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From: ricker@bunker.UUCP (James A. Ricker)
Newsgroups: net.ai,net.philosophy
Subject: Re: A halting problem
Message-ID: <1084@bunker.UUCP>
Date: Mon, 13-Jan-86 13:09:51 EST
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Posted: Mon Jan 13 13:09:51 1986
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> 
> 	There exists a proof that a computer procedure cannot be written
> such that given a procedure as input, it can tell you if that procedure
> contains an infinite loop. 
...
> For, if such a procedure existed, we
> could set up a paradox:
> 	PROCEDURE PARADOX:
> 		IF HALT(PARADOX) THEN PARADOX

Yes, I can agree so far.

> 
> 	The human mind, on the other hand, given enough time an
> practice, can find an endless loop in any procedure. (You doubt this?)

I don't doubt this. I think it's important that the "time and practice" clause
be accented.

> 
> 	This would mean that there is a set of problems no procedure
> can ever do, yet the human mind does.  The root of them is at the fact
> that the human brain has meta-cognizance (I can realize, "Hey! This
> loop is taking me no-where.") Or, that the root of intelligence
> can not be duplicated by machine.
 
Hold it right there! (Now hold it over here.) If you are going to restrict
the machine to a sequential processing architecture, of course the machine
will not be able to perform the task as well as a human mind. However, what
evidence is there that a machine with real-time multiprocessing and/or parallel processing capabilities is incapable of detecting an endless loop? Moreover,
as another person has already pointed out in a previous article
(using an example in C), if the procedure detecting the endless loop is not
the same procedure executing the endless loop, the endless loop is detectable. 

I don't know exactly how our minds do this "stepping back" from the problem.
My hunch is that you are correct about the importance of meta-cognizance.

What do you think of this reasoning?

1) You are capable of detecting an endless loop in a procedure which contains
   an endless loop.

2) You are capable of communicating your proof to me (through the use of
   symbols) that the endless loop exist.

3) Why can't it be possible to program your proof?

                                   Ricker
                                   in Connecticut