PREFACE

This logic book is designed for a first course in logic, and as the title suggests, a course in formal logic. Teachers often find themselves in a quandary about what logic text to use for their introductory course. They want to teach a real course in logic, that treats the laws and the methods of logic, to ordinary students across the curriculum, but they do not want to teach a more advanced course in formal logic. This is precisely the objective that this logic book is designed to achieve. The purpose of this logic course is to give students a comprehensive knowledge of the laws of logic, together with the method of logical deduction that uses these laws, in such a manner that people can make use of this knowledge in their ordinary reasoning. Of course, many other interesting and useful topics are covered as well (as the Table of Contents shows), but the focus is on the laws and method of logic. This focus, by itself, makes this course a course in formal logic, (in contrast to what is normally called informal logic), but naturally, it is formal logic in another sense as well. Logic is presented as a precise symbolic system, divided into the three areas of Propositional Logic, Traditional Logic, and Quantificational Logic. The nature of this symbolic system, is, of course, the very issue that creates the educational quandary. Our purpose requires that the symbolic system be formulated to correspond to the patterns and methods of ordinary reasoning. This may sound like a truism that hardly needs to be stated, but that is not so. Many introductory logic texts present logic systems that use special rules and formal techniques that do not correspond to ordinary reasoning, such as the now commonly presented method of semantic (truth) trees with open or closed branches to determine logical validity, which is an elegant and efficient technique, and an important tool for solving system-related theoretical questions, but which is artificial and unnatural, and ironically, incapable of being used in ordinary reasoning. By contrast, our presentation of logic gives students exact formal tools that are readily used in ordinary reasoning. The symbolic techniques will be natural, and the rules of logic will be ample, familiar, and readily usable. This book, then, presents logic as a formal, symbolic system, and includes a comprehensive presentation of the laws of logic and the method of logical deduction, all such as correspond to patterns of ordinary reasoning. The three areas of Propositional Logic, Traditional Logic, and Quanti­ficational Logic are presented, and treated in a standard way, except for Traditional Logic. Traditional Logic is standardly treated with much archaic detail and as an unserviceable truncated system, that has some rules but no method of deduction. Our treatment of Traditional Logic trims off all the archaic detail and replaces it with a simple, comprehensive, and commonsense method of syllogistic deduction identical to the deductive methods of the other areas of logic. This new treatment integrates Traditional Logic into the deductive framework of modern logic as a partner on equal footing with the other areas, which is some- thing that many teachers of logic will find to be a very satisfying result. The book has been designed to make good use of many exercises spaced throughout the book. All of the sections of the chapters include various sets of exercises, typically of varying degrees of difficulty. To achieve the pedagogical goals of the book, the students should be required to do many of these exercises on a daily basis. There are specially designed worksheets for these exercises

that facilitate the completion, as well as the correction, of these exercises. It is also recommended that the daily lectures review the exercise material to some extent. There is more material in this book than what is needed to have a good introductory course in logic. The material has been arranged so that the instructor can selectively choose various parts to achieve the desired content, the desired level of difficulty, and the desired pace of the course. The book has the following main divisions: Chapter 1. Basic logical concepts Chapter 2. Propositional Logic                   More advanced topics Chapter 3. Traditional Logic Chapter 4. Quantificational Logic                   More advanced topics Chapter 5. Logical Fallacies The order of the chapters is flexible. In particular, the chapters on Propositional Logic and Traditional Logic are independent of each other, and one may therefore reverse their order if desired. As a further alternative, since the chapters on Propositional Logic and Quantificational Logic are complete treatments of logic, one may simply opt not to do the chapter on Traditional Logic. But our treatment of that material is a much improved and useful version, and from the viewpoint of application, chapter 3 is highly re­commended. The chapter on Logical Fallacies is a stand-alone chapter, and one may take it at any point after chapter 1, or not at all. There is, then, significant flexibility in how one may use this book. Here are some examples: (1) For a more moderate course, do all the chapters 1 through 5, but skip the advan­ced sections of both chapters 2 and 4. (2) For a more relaxed course, do the material suggested for (1), except, also skip section 2.6 (additional uses of truth tables), section 3.8 (combined deductions of Propositional and Traditional Logic), and section 4.4 (quantificational deductions). (3) For a more intense course, do the entire book, chapters 1 through 4, including the advanced sections, but with chapter 5 optional. (4) For a course in formal logic, do chapters 1, 2, and 4, including the advanced sections, with chapter 3 optional, and skipping chapter 5. (5) For a course in applied logic, do chapters 1, 2, 3, and 5, with the advanced sections of chapter 2 optional, and skipping chapter 4.

Enjoy the book.
Arnold vander Nat