From newshub.ccs.yorku.ca!torn!utcsri!rpi!psinntp!psinntp!scylla!daryl Tue Nov 24 10:50:59 EST 1992
Article 7552 of comp.ai.philosophy:
Newsgroups: comp.ai.philosophy
Path: newshub.ccs.yorku.ca!torn!utcsri!rpi!psinntp!psinntp!scylla!daryl
>From: daryl@oracorp.com (Daryl McCullough)
Subject: Re: Human intelligence vs. Machine intelligence
Message-ID: <1992Nov9.165212.470@oracorp.com>
Organization: ORA Corporation
Date: Mon, 9 Nov 1992 16:52:12 GMT

A little bit of background to this silly little thread. I claimed that
there was a sentence G such that, assuming David Chalmers beliefs are
deductively closed (that means that he believes any statement that is
a consequence of his other beliefs), then the following equivalences
hold:

     G is true
     <-> David Chalmers' beliefs are consistent
     <-> David Chalmers never comes to believe G


In article <aV0TTB3w165w@CODEWKS.nacjack.gen.nz>,
system@CODEWKS.nacjack.gen.nz (Wayne McDougall) writes:

>> If it turns out that the reason David Chalmers doesn't believe G is
>> because he thinks G is a meaningless, self-referential sentence, fine.
>> That's just one way to not believe something, and any way is good enough
>> for G to be true.
>> 
>But surely now we are back to a paradox? Unless you are trying to 
>separate "believing" from "co-incidentally agreeing with". If David 
>Chalmers doesn't believe it because it is self-referential, than David 
>Chalmers is agreeing with it (ie he doesn't believe the sentence). 
>Surely if he agree with it, he believes it? But then he isn't agreeing 
>with it?

Notice that G is true if and only if David Chalmers *never* comes to
believe G. The fact that David Chalmers doesn't believe G now does not
imply that he will never come to believe G. Therefore, he cannot
conclude that G is true from the fact that he doesn't *currently*
believe G. There is no paradox.

However, a second implication is that if David Chalmers actually
believes that he is consistent, then either he is mistaken (his
beliefs are inconsistent), or his beliefs are not deductively closed.

Proof:

Under the assumption that David Chalmers' beliefs are deductively
closed, G is true if and only if David Chalmers is consistent.
Therefore, if David Chalmers believes that he is consistent, then he
must believe G. (It is a consequence of his belief that he is
consistent.) But G is true if and only if David Chalmers does not
believe G. So G must be false. But G is true if and only if David
Chalmers is consistent, so if G is false, then David Chalmers is
inconsistent. Therefore, if David Chalmers' beliefs are deductively
closed, and he believes that he is consistent, then he is not
consistent.

So if David Chalmers believes that he is consistent, then either he is
mistaken, or his beliefs are not deductively closed. I think the
latter, because he believes that he is consistent, and he doesn't
believe G (although G is a consequence of his belief that he is
consistent).

Daryl McCullough
ORA Corp.
Ithaca, NY




