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

3.86  ·  Rating Details ·  86 Ratings  ·  14 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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(showing 1-30 of 273)
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Kevin K
May 02, 2014 Kevin K rated it really liked it  ·  review of another edition
Shelves: logic-math
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
Barry
Aug 13, 2008 Barry rated it really liked it
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
Jan 20, 2015 Zoe Jackson rated it really liked it  ·  review of another edition
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
Charles
Apr 18, 2015 Charles rated it it was amazing  ·  review of another edition
Godel's Incompleteness Theorems were a revolution in mathematics and there were repercussions and misunderstandings that rippled out into other fields. The main theorem first appeared in an Austrian journal in 1931 and can be stated very simply.

In any consistent formal system S within which it is possible to perform a minimum amount of elementary arithmetic, there are statements that can neither be proved nor disproved.

The consequences are enormous, in that it means that in any system that can b
...more
Joseph
Jun 27, 2014 Joseph rated it really liked it
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
Ton van Gessel
May 10, 2015 Ton van Gessel rated it really liked it
Shelves: math
This book tells you what Godel's theorem really is about. It's not the easiest book to read if like me you don't have a formal math education. But if you take the time to read, reread, think about it en reread again you can eventually understand it (I could ). Godel's theorem is mentioned in passing in many books. This book gives you the tools to check if it really has anything to do with Godel's theorem ( to my surprise in many cases it doesn't ).
Babak
May 04, 2013 Babak rated it really liked it
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.
Cait
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.
NumberLord
May 09, 2008 NumberLord rated it really liked it
Shelves: mathematics
A nice description of Godel's Incompleteness Theorem. The book is notable for giving examples of the misuses of the Theorem.
Isk
Apr 02, 2009 Isk rated it it was ok
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.
Jeff
Jan 15, 2010 Jeff rated it it was ok
This is really poorly written.
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“In the quoted passage, the suggested conclusion is that a system of laws must be “inconsistent or incomplete.” Given the accompanying explanation of what “inconsistent” and “incomplete” mean here, it is an easy observation that all systems of laws, rules of living, and so on, are both inconsistent and incomplete and will remain so. In other words, in the case of legal systems, there will always be actions and procedures about which the law has nothing to say, and there will always be actions and procedures on which conflicting legal viewpoints can be brought to bear. Hence the need for courts and legal decisions. References to Gödel’s theorem can only add a rhetorical flourish to this simple observation.” 0 likes
“The incompleteness theorem is a mathematical theorem precisely because the relevant notions of truth and provability are mathematically definable. Nonmathematical “Gödel sentences” and Liar sentences give rise to prolonged (or endless) discussions of just what is meant by a proof, by a true statement, by sound reasoning, by showing something to be true, by convincing oneself of something, by believing something, by a meaningful statement, and so on.” 0 likes
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