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From: jeff@aiai.ed.ac.uk (Jeff Dalton)
Subject: Re: Penrose & Banach-Tarski/Axiom of Choice
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Date: Sun, 23 Oct 1994 22:25:47 GMT
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In article <38653l$ivf@mp.cs.niu.edu> rickert@cs.niu.edu (Neil Rickert) writes:
>In <385i1s$69h@toves.cs.city.ac.uk> jampel@cs.city.ac.uk (Michael Jampel) writes:
>>Penrose's argument against Strong AI is, I think, this: Humans know the
>>_truth_ of certain Goedel sentences despite the fact that the are not
>>_provable_. Unlike humans, computers have no semantic content/
>>understanding [i.e. computers are not the same as humans], so can only
>>use proof-theoretic techniques to decide if they believe something is
>>true. Therefore computers cannot be `intelligent'' in any sense of the
>>word which is applicable to humans [i.e. computers are not the same as
>>humans]
>
>Yes, I agree that this is the basic Penrose argument.  It is
>therefore the exact same point as Searle tries to make in his Chinese
>Room argument.  And the exact same "Systems Reply" is applicable.

An interesting suggestion.  Could you explain it further, please?

>>My question: is the Axiom of Choice TRUE.
>
>Of course the Axiom of Choice is TRUE.  In mathematical systems,
>axioms are true BY DEFINITION.  It is true in the sense of truth
>within a formal mathematical system.  It is not intended to say
>anything about the real world.

When I studied this stuff, "is the AC true" seemed to be a
legitimate question.  I find your instantly dismissive attitude
somewhat odd.

-- jeff
