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

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
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Paperback, 182 pages

Published
June 6th 2005
by AK Peters
(first published May 25th 2005)

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## Community Reviews

(showing 1-30 of 273)

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

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

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

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

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

I'll have to pull up some quotes as I go....

*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....

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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.”
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“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.”
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