Preface for Students
This book is intended to do several things for you. Most importantly it is intended to enhance your ability to reason correctly, and to evaluate the reasoning of others. To this end we will Ieam various forms of argument and rules for making valid inferences, learning also how to symbolize them and construct proofs of validity.
As far as possible we will be looking at real arguments that people have made, some of which have made vital contributions to the history of thought. But even those that haven’t are generally more interesting than logicians’ made-up examples. We will also learn methods for tackling natural arguments directly, i.e., for treating arguments as they actually appear in their original wording. In this way we will steer a judicious middle course between two approaches: a purely formal treatment, and the “informal logic” approach to treating arguments directly that has gained in popularity in recent years. On its own the first approach can be quite difficult and off-putting if you have had little training in formal methods, and may leave you at a loss when faced with the complexities of arguments given in their context; whereas the informal logic approach may do you a disservice in leaving you ignorant of the whole history of logic from Zeno of Elea and the early Buddhists to Bertrand Russell and the Intuitionists, and by ducking any acquaintance with the simple formal rules that have underlain some of the most exciting arguments in science and philosophy. So here I have tried to combine the best of both these approaches, natural deduction techniques and methods for grappling with natural arguments, while at the same time including enough material to help you get a sense of logic’s fascinating history.This text is bom out of the conviction that logic can be exhilarating. It can be frustrating; but it can also be emancipating. I have seen students who have spent long years in a cloud of “math anxiety” experience a kind of revelation when they suddenly see how to symbolize and do proofs. Likewise it can be very liberating when you have Ieamt to spot errors in the arguments of experts on subjects you know little about. But although it can be hard work, there is no reason logic cannot also be fun. It has a close relation with humour, and I have tried to build on this with liberal use of jokes and sketches. Γve enjoyed writing this book, and have tried to make it fun as well as instructive. I hope that comes through as you read and work from it.