Games for Your Mind by Jason Rosenhouse -- Read -- Imperial Library of Trantor

Index

Cover Title Page Copyright Contents Preface I: The Pain and Pleasure of Logic

1. Is Logic Boring and Pointless?

1.1. Logic in Practice, Logic in Theory 1.2. Enter the Philosophers 1.3. Notes and Further Reading

2. Logic Just for Fun

2.1. Sudoku and Mastermind 2.2. Some Classic Logic Puzzles 2.3. Puzzles in Propositional Logic 2.4. Notes and Further Reading 2.5. Solutions

II: Lewis Carroll and Aristotelian Logic

3. Aristotle’s Syllogistic

3.1. The Beginning of Formal Logic 3.2. Proposition Jargon 3.3. Operations on Propositions 3.4. Figures and Moods 3.5. Aristotle’s Proof Methods 3.6. Notes and Further Reading

4. The Empuzzlement of Aristotelian Logic

4.1. Diagrams for Propositions 4.2. Playing the Game 4.3. A Closer Look at Placing Counters 4.4. One More Example 4.5. Are We Having Fun Yet? 4.6. Puzzles for Solving 4.7. Solutions

5. Sorites Puzzles

5.1. A Quadriliteral Diagram? 5.2. Notation and Formulas 5.3. The Formalization in Action 5.4. The Method of Underscoring 5.5. The Method of Trees 5.6. Puzzles for Solving 5.7. Notes and Further Reading 5.8. Solutions

6. Carroll’s Contributions to Mind

6.1. The Barbershop Puzzle 6.2. Achilles and the Tortoise 6.3. Scholarly Responses to Carroll’s Regress 6.4. Does the Tortoise Have a Point? 6.5. Notes and Further Reading

III: Raymond Smullyan and Mathematical Logic

7. Liars and Truthtellers

7.1. Propositional Logic 7.2. A Knight/Knave Primer 7.3. A Selection of Knight/Knave Puzzles 7.4. Sane or Mad? 7.5. The Lady or the Tiger? 7.6. Some Unusual Knights and Knaves 7.7. Two Elaborate Puzzles 7.8. Notes and Further Reading 7.9. Solutions

8. From Aristotle to Russell

8.1. Aristotle’s Organon 8.2. Medieval Logic 8.3. Mill’s A System of Logic 8.4. Boole and Venn 8.5. Russell’s The Principles of Mathematics 8.6. Notes and Further Reading

9. Formal Systems in Life and Math

9.1. What Is a Formal System? 9.2. What Can Your Formal Language Say? 9.3. Formalizations of Arithmetic 9.4. Notes and Further Reading

10. The Empuzzlement of Gödel’s Theorems

10.1. Established Knights and Knaves 10.2. A Sentence That Is True but Unprovable 10.3. Establishment, Revisited 10.4. A Gödelian Machine 10.5. Gödel’s Second Incompleteness Theorem 10.6. Puzzles for Solving 10.7. Notes and Further Reading 10.8. Solutions

11. Question Puzzles

11.1. Three Warm-Ups 11.2. The Power of Indexical Questions 11.3. The Heaven/Hell Puzzle 11.4. The Nelson Goodman Principle 11.5. Generalized Nelson Goodman Principles 11.6. Coercive Logic 11.7. Smullyan as a Writer 11.8. Solutions

IV: Puzzles Based on Nonclassical Logics

12. Should “Logics” Be a Word?

12.1. Logical Pluralism? 12.2. Is Classical Logic Correct? 12.3. Applications of Nonclassical Logic 12.4. Notes and Further Reading

13. Many-Valued Knights and Knaves

13.1. The Transitional Phase 13.2. The Three-Valued Island 13.3. The Fuzzy Island 13.4. Modus Ponens and Sorites 13.5. Puzzles for Solving 13.6. Solutions

V: Miscellaneous Topics

14. The Saga of the Hardest Logic Puzzle Ever

14.1. Boolos Introduces the Puzzle 14.2. Is There a Simpler Solution? 14.3. Trivializing the Hardest Puzzle Ever 14.4. Are Three Questions Necessary? 14.5. Two Questions When Random Is Really Random 14.6. What If Random Can Remain Silent? 14.7. Notes and Further Reading

15. Metapuzzles

15.1. A Warm-Up Puzzle 15.2. The Playful Children and Caliban’s Will 15.3. Knight/Knave Metapuzzles 15.4. Solutions

16. Paradoxes

16.1. What Is a Paradox? 16.2. Paradoxes of Predication 16.3. The Paradox of the Preface 16.4. The Liar 16.5. Miscellaneous Paradoxes 16.6. Notes and Further Reading

17. A Guide to Some Literary Logic Puzzles

17.1. The Nine Mile Walk 17.2. The Early Days of “Logic Fiction” 17.3. A Gallery of Eccentric Detectives 17.4. The Anti-Logicians 17.5. Carr and Queen 17.6. The Thinking Machine

Glossary References Index