Games for your mind
the history and future of logic puzzles
- ISBN: 9780691242026
- Editorial: Princeton University Press
- Fecha de la edición: 2022
- Lugar de la edición: Princeton (NJ). Estados Unidos de Norteamérica
- Encuadernación: Rústica
- Medidas: 24 cm
- Nº Pág.: 352
- Idiomas: Inglés
A lively and engaging look at logic puzzles and their role in mathematics, philosophy, and recreation
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.
In this informative and entertaining book, 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.
I The Pain and Pleasure of Logic 1
1 Is Logic Boring and Pointless? 3
1.1 Logic in Practice, Logic in Theory 3
1.2 Enter the Philosophers 8
1.3 Notes and Further Reading 14
2 Logic Just for Fun 15
2.1 Sudoku and Mastermind 15
2.2 Some Classic Logic Puzzles 18
2.3 Puzzles in Propositional Logic 21
2.4 Notes and Further Reading 22
2.5 Solutions 23
II Lewis Carroll and Aristotelian Logic 29
3 Aristotle’s Syllogistic 31
3.1 The Beginning of Formal Logic 31
3.2 Proposition Jargon 34
3.3 Operations on Propositions 37
3.4 Figures and Moods 41
3.5 Aristotle’s Proof Methods 45
3.6 Notes and Further Reading 48
4 The Empuzzlement of Aristotelian Logic 50
4.1 Diagrams for Propositions 50
4.2 Playing the Game 53
4.3 A Closer Look at Placing Counters 56
4.4 One More Example 59
4.5 Are We Having Fun Yet? 61
4.6 Puzzles for Solving 64
4.7 Solutions 65
5 Sorites Puzzles 68
5.1 A Quadriliteral Diagram? 69
5.2 Notation and Formulas 72
5.3 The Formalization in Action 76
5.4 The Method of Underscoring 78
5.5 The Method of Trees 81
5.6 Puzzles for Solving 88
5.7 Notes and Further Reading 90
5.8 Solutions 90
6 Carroll’s Contributions to Mind 93
6.1 The Barbershop Puzzle 93
6.2 Achilles and the Tortoise 97
6.3 Scholarly Responses to Carroll’s Regress 99
6.4 Does the Tortoise Have a Point? 107
6.5 Notes and Further Reading 110
III Raymond Smullyan and Mathematical Logic 113
7 Liars and Truthtellers 115
7.1 Propositional Logic 115
7.2 A Knight/Knave Primer 120
7.3 A Selection of Knight/Knave Puzzles 122
7.4 Sane or Mad? 123
7.5 The Lady or the Tiger? 125
7.6 Some Unusual Knights and Knaves 127
7.7 Two Elaborate Puzzles 128
7.8 Notes and Further Reading 129
7.9 Solutions 131
8 From Aristotle to Russell 137
8.1 Aristotle’s Organon 138
8.2 Medieval Logic 140
8.3 Mill’s A System of Logic 144
8.4 Boole and Venn 146
8.5 Russell’s The Principles of Mathematics 151
8.6 Notes and Further Reading 153
9 Formal Systems in Life and Math 154
9.1 What Is a Formal System? 154
9.2 What Can Your Formal Language Say? 159
9.3 Formalizations of Arithmetic 161
9.4 Notes and Further Reading 163
10 The Empuzzlement of Gödel’s Theorems 164
10.1 Established Knights and Knaves 164
10.2 A Sentence That Is True but Unprovable 166
10.3 Establishment, Revisited 169
10.4 A Gödelian Machine 172
10.5 Gödel’s Second Incompleteness Theorem 174
10.6 Puzzles for Solving 177
10.7 Notes and Further Reading 180
10.8 Solutions 181
11 Question Puzzles 184
11.1 Three Warm-Ups 184
11.2 The Power of Indexical Questions 185
11.3 The Heaven/Hell Puzzle 186
11.4 The Nelson Goodman Principle 189
11.5 Generalized Nelson Goodman Principles 191
11.6 Coercive Logic 194
11.7 Smullyan as a Writer 195
11.8 Solutions 196
IV Puzzles Based on Nonclassical Logics 199
12 Should “Logics” Be a Word? 201
12.1 Logical Pluralism? 202
12.2 Is Classical Logic Correct? 206
12.3 Applications of Nonclassical Logic 208
12.4 Notes and Further Reading 210
13 Many-Valued Knights and Knaves 212
13.1 The Transitional Phase 212
13.2 The Three-Valued Island 214
13.3 The Fuzzy Island 220
13.4 Modus Ponens and Sorites 225
13.5 Puzzles for Solving 228
13.6 Solutions 231
V Miscellaneous Topics 237
14 The Saga of the Hardest Logic Puzzle Ever 239
14.1 Boolos Introduces the Puzzle 239
14.2 Is There a Simpler Solution? 245
14.3 Trivializing the Hardest Puzzle Ever 250
14.4 Are Three Questions Necessary? 253
14.5 Two Questions When Random Is Really Random 255
14.6 What If Random Can Remain Silent? 259
14.7 Notes and Further Reading 265
15 Metapuzzles 266
15.1 A Warm-Up Puzzle 266
15.2 The Playful Children and Caliban’s Will 267
15.3 Knight/Knave Metapuzzles 269
15.4 Solutions 270
16 Paradoxes 274
16.1 What Is a Paradox? 275
16.2 Paradoxes of Predication 276
16.3 The Paradox of the Preface 279
16.4 The Liar 282
16.5 Miscellaneous Paradoxes 289
16.6 Notes and Further Reading 290
17 A Guide to Some Literary Logic Puzzles 292
17.1 The Nine Mile Walk 293
17.2 The Early Days of “Logic Fiction” 295
17.3 A Gallery of Eccentric Detectives 300
17.4 The Anti-Logicians 303
17.5 Carr and Queen 305
17.6 The Thinking Machine 307
