Gödel's Theorem: An Incomplete Guide to Its Use and AbuseCRC Press, 6 giu 2005 - 182 pagine "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 |
Sommario
An Overview | 9 |
Computability Formal Systems and Incompleteness | 59 |
Incompleteness Everywhere | 77 |
Skepticism and Confidence | 97 |
Gödel Minds and Computers | 115 |
Gödels Completeness Theorem | 127 |
Incompleteness Complexity and Infinity | 137 |
A Appendix | 155 |
References | 165 |
Altre edizioni - Visualizza tutto
Gödel's Theorem: An Incomplete Guide to Its Use and Abuse Torkel Franzén Anteprima non disponibile - 2005 |
Gödel's Theorem: An Incomplete Guide to Its Use and Abuse Torkel Franzén Anteprima non disponibile - 2017 |
Parole e frasi comuni
accept algorithm amount apply argument arithmetical arithmetical statement assume axioms basic basis called carried Chaitin Chapter claim complexity computably enumerable concept conclusion conjecture connection consequence consider consistency proof consistent contains course decidable defined definition Diophantine equation discussion disproved doubts elementary equivalent establish example existence expressed extend fact false finite first-order follows formal system further give given Gödel number Gödel's proof Gödel's theorem Goldbach-like statement greater human mind idea implies inconsistent infinite interest interpretation introduced kind knowledge known language length logic mathematical mathematicians matter means natural numbers noted observation obtained ordinary particular philosophical possible presented prime principles problem proof provable proved question reasoning refer regard result rules second incompleteness theorem sense sentence sequence shows simple solution sound specify statement strings stronger Suppose symbols theory thought true truth undecidable unprovable