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Proof has been formalised into a program
SupportiveArgument
1
#1115
Using the Boyer-Moore theorem prover, Gödel’s theorem has been derived from a basic set of axioms by a computer in basically the same way that Gödel proved it himself.
Natarajan Shankar at (1994), as articulated by Stewart Russell 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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Improved machines »
Improved machines
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
▲
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
■
Proof has been formalised into a program
Proof has been formalised into a program☜Using the Boyer-Moore theorem prover, Gödel’s theorem has been derived from a basic set of axioms by a computer in basically the same way that Gödel proved it himself.☜98CE71
●
Boyer-Moore theorem prover »
Boyer-Moore theorem prover
Boyer-Moore theorem prover☜A LISP-driven theorem proving engine that has been used to derive many novel mathematical results, including decisions on some open questions in mathematics.☜98CE71
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Entered by:-
David Price
NodeID:
#1115
Node type:
SupportiveArgument
Entry date (GMT):
8/30/2006 10:55:00 AM
Last edit date (GMT):
12/8/2007 7:05:00 PM
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