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From: chalmers@bronze.ucs.indiana.edu (David Chalmers)
Newsgroups: comp.ai.philosophy
Subject: Re: Minds, machines, and Godel
Message-ID: <1991Jan18.180455.3268@bronze.ucs.indiana.edu>
Date: 18 Jan 91 18:04:55 GMT
References: <91Jan16.135532edt.1132@neuron.ai.toronto.edu> <1991Jan17.040803.8205@bronze.ucs.indiana.edu> <3857@aipna.ed.ac.uk>
Organization: Indiana University, Bloomington
Lines: 25

In article <3857@aipna.ed.ac.uk> cam@aipna.ed.ac.uk (Chris Malcolm) writes:

>Only if you have decided to limit your TM, as others have pointed out,
>to working exclusively from one set of axioms, and to being consistent.
>But even if you do decide to limit your TM in this way, all your
>argument claims is that people can't be such machines -- and who ever
>proposed that they might be?

All I need is the assumption that humans are computationally simulable
(and, as I've said a couple of times, the perhaps disputable idealization
to consistency).  The computational foundation of the TM that simulates a
human mathematician will probably look nothing like any normal axiomatic
system.  Perhaps e.g. it will involve the computations of a simulated
neural network.  Various mathematical axiomatic systems that the human
may be consciously using at a higher level (e.g. ZFC & Principia Mathematica)
may well be only a very small part of the story.  If we have a perfect
computational simulation of the human, then the ability to "change" such
higher-level axiomatic systems will come along as part of the package.
But it's still a TM (flexible, universal, or not), and so the argument
applies.

-- 
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."