Gödel's theorem : an incomplete guide to its use and abuse /

Gödel's theorem : an incomplete guide to its use and abuse /

Saved in:
Bibliographic Details
Author / Creator:Franzén, Torkel.
Imprint:Wellesley, MA : A K Peters, c2005.
Description:x, 172 p. ; 23 cm.
Language:English
Subject:
Gödel's theorem.
Incompleteness theorems.
Gödel's theorem.
Incompleteness theorems.
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/6234650
Hidden Bibliographic Details
ISBN:1568812388
Notes:Includes bibliographical references (p. 165-167) and index.
Table of Contents:
  • Preface
  • 1. Introduction
  • 1.1. The Incompleteness Theorem
  • 1.2. Godel's Life and Work
  • 1.3. The Rest of the Book
  • 2. The Incompleteness Theorem: An Overview
  • 2.1. Arithmetic
  • 2.2. The First Incompleteness Theorem
  • 2.3. Some Limitations of the First Incompleteness Theorem
  • 2.4. The First Incompleteness Theorem and Mathematical Truth
  • 2.5. The First Incompleteness Theorem and Hilbert's Non Ignorabimus
  • 2.6. The Second Incompleteness Theorem
  • 2.7. Proving the Incompleteness Theorem
  • 2.8. A "Postmodern Condition"?
  • 2.9. Mind vs. Computer
  • 2.10. Some Later Developments
  • 3. Computability, Formal Systems, and Incompleteness
  • 3.1. Strings of Symbols
  • 3.2. Computable Enumerability and Decidability
  • 3.3. Undecidable Sets
  • 3.4. Computability and the First Incompleteness Theorem
  • 4. Incompleteness Everywhere
  • 4.1. The Incompleteness Theorem Outside Mathematics
  • 4.2. "Human Thought" and the Incompleteness Theorem
  • 4.3. Generalized Godel Sentences
  • 4.4. Incompleteness and the TOE
  • 4.5. Theological Applications
  • 5. Skepticism and Confidence
  • 5.1. The Second Incompleteness Theorem
  • 5.2. Skepticism
  • 5.3. Consistency Proofs
  • 5.4. Inexhaustibility
  • 6. Godel, Minds, and Computers
  • 6.1. Godel and the UTM
  • 6.2. Penrose's "Second Argument"
  • 6.3. Inexhaustibility Revisited
  • 6.4. Understanding One's Own Mind
  • 7. Godel's Completeness Theorem
  • 7.1. The Theorem
  • 7.2. PA as a First-Order Theory
  • 7.3. Incompleteness and Nonstandard Models
  • 8. Incompleteness, Complexity, and Infinity
  • 8.1. Incompleteness and Complexity
  • 8.2. Incompleteness and Randomness
  • 8.3. Incompleteness and Infinity
  • A. Appendix
  • A.1. The Language of Elementary Arithmetic
  • A.2. The First Incompleteness Theorem
  • A.3. Goldbach-Like Statements
  • References
  • Index

Similar Items