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The field of modern logic is too extensive to be worked through by open cast mining. To open it up, we need to sink shafts and construct adits. This is the method of most text books: a systematic exposition of a number of main topics, supplemented by exercises to teach skill in the appurtenant techniques, lays a secure foundation for subsequent dis cussion of selected questions. Compared with this, the present treatment is more like a network of exploratory drillings to show that it would be worthwhile to start mining operations, or to work the existing shafts and adits, as the case may be. Within this metaphor we may also describe the inherent weakness of this conception: once a cavity is pierced, the duct's capacity will in general not be sufficient to carry away the discovered riches. But whether we are concerned with a new or an already worked mine - at any rate, the experience should stimulate us into either reviving an existing system of shafts or even, in particularly fortunate cases, designing a new ap proach.
Formal logic provides us with a powerful set of techniques for criticizing some arguments and showing others to be valid. These techniques are relevant to all of us with an interest in being skilful and accurate reasoners. In this highly accessible book, Peter Smith presents a guide to the fundamental aims and basic elements of formal logic. He introduces the reader to the languages of propositional and predicate logic, and then develops formal systems for evaluating arguments translated into these languages, concentrating on the easily comprehensible 'tree' method. His discussion is richly illustrated with worked examples and exercises. A distinctive feature is that, alongside the formal work, there is illuminating philosophical commentary. This book will make an ideal text for a first logic course, and will provide a firm basis for further work in formal and philosophical logic.
This text presents a clear and philosophically sound method for identifying, interpreting, and evaluating arguments as they appear in non-technical sources. It focuses on a more functional, real-world goal of argument analysis as a tool for figuring out what is reasonable to believe rather than as an instrument of persuasion. Methods are illustrated by applying them to arguments about different topics as they appear in a variety of contexts — e.g., newspaper editorials and columns, short essays, informal reports of scientific results, etc.
This classic undergraduate treatment examines the deductive method in its first part and explores applications of logic and methodology in constructing mathematical theories in its second part. Exercises appear throughout.
Introductory logic is generally taught as a straightforward technical discipline. In this book, John MacFarlane helps the reader think about the limitations of, presuppositions of, and alternatives to classical first-order predicate logic, making this an ideal introduction to philosophical logic for any student who already has completed an introductory logic course. The book explores the following questions. Are there quantificational idioms that cannot be expressed with the familiar universal and existential quantifiers? How can logic be extended to capture modal notions like necessity and obligation? Does the material conditional adequately capture the meaning of 'if'—and if not, what are the alternatives? Should logical consequence be understood in terms of models or in terms of proofs? Can one intelligibly question the validity of basic logical principles like Modus Ponens or Double Negation Elimination? Is the fact that classical logic validates the inference from a contradiction to anything a flaw, and if so, how can logic be modified to repair it? How, exactly, is logic related to reasoning? Must classical logic be revised in order to be applied to vague language, and if so how? Each chapter is organized around suggested readings and includes exercises designed to deepen the reader's understanding. Key Features: An integrated treatment of the technical and philosophical issues comprising philosophical logic Designed to serve students taking only one course in logic beyond the introductory level Provides tools and concepts necessary to understand work in many areas of analytic philosophy Includes exercises, suggested readings, and suggestions for further exploration in each chapter
Modern Logic fills the strong need for a highly accessible, carefully structured introductory text in symbolic logic. The natural deduction system Forbes uses will be easy for students to understand, and the material is carefully structured, with graded exercises at the end of each section, selected answers to which are provided at the back of the book. The book's emphasis is on giving the student a thorough understanding of the concepts rather than just a facilitywith formal procedures.