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Logic from Russell to Church

Author: Dov M. Gabbay
Publisher: Elsevier
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This volume is number five in the 11-volume Handbook of the History of Logic. It covers the first 50 years of the development of mathematical logic in the 20th century, and concentrates on the achievements of the great names of the period--Russell, Post, Gödel, Tarski, Church, and the like. This was the period in which mathematical logic gave mature expression to its four main parts: set theory, model theory, proof theory and recursion theory. Collectively, this work ranks as one of the greatest achievements of our intellectual history. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in the history of logic, the history of philosophy, and any discipline, such as mathematics, computer science, and artificial intelligence, for whom the historical background of his or her work is a salient consideration. • The entire range of modal logic is covered • Serves as a singular contribution to the intellectual history of the 20th century • Contains the latest scholarly discoveries and interpretative insights


Elements of Logical Reasoning

Author: Jan von Plato
Publisher: Cambridge University Press
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Some of our earliest experiences of the conclusive force of an argument come from school mathematics: faced with a mathematical proof, we cannot deny the conclusion once the premises have been accepted. Behind such arguments lies a more general pattern of 'demonstrative arguments' that is studied in the science of logic. Logical reasoning is applied at all levels, from everyday life to advanced sciences, and a remarkable level of complexity is achieved in everyday logical reasoning, even if the principles behind it remain intuitive. Jan von Plato provides an accessible but rigorous introduction to an important aspect of contemporary logic: its deductive machinery. He shows that when the forms of logical reasoning are analysed, it turns out that a limited set of first principles can represent any logical argument. His book will be valuable for students of logic, mathematics and computer science.


Lambda Calculus with Types

Author: Henk Barendregt
Publisher: Cambridge University Press
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This handbook with exercises reveals in formalisms, hitherto mainly used for hardware and software design and verification, unexpected mathematical beauty. The lambda calculus forms a prototype universal programming language, which in its untyped version is related to Lisp, and was treated in the first author's classic The Lambda Calculus (1984). The formalism has since been extended with types and used in functional programming (Haskell, Clean) and proof assistants (Coq, Isabelle, HOL), used in designing and verifying IT products and mathematical proofs. In this book, the authors focus on three classes of typing for lambda terms: simple types, recursive types and intersection types. It is in these three formalisms of terms and types that the unexpected mathematical beauty is revealed. The treatment is authoritative and comprehensive, complemented by an exhaustive bibliography, and numerous exercises are provided to deepen the readers' understanding and increase their confidence using types.


Proof Analysis

Author: Sara Negri
Publisher: Cambridge University Press
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This book continues from where the authors' previous book, Structural Proof Theory, ended. It presents an extension of the methods of analysis of proofs in pure logic to elementary axiomatic systems and to what is known as philosophical logic. A self-contained brief introduction to the proof theory of pure logic is included that serves both the mathematically and philosophically oriented reader. The method is built up gradually, with examples drawn from theories of order, lattice theory and elementary geometry. The aim is, in each of the examples, to help the reader grasp the combinatorial behaviour of an axiom system, which typically leads to decidability results. The last part presents, as an application and extension of all that precedes it, a proof-theoretical approach to the Kripke semantics of modal and related logics, with a great number of new results, providing essential reading for mathematical and philosophical logicians.


Logic A History of its Central Concepts

Author: Dov M. Gabbay
Publisher: Newnes
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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


Perspectives on the History of Mathematical Logic

Author: Thomas Drucker
Publisher: Springer Science & Business Media
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This volume offers insights into the development of mathematical logic over the last century. Arising from a special session of the history of logic at an American Mathematical Society meeting, the chapters explore technical innovations, the philosophical consequences of work during the period, and the historical and social context in which the logicians worked. The discussions herein will appeal to mathematical logicians and historians of mathematics, as well as philosophers and historians of science.


Handbook of Logic and Language

Author: J. F. A. K. van Benthem
Publisher: Elsevier
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This Handbook documents the main trends in current research between logic and language, including its broader influence in computer science, linguistic theory and cognitive science. The history of the combined study of Logic and Linguistics goes back a long way, at least to the work of the scholastic philosophers in the Middle Ages. At the beginning of this century, the subject was revitalized through the pioneering efforts of Gottlob Frege, Bertrand Russell, and Polish philosophical logicians such as Kazimierz Ajdukiewicz. Around 1970, the landmark achievements of Richard Montague established a junction between state-of-the-art mathematical logic and generative linguistic theory. Over the subsequent decades, this enterprise of Montague Grammar has flourished and diversified into a number of research programs with empirical and theoretical substance. This appears to be the first Handbook to bring logic-language interface to the fore. Both aspects of the interaction between logic and language are demonstrated in the book i.e. firstly, how logical systems are designed and modified in response to linguistic needs and secondly, how mathematical theory arises in this process and how it affects subsequent linguistic theory. The Handbook presents concise, impartial accounts of the topics covered. Where possible, an author and a commentator have cooperated to ensure the proper breadth and technical content of the papers. The Handbook is self-contained, and individual articles are of the highest quality.


The Evolution of Logic

Author: W. D. Hart
Publisher: Cambridge University Press
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Examines the relations between logic and philosophy over the last 150 years. Logic underwent a major renaissance beginning in the nineteenth century. Cantor almost tamed the infinite, and Frege aimed to undercut Kant by reducing mathematics to logic. These achievements were threatened by the paradoxes, like Russell's. This ferment generated excellent philosophy (and mathematics) by excellent philosophers (and mathematicians) up to World War II. This book provides a selective, critical history of the collaboration between logic and philosophy during this period. After World War II, mathematical logic became a recognized subdiscipline in mathematics departments, and consequently but unfortunately philosophers have lost touch with its monuments. This book aims to make four of them (consistency and independence of the continuum hypothesis, Post's problem, and Morley's theorem) more accessible to philosophers, making available the tools necessary for modern scholars of philosophy to renew a productive dialogue between logic and philosophy.


Origins of Analytic Philosophy

Author: Delbert Reed
Publisher: A&C Black
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History of Western Philosophy

Author: Bertrand Russell
Publisher: Routledge
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Now in a special gift edition, and featuring a brand new foreword by Anthony Gottlieb, this is a dazzlingly unique exploration of the works of significant philosophers throughout the ages and a definitive must-have title that deserves a revered place on every bookshelf.