Gödel was not a machine

Paolo Caressa (2002)

I won't pretend to have written an essay on the complex theme of relationship between minds, machines and all that stuff; these reflections include some of my feelings about the opinions expressed by Hofstadter in his famous book Gödel, Escher, Bach and subsequent works. Just take them as a review on Hofstadter's book.

1. Hofstadter's book is not what it professes to be.

Let me talk about Hofstadter's celebrated book Gödel, Escher, Bach: I agree that this is a deep, funny and well-written book, with a clear exposition of Gödel's technical ideas (along with a lot of other things); but I think also it's a shifty philosophical operation: indeed the theme of the book is to prove the materialistic thesis (which dates back in the ages with the name of Mechanism) of the non existence of the soul, in the sense of spirit, thus non material counterpart of the mind and of the human thought; namely Hofstadter tries to confute the opinion according to which an artificial machine (like a computer) is essentially different from the human mind, or, more precisely, that human mind will never reveal, at last, to be a machine. Of course, confutations to such a possibility of proof were already expressed (in a somewhat definitive way) by Kant (along with confutations of the possibility of proof the contrary); however this thesis regained attention when Alan Turing expressed it in a famous paper [Proc.London Math Soc. 42 (1936)]

Now, I believe Hofstadter should have called his book something like A Vindication of Minds=Machines or better Zen, Minds and Machines, without enlisting in his philosophical army Gödel, Escher nor Bach; indeed Gödel and Bach (I do not know about Escher metaphysical opinions) had completely different viewpoints on that matter.

Johann Sebastian Bach was the great musician we all know: he was a very religious and devout man, who dedicated his great musical works to God and Christ; surely he believed that minds are not machine, but that they are a rational manifestation of the eternal soul granted from God to man.

Gödel was a strong asserter of the essential difference between minds and machines: for example he believed [Bull. Amer. Math. Soc. 58 (1952)] that human mind is intrinsically better than any machine or (exclusive disjunction) there are problems in number theory which are not decidable by human mind; he adds that the second assertion of this disjunction is false (and also adds that this opinion is in agreement with that of David Hilbert); moreover Gödel believed in an essential non physical component of the human mind: Gödel opinions are quoted by Hao Wang in his book From Mathematics to Philosophy [1974] chapter 10.

Hence it's rather irritating to read in Hofstadter bibliography that it has been a fight Lucas-Gödel; Gödel didn't share the equation minds=machines, so to ascribe it to him is definitely deceitful.

On the contrary Hofstadter's book pretends to introduce you to a mystery which lies beyond Gödel theorems, Bach's compositions and Escher's pictures, and that, at last, is revealed in the coincidence of minds and machines, which should spring from these great men works.

Let me make an example to explain why I think to this book as an underhand trick: suppose you want to write a book to confute the opinion of an author, say Feuerbach, that God does not exist; indeed, for some reason, you think that God does exist, and you want to communicate this eternal truth to human-kind; you are obsessed by this idea: when you contemplates the sky at night, when you see a picture or listen to a symphony you always think to the existence of God; so you invent a lot of interesting arguments to support your thesis, and create a lot of connections between science, theology and art; at last your chief-work is complete and you publish it with the following title: Giotto, Einstein, Beethoven: an eternal rolling die; should your book be listed between relativity's books, even if you wrote it to prove the existence of God, only because, among other thing, you devote a lot of its pages to the general theory of relativity?

So I think Hofstadter's book definitely does not belong to Logic, Art nor Music books; it's a philosophical essay on human mind disguised as a scientific book; it's a pity, since Hofstadter could have written at least three good books: one of Art, one of Music, one of Logic; but moreover it's a pity (not to say a sin) that if a guy does not know anything about Gödel theorems he will surely read this book, and will believe that Gödel proved that minds are machines; and this is dishonest.

2. To Be short is a virtue.

Moreover, also from an aesthetic viewpoint the book is unsatisfactory: indeed, whether you agree or not with the author, who, however, always writes non trivial and interesting arguments to support his thesis, the point is that the book is huge; this is not, of course, an intrinsic fault, but in this case it is, if you consider that the all book arose, as the author himself confesses, as a confutation of a paper by J.R. Lucas (Minds, machines and Gödel Philosophy 36 (1961)) which is 15 pages long. I remind Borges's suggestion

Desvarío laborioso y empobrecedor el de componer vastos libros; el de explayar en quinientas páginas una idea cuya perfecta exposicíon oral cabe en pocos minutos. Meyor procedimiento es simular que estos libros ya existen y ofrecer un resumen, un comentario.

[Depreciating and laborious raving is that of composing vast books; is that of explaining in five hundred pages an idea whose complete exposition takes few minutes. Better procedure is to simulate that these books already exist and to give a summary, a commentary].

Unfortunately, Hofstadter did not accept this suggestion: his book should be based not on Gödel, nor Escher, nor Bach, but on an imaginary scientist, or painter or composer (or a mix of these three, power of fiction!) author of an imaginary confutation of Lucas argument; an even huge commentary to this imaginary work would have been much a better book than the heterogeneous medley called Gödel, Escher, Bach.

For example that's what Thomas Carlyle did in Sartor Resartus: The Life and Opinions of Herr Teufelsdrockh.

[Notice that this has been a short section.]

3. (minds=machines)=mechanism.

Now I have the duty to explain why I think that the pseudo-gödelian proof by Hofstadter of the materialistic thesis is wrong (but I also think that Lucas' proof that minds are not machine is wrong, as based on Gödel theorem: it is good as a confutation argument against the possibility of proving that minds=machines).

First of all recall that mechanism (which I think is accepted by many scientists) has a long history: for example, in the past, Epicurean philosophers wrote about it (it's expressed in immortal verses in Lucretius' De rerum natura); however it's better to distinguish between different areas: for example mechanism can be understood as the Pierre-Simon Laplace's doctrine of the complete determination of all events in the universe by means of differential equations and boundary conditions [Turing said: Science is a differential equation and Religion the boundary condition]; it's well known what Laplace answered to Napoleon, who asked why in his book about Celestial Mechanics he never talk about God: because I didn't need that hypothesis.

The mechanical interpretation of the universe (at large scale) is said to be broken by the quantum mechanical description; one of the principle of quantum mechanics, the celebrated Heisenberg's statement, is a confutation of the possibility to compute all the events in the Laplace's sense. But of course one could say that the impossibility for us to compute position and momentum of an elementary particle does not imply that mechanism is false, but simply that a complete description of the universe is impossible to us (I wonder why one would know the motion and position of every particle: for instance the ones that compose my chair...)

[I would like to add that also Heisenberg principle has been charged of metaphysical meanings: now, if you know what I am talking about, you'll recognize that Heisenberg principle amounts to say that a certain algebraic operation does not satisfy commutative rule; if you find natural to argue from this a lot of metaphysical inferences, then you see something that is hidden to my poor eyes.]

4. A difference between living beings and machines.

I think that quantum physics is not a confutation of mechanism, but a confutation of the pretence to prove that the world is nothing more than particles with position and speed; Berkeley, Kant and Schopenhauer said definitive things on these arguments, according to my opinion; so invoking quantum mechanics may not be needed.

The same is true for mental mechanism: maybe this conception corresponds to the truth of mental processes, but the machine-theoretic proof seems to me to be false; there have been a lot of arguments against the equation minds=machines; I propose here an intuitive reason of the intrinsic difference between machines and minds, which arises naturally in me when thinking to this puzzling questions, and which I didn't read before: machine have an intrinsic teleology, minds have not.

I mean that a machine is built by us for some reason, to achieve some purpose, that we know, because is fixed by us; this is a trivial but essential remark: the machine is what it must do, thus we can completely define it according to the reason of its existence; for example I ignore how a television works, I do not know anything about electronics, but I have a complete idea of the television, since I know its purpose; indeed I can use it, and in some sense it exists just to be used by me (or by any other guy who bought it).

But, as far as I know (maybe Hofstadter is aware of some truth hidden to ordinary mortals) men, in particular their minds, have not a manifest aim; of course a man sharing some religious viewpoint will tell you that he believes human beings, say, to be created for the glory of God, or something similar; but this t(h)e(le)ology is not common to all men, so it is not intrinsic (I mean it is not part of the concept of a man or of a mind); on the other hand, a refrigerator is built for a precise purpose. The same is true for computers, and for software.

Indeed computers and computer's programs (like AI ones) are the most teleological artificial creatures ever conceived: each AI program has one or several precise goals to achieve; it's a machine in the purest sense, the most different thing I can imagine from a stone, an animal, a man.

Why to have a purpose is such a difference between artificial things and natural things? This is the same thing as before: we talked about mechanism as the possibility to know all positions and velocities of particles; that's a God's job; I believe the same is true for human aim; God knows it (or nobody knows if you are atheist). So, from our point of view, minds are essentially different from machines: we know something (maybe the verb "know" makes not sense when applied to a machine) they can't conceive: their purpose; they can't do nothing else but their purpose; and we are the makers of their purpose.

One could object that a slave in ancient Rome was in the same condition: but this is not true; the aim of the slave is to be useful to the master, if we consider it a slave, but if we consider him as a man (thus if we consider him as a man with his mind) its aim is unknown; perhaps to be rebel against the master, who knows? The slave could be, alas, an object owned by the master, but certainly not created by the master himself, who pretended the purpose of the slave to be his slave, being wrong.

Of course if men have been created by someone, God for example (who else?), then we are machine from the viewpoint of God (or better we are God's computers): he created us for some purpose, unknown to us; at this point one can assume that Hofstadter's proof fits very well in a theistic metaphysical arena in which there's no space for human souls (for example Sadduceans believed something like that: God does exist, but there's no life after death, and no other world than this one). Notice that this same assumption can be used to make mechanism and quantum mechanics to agree: suppose God to exists: then he surely knows position and speed of each particle in the universe (maybe this could be taken as a definition of God); in other words God is the only creature who can be mechanist. So accepting the axiom God exists (another proposition which is a conceit to try to prove) mechanism seems to be reasonable and in agreement with many different doctrines.

You may think that the previous thought are visionary, but I think that mechanism, atheism, materialism are not less dogmatic than a religious Weltanschaunng. And this is good: we need dogmata, after all mathematical axioms are nothing else than formalized dogmata; a man without dogmata (say, a skeptical) can't say nothing about nothing, and indeed he should be silent; I prefer people with dogmata; of course few dogmata are better than a lot of dogmata, and indeed also in Mathematics independence questions are essentials; in some sense I think a man is a more or less refined person (as far as his intelligence is concerned) according to the number of independent axioms of his Weltanschauung; but in any case I like people who admit their dogmata in a clear and honest way (and, after all, I do not believe to people who say they have no dogmata...)

Usually asserters of minds=machines say that a very complicated Turing machine could emulate each mental process; of course a Turing machine needs a program to work, and they would say that the program is its thelos, its aim; but this is false: a program is a sequence of symbols; it is its meaning to be (or better to represent) the thelos, and this meaning is a projection of our minds onto the machine; symbols in themselves mean nothing: meaning is a human fiction. I can't look to clouds or to stars in the sky without arranging them in imaginary images: meanings are no more real than constellations.

When we see a computer program which prints messages on the screen and answers to our questions, we imagine that it understands what we are saying; but there's only an electron's beam on a screen, and a lot of bits inside a box, no more; it's our imagination which makes us to consider the beam as a sequence of characters and these characters as words and these words as concepts and so we have the impression that someone is talking to us. What the computer does is to perform computations: computations to process strings, computations to print messages inside a window, and so on.

You may say that a man is the same thing: some waters, proteins and so on arranged in such a way that when we interact with him we have the impression that he is talking to us; but the difference is that we attach the meaning to computers, not vice versa, while two interacting men, attach meanings to each other; if you try to listen to a person talking in an unknown language, the most natural thing will be to try to recognize his words as yours: for example if he says "mano" (the italian word for "hand"), you'll reply "Man? Have you said man?" [it is well known that the name Yucatan was given by Spanish explorers: they met some Americans and asked them, in Spanish: "What is the name of this place?"; they answered, in their pre-columbian idiom, something like "I don't understand", and the sound for this expression was "yucatan"; the Spanish were satisfied by this answer: they considered American people like things, and indeed they slayed them and used them as slaves.]

Of course my proposal to shift attention to teleology induces to ask to ourselves some deeper questions: for example, what is the aim of life, the meaning of life? Probably the answer is who knows? and we should accept Voltaire's suggestion when he writes (talking about this question, in the article Ame of his Dictionnaire Philosophique)

O homme! ce Dieu t'a donné l'entendement pour te bien conduire, et non pour pénétrer dans l'essence des choses qu'il a créées.

[O man! this God gave to you the discernment to behave well, and not to penetrate into the essence of the things he created.]

5. Strong AI as nouvelle cuisine.

A lot of people say that mental mechanism is true because they work in computer science, namely in AI (the field called, with a bit of presumption, Artificial Intelligence), and hope to be the first to construct a computer (or to write a program or both) which is able to win a Turing test.

This means a computer which can reason by itself, which can learn from the environment and interact with human beings (or other animals) as if it is a human being (or an animal) too. The faith in the possibility of assembling such a robot is usually called strong AI.

Now: I think to a computer program, much as a cooking recipe: the computer can handle some ingredients, essentially binary numbers, and follows a recipe called program to combine these elements and, finally, produce a dish.

I think that a cooking automata has the same power of a Turing machine (with finite memory); for example you may represent numbers as sequences of dishes: if the dish is, say, spicy, then the bit is on, otherwise it's off; then to add two bits means to produce, given two dishes D and E, other two dishes S and R: S will be spice if both D and E are or if neither D nor E are, and R will be spicy only if both D and E are.

Of course this is a rough example, and one can surely imagine a better way to optimize ingredients and time, but the point is that cooking for a lot of people resembles doing complicated computations; after all the computer is unaware of computations, numbers and all that: it only sets and resets bits according to some recipe.

Now: one can say that cooking is useful, is beautiful, can be a delight for human-kind, but not that it's "intelligent": the same, I think, does apply to computer science, so that "Artificial Intelligence" should be called "Symbolic Cooking" or something similar; now when thinking to strong AI I can't resist to call it "strong symbolic cooking", which is rather grotesque; for this reason is better for me to stop here: I didn't want to convince people that AI is bad or that computer scientists are dummies, but only that AI is a bad name for a noble and interesting part of computer science, and that computer scientists who do AI should not think about themselves as philosophers, psychologists or theologians of modern times, but simply as engineers, not much different from people working in databases, Internet applications, etc.

6. Leave Gödel alone.

Be as it is: you can accept the axiom minds=machines or you can accept its negation; the irritating point (at least according to me) is: what does Gödel's theorem have to do with all these questions? This theorem is the assertion that a certain formal system (1st order arithmetic in the original paper, but the majority of mathematical theories share the same doom) if assumed to be consistent (thus without contradictions) reveals to be incomplete, in the sense that there are true statements which can't be proved: indeed Gödel constructs a statement which says "I can't be proved" and shows that, if the theory is consistent, this statement is true. But what does it mean to be "true"? It means not an absolute truth, but "to be true inside a certain formal system".

Thus: we have a formalized theory, for example arithmetics; to be formalized means that we have precise rules to compose formulas and precise rules to infer new formulas from given ones; then we fix a set of axioms and we start to deduce formulas from these axioms by means of the inference rules.

Then Gödel built inside the formal system its very description: the idea is the beautiful process of gödelization, which is a way to transform strings of symbols representing theorems into numbers; then operations on strings, like concatenating two strings, become arithmetical operations; but the theory formalized by those string is number theory, so that it can talk about these numbers which in turn represent its own formulas; so the theory can speak about itself, and the proposition "this formula is provable" for example becomes expressible within the theory itself, and one may wonder whether it is true or not, whether it is provable or not.

Now Gödel constructs a formula which, if interpreted in this way, asserts "I can't be proved" and show that this formula is true if we agree that the theory is consistent. This shows that not all true formulas are provable inside the theory.

Now some people think that this argument may be applied to prove that minds are essentially different from machines; some other guys think that this argument may be applied to prove that minds are machines; I think that this argument only tells us that arithmetics is a very interesting theory, since to discover its truths one could not proceed merely in a mechanical way, but has to use something which escapes from formalized languages: intuition, ideas, genius.

So the problem about machines and minds must be faced with purely philosophical arguments, not scientific ones; leave Gödel alone and try to find out some argument by yourself!

Here are some links about this brief discussion:

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