Gödel's Theorem: An Incomplete Guide to Its Use and Abuse
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Gödel's Theorem: An Incomplete Guide to Its Use and Abuse

3.86 of 5 stars 3.86  ·  rating details  ·  59 ratings  ·  12 reviews
Among the many expositions of Gödel's incompleteness theorems written for non-specialists, this book stands apart. With exceptional clarity, Franz n gives careful, non-technical explanations both of what those theorems say and, more importantly, what they do not. No other book aims, as his does, to address in detail the misunderstandings and abuses of the incompleteness th...more
Paperback, 182 pages
Published June 6th 2005 by AK Peters (first published May 25th 2005)
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Kevin K
Important: Contrary to the claims, THIS BOOK IS NOT WRITTEN FOR GENERAL READERS OR NON-MATHEMATICIANS. I myself have a math degree and found the book quite challenging. A person with little math experience will be in for a very tough slog.

That said, this is a concise and well-written overview. It covers Godel's two incompleteness theorems, and a number of important related topics (e.g., the completeness theorem, compactness theorem, non-standard analysis, large cardinals). The level of detail wa...more
Leo Horovitz
I think my first real encounter of a clear abuse of Gödel's incompleteness theorem came when I was engaged (as I so often am) in the debate on religion, online as well as elsewhere. This was one of the former kind and in one of the lower subcategories of the bigger category of online venues for the exchange of ideas: YouTube... Some atheist or number of atheists had argued against religion, presumably (because the response regarded this aspect of the religious question, but it wouldn't surprise...more
Aug 13, 2008 Barry rated it 4 of 5 stars
Shelves: math
Having had more classes than I care to remember in various aspects of computational theory (and trust me, I'm fast forgetting all of them), I've been exposed to Turing machines and the Incompleteness Theorem. I may have even on occasion said something to the effect that such-and-such was not possible due to said theorem. No more.

This book makes Godel about as approachable as it can be made. This is to say that it's certainly possible to sit down and read it over a good spaghetti dinner and thin...more
Zoe Jackson
A boon for anyone who's read a populist account of Gödel's incompleteness theorems and been left with a vague sense of unease from the amount of technical detail glossed over, and the sweeping claims made for the theorems' consequences. This book, if given close attention, will reward even the lay-reader with a precise, technical working of the proofs and their proper (and surprisingly limited) spheres of application. Spoiler alert: anyone who tries to use these theorems to argue for the relativ...more
Neat little book, it helped dispel some of my own misconceptions around
Gödel's work.

It's definitely not a simple book to read, you'll need to dig in an grapple with the logical, algebraic language. It doesn't presuppose that you understand a lot of math, but people who have done a lot of math are a lot more used to reading a lot of dense sentences, so they'll have an easier time.

Once you can get through the in-depth logical stuff, you'll reach the pretty obvious takeaway: that an unfortunate nu...more
An elegant book on clarifying the Gödel's incompleteness theorems, and their margins. It also well clarifies some of the common misconceptions on these theorems.

However and contrary to what is somewhat implied in introduction, the content is compact! and one can't understand it without picking up a pen and a piece of paper, and opening the details of the explained subjects by oneself.
Jun 11, 2008 Cait is currently reading it
So far I'm enjoying this book but not respecting it. For a book intended as a non-mathematician's guide to Gödel's work, it reads like many a textbook I've had. I personally like that -- I find theorems on prime numbers very soothing -- but it leaves me suspicious of the book's self-awareness.

I'll have to pull up some quotes as I go....
Muhammad al-Khwarizmi
Can't give this book two stars. I'd like to give it 2.5. Franzén explains some of the ways Gödel's theorems are misused well enough but his mathematical prose is confusing. I've read much clearer expositions of the same / similar topics.
A nice description of Godel's Incompleteness Theorem. The book is notable for giving examples of the misuses of the Theorem.
Unfinished. The math isn't well-explained, and it's annoyingly obvious that the abuses of Goedel's Theorem are abuses.
Najamuddin Mohammed
I am quoted on pages 94 and 95 of this book.
This is really poorly written.
Jared Davis
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Sep 09, 2014
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