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From: erwin@trwacs.UUCP (Harry Erwin)
Newsgroups: comp.ai.philosophy
Subject: Re: how many distinct thoughts can a person have?
Message-ID: <315@trwacs.UUCP>
Date: 20 Jun 91 19:46:32 GMT
References: <1991Jun19.033316.18773@athena.mit.edu> <314@trwacs.UUCP> <1991Jun19.232912.17871@cs.ubc.ca>
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alphonce@cs.ubc.ca (Carl Alphonce) writes:

. . . . 
>> The number of distinct human thoughts isn't even countably infinite
>>in a quantum-mechanical universe, let alone uncountable. However,
>>if we ignore that argument, the question boils down to whether the
>>state of the brain is sensitively dependent to its state on a
>>cauchy surface. I believe Paul Rapp has evidence that it is. So,
>>although the number isn't infinite, it looks like it's uncountable.
                                         -----
>>
>>-- 
>>Harry Erwin
>>Internet: erwin@trwacs.fp.trw.com

>A minor point: if something is uncountable, it is infinite.  In fact,

>    finite < countable (countable infinite) < uncountable (uncoutably infinite)

>at least as far as I can recall from my logic / set theory courses.

You're correct, which is why I said "it looks like it's uncountable."
There is some very recent work that indicates you can simulate chaos
satisfactorily with a 16-bit word size. For all practical purposes,
there are an uncountable number of thoughts, but if you look at it
carefully, there are probably only a finite (but very large) number.

-- 
Harry Erwin
Internet: erwin@trwacs.fp.trw.com