It is with great pleasure that we are presenting to the community the second edition of this extraordinary handbook. It has been over 15 years since the publication of the first edition and there have been great changes in the landscape of philosophical logic since then. The first edition has proved invaluable to generations of students and researchers in formal philosophy and language, as well as to consumers of logic in many applied areas. The main logic article in the Encyclopaedia Britannica 1999 has described the first edition as 'the best starting point for exploring any of the topics in logic'. We are confident that the second edition will prove to be just as good, The first edition was the second handbook published for the logic commu nity. It followed the North Holland one volume Handbook of Mathematical Logic, published in 1977, edited by the late Jon Barwise. The four volume Handbook of Philosophical Logic, published 1983-1989 came at a fortunate temporal junction at the evolution of logic. This was the time when logic was gaining ground in computer science and artificial intelligence circles. These areas were under increasing commercial pressure to provide devices which help and/or replace the human in his daily activity. This pressure required the use of logic in the modelling of human activity and organisa tion on the one hand and to provide the theoretical basis for the computer program constructs on the other."

The relation between logic and knowledge provoked a heated debate since the 1960s. The epistemic approaches, found their formal argument in the mathematics of Brouwer and intuitionistic logic. And following Michael Dummett - started to call themselves: antirealists'. Others persisted with the formal background of the Frege-Tarski tradition, where Cantorian set theory is linked via model theory to classical logic. Jaakko Hintikka tried to join both traditions by means of what is now known as explicit epistemic logic'. Here the epistemic content is introduced into the object language as an operator which yield propositions from propositions rather than as metalogical constraint on the notion of inference. The Realism-Antirealism debate had thus three players: classical logicians, intuitionists and explicit epistemic logicians. The editors of the present volume think that in these days and age of Alternative Logics, where manifold developments in logic happen in a breathtaking pace, this debate should be revisited. Using the most recent logical and epistemological tools, this book provides a novel and refreshing view on the most important topics of the Realism vs. Antirealism debate. Its general scope is to show the most recent developments in philosophical logic to deal with problems inherited from this debate. It is meant for researcher and advanced students in philosophy, logic, formal methods. It's complete collection with a variety of approaches, it is written by leading authors in the fields, every chapter is self-contained.

Alexander Broadie explains the theories of truth and validity of the great logicians of the fourteenth century. He shows how far they advanced beyond the logic of Aristotle, and reveals that much of what seems characteristically twentieth-century logic was familiar long ago. He has extensively revised his text for this second edition, while preserving the character of the first. There are now fuller accounts of supposition of intentional contexts, and of medieval syllogistics, and the conclusion has been substantially expanded.

The present volume of the "Handbook of the History of Logic" is designed to establish 19th century Britain as a substantial force in logic, developing new ideas, some of which would be overtaken by, and other that would anticipate, the century's later capitulation to the mathematization of logic.
"British Logic in the Nineteenth Century" is indispensable reading and a definitive research resource for anyone with an interest in the history of logic.
- Detailed and comprehensive chapters covering the entire range of modal logic
- Contains the latest scholarly discoveries and interpretative insights that answer many questions in the field of logic

This study looks to the work of Tarski's mentors Stanislaw Lesniewski and Tadeusz Kotarbinski, and reconsiders all of the major issues in Tarski scholarship in light of the conception of Intuitionistic Formalism developed: semantics, truth, paradox, logical consequence.

This volume contains a selection of papers presented at a Seminar on Intensional Logic held at the University of Amsterdam during the period September 1990-May 1991. Modal logic, either as a topic or as a tool, is common to most of the papers in this volume. A number of the papers are con cerned with what may be called well-known or traditional modal systems, but, as a quick glance through this volume will reveal, this by no means implies that they walk the beaten tracks. In deed, such contributions display new directions, new results, and new techniques to obtain familiar results. Other papers in this volume are representative examples of a current trend in modal logic: the study of extensions or adaptations of the standard sys tems that have been introduced to overcome various shortcomings of the latter, especially their limited expressive power. Finally, there is another major theme that can be discerned in the vol ume, a theme that may be described by the slogan 'representing changing information. ' Papers falling under this heading address long-standing issues in the area, or present a systematic approach, while a critical survey and a report contributing new techniques are also included. The bulk of the papers on pure modal logic deal with theoreti calor even foundational aspects of modal systems."

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."

First published in 2005. Routledge is an imprint of Taylor & Francis, an informa company.

Law is traditionally conceived as consisting of norms of conduct and power-conferring norms. This conception, however, is unable to account for a variety of elements of modern legal systems that differ significantly from the classical notions. This book concerns the problem of which results of human activity can obtain legal validity. The author makes use of recent findings in speech act theory, especially John R. Searle and Daniel Vanderveken's illocutionary logic. He sets out a theory of legal norms conceived as institutional legal facts resulting from performances of speech acts specified in power-conferring norms. The theory provides a classification of acts-in-the-law and of legal norms resulting from performances of these. Finally, the transition is made from institutional legal facts to legal institutions. The book is a contribution to the institutional theory of law as developed by N. MacCormick and O. Weinberger.

The Laws of Thought is an exploration of the deductive and inductive foundations of rational thought. The author here clarifies and defends Aristotle's Three Laws of Thought, called the Laws of Identity, Non-contradiction and Exclusion of the Middle - and introduces two more, which are implicit in and crucial to them: the Fourth Law of Thought, called the Principle of Induction, and the Fifth Law of Thought, called the Principle of Deduction. This book is a thematic compilation drawn from past works by the author over a period of twenty-three years.

Reasoning is an integral part of intelligent systems in fields like databases, logic programming, robotics, knowledge engineering, human/computer interfaces, programming environments, etc. In reality any such system has to cope with a changing world and its dynamics. Hence it is of great importance that reasoning must account for coping with change in order to be truly useful in practice. The book comprises several contributions to current ways of approaching this problem. On the one hand it surveys and synthesizes recent research work, while on the other hand new research results are included. Among the topics treated are logics for reasoning about actions and planning, belief revision and the reconciliation of logically conflicting inputs, resolving of conflicts by merging of knowledge and issues in the evolution in object-oriented databases. The book is aimed at the researcher and advanced student active in this field.

Constructibility and complexity play central roles in recent research in computer science, mathematics and physics. For example, scientists are investigating the complexity of computer programs, constructive proofs in mathematics and the randomness of physical processes. But there are different approaches to the explication of these concepts. This volume presents important research on the state of this discussion, especially as it refers to quantum mechanics. This foundational debate' in computer science, mathematics and physics was already fully developed in 1930 in the Vienna Circle. A special section is devoted to its real founder Hans Hahn, referring to his contribution to the history and philosophy of science. The documentation section presents articles on the early Philipp Frank and on the Vienna Circle in exile. Reviews cover important recent literature on logical empiricism and related topics.

This book seeks to arrive at a better understanding of the relationships between the objective and subjective aspects of time. It discusses the existence of fluent time, a controversial concept in many areas, from philosophy to physics. Fluent time is understood as directional time with a past, a present and a future. We experience fluent time in our lives and we adopt a temporal perspective in our ways of knowing and acting. Nevertheless, the existence of fluent time has been debated for both philosophical and scientific reasons, thus creating a rift between the subjective and objective aspects of time. Starting from the basic notion of points of view, or perspectives, this book explores the relationships between objective or external time, as it has been conceptualized by science, and subjective or internal time, which is involved in our lived experiences. It establishes a general framework encompassing the nature, structure and mode of existence of points of view, in which the objective and subjective aspects of time can be integrated. The book mainly addresses researchers and postgraduates in philosophy and logic. Additionally, it offers inspiration for physicists and computer scientists involved in the modeling and simulation of complex behaviors for which the representation of internal time should be considered together with the notion of objective, external time.

This introduction to modality places the emphasis on the metaphysics of modality rather than on the formal semetics of quantified modal logic. The text begins by introducing students to the "de re/de dicto" distinction, conventionalist and conceptualist theories of modality and some of the key problems in modality, particularly Quine's criticisms. It then moves on to explain how possible worlds provide a solution to many of the problems in modality and how possible worlds themselves have been used to analyse notions outside modality such as properties and propositions. Possible worlds introduce problems of their own and the book argues that to make progress with these problems a theory of possible worlds is required. The pros and cons of various theories of possible worlds are then examined in turn, including those of Lewis, Kripke, Adams, Stalnaker and Plantinga.

This introduction to modality places the emphasis on the metaphysics of modality rather than on the formal semetics of quantified modal logic. The text begins by introducing students to the "de re/de dicto" distinction, conventionalist and conceptualist theories of modality and some of the key problems in modality, particularly Quine's criticisms. It then moves on to explain how possible worlds provide a solution to many of the problems in modality and how possible worlds themselves have been used to analyse notions outside modality such as properties and propositions. Possible worlds introduce problems of their own and the book argues that to make progress with these problems a theory of possible worlds is required. The pros and cons of various theories of possible worlds are then examined in turn, including those of Lewis, Kripke, Adams, Stalnaker and Plantinga.

Paradoxes are more than just intellectual puzzles - they raise substantive philosophical issues and offer the promise of increased philosophical knowledge. In this introduction to paradox and paradoxes, Doris Olin shows how seductive paradoxes can be, why they confuse and confound, and why they continue to fascinate. Olin examines the nature of paradox, outlining a rigorous definition and providing a clear and incisive statement of what does and does not count as a resolution of a paradox. The view that a statement can be both true and false, that contradictions can be true, is seen to provide a challenge to the account of paradox resolution, and is explored. With this framework in place, the book then turns to an in-depth treatment of the Prediction Paradox, versions of the Preface/Fallibility Paradox, the Lottery Paradox, Newcomb's Problem, the Prisoner's Dilemma and the Sorites Paradox. Each of these paradoxes is shown to have considerable philosophical punch. Olin unpacks the central arguments in a clear and systematic fashion, offers original analyses and solutions, and exposes further unsettling implications for some of our most deep-seated principles and convictions.

Paradoxes are more than just intellectual puzzles - they raise substantive philosophical issues and offer the promise of increased philosophical knowledge. In this introduction to paradox and paradoxes, Doris Olin shows how seductive paradoxes can be, why they confuse and confound, and why they continue to fascinate. Olin examines the nature of paradox, outlining a rigorous definition and providing a clear and incisive statement of what does and does not count as a resolution of a paradox. The view that a statement can be both true and false, that contradictions can be true, is seen to provide a challenge to the account of paradox resolution, and is explored. With this framework in place, the book then turns to an in-depth treatment of the Prediction Paradox, versions of the Preface/Fallibility Paradox, the Lottery Paradox, Newcomb's Problem, the Prisoner's Dilemma and the Sorites Paradox. Each of these paradoxes is shown to have considerable philosophical punch. Olin unpacks the central arguments in a clear and systematic fashion, offers original analyses and solutions, and exposes further unsettling implications for some of our most deep-seated principles and convictions.

This book is a study in the logic of questions (sometimes called erotetic logic). The central topics in erotetic logic have been the structure of questions and the question-answer relationship. This book doesn't neglect these problems, but much of it is focussed on other issues. The main subject is the logical analysis of certain relations between questions and the contexts of their appearance. And our aim is to elaborate the conceptual apparatus of the inferential approach to the logic of questions. Questions are asked for many reasons and for different purposes. Yet, before a question is asked or posed, a questioner must arrive at it. In many cases arriving at a question resembles coming to a conclusion: there are some premises involved and some inferential thought processes take place. If we agree that a conclusion need not be "conclusive," we may say that sometimes questions can play the role of conclusions. But questions can also perform the role of premises: we often pass from some "initial" question to another question. In other words, there are inferential thought processes - we shall call them erotetic inferences - in which questions play the roles of conclusions or conclusions and premises. The inferential approach to the logic of questions focusses its attention on the analysis of erotetic inferences. This book consists of eight chapters.

This book deals with a previously neglected episode in the history of logic and theories of cognition: the way in which conceptions of inference changed during the 17th century. Gaukroger focuses on the work of Descartes, contrasting his explanation of inference as an instantaneous grasp in accord with the natural light of reason with the Aristotelian view of inference as a discursive process. He offers a new interpretation of Descartes' contribution to the question, revealing it to be a significant advance over humanist and late Scholastic conceptions, and argues that the Cartesian account played a pivotal role in the development of our understanding of the nature of inference.

The fourteenth volume of the Second Edition covers central topics in philosophical logic that have been studied for thousands of years, since Aristotle: Inconsistency, Causality, Conditionals, and Quantifiers. These topics are central in many applications of logic in central disciplines and this book is indispensable to any advanced student or researcher using logic in these areas. The chapters are comprehensive and written by major figures in the field.

somewhat like Henkin's nonstandard interpretation of higher-order logics, while the right semantics [or logical modalities is an analogue to the standard of type theory in Henkin's sense. interpretation Another possibility would be to follow W.V. Quine's advice to give up logi- cal modalities as being beyond repair. Or we could also try to develop a logic of conceptual possibility, restricting the range of our "possible worlds" to those compatible with the transcendental presuppositions of our own conceptual sys- tem. This looks in fact like one of the most interesting possible theories I have dreamt of developing but undoubtedly never will. Its kinship with Kant's way of thinking should be obvious. Besides putting the entire enterprise of possible-worlds semantics into a perspective, we can also see that the actual history of possible-worlds seman- tics is more complicated than it might first appear to be. For the standard in- terpretation of modal logics has reared its beautiful head repeatedly in the writings of Stig Kanger, Richard Montague the pre-Montague-semantics theorist, and Nino Cocchiarella.

Category theory is a branch of abstract algebra with incredibly diverse applications. This text and reference book is aimed not only at mathematicians, but also researchers and students of computer science, logic, linguistics, cognitive science, philosophy, and any of the other fields in which the ideas are being applied. Containing clear definitions of the essential concepts, illuminated with numerous accessible examples, and providing full proofs of all important propositions and theorems, this book aims to make the basic ideas, theorems, and methods of category theory understandable to this broad readership.
Although assuming few mathematical pre-requisites, the standard of mathematical rigour is not compromised. The material covered includes the standard core of categories; functors; natural transformations; equivalence; limits and colimits; functor categories; representables; Yoneda's lemma; adjoints; monads. An extra topic of cartesian closed categories and the lambda-calculus is also provided - a must for computer scientists, logicians and linguists
This Second Edition contains numerous revisions to the original text, including expanding the exposition, revising and elaborating the proofs, providing additional diagrams, correcting typographical errors and, finally, adding an entirely new section on monoidal categories. Nearly a hundred new exercises have also been added, many with solutions, to make the book more useful as a course text and for self-study.