Infinity and the Mind

Portada
Рипол Классик, 1978 - 137 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

INFINITY
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
Bibliography
354
Index
363
Derechos de autor

Términos y frases comunes

Información bibliográfica