336 Pages
    by A K Peters/CRC Press

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    This book features a unique approach to the teaching of mathematical logic by putting it in the context of the puzzles and paradoxes of common language and rational thought. It serves as a bridge from the author’s puzzle books to his technical writing in the fascinating field of mathematical logic. Using the logic of lying and truth-telling, the author introduces the readers to informal reasoning preparing them for the formal study of symbolic logic, from propositional logic to first-order logic, a subject that has many important applications to philosophy, mathematics, and computer science. The book includes a journey through the amazing labyrinths of infinity, which have stirred the imagination of mankind as much, if not more, than any other subject.


    Be Wise, Generalize!
    The Logic of Lying and Truth-Telling
    Male or Female?
    Silent Knights and Knaves
    Mad or Sane?
    The Difficulties Double!
    A Unification

    Be Wise, Symbolize!
    Beginning Propositional Logic
    Liars, Truth-Tellers, and Propositional Logic
    Variable Liars
    Logical Connectives and Variable Liars
    The Tableau Method
    All and Some
    Beginning First-Order Logic

    The Nature of Infinity
    Mathematical Induction
    Generalized Induction, K¨onig’s Lemma, Compactness

    Fundamental Results in First-Order Logic
    Fundamental Results in Propositional Logic
    First-Order Logic: Completeness, Compactness, Skolem-L¨owenheim Theorem
    The Regularity Theorem

    Axiom Systems
    Beginning Axiomatics
    More Propositional Axiomatics
    Axiom Systems for First-Order Logic

    More on First-Order Logic
    Craig’s Interpolation Lemma
    Robinson’s Theorem
    Beth’s Definability Theorem
    A Unification
    Looking Ahead


    Raymond Smullyan

    With the various bridge courses springing around campuses, this book could be used for a first glimpse into mathematical logic. The author has reached a delicate balance between simple fun with the various puzzles that fill the book and the formality of an introductory course on mathematical logic.
    MAA Reviews, March 2009

    In addition to being one of the most important mathematical logicians of our time, Raymond Smullyan is also a master inventor and purveyor of logic puzzles... Much of Smullyan's technical work consists of ingenious ways to generalize features of formal systems and crucial results in mathematical logic. That is what is highlighted in this book. Indeed, to motivate the presentation of the logic, he presents a clean and insightful generalization of many of the logic puzzles themselves. ... Given Smullyan's vitality, we can all hope for the sequel.
    —Stewart Shapiro, Mathematical Reviews, October 2009

    If mathematics educators wish to narrow the gap between expert and novice, they must understand the factors in the teaching and learning of proof, design rich explorations, and establish an environment in which these explorations are possible. The author accomplishes this admirably.
    —Premalatha Junius, Mathematics Teacher, November 2009

    Smullyan ... has earned fame for writing a small shelf of puzzle books. ... [Here] he provides a textbook on first-order logic, suitable for classroom use but animated with the lively imagination that makes his puzzle books a delight.
    —D.V. Feldman, CHOICE, February 2010