Godel's Theorem: An Incomplete Guide to Its Use and Abuse [NOOK Book]

Overview

Among the many expositions of Goedel's incompleteness theorems written for non-specialists, this book stands apart. With exceptional clarity, Franzen 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 ...
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Godel's Theorem: An Incomplete Guide to Its Use and Abuse

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Overview

Among the many expositions of Goedel's incompleteness theorems written for non-specialists, this book stands apart. With exceptional clarity, Franzen 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 Goedel
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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: 9781568815008
  • Publisher: A K Peters
  • Publication date: 10/1/2009
  • Sold by: Barnes & Noble
  • Format: eBook
  • Pages: 182
  • Sales rank: 1,109,346
  • File size: 234 KB

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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