The ``Many Sides of Logic'' is a volume containing a selection of the papers delivered at three simultaneous events held between 11-17 May 2008 in Paraty, RJ, Brazil, continuing a tradition of three decades of Brazilian and Latin-American meetings and celebrating the 30th anniversary of an institution congenital with the mature interest for logic, epistemology and history of sciences in Brazil: CLE 30 - 30th Anniversary of the Centre for Logic, Epistemology and the History of Science at the State University of Campinas (UNICAMP) XV EBL -15th Brazilian Logic Conference XIV SLALM - 14th Latin-American Symposium on Mathematical Logic Several renowned logicians, philosophers and mathematicians gathered in colonial Paraty, a historic village on the Brazilian coast founded in the 17th Century and surrounded by the luscious Atlantic rain forest to deliver lectures and talks celebrating the many sides of logic: the philosophical, the mathematical, the computational, the historical, and the multiple facets therein. The topics of the joint conferences, well represented here, included philosophical and mathematical Logic and applications with emphasis on model theory and proof theory, set theory, non-classical logics and applications, history and philosophy of logic, philosophy of the formal sciences and issues on the foundations of mathematics. The events have been preceded by a Logic School planned for students and young researchers held at the UNICAMP campus in Campinas, SP.

Many Sides is the first full-length study of Protagorean antilogic, an argumentative practice with deep roots in rhetorical history and renewed relevance for contemporary culture. Founded on the philosophical relativism of Protagoras, antilogic is a dynamic rather than a formal approach to argument, focused principally on the dialogical interaction of opposing positions (anti-logoi) in controversy. In ancient Athens, antilogic was the cardinal feature of Sophistic rhetoric. In Rome, Cicero redefined Sophistic argument in a concrete set of dialogical procedures. In turn, Quintilian inherited this dialogical tradition and made it the centrepiece of his own rhetorical practice and pedagogy. Many Sides explores the history, theory, and pedagogy of this neglected rhetorical tradition and, by appeal to recent rhetorical and philosophical theory, reconceives the enduring features of antilogical practice in a dialogical approach to argumentation especially suited to the pluralism of our own age and the diversity of modern classrooms.

The Handbook of the History of Logic is a multi-volume research instrument that brings to the development of logic the best in modern techniques of historical and interpretative scholarship. It is the first work in English in which the history of logic is presented so extensively. The volumes are numerous and large. Authors have been given considerable latitude to produce chapters of a length, and a level of detail, that would lay fair claim on the ambitions of the project to be a definitive research work. Authors have been carefully selected with this aim in mind. They and the Editors join in the conviction that a knowledge of the history of logic is nothing but beneficial to the subject's present-day research programmes. One of the attractions of the Handbook's several volumes is the emphasis they give to the enduring relevance of developments in logic throughout the ages, including some of the earliest manifestations of the subject. - Covers in depth the notion of logical consequence - Discusses the central concept in logic of modality - Includes the use of diagrams in logical reasoning

In this challenging and provocative analysis, Dale Jacquette argues that contemporary philosophy labours under a number of historically inherited delusions about the nature of logic and the philosophical significance of certain formal properties of specific types of logical constructions. Exposing some of the key misconceptions about formal symbolic logic and its relation to thought, language and the world, Jacquette clears the ground of some very well-entrenched philosophical doctrines about the nature of logic, including some of the most fundamental seldom-questioned parts of elementary propositional and predicate-quantificational logic. Having presented difficulties for conventional ways of thinking about truth functionality, the metaphysics of reference and predication, the role of a concept of truth in a theory of meaning, among others, Jacquette proceeds to reshape the network of ideas about traditional logic that philosophy has acquired along with modern logic itself. In so doing Jacquette is able to offer a new perspective on a number of existing problems in logic and philosophy of logic.

A presentation of current work that systematically explores and articulates the nature, origin and development of reasoning, this volume's primary aim is to describe and examine contemporary theory and research findings on the topic of deductive reasoning. Many contributors believe concepts such as "structure," "competence," and "mental logic" are necessary features for a complete understanding of reasoning. As the book emanates from a Jean Piaget Symposium, his theory of intellectual development as the standard contemporary treatment of deductive reasoning is used as the context in which the contributors elaborate on their own perceptions.

The Lvov-Warsaw School was active in all spheres of philosophy. Its members worked in the border area between philosophy and disci plines such as psychology, linguistics, and literary theory. But its most important achievements were without doubt in logic and philosophical analysis based on logic. The present book is concerned with fields to which the Lvov-Warsaw School made its most important and famous contributions. Data on the School as a whole are included only in the first and last part of the book. This work is based on my monograph (1985), which appeared in Polish. But it is not merely a translation, because some fragments of the Polish version have been omitted (e. g., the chapter on ethics), and some have been revised. Many persons helped me in my work on the book in Polish as well as on the present edition. I must first mention the late Izydora D~mbska, to whom this book is dedicated. On various detailed issues I have availed myself of advice and information given to me by Stefan Amsterdamski, Zdzislaw Augustynek, Kazimierz Czarnota, Henryk Hii, Boleslaw Iwanus, Jacek Jadacki, Jacek KabziIiski, Stanislaw Kiczuk, Tomasz Komendzinski, Janina Kotarbinska, Czeslaw Lejewski, Jerzy Perzanowski, Marian Przet~cki, the late Jerzy Slupecki, Klemens Szaniawski, Stefan Zamecki, Zbigniew Zwinogrodzki i Jan Zygmunt. I am indebted to Jaakko Hintikka for suggesting that my book be trans lated into English and published by Reidel. Olgierd Wojtasiewicz helped me to prepare the English text.

The present volume of the Handbook of the History of Logic brings together two of the most important developments in 20th century non-classical logic. These are many-valuedness and non-monotonicity. On the one approach, in deference to vagueness, temporal or quantum indeterminacy or reference-failure, sentences that are classically non-bivalent are allowed as inputs and outputs to consequence relations. Many-valued, dialetheic, fuzzy and quantum logics are, among other things, principled attempts to regulate the flow-through of sentences that are neither true nor false. On the second, or non-monotonic, approach, constraints are placed on inputs (and sometimes on outputs) of a classical consequence relation, with a view to producing a notion of consequence that serves in a more realistic way the requirements of real-life inference. Many-valued logics produce an interesting problem. Non-bivalent inputs produce classically valid consequence statements, for any choice of outputs. A major task of many-valued logics of all stripes is to fashion an appropriately non-classical relation of consequence.The chief preoccupation of non-monotonic (and default) logicians is how to constrain inputs and outputs of the consequence relation. In what is called "left non-monotonicity, it is forbidden to add new sentences to the inputs of true consequence-statements. The restriction takes notice of the fact that new information will sometimes override an antecedently (and reasonably) derived consequence. In what is called "right non-monotonicity, limitations are imposed on outputs of the consequence relation. Most notably, perhaps, is the requirement that the rule of or-introduction not be given free sway on outputs. Also prominent is the effort of paraconsistent logicians, both preservationist and dialetheic, to limit the outputs of inconsistent inputs, which in classical contexts are wholly unconstrained.In some instances, our two themes coincide. Dialetheic logics are a case in point. Dialetheic logics allow certain selected sentences to have, as a third truth value, the classical values of truth and falsity together. So such logics also admit classically inconsistent inputs. A central task is to construct a right non-monotonic consequence relation that allows for these many-valued, and inconsistent, inputs.The Many Valued and Non-Monotonic Turn in Logic is an indispensable research tool for anyone interested in the development of logic, including researchers, graduate and senior undergraduate students in logic, history of logic, mathematics, history of mathematics, computer science, AI, linguistics, cognitive science, argumentation theory, and the history of ideas. - Detailed and comprehensive chapters covering the entire range of modal logic. - Contains the latest scholarly discoveries and interprative insights that answers many questions in the field of logic.

This edited volume presents a comprehensive history of modern logic from the Middle Ages through the end of the twentieth century. In addition to a history of symbolic logic, the contributors also examine developments in the philosophy of logic and philosophical logic in modern times. The book begins with chapters on late medieval developments and logic and philosophy of logic from Humanism to Kant. The following chapters focus on the emergence of symbolic logic with special emphasis on the relations between logic and mathematics, on the one hand, and on logic and philosophy, on the other. This discussion is completed by a chapter on the themes of judgment and inference from 1837-1936. The volume contains a section on the development of mathematical logic from 1900-1935, followed by a section on main trends in mathematical logic after the 1930s. The volume goes on to discuss modal logic from Kant till the late twentieth century, and logic and semantics in the twentieth century; the philosophy of alternative logics; the philosophical aspects of inductive logic; the relations between logic and linguistics in the twentieth century; the relationship between logic and artificial intelligence; and ends with a presentation of the main schools of Indian logic. The Development of Modern Logic includes many prominent philosophers from around the world who work in the philosophy and history of mathematics and logic, who not only survey developments in a given period or area but also seek to make new contributions to contemporary research in the field. It is the first volume to discuss the field with this breadth of coverage and depth, and will appeal to scholars and students of logic and its philosophy.