**From:** Jef Allbright (*jef@jefallbright.net*)

**Date:** Sun Feb 25 2007 - 13:41:38 MST

**Next message:**Jey Kottalam: "Re: Meta: Minds, Machines and Gödel"**Previous message:**Mohsen Ravanbakhsh: "Meta: Minds, Machines and Gödel"**In reply to:**Mohsen Ravanbakhsh: "Meta: Minds, Machines and Gödel"**Next in thread:**Jey Kottalam: "Re: Meta: Minds, Machines and Gödel"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

On 2/25/07, Mohsen Ravanbakhsh <ravanbakhsh@gmail.com> wrote:

*> What's wrong with this argument?!!! If it's true, making a (supper)human is
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*> impossible!
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*>
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*>
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*>
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*> Minds, Machines and GÃ¶del is J. R. Lucas's 1959 philosophical paper in which
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*> he argues that a human mathematician cannot be accurately represented by an
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*> algorithmic automaton. Appealing to GÃ¶del's incompleteness theorem, he
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*> argues that for any such automaton, there would be some mathematical formula
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*> which it could not prove, but which the human mathematician could both see,
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*> and show, to be true.
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*>
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*> The paper is a GÃ¶delian argument over mechanism.
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As it seems I'm always saying, it's a matter of context.

Lucas applies different standards to the machine and the human,

apparently with the implicit assumption that while machines, by

definition, must be consistent, humans are somehow exempt (else how

could they have "free-will" which is "obvious" beyond dispute?)

Lucas argues

Godel's theorem states that in any consistent system which is

strong enough to produce simple arithmetic there are formulae

which cannot be proved-in-the- system, but which we [standing

outside the system] can see to be true.

Godel's theorem must apply to cybernetical machines, because

it is of the essence of being a machine, that it should be a concrete

instantiation of a formal system. It follows that given any machine

which is consistent and capable of doing simple arithmetic, there

is a formula which it is incapable of producing as being true -- but

which we can see to be true. It follows that no machine can be a

complete or adequate model of the mind, that minds are essentially

different from machines.

Lucas is correct in pointing out that the consistency of a system can

be proved only from within a context greater than and encompassing the

system of interest, but he fails to apply the same principle to the

human system. On what basis does he think human knowledge and

certainty of "truth" is warranted, given that both machines and humans

are similarly context-limited?

Another way to look at this is to agree with his statement that "given

any machine which is consistent and capable of doing simple

arithmetic, there is a formula which it is incapable of producing as

being true -- but which we [humans] can see to be true" and extend the

argument by applying a slightly more advanced machine that can prove

the more limited statements that stumped its predecessor, and imagine

doing this recursively as far as desired. It might then become clear

that that this hypothetical machine could in fact surpass the human in

context of understanding while remaining consistent but limited, and

that the provability of any statement, by human or machine, is a

matter of context.

Of course, given that your context and mine are necessarily disjoint

to some extent, the foregoing "proves" nothing. ;-)

- Jef

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