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From: lambert@boring.UUCP
Newsgroups: net.philosophy,net.math
Subject: Re: Sc--nce Attack (self-awareness)
Message-ID: <6657@boring.UUCP>
Date: Thu, 17-Oct-85 22:45:48 EDT
Article-I.D.: boring.6657
Posted: Thu Oct 17 22:45:48 1985
Date-Received: Sun, 20-Oct-85 06:20:10 EDT
References: <45200016@hpfcms.UUCP> <1605@pyuxd.UUCP>
Reply-To: lambert@boring.UUCP (Lambert Meertens)
Organization: CWI, Amsterdam
Lines: 91
Keywords: Turing machines vs. the mind
Xref: watmath net.philosophy:2888 net.math:2393
Apparently-To: rnews@mcvax.LOCAL

(I have missed most of the discussion, since American net philosophy does
not make it to this side of the Atlantic.)

> I don't understand your argument. I claim that the human mind
> cannot be essentially a turing machine. If we assume that a
> partcular mind is equivalant to a particular turing machine,
> then we immediately get a contradiction, namely there exists
> a statement recognizable as true by that human mind which is
> not recognizable as true by that turing machine.

> Can anyone explain to me what if anything is wrong with my
> reasoning?

The following attempt uses a device that is, unless I am mistaken, due to
Quine.

Consider texts (some of which represent statements, such as: "Two times two
equals four" and "`Two times two equals four' is a true statement about
natural numbers", and some of which do not, like "Who? Me?"  and "Don't
`Aw, mom' me".).  Some of these texts contain *internal* quoted texts.  If
T is a text, then let Q(T), or, in words, T *quoted*, stand for another
text, consisting of T put between the quotes "`" and "'". So if T is

    "Two times two equals for",

Q(T) is

    "`Two times two equals for'".

Let SQ(T), or T *self*quoted, mean: Q(T) followed by T.

So if T is

    " contains no digits"

then T, selfquoted, is

    "` contains no digits' contains no digits"

(which is a true statement).

Now consider the text S =

    "`, selfquoted, is not recognizable as true by the mind of Tom',
     selfquoted, is not recognizable as true by the mind of Tom".

S is a statement, and states that some text T, selfquoted, is not
recognizable as true by the mind of Tom.

So can Tom (or his mind) recognize SQ(T) as true, and is SQ(T) true in the
first place?

If Tom can recognize SQ(T) as true, then S is apparently false.  But note
that T is the text

    ", selfquoted, is not recognizable as true by the mind of Tom",

so SQ(T) = S.  So Tom would have recognized a false statement as true.  If
we collectively assume that Tom would never do such a thing, then all of us
non-Toms can now recognize S as true, something Tom can not.

If "Tom" is consistently replaced by "human being", then the argument still
goes through.  Neither I, nor you, or anyone else, can recognize that
statement as true without showing its falsehood (and human fallibility).
We would have to wait for some non-human intelligence telling us it is
true, but although we might believe it, we still could not recognize it as
being true.  (Now we might think that it is false, which may or may not be
quite true, but than it follows again that not all humans can be
infallible.)

This may all seem shallow.  But for me (to take an arbitrary example:-) to
assert that the mind of a fellow human being can recognize something as
true, with the same level of certainty as in mathematical proofs, requires
a rather total understanding of that mind, that, at least for me, is still
lacking.  More so, if I would also have to recognize the infallibility of
that mind (which is all the time an implicit argument).  With my own mind,
I thus far have not succeeded.  I guess it is the same for other people.

What the original reasoning really shows is that if we would, somehow,
construct a Turing-machine description of the workings of our own mind, we
could not with mathematical certainty recognize it as being that.  Neither
can a Turing machine do this for its own construction, or if it can, then
it is either fallible or has glaring defects in its logical power.  Applied
to human beings, the conclusion is not a big surprise.  It does not follow
that human minds are not Turing machines (although their memory tapes seem
not to be infinite:-).
-- 

     Lambert Meertens
     ...!{seismo,okstate,garfield,decvax,philabs}!lambert@mcvax.UUCP
     CWI (Centre for Mathematics and Computer Science), Amsterdam