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Gödel, Penrose and the possibility of AI

✍ Scribed by T. Dodd

Publisher
Springer Netherlands
Year
1991
Tongue
English
Weight
866 KB
Volume
5
Category
Article
ISSN
0269-2821

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✦ Synopsis

It is argued that Penrose's use of G6del's theorem to show that no machine can reproduce the achievements of a human mathematician depends on extra assumptions that would also show that no machine could ever check the validity of mathematical proofs: and it is claimed that the latter result contradicts views about the possibility of communicating mathematical proofs that are widely held and that are endorsed by Penrose.

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## Abstract After a brief review of Gödel‐type universes in string theory, we discuss some intriguing properties of black holes immersed in such backgrounds. Among these are the upper bound on the entropy that points towards a finite‐dimensional Hilbert space of a holographically dual theory, and t