The Gödelian insight has already been formalised
Programs have been developed that can derive Gödel's theorems. The Gödelian insight has, in effect, been formalised.
Stuart Russel and Peter Norvig (1995).
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Are thinking computers mathematically possible? [7] »Are thinking computers mathematically possible? [7]
No: computers are limited by Gödel's theorems »No: computers are limited by Gödel's theorems
The problem of consistency »The problem of consistency
We don't know that mathematics is consistent »We don't know that mathematics is consistent
The Gödelian insight is all that we need »The Gödelian insight is all that we need
The Gödelian insight has already been formalised
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