Vladimir Aleksandrovich Smirnov was born on March 2, 1931. He graduated from Moscow State University in 1954. From 1957 till 1961 he was a lecturer in philosophy and logic at the Tomsk University. Since 1961 his scientific activity continued in Moscow at the Institute of Philosophy of Academy of Sciences of the USSR. From 1970 and till the last days of his life V. A. Smirnov was lecturer and then Professor at the Chair of Logic at Moscow State University. V. A. Smirnov played an important role at the Institute of Philosophy of Russian Academy of Sciences being the Head of Department of Epistemology, Logic and Philosophy of Science and Technology, and the Head of Section of Logic. Last years he was the leader of the Centre of Logical Investigations of Russsian Academy of Sciences. In 1990-91 he founded a new non-goverment Institute of Logic, Cognitive Sciences and Development of Personality for performing research, teaching, editorial and organization activity in the field of humanities. At the Department of Philosophy of Moscow State University and at the Institute of Philosophy V. A. Smirnov and his close colleagues have founded a Russian logical school which brought up many talented researchers who work at several scientific centres in various countries.

Hard as it is to believe, what is possibly Galileo's most important Latin manuscript was not transcribed for the National Edition of his works and so has remained hidden from scholars for centuries. In this volume William A. Wallace translates the logical treatises contained in that manuscript and makes them intelligible to the modern reader. He prefaces his translation with a lengthy introduction describing the contents of the manuscript, the sources from which it derives, its dating, and how it relates to Galileo's other Pisan writings. The translation is accompanied by extensive notes and commentary; these explain the text and tie it to the fuller exposition of Galileo's logical methodology in the author's companion volume, Galileo's Logic of Discovery and Proof. The result is a research tool that is indispensable for anyone intent on understanding Galileo's logic as described in that volume and the documentary evidence on which it is based.

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 artiele in the Encyelopaedia 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 0/ Mathematical Logic, published in 1977, edited by the late Jon Barwise. The four volume Handbook 0/ 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 cireles. These areas were under increasing commercial press ure 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.

This volume contains a selection of papers (keynote addresses and other important papers) from the International Conference on Argumentation at Amsterdam of 2002 by prominent international scholars of argumentation theory. The contributions are representative of the main approaches to the study of argumentation: the informal logical approach, the logical approach, the dialectical approach, the rhetorical and the communicative approach. Taken together the papers in this volume provide an insightful cross-section of the current state of affairs in argumentation research.
The collection of essays as a whole will be of interest to all those working in the field of argumentation theory and to all scholars who are interested in recent developments in this field.

Intellectics' seeks to understand the functions, structure and operation of the human intellect and to test artificial systems to see the extent to which they can substitute or complement such functions. The word itself was introduced in the early 1980s by Wolfgang Bibel to describe the united fields of artificial intelligence and cognitive science. The book collects papers by distinguished researchers, colleagues and former students of Bibel's, all of whom have worked together with him, and who present their work to him here to mark his 60th birthday. The papers discuss significant issues in intellectics and computational logic, ranging across automated deduction, logic programming, the logic-based approach to intellectics, cognitive robotics, knowledge representation and reasoning. Each paper contains new, previously unpublished, reviewed results. The collection is a state of the art account of the current capabilities and limitations of a computational-logic-based approach to intellectics. Readership: Researchers who are convinced that the intelligent behaviour of machines should be based on a rigid formal treatment of knowledge representation and reasoning.

The aim of this book is to present and analyze philosophical conceptions concerning mathematics and logic as formulated by Polish logicians, mathematicians and philosophers in the 1920s and 1930s. It was a remarkable period in the history of Polish science, in particular in the history of Polish logic and mathematics. Therefore, it is justified to ask whether and to what extent the development of logic and mathematics was accompanied by a philosophical reflection. We try to answer those questions by analyzing both works of Polish logicians and mathematicians who have a philosophical temperament as well as their research practice. Works and philosophical views of the following Polish scientists will be analyzed: Waclaw Sierpinski, Zygmunt Janiszewski, Stefan Mazurkiewicz, Stefan Banach Hugo Steinhaus, Eustachy Zylinsk and Leon Chwistek, Jan Lukasiewicz, Zygmunt Zawirski, Stanislaw Lesniewski, Tadeusz Kotarbinski, Kazimierz Ajdukiewicz, Alfred Tarski, Andrzej Mostowski and Henryk Mehlberg, Jan Sleszynski, Stanislaw Zaremba and Witold Wilkosz. To indicate the background of scientists being active in the 1920s and 1930s we consider in Chapter 1 some predecessors, in particular: Jan Sniadecki, Jozef Maria Hoene-Wronski, Samuel Dickstein and Edward Stamm.

"Foundations of the Formal Sciences" (FotFS) is a series of interdisciplinary conferences in mathematics, philosophy, computer science and linguistics. The main goal is to reestablish the traditionally strong links between these areas of research that have been lost in the past decades.

The second conference in the series had the subtitle "Applications of Mathematical Logic in Philosophy and Linguistics" and brought speakers from all parts of the Formal Sciences together to give a holistic view of how mathematical methods can improve our philosophical and technical understanding of language and scientific discourse, ranging from the theoretical level up to applications in language recognition software.

Audience: This volume is of interest to all formal philosophers and theoretical linguists. In addition to that, logicians interested in the applications of their field and logic students in mathematics, computer science, philosophy and linguistics can use the volume to broaden their knowledge of applications of logic.

This monograph is designed to provide an introduction to the principal areas of tense logic. Many of the developments in this ever-growing field have been intentionally excluded to fulfill this aim. Length also dictated a choice between the alternative notations of A. N. Prior and Nicholas Rescher - two pioneers of the subject. I choose Prior's because of the syntactical parallels with the language it symbolizes and its close ties with other branches of logi cal theory, especially modal logic. The first chapter presents a wider view of the material than later chapters. Several lines of development are consequently not followed through the remainder of the book, most notably metric systems. Although it is import ant to recognize that the unadorned Prior-symbolism can be enriched in vari ous ways it is an advanced subject as to how to actually carry off these enrichments. Readers desiring more information are referred to the appropri ate literature. Specialists will notice that only the first of several quantifi cational versions of tense logic is proven complete in the final chapter. Again constraints of space are partly to blame. The proof for the 'star' systems is wildly complex and at the time of this writing is not yet ready for publi cation."

Constructive mathematics is based on the thesis that the meaning of a mathematical formula is given, not by its truth-conditions, but in terms of what constructions count as a proof of it. However, the meaning of the terms `construction' and `proof' has never been adequately explained (although Kriesel, Goodman and Martin-Loef have attempted axiomatisations). This monograph develops precise (though not wholly formal) definitions of construction and proof, and describes the algorithmic substructure underlying intuitionistic logic. Interpretations of Heyting arithmetic and constructive analysis are given. The philosophical basis of constructivism is explored thoroughly in Part I. The author seeks to answer objections from platonists and to reconcile his position with the central insights of Hilbert's formalism and logic. Audience: Philosophers of mathematics and logicians, both academic and graduate students, particularly those interested in Brouwer and Hilbert; theoretical computer scientists interested in the foundations of functional programming languages and program correctness calculi.

We are happy to present the second volume of the Handbook of Defeasible Reasoning and Uncertainty Management Systems. Uncertainty pervades the real world and must therefore be addressed by every system that attempts to represent reality. The representation of un certainty is a major concern of philosophers, logicians, artificial intelligence researchers and computer sciencists, psychologists, statisticians, economists and engineers. The present Handbook volumes provide frontline coverage of this area. This Handbook was produced in the style of previous handbook series like the Handbook of Philosophical Logic, the Handbook of Logic in Computer Science, the Handbook of Logic in Artificial Intelligence and Logic Programming, and can be seen as a companion to them in covering the wide applications of logic and reasoning. We hope it will answer the needs for adequate representations of uncertainty. This Handbook series grew out of the ESPRIT Basic Research Project DRUMS II, where the acronym is made out of the Handbook series title. This project was financially supported by the European Union and regroups 20 major European research teams working in the general domain of uncer tainty. As a fringe benefit of the DRUMS project, the research community was able to create this Handbook series, relying on the DRUMS partici pants as the core of the authors for the Handbook together with external international experts."

Truth and Paradox offers a comprehensive account of truth values and the norms governing claims about truth, based on a new approach to logic and semantics. Since the seminal work of Tarski in the mid-twentieth century, the Liar paradox and other related paradoxes have stood in the way of a precise philosophical account of truth. Tim Maudlin draws on analogies from mathematical physics to explicate the origin of classical truth-value gaps, and to provide an account of truth that avoids any hierarchy of languages or of truth predicates. He also closely investigates our reasoning about truth, including apparently unobjectionable reasoning about the paradoxical sentences. The fallacies in that reasoning are located not in any inferences concerning truth, but in the foundations of standard logic. Blocking the paradoxical arguments requires emendation of classical logic, and the requisite emendations call into question the existence of any a priori logical truths. Maudlin also includes a discussion of facts and factuality, most particularly the question of whether there are any facts about truth. All philosophers interested in logic and language will find this a stimulating read.

Infinite regresses (e.g., event3 caused event2, event2 caused event1, ad infinitum; statement3 justifies statement2, statement2 justifies statement1, ad infinitum) have been used as premises in arguments on a great variety of topics in both Eastern and Western philosophy since ancient times. They are part of a philosopher's tool kit of argumentation. But how sharp or strong is this tool? How effectively is it used? The typical presentation of infinite regress arguments throughout history is so succinct and has so many gaps that it is often unclear how an infinite regress is derived, and why an infinite regress is logically problematic, and as a result, it is often difficult to evaluate infinite regress arguments. These prevalent consequences indicate that there is a need for a theory to re-orient our practice. After well over two thousand years of using infinite regresses as premises, one would have expected that at least some theory of infinite regress arguments would have emerged. None exists. There have been only a few articles on infinite regress arguments, but they are based on the examination of only a small number of examples, discuss only a few logical or rhetorical aspects of infinite regress arguments, and so they help to meet the need for a theory in only a limited way.

Given the situation, I examined many infinite regress arguments to clarify the various aspects of the derivation of infinite regresses, and explain the different ways in which certain infinite regresses are unacceptable. My general approach consisted of collecting and evaluating as many infinite regress arguments as possible, comparing and contrasting many of the formal and non-formal properties, looking for recurring patterns, and identifying the properties that appeared essential to those patterns. The six chapters of this book gradually emerged from this approach. Two very general questions guided this work: (1) How are infinite regresses generated in infinite regress arguments? (2) How do infinite regresses logically function in an argument? In answering these questions I avoided as much as possible addressing the philosophical content and historical background of the arguments examined. Due to the already extensive work done on causal regresses and regresses of justification, only a few references are made to them. However, the focus is on other issues that have been neglected, and that do contribute to a general theory of infinite regress arguments: I clarify the notion of an infinite regress; identify different logical forms of infinite regresses; describe different kinds of infinite regress arguments; distinguish the rhetoric from the logic in infinite regress arguments; and discuss the function of infinite regresses in arguments. The unexamined derivation of infinite regresses is worth deriving to discover what we have kept hidden from ourselves, improve our ways of constructing and evaluating these arguments, and sharpen and strengthen one of our argumentative tools. This work is one example of empirical logic applied to infinite regress arguments: "the attempt to formulate, to test, to clarify, and to systematize concepts and principles for the interpretation, the evaluation, and the sound practice of reasoning" (Finocchiaro, M. Arguments about Arguments, Systematic, Critical and Historical Essays in Logical Theory. P48). "

Find out what connects logic and humor in this alternative guide to logical reasoning. Combining jokes, stories, and ironic situations, Stan Baronett shows how it is possible to ground the language of logic in everyday experience. Each chapter introduces a basic logical reasoning concept based on happenings in daily life. Using jokes as his examples, Baronett reveals the inner workings of logic. After all an effective joke often relies on an unanticipated assumption that leads to an unexpected result. The assumption changes the normal context of an everyday situation, so we are surprised by the ending. A complex mind that learns from experience, and builds a storehouse of regularly recurring patterns, is a great survival tool. But for a joke to work, the punch line has to be something our minds don't logically anticipate. The ending jolts our minds for a split second while we grasp the absurdity of the situation. This is how logic works: one part of your mind determines whether the information you are receiving is true or false, while another part of your mind deals with logical consequences. Injecting a sense of humor into logical language, Baronett helps us understand how to analyze basic logical reasoning and provides light relief for anyone daunted by the complex world of logic.

The studies that make up this book were written and brought together to honor the memory of Jan Pinborg. His unexpected death in 1982 at the age of forty-five shocked and saddened students of medieval philosophy everywhere and left them with a keen sense of disappoint ment. In his fifteen-year career Jan Pinborg had done so much for our field with his more than ninety books, editions, articles, and reviews and had done it all so well that we recognized him as a leader and counted on many more years of his scholarship, his help, and his friendship. To be missed so sorely by his international colleagues in an academic field is a mark of Jan's achievement, but only of one aspect of it, for historians of philosophy are not the only scholars who have reacted in this way to Jan's death. In his decade and a half of intense productivity he also acquired the same sort of special status among historians of linguistics, whose volume of essays in his memory is being G. L. Bursill-Hall almost simultane published under the editorship of ously with this one. Sten Ebbesen, Jan's student, colleague, and successor as Director of the Institute of Medieval Greek and Latin Philology at the University of Copenhagen, has earned the gratitude of all of us by memorializing Jan 1 in various biographical sketches, one of which is accompanied by a 2 complete bibliography of his publications."

This book is the first English version of Prolegomena zu einer kritischen Grammatik, published by Julius Springer, Vienna, 1935, as Volume 10 of the Vienna Circle's series Schriften zur wissenschaftlichen Weltauffassung. The prefatory remarks of both editor and author acknowledge the influence ofWittgenstein in a general way. However, in aim and approach, the work differs from Wittgenstein's Philosophische Grammatik (l969). This is indeed based on material going back to 1932, some of which Schachter must have known. On the other hand, the present Prolegomena not only explains the general, philosophical principles to be followed, but in the light of these proceeds to cover the entire range of conventional grammar, showing where that is uncritical. Whether Wittgenstein in his turn knew of Schachter's work has never been explored. Schachter's object is universal grammar. As is natural, the examples in the original are largely drawn from German grammar, with occasional minor excursions into other languages. For English readers, what matters are the general problems of grammar: there is no point in tying these to the linguistic peculiarities of German, let alone a local variety of it. One who can grasp German at that level might as well read the original. The translation is therefore twofold: the text as a whole has been rendered into English, and the entire apparatus of examples has been replaced, as far as this can be done, by illustrations from English grammar, chosen so as to bring out the same kinds of problem as in the original.

This book presents the New Theory of Argumentation, popularly known as the New Rhetoric, as an innovative theoretical and methodological system which will become increasingly important. Two factors determine the importance of this philosophy: (1) The collapse of all modern ideologies, many sociopolitical systems and their associated philosophies, whether of the right or the left, means that the era of the quick, dogmatic perception of how to force people to feel free and happy is over. (2) New forms and institutions of social and economic life must be found among the wreckage. The solutions sought must work best for the greatest number of people and must be flexible enough to allow the reinterpretation of all our determinations, from the very beginning. The New Rhetoric rejects all absolutist and dogmatic ideas. But neither does it support absolute relativism. It constitutes a method for the endless search for truthful explanations and for enlightened practical activity. Truth is only the process of approaching it. While critical of formal logic, the New Rhetoric develops the concepts of other', experimental', flexible', and logic of good sense'. The introduction and elaboration of the concept of reasonableness' is presented as a milestone in the evolution of scientific methodology. The New Rhetoric has overcome the traditional contradictions between logic, rationalism and dialectic and has laid new foundations for a modern theory of morality, law, legal interpretation, and human rights. This book discusses such problems as: new moral notions, the new dilemma of Cain, the spurious notions of 'centrism', Antigone's new arguments, 'argumentation is not bargaining', new foundations oftolerance and justice. It ends with a section on 'Resolutions for the New Century', written in the spirit of traditional enlightenment, rule of reason and humanism, but which goes beyond them.

The popular literature on mathematical logic is rather extensive and written for the most varied categories of readers. College students or adults who read it in their free time may find here a vast number of thought-provoking logical problems. The reader who wishes to enrich his mathematical background in the hope that this will help him in his everyday life can discover detailed descriptions of practical (and quite often -- not so practical ) applications of logic. The large number of popular books on logic has given rise to the hope that by applying mathematical logic, students will finally learn how to distinguish between necessary and sufficient conditions and other points of logic in the college course in mathematics. But the habit of teachers of mathematical analysis, for example, to stick to problems dealing with sequences without limit, uniformly continuous functions, etc. has, unfortunately, led to the writing of textbooks that present prescriptions for the mechanical construction of definitions of negative concepts which seem to obviate the need for any thinking on the reader's part. We are most certainly not able to enumerate everything the reader may draw out of existing books on mathematical logic, however.

This is a single volume reference guide to the latest work and potential future directions in Philosophical Logic, written by an international team of leading scholars. "The Continuum Companion to Philosophical Logic" offers the definitive guide to a key area of contemporary philosophy. The book covers all the fundamental areas of philosophical logic - topics that have continued to attract interest historically as well as topics that have emerged more recently as active areas of research. Seventeen specially commissioned essays from an international team of experts reveal where important work continues to be done in the area and, most valuably, the exciting new directions the field is taking. The Companion explores issues pertaining to classical logic and its rivals, extensional and intensional extensions of classical logic, semantics for parts of natural language, and the application of logic in the theory of rationality. Crucially the emphasis is on the role that logic plays in understanding philosophical problems. Featuring a series of indispensable research tools, including an A to Z of key terms and concepts, a detailed list of resources, a bibliography and a companion website, this is the essential reference tool for anyone working in contemporary philosophical logic. "The Continuum Companions" series is a major series of single volume companions to key research fields in the humanities aimed at postgraduate students, scholars and libraries. Each companion offers a comprehensive reference resource giving an overview of key topics, research areas, new directions and a manageable guide to beginning or developing research in the field. A distinctive feature of the series is that each companion provides practical guidance on advanced study and research in the field, including research methods and subject-specific resources.

In this book, the contributors present an overview of recent developments in philosophy of science by providing a collection of articles that together constitute a systematic and comprehensive investigation of how to understand the relation between the social sciences and democracy.

This book, translated from the French, is an introduction to first-order model theory. The first six chapters are very basic: starting from scratch, they quickly reach the essential, namely, the back-and-forth method and compactness, which are illustrated with examples taken from algebra. The next chapter introduces logic via the study of the models of arithmetic, and the following is a combinatorial tool-box preparing for the chapters on saturated and prime models. The last ten chapters form a rather complete but nevertheless accessible exposition of stability theory, which is the core of the subject.

This book aids in the rehabilitation of the wrongfully deprecated work of William Parry, and is the only full-length investigation into Parry-type propositional logics. A central tenet of the monograph is that the sheer diversity of the contexts in which the mereological analogy emerges - its effervescence with respect to fields ranging from metaphysics to computer programming - provides compelling evidence that the study of logics of analytic implication can be instrumental in identifying connections between topics that would otherwise remain hidden. More concretely, the book identifies and discusses a host of cases in which analytic implication can play an important role in revealing distinct problems to be facets of a larger, cross-disciplinary problem. It introduces an element of constancy and cohesion that has previously been absent in a regrettably fractured field, shoring up those who are sympathetic to the worth of mereological analogy. Moreover, it generates new interest in the field by illustrating a wide range of interesting features present in such logics - and highlighting these features to appeal to researchers in many fields.

I was very happy when in 1997 Fiachra Long came to spend part of his sabbatical leave at the Archives Maurice Blondel at Louvain-Ia-Neuve. This allowed him to bring together and complete his translation of three important articles from Maurice Blondel, known as the philosopher of Aix-en-Province. These three articles fonn a unity: they make explicit certain aspects of the method used in the great thesis of 1893, Action. This thesis, it is well known, aroused many polemic debates after its appearance. Thomist theologians accused Blondel of turning back towards Kantian idealism whereas the philosophers of the Revue de metaphysique et de morale accused him on the contrary of falling back on a pre-critical realism. The three articles translated here, each in its own way, attempt to pass beyond these two opposite charges. The Idealist Illusion (1898) underlines the fact that the content of consciousness should be unfurled as it appears, by withdrawing from any idealist or realist prejudice, before judging the consistency of its content as a whole. In this way Blondel supports the "phenomenological" method used in his thesis. The Elementary Principle of a Logic of the Moral Life (1903) is a very well-worked text which shows that "the logic of possession and privation" is broader than "the logic of amnnation and negation. " Using these words, Blondel develops certain striking laws of action such as that of the "parallelogram of contrary forces.

The notion of truth has become much discussed in philosophy over the last few decade, with many senior figures grappling with the relativist and constructivist notions of truth popular in other parts of the academy. It continues to be a subject enjoying vibrant debate. Despite the varieties of views on truth, most of the discussion has agreed that truth has a uniform, stable nature, ranging across the boundaries of human knowledge. The editors and contributors to this volume challenge this very basic assumption, putting forth the idea of what is called alethic pluralism - that there is more than one way of being true. While it is uncontroversial that there are different kinds of truth (moral truth, scientific truth etc), these pluralist views propose that truth itself can vary and that bearers of truth can literally be true in different ways. This volume presents new essays by some of the world's leading philosophers to explore this new view and its implications for the philosophy of language, epistemology, metaphysics, and logic.

Intuitionistic type theory can be described, somewhat boldly, as a partial fulfillment of the dream of a universal language for science. This book expounds several aspects of intuitionistic type theory, such as the notion of set, reference vs. computation, assumption, and substitution. Moreover, the book includes philosophically relevant sections on the principle of compositionality, lingua characteristica, epistemology, propositional logic, intuitionism, and the law of excluded middle. Ample historical references are given throughout the book.