This book is an example of fruitful interaction between (non-classical) propo sitionallogics and (classical) model theory which was made possible due to categorical logic. Its main aim consists in investigating the existence of model completions for equational theories arising from propositional logics (such as the theory of Heyting algebras and various kinds of theories related to proposi tional modal logic ). The existence of model-completions turns out to be related to proof-theoretic facts concerning interpretability of second order propositional logic into ordinary propositional logic through the so-called 'Pitts' quantifiers' or 'bisimulation quantifiers'. On the other hand, the book develops a large number of topics concerning the categorical structure of finitely presented al gebras, with related applications to propositional logics, both standard (like Beth's theorems) and new (like effectiveness of internal equivalence relations, projectivity and definability of dual connectives such as difference). A special emphasis is put on sheaf representation, showing that much of the nice categor ical structure of finitely presented algebras is in fact only a restriction of natural structure in sheaves. Applications to the theory of classifying toposes are also covered, yielding new examples. The book has to be considered mainly as a research book, reporting recent and often completely new results in the field; we believe it can also be fruitfully used as a complementary book for graduate courses in categorical and algebraic logic, universal algebra, model theory, and non-classical logics. 1."

The subject of Time has a wide intellectual appeal across different dis ciplines. This has shown in the variety of reactions received from readers of the first edition of the present Book. Many have reacted to issues raised in its philosophical discussions, while some have even solved a number of the open technical questions raised in the logical elaboration of the latter. These results will be recorded below, at a more convenient place. In the seven years after the first publication, there have been some noticeable newer developments in the logical study of Time and temporal expressions. As far as Temporal Logic proper is concerned, it seems fair to say that these amount to an increase in coverage and sophistication, rather than further break-through innovation. In fact, perhaps the most significant sources of new activity have been the applied areas of Linguistics and Computer Science (including Artificial Intelligence), where many intriguing new ideas have appeared presenting further challenges to temporal logic. Now, since this Book has a rather tight composition, it would have been difficult to interpolate this new material without endangering intelligibility."

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.

The problem of truth and the liar paradox is one of the most extensive problems of philosophy. The liar paradox can be avoided by assuming a so-called theory of partial truth instead of a classical theory of truth. Theories of partial truth, however, cannot solve the so-called strengthened liar paradox, which is the problem that many semantic statements about the so-called strengthened liar cannot be true in a theory of partial truth. If such semantic statements were true in the theory, another paradox would emerge. To proponents of contextual accounts, which assume that the concept of truth is context-dependent, the strengthened liar paradox is the core of the liar problem. This book provides an overview of current contextual approaches to the strengthened liar paradox. For this purpose, the author investigates formal theories of truth that result from formal reconstructions of such contextual approaches.

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.

Metamathematics and the Philosophical Tradition is the first work to explore in such historical depth the relationship between fundamental philosophical quandaries regarding self-reference and meta-mathematical notions of consistency and incompleteness. Using the insights of twentieth-century logicians from Goedel through Hilbert and their successors, this volume revisits the writings of Aristotle, the ancient skeptics, Anselm, and enlightenment and seventeenth and eighteenth century philosophers Leibniz, Berkeley, Hume, Pascal, Descartes, and Kant to identify ways in which these both encode and evade problems of a priori definition and self-reference. The final chapters critique and extend more recent insights of late 20th-century logicians and quantum physicists, and offer new applications of the completeness theorem as a means of exploring "metatheoretical ascent" and the limitations of scientific certainty. Broadly syncretic in range, Metamathematics and the Philosophical Tradition addresses central and recurring problems within epistemology. The volume's elegant, condensed writing style renders accessible its wealth of citations and allusions from varied traditions and in several languages. Its arguments will be of special interest to historians and philosophers of science and mathematics, particularly scholars of classical skepticism, the Enlightenment, Kant, ethics, and mathematical logic.

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.

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.

"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.

The volume contains almost thirty papers by Kazimierz Twardowski (1866-1938), the founder of the Lvov-Warsaw School. The papers are published in English for the first time. The papers concern fundamental problems of philosophy: the methods of philosophizing, the boundary of psychology and semiotics, the conceptual apparatus of metaphysics, ethical skepticism, the question of free will and ethical obligation, the aesthetics of music and so on. The systematic considerations are complemented by concise but excellent sketches of the philosophical views of Socrates, Aquinas, Leibniz, Spencer, Nietzsche, and Bergson.

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). "

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.