From newshub.ccs.yorku.ca!torn!cs.utexas.edu!sdd.hp.com!ux1.cso.uiuc.edu!usenet.ucs.indiana.edu!bronze.ucs.indiana.edu!chalmers Mon Oct 19 16:59:44 EDT 1992
Article 7323 of comp.ai.philosophy:
Newsgroups: comp.ai.philosophy
Path: newshub.ccs.yorku.ca!torn!cs.utexas.edu!sdd.hp.com!ux1.cso.uiuc.edu!usenet.ucs.indiana.edu!bronze.ucs.indiana.edu!chalmers
>From: chalmers@bronze.ucs.indiana.edu (David Chalmers)
Subject: Re: Human intelligence vs. Machine intelligence
Message-ID: <BwAHB0.7Ho@usenet.ucs.indiana.edu>
Sender: news@usenet.ucs.indiana.edu (USENET News System)
Nntp-Posting-Host: bronze.ucs.indiana.edu
Organization: Indiana University
References: <1992Oct15.185041.19681@oracorp.com>
Date: Sat, 17 Oct 1992 23:30:36 GMT
Lines: 58

In article <1992Oct15.185041.19681@oracorp.com> daryl@oracorp.com (Daryl McCullough) writes:

>Consider the following sentence G:
>
>    David Chalmers will never believe this sentence.

It seems to me that nothing you say rules out the possibility:

(1) I am sound (I never believe anything false);
(2) I know I am sound;
(3) I am not sure about G.

[In fact I think this may roughly describe the real situation, except
that I'm not of course perfectly sound, but I don't think that lack
of soundness or my knowledge thereof plays a role in my unsureness
about G.  For the purposes of this newsgroup, let's assume that
I'm perfectly sound and know it (so you can all go home now :-) ).]

Now, your argument says: well, you ought to be able to *infer* from
(1) and (2) that G is true.  But this is to ignore the fact that
I can equally well infer that G is false.  Faced with this situation,
I *could* drop my belief that I am sound, but I can equally well
retain them and simply be unsure about G and my epistemic relation
to it.

The point is that from my point of view, G is paradoxical.  It's like
the paradox of the unexpected hanging -- there's what appears to be
a sound argument that I will never be hanged, but there's also the
very clear possibility that I will be.  Faced with such a contradiction,
one doesn't just follow one sound side of the argument to its
conclusion, irrespective of the other side.  Rather one suspends
judgment, precisely because of the paradoxical conclusion, and hopes
that the problem will be resolved some other way, e.g. by uncovering
a subtle error in the processes of inference that led to the conclusions
in question.

Now, maybe this is a weak-kneed way of reasoning, but the point is
that it is a coherent way to be, and if it is indeed the way my
reasoning works, then there's nothing about this that contradicts
(1), (2), or (3).  Perhaps you might say that I *ought* to believe
G, but that is arguable at best, and in any case irrelevant.  The
fact is, I'm just very confused about G -- maybe I believe it,
maybe I don't, maybe it's meaningless, I'm not sure.  So I may be
an incomplete system, but I'm not an unsound one.

In any case this example is somewhat off the point, as I intended
my original claim to be that a system could be entirely sound
*in its arithmetical competence* and could know it.  Sentence G
here doesn't have anything to do with arithmetic, so doesn't
bear on this.  But I recall you had a formalization of this
argument that showed that even the claim about arithmetical
competence led to a contradiction.  I don't recall the details
perfectly, so maybe you could give them.

-- 
Dave Chalmers                            (dave@cogsci.indiana.edu)      
Center for Research on Concepts and Cognition, Indiana University.
"It is not the least charm of a theory that it is refutable."


