On 14 Aug 2012, at 20:16, William R. Buckley wrote:
John:
Regardless of your dislike for the term omniscience versus
universality, the Turing machine
can compute all computable computations, and this simply by virtue
of its construction.
It is deeper than that. It is in virtue of the fact that the set of
computable functions, unlike all other sets in math, is closed for the
diagonalization, and the price for this is incompleteness. It is not
trivial, and makes computational universality rather exceptional and
unexpected. The discovery of the universal machine is a very big
discovery, of the type: it changes everything we knew. I think.
For beliefs, knowledge, proofs, definability, etc. This never happens,
and the corresponding formal systems can always been extended.
Bruno
wrb
From: everything-list@googlegroups.com [mailto:everything-list@googlegroups.com
] On Behalf Of John Clark
Sent: Tuesday, August 14, 2012 9:39 AM
To: everything-list@googlegroups.com
Subject: Re: Why AI is impossible
On Mon, Aug 13, 2012 at 8:09 PM, William R. Buckley <bill.buck...@gmail.com
> wrote:
> Consider that the Turing machine is computational omniscient[...]
Turing's entire reason for inventing what we now call a Turing
Machine was to prove that computational omniscience is NOT possible.
He rigorously proved that no Turing Machine, that is to say no
computer, can determine in advance if any given computer program
will eventually stop.
For example, it would be very easy to write a program to look for
the first even number greater than 2 that is not the sum of two
prime numbers and then stop. But will the machine ever stop? The
Turing Machine doesn't know, I don't know, you don't know, nobody
knows. Maybe it will stop in the next 5 seconds, maybe it will stop
in 5 billion years, maybe it will never stop. If you want to know
what the machine will do you just have to watch it and see, and even
the machine doesn't know what it will do until it does it.
John K Clark
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