The Gödelian Puzzle Book: Puzzles, Paradoxes and Proofs by Raymond M. Smullyan (PDF)

Description

These brand-new recreational logic puzzles provide entertaining variations on Gödel’s incompleteness theorems, offering ingenious challenges related to infinity, truth and provability, undecidability, and other concepts. Created by the celebrated logician Raymond Smullyan, the puzzles require no background in formal logic and will delight readers of all ages.The two-part selection of puzzles and paradoxes begins with examinations of the nature of infinity and some curious systems related to Gödel’s theorem. The first three chapters of Part II contain generalized Gödel theorems. Symbolic logic is deferred until the last three chapters, which give explanations and examples of first-order arithmetic, Peano arithmetic, and a complete proof of Gödel’s celebrated result involving statements that cannot be proved or disproved. The book also includes a lively look at decision theory, better known as recursion theory, which plays a vital role in computer science.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book is extremely entertaining, full of educational, thought-provoking, and sometimes difficult logic puzzles. I’m a huge fan of Smullyan and his work and this book certainly did not disappoint. This book is a great way to learn about Godel’s theorems without any risk of falling asleep.That said, I am not a fan of typos and errors, and this book is full of them. Several of the puzzles are impossible to solve because a wrong name is used in the scenario, and some of the proofs are equally problematic. Anyone paying close attention will be able to work around the issues, but that should not be required of the reader. I’m not sure why these problems weren’t caught during a review phase.Were this book any less excellent I would have given it three or perhaps even two stars as a result of the errors. I’m disappointed by the issues, but would still highly recommend the book. Just be extra-alert as you work through it.

⭐The content of the book is excellent. I’m halfway through it and can’t put it down.However there are (so far) a few errors which are kind of annoying. In the pictures you see a repeated paragraph and inconsistent quoting. The last might seem like a nit, but given that a big subject in the book is self-reference it can throw the reader off balance. I also found some wrong solutions to the puzzle, particularly in chapter 9, but I don’t think the editing is to be blamed for that part.So I’d say buy it! But I really hope a new edition is made with corrections.

⭐The author here analyzes particularly the Godel theorem.So we observe how this theorem has earned its fame, because it correlates the logics with the meta-mathematics. Particularly that results from the fact that a proposition can tell something about it-self. The book is reach of exercises and applications, particularly about the fixed point and the Zeno paradox.

⭐If you’re a math nerd who loves logical puzzles, then you might like this book. A lot of it is theory and has no straight answers, or even possibly infinite answers to many of the “riddles”. It’s pretty dry for my tastes, most of them seem way too similar to each other and I find myself skipping my way through most of the chapters to find something different. All in all, it’s okay, if you loved math in high school, you’ll probably like this book.

⭐Each time I think that Raymond Smullyan has reached his upper limit, he produces a book even more amazing, wondrous, and stupendous. He is a boundless source of creativity and ingenuity, and not even his advanced years deter him in the slightest. His latest “Godelian Puzzle Book” is a true masterpiece – a mixture of humor and brilliance which entertainingly bares the very mind and soul of the eminent logician Kurt Gödel. I can not recommend this book enough!

⭐The first few chapters are great, but then it gets a little technical and and the puzzles get a little monotonous. Nevertheless and all around good read.

⭐I am not a professional student of Logic but Smullyan’s other books have kept very busyover a long time span. This book takes me just where I wanted to go to apractical account of why Godel has made such a tremendous impact

⭐If you enjoy this way of thinking, the inherent self-contradictions of logic in self-referential environments.

⭐This is the greatest mathematical logic book I have ever seen.The “step by step” style which clearly shown the background and gives you the chance to challenge yourself and experience the whole process to discover this subject like a mathematician.And I think this is the best way to study mathematics rather than without following the historical process.

⭐Ein wunderschönes Einführungsbuch in die Welt des ersten Gödelschen Theorems. Man kann sich keine schönere Einführung vorstellen.Im ersten Teil führt Smullyan anhand von logischen Rätseln und ausgewählten formalen Systemen sehr eng an die Grundgedanken des Theorems heran. Hervorzuheben ist, daß der für die diversen Rätsel und Probleme stets auch genaue Lösungen angibt. Er läßt den Leser nicht im Stich.Der zweite Teil enthält eine genaue und originelle Darstellung aller Beweisschritte. Das Bemerkenswerte an dieser Darstellung ist, daß es Smullyan gelingt, den Beweisgang so zu vereinfachen, daß er gegenüber den üblichen Darstellungen in der Standardliteratur wirklich durchsichtig erscheint. Dabei machen sich u.a. die enormen Vorzüge der von Smullyan gewählten Gödelisierung (im Rahmen der von ihm entwickelten dyadischen Zifferndarstellung) sowie die Anwendung seiner elementar-formalen Systeme stark bemerkbar.Es gelingt Smullyan, einen wirklich vollständigen Beweis des ersten Gödelschen Unvollständigkeitstheorems zu erbringen, der auch für Leser ohne spezielle logisch-mathematische Schulung nachvollziehbar ist.Eine Meisterleistung! Faszinierend!

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⭐It says it’s entertaining for all all ages, so I took that at face value. Very disappointed to discover the language was that of a postgraduate degree in maths. Maybe child geniuses would enjoy it. Not suitable as a Christmas present for someone who likes sudoku and the like.

⭐Me gustó mucho, tiene de todo. El único detalle que no me agradó tanto es el estilo del libro (fuente, tamaño de texto y demás) pero es algo aparte.

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⭐Just the perfect(At least tends to ) book to stimulate your brain.Suitable for any person who has the maturity to accept intellectual challengea.

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