Newsgroups: comp.ai.philosophy
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From: dirish@csc-sun.math.utah.edu (Dudley Irish)
Subject: Re: how many distinct thoughts can a person have?
In-Reply-To: thomas@ckgp.UUCP's message of 20 Jun 91 23:28:54 GMT
Message-ID: <DIRISH.91Jun21074138@csc-sun.math.utah.edu>
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Organization: Department of Mathematics, University of Utah
References: <1991Jun19.033316.18773@athena.mit.edu>
	<1991Jun19.195149.19583@panix.uucp> <607@ckgp.UUCP>
Distribution: usa
Date: 21 Jun 91 07:41:38

I am sure that that you have all heard the old saw, "You can never
step into the same river twice."  I would similarly argue that you can
never have the same thought twice.  Thus, for as long as you live you
are constantly having different thoughts.  There are two questions
here.  First, does this sequence map to the integers or to the real
numbers, in other words, is the sequence of brain states countably
infinite or uncountably infinite.  The other question is whether
because people only live a finite time we want to accept that the
sequence of thoughts has an end or whether we want to take a
theoretical stance where we don't view the sequence as ending.

Now, be careful.  Remember the number of real numbers from zero to one
is uncountably infinite.  If you believe that thoughts map to the
real numbers rather than the integers this still leaves you with an
uncountable number of thoughts.  Also, the number of rational numbers
from zero to one is countably infinite.  Thus if between every pair of
thoughts there is another thought, then even if we take the sequence
as ending, it still is countably infinite.

So you simply must decide whether thoughts are continuous or not.  I
don't have a clue as to how to decide this issue.

Now, before you think to flame me for a screwup in my understanding of
cardinal number theory, I will warn you that my favorite mathematics
professor taught a set theory class two quarters ago that I sat in on.
I seriously believe that I remember all this stuff correctly.  Though
what it has to do with AI, I don't know.

--
Dudley Irish / dirish@math.utah.edu / Manager Computer Operations
Center for Scientific Computing, Dept of Mathematics, University of Utah

The views expressed in this message do not reflect the views of the
Dept of Mathematics, the University of Utah, or the State of Utah.
