From newshub.ccs.yorku.ca!torn!cs.utexas.edu!uunet!secapl!Cookie!frank Tue Nov 24 10:51:55 EST 1992
Article 7627 of comp.ai.philosophy:
Newsgroups: comp.ai.philosophy
Path: newshub.ccs.yorku.ca!torn!cs.utexas.edu!uunet!secapl!Cookie!frank
>From: frank@Cookie.secapl.com (Frank Adams)
Subject: Re: Human intelligence vs. Machine intelligence
Message-ID: <1992Nov12.212403.32326@Cookie.secapl.com>
Date: Thu, 12 Nov 1992 21:24:03 GMT
References: <1992Nov11.140249.22979@oracorp.com>
Organization: Security APL, Inc.
Lines: 50

In article <1992Nov11.140249.22979@oracorp.com> daryl@oracorp.com (Daryl McCullough) writes:
>In article <1992Nov10.025040.117799@Cookie.secapl.com>,
>frank@Cookie.secapl.com (Frank Adams) writes:
>
>Statement G:
>
>     `Diagonalizing `Diagonalizing this sentence produces a string of words
>      that will never be believed by David Chalmers.' produces a
>      string of words that will never be believed by David Chalmers.'

By the way, this statement as is can easily be falsified by David Chalmers.
All he has to do is believe *once* -- thereafter he, and everybody else, can
consistently recognize it as false.

>>And as a statement, G is self-referential in an unacceptable way.  Consider
>>sentence H:
>>
>>`Diagonalizing `Diagonalizing this sentence produces a string of words which
>>is false when interpreted as a statement.' produces a string of words which
>>is false when interpreted as a statement.'
>>
>>If we can interpret G as a statement, we can interpret H likewise; but this
>>produces a flat-out contradiction.  Thus it is *not* legitimate to interpret
>>G as a statement, however clear its meaning may seem.
>
>I disagree. The problem with statement H is *not* its self-reference.
>G and H both have the same form, roughly:
>
>     G <-> not(G in B)
>     H <-> not(H in T)
>
>where B is the set of believed sentences, and T is the set of true
>sentences. The problem is *not* that G or H is self-referential, it is
>the fact that there is no consistent notion of the set of all true
>sentences. As a matter of fact, your sentence H shows that there can
>be no such set.

Wait a minute!  Where did these sets come from?  I didn't commit myself to
the existence of any particular sets.

Even so, you have done nothing to argue that there *is* a set of believed
sentences -- you have just failed to derive a contradiction from the
assumption that there is.

Note the contrast with provability for a formal system.  G"odel's sentence
can be shown to be equivalent to provability in the formal system.  By
contrast, you are blandly asserting the right to do so with the word
"believe".

I still believe that sentences like G are invalid.


