Book on Godel's Theorem

I'd like to recommend a new book for those interested in Gödel's Incompleteness theorems. It is by Torkel Franzén, and is entitled Gödel's Theorem: An Incomplete Guide to Its Use and Abuse. [ISBN 1568812388] As evidenced from the title, the primary focus of the book is to identify the specific nature of these theorems, where they apply directly, and where they do not apply directly, and where they are interpreted entirely erroneously.

Although the book is aimed at non-mathematicians and those with no knowledge of formal logic, I can't really imagine someone with no understanding of logic and some fair amount of math comprehension benefitting alot from this book. I mean, by p. 10 he talking about Diophantine equations and Goldbach-like conjectures, and soon after, "PA" and "ZFC" are tossed about as if they were practically everyday acronyms for most people. The book is however, largely free of formulas and proofs, for those who are dissuaded by such. The overviews of the theorems themselves is not as lucid as I imagine they could be. The overviews will also seem a bit alien to someone expecting and Nagel & Newman kind of treatment; instead, this is discussed from a more abstract perspective of the characteristics and properties of formal systems, which avoids getting into the gritty details (even Gödel-numbering is not explained in detail!) but may be hard to grasp for someone not used to thinking at this level of abstraction about mathematical systems.

With that said, I still think it is quite worthwhile reading, and at a slim 170ish pages, it is a fairly quick read. After the overviews, he takes on various applications/misapplications of the theorems by topic. So, there are discussion of the theorems' relevance or applicability to things such as TOE (Theory of Everything), Turing machines, skepticism, minds, inexhaustibility, computability and so on. He does so typically by first giving several quotes that appear either in the literature or commonly on the internet, and then proceeds to either correct or clarify those quotes. Such notables as Roger Penrose, Freeman Dyson, and Stephen Hawking are among the quoted who are scrutinized.

I think the primary goal of the book is accomplished in its debunking of outright misuses of the theorems, and by way of correction and clarification of other uses, it accomplishes its pedagogical goal. I know it will cause me to strive to be more precise in any future invocations of these theorems.