G�del's Theorem An Incomplete Guide to Its Use and Abuse

ISBN-10: 1568812388

ISBN-13: 9781568812380

Edition: 2005

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Description:

G?del's Theorem has been used to argue that a computer can never be as smart as a human being because the extent of its knowledge is limited by a fixed set of axioms, whereas people can discover unexpected truths ... It plays a part in modern linguistic theories, which emphasize the power of language to come up with new ways to express ideas. And it has been taken to imply that you'll never entirely understand yourself, since your mind, like any other closed system, can only be sure of what it knows about itself by relying on what it knows about itself- An Incomplete Education, by Judy Jones and William Wilson. A philosopher by training (PhD, University of Stockholm), Torkel Franz?n has for the past twenty years been active working in computer science (at the Swedish Institute of Computer Science) and teaching programming (at Lule? University of Technology). He is the author of a number of books, among them Inexhaustibility:
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Book details

List price: $35.95
Copyright year: 2005
Publisher: A K Peters, Limited
Publication date: 6/6/2005
Binding: Paperback
Pages: 182
Size: 6.00" wide x 8.75" long x 0.50" tall
Weight: 0.550
Language: English

Preface
Introduction
The Incompleteness Theorem
Godel's Life and Work
The Rest of the Book
The Incompleteness Theorem: An Overview
Arithmetic
The First Incompleteness Theorem
Some Limitations of the First Incompleteness Theorem
The First Incompleteness Theorem and Mathematical Truth
The First Incompleteness Theorem and Hilbert's Non Ignorabimus
The Second Incompleteness Theorem
Proving the Incompleteness Theorem
A "Postmodern Condition"?
Mind vs. Computer
Some Later Developments
Computability, Formal Systems, and Incompleteness
Strings of Symbols
Computable Enumerability and Decidability
Undecidable Sets
Computability and the First Incompleteness Theorem
Incompleteness Everywhere
The Incompleteness Theorem Outside Mathematics
"Human Thought" and the Incompleteness Theorem
Generalized Godel Sentences
Incompleteness and the TOE
Theological Applications
Skepticism and Confidence
The Second Incompleteness Theorem
Skepticism
Consistency Proofs
Inexhaustibility
Godel, Minds, and Computers
Godel and the UTM
Penrose's "Second Argument"
Inexhaustibility Revisited
Understanding One's Own Mind
Godel's Completeness Theorem
The Theorem
PA as a First-Order Theory
Incompleteness and Nonstandard Models
Incompleteness, Complexity, and Infinity
Incompleteness and Complexity
Incompleteness and Randomness
Incompleteness and Infinity
Appendix
The Language of Elementary Arithmetic
The First Incompleteness Theorem
Goldbach-Like Statements
References
Index
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