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Article 5896 of comp.ai.philosophy:
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>From: pl160988@mtecv2.mty.itesm.mx (Ivan Ordonez-Reinoso)
Newsgroups: comp.ai.philosophy
Subject: Re: penrose
Message-ID: <5819@mtecv2.mty.itesm.mx>
Date: 25 May 92 19:25:29 GMT
References: <1992May8.015202.10792@news.media.mit.edu> <1992May18.194416.27171@hellgate.utah.edu> <1992May19.025328.5332@news.media.mit.edu>
Organization: I.T.E.S.M. Campus Monterrey
Lines: 53

In article <1992May19.025328.5332@news.media.mit.edu> 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:
[...]
:>
:>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!
:
I think that the words "algorithms are fundamentally incomplete" are not
hard to interpret. I think that what Kenneth Tolman meant is that there
are things that cannot be done, even in principle, just by using an
algorithm. Maybe some physical phenomena are not computable at all, but
I'm no expert on this subject.
:
: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.
Excuse my ignorance, but, how could us be inconsistent? At which level
would this inconsistence be? At the chemical level? I don't think so,
unless you think the laws of physics are inconsistent. At the mind, or
abstract level? Then our logic, our math, all human reasoning is worth
nothing.
:  (2) There's no reason to program a machine to be, either.
As far as I know, all computer programs are nothing but bit
manipulation, according to simple logical rules (floating point
arithmetic may not be exact, but the logic that governs it is
consistent).
But again, excuse my ignorance on this subject, all I ask is to be
clarified.
[...]
:
: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!

Once again, a humble question. Could you show me the proof that people
are formal systems that cannot escape "Goedelization"?

Ivan Ordonez-Reinoso
Centro de Inteligencia Artificial
ITESM, Campus Monterrey, Mexico
pl160988@mtecv2.mty.itesm.mx



