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. Contents......Page 6 Preface......Page 8 I. Be Wise, Generalize!......Page 11 1. The Logic of Lying and Truth-Telling......Page 13 2. Male or Female?......Page 27 3. Silent Knights and Knaves......Page 31 4. Mad or Sane?......Page 35 5. The Difficulties Double......Page 41 6. A Unification......Page 47 II. Be Wise, Symbolize!......Page 51 7. Beginning Propositional Logic......Page 53 8. Liars, Truth-Tellers, and Propositional Logic......Page 65 9. Variable Liars......Page 77 10. Logical Connectives and Variable Liars......Page 83 11. The Tableau Method......Page 93 12. All and Some......Page 109 13. Beginning First-Order Logic......Page 121 III. Infinity......Page 143 14. The Nature of Infinity......Page 145 15. Mathematical Induction......Page 167 16. Generalized Induction, König's Lemma, Compactness......Page 183 IV. Fundamental Results in First-Order Logic......Page 199 17. Fundamental Results in Propositional Logic......Page 201 18. First-Order Logic: Completeness, Compactness,Skolem-Löwenheim Theorem......Page 215 19. The Regularity Theorem......Page 227 V. Axiom Systems......Page 237 20. Beginning Axiomatics......Page 238 21. More Propositional Axiomatics......Page 255 22. Axiom Systems for First-Order Logic......Page 277 VI. More on First-Order Logic......Page 285 23. Craig’s Interpolation Lemma......Page 287 24. Robinson's Theorem......Page 295 25. Beth's Definability Theorem......Page 301 26. A Unification......Page 307 27. Looking Ahead......Page 319 References......Page 331 Index......Page 333 Contents 6 Preface 8 I. Be Wise, Generalize! 11 1. The Logic of Lying and Truth-Telling 13 2. Male or Female? 27 3. Silent Knights and Knaves 31 4. Mad or Sane? 35 5. The Difficulties Double 41 6. A Unification 47 II. Be Wise, Symbolize! 51 7. Beginning Propositional Logic 53 8. Liars, Truth-Tellers, and Propositional Logic 65 9. Variable Liars 77 10. Logical Connectives and Variable Liars 83 11. The Tableau Method 93 12. All and Some 109 13. Beginning First-Order Logic 121 III. Infinity 143 14. The Nature of Infinity 145 15. Mathematical Induction 167 16. Generalized Induction, König's Lemma, Compactness 183 IV. Fundamental Results in First-Order Logic 199 17. Fundamental Results in Propositional Logic 201 18. First-Order Logic: Completeness, Compactness,Skolem-Löwenheim Theorem 215 19. The Regularity Theorem 227 V. Axiom Systems 237 20. Beginning Axiomatics 238 21. More Propositional Axiomatics 255 22. Axiom Systems for First-Order Logic 277 VI. More on First-Order Logic 285 23. Craig’s Interpolation Lemma 287 24. Robinson's Theorem 295 25. Beth's Definability Theorem 301 26. A Unification 307 27. Looking Ahead 319 References 331 Index 333 9781568814438 A K Peters

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.