This book collects, for the first time in one volume, contributions honoring Professor Raymond Smullyan's work on self-reference. It serves not only as a tribute to one of the great thinkers in logic, but also as a celebration of self-reference in general, to be enjoyed by all lovers of this field. Raymond Smullyan, mathematician, philosopher, musician and inventor of logic puzzles, made a lasting impact on the study of mathematical logic; accordingly, this book spans the many personalities through which Professor Smullyan operated, offering extensions and re-evaluations of his academic work on self-reference, applying self-referential logic to art and nature, and lastly, offering new puzzles designed to communicate otherwise esoteric concepts in mathematical logic, in the manner for which Professor Smullyan was so well known. This book is suitable for students, scholars and logicians who are interested in learning more about Raymond Smullyan's work and life.

This volume contains English translations of Frege's early writings in logic and philosophy and of relevant reviews by other leading logicians. Professor Bynum has contributed a biographical essay, introduction, and extensive bibliography.

This volume is dedicated to Prof. Dag Prawitz and his outstanding contributions to philosophical and mathematical logic. Prawitz's eminent contributions to structural proof theory, or general proof theory, as he calls it, and inference-based meaning theories have been extremely influential in the development of modern proof theory and anti-realistic semantics. In particular, Prawitz is the main author on natural deduction in addition to Gerhard Gentzen, who defined natural deduction in his PhD thesis published in 1934. The book opens with an introductory paper that surveys Prawitz's numerous contributions to proof theory and proof-theoretic semantics and puts his work into a somewhat broader perspective, both historically and systematically. Chapters include either in-depth studies of certain aspects of Dag Prawitz's work or address open research problems that are concerned with core issues in structural proof theory and range from philosophical essays to papers of a mathematical nature. Investigations into the necessity of thought and the theory of grounds and computational justifications as well as an examination of Prawitz's conception of the validity of inferences in the light of three "dogmas of proof-theoretic semantics" are included. More formal papers deal with the constructive behaviour of fragments of classical logic and fragments of the modal logic S4 among other topics. In addition, there are chapters about inversion principles, normalization of p roofs, and the notion of proof-theoretic harmony and other areas of a more mathematical persuasion. Dag Prawitz also writes a chapter in which he explains his current views on the epistemic dimension of proofs and addresses the question why some inferences succeed in conferring evidence on their conclusions when applied to premises for which one already possesses evidence.

This volume describes and analyzes in a systematic way the great contributions of the philosopher Krister Segerberg to the study of real and doxastic actions. Following an introduction which functions as a roadmap to Segerberg's works on actions, the first part of the book covers relations between actions, intentions and routines, dynamic logic as a theory of action, agency, and deontic logics built upon the logics of actions. The second section explores belief revision and update, iterated and irrevocable beliefs change, dynamic doxastic logic and hypertheories. Segerberg has worked for more than thirty years to analyze the intricacies of real and doxastic actions using formal tools - mostly modal (dynamic) logic and its semantics. He has had such a significant impact on modal logic that "It is hard to roam for long in modal logic without finding Krister Segerberg's traces," as Johan van Benthem notes in his chapter of this book.

Themes from Ontology, Mind and Logic celebrates Peter Simons's admirable career. The book contains seventeen essays with themes ranging from metaphysics to phenomenology. The contributions by Fabrice Correia, Bob Hale and Crispin Wright, Ingvar Johansson, Kathrin Koslicki, Uriah Kriegel, Wolfgang Kunne, Edgar Morscher, Kevin Mulligan, Maria Elisabeth Reicher, Maria van der Schaar, Benjamin Schnieder, Johanna Seibt, Ted Sider, David Woodruff Smith, Mark Textor and Jan Wolenski, tackle the problems that defined Simons's work and insights into some of today's most interesting and significant philosophical questions.

This is not quite the book I originally intended to write. Since I first felt that linguistic application of categorial grammar merited a system- atic presentation, I have been subject to (what seemed to be) a series of demanding technical and foundational distractions. Inspite of a prej- udice that mathematical elegance was even inconsistent with linguistic practicality, repeated illumination of the latter by the former implied a new perspective on the field, one prompting formal innovation, and some re-examination of methods and goals. This piece collects and extends work over the last four years general- ising categorial grammar to a categorial logic. The state of the art at the beginning of that period was represented by the edited collections Oehrle, Bach and Wheeler (1988) and Buszkowski, Marciszewski and van Benthem (1988) (see Morrill 1991a, b), and by Moortgat (1988b). Familiarity with such work however is not strictly necessary for an un- derstanding of the present one, which attempts to map a self-contained, if intensive, course with Montague Grammar as its point of departure. This being the case, the reader should have an understanding of logical semantics and its technicalities, such as would be obtained from Dowty, Wall and Peters (1981), or Gamut (1991). Some familiarity with the issues raised by contemporary syntactic theories would also be useful, as would some familiarity with logical deduction.

A comprehensive survey of Martin-Loef's constructive type theory, considerable parts of which have only been presented by Martin-Loef in lecture form or as part of conference talks. Sommaruga surveys the prehistory of type theory and its highly complex development through eight different stages from 1970 to 1995. He also provides a systematic presentation of the latest version of the theory, as offered by Martin-Loef at Leiden University in Fall 1993. This presentation gives a fuller and updated account of the system. Earlier, brief presentations took no account of the issues related to the type-theoretical approach to logic and the foundations of mathematics, while here they are accorded an entire part of the book. Readership: Comprehensive accounts of the history and philosophy of constructive type theory and a considerable amount of related material. Readers need a solid background in standard logic and a first, basic acquaintance with type theory.

Graham Priest presents an original exploration of philosophical questions concerning the one and the many. He covers a wide range of issues in metaphysics-including unity, identity, grounding, mereology, universals, being, intentionality, and nothingness-and deploys the techniques of paraconsistent logic in order to offer a radically new treatment of unity. Priest brings together traditions of Western and Asian thought that are usually kept separate in academic philosophy: he draws on ideas from Plato, Heidegger, and Nagarjuna, among other philosophers.

The first Symposium consisted of three people in a cafe in Warsaw in 1973. Since then, meetings have grown in size and have been held in Leyden, Copenhagen, Nijmegen, Rome, Oxford, Poitiers and Freiburg am-Breisgau. The ninth Symposium was held in St Andrews in June 1990, with 57 participants who listened to addresses by 28 speakers. It was very fitting that Scotland's oldest university, founded in the heyday of medievalleaming in 1411, should have been given the chance to bring together scholars from all over Europe and beyond to present their researches on the glorious past of scholastic rational thought. The topic of the Symposium was "Sophisms in Medieval Logic and Grammar." The present volume consists, for the most part, of the papers presented at the Symposium. In fact, however, it proved impossible to include five of the contributions. Two of the papers included here were intended for the Symposium but in the event not delivered, because of the unavoidable absence of the speakers. The Symposium received very helpful financial support from one of the major philosophical associations in Britain, the Mind Association, from the Philosophical Quarterly, a journal published at St Andrews, from the University of St Andrews, from the British Academy, and from Low and Bonarplc. In organising the programme for the conference and in preparing the papers for publication I received invaluable help from: Professor E.J."

Action is conceived of as an intentional behavior of an individual or of an institutional subject; it is determined by information processing, namely by a process in which pieces of descriptive and practical information are involved. Action is explained by a formal and finalistic theory which is connected with a specific theory of institutions. The philosophical basis of the logic of norm sentences and of other systems of practical thinking (formal teleology, axiology, logic of preferences) is discussed. The author criticizes traditional deontic logic and argues in favor of a genuine logic of norms. The book gives a structure analysis of the so-called practical inference and of nomic causal propositions. Besides a critical account of von Wright's practical philosophy the author offers critical analyses of discourse rationality (Habermas, Apel, Alexy) and of Wittgenstein's views on philosophizing. The book addresses readers interested in philosophical logic, practical philosophy, sociology of institutions, legal philosophy, and theory democracy.

Mathematics and logic have been central topics of concern since the dawn of philosophy. Since logic is the study of correct reasoning, it is a fundamental branch of epistemology and a priority in any philosophical system. Philosophers have focused on mathematics as a case study for general philosophical issues and for its role in overall knowledge- gathering. Today, philosophy of mathematics and logic remain central disciplines in contemporary philosophy, as evidenced by the regular appearance of articles on these topics in the best mainstream philosophical journals; in fact, the last decade has seen an explosion of scholarly work in these areas.
This volume covers these disciplines in a comprehensive and accessible manner, giving the reader an overview of the major problems, positions, and battle lines. The 26 contributed chapters are by established experts in the field, and their articles contain both exposition and criticism as well as substantial development of their own positions. The essays, which are substantially self-contained, serve both to introduce the reader to the subject and to engage in it at its frontiers. Certain major positions are represented by two chapters--one supportive and one critical.
The Oxford Handbook of Philosophy of Math and Logic is a ground-breaking reference like no other in its field. It is a central resource to those wishing to learn about the philosophy of mathematics and the philosophy of logic, or some aspect thereof, and to those who actively engage in the discipline, from advanced undergraduates to professional philosophers, mathematicians, and historians.

Essays on Husserl's Logic and Philosophy of Mathematics sets out to fill up a lacuna in the present research on Husserl by presenting a precise account of Husserl's work in the field of logic, of the philosophy of logic and of the philosophy of mathematics. The aim is to provide an in-depth reconstruction and analysis of the discussion between Husserl and his most important interlocutors, and to clarify pivotal ideas of Husserl's by considering their reception and elaboration by some of his disciples and followers, such as Oskar Becker and Jacob Klein, as well as their influence on some of the most significant logicians and mathematicians of the past century, such as Luitzen E. J. Brouwer, Rudolf Carnap, Kurt Goedel and Hermann Weyl. Most of the papers consider Husserl and another scholar - e.g. Leibniz, Kant, Bolzano, Brentano, Cantor, Frege - and trace out and contextualize lines of influence, points of contact, and points of disagreement. Each essay is written by an expert of the field, and the volume includes contributions both from the analytical tradition and from the phenomenological one.

Aristotle's modal syllogistic has been an object of study ever since the time of Theophrastus; but these studies (apart from an intense flowering in the Middle Ages) have been somewhat desultory. Remarkably, in the 1990s several new lines of research have appeared, with series of original publications by Fred Johnson, Richard Patterson and Ulrich Nortmann. Johnson presented for the first time a formal semantics adequate to a de re reading of the apodeictic syllogistic; this was based on a simple intuition linking the modal syllogistic to Aristotelian metaphysics. Nortmann developed an ingenious de dicto analysis. Patterson articulated the links (both theoretical and genetic) between the modal syllogistic and the metaphysics, using an analysis which strictly speaking is neither de re nor de dicto. My own studies in this field date from 1976, when my colleague Peter Roeper and I jointly wrote a paper "Aristotle's apodeictic syllogisms" for the XXIInd History of Logic Conference in Krakow. This paper contained the disjunctive reading of particular affirmative apodeictic propositions, which I still favour. Nonetheless, I did not consider that paper's results decisive or comprehensive enough to publish, and my 1981 book The Syllogism contained no treatment of the modal syllogism. The paper's ideas lay dormant till 1989, when I read Johnson's and Patterson's initial articles. I began publishing on the topic in 1991. Gradually my thoughts acquired a certain comprehensiveness and systematicity, till in 1993 I was able to take a semester's sabbatical to write up a draft of this book.

Poland has played an enormous role in the development of mathematical logic. Leading Polish logicians, like Lesniewski, Lukasiewicz and Tarski, produced several works related to philosophical logic, a field covering different topics relevant to philosophical foundations of logic itself, as well as various individual sciences. This collection presents contemporary Polish work in philosophical logic which in many respects continue the Polish way of doing philosophical logic. This book will be of interest to logicians, mathematicians, philosophers, and linguists.

The distinguished scholar of ancient philosophy J.L. Ackrill here presents the best of his essays on Plato and Aristotle from the past forty years. He brings philosophical acuity and philological expertise to a range of texts and topics in ancient thought - from ethics and logic to epistemology and metaphysics - which continue to be widely discussed today.

The articles in this volume deal with the main inferential methods that can be applied to different kinds of experimental evidence. These contributions - accompanied with critical comments - by renowned scholars in the field of philosophy of science aim at removing the traditional opposition between inductivists and deductivists. They explore the different methods of explanation and justification in the sciences in different contexts and with different objectives.
The volume contains contributions on methods of the sciences, especially on induction, deduction, abduction, laws, probability and explanation, ranging from logic, mathematics, natural to the social sciences. They present a highly topical pluralist re-evaluation of methodological and foundational procedures and reasoning, e.g. focusing in Bayesianism and Artificial Intelligence.
They document the second international conference in Vienna on "Induction and Deduction in the Sciences" as part of the Scientific Network on "Historical and Contemporary Perspectives of Philosophy of Science in Europe," funded by the European Science Foundation (ESF).

This volume is a culmination of years of development, and the first to introduce the concepts of superoptimum evaluative and explanatory reasoning. Stuart Nagel's new Quorum book will help academic and practicing attorneys in two important ways. First, by understanding evaluative reasoning, they will gain a better grasp of the appropriate behavior to be adopted if they wish to achieve certain desired goals. Second, by understanding the elements of explanatory reasoning, they will understand how and why decisions are reached.

Evaluative reasoning can take several forms. It can help decision-makers select from among several public policy choices. It can enhance individual decision-making and provide means to allocate scarce resources. It can also assist in advocating and influencing decisions, mediating disputes, representing divergent viewpoints, and in assigning people to specific tasks. Explanatory reasoning, on the other hand, will help explain public policy making, and assist users in generalizing from cases and facts, and in understanding relationships. The purpose of explanatory reasoning is also to explain why superoptimum solutions are infrequently adopted and why they are seldom successfully implemented. The use of both kinds of reasoning, says Nagel, are particularly important to those who want a better understanding and want to improve the legal system.

The goal of this work is twofold. First, it aims to account for double genitive constructions in Serbian. Second, it aims to re-evaluate the DP hypothesis in light of their existence in Serbian. Based on evidence from the categorial status of possessives, argumenthood in the nominal domain, the morphosyntactic structure of nominalizations, and the assignment of the genitive case, it is argued that DP projection must be assumed in Serbian.

Aristotle's modal syllogistic is his study of patterns of reasoning about necessity and possibility. Many scholars think the modal syllogistic is incoherent, a 'realm of darkness'. Others think it is coherent, but devise complicated formal modellings to mimic Aristotle's results. This volume provides a simple interpretation of Aristotle's modal syllogistic using standard predicate logic. Rini distinguishes between red terms, such as 'horse', 'plant' or 'man', which name things in virtue of features those things must have, and green terms, such as 'moving', which name things in virtue of their non-necessary features. By applying this distinction to the "Prior Analytics," Rini shows how traditional interpretive puzzles about the modal syllogistic melt away and the simple structure of Aristotle's own proofs is revealed. The result is an applied logic which provides needed links between Aristotle's views of science and logical demonstration. The volume is particularly valuable to researchers and students of the history of logic, Aristotle's theory of modality, and the philosophy of logic in general.

Temporal Logic: From Ancient Ideas to Artificial Intelligence deals with the history of temporal logic as well as the crucial systematic questions within the field. The book studies the rich contributions from ancient and medieval philosophy up to the downfall of temporal logic in the Renaissance. The modern rediscovery of the subject, which is especially due to the work of A. N. Prior, is described, leading into a thorough discussion of the use of temporal logic in computer science and the understanding of natural language. Temporal Logic: From Ancient Ideas to Artificial Intelligence thus interweaves linguistic, philosophical and computational aspects into an informative and inspiring whole.

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."