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Gödelian insight is a slippery character
ArgumentOpposé
1
#1113
The Gödelian insight can attach itself to any system that has been algorithmically specified, including an algorithmic specification of the Gödelization procedure.
Roger Penrose (1990).
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Are thinking computers mathematically possible? [7] »
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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
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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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Improved machines »
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Improved machines☜A beefed-up machine can recognise the truth of the Gödel sentence. Such a machine defeats Lucass argument, because it shows that a formal system can evade Lucass Gödelizing ability.☜EF597B
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The Gödelian insight has already been formalised »
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.☜98CE71
▲
Gödelization procedure algorithmically specifiable »
Gödelization procedure algorithmically specifiable
Gödelization procedure algorithmically specifiable☜The mathematical Gödelization process can be formalised. It is meta in the sense that a formal mathematical processes is being used to reason about a mathematical process.☜98CE71
■
Gödelian insight is a slippery character
Gödelian insight is a slippery character☜The Gödelian insight can attach itself to any system that has been algorithmically specified, including an algorithmic specification of the Gödelization procedure.☜EF597B
◄
Roger Penrose »
Roger Penrose
Roger Penrose☜Arguments advanced by Roger Penrose.☜FFFACD
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Entrée par:
David Price
NodeID:
#1113
Node type:
OpposingArgument
Date d'entrée (GMT):
8/30/2006 10:50:00 AM
Date de la dernière modification (Heure GMT):
10/23/2007 1:59:00 PM
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