Introduction to Logic

Book Preface

This textbook was written with the fully onlinc student and the independent learner in mind. The explanations are more thorough, more “from the ground up” than usual; the examples and applications are more numerous; and the relations be­tween each unit arc carefully explained to make the text an interconnected whole. ln short, much of the explanatory work one would ordinarily do in the classroom is provided within this text. ln addition, optional appendices, sidebars, and inter­ludes take the interested student beyond the introductory level, offering food for thought as well as opportunities for advanced research not usually available in the introduction to logic text.

Not that this book is unsuitable for the face-to-face class. lam confident it will serve both populations of students very well. l plan to use this text in the classroom as well as in my fully online logic classes. The fact that this book was written with the online learner in mind means less content will need to be explained in the classroom, leaving more time for discussion and practice.  I hope that the addition of an integrated history track running from the begin­ning to the end of the book adds realism, gives a personal touch, and makes it a little more fun to teach as well as to learn logic. ln this text, the history of logic is not confined to occasional sidebars; it is built into the content. Logical theory unfolds historically, as a story starting in ancient Athens and reaching undreamed of heights in the late twentieth century. I hope you will agree that historical context not only adds personality to a course that can be pretty dry if you let it be, it also makes the logic course more interesting. Many of the great logicians of history were interesting characters, and the conceptual problems they sought to solve were serious ones. ln short, l have tried to present logic as a human endeavor and not merely as a collection of techniques.

Some of the material in this book appeared in an earlier textbook that I wrote, Tlte Many Worlds of Logic, first published in 1993. Oxford University Press published the second edition of that book. This new book covers everything treated in Many Worlds and more. The difference between my earlier book and this book stems from two intervening experiences. First, in the 12 years since the second edition of Many Worlds appeared, I have been teaching fully online logic classes every quarter, in ad­dition to face-to-face logic classes. It was my experiences as an online logic teacher that inspired me to begin this textbook. My online students, and their struggles to learn logic in a fully online environment, inspired me to aim for a text with expla­nations so crystal dear, so thorough, so from the ground up, that the independent online student would find in the text all he or she needs to fully master the subject outside the traditional classroom.

Second, at some point I became convinced that the history of logic adds real­world context as well as a wonderful human element to the introductory logic course. Most of us move through the subject in a roughly historical order anyway. After laying down fundamental concepts, we often progress from Aristotelian to truth-functional to predicate logic, perhaps visiting informal and inductive logic along the way. I have found that adding historical context as the course proceeds takes very little class time while adding the nice touches already mentioned The history of logic is more in­teresting than many might initially suppose. With this new text I plan to teach logic as a fascinating, human story unfolding over time, as well as a body of important technical information with applications to every area of human thought. The two approaches-the historical and the technical-do not have to be kept separate. They are intertwined in this book.

Every quarter, one or two students always ask about advanced logic. What comes next in logical theory’ What sort of class can I take if I want to study more logic? I am sure you have been asked the same questions. In the past, I have recommended Hunters Metalogic and Mates’s Elementary Logic. With this new textbook I will no longer have to send the student off to a university library. Accessible, nontechnical appendices on metalogic, Godel, Turing, and logic and computing will now mean that the student who seeks to go beyond the introductory level has a place to start­right here in this textbook.  Students also often ask questions like these: Why does logic have to be so techni­cal’ What is the point of all of this really abstract stuff? What difference does it all make anyway? I am sure you have been asked these or similar questions, perhaps even in front of the class. I hope that the nontechnical appendix on logic and com­puting, and the applications oflogic to real-world issues within the text, will help you answer those who call into question the very worth oflogic as an academic subject.