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Article 7611 of comp.ai.philosophy:
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>From: daryl@oracorp.com (Daryl McCullough)
Subject: Re: Human intelligence vs. Machine intelligence
Message-ID: <1992Nov11.140249.22979@oracorp.com>
Organization: ORA Corporation
Date: Wed, 11 Nov 1992 14:02:49 GMT
Lines: 42

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.'

>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.

However, given that there is a set A of strings, there is no problem
with the existence of a self-referential sentence G such that
   G <-> The string expressing G is in A

Daryl McCullough
ORA Corp.
Ithaca, NY





