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The Gödelian insight has already been formalised
OpposingArgument
1
#1154
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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Artificial Intelligence »
Artificial Intelligence
Artificial Intelligence☜A collaboratively editable version of Robert Horns brilliant and pioneering debate map Can Computers Think?—exploring 50 years of philosophical argument about the possibility of computer thought.☜F1CEB7
▲
Are thinking computers mathematically possible? [7] »
Are thinking computers mathematically possible? [7]
Are thinking computers mathematically possible? [7]☜Is it mathematically possible for a computer to think as well as a human can? Does the mathematics of computation contain anything to prohibit machines from thinking?☜FFB597
▲
No: computers are limited by Gödel's theorems »
No: computers are limited by Gödel's theorems
No: computers are limited by Gödel's theorems☜Gödels theorem proves that a computer cant in principle operate with human understanding (see detailed text). Gödels incompleteness theorems are the Achilles heel of mechanism. John Lucas (1961).☜59C6EF
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The problem of consistency »
The problem of consistency
The problem of consistency☜The notion of consistency involved in Lucass argument runs into difficulties for humans and/or machines.☜EF597B
▲
We don't know that mathematics is consistent »
We don't know that mathematics is consistent
We don't know that mathematics is consistent☜Gödel’s theorem rests on the assumption of a consistent formal theory. But many theories in the history of mathematics have been flawed, and even today the best theories are sometimes called into question.☜98CE71
▲
The Gödelian insight is all that we need »
The Gödelian insight is all that we need
The Gödelian insight is all that we need☜Its not necessary to see the consistency of an entire formal system. The ability to pass from one formal system to the Gödel sentence of that formal system is enough.☜EF597B
■
The Gödelian insight has already been formalised
The Gödelian insight has already been formalised☜Programs have been developed that can derive Gödels theorems. The Gödelian insight has, in effect, been formalised.☜EF597B
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Entered by:-
David Price
NodeID:
#1154
Node type:
OpposingArgument
Entry date (GMT):
8/30/2006 6:57:00 PM
Last edit date (GMT):
8/30/2006 6:57:00 PM
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