"This sentence cannot be confirmed to be true by a 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
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
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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