Introduction to Logic Predicate Logic

by Pospesel, Howard

• ISBN13: 9780131649897
• ISBN10: 0131649892
• Edition: 2nd
• Format: Paperback
• Copyright: 2002-06-19
• Publisher: Pearson

Summary

This clearly written, new edition by Howard Pospesel extends to general statements the system developed in Propositional Logic, revised Third Edition. This new edition covers symbolization, proofs, counterexamples, and truth trees. These topics are presented in graded steps, beginning with the symbolization of categorical propositions and concluding with the properties of relations. Examples and exercises are drawn from such sources as newspapers, television broadcasts, films, books, and exams. The book enhances students' ability to recognize and evaluate the predicate arguments they encounter outside the logic classroom. Logic is made accessible without sacrificing rigor. Among the new and revised elements in the Second Edition: bull; bull;Many new exercises and examples bull;A chapter on truth trees bull;New sections treating possible-world counterexamples, intensional contexts, quantifier scope, and quantifier order bull;An appendix on metatheory by William G. Lycan Also, with this new Second Edition! PredLogic, Windows-based software provides an environment in which students symbolize sentences, construct proofs of validity, devise counterexamples, and create truth trees. The program enables students to catch errors as they are made, and it offers hints for solving problems.

Table of Contents

1. Introduction.
2. Basic Symbolization.
3. Proofs: …"O and $O.
4. Proofs: …$I and QE.
5. Intermediate Symbolization.
6. Intermediate Proofs.
7. Counterexamples.
8. Truth Trees.
9. Property-Logic Refinements.
10. Relational Symbolization.
11. Relational Proofs.
12. Relational CEXes and Trees.
13. Relational-Logic Refinements.
14. Natural Arguments.
Appendix 1. Propositional Logic:
A Brief Review.
Appendix 2. Metatheory.
Appendix 3. Using PredLogic.
Appendix 4. Solutions to Starred Exercises.
Index.
Proof Rules.
Truth-Tree Rules.

Excerpts

Student''s Preface I have three aims for this book. The firstgoal is to teach you the vocabulary and grammar of predicate logic so that you will be able to translate the sentences of English (or other natural languages) into the notation of this important branch of symbolic logic. The secondgoal concerns three techniques for evaluating predicate arguments: formal proofs, counterexamples, and truth trees. I aim to help you become proficient in employing these logical methods. The thirdgoal of the book is to develop your ability to identify and assess those predicate arguments you encounter daily as you read books and newspapers, carry on conversations, and watch television. Most of the examples and exercises in the text involve arguments of this everyday variety. I enjoyed writing the book. If you enjoy studying it (as I hope you will), I think my goals will be achieved. Howard Pospesel University of Miami Teacher''s Preface This text presupposes familiarity with propositional logic and, in particular, acquaintance with the natural-deduction approach to formal proofs and the technique of two-sided truth trees. Appendix One contains a review of this material, but it is too compact to be fully intelligible to the complete novice. A discussion of these techniques is provided in the companion volume, Introduction to Logic: Propositional Logic,revised third edition. Predicate logic is developed gradually in this book, starting with the simplest monadic symbolizations and proceeding through multiple quantification to the logic of relations. Students learn to symbolize andevaluate arguments of a given degree of complexity before addressing the symbolization of more complex problems. The formal-proof. system presented here does not include a universal-quantifier introduction rule. The advantages of this approach are that the quantifier rules can be stated more simply and that proofs (although often longer) are often easier to devise. A universal-quantifier introduction rule is provided in a footnote at the start of section 4.2 to accommodate students of teachers who prefer to include this rule. Most of the examples and exercises center around arguments similar to those encountered by students. The majority of these arguments are natural,rather than contrived; many are presented by direct quotation from newspapers and other sources. My purposes in employing natural everyday arguments are (1) to evoke the reader''s interest, (2) to counter the common but mistaken view that formal logic is just an impractical academic diversion, and (3) to improve students'' capacity to notice and assess the arguments they encounter. The final chapter explicitly addresses the problems that arise when predicate logic is applied to natural arguments. The second edition has been extensively revised. It differs from the first edition mainly in these ways: The book has been reorganized to allow students to develop symbolization and proof-construction skills even more gradually. There is a chapter on two-sided truth trees. Some instructors prefer to teach one-sided trees; a chapter explaining that technique is included on the CD-ROM disk packaged with the book. New sections treat possible-world counterexamples, intensional contexts, quantifier scope, and quantifier order. There are more exercises, and most of the original exercises and examples have been replaced by better and more current ones. The book is accompanied by a tutorial program, "PredLogic," written by Mark Pospesel and me. This Windows-based software provides an environment in which students symbolize sentences, construct proofs of validity, devise counterexamples, and create truth trees. The program enables students to catch errors as they are made, and it offers hints for solving problems. William G. Lycan has provided an appendix on the metatheory of predicate logic. This edition uses parenthesis-free quantifier symbols. These symbols have become standard since the first edition was published, and they are more suitable for doing logic on a computer. Gender-neutral language is used throughout. The chapter on logic diagrams (that appeared in the first edition) has been moved to the CD-ROM disk that accompanies the book.