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Logic and Philosophy of Mathematics in the Early Husserl (Synthese Library #345)
by Stefania CentroneLogic and Philosophy of Mathematics in the Early Husserl focuses on the first ten years of Edmund Husserl’s work, from the publication of his Philosophy of Arithmetic (1891) to that of his Logical Investigations (1900/01), and aims to precisely locate his early work in the fields of logic, philosophy of logic and philosophy of mathematics. Unlike most phenomenologists, the author refrains from reading Husserl’s early work as a more or less immature sketch of claims consolidated only in his later phenomenology, and unlike the majority of historians of logic she emphasizes the systematic strength and the originality of Husserl’s logico-mathematical work. The book attempts to reconstruct the discussion between Husserl and those philosophers and mathematicians who contributed to new developments in logic, such as Leibniz, Bolzano, the logical algebraists (especially Boole and Schröder), Frege, and Hilbert and his school. It presents both a comprehensive critical examination of some of the major works produced by Husserl and his antagonists in the last decade of the 19th century and a formal reconstruction of many texts from Husserl’s Nachlaß that have not yet been the object of systematical scrutiny. This volume will be of particular interest to researchers working in the history, and in the philosophy, of logic and mathematics, and more generally, to analytical philosophers and phenomenologists with a background in standard logic.
Logic and Science: An Exploration of Logical Anti-Exceptionalism (Elements in Philosophy and Logic)
by Filippo Ferrari Massimiliano CarraraThis Element delves into the relationship between logic and the sciences, a topic brought to prominence by Quine, who regarded logic as methodologically and epistemologically akin to the sciences. For this reason, Quine is seen as the forefather of anti-exceptionalism about logic (AEL), a stance that has become prevalent in the philosophy of logic today. Despite its popularity and the volume of research it inspires, some core issues still lack clarity. For one thing, most works in the debate remain vague on what should count as logic and what should count as a science. Furthermore, the terms of the comparison are rarely specified and discussed in a systematic way. This Element purports to advance the debate on these crucial issues with the hope of fostering our understanding of the fundamentals of AEL. This title is also available as Open Access on Cambridge Core.
Logic and the Limits of Philosophy in Kant and Hegel
by Clayton BohnetThis text examines the boundary between philosophy and formal logic in Kant and Hegel. It takes up the particular category of 'quantity' as a point around which to explore Kant's and Hegel's larger architectonic concerns. Analysis of the relation in Kant between quantity in formal logic and in his transcendental logic reveals two complementary but distinct approaches that preserve the boundary between philosophy and formal logic. By contrast, in Hegel's Science of Logic we find both a novelapproach to the traditional treatment of quantity in logic, and a reconstruction of the relation of logic to all other determinations of thought. By basing its examination of the relation of formal logic and philosophy in Kant and Hegel on a detailed analysis of quantity, Logic and the Limits of Philosophy in Kant and Hegel provides a resource for an historically informed interpretation of the revolutions in logic that marked the onset of our digital age.
Logic and Transcendence: A New Translation with Selected Letters
by Frithjof SchuonIn this new edition of his most important philosophical work, Frithjof Schuon confronts the pitfalls of rationalism and relativism within modern philosophy. This new edition comprises a fully revised translation from the French original and contains an extensive Appendix with previously unpublished letters and other private writings.
Logic as a Tool: A Guide to Formal Logical Reasoning (Wiley Desktop Editions Ser.)
by Valentin GorankoWritten in a clear, precise and user-friendly style, Logic as a Tool: A Guide to Formal Logical Reasoning is intended for undergraduates in both mathematics and computer science, and will guide them to learn, understand and master the use of classical logic as a tool for doing correct reasoning. It offers a systematic and precise exposition of classical logic with many examples and exercises, and only the necessary minimum of theory. The book explains the grammar, semantics and use of classical logical languages and teaches the reader how grasp the meaning and translate them to and from natural language. It illustrates with extensive examples the use of the most popular deductive systems -- axiomatic systems, semantic tableaux, natural deduction, and resolution -- for formalising and automating logical reasoning both on propositional and on first-order level, and provides the reader with technical skills needed for practical derivations in them. Systematic guidelines are offered on how to perform logically correct and well-structured reasoning using these deductive systems and the reasoning techniques that they employ. •Concise and systematic exposition, with semi-formal but rigorous treatment of the minimum necessary theory, amply illustrated with examples •Emphasis both on conceptual understanding and on developing practical skills •Solid and balanced coverage of syntactic, semantic, and deductive aspects of logic •Includes extensive sets of exercises, many of them provided with solutions or answers•Supplemented by a website including detailed slides, additional exercises and solutionsFor more information browse the book's website at: https://logicasatool.wordpress.com
Logic as Universal Science
by Anssi KorhonenLogic as Universal Science offers a detailed reconstruction of the underlying philosophy in The Principles of Mathematics showing how Russell sought to deliver a death blow to the dominant Kantian view that formal logic is a concise and dry science and unable to enlarge our understanding.
Logic-Based Program Synthesis and Transformation: 30th International Symposium, LOPSTR 2020, Bologna, Italy, September 7–9, 2020, Proceedings (Lecture Notes in Computer Science #12561)
by Maribel FernándezThis book constitutes the refereed proceedings of the 30th International Conference on Logic-Based Program Synthesis and Transformation, LOPSTR 2020, which was held during September 7-9, 2020. The 15 papers presented in this volume were carefully reviewed and selected from a total of 31 submissions. The book also contains two invited talks in full paper length. The contributions were organized in topical sections named: rewriting; unification; types; verification; model checking and probabilistic programming; program analysis and testing; and logics.
Logic-Based Program Synthesis and Transformation: 27th International Symposium, LOPSTR 2017, Namur, Belgium, October 10-12, 2017, Revised Selected Papers (Lecture Notes in Computer Science #10855)
by Fabio Fioravanti John P. GallagherThis book constitutes the thoroughly refereed post-conference proceedings of the 27th International Symposium on Logic-Based Program Synthesis and Transformation, LOPSTR 2017, held in Namur, Belgium, in October 2017. The 19 revised full papers were carefully reviewed and selected from 29 submissions. In addition to the 19 revised papers, this volume includes the abstracts of the invited talks by three outstanding speakers: Sumit Gulwani, Marieke Huisman, and Grigore Roşu. The aim of the LOPSTR series is to stimulate and promote international research and collaboration on logic-based program development. LOPSTR is open to contributions in all aspects of logic-based program development, all stages of the software life cycle, and issues of both programming-in-the-small and programming-in-the-large. LOPSTR traditionally solicits contributions, in any language paradigm, in the areas of synthesis, specification, transformation, analysis and verification, specialization, testing and certification, composition, program/model manipulation, optimization, transformational techniques in SE, inversion, applications, and tools.
Logic-Based Program Synthesis and Transformation: 28th International Symposium, LOPSTR 2018, Frankfurt/Main, Germany, September 4-6, 2018, Revised Selected Papers (Lecture Notes in Computer Science #11408)
by Fred Mesnard Peter J. StuckeyThis book constitutes the thoroughly refereed post-conference proceedings of the 28th International Symposium on Logic-Based Program Synthesis and Transformation, LOPSTR 2018, held in Frankfurt/Main, Germany, in September 2018.The 11 revised full papers were carefully reviewed and selected from 29 submissions. In addition to the 11 papers, this volume includes 3 abstracts of invited talks and 2 abstracts of invited tutorials. The papers are grouped into the following topics: analysis of term rewriting; logic-based distributed/concurrent programming; analysis of logic programming; and program analysis.
Logic: Bullet Guides
by Joe MorrisonOpen this book and you will Learn what logic is Use truth tables and truth trees Make sense of complex arguments Use logic every day
Logic: A Complete Introduction: Teach Yourself
by Siu-Fan LeeUnderstand Logic is a comprehensive introduction to this fascinating though sometimes challenging subject. As well as looking at logic in theoretical terms the book considers its everyday uses and demonstrates how it has genuine practical applications. It will take you step by step through the most difficult concepts and is packed with exercises to help you consolidate your learning at every stage. Covering everything from syllogistic logic to logical paradoxes and even looking at logic in Alice in Wonderland, this is the only guide you will ever need.
Logic, Computation and Rigorous Methods: Essays Dedicated to Egon Börger on the Occasion of His 75th Birthday (Lecture Notes in Computer Science #12750)
by Alexander Raschke Elvinia Riccobene Klaus-Dieter ScheweThis Festschrift was published in honor of Egon Börger on the occasion of his 75th birthday.It acknowledges Prof. Börger's inspiration as a scientist, author, mentor, and community organizer. Dedicated to a pioneer in the fields of logic and computer science, Egon Börger's research interests are unusual in scope, from programming languages to hardware architectures, software architectures, control systems, workflow and interaction patterns, business processes, web applications, and concurrent systems.The 18 invited contributions in this volume are by leading researchers in the areas of software engineering, programming languages, business information systems, and computer science logic.
Logic, Epistemology, and Scientific Theories - From Peano to the Vienna Circle (Vienna Circle Institute Yearbook #29)
by Paola Cantù Georg SchiemerThis book provides a collection of chapters on the development of scientific philosophy and symbolic logic in the early twentieth century. The turn of the last century was a key transitional period for the development of symbolic logic and scientific philosophy. The Peano school, the editorial board of the Revue de Métaphysique et de Morale, and the members of the Vienna Circle are generally mentioned as champions of this transformation of the role of logic in mathematics and in the sciences. The scholarship contained provides a rich historical and philosophical understanding of these groups and research areas. Specifically, the contributions focus on a detailed investigation of the relation between structuralism and modern mathematics. In addition, this book provides a closer understanding of the relation between symbolic logic and previous traditions such as syllogistics. This volume also informs the reader on the relation between logic, the history and didactics in the Peano School. This edition appeals to students and researchers working in the history of philosophy and of logic, philosophy of science, as well as to researchers on the Vienna Circle and the Peano School.
Logic Essentials
by W. Kent WilsonREA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Logic covers the basic concepts of logic, including sentences, arguments, and the evaluation of arguments. This book will give the reader a clear understanding of sentence logic such as symbolization, semantics, and truth trees by giving concise definitions and examples of each.
Logic, Everyday Discourse, and Metaphysics (UNIPA Springer Series)
by Gianni RigamontiThis book applies the formal discipline of logic to everyday discourse. It offers a new analysis of the notion of individual, suggesting that this notion is linguistic, not ontological, and that anything denoted by a proper name in a well-functioning language game is an individual. It further posits that everyday discourse is non-compositional, i.e., its complex expressions are not just the result of putting simpler ones together but react on the latter, modifying their meaning through feedback. The book theorizes that in everyday discourse, there is no algebra of truth values, but the latter can be both input and output of something which has no truth value at all. It suggests that an elementary proposition of everyday discourse (defined as having exactly one predicate) can, in principle, be indefinitely expanded by adding new components, belonging neither to subject nor to predicate, but remain elementary. This book is of interest to logicians and philosophers of language.
Logic for Computer Science: Foundations of Automatic Theorem Proving, Second Edition (Dover Books on Computer Science)
by Jean H. GallierThis advanced text for undergraduate and graduate students introduces mathematical logic with an emphasis on proof theory and procedures for algorithmic construction of formal proofs. The self-contained treatment is also useful for computer scientists and mathematically inclined readers interested in the formalization of proofs and basics of automatic theorem proving. Topics include propositional logic and its resolution, first-order logic, Gentzen's cut elimination theorem and applications, and Gentzen's sharpened Hauptsatz and Herbrand's theorem. Additional subjects include resolution in first-order logic; SLD-resolution, logic programming, and the foundations of PROLOG; and many-sorted first-order logic. Numerous problems appear throughout the book, and two Appendixes provide practical background information.
Logic for Justice: An Introduction to Formal Logic with an Emphasis on Political Reform
by Isaac WilhelmAn introductory textbook, Logic for Justice covers, in full detail, the language and semantics of both propositional logic and first-order logic. It motivates the study of those logical systems by drawing on social and political issues. Basically, Logic for Justice frames propositional logic and first-order logic as two theories of the distinction between good arguments and bad arguments. And the book explains why, for the purposes of social justice and political reform, we need theories of that distinction. In addition, Logic for Justice is extremely lucid, thorough, and clear. It explains, and motivates, many different features of the formalism of propositional logic and first-order logic, always connecting those features back to real-world issues. Key Features Connects the study of logic to real-world social and political issues, drawing in students who might not otherwise be attracted to the subject. Offers extremely clear and thorough presentations of technical material, allowing students to learn directly from the book without having to rely on instructor explanations. Carefully explains the value of arguing well throughout one’s life, with several discussions about how to argue and how arguments – when done with care – can be helpful personally. Includes examples that appear throughout the entire book, allowing students to see how the ideas presented in the book build on each other. Provides a large and diverse set of problems for each chapter. Teaches logic by connecting formal languages to natural languages with which students are already familiar, making it much easier for students to learn how logic works.
Logic, Form and Grammar (International Library of Philosophy)
by Peter LongThis work contains Peter Long's important essay, Logic, Form and Grammar, which resolves many difficulties for the logical form of an argument where the reasoning is hypothetical. Also included are two essays on classical problems in philosophical logic, relating to logical form and formal relations. All of the essays provide clear thinking and philosophical explanations, overturning many unchallenged suggestions in philosophical logic.
Logic from Kant to Russell: Laying the Foundations for Analytic Philosophy (Routledge Studies in Nineteenth-Century Philosophy)
by Sandra LapointeThe 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
by John B. Bacon Michael Detlefsen David Charles McCartyFirst 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 in Computer Science: Modelling and Reasoning about Systems
by Michael Huth Mark RyanIn recent years, powerful tools for verifying hardware and software systems have been developed. Major companies, such as Intel, Siemens, BT, AT & T, and IBM have increasingly become interested in that technology. Students need a basic formal training that allows them to gain sufficient proficiency in using logic-based verification methods. This book addresses these needs by providing a sound basis in logic and an introduction to the logical frameworks used in modeling, specifying and verifying computer systems. Coverage provides a simple and clear presentation, detailing propositional and predicate logic as well as some specialized logics used for reasoning about the correctness of computer systems. The authors introduce a carefully chosen core of essential terminology; further technicalities are introduced only where they are required by the applications. Numerous examples are given, as well as a full exposition of a fast-growing technique for modeling and verifying computer systems, known as symbolic model checking. It will be an ideal introduction for undergraduate students. A worldwide web tutorial that supports the course activities and provides solutions to the sample exercises is available to instructors.
Logic in Computer Science
by Hantao Zhang Jian ZhangMathematical logic is an important basis for mathematics, computer science and artificial intelligence alike. This book provides a comprehensive introduction to various logics, including classical propositional logic and first-order predicate logic, as well as equational logic, temporal logic, and Hoare logic. In addition, it presents proof procedures for classical logics and decision procedures for checking the satisfiability of logical formulas. The book assumes no background in logic. It presents logics as practical tools for solving various problems in artificial intelligence and formal verification. Accordingly, it is well suited for (junior and senior) undergraduate and graduate students majoring in computer science or mathematics. Each chapter includes roughly a dozen exercise problems, so as to help the reader understand the concepts and techniques discussed.
Logic in Elementary Mathematics (Dover Books on Mathematics)
by Robert M. Exner Myron F. RosskopfThis 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)
by Alessandro Giordani Jacek MalinowskiThis 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.
The Logic in Philosophy of Science
by Hans HalvorsonMajor figures of twentieth-century philosophy were enthralled by the revolution in formal logic, and many of their arguments are based on novel mathematical discoveries. Hilary Putnam claimed that the Löwenheim-Skølem theorem refutes the existence of an objective, observer-independent world; Bas van Fraassen claimed that arguments against empiricism in philosophy of science are ineffective against a semantic approach to scientific theories; W. V. O. Quine claimed that the distinction between analytic and synthetic truths is trivialized by the fact that any theory can be reduced to one in which all truths are analytic. This book dissects these and other arguments through in-depth investigation of the mathematical facts undergirding them. It presents a systematic, mathematically rigorous account of the key notions arising from such debates, including theory, equivalence, translation, reduction, and model. The result is a far-reaching reconceptualization of the role of formal methods in answering philosophical questions.