Path: utzoo!utgpu!news-server.csri.toronto.edu!cs.utexas.edu!usc!zaphod.mps.ohio-state.edu!sol.ctr.columbia.edu!bronze!chalmers
From: chalmers@bronze.ucs.indiana.edu (David Chalmers)
Newsgroups: comp.ai.philosophy
Subject: Re: Minds, machines, and Godel
Message-ID: <1991Jan19.045559.25936@bronze.ucs.indiana.edu>
Date: 19 Jan 91 04:55:59 GMT
References: <1991Jan18.203249.7022@sics.se> <1991Jan18.223602.15474@bronze.ucs.indiana.edu> <14733@milton.u.washington.edu>
Organization: Indiana University, Bloomington
Lines: 64

In article <14733@milton.u.washington.edu> forbis@milton.u.washington.edu (Gary Forbis) writes:

>[Idealizations:]
>(1) I am consistent.
>(2) I know I am consistent.
>(3) I am capable of empirically discovering enough about my mind that I can
>    tell when a given TM simulates me.
>
>If I understand your argument correctly you want to hold these to be true when
>you have already argued they cannot all be true.  I think you have also made
>another idealization.  That is (4) The individual and the collective are 
>arbitrary.

Actually, the argument claimed not that (1)-(3) are inconsistent, but rather
that they are not consistent with the fact that I am a TM.  (NB Certain
other background assumptions are also needed, esp the fact that I have at
least a basic arithmetical ability.  I hope this isn't controversial :-). )

Those who base their counter to the Lucas argument on the fact that one of
(1)-(3) is fundamentally false would appear to accept that argument.
(Indeed, Minsky appears to claim that the Lucas/Godel argument shows that
consistent systems are fundamentally limited in a way that we are not.)
I think that this is far too much of a concession to Lucas, however.

>without affecting the consistancy of the set.  This being so, I can imagine
>another individual who is consistant, knows he or she is consistant, and know
>the TM that simulates him or her.  When the two of us are considered together
>we may no longer be consistent.  The difference between the individual and
>the collective is not arbitrary.

True.  Doesn't matter.  I'll decide in advance what it is that I want to
simulate, whether it's a single mathematician or an army of them.  Preferably
the latter.  They'll work on judging truth for an indefinite period of time,
until they come to a joint, carefully-considered decision.  Individual
mathematicians may at first have differences, but we assume that the process
will eventually settle them.  Statements of number theory (unlike those of
set theory) don't seem to cause radical differences in standards of
justification, presumably because mathematicians share a set of common
intuitions about the integers.  There might still be a minute amount of
random noise in this system causing mistakes, but this is what I'm prepared
to idealize away from

>I am not the same TM I was a moment ago.  The difference between the TMs at
>any two moments is chaotic or random.

If you're making an appeal to low-level chaos, I'm idealizing away from that
too.  (I wish I was Noam Chomsky so I could make these idealizations
with a straight face.  They always seem to bring on this feeling of
defensiveness.  I don't know how he does it.)  I think it's fairly widely
accepted that chaos doesn't give us any extra capacities that a simulation at
a very fine but discrete level wouldn't have.  (Because of chaos, such
a simulation gives you a way that the system could have gone, rather than
the way that in fact does go on a particular occasion.  No difference
in competence.)  As with consistency but more clearly, I don't think you
want to base an argument against Lucas solely on chaos.

(Actually, your argument from chaos might be construed as an argument *for*
Lucas, saying "Hey, we're really not TM simulable after all.  So Lucas was
right.")

-- 
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."