Demonstrating the different roles that logic plays in the disciplines of computer science, mathematics, and philosophy, this concise undergraduate textbook covers select topics from three different areas of logic: proof theory, computability theory, and nonclassical logic. The book balances accessibility, breadth, and rigor, and is designed so that its materials will fit into a single semester. Its distinctive presentation of traditional logic material will enhance readers' capabilities and mathematical maturity. The proof theory portion presents classical propositional logic and first-order logic using a computer-oriented (resolution) formal system. Linear resolution and its connection to the programming language Prolog are also treated. The computability component offers a machine model and mathematical model for computation, proves the equivalence of the two approaches, and includes famous decision problems unsolvable by an algorithm. The section on nonclassical logic discusses the shortcomings of classical logic in its treatment of implication and an alternate approach that improves upon it: Anderson and Belnap's relevance logic. Applications are included in each section. The material on a four-valued semantics for relevance logic is presented in textbook form for the first time. Aimed at upper-level undergraduates of moderate analytical background, Three Views of Logic will be useful in a variety of classroom settings. Gives an exceptionally broad view of logic Treats traditional logic in a modern format Presents relevance logic with applications Provides an ideal text for a variety of one-semester upper-level undergraduate courses

This book examines positions that challenge the Fregean logic-first view. It raises critical questions about logic by examining various ways in which logic may be entangled with mathematics and metaphysics. Is logic topic-neutral and general? Can we take the application of logic for granted? This book suggests that we should not be dogmatic about logic but ask similar critical questions about logic as those Kant raised about metaphysics and mathematics. It challenges the Fregean logic-first view according to which logic is fundamental and hence independent of any extra-logical considerations. Whereas Quine assimilated logic and mathematics to the theoretical parts of empirical science, the present volume explores views that stop short of his thoroughgoing holism but instead take logic to be answerable to or entangled with some particular disciplines. The contributions provide views that assign primacy to mathematical reasons, Kantian metaphysical grounds, Husserlian transcendental phenomenological reflection, or normative considerations about how terms ought to be defined in various fields of empirical science or mathematics. Space is thereby carved out between a Fregean position on the one hand and Quinean holism on the other. Critical Views of Logic will be a key resource for academics, researchers, and advanced students of philosophy, linguistics, mathematics, and computer science, as well as those engaged in various fields of empirical science. The chapters in this book, except for chapter 4, were originally published in the journal Inquiry.

This book examines positions that challenge the Fregean logic-first view. It raises critical questions about logic by examining various ways in which logic may be entangled with mathematics and metaphysics. Is logic topic-neutral and general? Can we take the application of logic for granted? This book suggests that we should not be dogmatic about logic but ask similar critical questions about logic as those Kant raised about metaphysics and mathematics. It challenges the Fregean logic-first view according to which logic is fundamental and hence independent of any extra-logical considerations. Whereas Quine assimilated logic and mathematics to the theoretical parts of empirical science, the present volume explores views that stop short of his thoroughgoing holism but instead take logic to be answerable to or entangled with some particular disciplines. The contributions provide views that assign primacy to mathematical reasons, Kantian metaphysical grounds, Husserlian transcendental phenomenological reflection, or normative considerations about how terms ought to be defined in various fields of empirical science or mathematics. Space is thereby carved out between a Fregean position on the one hand and Quinean holism on the other. Critical Views of Logic will be a key resource for academics, researchers, and advanced students of philosophy, linguistics, mathematics, and computer science, as well as those engaged in various fields of empirical science. The chapters in this book, except for chapter 4, were originally published in the journal Inquiry.

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Since his inaugural lecture at Freiburg in 1929 in which Heidegger delivered his most celebrated salvo against logic, he has frequently been portrayed as an anti-logician, a classic example of the obscurity resultant upon a rejection of the discipline of logic, a champion of the irrational, and a variety of similar things. Because many of Heidegger's statements on logic are polemical in tone, there has been no little misunderstanding of his position in regard to logic, and a great deal of distortion of it. All too frequently the position which is attacked as Heidegger's is a barely recognizable caricature of it. Heidegger has, from the very beginning of his career, written and said much on logic. Strangely enough, in view of all that he has said, his critique of logic has not been singled out as the subject of any of the longer, more detailed studies on the various aspects of his thought.

This robust, clear, and well-researched textbook for classes in logic introduces students to both formal logic and to the virtues of intellectual inquiry. Part 1 challenges students to develop the analytical skills of deductive and inductive reasoning, showing them how to identify and evaluate arguments. Part 2 helps students develop the intellectual virtues of the wise inquirer. The book includes helpful pedagogical features such as practice exercises and a concluding summary with definitions of key concepts for each chapter. Resources for professors and students are available through Baker Academic's Textbook eSources.

The Elements of Arguments introduces such central critical thinking topics as informal fallacies, the difference between validity and truth, basic formal propositional logic, and how to extract arguments from texts. Turetzky aims to prevent common confusions by clearly explaining a number of important distinctions, including propositions vs. propositional attitudes, propositions vs. states of affairs, and logic vs. rhetoric vs. psychology. Exercises are provided throughout, including numerous informal arguments that can be assessed using the skills and strategies presented within the text.