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Games for Your Mind

The History and Future of Logic Puzzles
  • and
Language: English
Published/Copyright: 2020

About this book

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.

Author / Editor information

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. 1–3) (Princeton).

Reviews

"Jason Rosenhouse’s 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 Rosenhouse’s solution is surely a high for any mathematician out there."---Holly A. J. Middleton-Spencer, London Mathematical Society --- "It’s 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 --- "Excellent."---Elizabeth Palmer, Christian Century --- "Fascinating. . . . Part philosophy, part maths, part activity book; Games for Your Mind is an ingenious thing."---Amy Barrett, BBC Science Focus

Topics

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    Frontmatter

    i
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  • Publicly Available

    CONTENTS

    vii
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  • Publicly Available

    Preface

    xi
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  • I. The Pain and Pleasure of Logic
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    1. Is Logic Boring and Pointless?

    3
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    2. Logic Just for Fun

    15
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  • II. Lewis Carroll and Aristotelian Logic
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    3. Aristotle’s Syllogistic

    31
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    4. The Empuzzlement of Aristotelian Logic

    50
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    5. Sorites Puzzles

    68
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    6. Carroll’s Contributions to Mind

    93
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  • III. Raymond Smullyan and Mathematical Logic
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    7. Liars and Truthtellers

    115
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    8. From Aristotle to Russell

    137
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    9. Formal Systems in Life and Math

    154
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    10. The Empuzzlement of Gödel’s Theorems

    164
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    11. Question Puzzles

    184
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  • IV. Puzzles Based on Nonclassical Logics
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    12. Should “Logics” Be a Word?

    201
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    13. Many-Valued Knights and Knaves

    212
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  • V. Miscellaneous Topics
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    14. The Saga of the Hardest Logic Puzzle Ever

    239
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    15. Metapuzzles

    266
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    16. Paradoxes

    274
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    17. A Guide to Some Literary Logic Puzzles

    292
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    Glossary

    311
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    References

    319
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    Index

    327
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Publishing information
Pages and Images/Illustrations in book
eBook published on:
November 11, 2020
eBook ISBN:
9780691200347
Pages and Images/Illustrations in book
View content
https://doi.org/10.1515/9780691200347
eBook ISBN: 9780691200347
Keywords for this book
Syllogism; Logic; Philosopher; Inference; Mathematician; Classical logic; Mathematics; Theorem; Contradiction; Premise; Truth value; Reason; Lewis Carroll; Premises; Falsity; Propositional calculus; Mathematical logic; Categorical proposition; Term logic; Logical consequence; Natural language; Logical connective; Raymond Smullyan; Natural number; Axiom; Deductive reasoning; Principle; Notation; Aristotle; Thought; Predicate (mathematical logic); The Philosopher; Writing; Addition; Negation; Explanation; Logical reasoning; Logical disjunction; Bertrand Russell; Consequent; Knights and Knaves; Philosophy; Formal system; Result; Ambiguity; Literature; Theory; Textbook; Inductive reasoning; Gödel's incompleteness theorems; Liar paradox; Paradox; Instance (computer science); Coercive logic; Diagram; Dushanbe; Fiction; Prosecutor; Analogy; Instrumentalism; Formal language; Diagram (category theory); Understanding; Logical form; Asymmetry; Relevance; Kyrgyzstan; Peano axioms; Geometry; Prose
Audience(s) for this book
For a non-specialist adult audience
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