Godel's Theorem: An Incomplete Guide to Its Use and Abuseby Torkel Franzen
Pub. Date: 06/28/2005
Publisher: Taylor & Francis
"Among the many expositions of Gödel's incompleteness theorems written for non-specialists, this book stands apart. With exceptional clarity, Franzén 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… See more details below
"Among the many expositions of Gödel's incompleteness theorems written for non-specialists, this book stands apart. With exceptional clarity, Franzén 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 theorems that are so rife in popular discussions of their significance. As an antidote to the many spurious appeals to incompleteness in theological, anti-mechanist and post-modernist debates, it is a valuable addition to the literature." - John W. Dawson, author of Logical Dilemmas: The Life and Work of Kurt Gödel
- Taylor & Francis
- Publication date:
- Edition description:
- New Edition
- Sales rank:
- Product dimensions:
- 6.16(w) x 9.08(h) x 0.39(d)
Table of Contents
|2||The incompleteness theorem : an overview||9|
|3||Computability, formal systems, and incompleteness||59|
|5||Skepticism and confidence||97|
|6||Godel, minds, and computers||115|
|7||Godel's completeness theorem||127|
|8||Incompleteness, complexity, and infinity||137|
|App. 1||The language of elementary arithmetic||155|
|App. 2||The first incompleteness theorem||157|
|App. 3||Goldbach-like statements||160|
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I bought the book after reading a review in the MAA Monthly, which I found to be incredibly fascinating. Unfortunately, the book did not continue where the review left off as I had hoped.
The writing is *very* technical and hard to understand. I can see that the author tried to make large passages as easy-to-read as possible, but the effect is that large passages are incomprehensible to the trained mathematics student (the most important definitions appear much later on if you are looking for them, as I was), and not so useful for the "general reader" (without the definitions, it is hard to fully understand the metaphors).
The back of the book says that the book was written for a "general audience", but I would say that it is meant more for the advanced undergraduate to beginning-intermediate graduate.
As one other point, the book is hard to read because of the writing *and* typesetting; it appears that an article-style LaTeX file was simply published, when the LaTeX file should have been rendered in book-style (so as to have a wider inner margin and a thinner outer margin).
Hopefully the author will make a second addition that has better organization (made more like a math textbook), because the concept of creating a guide to the Incompleteness Theorems is a good one, I think, and this text has potential.
I recognized Torkel Franzen's name from his participation on many Usenet groups over the years and associated his name with informative discussion. With the jacket blurbs to this book I was looking forward to something really helpful. I'm not sure the book quite delivers. I came to the subject with some background and some questions. The book helps to raise additional questions, but it is so informal that the questions are never quite argued or answered. I would not want to defend the questions (or such answers as are attempted) in full-on academic or peer-reviewed forums. Even the writing is informal as most Usenet posts, and a little short of what one expects in book form. If you are desparate for some unconventional perspectives on Godel's Theorem you will find some leads here, but what to do with them, starting with fully understanding and validating them, is left as a very significant exercise for the reader.