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Possibilities and Paradox

An Introduction to Modal and Many-Valued Logic

J. C. Beall and Bas C. van Fraassen

Publication Date - April 2003

ISBN: 9780199259878

256 pages

Retail Price to Students: $51.95


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.


  • Clearly targeted at students with no previous exposure to the subject matter and has an accessible and user-friendly approach
  • Covers not only the basic formal machinery involved in modal and many-valued logic, but also enlivens the discussion of different systems of logic by considering their philosophical motivations and implications
  • Innovative learning aids throughout, including exercises, examples, and guides to further reading
  • Bas van Fraassen is a world-renowned philosopher of logic and JC Beall is a well-known and highly respected academic


"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

Table of Contents

    1. Philosophical Motives
    2. Set-Theoretic Tools
    3. Languages and Logics
    4. Tableaux
    5. Normal Modal Logics
    6. Variations on a Theme
    7. Around Truth and Falsity
    8. Gaps, Gluts, and Liars
    9. Heaps, Supertruth, and the Continuum
    10. Further Tools
    11. Logical Systems and Completeness
    12. Meta-Theorems for Non-Classical Logics

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