Logical Labyrinths 1st Edition by Raymond Smullyan (PDF)

Description

This book features a unique approach to the teaching of mathematical logic by putting it in the context of the puzzles and paradoxes of common language and rational thought. It serves as a bridge from the author’s puzzle books to his technical writing in the fascinating field of mathematical logic. Using the logic of lying and truth-telling, the author introduces the readers to informal reasoning preparing them for the formal study of symbolic logic, from propositional logic to first-order logic, a subject that has many important applications to philosophy, mathematics, and computer science. The book includes a journey through the amazing labyrinths of infinity, which have stirred the imagination of mankind as much, if not more, than any other subject.

User’s Reviews

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

⭐Smullyan is amazing in this book, but the mistakes! It’s so awful to see such a nice work be plagued by typos (missing parentheses) and mistakes (wrong formulas sometimes) and the guy saying “it’s obvious” every few problems. I really hope they come out with a revised edition. It’s really much better as an intro to logic than most other books I purchased which go into long drawn and boring argument about old political debates which avoid as much controversies as possible not to offend the sensibilities of either side of the isle. This one is about puzzles! Solve this, try that. Fun stuff! I highly recommend it… 40$ with all the mistakes though… I wonder who was A.K. Peters (the publisher) targeting with this book. Smullyan is in his 90’s now. It’s fascinating to peak in his mind through this book; he’s still sharp for his age strangely enough.

⭐Classic. Read it and recommend it. You will want all of them.

⭐I’ll keep this short. It’s a great book with lots of problems. I mean both that you will be solving a lot of problems (puzzles), as well as that there are many errors. The author obviously used LaTax in writing it, and he obviously misused copy and paste in several instances (oops, I meant AND instead of OR). Its a first edition, so I would excuse the errors if he wasn’t falling into the common math professor trap of implying things should be obvious every chapter or so. But its worth it for its approach to logic; I would recommend it, especially when a second (fixed) edition comes out.

⭐スマリヤンの自叙伝「天才スマリヤンのパラドックス人生」の訳者あとがきにおいてスマリヤンが本書を執筆中であることを知って以来、出版を心待ちにしていました。本書は、これまで出版してきたパズルブックから数理論理学の専門書への架け橋と位置づけられており、読者層として大学生や社会人を想定しているようです。その内容を一行で表すと、論理パズル＋”First-Order Logic”＋無限集合の話題でしょうか。論理パズルの章では、様々なタイプの論理パズルから始まり、ネルソン・グッドマン原理を一般化してその幕を閉じます。本論に入り、命題論理と述語論理の初歩から歩みを始めて、タブロー法を紹介。無限集合に関する話題において、数学的帰納法、Konigの補題、コンパクト定理などが説明された後、タブロー法の完全性と正確性が証明されます。その後、公理系の話題となり、ヒルベルト公理系の完全性と正確性が証明されます。述語論理の応用編ではCraigの補題を含めて複数の有名な定理が証明され、最後にこれまで証明してきた様々な定理を一般的に導く一つの原理が紹介されます。この部分が本書の華です。本書は大学におけるスマリヤン独特の講義内容を一冊にまとめた本です。彼のパズルブックを読んだことがある人もない人も十分楽しめる内容であり、ご一読をおすすめします。

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⭐1919年生まれ、ご存知スマリヤン博士の集大成であり、事実上の最終講義でしょう。内容については多くを語る必要は・・・・ともあれ極上のテキストです。”That’s all for now. Good reading! I am a bit sad that this book must end. Perhaps one day I might write a sequel. Who knows?”結びの言葉からも万感の思いが伝わります。必読。

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