Understanding Symbolic Logic

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9780139364686: Understanding Symbolic Logic

Designed for those who have no prior background in logic, philosophy, or mathematics, this comprehensive introduction covers all the standard topics of symbolic logic through relational predicate logic with identity. Understanding Symbolic Logic, Fourth Edition, is completely reader-friendly. All concepts and theories are presented in small "bites," helping you to master the concepts of symbolic logic with confidence. Understanding Symbolic Logic, Fourth Edition, features: *Explanations keyed to the difficulty of the topics covered; *Numerous worked-out examples; many detailed, step-by-step symbolizations; over 50 fully worked-out proofs; additional exercises; and *"Extra credit" units that offer a glimpse into alternative methods of logic and more advanced topics; *New for the Fourth Edition: New explanatory material on logical form and other topics; many updates and clarifications; a new exercise set; and more. Pearson Education

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This comprehensive introduction to symbolic logic is designed for students with no prior background in logic, philosophy, or mathematics.

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This book is intended as a comprehensive introduction to symbolic logic. It presupposes no prior acquaintance with either logic or mathematics, and it includes all the standard topics through relational predicate logic with identity. The book was written in the conviction that any student can master symbolic logic, and it is designed to give the student as much help as possible in attaining that mastery.

The main part of the book is divided into twenty units, each of which has an introduction and a statement of study objectives so that the student has an overview of what is to come and knows exactly what is required in order to master the unit. The explanatory material for each unit is divided into several subsections, each of which has a specific function and covers one relatively small, clearly defined topic. The clear separation of topics and the division into easily comprehended small "bites" allow the student to master the material step by step without being overwhelmed by an indigestible mass of information.

One-variable predicate logic is developed, in detail, independently of relational predicate logic, and identity is presented in two separate units. The semantics of predicate logic is also developed in a separate unit, as is the semantics for sentential logic. In addition to the basic material, there are several "extra credit" units, which provide a glimpse into alternative methods of logic and more advanced topics.

I have tried to give as detailed explanations as possible, both for specific techniques, such as drawing up truth tables or constructing proofs, and for the rationale behind these techniques. It seems to me as important for a student to understand why things are done in a certain way as to learn the techniques themselves, and in this book I have tried to supply the "why's" as well as the "how's."

The book does, however, supply the "how's" in abundance. Aside from the detailed explanations, there are numerous examples worked out in the text: various types of truth tables, a great many detailed, step-by-step symbolizations, and over fifty fully worked out proofs. In addition, there are copious exercises, with answers to fully half of these provided at the back of the book. Problems for which answers are given are indicated by stars.

Because of the detailed explanations, the extensive coverage, and the clear division of topics, the book is extremely flexible. It can be used in either freshman courses or upper-division courses and is suitable for quarter, semester, or even two-quarter courses. In one quarter, for instance, one might cover just Units 1 through 14; in a semester course, Units 1 through 15, 17, and 18; and in a two-quarter course one might cover the entire book, including the supplementary units. Because of the step-by-step approach and the numerous examples and exercises, the book can also be used in self-paced classes. Suggestions on how to structure such a course are included in the Instructor's Manual.

A new edition has given me the opportunity to make numerous changes that should clarify and streamline the presentation. In addition to updating examples and exercises, I have provided new or expanded explanations for many topics that students might find puzzling and have made scores of relatively minor changes that significantly clarify the material. The most substantial changes are in sections covering logical form and the distinction between form and substitution instance. I have also expanded and clarified various examples and problems in the text and have added new exercises in Unit 19.

It is a great pleasure to acknowledge at this point my considerable debt to the many people who helped make this book what it is. My greatest debt, both in general and in particular, is to Nuel D. Belnap, Jr., from whom I absorbed most of what I know about logic and much of my interest in pedagogy. In addition to these general contributions, the rule system for predicate logic is a slightly modified version of one of his systems. He also read the initial version of the entire manuscript and made numerous valuable suggestions, most of which have been incorporated here. Without him the book would not have been written, and without his astute commentary it would not have been as useful as I hope it will be.

I would like to thank Nicholas D. Smith, of the Department of Philosophy of Virginia Polytechnic Institute & State University, for the many excellent comments and suggestions he made in reviewing the first edition manuscript. I would also like to thank numerous colleagues at West Virginia University and students at both WVU and the University of Pittsburgh for many valuable suggestions and for catching many misprints and outright errors. I would especially like to thank Shirley Dowdy, Henry Ruf, and Patricia Long for their time and expertise. Special thanks go to Myrtle Dodge and Kellie Zurzolo for their patient, expert, and good-humored typing of a manuscript that must have been at times enormously frustrating. The Lilly Foundation provided partial summer funding during 1977, and I would like to thank that organization and Gene D'Amour for the initial impetus for the book. I would also like to thank the West Virginia University Foundation for making possible in-house publication of an earlier, partial version, which encouraged me to complete the project. Finally, I wish to thank the following for their valuable comments when reviewing the manuscript for this fourth edition: Joseph J. Tarala, Ocean County College; Richard L. Wilson, Towson State University; and W. Jay Wood, Wheaton College.

Finally, this book is dedicated to the memory of my mother, Helen Crooker Klenk, who always encouraged my interest in formal studies, and my sister, Nancy Klenk Hill, who was my mentor and friend.

VIRGINIA KLENK

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