An Introduction To Symbolic Logic

Famous classic has introduced countless readers to symbolic logic with its thorough and precise exposition. Starts with simple symbols and conventions and concludes with the Boole-Schroeder and Russell-Whitehead systems. No special knowledge of mathematics necessary. "One of the clearest and simplest introductions to a subject which is very much alive." — Mathematics Gazette.

This accessible, SHORT introduction to symbolic logic includes coverage of sentential and predicate logic, translations, truth tables, and derivations. The author’s engaging style makes this the most informal of introductions to formal logic. Topics are explained in a conversational, easy-to-understand way for readers not familiar with mathematics or formal systems, and the author provides patient, reader-friendly explanations—even with the occasional bit of humour. The first half of the book deals with all the basic elements of Sentential Logic: the five truth-functional connectives, formation rules and translation into this language, truth-tables for validity, logical truth/falsity, equivalency, consistency and derivations. The second half deals with Quantifier Logic: the two quantifiers, formation rules and translation, demonstrating certain logical characteristics by “Finding an Interpretation” and derivations. There are plenty of exercises scattered throughout, more than in many texts, arranged in order of increasing difficulty and including separate answer keys.

Clear, comprehensive, and rigorous treatment develops the subject from elementary concepts to the construction and analysis of relatively complex logical languages. Hundreds of problems, examples, and exercises. 1958 edition.

Logic With Trees is a new and original introduction to modern formal logic. Unlike most texts, it also contains discussions on more philosophical issues such as truth, conditionals and modal logic. It presents the formal material with clarity, preferring informal explanations and arguments to intimidatingly rigorous development. Worked examples and excercises enable the readers to check their progress. Logic With Trees equips students with * a complete and clear account of the truth-tree system for first order logic * the importance of logic and its relevance to many different disciplines * the skills to grasp sophisticated formal reasoning techniques necessary to explore complex metalogic * the ability to contest claims that `ordinary' reasoning is well represented by formal first order logic The issues covered include a thorough discussion of truth-functional and full first order logic, using the truth-tree or semantic tableau approach. Completeness and Soundness proofs are given for both truth-functional and first order trees. Much use is made of induction, which is presented in a clear and consistent manner. There is also discussion of alternative deductive systems, an introduction to transfinite numbers and categoricity, the Lowenhein-Skolem theories and the celebrated findings of Godel and Church. The book concludes with an account of Kripke's attempted solution of the liar paradox and a discussion of the weakness of truth-functional account of conditionals. Particularly useful to those who favour critical accounts of formal reasoning, it will be of interest to students of philosophy at first level and beyond and also students of mathematics and computer science.

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.

The Logic of Our Language teaches the practical and everyday application of formal logic. Rather than overwhelming the reader with abstract theory, Jackson and McLeod show how the skills developed through the practice of logic can help us to better understand our own language and reasoning processes. The authors’ goal is to draw attention to the patterns and logical structures inherent in our spoken and written language by teaching the reader how to translate English sentences into formal symbols. Other logical tools, including truth tables, truth trees, and natural deduction, are then introduced as techniques for examining the properties of symbolized sentences and assessing the validity of arguments. A substantial number of practice questions are offered both within the book itself and as interactive activities on a companion website.