Muutke küpsiste eelistusi

Games for Your Mind: The History and Future of Logic Puzzles [Kõva köide]

4.00/5 (59 hinnangut Goodreads-ist)
  • Formaat: Hardback, 352 pages, kõrgus x laius: 235x155 mm, 35 b/w illus. 32 tables.
  • Ilmumisaeg: 24-Nov-2020
  • Kirjastus: Princeton University Press
  • ISBN-10: 0691174075
  • ISBN-13: 9780691174075
Teised raamatud teemal:
Games for Your Mind: The History and Future of Logic PuzzlesSuurem pilt
  • Formaat: Hardback, 352 pages, kõrgus x laius: 235x155 mm, 35 b/w illus. 32 tables.
  • Ilmumisaeg: 24-Nov-2020
  • Kirjastus: Princeton University Press
  • ISBN-10: 0691174075
  • ISBN-13: 9780691174075
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780691174075.html
Märksõnad:
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.

Arvustused

"Fascinating. . . . Part philosophy, part maths, part activity book; Games for Your Mind is an ingenious thing."---Amy Barrett, BBC Science Focus "Excellent."---Elizabeth Palmer, Christian Century "Its a serious and at times technical book, specifically about logic puzzles, though beneath its concern with matters such as obversion and epistemic obligations it has an unexpected jauntiness."---Henry Hitchings, Times Literary Supplement "Jason Rosenhouses Games for Your Mind is an engaging popular mathematics book written to enlighten the reader on the mathematics and logic behind popular puzzles. . . .overall, the reviewer would recommend this book to all people who want a puzzling challenge. Although the puzzles towards the end of the book feel impossible, the thrill of that ah! moment when you work through Rosenhouses solution is surely a high for any mathematician out there."---Holly A. J. Middleton-Spencer, London Mathematical Society

Preface xi
I The Pain and Pleasure of Logic
1(28)
1 Is Logic Boring and Pointless?
3(12)
1.1 Logic in Practice, Logic in Theory
3(5)
1.2 Enter the Philosophers
8(6)
1.3 Notes and Further Reading
14(1)
2 Logic Just for Fun
15(14)
2.1 Sudoku and Mastermind
15(3)
2.2 Some Classic Logic Puzzles
18(3)
2.3 Puzzles in Propositional Logic
21(1)
2.4 Notes and Further Reading
22(1)
2.5 Solutions
23(6)
II Lewis Carroll and Aristotelian Logic
29(84)
3 Aristotle's Syllogistic
31(19)
3.1 The Beginning of Formal Logic
31(3)
3.2 Proposition Jargon
34(3)
3.3 Operations on Propositions
37(4)
3.4 Figures and Moods
41(4)
3.5 Aristotle's Proof Methods
45(3)
3.6 Notes and Further Reading
48(2)
4 The Empuzzlement of Aristotelian Logic
50(18)
4.1 Diagrams for Propositions
50(3)
4.2 Playing the Game
53(3)
4.3 A Closer Look at Placing Counters
56(3)
4.4 One More Example
59(2)
4.5 Are We Having Fun Yet?
61(3)
4.6 Puzzles for Solving
64(1)
4.7 Solutions
65(3)
5 Sorites Puzzles
68(25)
5.1 A Quadriliteral Diagram?
69(3)
5.2 Notation and Formulas
72(4)
5.3 The Formalization in Action
76(2)
5.4 The Method of Underscoring
78(3)
5.5 The Method of Trees
81(7)
5.6 Puzzles for Solving
88(2)
5.7 Notes and Further Reading
90(1)
5.8 Solutions
90(3)
6 Carroll's Contributions to Mind
93(20)
6.1 The Barbershop Puzzle
93(4)
6.2 Achilles and the Tortoise
97(2)
6.3 Scholarly Responses to Carroll's Regress
99(8)
6.4 Does the Tortoise Have a Point?
107(3)
6.5 Notes and Further Reading
110(3)
III Raymond Smullyan and Mathematical Logic
113(86)
7 Liars and Truthtellers
115(22)
7.1 Propositional Logic
115(5)
7.2 A Knight/Knave Primer
120(2)
7.3 A Selection of Knight/Knave Puzzles
122(1)
7.4 Sane or Mad?
123(2)
7.5 The Lady or the Tiger?
125(2)
7.6 Some Unusual Knights and Knaves
127(1)
7.7 Two Elaborate Puzzles
128(1)
7.8 Notes and Further Reading
129(2)
7.9 Solutions
131(6)
8 From Aristotle to Russell
137(17)
8.1 Aristotle's Organon
138(2)
8.2 Medieval Logic
140(4)
8.3 Mill's A System of Logic
144(2)
8.4 Boole and Venn
146(5)
8.5 Russell's The Principles of Mathematics
151(2)
8.6 Notes and Further Reading
153(1)
9 Formal Systems in Life and Math
154(10)
9.1 What Is a Formal System?
154(5)
9.2 What Can Your Formal Language Say?
159(2)
9.3 Formalizations of Arithmetic
161(2)
9.4 Notes and Further Reading
163(1)
10 The Empuzzlement of Godel's Theorems
164(20)
10.1 Established Knights and Knaves
164(2)
10.2 A Sentence That Is True but Unprovable
166(3)
10.3 Establishment, Revisited
169(3)
10.4 A Godelian Machine
172(2)
10.5 Godel's Second Incompleteness Theorem
174(3)
10.6 Puzzles for Solving
177(3)
10.7 Notes and Further Reading
180(1)
10.8 Solutions
181(3)
11 Question Puzzles
184(15)
11.1 Three Warm-Ups
184(1)
11.2 The Power of Indexical Questions
185(1)
11.3 The Heaven/Hell Puzzle
186(3)
11.4 The Nelson Goodman Principle
189(2)
11.5 Generalized Nelson Goodman Principles
191(3)
11.6 Coercive Logic
194(1)
11.7 Smullyan as a Writer
195(1)
11.8 Solutions
196(3)
IV Puzzles Based on Nonclassical Logics
199(38)
12 Should "Logics" Be a Word?
201(11)
12.1 Logical Pluralism?
202(4)
12.2 Is Classical Logic Correct?
206(2)
12.3 Applications of Nonclassical Logic
208(2)
12.4 Notes and Further Reading
210(2)
13 Many-Valued Knights and Knaves
212(25)
13.1 The Transitional Phase
212(2)
13.2 The Three-Valued Island
214(6)
13.3 The Fuzzy Island
220(5)
13.4 Modus Ponens and Sorites
225(3)
13.5 Puzzles for Solving
228(3)
13.6 Solutions
231(6)
V Miscellaneous Topics
237(74)
14 The Saga of the Hardest Logic Puzzle Ever
239(27)
14.1 Boolos Introduces the Puzzle
239(6)
14.2 Is There a Simpler Solution?
245(5)
14.3 Trivializing the Hardest Puzzle Ever
250(3)
14.4 Are Three Questions Necessary?
253(2)
14.5 Two Questions When Random Is Really Random
255(4)
14.6 What If Random Can Remain Silent?
259(6)
14.7 Notes and Further Reading
265(1)
15 Metapuzzles
266(8)
15.1 A Warm-Up Puzzle
266(1)
15.2 The Playful Children and Caliban's Will
267(2)
15.3 Knight/Knave Metapuzzles
269(1)
15.4 Solutions
270(4)
16 Paradoxes
274(18)
16.1 What Is a Paradox?
275(1)
16.2 Paradoxes of Predication
276(3)
16.3 The Paradox of the Preface
279(3)
16.4 The Liar
282(7)
16.5 Miscellaneous Paradoxes
289(1)
16.6 Notes and Further Reading
290(2)
17 A Guide to Some Literary Logic Puzzles
292(19)
17.1 The Nine Mile Walk
293(2)
17.2 The Early Days of "Logic Fiction"
295(5)
17.3 A Gallery of Eccentric Detectives
300(3)
17.4 The Anti-Logicians
303(2)
17.5 Carr and Queen
305(2)
17.6 The Thinking Machine
307(4)
Glossary 311(8)
References 319(8)
Index 327
Jason Rosenhouse is professor of mathematics at James Madison University. He is the author of The Monty Hall Problem: The Remarkable Story of Math's Most Contentious Brain Teaser and Among the Creationists: Dispatches from the Anti-Evolutionist Front Line. He is the coauthor (with Laura Taalman) of Taking Sudoku Seriously: The Math behind the World's Most Popular Pencil Puzzle and the coeditor (with Jennifer Beineke) of The Mathematics of Various Entertaining Subjects (Vols. 13) (Princeton).