Path: utzoo!utgpu!news-server.csri.toronto.edu!cs.utexas.edu!samsung!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: <1991Jan19.185303.25410@bronze.ucs.indiana.edu>
Date: 19 Jan 91 18:53:03 GMT
References: <1991Jan18.203249.7022@sics.se> <1991Jan18.223602.15474@bronze.ucs.indiana.edu> <1991Jan19.112854.28632@sics.se>
Organization: Indiana University, Bloomington
Lines: 53

In article <1991Jan19.112854.28632@sics.se> torkel@sics.se (Torkel Franzen) writes:

>  Just what do you mean by a refutation of the Lucas argument? What I
>mean by refuting the Lucas/Penrose argument is to establish that it is
>inconclusive.  I believe this is what is generally meant by refuting
>an argument. I am not concerned with either accepting or rejecting
>vague speculations about the possibility of our establishing that the
>human mind is simulated by some Turing machine. My argument is just
>this, that the Lucas/Penrose argument preupposes a claim for which no
>justification whatever has been presented, namely the claim that if
>the humanly provable statements of arithmetic are exactly the theorems
>of a formal system T, it must be possible for human beings to convince
>themselves of this fact.

The trouble with this refutation through inconclusiveness is that if it does
in fact turn out that we are able to discover enough about the human mind
(an empirical matter), then the Lucas argument applies as strongly as ever.
I'd prefer to find a refutation that isn't subject to such empirical
vagaries.  (Unless, in fact, you believe that the argument would be valid
given such an assumption.)

>  If we leave the Lucas/Penrose argument to one side and consider on
>its own merits the idea of simulating the mathematical activity of the
>human mind by a Turing machine or formal system, my general attitude
>is that there is no such thing as a well-defined "capacity of the
>human mind" for realizing mathematical truths or proving mathematical
>statements. The question of the possibility or impossibility of
>simulating the human mind by a Turing machine (in the sense and the
>area here at issue) is not an empirical question at all, but the
>outcome of a misunderstanding of or lack of attention to such concepts
>as mathematical provability and mathematical evidence.

Your first sentence is quite true, and that's why I've done it by stipulation.
Pick an army of mathematicians that I want to simulate, set them to work on
judging the truth of a statement, and when they've convinced themselves that
the statement is "certainly true" (by their own standards, but they must be
conservative standards), they lodge an offical judgment.  The TM that simulates
this process (and produces as final output their judgment) is the TM that is
being used.  [And I'm idealizing away from the possibility of mistakes,
somewhat controversially, as well as from factors like death and boredom,
I hope less controversially.]

As for simulating the mind by a TM not being an empirical question; I don't
see why.  I'm talking about a complete simulation of human action, not just
some ill-specified notion of "mathematical judgment".  Then *given* such
a simulation ability, we can produce simulation of some stipulated aspect of
mathematical judgment without difficulty, as outlined in the previous
paragraph.

-- 
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."