Newsgroups: comp.ai.philosophy
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From: alphonce@cs.ubc.ca (Carl Alphonce)
Subject: Re: how many distinct thoughts can a person have?
Message-ID: <1991Jun19.232912.17871@cs.ubc.ca>
Sender: usenet@cs.ubc.ca (Usenet News)
Organization: UBC Department of Computer Science, Vancouver, B.C., Canada
References: <1991Jun19.033316.18773@athena.mit.edu> <314@trwacs.UUCP>
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Date: Wed, 19 Jun 91 23:29:12 GMT

In article <314@trwacs.UUCP> erwin@trwacs.UUCP (Harry Erwin) writes:
>mlevin@jade.tufts.edu writes:
>
>
>>   I was just reading Z. Pylyshin's "Computation and Cognition", and
>>at one point, he states something like: "the number of distinct human
>>thoughts is uncountable." Does anyone have any arguments for or
>>against the idea that the number of possible distinct human thoughts
>>(or mental states) is uncountably infinite? Note I do not mean
>>"astronomicallly large" - I mean infinite (and perhaps uncountably so)
>>in the strict mathematical sense. It seems plausible to me; does
>>anyone have a good argument either way?
>
>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.