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Article 5897 of comp.ai.philosophy:
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>From: rickert@mp.cs.niu.edu (Neil Rickert)
Subject: Re: penrose
Message-ID: <1992May25.203925.30868@mp.cs.niu.edu>
Organization: Northern Illinois University
References: <1992May18.194416.27171@hellgate.utah.edu> <1992May19.025328.5332@news.media.mit.edu> <5819@mtecv2.mty.itesm.mx>
Date: Mon, 25 May 1992 20:39:25 GMT
Lines: 64

In article <5819@mtecv2.mty.itesm.mx> pl160988@mtecv2.mty.itesm.mx (Ivan Ordonez-Reinoso) writes:
>In article <1992May19.025328.5332@news.media.mit.edu> minsky@media.mit.edu (Marvin Minsky) writes:

>: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.

  The interpretation of this might depend on what you mean by an "algorithm."
For example, is a Monte Carlo simulation method an algorithm?

>:  (1) There's no good reason to assume humans are consistent.

>Excuse my ignorance, but, how could us be inconsistent?

  Perhaps you have had unusual experiences.  But I can't say that I have
ever met a human who was fully consistent.  Rumor has it that I have even
displayed some inconsistency myself.

>                                                       At the mind, or
>abstract level? Then our logic, our math, all human reasoning is worth
>nothing.

  Just because people are inconsistent and illogical, it does not follow
that they are incapable of producing consistent useful logical mathematics.

>:  (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).

  If you have not yet come across an inconsistent computer program, your
experience with programming must be quite limited :-(.

  More seriously, consider a program which uses a random number generator,
and initially seeds the random numbers from the system clock.  It will
produce different sequences of random numbers each time, so it is
inconsistent.

>: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"?

 I think you misread Minsky's implication.  His point was that computers
can do very informal things for which Goedel is irrelevant, just as people
can.  But when people work formally they are just as much limited by
Goedel as would a computer.

-- 
=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=
  Neil W. Rickert, Computer Science               <rickert@cs.niu.edu>
  Northern Illinois Univ.
  DeKalb, IL 60115                                   +1-815-753-6940


