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From: throopw@rtp47.UUCP (Wayne Throop)
Newsgroups: net.philosophy
Subject: Godel and Turing
Message-ID: <220@rtp47.UUCP>
Date: Tue, 15-Oct-85 23:12:13 EDT
Article-I.D.: rtp47.220
Posted: Tue Oct 15 23:12:13 1985
Date-Received: Sat, 19-Oct-85 07:40:00 EDT
References: <10642@ucbvax.ARPA>
Organization: Data General, RTP, NC
Lines: 41

> My understanding is that Godel's incompleteness theorems prove
> (assuming the consistency of Arithmetic) that no Turing machine
> can possibly simulate the human mind.
>
> This is because for any particular Turing machine there are certain
> statements that the human mind can recognize as true (again with
> the consistency assumption), that the machine cannot recognize
> as true.
>
> Does anyone dispute this?
>
>   tedrick@ucbernie.ARPA

I do.  For several reasons.

First, there is no reason for the simulation to be consistant.  Unless
the claim is made that Humans are consistant, which I find hard to
beleive.

Second, assuming that physical laws are consistant (in about the same
way that formal systems are consistant), there is reason to think that
Humans are "simulated" or "implemented" using consistant, formal,
physical laws.  Thus, Humans are arguably *already* implemented in
a "consistant formal system", so I see no reason that they couldn't
be simulated to any degree of accuracy you please in another formal
system.

Thirdly, there is no particular reason to beleive that there is no
"Godel Sentence" for Humanity, such that no human (or perhaps some humans)
cannot "see it to be true", that some other being *can* so see it.

I also note in passing (as I understand things) that nobody has ever
actually found a Godel sentence for the formal system of "mathematics"
or "logic".  It has simply been proven that such sentences exist.
So the claim that "there are certain statements that the human mind
can recognize as true [that a machine cannot]" is quite suspect.
In fact, I suspect that no unaided human could find a Godel sentence
for even the most limited and basic (but serious) attempt at
"artificial intelligence".
-- 
Wayne Throop at Data General, RTP, NC
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