The second volume is devoted to issues of compositionality that arouse in the sciences of language, the investigation of the mind, and the modeling of representational brain functions. How could compositional languages evolve? How many sentences are needed to learn a compositional language? How does compositionality relate to the interpretation of texts, the generation of idioms and metaphors, and the understanding of aberrant expressions? What psychological mechanism underlies the combination of complex concepts? And finally, what neuronal structure can possibly realize a compositional system of mental representations?

Alfred Tarski was one of the two giants of the twentieth-century development of logic, along with Kurt Goedel. The four volumes of this collection contain all of Tarski's published papers and abstracts, as well as a comprehensive bibliography. Here will be found many of the works, spanning the period 1921 through 1979, which are the bedrock of contemporary areas of logic, whether in mathematics or philosophy. These areas include the theory of truth in formalized languages, decision methods and undecidable theories, foundations of geometry, set theory, and model theory, algebraic logic, and universal algebra.

Pondering on Problems of Argumentation is a collection of twenty essays brought together for anyone who is interested in theoretical issues in the study of argumentation. This collection of papers gives the reader an insightful and balanced view of the kind of theoretical issues argumentation theorists are currently concerned with. Because most of the perspectives on argumentation that are en vogue are represented, this volume provides a multidisciplinary and even interdisciplinary outlook on the current state of affairs in argumentation theory. Some of the contributions in Pondering on Problems of Argumentation deal with problems of argumentation that have been recognized as theoretical issues for a considerable time, like the problems of fallaciousness and identifying argumentation structures. Other contributions discuss issues that have become a focus of attention only recently or regained their prominence, such as the relationship between dialectic and rhetoric, and the strategic use of the argumentative technique of dissociation. In five separate sections papers are included dealing with argumentative strategies, problems of norms of reasonableness and fallaciousness, types of argument and argument schemes the structure of argumentation and rules for advocacy and discussion.

This collection of papers, celebrating the contributions of Swedish logician Dag Prawitz to Proof Theory, has been assembled from those presented at the Natural Deduction conference organized in Rio de Janeiro to honour his seminal research. Dag Prawitz's work forms the basis of intuitionistic type theory and his inversion principle constitutes the foundation of most modern accounts of proof-theoretic semantics in Logic, Linguistics and Theoretical Computer Science.

The range of contributions includes material on the extension of natural deduction with higher-order rules, as opposed to higher-order connectives, and a paper discussing the application of natural deduction rules to dealing with equality in predicate calculus. The volume continues with a key chapter summarizing work on the extension of the Curry-Howard isomorphism (itself a by-product of the work on natural deduction), via methods of category theory that have been successfully applied to linear logic, as well as many other contributions from highly regarded authorities. With an illustrious group of contributors addressing a wealth of topics and applications, this volume is a valuable addition to the libraries of academics in the multiple disciplines whose development has been given added scope by the methodologies supplied by natural deduction. The volume is representative of the rich and varied directions that Prawitz work has inspired in the area of natural deduction.
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Thetitleofthisbookmentionstheconceptsofparaconsistencyandconstr- tive logic. However, the presented material belongs to the ?eld of parac- sistency, not to constructive logic. At the level of metatheory, the classical methods are used. We will consider two concepts of negation: the ne- tion as reduction to absurdity and the strong negation. Both concepts were developed in the setting of constrictive logic, which explains our choice of the title of the book. The paraconsistent logics are those, which admit - consistent but non-trivial theories, i. e. , the logics which allow one to make inferences in a non-trivial fashion from an inconsistent set of hypotheses. Logics in which all inconsistent theories are trivial are called explosive. The indicated property of paraconsistent logics yields the possibility to apply them in di?erent situations, where we encounter phenomena relevant (to some extent) to the logical notion of inconsistency. Examples of these si- ations are (see [86]): information in a computer data base; various scienti?c theories; constitutions and other legal documents; descriptions of ?ctional (and other non-existent) objects; descriptions of counterfactual situations; etc. The mentioned survey by G. Priest [86] may also be recommended for a ?rst acquaintance with paraconsistent logic. The study of the paracons- tency phenomenon may be based on di?erent philosophical presuppositions (see, e. g. , [87]). At this point, we emphasize only one fundamental aspect of investigations in the ?eld of paraconsistency. It was noted by D. Nelson in [65, p.

such questions for centuries (unrestricted by the capabilities of any hard ware). The principles governing the interaction of several processes, for example, are abstract an similar to principles governing the cooperation of two large organisation. A detailed rule based effective but rigid bureaucracy is very much similar to a complex computer program handling and manipulating data. My guess is that the principles underlying one are very much the same as those underlying the other. I believe the day is not far away in the future when the computer scientist will wake up one morning with the realisation that he is actually a kind of formal philosopher The projected number of volumes for this Handbook is about 18. The subject has evolved and its areas have become interrelated to such an extent that it no longer makes sense to dedicate volumes to topics. However, the volumes do follow some natural groupings of chapters. I would like to thank our authors are readers for their contributions and their commitment in making this Handbook a success. Thanks also to our publication administrator Mrs J. Spurr for her usual dedication and excellence and to Kluwer Academic Publishers for their continuing support for the Handbook."

The notion of complexity is an important contribution of logic to theoretical computer science and mathematics. This volume attempts to approach complexity in a holistic way, investigating mathematical properties of complexity hierarchies at the same time as discussing algorithms and computational properties. A main focus of the volume is on some of the new paradigms of computation, among them Quantum Computing and Infinitary Computation. The papers in the volume are tied together by an introductory article describing abstract properties of complexity hierarchies.

This volume will be of great interest to both mathematical logicians and theoretical computer scientists, providing them with new insights into the various views of complexity and thus shedding new light on their own research.

This monograph first presents a method of diagramming argument macrostructure, synthesizing the standard circle and arrow approach with the Toulmin model. A theoretical justification of this method through a dialectical understanding of argument, a critical examination of Toulmin on warrants, a thorough discussion of the linked-convergent distinction, and an account of the proper reconstruction of enthymemes follows.

Offers an extremely bold, far-reaching, and unsuspected thesis in the history of philosophy: Aristotelianism was a dominant movement of the British philosophical landscape, especially in the field of logic, and it had a long survival. British Aristotelian doctrines were strongly empiricist in nature, both in the theory of knowledge and in scientific method; this character marked and influenced further developments in British philosophy at the end of the century, and eventually gave rise to what we now call British empiricism, which is represented by philosophers such as John Locke, George Berkeley and David Hume. Beyond the apparent and explicit criticism of the old Scholastic and Aristotelian philosophy, which has been very well recognized by the scholarship in the twentieth century and which has contributed to the false notion that early modern philosophy emerged as a reaction to Aristotelianism, the present research examines the continuity, the original developments and the impact of Aristotelian doctrines and terminology in logic and epistemology as the background for the rise of empiricism.Without the Aristotelian tradition, without its doctrines, and without its conceptual elaborations, British empiricism would never have been born. The book emphasizes that philosophy is not defined only by the great names, but also by minor authors, who determine the intellectual milieu from which the canonical names emerge. It considers every single published work of logic between the middle of the sixteenth and the end of the seventeenth century, being acquainted with a number of surviving manuscripts and being well-informed about the best existing scholarship in the field. "

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 book provides a collection of essays representing the state of the art in the research into argumentation in classical antiquity. It contains essays from leading and up and coming scholars on figures as diverse as Parmenides, Gorgias, Seneca, and Classical Chinese "wandering persuaders." The book includes contributions from specialists in the history of philosophy as well as specialists in contemporary argumentation theory, and stimulates the dialogue between scholars studying issues relating to argumentation theory in ancient philosophy and contemporary argumentation theorists. Furthermore, the book sets the direction for research into argumentation in antiquity by encouraging an engagement with a broader range of historical figures, and closer collaboration between contemporary concerns and the history of philosophy.

This volume deals with the connection between thinking-and-speaking and our form(s) of life. All contributions engage with Wittgenstein's approach to this topic. As a whole, the volume takes a stance against both biological and ethnological interpretations of the notion "form of life" and seeks to promote a broadly logico-linguistic understanding instead. The structure of this book is threefold. Part one focuses on lines of thinking that lead from Wittgenstein's earlier thought to the concept of form of life in his later work. Contributions to part two examine the concrete philosophical function of this notion as well as the ways in which it differs from cognate concepts. Contributions to part three put Wittgenstein's notion of form of life in perspective by relating it to phenomenology, ordinary language philosophy and problems in contemporary analytic philosophy.

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.

CENGAGE ADVANTAGE BOOKS: UNDERSTANDING ARGUMENTS, CONCISE EDITION, 1E uses everyday life experiences to teach the basics of informal logic. By taking out the non-essential instruction, this edition hones in on the "argument construction" involved in day-to-day life, and how to do it better. Plus, to round out the discussion, CENGAGE ADVANTAGE BOOKS: UNDERSTANDING ARGUMENTS, CONCISE EDITION, 1E includes a three-chapter overview of formal logic as well.

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 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.

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.

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.

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.

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.

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."

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.