Classical and Nonclassical Logics: An Introduction to the Mathematics of Propositions - Hardcover

Schechter, Eric

Hardcover

ISBN 10: 0691122792 ISBN 13: 9780691122793

Publisher: Princeton University Press, 2005

Synopsis

So-called classical logic--the logic developed in the early twentieth century by Gottlob Frege, Bertrand Russell, and others--is computationally the simplest of the major logics, and it is adequate for the needs of most mathematicians. But it is just one of the many kinds of reasoning in everyday thought. Consequently, when presented by itself--as in most introductory texts on logic--it seems arbitrary and unnatural to students new to the subject.

In Classical and Nonclassical Logics, Eric Schechter introduces classical logic alongside constructive, relevant, comparative, and other nonclassical logics. Such logics have been investigated for decades in research journals and advanced books, but this is the first textbook to make this subject accessible to beginners. While presenting an assortment of logics separately, it also conveys the deeper ideas (such as derivations and soundness) that apply to all logics. The book leads up to proofs of the Disjunction Property of constructive logic and completeness for several logics.

The book begins with brief introductions to informal set theory and general topology, and avoids advanced algebra; thus it is self-contained and suitable for readers with little background in mathematics. It is intended primarily for undergraduate students with no previous experience of formal logic, but advanced students as well as researchers will also profit from this book.

About this title

From the Back Cover

"Offering a rich combination and breadth of material, this book is practically an encyclopedia of schools of logic; it is a convenient reference, lucidly describing complex ideas in various schools of logic that are traditionally not treated in a single book. The writing is fluent, clear, and detailed; the exposition is solid and successfully clarifies topics that are usually difficult for beginners to understand."--Iraj Kalantari, Western Illinois University

"This is a fine introduction to relevance and intuitionist logics and the basic notions of metalogic, with classical logic introduced as a necessary contrast. It will be a valuable addition to the literature, especially as some of the topics covered have long been the preserve of specialists. Though I have worked in philosophical logic for many years, it taught me things I should have known long ago."--Bernard Linsky, University of Alberta, author of Russell's Metaphysical Logic

"This is a very good introduction to a broad array of logics. Particularly interesting is the treatment of algebraic and topological semantics, which are only found in more advanced treatments of the same topics. The author does a great job motivating, presenting, and addressing the different formalisms."--G. Aldo Antonelli, University of California, Irvine; Editor, Journal of Philosophical Logic

About the Author

Eric Schechter, Associate Professor of Mathematics at Vanderbilt University, is the author of Handbook of Analysis and Its Foundations.

Edition details

• Publisher: Princeton University Press
• Publication date: 2005
• ISBN 10: 0691122792
• ISBN 13: 9780691122793
• Binding: Hardcover
• Language: English
• Number of pages: 520