From newshub.ccs.yorku.ca!torn!cs.utexas.edu!sdd.hp.com!zaphod.mps.ohio-state.edu!rpi!psinntp!psinntp!scylla!daryl Fri Oct 30 15:17:32 EST 1992
Article 7389 of comp.ai.philosophy:
Newsgroups: comp.ai.philosophy
Path: newshub.ccs.yorku.ca!torn!cs.utexas.edu!sdd.hp.com!zaphod.mps.ohio-state.edu!rpi!psinntp!psinntp!scylla!daryl
>From: daryl@oracorp.com (Daryl McCullough)
Subject: Re: Human intelligence vs. Machine intelligence
Message-ID: <1992Oct24.144617.20159@oracorp.com>
Organization: ORA Corporation
Date: Sat, 24 Oct 1992 14:46:17 GMT
Lines: 69

In article <1992Oct15.185041.19681@oracorp.com>,
system@CODEWKS.nacjack.gen.nz (Wayne McDougall) writes:

>> Consider the following sentence G:
>> 
>>     David Chalmers will never believe this sentence.
>> 
>
>While it is clear enough what the sentence means, it is still a 
>meta-reference, and IMO your little trick with the email message still 
>leaves it a meta-reference (a sentence talking about a sentence). For 
>that reason, I personally, don't find your argument persuasive, or 
>valid.

I think you are wrong. G is not a meta-statement at all. It is a
statement about the relationship between David Chalmers' brain and the
string of symbols "David Chalmers will never believe this statement."

In what follows, I try to make it more obvious that G is *not* a
meta-statement (or need not be). It is much more tedious if you have
to be precise, but it has the same conclusion.

First, let's get away from talk about statements (which makes people
use words like "meta-reference") and stick to a discussion of strings
of words. We will say that David Chalmers believes a certain string of
words if his brain is in such a state that he eventually will come to
the conclusion that, yes, that string of words has meaning (to David
Chalmers) and yes, that meaning is something that he thinks is true
about the world. Clear enough? To say David Chalmers believes X is
simply a statement about what is going on inside David Chalmers'
brain, and X is simply a string of words (which we can sometimes
interpret to be a statement).

Now, let me define an operation on strings of words called
diagonalization. Essentially, when you diagonalize a string of words,
you search for any occurrence of the words "this sentence"
and replace them by the entire string of words, enclosed by quotes.
Notice that diagonalization takes a self-referential sentence, and
returns a sentence that is *not* self-referential. For example:
diagonalizing `This sentence is six words long' gives you ``This
sentence is six words long' is six words long'. The first sentence
seems to be talking about itself, while the second is talking about
the string of words `This sentence is six words long'.

Okay, now consider a self-referential sentence G0: `Diagonalizing this
sentence produces a string of words that will never be believed by
David Chalmers'. If we diagonalize G0 we get the following long and
complicated sentence (call it 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.'

Now what exactly does G say? Well, it says that a certain string of
will never be believed by David Chalmers. So G is no meta-statement,
it is simply a statement about strings of words and David Chalmers
beliefs. However, let's find out exactly what string of words G is
claiming that David Chalmers will never believe. Well, it is the
diagonalization of `Diagonalizing this sentence produces a string of
words that will never be believed by David Chalmers.', which is just
G0. Therefore G is saying that David Chalmers will never believe the
diagonalization of G0. However, G *is* the diagonalization of G0!
Therefore, G, which is no meta-statement, but is simply a statement
about brains and strings, nevertheless implies that G will never be
believed by David Chalmers.

Daryl McCullough
ORA Corp.
Ithaca, NY


