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From: chalmers@bronze.ucs.indiana.edu (David Chalmers)
Newsgroups: comp.ai.philosophy
Subject: Re: Minds, machines, and Godel
Message-ID: <1991Jan29.234146.26158@bronze.ucs.indiana.edu>
Date: 29 Jan 91 23:41:46 GMT
References: <28203@cs.yale.edu> <1991Jan21.022919.13895@bronze.ucs.indiana.edu> <1991Jan29.211200.29482@uncecs.edu>
Organization: Indiana University, Bloomington
Lines: 35

In article <1991Jan29.211200.29482@uncecs.edu> james@uncecs.edu (J. Smith) writes:

>Would the argument make any claims regarding: "human capabilities
>differ from those of any given human being" or "the set of arithmetical
>statements encompassed by human competence includes statements that are
>outside the capacities of any given human being"?

No, it wouldn't.  The Godelian argument only applies to TM's, not humans,
so it would only yield such a conclusion if we beg the question and assume
that humans are TM's.

The given statements (particularly the second) might well be true, but only
because of "performance noise" in the capacities of a given human.  It's not
impossible from the standpoint of the argument that there could exist a human
without such performance limitations (except the trivial limitations like
death).  In any case, this empirical competence/performance distinction is
different in kind to the fundamental difference in capacities that the
argument purports to find between humans and TM's.

>Is there a notion of "TM capabilities" or "TM competence" we might
>contrast with any "given TM" in the same way?

That's an interesting question.  There are any number of different ways of
drawing competence/performance distinctions, depending on what we want to
idealize away from.  The question of whether the idealization preserves
the "essence" of a given capacity is a tricky one.  Presumably in the given
context, some such idealizations will sometimes be able to be drawn, just
as they can be from humans.  But I don't think that will affect the argument,
as the argument applies to a TM (the purported TM model of human competence)
for which all the relevant idealizations have already been made.

-- 
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."