Newsgroups: comp.ai.philosophy
From: Lupton@luptonpj.demon.co.uk (Peter Lupton)
Path: cantaloupe.srv.cs.cmu.edu!das-news2.harvard.edu!news2.near.net!howland.reston.ans.net!swrinde!pipex!demon!luptonpj.demon.co.uk!Lupton
Subject: Re: Strong AI and consciousness
References: <jqbD0D7ou.56I@netcom.com> <1994Dec2.143356.8747@oracorp.com> <3bq5oq$g06@news1.shell>
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Date: Thu, 8 Dec 1994 00:35:40 +0000
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In article: <jqbD0D7ou.56I@netcom.com>  jqb@netcom.com (Jim Balter) writes:
> 
> In article <3bq5oq$g06@news1.shell>, Hal <hfinney@shell.portal.com> wrote:
> >A more important criticism of the AC approach is simply that there is no
> >algorithmic way to calculate the algorithmic complexity of any given data
> >set.  Because of the halting problem, there is no way of being sure that
> >some program shorter than the best one known would generate the same
> >data.  So at best we can give an upper bound to the AC of a string.  I
> >still think this may be a useful concept in giving a foundation to our
> >intuitive notions of reasonableness of theories and interpretations.
> 
> I don't want to comment on the rest of the AC issues, but I do take exception
> to this.  The halting problem says that no Turing Machine can determine
> whether every Turing Machine halts.  But that doesn't apply here.  We have a
> program and a finite data set.  We can enumerate all shorter programs.  We can
> analyze each of those shorter programs working on that finite data set.  The
> HP does not say that we cannot determine, for each such case, whether it
> terminates.  In fact, I'm fairly certain we always can.  (I'm way too rusty
> and too lazy to prove such a thing, but if I'm wrong the HP is a much stronger
> statement than necessary.)
> -- 
> <J Q B>

Well, we could just guess right! We could, in such a case, add that
guess as an axiom. Leaving that aside, if our abilities were limited 
to some given machine, and since C and K are co-enumerable and not 
recursive, there must be some data for which we (given our limitations) 
could not get the right answer. What is theoretically possible is to 
carry on compressing and, eventually, one's guesses would become
right. It's just one would never know when.

Cheers,
Pete Lupton
