This volume examines the entire logical and philosophical production of Nicolai A. Vasil'ev, studying his life and activities as a historian and man of letters. Readers will gain a comprehensive understanding of this influential Russian logician, philosopher, psychologist, and poet. The author frames Vasil'ev's work within its historical and cultural context. He takes into consideration both the situation of logic in Russia and the state of logic in Western Europe, from the end of the 19th century to the beginning of the 20th. Following this, the book considers the attempts to develop non-Aristotelian logics or ideas that present affinities with imaginary logic. It then looks at the contribution of traditional logic in elaborating non-classical ideas. This logic allows the author to deal with incomplete objects just as imaginary logic does with contradictory ones. Both logics are objects of interesting analysis by modern researchers. This volume will appeal to graduate students and scholars interested not only in Vasil'ev's work, but also in the history of non-classical logics.

Many systems of logic diagrams have been offered both historically and more recently. Each of them has clear limitations. An original alternative system is offered here. It is simpler, more natural, and more expressively and inferentially powerful. It can be used to analyze not only syllogisms but arguments involving relational terms and unanalyzed statement terms.

Friedrich Ueberweg (1826-71) is best remembered for both his compendious "History of Philosophy" and his "System of Logic", both of which went through several editions in the original German. It was the latter's remarkable popularity as a textbook in Germany that led Lindsay to translate it to fill a gap in the English market. As well as incorporating the most up-to-date revisions and additons to the German edition he inserted the opinions of the more important English logicians. As such this is a valuable textbook for the understanding of logic systems as taught in England and Germany before symbolic logic was a formal and distinct discipline.

Published in honor of Sergio Galvan, this collection concentrates on the application of logical and mathematical methods for the study of central issues in formal philosophy. The volume is subdivided into four sections, dedicated to logic and philosophy of logic, philosophy of mathematics, philosophy of science, metaphysics and philosophy of religion. The contributions adress, from a logical point of view, some of the main topics in these areas. The first two sections include formal treatments of: truth and paradoxes; definitions by abstraction; the status of abstract objects, such as mathematical objects and universal concepts; and the structure of explicit knowledge. The last two sections include papers on classical problems in philosophy of science, such as the status of subjective probability, the notion of verisimilitude, the notion of approximation, and the theory of mind and mental causation, and specific issues in metaphysics and philosophy of religion, such as the ontology of species, actions, and intelligible worlds, and the logic of religious belonging.

This book is dedicated to Dov Gabbay, one of the most outstanding and most productive researchers in the area of logic, language and reasoning. He has exerted a profound influence in the major fields of logic, linguistics and computer science. Most of the chapters included, therefore, build on his work and present results or summarize areas where Dov has made major contributions. In particular his work on Labelled Deductive Systems is addressed in most of the contributions. The chapters on computational linguistics address logical and deductive aspects of linguistic problems. The papers by van Benthem Lambek and Moortgat investigate categorial considerations and the use of labels within the "parsing as deduction" approach. Analyses of particular linguistic problems are given in the remaining papers by Kamp, Kempson, Moravcsik, Konig and Reyle. They address the logic of generalized quantifiers, the treatment of cross-over phenomena and temporal/aspectual interpretation, as well as applicability of underspecified deduction in linguistic formalisms. The more logic-oriented chapters address philosophical and proof-theoretic problems and give algorithmic solutions for most of them. The spectrum ranges from K. Segerberg's contribution which brings together the two traditions of epistemic and doxastic logics of belief, to M. Finger and M. Reynold's chapter on two-dimensional executable logics with applications to temporal databases. The book demonstrates that a relatively small number of basic techniques and ideas, in particular the idea of labelled deductive systems, can be successfully applied in many different areas.

Ordinal Computability discusses models of computation obtained by generalizing classical models, such as Turing machines or register machines, to transfinite working time and space. In particular, recognizability, randomness, and applications to other areas of mathematics are covered.

The aim of this volume is to collect original contributions by the best specialists from the area of proof theory, constructivity, and computation and discuss recent trends and results in these areas. Some emphasis will be put on ordinal analysis, reductive proof theory, explicit mathematics and type-theoretic formalisms, and abstract computations. The volume is dedicated to the 60th birthday of Professor Gerhard Jager, who has been instrumental in shaping and promoting logic in Switzerland for the last 25 years. It comprises contributions from the symposium "Advances in Proof Theory", which was held in Bern in December 2013. Proof theory came into being in the twenties of the last century, when it was inaugurated by David Hilbert in order to secure the foundations of mathematics. It was substantially influenced by Goedel's famous incompleteness theorems of 1930 and Gentzen's new consistency proof for the axiom system of first order number theory in 1936. Today, proof theory is a well-established branch of mathematical and philosophical logic and one of the pillars of the foundations of mathematics. Proof theory explores constructive and computational aspects of mathematical reasoning; it is particularly suitable for dealing with various questions in computer science.

This is a concise and readable study of five intertwined themes at the heart of Wittgenstein's thought, written by one of his most eminent interpreters. David Pears offers penetrating investigations and lucid explications of some of the most influential and yet puzzling writings of twentieth-century philosophy. He focuses on the idea of language as a picture of the world; the phenomenon of linguistic regularity; the famous "private language argument"; logical necessity; and ego and the self.

This volume collects the most important articles on the metaphysics of modality by noted philosopher Alvin Plantinga. The book chronicles Plantinga's thought from the late 1960's to the present. Plantinga is here concerned with fundamental issues in metaphysics: what is the nature of abstract objects like possible worlds,properties, propositions, and such phenomena? Are there possible but non-actual objects? Can objects that do not exist exemplify properties? In this thorough and searching book, Plantinga addresses these and many other questions that continue to preoccupy philosophers in the field. This volume contains some of the best work in metaphysics from the past 30 years, and will remain a source of critical contention and keen interest among philosophers of metaphysics and philosophical logic for years to come.

This book provides a general survey of the main concepts, questions and results that have been developed in the recent interactions between quantum information, quantum computation and logic. Divided into 10 chapters, the books starts with an introduction of the main concepts of the quantum-theoretic formalism used in quantum information. It then gives a synthetic presentation of the main "mathematical characters" of the quantum computational game: qubits, quregisters, mixtures of quregisters, quantum logical gates. Next, the book investigates the puzzling entanglement-phenomena and logically analyses the Einstein-Podolsky-Rosen paradox and introduces the reader to quantum computational logics, and new forms of quantum logic. The middle chapters investigate the possibility of a quantum computational semantics for a language that can express sentences like "Alice knows that everybody knows that she is pretty", explore the mathematical concept of quantum Turing machine, and illustrate some characteristic examples that arise in the framework of musical languages. The book concludes with an analysis of recent discussions, and contains a Mathematical Appendix which is a survey of the definitions of all main mathematical concepts used in the book.

From Concept to Objectivity uncovers the nature and authority of conceptual determination by critically thinking through neglected arguments in Hegel's Science of Logic pivotal for understanding reason and its role in philosophy. Winfield clarifies the logical problems of presuppositionlessness and determinacy that prepare the way for conceiving the concept, examines how universality, particularity, and individuality are determined, investigates how judgment and syllogism are exhaustively differentiated, and, on that basis, explores how objectivity can be categorized without casting thought in irrevocable opposition to reality. Winfield's book will be of interest to readers of Hegel as well as anyone wondering how thought can be objective.

Barry Taylor's book mounts an argument against one of the fundamental tenets of much contemporary philosophy, the idea that we can make sense of reality as existing objectively, independently of our capacities to come to know it. Part One sets the scene by arguings that traditional realism can be explicated as a doctrine about truth - that truth is objective, that is, public, bivalent, and epistemically independent. Part Two, the centrepiece of the book, shows how a form of Hilary Putnam's model-theoretic argument demonstrates that no such notion of truth can be founded on the idea of correspondence, as explained in model-theoretic terms (more traditional accounts of correspondence having been already disposed of in Part One). Part Three argues that non-correspondence accounts of truth - truth as superassertibility or idealized rational acceptability, formal conceptions of truth, Tarskian truth - also fail to meet the criteria for objectivity; along the way, it also dismisses the claims of the latterday views of Putnam, and of similar views articulated by John McDowell, to constitute a new, less traditional form of realism. In the Coda, Taylor bolsters some of the considerations advanced in Part Three in evaluating formal conceptions of truth, by assessing and rejecting the claims of Robert Brandom to have combined such an account of truth with a satisfactory account of semantic structure. He concludes that there is no defensible notion of truth which preserves the theses of traditional realism, nor any extant position sufficiently true to the ideals of that doctrine to inherit its title. So the only question remaining is which form of antirealism to adopt.

Aristotle's Topics is a handbook for dialectic, which can be understood as a philosophical debate between a questioner and a respondent. In book 2, Aristotle mainly develops strategies for making deductions about 'accidents', which are properties that might or might not belong to a subject (for instance, Socrates has five fingers, but might have had six), and about properties that simply belong to a subject without further specification. In the present commentary, here translated into English for the first time, Alexander develops a careful study of Aristotle's text. He preserves objections and replies from other philosophers whose work is now lost, such as the Stoics. He also offers an invaluable picture of the tradition of Aristotelian logic down to his time, including innovative attempts to unify Aristotle's guidance for dialectic with his general theory of deductive argument (the syllogism), found in the Analytics. The work will be of interest not only for its perspective on ancient logic, rhetoric, and debate, but also for its continuing influence on argument in the Middle Ages and later.

Kit Fine has since the 1970s been one of the leading contributors to work at the intersection of logic and metaphysics. This is his eagerly-awaited first book in the area. It draws together a series of essays, three of them previously unpublished, on possibility, necessity, and tense. These puzzling aspects of the way the world is have been the focus of considerable philosophical attention in recent decades. Fine gives here the definitive exposition and defence of certain positions for which he is well known: the intelligibility of modality de re; the primitiveness of the modal; and the primacy of the actual over the possible. But the book also argues for several positions that are not so familiar: the existence of distinctive forms of natural and normative necessity, not reducible to any form of metaphysical necessity; the need to make a distinction between the worldly and the unworldly, analogous to the distinction between the tensed and the tenseless; and the viability of a non-standard form of realism about tense, which recognizes the tensed character of reality without conceding that there is any privileged standpoint from which it is to be viewed. Modality and Tense covers a wide range of topics from many different areas: the possible-worlds analysis of counterfactuals; the compatibility of special relativity with presentism; the implications of ethical naturalism; and the nature of first-personal experience. A helpful introduction orients the reader and offers a way into some of the most original work in contemporary philosophy.

This contributed volume explores the ways logical skills have been perceived over the course of history. The authors approach the topic from the lenses of philosophy, anthropology, sociology, and history to examine two opposing perceptions of logic: the first as an innate human ability and the second as a skill that can be learned and mastered. Chapters focus on the social and political dynamics of the use of logic throughout history, utilizing case studies and critical analyses. Specific topics covered include: the rise of logical skills problems concerning medieval notions of idiocy and rationality decolonizing natural logic natural logic and the course of time Logical Skills: Social-Historical Perspectives will appeal to undergraduate and graduate students, as well as researchers in the fields of history, sociology, philosophy, and logic. Psychology and colonial studies scholars will also find this volume to be of particular interest.

A comprehensive philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true.

This book is dedicated to the life and work of the mathematician Joachim Lambek (1922-2014). The editors gather together noted experts to discuss the state of the art of various of Lambek's works in logic, category theory, and linguistics and to celebrate his contributions to those areas over the course of his multifaceted career. After early work in combinatorics and elementary number theory, Lambek became a distinguished algebraist (notably in ring theory). In the 1960s, he began to work in category theory, categorical algebra, logic, proof theory, and foundations of computability. In a parallel development, beginning in the late 1950s and for the rest of his career, Lambek also worked extensively in mathematical linguistics and computational approaches to natural languages. He and his collaborators perfected production and type grammars for numerous natural languages. Lambek grammars form an early noncommutative precursor to Girard's linear logic. In a surprising development (2000), he introduced a novel and deeper algebraic framework (which he called pregroup grammars) for analyzing natural language, along with algebraic, higher category, and proof-theoretic semantics. This book is of interest to mathematicians, logicians, linguists, and computer scientists.

This book presents reflections on the relationship between narratives and argumentative discourse. It focuses on their functional and structural similarities or dissimilarities, and offers diverse perspectives and conceptual tools for analyzing the narratives' potential power for justification, explanation and persuasion. Divided into two sections, the first Part, under the title "Narratives as Sources of Knowledge and Argument", includes five chapters addressing rather general, theoretical and characteristically philosophical issues related to the argumentative analysis and understanding of narratives. We may perceive here how scholars in Argumentation Theory have recently approached certain topics that have a close connection with mainstream discussions in epistemology and the cognitive sciences about the justificatory potential of narratives. The second Part, entitled "Argumentative Narratives in Context", brings us six more chapters that concentrate on either particular functions played by argumentatively-oriented narratives or particular practices that may benefit from the use of special kinds of narratives. Here the focus is either on the detailed analysis of contextualized examples of narratives with argumentative qualities or on the careful understanding of the particular demands of certain well-defined situated activities, as diverse as scientific theorizing or war policing, that may be satisfied by certain uses of narrative discourse.

F. H. Bradley was the greatest of the British Idealists, but for much of this century his views have been neglected, primarily as a result of the severe criticism to which they were subjected by Russell and Moore. In recent years, however, there has been a resurgence of interest in and a widespread reappraisal of his work. W. J. Mander offers a general introduction to Bradley's metaphysics and its logical foundations, and shows that much of his philosophy has been seriously misunderstood. Dr Mander argues that any adequate treatment of Bradley's thought must take full account of his unique dual inheritance from the traditions of British empiricism and Hegelian rationalism. The scholarship of recent years is assessed, and new interpretations are offered of Bradley's views about truth, predication, and relations, and of his arguments for idealism. This book is a clear and helpful guide for those new to this difficult but fascinating thinker, and at the same time an original and stimulating contribution to the re-evaluation of his work.

Critical thinking is becoming increasingly prominent as an academic discipline taught and examined in schools and universities, as well as a crucial skill for everyday life. To be a successful critical thinker it is vital to understand how the different concepts and terms are defined and used. The terminology often presents a stumbling block for the beginner, since much of it is used imprecisely in everyday language. This definitive A to Z guide provides precise definitions for over 130 terms and concepts used in critical thinking. Each entry presents a short definition followed by a more detailed explanation and authoritative clarification. Armed with the tools and knowledge provided in these pages, the reader will be able to distinguish an assertion from an argument, a flaw from a fallacy, a correlation from a cause and a fact from an opinion. The book is an invaluable resource for teachers and students of critical thinking, providing all the tools necessary to effectively analyse, evaluate, question and reason for yourself.