Possibilities and Paradox: An Introduction to Modal and Many-Valued Logic [Paperback]

J. C. Beall (Author), Bas C. van Fraassen (Author)

Book Description

Publication Date: April 24, 2003

Extensively classroom-tested, Possibilities and Paradox provides an accessible and carefully structured introduction to modal and many-valued logic. The authors cover the basic formal frameworks, enlivening the discussion of these different systems of logic by considering their philosophical motivations and implications. Easily accessible to students with no background in the subject, the text features innovative learning aids in each chapter, including exercises that provide hands-on experience, examples that demonstrate the application of concepts, and guides to further reading.

Editorial Reviews

Review

"A clear, self-contained, unified introduction to a variety of extensions and alternatives to classical logic. Philosophically engaging and technically accomplished, it will serve as an excellent textbook for beginners as well as a valuable reference for advanced students and researchers."--Achille Varzi, Associate Professor of Philosophy, Columbia University

"An exciting new logic text that investigates non-classical propositional logics in an unusual way. Propositional model, intuitionistic, multivalued, relevance, and conditional logics are developed in detail. This book should be invaluable to any member of the profession interested in these topics at any level."--Edmund L. Gettier, Professor Emeritus, University of Massachusetts

"A well-organized introduction to the variety of logics extending or departing from classical propositional logic that have been of interest to logically-minded philosophers and philosophically-minded logicians. An extremely useful book. Written in a concise yet highly accessible style that provides a clear and well-motivated treatment of an impressively wide range of material."--Michael Glanzberg, Associate Professor of Philosophy, Massachusetts Institute of Technology

About the Author

JC Beall is an Assistant Professor in Philosophy at the University of Connecticut. Forthcoming publications include 'Logical Pluralism' (with Greg Restall) and 'Deflationism and Paradox' (edited with Bradley Armour-Garb). Bas C. van Fraassen is the McCosh Professor of Philosophy at Princeton University. Past publications include 'The Empirical Stance' (2002), 'Topics in the Foundation of Statistics' (1997) and 'Quantum Mechanics: An Empiricist View' (1991).

Product Details

• Paperback: 256 pages
• Publisher: Oxford University Press, USA; First Edition edition (April 24, 2003)
• Language: English
• ISBN-10: 0199259879
• ISBN-13: 978-0199259878
• Product Dimensions: 9.2 x 6.1 x 0.5 inches
• Shipping Weight: 13.4 ounces (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #1,078,923 in Books (See Top 100 in Books)

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22 of 22 people found the following review helpful:

4.0 out of 5 stars Not for the faint of heart, but a valuable resource nonetheless., January 9, 2006

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J. Wisdom - See all my reviews
(REAL NAME)   

This review is from: Possibilities and Paradox: An Introduction to Modal and Many-Valued Logic (Paperback)

In Possibilities and Paradox, J.C. Beall and Bas Van Fraassen team up to present a rigorous introduction to modal and many-valued logic. After presenting a brief motivation for the development of modal logic (chapter 1), the authors provide a discussion of set theory (chapter 2), logical semantics (chapter 3), the tableau or "tree" method of proof (chapter 4), normal modal logics (chapter 5), and intuitionistic and non-normal modal logics (chapter 6). These chapters prepare the reader for future topics, including many-valued logics (chapter 7), the Sorites and Liar paradoxes (chapter 8), and supervaluations and continuum-valued logics (chapter 9). The final section is devoted to metatheory and includes further tools for understanding and working with, among other things, functions, sentences, and soundness and completeness proofs.

For the student with only a basic logic course or two under his or her belt, Possibilities and Paradox is going to be a tough read. Despite its brevity (233 total pages), the book is extremely information dense--the philosophical equivalent of Grape Nuts cereal, if you will. Virtually every sentence of every chapter contains an essential point or concept that merits a careful reading, re-reading, re-re-reading, and perhaps two or three readings on top of that before an exam if it is a required text, as it was in my case. While this makes the book exemplary when it comes to an efficient presentation of the material, since it is an introductory text it would have benefited from at least three additional features. First, I would have liked to see the authors provide more of a "big picture" framework for approaching the mechanics of logic- what a good logical language should do, why we'd want a syntax to work a certain way, etc. The authors do a fairly good job of this in the later chapters, but bit more attention to this in the first three or four would make the book even more accessible to students. Second, a chapter or two on proofs would be especially helpful to students without a strong background in this aspect of logic; something like a brief, modal and many-valued version of Daniel Velleman's, How to Prove It. Finally, a chapter or two on quantification would be a nice addition to future editions of the book.

One last thing (note well): as of the writing of this review, a helpful list of corrections to various errata is available on professor Van Fraassen's website.