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Boyer-Moore theorem prover
VoorArgument
1
#1116
A LISP-driven theorem proving engine that has been used to derive many novel mathematical results, including decisions on some open questions in mathematics.
R. S. Boyer and J. S. Moore (1979).
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Artificial Intelligence »
Artificial Intelligence
Artificial IntelligenceâA collaboratively editable version of Robert Horns brilliant and pioneering debate map Can Computers Think?âexploring 50 years of philosophical argument about the possibility of computer thought.âF1CEB7
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Are thinking computers mathematically possible? [7] »
Are thinking computers mathematically possible? [7]
Are thinking computers mathematically possible? [7]âIs 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?âFFB597
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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 theoremsâGödels 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).â59C6EF
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Improved machines »
Improved machines
Improved machinesâA 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.âEF597B
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The Gödelian insight has already been formalised »
The Gödelian insight has already been formalised
The Gödelian insight has already been formalisedâPrograms have been developed that can derive Gödels theorems. The Gödelian insight has, in effect, been formalised.â98CE71
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Gödelization procedure algorithmically specifiable »
Gödelization procedure algorithmically specifiable
Gödelization procedure algorithmically specifiableâThe 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.â98CE71
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Proof has been formalised into a program »
Proof has been formalised into a program
Proof has been formalised into a programâUsing the Boyer-Moore theorem prover, Gödelâs theorem has been derived from a basic set of axioms by a computer in basically the same way that Gödel proved it himself.â98CE71
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Boyer-Moore theorem prover
Boyer-Moore theorem proverâA LISP-driven theorem proving engine that has been used to derive many novel mathematical results, including decisions on some open questions in mathematics.â98CE71
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Gemaakt door:
David Price
NodeID:
#1116
Node type:
SupportiveArgument
Gemaakt op (GMT):
8/30/2006 10:58:00 AM
Laatste bewerking (GMT):
12/8/2007 6:41:00 PM
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