From: frank@Cookie.secapl.com (Frank Adams)
Subject: Re: Human intelligence vs. Machine intelligence
Date: Mon, 16 Nov 1992 23:20:11 GMT
Organization: Security APL, Inc.

In article <1992Nov14.134537.2170@oracorp.com> daryl@oracorp.com (Daryl McCullough) writes:
>In article <1992Nov12.212403.32326@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.
>
>Exactly. G is true if and only if David Chalmers does not believe G.
>If David Chalmers *does* believe G, then G is false (and David
>Chalmers happens to believe a manifestly false statement).
>
>The fact that G *can* meaningfully be false shows that G is not a
>paradoxical statement. And it can meaningfully be true, as well.
>It all depends on whether David Chalmers' beliefs are consistent.

You missed my point -- I was complaining about your wording.  Specifically,
the phrase "will never be believed".  Mr. Chalmers need only only believe
G momentarily in order thereafter to have a consisent view of its truth.
But this is all by the way, since I think G is NOT meaningful.

>>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 didn't blandly assert it. I constructed the sentence G so that it
>has this property. If you would read Godel's proof, you will find the
>construction almost identical; the only differences are (1) instead of
>the predicate "is believable", he uses the predicate "is provable" (2)
>instead of coding statements by strings, he codes them by numbers.

I am quite familiar with G"odel's proof; also the relevant paper by
Smullyan.  The point is that in G"odel's proof, he can construct the whole
machinery formally, and then put the interpretation on it.  Although you
claim to have done this, you have failed (IMO).

>>I still believe that sentences like G are invalid.
>
>Invalid in what sense? Is the notion of diagonalizing a string
>invalid? Is the notion of David Chalmers believing something invalid?
>G is a simple combination of these two notions.

The notion of David Chalmers believing something is only valid if the
*something* is meaningful.  Does he "believe" or "disbelieve" the sun?

When you try to understand what G means, by interpreting the "diagonalizing"
operator, you get an infinite regress (in fact, a simple self-reference, but
it is not difficult to construct examples using diagonalization where the
references are not self-referential, but do produce an infinite regress).

Note that "This sentence has six words." has a different status, because its
correctness does not involve a recursive reference to its meaning.
Newsgroups: comp.ai.philosophy,sci.logic