Logic puzzles were first introduced to the public by Lewis Carroll in the late nineteenth century and have been popular ever since. Games like Sudoku and Mastermind are fun and engrossing recreational activities, but they also share deep foundations in mathematical logic and are worthy of serious intellectual inquiry. Games for Your Mind explores the history and future of logic puzzles while enabling you to test your skill against a variety of puzzles yourself. Jason Rosenhouse begins by introducing readers to logic and logic puzzles and goes on to reveal the rich history of these puzzles. He shows how Carroll's puzzles presented Aristotelian logic as a game for children, yet also informed his scholarly work on logic. He reveals how another pioneer of logic puzzles, Raymond Smullyan, drew on classic puzzles about liars and truthtellers to illustrate Kurt Gödel's theorems and illuminate profound questions in mathematical logic. Rosenhouse then presents a new vision for the future of logic puzzles based on nonclassical logic, which is used today in computer science and automated reasoning to manipulate large and sometimes contradictory sets of data. Featuring a wealth of sample puzzles ranging from simple to extremely challenging, this lively and engaging book brings together many of the most ingenious puzzles ever devised, including the "Hardest Logic Puzzle Ever," metapuzzles, paradoxes, and the logic puzzles in detective stories.

• Cover
• 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