Logical Labyrinths

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 in 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. As much as a textbook for undergraduate courses in logic, in particular to a liberal- arts audience, this book will succeed as a trade book for anyone who has an interest in a more rigorous understanding of rational thought.

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.

Índice: I. Be wise, generalize! 1. The logic of lying and truth-telling 2. Male or female? 3. Silent knights and knaves 4. Mad or sane? 5. The difficulties double! 6. A unification II. Be wise, simbolize! 7. Beginning propositional logic 8. Liars, truth-tellers, and propositional logic 9. Variable liars 10. Logical connectives and variable liars 11. The tableau method 12. All and some 13. Beginning first-order logic. III. Infinity 14. The nature of infinity 15. Mathematical induction 16. Generalized induction, König's Lemma, compactness IV. Fundamentals results in first-order logic 17. Fundamental results in propositional logic .. Front Cover; Table of Contents; Preface; I. Be Wise, Generalize!; 1. The Logic of Lying and Truth-Telling; 2. Male or Female?; 3. Silent Knights and Knaves; 4. Mad or Sane?; 5. The Difficulties Double!; 6. A Unification; II. Be Wise, Symbolize!; 7. Beginning Propositional Logic; 8. Liars, Truth-Tellers, and Propositional Logic; 9. Variable Liars; 10. Logical Connectives and Variable Liars; 11. The Tableau Method; 12. All and Some; 13. Beginning First-Order Logic; III. Infinity; 14. The Nature of Infinity; 15. Mathematical Induction; 16. Generalized Induction, Konig's Lemma, Compactness Features an approach to the teaching of mathematical logic by putting it in the context of the puzzles and paradoxes of common language and rational thought. Using the logic of lying and truth-telling, this book introduces the informal reasoning preparing them for the formal study of symbolic logic, from propositional logic to first-order logic.