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From: throopw@rtp47.UUCP (Wayne Throop)
Newsgroups: net.philosophy
Subject: Godel and Turing
Message-ID: <222@rtp47.UUCP>
Date: Thu, 17-Oct-85 17:32:51 EDT
Article-I.D.: rtp47.222
Posted: Thu Oct 17 17:32:51 1985
Date-Received: Sun, 20-Oct-85 05:55:03 EDT
References: <1949@aecom.UUCP> <10675@ucbvax.ARPA>
Organization: Data General, RTP, NC
Lines: 49

> I claim that if we make the consistency assumption, and assume
> that the mind is equivalent to a Turing machine, we get a
> contradiction in that there are true statements recognizable
> by the mind which are not recognizable by the machine.
> Maybe I'm wrong but if I am I hope someone can explain to
> me why I am wrong.
>                       -Tom    tedrick@ucbernie.ARPA

I can see three ways out of the dilemma.  I've mentioned them before,
implicitly, but I'll try to make them more explicit, and state exactly
why each scenario is an escape from contradiction.

One is to note that "Turing machines" need not implement consistant
formal systems, thus contradicting one of the assumptions.  This is the
position that minds are not consistant, thus Godel's theorem doesn't
apply.

Another is to note that (if minds are consistant) Godel's theorem
applies to the entire simulation, including the underlying Turing
machine.  That is, assuming that "the mind" is a consistant formal
system, there will be statements that the particular mind in question
cannot recognize as true, but which indeed are true.  The fact that some
other mind can see the truth of these statements is irrelevant.  The
fact that "the mind" is "running on" a Turing machine rather than on a
"neural network" is likewise irrelevant.  This is the position that the
Turing simulation is not subject to scrutiny by the mind it is
simulating... that they are one and the same thing.

Yet another is to note that human minds have finite capacity.  Assume
that the Turing simulation is a formal system subject to scrutiny by the
mind it is simulating.  Nevertheless, it might be far beyond the
capacity of that mind to discover the Godel sentence of the formal
system upon which it is simulated.


All of these call into question the claim that "there are true
statements recognizable by the mind which are not recognizable by the
machine." The first says that the conditions under which this is true
are not met.  The second says that there is no seperate "machine" and
"mind" such that one can do something the other cannot.  And the third
says that the capacity of the simulated mind will simply be limited by
the complexity of the formal system.

I'm rather partial to the first refutation myself.  The examples of
"minds" that I've seen don't seem very consistant to me.  (And, alas,
the "Turing machine" I'm writing this note on seems inconsistant all too
often... :-)
-- 
Wayne Throop at Data General, RTP, NC
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