On 21 Aug 2012, at 20:15, meekerdb wrote:
"This sentence cannot be confirmed to be true by a human being."
The Computer
LOL.
Of course, Clark is right, you should add "consistently" before
confirmed, to avoid the refutation of a human claiming confirming that
sentence. Or put "consistent" before human being.
On 8/21/2012 9:54 AM, benjayk wrote:
In this post I present an example of a problem that we can (quite
easily)
solve, yet a computer can't, even in principle, thus showing that our
intelligence transcends that of a computer. It doesn't necessarily
show that
human intelligence transcend computer intelligence, since the human
may have
received the answer from something beyond itself (even though I am
quite
confident human intelligence does transcend computer intelligence).
It is, in some sense, a variant of the Gödel sentence, yet it more
directly
relates to computers, thus avoiding the ambiguities in interpreting
the
relevance of Gödel to computer intelligence.
Is the following statement true?
'This statement can't be confirmed to be true solely by utilizing a
computer'
Imagine a computer trying to solve this problem:
If it says yes, it leads to a contradiction, since a computer has
been
trying to confirm it, so its answer is wrong.
If it says no, that is, it claims that it CAN be confirmed by a
computer,
again leading to a contradiction.
But from this we can derive that a computer cannot correctly answer
the
statement, and so cannot solve the problem in question! So the
solution to
the problem is YES, yet no computer can really confirm the truth of
the
sentence.
Nevertheless it can utter it. A computer can say "The following
statement is
true: 'This statement can't be confirmed to be true by utilizing a
computer'", but when it does this doesn't help to answer the question
whether it is correct about that, since we could just as well
program it to
say the opposite.
So, yes, our intelligence (whatever we truly are) definitely
transcends the
intelligence of a computer and the quest for strong AI or even
superhuman AI
seems futile based on that.
This has also relevance for AI development, especially yet-to-come
more
powerful AI. We should hardcode the fact "Some things cannot be
understood
using computers" into the computer, so it reminds us of its own
limits. This
will help us to use it correctly and not get lost in a illusion of
all-knowing, all-powerful computers (which to an extend is already
happening
as you can see by looking at concepts like "singularity").
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