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Article 5677 of comp.ai.philosophy:
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>From: alliot@cenatls.cena.dgac.fr (Jean-Marc Alliot)
Newsgroups: comp.ai.philosophy
Subject: Re: penrose
Message-ID: <1992May15.100034.20472@cenatls.cena.dgac.fr>
Date: 15 May 92 10:00:34 GMT
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In-Reply-To: minsky@media.mit.edu's message of 9 May 92 15:12:03 GMT


This is an article I wrote a few months ago. It is related to the
problem discussed here. It was once submitted to a conference, the first
reviewer liked it (3/5) the other did not (1/5). I would be interested
in discussing about it. So, if you are interested, just send me a mail
(do not hesitate to point out mistakes. Ai philosophy is not my usual
job, I am working in the field of non-classical logic).

Moreover, if the first reviewer of this article reads this group, I
would like to get in touch with him to discuss some points with him.

Thanks.


\documentstyle{article}
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\newtheorem{hypot}{Hypothesis}
\title{The Strong AI hypothesis, Chaitin's theorem and Undecidability}
\author{Jean-Marc Alliot\\\footnotesize{(alliot@irit.fr)}\and Institut
de Recherche en Informatique de 
Toulouse \\ 118 Route de Narbonne\\ 31062 Toulouse CEDEX France }
\date{25/11/90}
\begin{document}
\bibliographystyle{alpha}
\maketitle
\abstract{This paper clarifies the distinction between what is
usually called {\em Strong AI\/} and {\em Weak AI} and
shows that inside the Strong AI paradigm there exist different points
of view. It then shows that one of them, the computational
model of AI, which has been widely criticized
(\cite{Searle0}), can be looked upon as an undecidable statement.
Finally, it discusses the consequences of this undecidability.}

\begin{description}
\item[Area:] Philosophical foundation.
\item[Presentation:] I am not sure I could physically attend the
conference, as I must go to FGCS (Tokyo) in June to present a paper,
and missions to Japan are expensive. So, a poster will be OK.
\item[Student:] No 
\end{description}
\newpage

\section{A few lines of history}
The word ``Artificial Intelligence'' was invented by John McCarthy at the
Dartmouth conference. In 1976,  John Newell and Herbert Simon (\cite{Newell3})
gave a theoretical ground for AI, the Physical Symbol
System Hypothesis, or PSSH. This hypothesis can be summarized by one sentence:
``Intelligence can be reduced to the manipulation of physical symbols''.

William Rapaport (\cite{Rapa0}) in his
article for the {\em Encyclopedia of computer science and engineering}
gives a short definition of the strong computational view of
cognitive science :
\begin{quote}
Mental states and processes {\em are\/} expressible as algorithms:
``cognition {\it is\/} a type of computation'' (\cite{Pylyshin0}).
\end{quote}

>From the early 70s and Hubert Dreyfus book publication (\cite{Dreyfusvo0}) until now, 
this materialist approach of intelligence has been widely discussed by
computer scientists but also specialists of psychology or philosophy. As
John Haugeland noted (\cite{Haugelandvo1}), there are both unbelievers
and devoted followers of this hypothesis, each being sure that their
opponents have to be fanatics to oppose to (respectively to believe in)
such theories. 

A lot of arguments have been raised in the last years against strong
AI; if Dreyfus is one of the oldest opponents, he has been followed by
many others including famous scientists like Roger Penrose
(\cite{Penrose0}, Joseph Weizenbaum (\cite{Weizenbaum0}), or in France
Jacques Arsac (\cite{Arsac0}).

One of AI opponents, Professor John Searle
(\cite{Searlevo5}, \cite{Searle0},\ldots) makes an
interesting distinction in AI. He calls {\em Weak AI\/} the part of AI
dedicated to the development of efficient algorithms (such as game playing
algorithms).  This part of AI has little to do with the PSSH, and according
to Searle himself can be accepted. The other part of AI is called
{\em Strong AI\/} by Searle. It is the part of AI whose goal is either to
mimic human Intelligence or to develop a true Artificial Intelligence.

We are first going to be more precise about the strong AI hypothesis,
before discussing it.


\section{A reformulation of the strong AI hypothesis}
I am going to accept in this paper the PSSH, but in a very weak
meaning, and I will call it the {\em Weak PSSH Hypothesis}:

\begin{hypot}[Weak PSSH]
 The brain is a physical system containing a finite number of
physical components. If my level of description is low enough (the neuron
for example), each component of the system and its connections with other
components can be emulated by a programmed device.
\end{hypot}

John Haugeland, when discussing Searle's ``Chinese room
argument''
used a system (the H-demon), that Hofstadter and Dennet
(\cite{Hofstadtervo0}) changed into an S-demon which is almost
identical to the Weak PSSH hypothesis.
If we accept this hypothesis, we accept the PSSH, but in such a weak sense,
that it becomes almost useless. In fact, it just states that
an exact copy of the brain is possible, with each component being
electronic and digital instead of biological and analog.
This is a called by Hubert Dreyfus an {\em artifact}; 
Dreyfus accepts the possibility of rebuilding the brain with analog et
biological components (he is a materialist), but he denies the
possibility for digital processes to model analog ones with enough
accuracy to achieve intelligence. Penrose's quantic argument makes
a somewhat similar claim. However, the discussion of this point is not
the goal of this paper, and we will not concentrate on it.


In fact, strong AI followers wants more than a pure copy, even if it
is a digital copy.
According to them, human reasoning can be described on an other
level than this elementary one. Cognitive psychology uses the expression:
``cognitive models'' for that idea. For a specialist of cognitive psychology,
we are able to give a model of reasoning with a high level
description language. This idea is as old as AI and relies on a
computer science metaphor: there is a low level system executing a low
level program (hardware using machine code, which is both program and
data), but this can easily
(and elegantly) be reduced to an abstract machine running high level
code (this idea is discussed in an almost identical sense in
\cite{Hofstadtervo0}). Of course, the brain is the low level system
and the cognitive theory the high level description language. 

We can now reformulate the strong AI hypothesis: 
\begin{hypot}[The very strong AI hypothesis]
The brain is a physical structure (the hardware) using chemical
molecules (the data) which can be reduced to a much simpler system.
\end{hypot}
The opponents of strong AI claim that this theory is wrong:
they refuse the possibility of reducing this system to a simpler one. 

This is mainly the idea of John Searle in his Chinese room argument.
Searle does not discuss the problem of analog to digital reduction (as
Penrose or Dreyfus), but the possibility of reducing human reasoning
to a (simpler) formal description.

We are going to try to show that no formal reasoning can prove the
very strong AI hypothesis false.


\section{System complexity and minimal programs}
The definition of system complexity that we present here is called 
the Chaitin-Kolmogorov complexity. It was independently developed 
by A. N. Kolmogorov and G. Chaitin about 1965, and is now 
widely known and used. We just mention in this paragraph fundamental results,
more complete information can be easily found (\cite{Chaitinvo0},
\cite{Chaitinvo1}, \cite{Chaitin3}, \cite{Chaitin4}, \cite{Chaitin5},
\cite{Chaitin6}, \cite{Kolmogorov0}, \cite{Kolmogorov1}, \cite{Martin0}).

The Chaitin-Kolmogorov complexity derives from the theory of
information, and gives a formal definition of randomness;
given a sequence of bits, let's suppose we want to write a computer
program that can generate it as an output.
There exists of course a set of different programs
that can generate this sequence. All programs in this set have a
size that can be 
itself measured in bits\footnote{We do not discuss here the peripheral 
problems of the choice of the programming language or the choice of the
computer.}. The smaller program that can generate 
the output sequence is called the {\em minimal program}.
The complexity of the sequence of bits is the size of this program.
A sequence of bits is called {\em random} if its complexity approaches
its size in bits. We can also say that a random sequence can not be
reduced to a shorter one.

A minimal program is itself random, whether it generates a random
sequence or not. It is Chaitin's first theorem. If we suppose that we
have a minimal program $P$ that is not random, then we 
can write a program $P'$ much smaller than $P$ that generates $P$, and
derives from this program $P$ a program defined by: ``using $P'$,
generates $P$ then calculates its output''. This program being only a
few bits longer than $P'$, it is smaller than $P$. Thus $P$ would not
be minimal. QED: a minimal program is random.

There is of course a good question about randomness: is it possible to
prove that a given sequence is random? Or, if we say it the other way, to
prove that a given program is minimal? 

Proving that a program is not minimal is easy: we just have to find an
other program, shorter, and calculating the same output. An other
interesting property is that we always have an upper bound for the
complexity of a sequence of bits, the size of the sequence
itself\footnote{To be absolutely correct, it is the size in bits of
the program {\tt PRINT sequence}, which is a little larger.}.
But we can not even find a random sequence. The core of Chaitin's
demonstration is easy to understand: let's suppose that we
write the program: ``Find a sequence of bits such as we can prove that
its complexity is greater that the complexity of this program''. This
program can not stop: if it finds a sequence of complexity greater
than the program itself, then it has calculated the sequence, which
means the sequence has a complexity lesser or equal to the program
complexity (by definition)\footnote{This kind of recursive argument is
always at the base of undecidability, as shown by Kleene for the
building of non-calculable functions (\cite{Kleenevo0}).}.

Chaintin's theorems can be applied to random sequences, but is also
useful for the interpretation of some of classical undecidability
theorems, as shown in \cite{Chaitinvo0}, \cite{Chaitin6}.


\section{An application to the strong AI controversy}
\subsection{The unfalsifiability of the Strong AI thesis}
If we accept the Weak PSSH hypothesis, then discussion clearly falls under
Chaitin's theorem grasp. The low level model is a large set of number (bits)
which describes our formal system (the brain) in which we want to do our 
proof. This is an upper bound of the system
complexity, because, as we have stated above, the size of a sequence
is always an upper bound of its complexity. But if opponents of strong
AI are right, this is also 
the {\em complexity of the brain}, and it can not be reduced to the
smaller set (the cognitive model) of strong AI supporters: this
sequence of bits is random. However,
this is unfalsifiable, as Chaitin's theorem holds: if the complexity of
the brain is equivalent to the low level model, then it can not be
proved in this model.

Then, if my proof is correct, the strong AI thesis is either true or
undecidable: if AI 
scientists succeed in building an artificial intelligence based on
cognitive models, then it would prove that  Strong AI is correct. But,
it is impossible to prove formally that the Strong AI thesis is wrong, and
it is useless to try. 

\subsection{Can we accept the Weak PSSH hypothesis?}
The Weak PSSH principle is not a new idea. 
A. M. Turing in a famous paper (\cite{Turingvo0}) already presents the 
possibility of rebuilding completely a brain.
The Weak PSSH states that it is possible to build mechanical,
electronic devices which have the functions of biological ones, from
an electronic brain to a mechanical arm. 
Even if we have not yet succeeded in building such an arm,
few people would deny the possibility of doing it. If neuro-biology is
successful enough, we could in a few years accept as well 
the {\em theoretical possibility} of 
an artificial brain: neural nets and neuro-biology
seem to have a good convergence (\cite{Mahowaldvo0}, \cite{chho}), and both
neuro-biologists and neural network specialists seem to be willing to
accept the possibility of a mathematical programmable model of
the neuron. 

There are however arguments against that hypothesis. Brooks (\cite{Brooks0})
advocates that we have no proof that the neuron is really the functional
unit of the brain (\cite{CohenWu0}); \
We have already said a word about Hubert Dreyfus and Roger Penrose
belief in the impossibility of simulating analog processes with
digital systems. A large collection of arguments
opposed to a digital model of the brain can be found in \cite{Born0}.
We do not intend to discuss them here.

\section{Discussions}
\subsection{Is Strong AI stronger?}
One can ask if after this demonstration, Strong AI is not living on a
more solid ground. In fact, I think it is exactly the contrary. Strong
AI opponents would not any more have 
to prove formally that Strong AI is false, 
because
it is not provable. However, they would be able to concentrate on 
Strong AI achievements and Strong AI philosophical implications.
It is now the burden of Strong AI to prove its soundness.

Looking for Strong AI is like looking for God. Nobody can formally prove 
that He doesn't exist, and if somebody could find a proof of His 
existence, then that proof would hold. However, it seems that less and
less people seem to look actively for Him, 
due probably to the repeated failures of such quests in the 
previous centuries. Strong AI supporters have now to show that they have
a serious chance of finding their mechanical god, 
if they want people to believe in It. Repeated failures could also lead
to the loss of Faith.


\subsection{Strong AI ``demonstration''}
The current ``demonstration'' of Strong AI soundness that can be found
in a lot of articles relies on a false reasoning. Its argument is,
more or less: ``We have found that a large number of behaviors are
consistent with our model''.

Let's
consider a large set of numbers, all in the range 1 to 1,000,000, which
includes all even numbers in this range and a thousand random odd numbers.
In this set, the complexity comes from the relatively small set of odd
numbers. Writing a program that can print all even numbers does
not account for the complexity of the system
and {\em is not even a valid approximation}.

I think that every person who has worked in the Expert System field 
has lived experiences almost similar\footnote{And the author of these
lines has experienced that (\cite{erato0})~!}.
An Expert System development has usually two stages. The first one 
is exciting; expertise is easily captured and put into the system. Few 
rules describe a large part of knowledge. But in fact 
it is only the elementary part of
the knowledge (what Hubert and Stuart Dreyfus (\cite{Dreyfus1}) 
would call the {\em 
advanced beginner expertise}) which is captured. Then comes the second stage,
and it is much more difficult to go through it. A
new rule added to the basis creates inconsistency, there are always some
cases that the system does not correctly handle according to the Expert, 
and soon the amount of rules that have to be added or modified becomes
so important that the system becomes unmaintainable. 

Writing the program 
which prints all the even numbers is easy, but printing all the random
odd numbers 
require to write {\em all of them} explicitly in the program, and  is 
much more difficult.

If Strong AI ever finds some regular structures that seem to
describe partially human thoughts, it does not demonstrate at all that
it describes the really meaningful (complex) part of the system. 
What cognitive psychology calls ``Human variability'' might well be
the only interesting part of the problem, and is exactly what
cognitive psychology can not describe, because it is interested only
in the general behavior of the system. This does not deny the possibility
of creating cognitive models, but seriously weakens their so-called 
validation. 


\end{document}


