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Article 5734 of comp.ai.philosophy:
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>From: minsky@media.mit.edu (Marvin Minsky)
Newsgroups: comp.ai.philosophy
Subject: Re: penrose
Message-ID: <1992May19.025328.5332@news.media.mit.edu>
Date: 19 May 92 02:53:28 GMT
References: <1992May6.220605.26774@unixg.ubc.ca> <1992May8.015202.10792@news.media.mit.edu> <1992May18.194416.27171@hellgate.utah.edu>
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In article <1992May18.194416.27171@hellgate.utah.edu> tolman%asylum.utah.edu@cs.utah.edu (Kenneth Tolman) writes:
>In article <1992May8.015202.10792@news.media.mit.edu> minsky@media.mit.edu (Marvin Minsky) writes:
>
>>Now here's one of the things worng with what follows.  Penrose
>>presents a proof of Godel's theorem, shows how to make a godel
>>any algorithm.  I cannot follow this argument, which is based on a new
>> [etc]
>If you cannot follow this argument, check out Hilbert's attempt to do it,
>the Entsheidungsproblem.  (The very problem Turing was trying to solve)
>Then check out why algorithms are incapable of it.
>
>Algorithms are fundamentally incomplete.  Turing machines are fundamentally
>incomplete.  Think.

I cannot follow this, either.  The predicate "incomplete" doesn't
apply to either a procedure or a machine.  It applies only to
consistent logical systems. Think!  All inconsistent systems are complete.
The trouble is that they can prove "false" statements as well as true ones!

Your problem appears to be the same as Penrose's: the grandiose
illusion of being able to make self-referent statements rather freely,
yet maintaining consistency.  

Look again at Godel's theorem. It starts by assuming a system that is
"rich enough to express arithmetic."  Then Godel observes that this
permits a form of self-reference, namely by using a trick like godel
numbering.  And proves that if the result is consistent, then it is
incomplete.  My point is simply, so what!  Because

  (1) There's no good reason to assume humans are consistent.
  (2) There's no reason to program a machine to be, either.

So I can't follow the remaining arguments.  They all slip into the
usual commonsense arguments that humans can make infinite clusures of
extensions, whereas machines can only do it step-by-step.  But
remember Russell's paradox.  Your commonsense closures -- Penrose calls
them "informal", are richly self-referent.  Are you (and him) really
claiming
  (1) You can do this without becoming inconsistent?
  (2) That you can't write algorithms -- that is, programs -- which do
the same sorts of verbal self-references?

All this nonsense seems to depend on these two absurd assumptions.
I've had it with people who say that only people can be "informal" and
also that people can magically escape the consequences of what Godel
discovered!  Yes, I know, Godel said he thought so, too.  That's not a
convincing proof, though!


