Path: utzoo!utgpu!news-server.csri.toronto.edu!bonnie.concordia.ca!uunet!spool2.mu.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: <1991Jan18.191303.6840@bronze.ucs.indiana.edu>
Date: 18 Jan 91 19:13:03 GMT
References: <1991Jan16.182120.20961@sics.se> <1991Jan18.012527.20104@news.cs.indiana.edu> <1991Jan18.083759.19131@sics.se>
Organization: Indiana University, Bloomington
Lines: 44

In article <1991Jan18.083759.19131@sics.se> torkel@sics.se (Torkel Franzen) writes:

>  In spite of your later remarks I fail to see that you have in any way
>substantiated the claim that we are not Turing machines. You are postulating
>that if the arithmetical theorems provable by by us are exactly those
>of a theory T, then we must be able to recognize that "we are that machine"
>and therefore T is consistent. Exactly what you mean by this is unclear,
>but you have given no justification for it.

This is now getting very close to the bone.  Judgment of the truth of the
Godel sentence is parasitical on a judgment of consistency, which in turn
is parasitical on our knowledge that the TM in question is in fact an accurate
simulation of us.  Now, I don't know in practice whether we can know whether a
given TM is an accurate simulation of us or not, but it doesn't seem an
unreasonable claim, with the wonders of cognitive science and neurophysiology.
Importantly, to use this as your refutation of the argument, it is you who
have to make the strong claim (a la Benacerraf) that we necessarily cannot
discover the TM that we are (or more precisely, a TM that accurately
simulates us).  I don't see any independently-supported reason for such a
claim, although it's certainly a logical possibility.

This is a bit like the inconsistency counter.  If we in fact couldn't
discover what TM we are, then the argument wouldn't apply, but on the
face of it it seems to be a bit too much of an easy way out.

>  Suppose I claim that the arithmetical theorems provable by human beings
>are precisely those of ZFC+'there is an uncountable measurable cardinal'
>(even if we have so far only managed to arrive at the truth of a tiny
>fraction of this wealth of arithmetic). How do you propose to use Godel's
>theorem to refute this claim?

Well, the form of the argument is a reductio.  If you did this, and you
provided convincing evidence for this claim, and I had good reason to
believe that I was consistent (the role of the last two assumptions has been
gone over in this and the previous posts), then I could then assert the
statement "ZFC+UM is consistent", and its arithmetical analog (or
alternatively, I could assert the Godel sentence of the theory).  I would
thus have asserted a statement outside the bounds of the theory.  
Contradiction.

-- 
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."