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Improved machines
OpposingArgument
1
#1093
A beefedup machine can recognise the truth of the Gödel sentence. Such a machine defeats Lucas's argument, because it shows that a formal system can evade Lucas's Gödelizing ability.
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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
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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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Improved machines
Improved machines☜A beefedup 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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Connectionist machine may evade Gödelization »
Connectionist machine may evade Gödelization
Connectionist machine may evade Gödelization☜A connectionist machine with massively parallel distributed processing capability could in principle reconfigure its own parameters while in the process of computation and arrive at its own semantic metalanguage by inductive means.☜98CE71
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Highly complex machine may not be Gödelizable »
Highly complex machine may not be Gödelizable
Highly complex machine may not be Gödelizable☜A qualitative difference in the way computers think may be introduced when they have advanced to a high enough degree of complexity. Such a highly complex machine may recognise the truth of its own Gödel sentence.☜98CE71
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Inductive machines immune to Gödelization »
Inductive machines immune to Gödelization
Inductive machines immune to Gödelization☜Inductive thinking, which humans can do, would allow computers to understand their own Gödel sentences.☜98CE71
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Ingenious machines could evade the Gödel argument »
Ingenious machines could evade the Gödel argument
Ingenious machines could evade the Gödel argument☜Machines may have mathematical insight, if theyre properly programmed to gauge symmetry and simplicity in patterns of formulae. Such ingenious machines replicate abilities of human mathematicians, and so can evade Gödelization as well as any human.☜98CE71
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Selfreferential machines »
Selfreferential machines
Selfreferential machines☜A selfreferential machine can evaluate Gödel sentences for itself. Such a machine may evade the Lucas argument.☜98CE71
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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
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Entered by:
David Price
NodeID:
#1093
Node type:
OpposingArgument
Entry date (GMT):
8/29/2006 7:52:00 PM
Last edit date (GMT):
12/9/2007 4:17:00 PM
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