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Article 5769 of comp.ai.philosophy:
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>From: atten@phil.ruu.nl (Mark van Atten)
Newsgroups: comp.ai.philosophy
Subject: Re: penrose
Message-ID: <atten.706362138@groucho.phil.ruu.nl>
Date: 20 May 92 11:42:18 GMT
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References: <1992May6.220605.26774@unixg.ubc.ca> <1992May8.015202.10792@news.media.mit.edu> <1992May18.194416.27171@hellgate.utah.edu> <1992May19.025328.5332@news.media.mit.edu>
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minsky@media.mit.edu (Marvin Minsky) writes:

>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.

Good point! This has also been pointed out by Hao Wang, in From Mathematics
to Philosophy. He explains he is not convinced by Lucas, because all you
know is: if S is consistent, then <Goedel sentence>. But you have to prove
consistency first, and then the problem of your own consistency rises.

Best wishes,

Mark.


