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Logic from Kant to Russell: Laying the Foundations for Analytic Philosophy (Routledge Studies in Nineteenth-Century Philosophy)

The scope and method of logic as we know it today eminently reflect the ground-breaking developments of set theory and the logical foundations of mathematics at the turn of the 20th century. Unfortunately, little effort has been made to understand the idiosyncrasies of the philosophical context that led to these tremendous innovations in the 19thcentury beyond what is found in the works of mathematicians such as Frege, Hilbert, and Russell. This constitutes a monumental gap in our understanding of the central influences that shaped 19th-century thought, from Kant to Russell, and that helped to create the conditions in which analytic philosophy could emerge. The aim of Logic from Kant to Russell is to document the development of logic in the works of 19th-century philosophers. It contains thirteen original essays written by authors from a broad range of backgrounds—intellectual historians, historians of idealism, philosophers of science, and historians of logic and analytic philosophy. These essays question the standard narratives of analytic philosophy’s past and address concerns that are relevant to the contemporary philosophical study of language, mind, and cognition. The book covers a broad range of influential thinkers in 19th-century philosophy and analytic philosophy, including Kant, Bolzano, Hegel, Herbart, Lotze, the British Algebraists and Idealists, Moore, Russell, the Neo-Kantians, and Frege.

Logic from Kant to Russell: Laying the Foundations for Analytic Philosophy (Routledge Studies in Nineteenth-Century Philosophy)

The scope and method of logic as we know it today eminently reflect the ground-breaking developments of set theory and the logical foundations of mathematics at the turn of the 20th century. Unfortunately, little effort has been made to understand the idiosyncrasies of the philosophical context that led to these tremendous innovations in the 19thcentury beyond what is found in the works of mathematicians such as Frege, Hilbert, and Russell. This constitutes a monumental gap in our understanding of the central influences that shaped 19th-century thought, from Kant to Russell, and that helped to create the conditions in which analytic philosophy could emerge. The aim of Logic from Kant to Russell is to document the development of logic in the works of 19th-century philosophers. It contains thirteen original essays written by authors from a broad range of backgrounds—intellectual historians, historians of idealism, philosophers of science, and historians of logic and analytic philosophy. These essays question the standard narratives of analytic philosophy’s past and address concerns that are relevant to the contemporary philosophical study of language, mind, and cognition. The book covers a broad range of influential thinkers in 19th-century philosophy and analytic philosophy, including Kant, Bolzano, Hegel, Herbart, Lotze, the British Algebraists and Idealists, Moore, Russell, the Neo-Kantians, and Frege.

Logic from A to Z: The Routledge Encyclopedia of Philosophy Glossary of Logical and Mathematical Terms

First published in the most ambitious international philosophy project for a generation; the Routledge Encyclopedia of Philosophy.Logic from A to Z is a unique glossary of terms used in formal logic and the philosophy of mathematics.Over 500 entries include key terms found in the study of:* Logic: Argument, Turing Machine, Variable* Set and model theory: Isomorphism, Function* Computability theory: Algorithm, Turing Machine* Plus a table of logical symbols.Extensively cross-referenced to help comprehension and add detail, Logic from A to Z provides an indispensable reference source for students of all branches of logic.

Logic from A to Z: The Routledge Encyclopedia of Philosophy Glossary of Logical and Mathematical Terms

First published in the most ambitious international philosophy project for a generation; the Routledge Encyclopedia of Philosophy.Logic from A to Z is a unique glossary of terms used in formal logic and the philosophy of mathematics.Over 500 entries include key terms found in the study of:* Logic: Argument, Turing Machine, Variable* Set and model theory: Isomorphism, Function* Computability theory: Algorithm, Turing Machine* Plus a table of logical symbols.Extensively cross-referenced to help comprehension and add detail, Logic from A to Z provides an indispensable reference source for students of all branches of logic.

Logic Functions and Equations: Binary Models for Computer Science

The expanded and updated 2nd edition of this classic text offers the reader a comprehensive introduction to the concepts of logic functions and equations and their applications across computer science. The approach emphasizes a thorough understanding of the fundamental principles as well as numerical and computer-based solution methods. Updated throughout, some major additions for the 2nd edition include: - an expanded introductory section on logic equations; - a new chapter on sets, lattices, and classes of logic functions; - a new chapter about SAT-problems; - a new chapter about methods to solve extremely complex problems; and - an expanded section with new decomposition methods utilizing the Boolean Differential Calculus extended to lattices of logic functions. The book provides insight into applications across binary arithmetic, coding, complexity, logic design, programming, computer architecture, and artificial intelligence. Based on the extensive teaching experience of the authors, Logic Functions and Equations is highly recommended for a one- or two-semester course in computer science and related programs. It provides straightforward high-level access to these methods and enables sophisticated applications, elegantly bridging the gap between mathematics and the theoretical foundations of computer science.

Logic Functions and Equations: Binary Models for Computer Science

Logic functions and equations are (some of) the most important concepts of Computer Science with many applications such as Binary Arithmetics, Coding, Complexity, Logic Design, Programming, Computer Architecture and Artificial Intelligence. They are very often studied in a minimum way prior to or together with their respective applications. Based on our long-time teaching experience, a comprehensive presentation of these concepts is given, especially emphasising a thorough understanding as well as numerical and computer-based solution methods. Any applications and examples from all the respective areas are given that can be dealt with in a unified way. They offer a broad understanding of the recent developments in Computer Science and are directly applicable in professional life. Logic Functions and Equations is highly recommended for a one- or two-semester course in many Computer Science or computer Science-oriented programmes. It allows students an easy high-level access to these methods and enables sophisticated applications in many different areas. It elegantly bridges the gap between Mathematics and the required theoretical foundations of Computer Science.

Logic, God and Metaphysics (Studies in Philosophy and Religion #15)

The papers in this volume are in honor of Bowman L. Clarke. Bowman Clarke earned degrees from Millsaps College, the University of Mississippi, and Emory University in Atlanta, Georgia, including the PhD in philosophy from Emory in 1961. He spent most of his academic career, a total of twenty-nine years, as a member of the Philosophy Department of the University of Georgia, Athens, Georgia, from which he retired in 1990. He also served as Head of the Department for several years. He has held many positions of distinction in professional societies, including President of the Georgia Philosophical Society, President of the Society for the Philosophy of Religion, and President of the Southern Society for Philosophy and Psychology. He also served as Editor-in­ Chief of the International Journal for the Philosophy of Religion from 1975-1989. Professor Clarke is the author of Language and Natural Theology (The Hague: Mouton and Co. , 1966) as well as numerous articles in professional journals. He has made major contributions in the areas of the philosophy of religion, the study of the philosophy of Alfred North Whitehead, and the development of the calculus of individuals. ix J. F. Harris (ed. ), Logic, God and Metaphysics, ix. © 1992 Kluwer Academic Publishers. Introduction The title for this volume, Logic, God, and Metaphysics, was chosen very carefully and deliberately. The papers in this volume are directed at the issues and problems which lie in the domain of the juncture of these three different areas of philosophical inquiry.

Logic Grammars (Symbolic Computation)

Logic grammars have found wide application both in natural language processing and in formal applications such as compiler writing. This book introduces the main concepts involving natural and formal language processing in logic programming, and discusses typical problems which the reader may encounter, proposing various methods for solving them. The basic material is presented in depth; advanced material, involving new logic grammar formalisms and applications, is presented with a view towards breadth. Major sections of the book include: grammars for formal language and linguistic research, writing a simple logic grammar, different types of logic grammars, applications, and logic grammars and concurrency. This book is intended for those interested in logic programming, artificial intelligence, computational linguistics, Fifth Generation computing, formal languages and compiling techniques. It may be read profitably by upper-level undergraduates, post-graduate students, and active researchers on the above-named areas. Some familiarity with Prolog and logic programming would be helpful; the authors, however, briefly describe Prolog and its relation to logic grammars. After reading Logic Grammars, the reader will be able to cope with the ever-increasing literature of this new and exciting field.

Logic in Elementary Mathematics (Dover Books on Mathematics)

This applications-related introductory treatment explores facets of modern symbolic logic useful in the exposition of elementary mathematics. The authors convey the material in a manner accessible to those trained in standard elementary mathematics but lacking any formal background in logic. Topics include the statement calculus, proof and demonstration, abstract mathematical systems, and the restricted predicate calculus. The final chapter draws upon the methods of logical reasoning covered in previous chapters to develop solutions of linear and quadratic equations, definitions of order and absolute value, and other applications. Numerous examples and exercises aid in the mastery of the language of logic.

Logic in High Definition: Trends in Logical Semantics (Trends in Logic #56)

This volume clusters together issues centered upon the variety of types of intensional semantics. Consisting of 10 contributions, the volume is based on papers presented at the Trends in Logic 2019 conference. The various chapters introduce readers to the topic, or apply new types of logical semantics to elucidate subtleties of logical systems and natural language semantics.The book introduces hyperintentional systems that aim at solving some open philosophical problems. Specifically, the first three studies focus on relating semantics, while the following ones discuss fundamental issues related to hyper-intensional semantics or develop hyper-intensional frameworks to address issues in modal, epistemic, deontic and action logic. Authors in this volume present original results on logical systems but also extend beyond this by offering philosophical considerations on the topic as well. This volume will appeal to students and researchers in the field of logic.

Logic in Law: Remarks on Logic and Rationality in Normative Reasoning, Especially in Law (Law and Philosophy Library #6)

The study presented in this book was entered upon by me from a legal point of view. 'Legal logic' has been known for a long time, concerning itself with the methodology of legal and in particular judicial reasoning. In modern days, however, this 'legal logic' is sometimes also connected with modern formal logic, as it has been developed in the works of G. Boole, A. de Morgan, G. Frege, C.S. Peirce, E. Schroder, G. Peano, A.N. Whitehead, B. Russell and others. For me this gave rise to the as yet not very specific question about the meaning of modern symbolic logic for law. Already in an early stage it appeared that, although traditional legal logic and modern symbolic logic both concern logic, this may not create the misapprehension that a similar matter is at issue. Both concern themselves (among other things) with reasonings and reasoning. Traditional legal logic is, however, as it was said by the German legal theoretician K. Engisch: "a material logic that wants us to reflect on what we have to do if we -within the limits of actual possibility- wish to reach true, or at least correct judgements" (Engisch, 1964, p.5). Modern symbolic logic on the other hand is not concerned with the truth or correctness of the result of an argument, but with its validity, i.e. the question when or under which conditions the truth (correctness) of the conclusion is guaranteed by the truth (correctness) of the premisses.

Logic in Question: Talks from the Annual Sorbonne Logic Workshop (2011- 2019) (Studies in Universal Logic)

This contributed volume collects papers related to the Logic in Question workshop, which has taken place annually at Sorbonne University in Paris since 2011. Each year, the workshop brings together historians, philosophers, mathematicians, linguists, and computer scientists to explore questions related to the nature of logic and how it has developed over the years. As a result, chapter authors provide a thorough, interdisciplinary exploration of topics that have been studied in the workshop. Organized into three sections, the first part of the book focuses on historical questions related to logic, the second explores philosophical questions, and the third section is dedicated to mathematical discussions. Specific topics include:• logic and analogy• Chinese logic• nineteenth century British logic (in particular Boole and Lewis Carroll)• logical diagrams • the place and value of logic in Louis Couturat’s philosophical thinking• contributions of logical analysis for mathematics education• the exceptionality of logic• the logical expressive power of natural languages• the unification of mathematics via topos theoryLogic in Question will appeal to pure logicians, historians of logic, philosophers, linguists, and other researchers interested in the history of logic, making this volume a unique and valuable contribution to the field.

Logic in Reality

This book is both dif?cult and rewarding, affording a new perspective on logic and reality, basically seen in terms of change and stability, being and becoming. Most importantly it exemplifies a mode of doing philosophy of science that seems a welcome departure from the traditional focus on purely analytic arguments. The author approaches ontology, metaphysics, and logic as having offered a number of ways of constructing the description of reality, and aims at deepening their relationships in a new way. Going beyond the mere abstract and formal aspects of logical analysis, he offers a new architecture of logic that sees it as applied not only to the “reasoning processes” belonging to the first disciplinary group – ontology – but also directly concerned with en- ties, events, and phenomena studied by the second one – metaphysics. It is the task of the book to elaborate such a constructive logic, both by offering a lo- cal view of the structure of the reality in general and by proffering a wealth of models able to encompass its implications for science. In turning from the merely formal to the constructive account of logic Brenner overcomes the limitation of logic to linguistic concepts so that it can be not only a logic “of” reality but also “in” that reality which is constitutively characterized by a number of fundamental dualities (observer and observed, self and not-self, internal and external, etc.

Logic in the Theory and Practice of Lawmaking (Legisprudence Library #2)

This book presents the current state of the art regarding the application of logical tools to the problems of theory and practice of lawmaking. It shows how contemporary logic may be useful in the analysis of legislation, legislative drafting and legal reasoning concerning different contexts of law making.Elaborations of the process of law making have variously emphasised its political, social or economic aspects. Yet despite strong interest in logical analyses of law, questions remains about the role of logical tools in law making. This volume attempts to bridge that gap, or at least to narrow it, drawing together some important research problems—and some possible solutions—as seen through the work of leading contemporary academics.The volume encompasses 20 chapters written by authors from 16 countries and it presents diversified views on the understanding of logic (from strict mathematical approaches to the informal, argumentative ones) and differentiated choices concerning the aspects of law making taken into account. The book presents a broad set of perspectives, insights and results into the emerging field of research devoted to the logical analysis of the area of creation of law.How does logic inform lawmaking?Are legal systems consistent and complete?How can legal rules be represented by means of formal calculi and visualization techniques?Does the structure of statutes or of legal systems resemble the structure of deductive systems?What are the logical relations between the basic concepts of jurisprudence that constitute the system of law?How are theories of legal interpretation relevant to the process of legislation?How might the statutory text be analysed by means of contemporary computer programs?These and other questions, ranging from the theoretical to the immediately practical, are addressed in this definitive collection.

Logic, Language, and Computation: 10th International Tbilisi Symposium on Logic, Language, and Computation, TbiLLC 2013, Gudauri, Georgia, September 23-27, 2013. Revised Selected Papers (Lecture Notes in Computer Science #8984)

This book constitutes the refereed proceedings of the 10th International Tbilisi Symposium on Logic, Language and Computation, TbiLLC 2013, held in Gudauri, Georgia, in September 2013. The conference series is centered around the interaction between logic, language and computation. The contributions represent these three fields and the symposia aim to foster interaction between them.The book consists of 16 papers that were carefully reviewed and selected from 26 submissions. Each paper has passed through a rigorous peer-review process before being accepted for publication. The volume also contains two summaries of the tutorials that took place at the symposium: the one on admissible rules and the one on the formal semantics of aspectual meaning from a cross-linguistic perspective.

Logic, Language and Computation (Applied Logic Series #5)

The editors of the Applied Logic Series are happy to present to the reader the fifth volume in the series, a collection of papers on Logic, Language and Computation. One very striking feature of the application of logic to language and to computation is that it requires the combination, the integration and the use of many diverse systems and methodologies - all in the same single application. The papers in this volume will give the reader a glimpse into the problems of this active frontier of logic. The Editors CONTENTS Preface IX 1. S. AKAMA Recent Issues in Logic, Language and Computation 1 2. M. J. CRESSWELL Restricted Quantification 27 3. B. H. SLATER The Epsilon Calculus' Problematic 39 4. K. VON HEUSINGER Definite Descriptions and Choice Functions 61 5. N. ASHER Spatio-Temporal Structure in Text 93 6. Y. NAKAYAMA DRT and Many-Valued Logics 131 7. S. AKAMA On Constructive Modality 143 8. H. W ANSING Displaying as Temporalizing: Sequent Systems for Subintuitionistic Logics 159 9. L. FARINAS DEL CERRO AND V. LUGARDON 179 Quantification and Dependence Logics 10. R. SYLVAN Relevant Conditionals, and Relevant Application Thereof 191 Index 245 Preface This is a collection of papers by distinguished researchers on Logic, Lin­ guistics, Philosophy and Computer Science. The aim of this book is to address a broad picture of the recent research on related areas. In particular, the contributions focus on natural language semantics and non-classical logics from different viewpoints.

Logic, Language, and Computation: 9th International Tbilisi Symposium on Logic, Language, and Computation, TbiLLC 2011, Kutaisi, Georgia, September 26-30, 2011, Revised Selected Papers (Lecture Notes in Computer Science #7758)

This book constitutes the refereed proceedings of the 9th International Tbilisi Symposium on Logic, Language, and Computation, TbiLLC 2011, held in Kutaisi, Georgia, in September 2011. The book consists of summaries of 3 tutorials presented at the symposium together with 13 full papers that were carefully reviewed and selected from the submissions. The papers are organized in two sections, one on Language and one on Logic and Computation. The range of topics covered in the Language section includes natural language syntax, semantics, and pragmatics, frames in natural language semantics, linguistic typology, and discourse phenomena. The papers in the Logic and Computation section cover such topics as constructive, modal, algebraic, and philosophical logic, as well as logics for computer science applications.

Logic, Language, and Computation: 8th International Tbilisi Symposium on Logic, Language, and Computation, TbiLLC 2009, Bakuriani, Georgia, September 21-25, 2009. Revised Selected Papers (Lecture Notes in Computer Science #6618)

Edited in collaboration with FoLLI, the Association of Logic, Language and Information, this book constitutes the refereed proceedings of the 8th International Tbilisi Symposium on Logic, Language, and Computation, TbiLLC 2009, held in Bakuriani, Georgia, in September 2009. The 20 revised full papers included in the book were carefully reviewed and selected from numerous presentations given at the symposium. The focus of the papers is on the following topics: natural language syntax, semantics, and pragmatics; constructive, modal and algebraic logic; linguistic typology and semantic universals; logics for artificial intelligence; information retrieval, query answer systems; logic, games, and formal pragmatics; language evolution and learnability; computational social choice; historical linguistics, history of logic.

Logic, Language, and Computation: 7th International Tbilisi Symposium on Logic, Language, and Computation, TbiLLC 2007, Tbilisi, Georgia, October 1-5, 2007. Revised Selected Papers (Lecture Notes in Computer Science #5422)

Edited in collaboration with FoLLI, the Association of Logic, Language and Information, this book constitutes the refereed proceedings of the 7th International Tbilisi Symposium on Logic, Language, and Computation, TbiLLC 2007, held in Tbilisi, Georgia, in October 2007. The 22 revised full papers included in the book were carefully reviewed and selected from numerous presentations given at the symposium. The focus of the papers is on the following topics: conceptual modeling of spatial relations, pragmatics and game theory, atypical valency phenomena, lexical typology, formal semantics and experimental evidence, exceptional quantifier scope, Georgian focussing particles, polarity and pragmatics, dynamics of belief, learning theory, inquisitive semantics, modal logic, coalgebras, computational linguistics of Georgian, type-logical grammar and cross-serial dependencies, non-monotonic logic, Japanese quantifiers, intuitionistic logic, semantics of negated nominals, word sense disambiguation, semantics of question-embedding predicates, and reciprocals and computational complexity.

Logic, Language, and Computation: 6th International Tbilisi Symposium on Logic, Language, and Computation. Batumi, Georgia, September 12-16, 2005, Revised Selected Papers (Lecture Notes in Computer Science #4363)

Edited in collaboration with FoLLI, the Association of Logic, Language and Information, this book represents the thoroughly refereed post-proceedings of the 6th International Tbilisi Symposium on Logic, Language, and Computation, TbiLLC 2005, held in Batumi, Georgia. The 19 revised full papers presented were carefully reviewed and selected from numerous presentations at the symposium. The papers present current research in all aspects of linguistics, logic and computation.

Logic, Language, and Computation: 11th International Tbilisi Symposium on Logic, Language, and Computation, TbiLLC 2015, Tbilisi, Georgia, September 21-26, 2015, Revised Selected Papers (Lecture Notes in Computer Science #10148)

This book constitutes the refereed proceedings of the 11th International Tbilisi Symposium on Logic, Language and Computation, TbiLLC 2015, held in Tbilisi, Georgia, in September 2015.The 18 papers in this book were selected from the invited submissions of full, revised versions of the 37 short papers presented at the conference, and one invited talk. Each paper has passed through a rigorous peer-review process before being accepted for publication.The biennial conference series and the proceedings are representative of the aims of the organizing institutes: to promote the integrated study of logic, information and language. The scientific program consisted of tutorials, invited lectures, contributed talks, and two workshops.

Logic, Language, and Mathematics: Themes from the Philosophy of Crispin Wright

Crispin Wright is widely recognised as one of the most important and influential analytic philosophers of the twentieth and twenty-first centuries. This volume is a collective exploration of the major themes of his work in philosophy of language, philosophical logic, and philosophy of mathematics. It comprises specially written chapters by a group of internationally renowned thinkers, as well as four substantial responses from Wright. In these thematically organized replies, Wright summarizes his life's work and responds to the contributory essays collected in this book. In bringing together such scholarship, the present volume testifies to both the enormous interest in Wright's thought and the continued relevance of Wright's seminal contributions in analytic philosophy for present-day debates;

Logic, Language and Meaning: 17th Amsterdam Colloquium, Amsterdam, The Netherlands, December 16-18, 2009, Revised Selected Papers (Lecture Notes in Computer Science #6042)

Logic, Language and Meaning: 18th Amsterdam Colloquium, Amsterdam, The Netherlands, December 19-21, 2011, Revised Selected Papers (Lecture Notes in Computer Science #7218)

This book contains the revised papers presented at the 8th Amsterdam Colloquium 2011, held in Amsterdam, The Netherlands, in December 2011. The 46 thoroughly refereed and revised contributions out of 137 submissions presented together with 2 invited talks are organized in five sections. The first section contains the invited contributions. The second, third and fourth sections incorporate submitted contributions to the three thematic workshops that were hosted by the Colloquium and addressed the following topics: inquisitiveness; formal semantics and pragmatics of sign languages, formal semantic evidence. The final section presents the submitted contributions to the general program.

Logic, Language, and Meaning, Volume 1: Introduction to Logic

Although the two volumes of Logic, Language, and Meaning can be used independently of one another, together they provide a comprehensive overview of modern logic as it is used as a tool in the analysis of natural language. Both volumes provide exercises and their solutions. Volume 1, Introduction to Logic, begins with a historical overview and then offers a thorough introduction to standard propositional and first-order predicate logic. It provides both a syntactic and a semantic approach to inference and validity, and discusses their relationship. Although language and meaning receive special attention, this introduction is also accessible to those with a more general interest in logic. In addition, the volume contains a survey of such topics as definite descriptions, restricted quantification, second-order logic, and many-valued logic. The pragmatic approach to non-truthconditional and conventional implicatures are also discussed. Finally, the relation between logic and formal syntax is treated, and the notions of rewrite rule, automation, grammatical complexity, and language hierarchy are explained.