrounding 'possibilities and paradox'.

In order to aid understanding, each chapter provides the following features: exercises to give students hands-on experience, examples to demonstrate the application of concepts and a list of further readings.

After introducing the empiricist point of view in philosophy of science, and the concepts and methods of the semantic approach to scientific theories, Professor van Fraassen discusses quantum theory in three stages. He first examines the question of whether and how empirical phenomena require a non-classical theory, and what sort of theory they require. He then discusses the mathematical foundations of quantum theory with special reference to developments in the modelling of interaction, composite systems, and measurement. Finally, the author broaches the main questions of interpretation. After offering a critique of earlier interpretations, he develops a new one - the modal interpretation - which attempts to stay close to the original Copenhagen ideas without implying a radical incompleteness in quantum theory. He again gives special attention to the character of composite, many-body systems and especially to the peculiar character of assemblies of indentical particles in quantum statistics.;The work is aimed at philosophers of science, scientists and mathematicians interested in the philosophy of mathematics and science.

Bas C. van Fraassen presents an original exploration of how we represent the world. Science represents natural phenomena by means of theories, as well as in many concrete ways by such means as pictures, graphs, table-top models, and computer simulations. Scientific Representation begins with an inquiry into the nature of representation in general, drawing on such diverse sources as Plato's dialogues, the development of perspectival drawing in the Renaissance, and the geometric styles of modelling in modern physics. Starting with Mach's and Poincare's analyses of measurement and the 'problem of coordination', van Fraassen then presents a view of measurement outcomes as representations. With respect to the theories of contemporary science he defends an empiricist structuralist version of the 'picture theory' of science, through an inquiry into the paradoxes that came to light in twentieth-century philosophies of science. Van Fraassen concludes with an analysis of the complex relationship between appearance and reality in the scientific world-picture.

An innovative, multifaceted approach to scientific experiments as designed by and shaped through interaction with the modeling process The role of scientific modeling in mediation between theories and phenomena is a critical topic within the philosophy of science, touching on issues from climate modeling to synthetic models in biology, high energy particle physics, and cognitive sciences. Offering a radically new conception of the role of data in the scientific modeling process as well as a new awareness of the problematic aspects of data, this cutting-edge volume offers a multifaceted view on experiments as designed and shaped in interaction with the modeling process. Contributors address such issues as the construction of models in conjunction with scientific experimentation; the status of measurement and the function of experiment in the identification of relevant parameters; how the phenomena under study are reconceived when accounted for by a model; and the interplay between experimenting, modeling, and simulation when results do not mesh. Highlighting the mediating role of models and the model-dependence (as well as theory-dependence) of data measurement, this volume proposes a normative and conceptual innovation in scientific modeling-that the phenomena to be investigated and modeled must not be precisely identified at the start but specified during the course of the interactions arising between experimental and modeling activities. Contributors: Nancy D. Cartwright, U of California, San Diego; Anthony Chemero, U of Cincinnati; Ronald N. Giere, U of Minnesota; Jenann Ismael, U of Arizona; Tarja Knuuttila, U of South Carolina; Andrea Loettgers, U of Bern, Switzerland; Deborah Mayo, Virginia Tech; Joseph Rouse, Wesleyan U; Paul Teller, U of California, Davis; Michael Weisberg, U of Pennsylvania; Eric Winsberg, U of South Florida.

The Aim of 'The Scientific Image' is to develop an empiricist alternative to both logical positivism and scientific realism. The book presents three mutually supporting theories concerning science. The presentation of these three theses is preceded by two chapters which provide an informal introduction to current in the philosophy of science, particularly concerning scientific realism.

This is a book in the philosophy of science, which examines the concept of laws of nature. The author analyses and rejects arguments for the existence of such laws, and argues that there is no point in us believing that they exist. This has important implications for scientists, since he rejects the idea of law as an inadequate clue to science. In the second part of the book he develops a philosophical approach to science which takes account of these objections.

An innovative, multifaceted approach to scientific experiments as designed by and shaped through interaction with the modeling process The role of scientific modeling in mediation between theories and phenomena is a critical topic within the philosophy of science, touching on issues from climate modeling to synthetic models in biology, high energy particle physics, and cognitive sciences. Offering a radically new conception of the role of data in the scientific modeling process as well as a new awareness of the problematic aspects of data, this cutting-edge volume offers a multifaceted view on experiments as designed and shaped in interaction with the modeling process. Contributors address such issues as the construction of models in conjunction with scientific experimentation; the status of measurement and the function of experiment in the identification of relevant parameters; how the phenomena under study are reconceived when accounted for by a model; and the interplay between experimenting, modeling, and simulation when results do not mesh. Highlighting the mediating role of models and the model-dependence (as well as theory-dependence) of data measurement, this volume proposes a normative and conceptual innovation in scientific modeling—that the phenomena to be investigated and modeled must not be precisely identified at the start but specified during the course of the interactions arising between experimental and modeling activities. Contributors: Nancy D. Cartwright, U of California, San Diego; Anthony Chemero, U of Cincinnati; Ronald N. Giere, U of Minnesota; Jenann Ismael, U of Arizona; Tarja Knuuttila, U of South Carolina; Andrea Loettgers, U of Bern, Switzerland; Deborah Mayo, Virginia Tech; Joseph Rouse, Wesleyan U; Paul Teller, U of California, Davis; Michael Weisberg, U of Pennsylvania; Eric Winsberg, U of South Florida.

What is empiricism and what could it be? Bas C. van Fraassen, one of the world's foremost contributors to philosophical logic and the philosophy of science, here undertakes a fresh consideration of these questions and offers a program for renewal of the empiricist tradition. The empiricist tradition is not and could not be defined by common doctrines, but embodies a certain stance in philosophy, van Fraassen says. This stance is displayed first of all in a searing, recurrent critique of metaphysics, and second in a focus on experience that requires a voluntarist view of belief and opinion. Van Fraassen focuses on the philosophical problems of scientific and conceptual revolutions and on the not unrelated ruptures between religious and secular ways of seeing or conceiving of ourselves. He explores what it is to be or not be secular and points the way toward a new relationship between secularism and science within philosophy.