Logic has attained in our century a development incomparably greater than in any past age of its long history, and this has led to such an enrichment and proliferation of its aspects, that the problem of some kind of unified recom prehension of this discipline seems nowadays unavoidable. This splitting into several subdomains is the natural consequence of the fact that Logic has intended to adopt in our century the status of a science. This always implies that the general optics, under which a certain set of problems used to be con sidered, breaks into a lot of specialized sectors of inquiry, each of them being characterized by the introduction of specific viewpoints and of technical tools of its own. The first impression, that often accompanies the creation of one of such specialized branches in a diSCipline, is that one has succeeded in isolating the 'scientific core' of it, by restricting the somehow vague and redundant generality of its original 'philosophical' configuration. But, after a while, it appears that some of the discarded aspects are indeed important and a new specialized domain of investigation is created to explore them. By follOwing this procedure, one finally finds himself confronted with such a variety of independent fields of research, that one wonders whether the fact of labelling them under a common denomination be nothing but the contingent effect of a pure historical tradition."

This book intends to unite studies in different fields related to the development of the relations between logic, law and legal reasoning. Combining historical and philosophical studies on legal reasoning in Civil and Common Law, and on the often neglected Arabic and Talmudic traditions of jurisprudence, this project unites these areas with recent technical developments in computer science. This combination has resulted in renewed interest in deontic logic and logic of norms that stems from the interaction between artificial intelligence and law and their applications to these areas of logic. The book also aims to motivate and launch a more intense interaction between the historical and philosophical work of Arabic, Talmudic and European jurisprudence. The publication discusses new insights in the interaction between logic and law, and more precisely the study of different answers to the question: what role does logic play in legal reasoning? Varying perspectives include that of foundational studies (such as logical principles and frameworks) to applications, and historical perspectives.

"Intuition" has perhaps been the least understood and the most abused term in philosophy. It is often the term used when one has no plausible explanation for the source of a given belief or opinion. According to some sceptics, it is understood only in terms of what it is not, and it is not any of the better understood means for acquiring knowledge. In mathematics the term has also unfortunately been used in this way. Thus, intuition is sometimes portrayed as if it were the Third Eye, something only mathematical "mystics," like Ramanujan, possess. In mathematics the notion has also been used in a host of other senses: by "intuitive" one might mean informal, or non-rigourous, or visual, or holistic, or incomplete, or perhaps even convincing in spite of lack of proof. My aim in this book is to sweep all of this aside, to argue that there is a perfectly coherent, philosophically respectable notion of mathematical intuition according to which intuition is a condition necessary for mathemati cal knowledge. I shall argue that mathematical intuition is not any special or mysterious kind of faculty, and that it is possible to make progress in the philosophical analysis of this notion. This kind of undertaking has a precedent in the philosophy of Kant. While I shall be mostly developing ideas about intuition due to Edmund Husser there will be a kind of Kantian argument underlying the entire book."

One of the great minds of the English Renaissance, Francis Bacon was a scholar, politician, and early advocate of scientific thinking who set no limits on the scope of his enquiries. In these compact and vibrant essays, Bacon addresses an astonishingly diverse range of subjects including religion, politics, personal relationships, morality and even architecture. Evident throughout the volume is his considerable rhetorical skill, incisive wit, and an unwavering belief in the power of reason.

This book examines the nature, sources, and implications of fallacies in philosophical reasoning. In doing so, it illustrates and evaluates various historical instances of this phenomenon. There is widespread interest in the practice and products of philosophizing, yet the important issue of fallacious reasoning in these matters has been effectively untouched. Nicholas Rescher fills this gap by presenting a systematic account of the principal ways in which philosophizing can go astray.

Spanning the period between Wittgenstein's return to Cambridge in 1929 and the first version of Philosophical Investigations in 1936, Piotr Dehnel explores the middle stage in Ludwig Wittgenstein's philosophical development and identifies the major issues which engrossed him, including phenomenology, philosophy of mathematics and philosophy of language. Contrary to the dominant perspective, Dehnel argues that this period was intrinsically different from the early and late stages and should not be viewed as a mere transitional phase. The distinctiveness of Wittgenstein's middle work can be seen in his philosophical thinking as it unfolds in a non-linear trajectory: thoughts do not follow upon each other, ideas do not appear sequentially one by one, and insights do not form a straight chain. Dehnel portrays the diffused and multifarious quality of Wittgenstein's middle thinking, enabling readers to form a more comprehensive view of his entire philosophy and acquire a better grasp of his conceptual trajectory, complete with the intricacies and challenges that it poses.

The issue of a logic foundation for African thought connects well with the question of method. Do we need new methods for African philosophy and studies? Or, are the methods of Western thought adequate for African intellectual space? These questions are not some of the easiest to answer because they lead straight to the question of whether or not a logic tradition from African intellectual space is possible. Thus in charting the course of future direction in African philosophy and studies, one must be confronted with this question of logic. The author boldly takes up this challenge and becomes the first to do so in a book by introducing new concepts and formulating a new African culture-inspired system of logic called Ezumezu which he believes would ground new methods in African philosophy and studies. He develops this system to rescue African philosophy and, by extension, sundry fields in African Indigenous Knowledge Systems from the spell of Plato and the hegemony of Aristotle. African philosophers can now ground their discourses in Ezumezu logic which will distinguish their philosophy as a tradition in its own right. On the whole, the book engages with some of the lingering controversies in the idea of (an) African logic before unveiling Ezumezu as a philosophy of logic, methodology and formal system. The book also provides fresh arguments and insights on the themes of decolonisation and Africanisation for the intellectual transformation of scholarship in Africa. It will appeal to philosophers and logicians-undergraduates and post graduate researchers-as well as those in various areas of African studies.

For the most part, the papers collected in this volume stern from presentations given at a conference held in Tucson over the weekend of May 31 through June 2, 1985. We wish to record our gratitude to the participants in that conference, as well as to the National Science Foundation (Grant No. BNS-8418916) and the University of Arizona SBS Research Institute for their financial support. The advice we received from Susan Steele on organizational matters proved invaluable and had many felicitous consequences for the success of the con ference. We also would like to thank the staff of the Departments of Linguistics of the University of Arizona and the University of Massachusetts at Amherst for their help, as weIl as a number of individuals, including Lin Hall, Kathy Todd, and Jiazhen Hu, Sandra Fulmer, Maria Sandoval, Natsuko Tsujimura, Stuart Davis, Mark Lewis, Robin Schafer, Shi Zhang, Olivia Oehrle-Steele, and Paul Saka. Finally, we would like to express our gratitude to Martin Scrivener, our editor, for his patience and his encouragement. Vll INTRODUCTION The term 'categorial grammar' was introduced by Bar-Rillel (1964, page 99) as a handy way of grouping together some of his own earlier work (1953) and the work of the Polish logicians and philosophers Lesniewski (1929) and Ajdukiewicz (1935), in contrast to approaches to linguistic analysis based on phrase structure grammars."

Contemporary analytic philosophy can generally be characterized by the following tendencies: commitment to first-order predicate logic as the only viable formal logic; rejection of correspondence theories of truth; a view of existence as something expressed by the existential quantifier; a metaphysics that doesn t give the world as a whole its due. This book seeks to offer an alternative analytic theory, one that provides a unified account of what there is, how we speak about it, the underlying logic of our language, how the truth of what we say is determined, and the central role of the real world in all of this. The result is a robust account of reality. The inspiration for many of the ideas that constitute this overall theory comes from such sources as Aristotle, Leibniz, Ryle, and Sommers."

Games, Norms, and Reasons: Logic at the Crossroads provides an overview of modern logic focusing on its relationships with other disciplines, including new interfaces with rational choice theory, epistemology, game theory and informatics. This book continues a series called "Logic at the Crossroads" whose title reflects a view that the deep insights from the classical phase of mathematical logic can form a harmonious mixture with a new, more ambitious research agenda of understanding and enhancing human reasoning and intelligent interaction. The editors have gathered together articles from active authors in this new area that explore dynamic logical aspects of norms, reasons, preferences and beliefs in human agency, human interaction and groups. The book pays a special tribute to Professor Rohit Parikh, a pioneer in this movement.

Frontiers in Belief Revision is a unique collection of leading edge research in Belief Revision. It contains the latest innovative ideas of highly respected and pioneering experts in the area, including Isaac Levi, Krister Segerberg, Sven Ove Hansson, Didier Dubois, and Henri Prade. The book addresses foundational issues of inductive reasoning and minimal change, generalizations of the standard belief revision theories, strategies for iterated revisions, probabilistic beliefs, multiagent environments and a variety of data structures and mechanisms for implementations. This book is suitable for students and researchers interested in knowledge representation and in the state of the art of the theory and practice of belief revision.

Klemens Szaniawski was born in Warsaw on March 3, 1925. He began to study philosophy in the clandestine Warsaw University during World War II. Tadeusz Kotarbinski, Jan Lukasiewicz, Maria and Stanislaw Ossowskis, Wladyslaw Tatarkiewicz, and Henryk Hii: were among his teachers. Sza- niawski was also a member of the Polish Home Army (AK), one of the young- est. He was arrested and spent the last period of the war as a prisoner in Auschwitz. After 1945, he continued his studies in the University of L6dz; his Master thesis was devoted to French moral thought of the 17th and 18th cen- turies. Then he worked in the Department of Ethics in L6dZ. In 1950, he received his Ph. D. on the basis of the dissertation on the concept of honour in knight groups in the Middle Ages; Maria Ossowska was the supervisor. In the early fifties he moved to Warsaw to the Department of Logic, directed by Kotarbinski. He took his habilitation exams in 1961. In 1969 he became a professor. Since 1970 he was the head of Department of the Logic at the Warsaw University. In the sixties Szaniawski was also the Dean of the Faculty of Philosophy and Sociology. In 1984 he was elected the Rector Magnificus of the Warsaw University but the Ministry overruled the autonomous democra- tic vote of the academic community. He served as the President of the Polish (since 1977) taking this post after Kotarbinski.

1. The ?rst edition of this book was published in 1977. The text has been well received and is still used, although it has been out of print for some time. In the intervening three decades, a lot of interesting things have happened to mathematical logic: (i) Model theory has shown that insights acquired in the study of formal languages could be used fruitfully in solving old problems of conventional mathematics. (ii) Mathematics has been and is moving with growing acceleration from the set-theoretic language of structures to the language and intuition of (higher) categories, leaving behind old concerns about in?nities: a new view of foundations is now emerging. (iii) Computer science, a no-nonsense child of the abstract computability theory, has been creatively dealing with old challenges and providing new ones, such as the P/NP problem. Planning additional chapters for this second edition, I have decided to focus onmodeltheory, the conspicuousabsenceofwhichinthe ?rsteditionwasnoted in several reviews, and the theory of computation, including its categorical and quantum aspects. The whole Part IV: Model Theory, is new. I am very grateful to Boris I. Zilber, who kindly agreed to write it. It may be read directly after Chapter II. The contents of the ?rst edition are basically reproduced here as Chapters I-VIII. Section IV.7, on the cardinality of the continuum, is completed by Section IV.7.3, discussing H. Woodin's discovery.

An introductory textbook, Logic for Justice covers, in full detail, the language and semantics of both propositional logic and first-order logic. It motivates the study of those logical systems by drawing on social and political issues. Basically, Logic for Justice frames propositional logic and first-order logic as two theories of the distinction between good arguments and bad arguments. And the book explains why, for the purposes of social justice and political reform, we need theories of that distinction. In addition, Logic for Justice is extremely lucid, thorough, and clear. It explains, and motivates, many different features of the formalism of propositional logic and first-order logic, always connecting those features back to real-world issues. Key Features Connects the study of logic to real-world social and political issues, drawing in students who might not otherwise be attracted to the subject. Offers extremely clear and thorough presentations of technical material, allowing students to learn directly from the book without having to rely on instructor explanations. Carefully explains the value of arguing well throughout one’s life, with several discussions about how to argue and how arguments – when done with care – can be helpful personally. Includes examples that appear throughout the entire book, allowing students to see how the ideas presented in the book build on each other. Provides a large and diverse set of problems for each chapter. Teaches logic by connecting formal languages to natural languages with which students are already familiar, making it much easier for students to learn how logic works.

An introductory textbook, Logic for Justice covers, in full detail, the language and semantics of both propositional logic and first-order logic. It motivates the study of those logical systems by drawing on social and political issues. Basically, Logic for Justice frames propositional logic and first-order logic as two theories of the distinction between good arguments and bad arguments. And the book explains why, for the purposes of social justice and political reform, we need theories of that distinction. In addition, Logic for Justice is extremely lucid, thorough, and clear. It explains, and motivates, many different features of the formalism of propositional logic and first-order logic, always connecting those features back to real-world issues. Key Features Connects the study of logic to real-world social and political issues, drawing in students who might not otherwise be attracted to the subject. Offers extremely clear and thorough presentations of technical material, allowing students to learn directly from the book without having to rely on instructor explanations. Carefully explains the value of arguing well throughout one’s life, with several discussions about how to argue and how arguments – when done with care – can be helpful personally. Includes examples that appear throughout the entire book, allowing students to see how the ideas presented in the book build on each other. Provides a large and diverse set of problems for each chapter. Teaches logic by connecting formal languages to natural languages with which students are already familiar, making it much easier for students to learn how logic works.

In Fallacies and Judgments of Reasonableness, Frans H. van Eemeren, Bart Garssen and Bert Meuffels report on their systematic empirical research of the conventional validity of the pragma-dialectical discussion rules. The experimental studies they carried out during more than ten years start from the pragma-dialectical theory of argumentation developed at the University of Amsterdam, their home university. In these studies they test methodically the intersubjective acceptability of the rules for critical discussion proposed in this theory by confronting ordinary arguers who have not received any special education in argumentation and fallacies with discussion fragments containing both fallacious and non-fallacious argumentative moves. The research covers a wide range of informal fallacies. In this way, the authors create a basis for comparing the theoretical reasonableness conception of pragma-dialectics with the norms for judging argumentative moves prevailing in argumentative practice. Fallacies and Judgments of Reasonableness provides a unique insight into the relationship between theoretical and practical conceptions of reasonableness, supported by extensive empirical material gained by means of sophisticated experimental research.

Soren Kierkegaard and Friedrich Nietzsche remain two of the most interesting and compelling thinkers for contemporary readers. Rejecting the dry, dispassionate tone of most academic philosophy, these thinkers offer witty, penetrating critiques of many modern values as well as passionately moving portraits of alternative ideals. This work reveals that what Kierkegaard and Nietzsche most fundamentally share, and what can be their greatest contribution to contemporary ethics, is a method of illustrating and evaluating different ways of life considered as a whole. In asking what way of life is best, Kierkegaard and Nietzsche revive an ancient approach to ethics largely neglected throughout the modern era. This work offers a detailed elucidation of this method and of their respective ideals, Kierkegaard's life of faith and Nietzsche's life of individual sovereignty. These ideals are explored within each thinker's typology of different ways of life and then compared and contrasted with each other.

This wide-ranging book introduces information as a key concept not only in physics, from quantum mechanics to thermodynamics, but also in the neighboring sciences and in the humanities. The central part analyzes dynamical processes as manifestations of information flows between microscopic and macroscopic scales and between systems and their environment. Quantum mechanics is interpreted as a reconstruction of mechanics based on fundamental limitations of information processing on the smallest scales. These become particularly manifest in quantum chaos and in quantum computing. Covering subjects such as causality, prediction, undecidability, chaos, and quantum randomness, the book also provides an information-theoretical view of predictability. More than 180 illustrations visualize the concepts and arguments. The book takes inspiration from the author's graduate-level topical lecture but is also well suited for undergraduate studies and is a valuable resource for researchers and professionals.

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.