Infinity and the MindBantam Books, 1983 M01 1 - 342 páginas The book contains popular expositions (accessible to readers with no more than a high school mathematics background) on the mathematical theory of infinity, and a number of related topics. These include G?del's incompleteness theorems and their relationship to concepts of artificial intelligence and the human mind, as well as the conceivability of some unconventional cosmological models. The material is approached from a variety of viewpoints, some more conventionally mathematical and others being nearly mystical. There is a brief account of the author's personal contact with Kurt G?del.An appendix contains one of the few popular expositions on set theory research on what are known as "strong axioms of infinity." |
Contenido
10 | |
lnfinities in the Mindscape | 52 |
Transfinite Numbers | 69 |
lnfinitesimals and Surreal Numbers | 84 |
THE UNNAMEABLE | 99 |
Random Reals | 115 |
Higher Physical Infinities 93 | 140 |
What Is Truth? | 153 |
Interface Enlightenment | 221 |
Puzzles and Paradoxes | 236 |
Cardinality | 245 |
The Continuum | 257 |
Large Cardinals | 273 |
GCDELS INCOMPLETENESS | 287 |
SelfReference | 302 |
Godels Proof | 308 |
Conclusion | 163 |
Godels lncompleteness Theorem | 174 |
Towards Robot Consciousness | 184 |
Beyond Mechanism? | 198 |
What Is a Set? 206 | 206 |
Puzzles and Paradoxes 97 | 318 |
Notes | 333 |
354 | |
363 | |
Otras ediciones - Ver todas
Infinity and the Mind: The Science and Philosophy of the Infinite Rudy Rucker Vista previa limitada - 2004 |
Infinity and the Mind: The Science and Philosophy of the Infinite Rudy Rucker Vista previa limitada - 2019 |
Infinity and the Mind: The Science and Philosophy of the Infinite Rudy Rucker Vista previa limitada - 2019 |
Términos y frases comunes
Absolute Infinite actually infinite argument axioms Berry paradox billion words called Cantor cardinal number code numbers complete conceivable property concept consistent countable decimal expansion defined definite describe difficulty digits discussed exist extendible cardinals fact field Figure final find finding finite description finite number first first number fit formal system Georg Cantor given Godel human inaccessible cardinals Incompleteness Theorem infinite number infinite regress infinite sets infinitesimal Kurt Godel language large cardinals Liar paradox logical Mahlo cardinals mathematicians meaningful formulas means measurable cardinals mind Mindscape multiplicity mystical nameable natural numbers never notion object one-to-one One/Many ordinals less physical possible proof provable prove question rational real number Reflection Principle robots sense sentence sequence set theory simply sort space specific statement strings of symbols subsets tetration thing thought Total Library transfinite truth machine universe of set zero