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From: chalmers@bronze.ucs.indiana.edu (David Chalmers)
Newsgroups: comp.ai.philosophy
Subject: Re: Minds, machines, and Godel
Message-ID: <1991Jan18.223602.15474@bronze.ucs.indiana.edu>
Date: 18 Jan 91 22:36:02 GMT
References: <1991Jan18.083759.19131@sics.se> <1991Jan18.191303.6840@bronze.ucs.indiana.edu> <1991Jan18.203249.7022@sics.se>
Organization: Indiana University, Bloomington
Lines: 46

In article <1991Jan18.203249.7022@sics.se> torkel@sics.se (Torkel Franzen) writes:

>  I claim nothing concerning what we can or cannot necessarily discover.
>To refute your argument I need merely show that it is inconclusive. You
>still have said nothing to substantiate the claim that if ZFC+UM codifies
>the humanly provable arithmetical statements, we must be able to convince
>ourselves of this. Vague (or rather vacuous) appeals to "the wonders of
>cognitive science" carry no more weight than a bald claim that humans
>can establish the truth of any true arithmetical statement.

It's a fairly subtle point.  I have no idea whether or not we will
someday be able to discover enough about the mind to build a TM that
accurately simulates it.  But the point is that I don't think you want
the refutation of the Lucas argument to rest solely on the claim that we
cannot.  Do you think that if in fact we could discover the structure of the
mind in this way, the Lucas argument would hold?  It seems tenuous to base
the refutation on such a fragile empirical matter.

As with inconsistency, I think there is something more clearcut going wrong.
Say we assume that we could in fact discover empirically what TM we "are".
Would the Lucas argument then apply, giving a reductio?  I don't think so.

So, I've made so far a number of idealizations, all of which could be subject 
to dispute:

(1) Humans are consistent.
(2) Humans know they are consistent.
(3) Humans are capable of empirically discovering enough about the mind so
    that if they in fact are simulable by a TM, they will know that a given
    TM simulates them.

A reply to the argument could be based on denying the possibility of any of
these idealizations.  Minsky's response is based on the denial of the
possibility of the idealization to (1).  Your response above appears to be
based on the denial of the possibility of the idealization to (3).  I
believe that these replies miss the point, as they're based more on
empirical matters than the logical heart of the Lucas argument.

In fact I believe that even if we accept idealizations (1), (2) and (3)
we can still refute the Lucas argument, in a very clearcut fashion.
Want to have a go?

-- 
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."