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Originally published in 1969. This book is for undergraduates whether specializing in philosophy or not. It assumes no previous knowledge of logic but aims to show how logical notions arise from, or are abstracted from, everyday discourse, whether technical or non-technical. It sets out a knowledge of principles and, while not historical, gives an account of the reasons for which modern systems have emerged from the traditional syllogistic logic, demonstrating how certain central ideas have developed. The text explains the connections between everyday reasoning and formal logic and works up to a brief sketch of systems of propositional calculus and predicate-calculus, using both the axiomatic method and the method of natural deduction. It provides a self-contained introduction but for those who intend to study the subject further it contains many suggestions and a sound basis for more advanced study.
Originally published in 1967. The common aim of all logical enquiry is to discover and analyse correctly the forms of valid argument. In this book concise expositions of traditional, Aristotelian logic and of modern systems of propositional and predicative logic show how far that aim has been achieved.
As the author of this volume states, "the science of logic does not stand still." This book was intended to cover the advances made in the study of logic in the first half of the nineteenth century, during which time the author felt there to have been greater advances made than in the whole of the preceding period from the time of Aristotle. Advances which, in her eyes, were not present in contemporary text books. As such, this book offers a valuable insight into the progress of the subject, tracing this frenetic period in its development with a first-hand awareness of its documentary value.
In the twenty-first century there are two ways to study logic. The more recent approach is symbolic logic. The history of teaching logic since World War II, however, casts doubt on the idea that symbolic logic is best for a first logic course. Logic as a Liberal Art is designed as part of a minority approach, teaching logic in the "verbal" way, in the student's "natural" language, the approach invented by Aristotle. On utilitarian grounds alone, this "verbal" approach is superior for a first course in logic, for the whole range of students. For millennia, this "verbal" approach to logic was taught in conjunction with grammar and rhetoric, christened the trivium. The decline in teaching grammar and rhetoric in American secondary schools has led Dr. Rollen Edward Houser to develop this book. The first part treats grammar, rhetoric, and the essential nature of logic. Those teachers who look down upon rhetoric are free, of course, to skip those lessons. The treatment of logic itself follows Aristotle's division of the three acts of the mind (Prior Analytics 1.1). Formal logic is then taken up in Aristotle's order, with Parts on the logic of Terms, Propositions, and Arguments. The emphasis in Logic as a Liberal Art is on learning logic through doing problems. Consequently, there are more problems in each lesson than would be found, for example, in many textbooks. In addition, a special effort has been made to have easy, medium, and difficult problems in each Problem Set. In this way the problem sets are designed to offer a challenge to all students, from those most in need of a logic course to the very best students.