This book is intended to serve as an advanced text and reference work on modal logic, a subject of growing importance which has applications to philosophy and linguistics. Although it is based mainly on research which I carried out during the years 1969-1973, it also includes some related results obtained by other workers in the field (see the refer ences in Part 7). Parts 0, 1 and 2, can be used as the basis of a one year graduate course in modal logic. The material which they contain has been taught in such courses at Stanford since 1970. The remaining parts of the book contain more than enough material for a second course in modal logic. The exercises supplement the text and are usually difficult. I wish to thank Stanford University and Bar-Han University for making it possible for me to continue and finish this work, and A. Ungar for correcting the typescript. Bar-Ilan University, Israel Dov M. GABBA Y PART 0 AN INTRODUCTION TO GENERAL INTENSIONAL LOGICS CHAPTER 0 CONSEQUENCE RELATIONS Motivation We introduce the notions of a consequence relation (which is a generalization of the notion of a logical system) and of a semantics. We show that every consequence relation is complete for a canonical semantics. We define the notion of one semantics being Dian in another and study the basic properties of this notion. The concepts of this chapter are generalizations of the various notions of logical system and possible world semantics found in the literature.

How many miles to Babylon? Three-score and ten. Can I get there by candle-light? Yes, and back again. If your heels are nimble dnd light, You may get there by candle-light. Any philosopher who takes more than a fleeting interest in the sciences and their development must at some stage confront the issue of incommensurability in one or other of its many manifes tations. For the philosopher of science concerned with problems of conceptual change and the growth of knowledge, matters of incommensurability are of paramount concern. After many years of skating over, skimming through and skirting round this issue in my studies of intertheory relations in science, I decided to take the plunge and make the problem of incommensurability the central and unifying theme of a book. The present volume is the result of that decision. My interest in problems of comparability and commensurability in science was awakened in the formative years of my philosophi cal studies by my teacher, Jerzy Giedymin. From him I have learnt not only to enjoy philosophical problems but also to beware of simpleminded solutions to them. The vibrant seminars of Paul Feyerabend held at Sussex University in 1974 left me in no doubt that incommensurability was, and would remain, a major topic of debate and dispute in the philosophical study of human knowledge.

Dynamic Epistemic Logic is the logic of knowledge change. This book provides various logics to support such formal specifications, including proof systems. Concrete examples and epistemic puzzles enliven the exposition. The book also offers exercises with answers. It is suitable for graduate courses in logic. Many examples, exercises, and thorough completeness proofs and expressivity results are included. A companion web page offers slides for lecturers and exams for further practice.

This volume began as a remembrance of Alonzo Church while he was still with us and is now finally complete. It contains papers by many well-known scholars, most of whom have been directly influenced by Church's own work. Often the emphasis is on foundational issues in logic, mathematics, computation, and philosophy - as was the case with Church's contributions, now universally recognized as having been of profound fundamental significance in those areas. The volume will be of interest to logicians, computer scientists, philosophers, and linguists. The contributions concern classical first-order logic, higher-order logic, non-classical theories of implication, set theories with universal sets, the logical and semantical paradoxes, the lambda-calculus, especially as it is used in computation, philosophical issues about meaning and ontology in the abstract sciences and in natural language, and much else. The material will be accessible to specialists in these areas and to advanced graduate students in the respective fields.

This book introduces an important group of logics that have come to be known under the umbrella term 'susbstructural'. Substructural logics have independently led to significant developments in philosophy, computing and linguistics. An Introduction to Substrucural Logics is the first book to systematically survey the new results and the significant impact that this class of logics has had on a wide range of fields.The following topics are covered: * Proof Theory * Propositional Structures * Frames * Decidability * Coda Both students and professors of philosophy, computing, linguistics, and mathematics will find this to be an important addition to their reading.

This book defends the Direct Reference (DR) thesis in philosophy of language regarding proper names and indexical pronouns. It uniquely draws out the significant consequences of DR when it is conjoined with the fact that these singular terms sometimes fail to refer. Even though DR is widely endorsed by philosophers of language, many philosophically important and radically controversial consequences of the thesis have gone largely unexplored. This book makes an important contribution to the DR literature by explicitly addressing the consequences that follow from DR regarding failure of reference. Michael McKinsey argues that only a form of neutral free logic can capture a revised concept of logical truth that is consistent with the fact that any sentence of any form that contains a directly referring genuine term can fail to be either true or false on interpretations where that term fails to refer. He also explains how it is possible for there to be true (or false) sentences that contain non-referring names, even though this possibility seems inconsistent with DR. Consequences of Reference Failure will be of interest to philosophers of language and logic and linguists working on Direct Reference.

Among the several dozens of symposia held on the occasion of the quincentennial of U ppsala University, there was included one symposium devoted to the theme of 'Philosophy and Grammar'. A selection of the most important papers delivered at this symposium have been collected in this volume. The papers need no introduction, but the inclusion of two of them in this collection requires a brief comment. First, the paper by von Wright, although not directly concerned with the central topic of the symposium, has been included because it was the terminating speech of the six parallel symposia (including the symposium on 'Philosophy and Grammar') held by the Humanities Faculty and moreover, because the raison d'etre of the Humanities is analyzed in this paper by a very prominent Swedish-speaking philosopher. Second, Professor Hintikka was unable to participate. In view of his expertise in the field, we nevertheless requested him to contribute a paper, so to speak, post factum. This he very generously did. We wish to express our sincere appreciation to all who participated and/or helped to carry the sessions through to a successful conclusion. We also wish to extend a special thanks to Professor Roman lakobson of Harvard University, who assumed the responsibility of General Chairman of the symposium.