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

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Overview

"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

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Editorial Reviews

From the Publisher
" ""Franzén's book is accessible, well written, and often funny..."" -Richard Zach, History and Philosophy of Logic, July 2005

""Ich möchte allen meinen Lesern . . . ein Buch ans Herz legen, und zwar ""das Neue"" von Torkel Franzén: Gödel's Theorem - An Incomplete Guide to Its Use and Abuse..."" -Altpapier, October 2005

""If the reader is serious about understanding the scope and limitations of Gödel's theorems, this book will serve them well."" -Don Vestal, MAA Online, November 2005

"". . . This is an excellent book, carefully considered and well-written. It will be read by layman and expert alike with pleasure and profit."" -Peter A. Fillmore, CMS Notes, Volume 37 No. 8, December 2005

""... a welcome tourist's guide not only to the correct but also to many incorrect interpretations of the theorems, both in their immediate contexts and in wider circumstances."" -I. Grattan-Guinness, LMS, February 2007

""This is a marvelous book. It is both highly competent and yet enjoyably readable. ... At last there is available a book that one can wholeheartedly recommend for anyone interested in Gödel’s incompleteness theorem—one of the most exciting and wide-ranging achievements of scientific thought ever."" -Panu Raatikainen, Notices of the AMS, February 2007

""This is a marvelous book. It is both highly competent and yet enjoyably readable. ... At last there is available a book that one can wholeheartedly recommend for anyone interested in Gödel’s incompleteness theorem—one of the most exciting and wide-ranging achievements of scientific thought ever."" -Panu Raatikainen, Notices of the AMS, March 2007

""... an extraordinary addition to the literature. ... The book is ideal reading for people with a basic logical background, be they computer scientists, philosophers, mathematicians, physicists, cognitive psychologists, or engineers ... and a real desire to understand quite deeply one of the intellectual gems of the 20th century."" -Wilfried Sieg, Mathematiacl Reviews, March 2007

""... lively and a pleasure to read ... provides remarkably sharp formulations of the usual confusions. There is no doubt that readers of this journal should recommend this book to any friends or colleagues who ask about the ramifications of incompleteness."" -Stewart Shapiro, Philosophia Mathematica, June 2006

""Dawson's biography of Göodel is provocative and interesting on several fronts, and is highly recommended to anyone with an interest in logic, the foundations of mathematics or the history of mathematics."" -Samuel R. Buss Buss, December 1998

""This book presents an exceptional exposition of Gödel's incompleteness theorems for non-specialists ... a valuable addition to the literature."" -EMS, March 2006

""The book explains fully, without using any technical logical apparatus, Gödel's two theorems about the incompleteness of any formal system which includes elementary arithmetic ... It is a great success in the way that the proofs of the theorems, while not given in full, are outlined in sufficient detail to make a discussion of the different versions that have been given worthwhile. I do not think there is any non-specialist exposition comparable for clarity and thoroughness."" -Clive Kilmister, The Mathematical Gazette, March 2007

""Franzen touches upon contemporary issues in logic that otherwise only rarely find their way into books of an introductory character like this one."" -The Review of Modern Logic, March 2007

""Torkel Franzen's ""Goedel's Theorem"" is a wonderful book, destined to become a classic ... In ""Goedel's Theorem,"" Torkel Franzen does a superb job of explaining clearly and carefully what the incompleteness theorem says and its implications as well as skewering much of the nonsense that has been written about it. ... However, while ""Goedel's Theorem"" should be accessible to a general audience, ""Inexhaustibility"" may be rather rough going for a reader who has not seriously studied mathematical logic."" -Mathematics and Comupter Science, March 2008"

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Product Details

  • ISBN-13: 9781568812380
  • Publisher: Taylor & Francis
  • Publication date: 6/28/2005
  • Edition description: New Edition
  • Pages: 182
  • Sales rank: 1,417,477
  • Product dimensions: 6.16 (w) x 9.08 (h) x 0.39 (d)

Table of Contents

1 Introduction 1
2 The incompleteness theorem : an overview 9
3 Computability, formal systems, and incompleteness 59
4 Incompleteness everywhere 77
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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Customer Reviews

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Sort by: Showing all of 2 Customer Reviews
  • Posted December 24, 2008

    It's okay

    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.<BR/><BR/>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).<BR/><BR/>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.<BR/><BR/>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).<BR/><BR/>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.

    1 out of 1 people found this review helpful.

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  • Posted December 18, 2012

    An Incomplete Guide

    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.

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