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Ο Σατανάς, ο Cantor και το άπειρο: Και άλλοι γρίφοι μαθηματικής λογικής
Γεια σας και πάλι! Να ένας μικρός γρίφος για σας. Ας υποθέσουμε πως σας δίνω δύο χαρτονομίσματα των δέκα δολαρίων και ότι συμφωνείτε με το ακόλουθο: Θα κάνω μια δήλωση. Εάν η δήλωση είναι ψευδής, τότε υπόσχεστε να μου επιστρέψετε το ένα χαρτονόμισμα και να κρατήσετε το άλλο. Και αν η δήλωση είναι αληθής, τότε θα κρατήσετε και τα δύο χαρτονομίσματα. Δέχεστε; Φαίνεται να σας συμφέρει, έτσι δεν είναι; Θα πάρετε τουλάχιστον το ένα από τα χαρτονομίσματα, μπορεί και τα δύο! Τι καλύτερο; Λοιπόν, θα δεχόσασταν την προσφορά μου; Η απάντηση είναι "όχι"! Γιατί; Διότι, αν τη δεχόσασταν, θα μπορούσα να κάνω μια δήλωση τέτοια ώστε ο μόνος τρόπος που θα είχατε για να κρατήσετε το λόγο σας θα ήταν να μου δίνατε οποιοδήποτε ποσό - ένα δισεκατομμύριο δολάρια, ας πούμε! Ποια δήλωση θα μπορούσα να κάνω ώστε να σας εξαναγκάσω να μου δώσετε ένα δισεκατομμύριο δολάρια; Θα σας δώσω ,την απάντηση αργότερα. (Παρεμπιπτόντως, αυτός είναι ο πιο διαβολεμένος γρίφος που έχω ποτέ επινοήσει!) [...] (Από τον πρόλογο στην έκδοση)
"Σπινθηροβόλα συλλογή προβλημάτων και παραδόξων λογικής από τον πιο ψυχαγωγικό επαΐοντα της μαθηματικής λογικής και της θεωρίας συνόλων που έζησε ποτέ. Όπως σε όλα τα ανάλογα βιβλία του, ο καθηγητής Smullyan μας οδηγεί στις γκεντελιανές στοές που υπόκεινται των μαθηματικών γρίφων, και οι οποίες οδηγούν σε όμορφα θεωρήματα για την αλήθεια και την αποδειξιμότητα". (Martin Gardner)
"Ο Smullyan έχει το χάρισμα να μετατρέπει τα πιο αφηρημένα και γεμάτα μυστήριο πεδία των μαθηματικών και της λογικής σε απτές και ελκυστικές εικόνες [...]. Μακάρι να γράψει ακόμη πιο πολλές, αμίμητες, υπέροχες, ολοζώντανες μαθηματικές ιστορίες". (Douglas Hofstadter)
"Πιστεύω ότι ο Ray Smullyan είναι ο Lewis Carroll της εποχής μας. Τα βιβλία του θα εξακολουθούν να μαγεύουν για πολύ καιρό αφότου οι περισσότεροι από μας θα 'χουμε ξεχαστεί". (Peter Denning)
"Φαίνεται πως η φαντασία του Smullyan δεν γνωρίζει όρια [...]. Αυτοί οι διαβολικά έξυπνοι γρίφοι λογικής οδηγούν τον αναγνώστη σε όλο και υψηλότερα επίπεδα δυσκολίας, καθόσον χτίζεται μια δομή η οποία καταλήγει στο θεώρημα του Godel". (Lee Dembart, The Los Angeles Times)
"Ο Smullyan είναι ένας χαρισματικός δάσκαλος. Όλους μας, ακόμη και τους φίλους του, απ' όποια γωνιά και αν τον παρατηρούμε, πάντα καταφέρνει να μας μπερδεύει. Είναι ο τέλειος λογικολόγος. Οι αστραπιαίες ανατροπές ή οι απρόσμενες καταλήξεις των ιστοριών του μας πείθουν ότι είναι ένας μάγος της λογικής". (Willard Quine, The New York Times Book Review)
"Σπινθηροβόλα συλλογή προβλημάτων και παραδόξων λογικής από τον πιο ψυχαγωγικό επαΐοντα της μαθηματικής λογικής και της θεωρίας συνόλων που έζησε ποτέ. Όπως σε όλα τα ανάλογα βιβλία του, ο καθηγητής Smullyan μας οδηγεί στις γκεντελιανές στοές που υπόκεινται των μαθηματικών γρίφων, και οι οποίες οδηγούν σε όμορφα θεωρήματα για την αλήθεια και την αποδειξιμότητα". (Martin Gardner)
"Ο Smullyan έχει το χάρισμα να μετατρέπει τα πιο αφηρημένα και γεμάτα μυστήριο πεδία των μαθηματικών και της λογικής σε απτές και ελκυστικές εικόνες [...]. Μακάρι να γράψει ακόμη πιο πολλές, αμίμητες, υπέροχες, ολοζώντανες μαθηματικές ιστορίες". (Douglas Hofstadter)
"Πιστεύω ότι ο Ray Smullyan είναι ο Lewis Carroll της εποχής μας. Τα βιβλία του θα εξακολουθούν να μαγεύουν για πολύ καιρό αφότου οι περισσότεροι από μας θα 'χουμε ξεχαστεί". (Peter Denning)
"Φαίνεται πως η φαντασία του Smullyan δεν γνωρίζει όρια [...]. Αυτοί οι διαβολικά έξυπνοι γρίφοι λογικής οδηγούν τον αναγνώστη σε όλο και υψηλότερα επίπεδα δυσκολίας, καθόσον χτίζεται μια δομή η οποία καταλήγει στο θεώρημα του Godel". (Lee Dembart, The Los Angeles Times)
"Ο Smullyan είναι ένας χαρισματικός δάσκαλος. Όλους μας, ακόμη και τους φίλους του, απ' όποια γωνιά και αν τον παρατηρούμε, πάντα καταφέρνει να μας μπερδεύει. Είναι ο τέλειος λογικολόγος. Οι αστραπιαίες ανατροπές ή οι απρόσμενες καταλήξεις των ιστοριών του μας πείθουν ότι είναι ένας μάγος της λογικής". (Willard Quine, The New York Times Book Review)
320 pages, Hardcover
First published January 1, 1992
29 people are currently reading
586 people want to read
About the author
Raymond M. Smullyan
77 books281 followersRaymond M. Smullyan was a logician, musician, Zen master, puzzle master, and writer.
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Displaying 1 - 9 of 9 reviews
January 19, 2015
I absolutely loved this book. It was so fun to read even though it took a while to get through all of the puzzles. It isn’t your average puzzle-book -- it has chapters, and parts, but the plot is very loose and is absolutely filled with great logic problems. Not only is it entertaining but it exercises your mind a lot. It teaches you new ways of thinking using logical deduction.
The problems start off quite easy, and aren’t too far out of your comfort zone. But soon, there are more difficult reasonings to make. I found it tough when the problems got harder, but I got used to the strange way of completely rational thinking. By the end of the book, I felt like I had transformed my brain just by sitting down and thinking all the way through all of the problems. Yes, I had to look at plenty of the solutions before I understood the answer, but that just helped me move on to harder problems. Towards the end of the book, the problems become a little abstract and quite difficult, but I found that it’s okay if you don’t comprehend all of the problems. You can always come back to sections of the book after you’ve read parts you can understand.
Unlike a book with a puzzle on every page, each numbered and with a solution at the back of the book, Satan, Cantor, and Infinity had an actual plot to it. It’s not one that has suspense and a climax, as in most fiction books (and some non-fiction), but you do follow three characters: the Sorcerer, Prince Alexander, and Princess Annabelle. At the beginning of the book you must solve a few problems to introduce the Sorcerer and unite the two lovers, which is really neat in my opinion.
After reading this book, I went on to read many other fascinating books by mathematician Raymond Smullyan. All the ones that I have read are also amazing, so check them out as well. Also, the name Satan, Cantor, and Infinity may seem a little strange to you. However, you have to read until the end to figure out why it’s named that.
The problems start off quite easy, and aren’t too far out of your comfort zone. But soon, there are more difficult reasonings to make. I found it tough when the problems got harder, but I got used to the strange way of completely rational thinking. By the end of the book, I felt like I had transformed my brain just by sitting down and thinking all the way through all of the problems. Yes, I had to look at plenty of the solutions before I understood the answer, but that just helped me move on to harder problems. Towards the end of the book, the problems become a little abstract and quite difficult, but I found that it’s okay if you don’t comprehend all of the problems. You can always come back to sections of the book after you’ve read parts you can understand.
Unlike a book with a puzzle on every page, each numbered and with a solution at the back of the book, Satan, Cantor, and Infinity had an actual plot to it. It’s not one that has suspense and a climax, as in most fiction books (and some non-fiction), but you do follow three characters: the Sorcerer, Prince Alexander, and Princess Annabelle. At the beginning of the book you must solve a few problems to introduce the Sorcerer and unite the two lovers, which is really neat in my opinion.
After reading this book, I went on to read many other fascinating books by mathematician Raymond Smullyan. All the ones that I have read are also amazing, so check them out as well. Also, the name Satan, Cantor, and Infinity may seem a little strange to you. However, you have to read until the end to figure out why it’s named that.
December 15, 2025
Satan, Cantor, and Infinity is a fascinating book of logic puzzles and mathematical ideas wrapped in storytelling. Raymond Smullyan is a master at taking very difficult ideas about truth, lies, infinity, and mathematical logic and making them fun and interesting through puzzles and stories. This book is for anyone who loves to think hard, loves puzzles, and wants to understand how logic works.
The book uses a character called the Sorcerer to guide readers through different types of puzzles and ideas. The Sorcerer lives on an imaginary Island of Knights and Knaves, where knights always tell the truth and knaves always lie. Using this simple idea, Smullyan builds increasingly difficult and clever puzzles that teach real logic principles.
The best part of the book is how it makes you think in new ways. Simple puzzles at the start teach you how to reason about truth and lies. By the middle of the book, you are working with robots that create other robots, a concept called self-reference that connects to Godel's famous theorem. By the end, you are learning about infinity through the ideas of mathematician Georg Cantor.
The storytelling keeps you interested while you are learning. Instead of just giving you a dry math textbook, Smullyan tells stories about characters like Alexander and Annabelle who face logic puzzles to win their freedom. You care about whether they will succeed, which makes you want to solve the puzzles.
What Works Brilliantly
The organization of the book is excellent. You start with very simple puzzles you can solve in a few minutes, then move to harder ones. By the time you reach the chapters on infinity, your mind is already trained to think in the logical way needed to understand difficult mathematical ideas.
The humor in the book is genuine. The characters talk to each other, make jokes, and sometimes get frustrated. This makes the book feel human, not cold and empty like a textbook. When Alexander fails a test for the fourth time trying to win back Princess Annabelle, you laugh but also feel his disappointment.
Smullyan explains difficult ideas clearly. Take Cantor's discovery: There are more real numbers than whole numbers, even though both sets are infinite. Instead of using heavy mathematical notation, Smullyan explains this through clever counting arguments and shows why it matters.
The puzzles are genuinely challenging. Even experienced puzzle solvers will find some of these hard. But the book does not make you feel stupid if you cannot solve something. Smullyan always explains the answer clearly enough that you understand why it is right.
Where the Book Has Limits
Some readers will find the middle sections (about robots and Godel's theorem) harder to follow than the early sections. The jumps between different types of problems can feel sudden. A reader might breeze through the knight and knave puzzles, then hit the chapter about self-reproducing robots and feel lost.
Some of the later puzzles are so difficult that you might want to peek at the answer before you have really exhausted your own thinking. This is fine, but it means some readers may not get the full reward of solving hard problems themselves.
This book is perfect for people who love puzzles, logic, and thinking hard about problems.
If you enjoyed books like Godel Escher Bach or if you like logic puzzles from newspapers or magazines, you will probably love this.
Teachers and students of mathematics or philosophy will find valuable material here.
The book explains important ideas like self-reference and infinity in a way that makes them memorable.
People who feel like they are "not good at math" should not avoid this book. The math here is not about arithmetic or equations. It is about reasoning and thinking clearly. Anyone who can follow a logical argument can understand this book.
The final chapter is where everything comes together. Satan thinks he has created an unbreakable trap using the idea of sets that do not contain themselves (a concept from Cantor's work). But Cantor's student beats him not by solving the puzzle but by asking whether Satan's description is even valid. By questioning the rules and definitions, the student wins. This is a perfect ending because it teaches that sometimes the most important thinking is asking the right questions.
My Rating:4.5/5
The book uses a character called the Sorcerer to guide readers through different types of puzzles and ideas. The Sorcerer lives on an imaginary Island of Knights and Knaves, where knights always tell the truth and knaves always lie. Using this simple idea, Smullyan builds increasingly difficult and clever puzzles that teach real logic principles.
The best part of the book is how it makes you think in new ways. Simple puzzles at the start teach you how to reason about truth and lies. By the middle of the book, you are working with robots that create other robots, a concept called self-reference that connects to Godel's famous theorem. By the end, you are learning about infinity through the ideas of mathematician Georg Cantor.
The storytelling keeps you interested while you are learning. Instead of just giving you a dry math textbook, Smullyan tells stories about characters like Alexander and Annabelle who face logic puzzles to win their freedom. You care about whether they will succeed, which makes you want to solve the puzzles.
What Works Brilliantly
The organization of the book is excellent. You start with very simple puzzles you can solve in a few minutes, then move to harder ones. By the time you reach the chapters on infinity, your mind is already trained to think in the logical way needed to understand difficult mathematical ideas.
The humor in the book is genuine. The characters talk to each other, make jokes, and sometimes get frustrated. This makes the book feel human, not cold and empty like a textbook. When Alexander fails a test for the fourth time trying to win back Princess Annabelle, you laugh but also feel his disappointment.
Smullyan explains difficult ideas clearly. Take Cantor's discovery: There are more real numbers than whole numbers, even though both sets are infinite. Instead of using heavy mathematical notation, Smullyan explains this through clever counting arguments and shows why it matters.
The puzzles are genuinely challenging. Even experienced puzzle solvers will find some of these hard. But the book does not make you feel stupid if you cannot solve something. Smullyan always explains the answer clearly enough that you understand why it is right.
Where the Book Has Limits
Some readers will find the middle sections (about robots and Godel's theorem) harder to follow than the early sections. The jumps between different types of problems can feel sudden. A reader might breeze through the knight and knave puzzles, then hit the chapter about self-reproducing robots and feel lost.
Some of the later puzzles are so difficult that you might want to peek at the answer before you have really exhausted your own thinking. This is fine, but it means some readers may not get the full reward of solving hard problems themselves.
This book is perfect for people who love puzzles, logic, and thinking hard about problems.
If you enjoyed books like Godel Escher Bach or if you like logic puzzles from newspapers or magazines, you will probably love this.
Teachers and students of mathematics or philosophy will find valuable material here.
The book explains important ideas like self-reference and infinity in a way that makes them memorable.
People who feel like they are "not good at math" should not avoid this book. The math here is not about arithmetic or equations. It is about reasoning and thinking clearly. Anyone who can follow a logical argument can understand this book.
The final chapter is where everything comes together. Satan thinks he has created an unbreakable trap using the idea of sets that do not contain themselves (a concept from Cantor's work). But Cantor's student beats him not by solving the puzzle but by asking whether Satan's description is even valid. By questioning the rules and definitions, the student wins. This is a perfect ending because it teaches that sometimes the most important thinking is asking the right questions.
My Rating:4.5/5
October 29, 2018
I'm fonder of Smullyan's other books, although the discussions of set theory in the latter half of the book are pretty good.
May 19, 2021
This made my head hurt when i was trying to (and failed to) grasp its later chapters but it would definitely recommend it to everyone
December 9, 2021
Dazzling and thought-provoking.
June 25, 2015
My supervisor reccomended it. And I agree with him, it's a great book. There are funny puzzles and interesting looks on Gödel's incompletenest theorems. I reccomend it to read "Forever Undecided" too, to make your knowledhe of incompletenes more complete.
Last parts are about Set theory, for me it was uninteresting, becouse I knew this before, but I believe, that someone who has no knowledge about problematic, will enjoy it.
Last parts are about Set theory, for me it was uninteresting, becouse I knew this before, but I believe, that someone who has no knowledge about problematic, will enjoy it.
January 7, 2011
Raymond Smullyan is my Logician Dumbledore. I own and read every book of his I can get my hands on. Which is well over a dozen.
Want to read
May 25, 2011non è indicato il nome del traduttore
June 17, 2008
Logic puzzles: They're not just for the GRE.
Displaying 1 - 9 of 9 reviews