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🔎
Theorems show limitations of machine thought
SupportiveArgument
1
#1184
Gödel’s theorem, and other mathematical theorems like it, reveal essential limitations on the project of making machines that think.
Note
: This region covers those arguments that don't derive from Lucas or Penrose but still deal with Gödelian limitations; that is, with the limitations that Gödel’s theorem—and other similar theorems—impose on machine and/or human intelligence.
CONTEXT
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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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Theorems show limitations of machine thought
Theorems show limitations of machine thought☜Gödel’s theorem, and other mathematical theorems like it, reveal essential limitations on the project of making machines that think.☜98CE71
●
Gödel's first theorem »
Gödel's first theorem
Gödel's first theorem☜Gödels incompleteness theorem shows that any consistent formal system of axioms and rules of inference, provided its strong enough to produce arithmetic, will contain true statements that cant be proven by the procedures provided in the system. ☜98CE71
●
Gödel's second theorem »
Gödel's second theorem
Gödel's second theorem☜As a corollary to Gödels first theorem it follows that any consistent formal system strong enough to produce arithmetic cant prove itself consistent. ☜98CE71
●
Gödel's and Church's theorems are psychological laws »
Gödel's and Church's theorems are psychological laws
Gödel's and Church's theorems are psychological laws☜Gödel’s theorem shows that human creativity will always exceed human capacity to anticipate that creativity. Furthermore, the theorems also show humans are able to entertain and clearly conceive of ideas that are neither constructible nor effective.☜98CE71
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Machines can't understand language like humans »
Machines can't understand language like humans
Machines can't understand language like humans☜Machines inability to distinguish the negation of the Gödel sentence from the Gödel sentence itself shows that matchines arent able to distinguish any sentence from its negation—which is a requirement of natural language understanding.☜98CE71
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Mathematical thought can't be fully formalised »
Mathematical thought can't be fully formalised
Mathematical thought can't be fully formalised☜Gödel’s theorem shows that human creativity cant be fully formalised. The ingenuity of mathematicians in devising new methods cant be reduced to a precise logical form.☜98CE71
●
Mathematics is an essentially creative activity »
Mathematics is an essentially creative activity
Mathematics is an essentially creative activity☜The incompleteness and undecidability results support the idea that mathematics is essentially creative, and that its preferable to have multiple formal systems rather than a single universal system such as the Principia Mathematica.☜98CE71
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The argument from Church's theorem »
The argument from Church's theorem
The argument from Church's theorem☜According to Churchs theorem theres no decision procedure for predicate calculus. This means that there is no computable procedure by which a machine can decide whether a given sentence in predicate calculus is true or false.☜98CE71
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A human can't simultaneously beat all machines »
A human can't simultaneously beat all machines
A human can't simultaneously beat all machines☜Theorems like Churchs, Gödels, and Turings, show only that a human can beat one machine on a given occasion. But theres no reason to believe that a human can outthink all machines. ☜EF597B
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Machines may eventually have mathematical intuition »
Machines may eventually have mathematical intuition
Machines may eventually have mathematical intuition☜The incompleteness theorems only show that a machine cant be proven to possess mathematical intuition—not that machines cant in fact possess mathematical intuition.☜EF597B
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Entered by:
David Price
NodeID:
#1184
Node type:
SupportiveArgument
Entry date (GMT):
9/5/2006 10:43:00 AM
Last edit date (GMT):
12/14/2007 12:25:00 AM
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