"A Strange Piece of Work:" John Lucas On Complexities of Mind, Machines and Gödel
John R. Lucas
Best known for his Incompleteness Theorem, Kurt Gödel
(1906-1978) is considered one of the most important
mathematicians and logicians of the 20th century. By showing that
the establishment of a set of axioms encompassing all of
mathematics would never succeed, he revolutionized the world of
mathematics, logic and philosophy.
John Randolph Lucas is a former Fellow and Tutor of Merton
College, Oxford, and remains an emeritus member of the University
Faculty of Philosophy. He is a Fellow of the British Academy.
Although best known for his paper Minds, Machines and
Gödel, where he argues that an automaton cannot represent a
human mathematician, Lucas has written widely on a diverse range
of topics. His main area of research has focused on philosophy of
mathematics, especially the implications of Gödel’s
incompleteness theorem, the philosophy of mind, free will and
determinism, the philosophy of science with special reference to
special relativity, causality, political philosophy, ethics and
business ethics, and the philosophy of religion. He is the author of Reason and Reality, A Treatise on Time & Space, Spacetime and Electromagnetism and On Justice
Q: When did you first become acquainted with Kurt
Gödel and his Incompleteness Theorems? And what was is it about
his work that impressed you?
A: I first heard a mention of a strange piece of work that
coded things with prime numbers in June, 1948, talking to a tutor
about switching from Mathematics to "Greats"
(Philosophy and Ancient History). I probably was trying to
explain a thought that had come to me earlier at school when I
had been listening to an essay by one of my contemporaries, who
was putting forward an extremely materialistic world-view. I
countered that if such a view was true, there was no room for
truth or rational conviction: he could not hope to persuade me
that it was true; if I came to believe it, it would be only
because he had successfully manipulated my nervous system, not
because it was true, and I had been rationally convinced by his
arguments.
While I was reading philosophy as an undergraduate, I made
considerable use of this type of argument, using it to refute the
Verification Principle, Marxism and Freudianism. But I found
great difficulty in formulating it in a water-tight way. There
were great difficulties in securing self-reference. Russell’s
Theory of Types stood in the way of most of my efforts. Gödel,
however, had managed to circumvent the difficulties. So when my
Junior Research Fellowship at Merton was coming to an end, I
decided to go to Princeton, and really master it.
Q: How would you explain Gödel’s Theorems to a
layman?
Q: You’re best known for your paper Minds,
Machines and Gödel which was published in 1961 in the journal
Philosophy. In it you argue, with the help of Gödel’s proof,
that a mechanist or computationalist view of the mind is
untenable. Can you briefly explain the gist of your
argument?
A: It is a version of the Turing test, a dialogue between a
mind and a purported mechanist representation of it. The
principles on which the mechanist representation works are
subject to Gödel’s Theorem, and so there is a Gödelian
sentence which is true, but cannot be proved to be true by the
machine from the principles on which it was constructed. The
mind, however, informed of the principles on which the machine
was constructed, can work out that this is its Gödelian sentence,
and see that it is true. Thus there is something the mind can do
and the machine cannot do, and so the machine is not an adequate
representation of the mind.
Q: How did you come to apply a purely mathematical
proof like Gödel’s theorem to the problem of minds and
machines?
A: Because I needed my argument to be incontrovertible. Many
others had thought of the argument that the materialist is
somehow cutting off the branch on which he is sitting when he
argues for materialism (I list some of them in an appendix in my
book, The Freedom of the Will, Oxford, 1970); but their
arguments, though cogent, could not get a grip on a hard-nosed
skeptic. I needed to start from where the skeptic stood, and use
arguments he could not deny on pain of self-contradiction.
Gödel’s Theorem enabled me to do it.
Q: Minds, Machines and Gödel was attacked on
many fronts over the ensuing years by various critics - many of
whom weren’t in accord with where your argument supposedly
failed, if at all. How has your argument held up since it was
first presented?
A: I am not the best judge, being partial to my own case. It
seems to me that the Artificial Intelligence people have largely
conceded that a Turing machine cannot be an adequate
representation of the mind, but claim that this is a narrow
victory, because they are dreaming up artificial intelligences
that are not Turing machines.
Q: In Gödel, Escher, Bach, Richard Hofstadter
cites your paper as one of the driving forces behind many of the
ideas developed in his book. However, he diverges from the path
you paved. Can you briefly explain what his view is?
A: I find it difficult. He seems to be giving my sort of
argument, but then draws back from the conclusion to which he was
tending. I suspect he has not fully understood the import of the
Church-Kleene theorem, and thinks that because there is no
algorithm for naming transfinite numbers, a mind would be stumped
to name one. But a mind is not confined to algorithmic
procedures.
Q: Did you ever consider using Turing’s argument
instead of Gödel’s in developing your views in Minds,
Machines and Gödel?
A: Yes, but only to reject it. The great virtue of Gödel’s
theorem (and Tarski’s) is that it invokes the concept of
truth, which was crucial in my original schoolboy thoughts, and
is prominent in mental activities.
Q: In more recent times, mathematician Roger Penrose
has taken up the same problem you covered in your original paper
in his book The Emperor’s New Mind and more recently,
"Shadows of the Mind." Are you familiar with his
version? If so, how does his differ from yours?
A: Yes. I reviewed The Emperor’s New Mind in the
Oxford Magazine. I discuss Penrose’s version in "Turn Over the Page" as well as
Gödel’s own one. (I was quite unaware that Gödel had had
similar thoughts when I was developing my argument. I wish I had
been able to discuss them with him when I was in Princeton in
1957-8.)
Q: Since Gödel first presented his Incompleteness
Theorems over 75 years ago, the mathematical community has
proceeded unabated as if his findings were never announced.
Why?
A: Not so.
1. Hilbert’s program was abandoned.
2. Robinson was able to use non-standard numbers (whose existence
is a corollary of Gödel’s theorem) to re-establish
infinitesimals as respectable members of the mathematical
ontology.
3. Mathematical logic is now a vigorous part of mathematics.
Q: What other philosophical lessons may we draw from
Gödel’s work?
A: It vindicates a widespread belief in the creative power of
reason. Aristotle distinguishes reason generally, meta
logou, from algorithmic reason,
reason-in-accordance-with-the-correct-rule, kata ton orthon
logon. But the distinction is difficult to draw, and has been
denied by many who have assumed that for something to be
reasonable it must be in accordance with some rule. Gödel shows
that however many rules of inference we formulate, there will
still be some valid inferences not covered by them. I see this as
supporting a philosophy of "more-than-ism" rather than
the "nothing-but-ery" of the reductionists.
