The Transcendence of Reason

[00:00:00] HOST:
It’s my great pleasure to introduce our next speaker, Professor Hilary Putnam of, uh, Harvard University. Uh, Professor Putnam was educated as an undergraduate at the University of Pennsylvania, and he got his PhD from UCLA. He’s taught at a wide variety of places, at Northwestern, Princeton, MIT, and Harvard.

Uh, if you have never heard Hilary lecture before, I can tell you that you’re in for a treat. The first time I ever met Hilary, I don’t know if if he remembers this, but it was in a-an airport in some dreadful town. It was the Detroit, uh, Metropolitan Airport.

And, uh, we just immediately started talking to each other, and I guess we must have been shouting. At any rate, I noticed after a while that everybody else in the airport restaurant was, uh, looking at us very strangely, and a very pompous man got up here Hil– It was a brilliant part of the discussion when Hilary was demonstrating to me that the whole idea of reference was purely a syntactical notion, and I don’t know why those other people weren’t interested.

But at any rate-

(laughter)

this very pompous man came over in the Detroit airport and said, “You are disturbing me.” And I can guarantee you that I think H-Hilary will disturb you. Hilary Putnam.

(laughter)

[00:01:25] HILARY PUTNAM:
Hmm. This machine again. This talk has a beginning part which is written, and the rest of it I will talk at you.

Don’t fear that I will read to you for a whole hour. The question, this is called Philosophy in Our Mental Life. Mainly on account of that somewhat preposterous question is what I want to talk about.

The question which troubles laymen, and which has long troubled philosophers, even if it is somewhat disguised by today’s analytic style of writing philosophy, is this: Are we made of matter or soul stuff? To put it as bluntly as possible, are we just m-material beings or are we, quotes, something more? In this paper, I want to argue as strongly as possible that this whole question rests on false assumptions.

My purpose is not to dismiss the question, however, so much as to speak to the real concern which is behind the question. The real concern is, I believe, with the autonomy of our mental life. People are worried that we may be debunked, that our behavior may be exposed as really explained by something mechanical.

Not to be sure, mechanical in the old sense of cogs and pulleys, but in the newer sense of electricity and magnetism and quantum chemistry, and so forth. In this paper, part of what I want to do is to argue that this can’t happen. Mentality is a real and autonomous feature of our world.

But even more important, at least in my feeling, is the fact that this whole question has nothing to do with our substance. Strange as it may seem to common sense and sophisticated intuition alike, the question of the autonomy of our mental life does not hinge on and has nothing to do with that all too popular, all too old question about matter or soul stuff. We could be made of Swiss cheese, and it wouldn’t matter a damn.

I say that, that this is the most important point in this paper, in my opinion, because failure to see this insistence, stubborn insistence on formulating the question as matter or soul utterly prevents progress on these questions. Conversely, once we see that our substance is not the issue, I do not see how we can help but make progress. Now, the concept which is key to unraveling the mysteries in the philosophy of mind, I think, is the concept of functional isomorphism.

Two systems are functionally isomorphic if there is a correspondence between the states of one and the states of the other that preserves functional relations. For example, to start with machine examples, if the functional relations are just sequence relations, for example, state A is always followed by state B. Then if F is a functional isomorphism, it must be the case that state A is followed by state B in system one if and only if state F of A is followed by state F of B in system two.

If the functional relations are, say, data or printout relations, e.g., when print pi is printed on the tape, system one goes into state A, these must be preserved. When print pi is printed on the tape, system two goes into state F of A. If F is to be in functional isomorphism between system one and system two. More generally, if T is a correct theory of the functioning of system one.

In the functional– at the functional or psychological level, then an isomorphism between system one and system two must map each property and relation mentioned in T onto a property and relation defined in system two in such a way that T comes out true when all references to system one are replaced by references to system two And all property and relation symbols in T are reinterpreted according to the mapping. I think I could write that out for you in model theoretic notation, but I won’t.

You know, roughly speaking, it says that if, If, if, if, uh, that F of M is also a model of T. The difficulty with the notions of functional isomorphism, the difficulty with the notion of functional isomorphism is that it presupposes the notion of a thing’s being a functional or psychological description. It is for this reason that, you know, in various papers I’ve written on this stuff, I introduced and explained the notion in terms of Turing machines.

And at that time, I felt constrained, therefore, to defend the thesis that we are Turing machines, that is, a certain kind of abs– computing machine. For Turing machines come, so to speak, with a normal form for their functional description, the so-called machine table, which is just a standard style of program. But it does not seem fatally sloppy to me, although it is sloppy, if we apply the notion of functional isomorphism to systems for which we have no detailed idea at present what a normal form description would look like, systems like ourselves.

The point is that even if we don’t have any idea what a comprehensive psychological theory would look like, I claim that we know enough. and here analogies from computing machines, economic systems, games, and so forth are helpful to point out illuminating differences between any possible psychological theory of a human being or even a functional description of a computing machine or an economic system and a physical or chemical description. Indeed, Dennett and Fodor have done a great deal along these lines in recent books.

So that brings me back to this question of copper, cheese, or soul. One point we can make immediately, as soon as we have the bare concept of functional isomorphism, is this: two systems can have quite different physical constitutions and be functionally isomorphic. For example, a computer made of electrical components can be isomorphic to one made of cogs and wheels.

In other words, for each state in the first computer, there’s a corresponding state in the other, and these, as I, as, uh, I said before, the sequential relations are the same. If state A is followed by state B in the case of the electronic computer, state A will be followed by state B in the case of the computer made of cogs and wheels. And it doesn’t matter at all that the physical realizations of those states are totally different.

So a computer made of electrical components can be isomorphic to made– one made of cogs and wheels or of human being clerks using paper and pencil. A computer made of one sort of wire, say copper wire, and one sort of relay, et cetera, will be in a different physical and chemical state when it computes pi than a computer made of a different sort of wire and relay, but the functional states may be the same. We may extend this point still farther.

Assume that one thesis of materialism is correct, and we are as wholes just material systems obeying physical laws. Then another thesis of classical materialism cannot be correct. Namely, our mental states, e.g., thinking about next summer’s vacation, cannot be identical with any physical or chemical states.

For it is clear from what we already know about computers, et cetera, that whatever the program of the brain may be, it must be physically possible, though not necessarily feasible, to produce something with that same program and quite a different physical and chemical constitution. Now, imagine two possible universes. I’m sorry.

Then to identify the state in question with its physical or chemical realization would be quite absurd, given that that realization is, in a sense, quite accidental from the point of view of psychology anyway, which is the relevant science. It is as if we met Martians and discovered that they were in all functional respects isomorphic to us, but we refused to admit that they could feel pain because their C-fibers were different. Now imagine two possible universes, perhaps parallel worlds in the science fiction sense, in one of which people have good old-fashioned type souls, operating through pineal glands, perhaps, and in the other of which they have complicated brains.

And suppose that the souls in the soul world are functionally isomorphic to the brains in the brain world. Is there any more sense to attaching importance to this difference than to the difference between copper wires and some other wires in a computer? Does it matter that the soul people have, so to speak, immaterial brains and that the brain people have material souls?

What matters is the common structure, the theory T of which we are alas in deep ignorance, and not the hardware, be it ever so ethereal. Now, one may raise various objections to what I’ve said in the body of this talk, and when you try to get to some of them, though not all of them. But one might, for example, say, but look, uh, if the souls of the soul people are isomorphic to the brains of the brain people, then their souls must be automata-like, and that’s not the sort of souls we’re interested in.

All your argument really shows is that there’s no need to distinguish between an, a brain and an automata-like soul. But what precisely does that objection come to? Well, I think there are two ways of understanding it.

It might come to the claim that the notion of functional organization or functional isomorphism only makes sense for automata, but that’s clearly false. Sloppy as our notions are at present, We at least know this much, as Jerry Fodor has emphasized. We know that the notion of functional organization applies to anything to which the notion of a psychological theory applies.

Remember, I explained the most general notion of functional isomorphism by saying that two systems are functionally isomorphic if there’s an isomorphism that makes both of them models for the same psychological theory. They are not just– not– that’s stronger, by the way, than just saying that they are both models for the same psychological theory. They’re not just both models for the same psychological theory, they’re isomorphic realizations of the same abstract structure.

The– to say that souls, real good old-fashioned souls, would not be in the domain of definition of the concept of functional organization or of the concept of functional isomorphism would be to take the position that whatever we mean by the soul, it’s something for which there can be no theory. Well, that seems to be pure obscurantism. You know, I can’t reply to it.

I can only say, if you want that, go in the Black Woods and read Heidegger.

(laughter and background chatter)

But I will assume henceforth that it is not built into the notion of mind or soul or whatever, that it’s unintelligible or that there couldn’t be a theory of it. Secondly, however, someone might say more seriously that even if there is a theory of the soul, theory of the mind, that the soul, at least in the full, rich, old-fashioned sense, is supposed to have powers that no mechanical system could have. Well, later in the body of– in, in the latter part of this talk, I’ll give some reasons for thinking that that couldn’t be so.

For the moment, let me simply say that even if your desire for a soul is a desire after magic, or a desire after perhaps reincarnation, or a desire perhaps after resurrection, that the question of whether we’re m-made out of matter or soul stuff is still irrelevant to all of those questions. You know, to take– I mean, I speak to magic. Well, if it’s built into your notion of soul that s-the soul can do things that violate the laws of physics, then I admit I am stumped.

You know, I cannot, uh, produce a brain which is isomorphic to a soul if the soul can read the future clairvoyantly, you know, in a way that is not in any way explainable by physical laws. On the other hand, if you’re interested in more modest forms of magic like telepathy, well, it seems to me that there’s no reason in principle why we couldn’t construct a device which would project, uh, sub-vocalized thoughts from one brain to another. Of course, you might say, “Well, that wouldn’t be telepathy.”

Functionally, it would be. Um, reincarnation. Well, if we are, as I am urging, a certain kind of functional structure, if my identity is, as it were, my functional structure, seems to me no reason in principle why that couldn’t be reproduced after a thousand years or a million years or a billion years.

You might say, “Well, but you couldn’t produce the same atoms.” However, the view of quantum mechanics, it is extremely doubtful whether that notion even makes sense. Uh, resurrection, as you know, uh, both Jewish and Christian thought have sometimes believed in resurrection in the flesh, which completely bypasses the need for an immaterial vehicle.

So even if you’re interested in those questions, and I must say they are not my main concern, although I am concerned to speak to people who have those concerns, Uh, even there, you don’t need an immaterial brain or soul stuff. So why then, if I’m right and the question of matter or soul stuff is really irrelevant to any question of philosophical, or I would add religious significance, why so much attention to it? Why so much heat?

I think that both sides agree, this seems to be the crux of the matter, that both sides have agreed, both the Diderots of this world and the Descartes of this world have agreed, that if we are matter, then there’s a physical explanation for how we behave, disappointing or exciting. You know, I think the traditional dualist says, “Wouldn’t it be terrible if we turn out to be just matter,” then there’s a physical explanation of everything I do? And isn’t that terrible?”

And the, uh, traditional materialist says, “If we’re just matter, then there’s a physical explanation of everything we do.

(laughter)

And isn’t that exciting?”

(laughter)

You know, to… It’s like, uh, Joe Weizenbaum’s distinction between an optimist and a pessimist. You know, an optimist is a man who says, “This is the best of all possible worlds,” and a pessimist is a man who says, “You’re right.”

(laughter)

Well, I think they’re both wrong. I think the common premise of Diderot and Descartes, of Diderot was the French encyclopedist who said that mental properties are highly derived properties of matter, and are, we’re both wrong in assuming that if we are matter, our souls are material, then there’s a physical explanation of our behavior. Let me try to illustrate what I mean by a very simple analogy.

(laughter)

There you have a very simple physical system. It is a board in which there are two holes, a circle one inch in diameter and a square one inch high. And here I have a cubical peg, epsilon less than one inch high, coated with Vaseline.

And here- Oh, that’s all I need. And I want…

No, I, I… Make it le– make it a sixteenth of an inch less than one inch high So it passes through easily. I don’t want any contact.

And here we have a following s- very simple fact to explain. The peg passes through the square hole, and it doesn’t pass through the round hole. Now, what is the explanation of this?

Well, one might attempt the following. One might say that the peg is at– that, that the, that the peg is, after all, a cloud, or better, a rigid lattice of atoms. And one might even attempt to give a description of that lattice, compute its electrical potential energy, worry about why it doesn’t all collapse, you know, produce some quantum mechanics to explain why it’s stable, et cetera, et cetera, et cetera.

The, um, board is also a lattice of atoms. Now I could, in principle, supposedly, given the s- arrangement of this lattice, consider all possible trajectories which bring the lattice to the board. I will call this now system A and this region one, this region two.

I could compute all possible trajectories of the la– of this lattice. Let us assume, by the way, there are que– there are very serious questions about these comp-computations, their effectiveness, feasibility, and so on, but let’s assume that. And maybe I could deduce from just the laws of particle mechanics or quantum electrodynamics that system A never passes through region one.

And that there is at least one trajectory which enables it to pass through region two. So, in other words, I have a deduction of that from the positions, relative velocities, and so forth of all those atoms. Is that an explanation?

I mean, very often we are told that if something is made of matter, then its behavior must have a physical explanation. And the argument is that if it’s made of matter and you make a ton of assumptions, then there should be a deduction of its behavior from its material structure. What makes you call that deduction an explanation?

On the other hand– I’ll come back to that in a moment, but if you don’t ask, if you’re not hipped on the idea that the explanation must be at the level of the ultimate constituents. and that in fact, the explanation might have the property that the ultimate constituents don’t matter. that only the higher level structure matters, and there’s a very simple explanation.

The explanation is that the board is rigid, the peg is rigid, and as a matter of geometrical fact, this is smaller than the peg. This hole is bigger than the peg when the peg is coming straight on then the cross-section of the peg. The hole pass– the peg passes through the hole that is large enough to it– take its cross section and doesn’t pass through the hole that is too small to take its cross section.

That’s a correct explanation, whether the peg consists of molecules or continuous rigid substance, or for that matter, uh, ether. If you want to complete the explanation slightly, s– you might point out that, uh, the geometrical fact that a square one inch high is bigger than a circle one inch across um Now you can say in that explanation, certain relevant structural features of the situation are brought out. It is brought out, the geometrical features are brought out.

It is relevant that a square one inch high is bigger than a circle one inch around. And it is relevant that, you know, the relation between the size and shape of the peg and the size and shape of the holes is relevant. It is relevant that both the, um, board and the peg are rigid under transportation.

And nothing else is relevant. Same explanation will go in any world, whatever the microstructure, in which those higher level structural features are present. In that sense, this explanation is autonomous.

Now, one might argue with me. People have argued, uh, Professor Garfinkel, who’s in the audience, is doing a lot of work on this, that, well, you’re wrong to say that the deduction isn’t an explanation. Now, I think actually that in terms of the con– the purposes for which we use the notion of explanation in science, it isn’t an explanation.

But I don’t care to quibble. If you want to, let’s admit that the– for today that the deduction is also an explanation. It’s just a terrible explanation.

And why look for terrible explanations when good ones are available? And the good is not here a subjective matter. If one agrees, as even the positivists who saddled us with this notion of explanation, you know, as deduction from laws, wanted to stress that one of the things you do in science is look for laws.

That an explanation is superior, not just subjectively, but methodologically in terms of facilitating the aims of scientific inquiry if it brings out relevant laws. An explanation is superior if it’s more general. Just taking those two features, and there are many, many more you could think of, compare the explanation at the higher level of this phenomenon and the atomic explanation.

The explanation at the higher level brings out the relevant laws about rigid bodies and geometrical relationships. The lower level explanation conceals those laws.

(door slam)

Also notice that the higher level explanation applies to a much more interesting class of systems. Of course, that has to do with what we’re interested in. Because the fact is we’re much more interested in generalizing if, you know, to other structures which are rigid and have various geometrical relations than we are in generalizing to the next peg that has exactly this molecular structure.

For the very good reason that there isn’t going to be a next peg which has exactly this molecular structure. So in terms of, you know, real-life disciplines, real-life ways of slicing up scientific problems, the higher-level explanation is far more general. Now, once you think of this, once you have this idea of abstract structure and the idea that although things do have a lower level structure, physical constitution, that that’s not always relevant.

Sometimes only certain results of that are relevant. Then you start looking at a lot of these traditional reductionist claims in a new light. If you read, for example, Professor Ernest Nagel’s various papers on reduction and his book, uh, The Structure of Scientific Explanations, you find Professor Nagel said reduction is wonderful for the following reasons.

That what a reduction does, he says, is it enables you to deduce the laws of the reduced discipline from the laws of the reducing discipline. That’s fine. That sounds really great, you know.

Until you start thinking, uh, is Professor Nagel saying that the laws of economic theory are deducible from Hamilton’s equations or the Schrödinger equation? Now, I don’t care what your economic standpoint is, whether you’re conservative or a radical, whether you’re thinking whether economics means capital or it means Keynes or Friedman. Uh, trying to deduce the theories of any one of those gentlemen from the Schrödinger equation is a loser.

And that’s not a criticism of their economic theories either. Uh, and that leads, leads one to look back at Nagel’s claim. In fact, he makes it the definition of reduction, that in a reduction, you deduce the laws of the reducing discipline from from reduced discipline from the laws of the reducing discipline.

That, unfortunately, is not true. It’s not true in any of the classical examples of reduction. In every case, there’s not a single classical case, or maybe there is one, but there’s at most one, let us say, classical case, in which you literally de-deduce the laws from the laws.

In all the usual cases, chemistry from physics, um, classical thermodynamics from molecular structure, and so on. In all those cases, what you do is deduce the laws of the reduced discipline from the laws of the reducing discipline, plus facts which are accidental from the point of view of the reducing discipline. For example, in order to derive Boyle’s law from a model of a gas as a lot of billiard balls whizzing around, you have to use assumptions about the distribution of the velocities.

For example, that they are distributed in a normal curve, which is an accidental fact from the point of view of mechanics. It’s not a law of mechanics. In the case of theory of life, this is even more clear.

We have a great many people saying nowadays, “Someday, molecular biology, you know, will deduce all the laws of life from the properties of the DNA molecule.” Well, the answer is, without information about the boundary conditions, it won’t do it. You will not deduce just from the physics of the DNA molecule that, uh, a bat’s wings will enable it to fly without knowing that there’s some air.

The fact that there’s air, that air has a certain density and a certain temperature is an accidental fact from the point of view of the reducing discipline. What that illustrates, by the way, that comes in here. We were only able to deduce the law, a state which is lawful at the higher level.

That the peg goes through the hole which, whose cross-secti– wh-which is larger than the cross-section of the peg and not through the hole which is smaller than the cross-section of the peg. When we try to deduce it from statements about the individual atoms, we use premises which are totally accidental. This atom is here, and this carbon atom is there, you know, this, uh, atom is here, and so forth.

And that’s, by the way, why it’s very misleading to talk about a reduction of something like economics to the level of the elementary particles making up the players of the economic game. Because in fact, their motions, buying this, selling that, arriving at an equilibrium price, these motions cannot be deduced from just the equations of motion. Otherwise, they’d be physically necessitated, not economically necessitated, to arrive at an equilibrium price.

But they play that game because they are particular systems with particular boundary conditions which are totally accidental from the point of view of physics. That means that their derivation of the laws of economics from just the laws of physics is in principle impossible. A derivation of the laws of economics from the laws of physics and accidental statements about which particles were where or when by a Laplacian supermind might be in principle possible, but why want it?

You know, a few chapters of Edgeworth’s will tell you far more about the regularities at the level of economic structure than such a deduction ever could. Now, the conclusion I want to draw from this is that we do have the kind of autonomy that I think we’re looking for in the mental realm. There seems to be no serious reason to believe that whatever our mental organization may be, it’s deducible from anything law-like about our physical organization.

And what we’re interested in is not, you know, given that we consist of such and such particles, Could someone have predicted that we would have this mental organization? Because such a prediction is not explanatory, however great a feat it may be. What we’re interested in is knowing, given that we have this sort of structure, can we at this autonomous level say, well, of course, since we have this sort of structure, we have this sort of program, does it follow that using that sort of program, we will make these conclusions?

We will be able to learn this, we will not be able to learn that, and so on? These are the problems of mental life, the description of this autonomous level of mental organization. And that’s what’s to be discovered.

Now, going that far, let me take up this question of whether we’re computing machines or, in the technical sense, Turing machines. Well, I think that there are two– again there, there are two questions that have gotten blurred together and that have to be separated. There is the question of whether we are Turing machines.

That is to say, whether our functional organization is the functional organization of some Turing machine or other digital– fundamentally digital machine. And there is the question of whether we can be simulated by Turing machines. Can the machine– we do anything machines can’t?

I think very often those two questions are identified. The question of whether we are Turing machines and the whether– question of whether we can do anything machines can’t. I don’t see any rational basis for identifying those questions.

I mean, suppose it turns out that machines can do everything we can do. Does not– seems to me it would be a totally open question whether they do it in at the psychological level. I’m not talking about the physical level.

At the psychological level, whether they do it the same way or a totally different way. Now, you know, to tell you briefly what I think about these questions, although I’ll do this with hesitancy because these are hard empirical questions. It seems to me that in principle, we cannot do anything that Turing machines can’t.

And the argument here, it seems to me, is a straight physical argument. You see, when we talk about what we do, one has to say how one is going to measure this. How is one going to determine what we do?

Now, it seems to me that at the level people are talking about when they ask the question, what can we do, that people are thinking of very discrete descriptions of what we do. You know, no one would say that a description of what I do was wrong because it predicted– mispredicted where I would put my hand by a ten-thousandth of an inch, because it wasn’t in any sense up to my voluntary control, you know, whether it would be this ten thousandth of an inch or that ten thousandth of an inch. On the other hand, a theory which misdescribed where I would put my hand by saying I would put it on this sheet of paper rather than this sheet of paper got what I did wrong.

I think we would say that any theory that could predict the gross motions of a human body to a few thousandths of an inch, let us say, including the verbal motions, what the human body would say under, you know, no matter what you asked it, what conversation it got into, and so on, that any such theory would be certainly counted as much more correct than we ever h- realistically hope to be in predicting human behavior. Now, the situation is this. See, people who argue that we may not be Turing machines or may not be simulatable by Turing machines are arguing, in effect, that continuities in our construction may play a role in our behavior.

But to see that that, while that could be true, that that can’t be relevant to simulating our behavior at this level of accuracy, just observe the following. That we’ve agreed to measure what we do in a discrete way. In other words, really what we’ve done is to adopt, since we’re identifying motions that are within a threshold of each other, What we really have is a discrete space.

There are fi–, literally a finite number of people, things a people can, a person can do in the sense of motions of his body at a given time. We place a cutoff on human life. We just consider a model of what a human can, p-person can do in, say, two hundred years.

That means that you have a, a finite possibility space. Now, what does it mean to talk about what’s going on inside? Well, one way, I mean, now in the physicist sense of what’s going on inside.

One way of understanding that is you’re looking for causes. You’re looking for a causal model. What’s going on inside causally explains why the arm moved to those coordinates, why the voice produced those words, and so on.

But any cause whose effect is something observable, parameterizable, discretely describable, can be, you can be viewed as something being measured. You can view our behavior as a measurement of our inner state. The supposition that we could not be simulated by Turing machines, and here I’m assuming what I call the first thesis of materialism, that we as wholes are physical systems.

The supposition that

(clears throat)

We could not be simulated by a Turing machine. It’s equivalent to the supposition that while our outer states, our behavior, is parametrizable discretely, our inner– the relevant inner states are not. I mean, that needs a little spelling out.

The point is, if the relevant inner states can themselves be discretized, you can enumerate them, identify ones which are very close together, so that in some description, you know, you can replace the actual possibly continuous model or by a discrete model, possibly a probabilistic one, then you end up with what is called a probabilistic automaton. So the assumption that we are not simulated by a Turing machine means mathematically that arbitrarily small differences in the inner state might produce an observable difference in the discretely described outer behavior. For example, if you’re interested in verbal behavior and what the man says, this would, this hypothesis that we’re not simulatable by Turing machines would mean that arbitrarily fine differences in our inner state could result in my saying yes rather than no, or no rather than yes, right?

Well, that makes the thing a very definite physical question, namely, what characteristics does the system have to have to be able to carry out arbitrarily precise measurements? And that’s a question that’s been studied in quantum mechanics in considerable detail, and there are a lot of results. The system has to have an infinite number of degrees of freedom.

The energy required goes to infinity, and so on. In other words, unless current physics is wrong or we are exceptions to the laws of physics, it must be possible to approximate us arbitrarily well by discrete systems. So that means that there’s a general guarantee, of course, quite useless to artificial intelligence people, that in principle, we can be simulated by Turing machines.

But it doesn’t follow that we are Turing machines in any interesting sense. I mean, so what? As we said at the beginning, what we’re interested in is our mental structure.

Now, the one argument that I know for the view that we are Turing machines in some interest, interesting sense is the argument that Minsky and Papert have advanced. Now, I’m not convinced, and I don’t want to make that the main thrust of this talk, but I’ll say a couple of words about that. Uh, I’ve heard Professor Minsky give that argument in a number of ways.

I, I do find it somewhat persuasive. I say I’m not convinced. That doesn’t mean I don’t feel the pull at all.

One way in which Minsky has expressed the argument, it’s very closely related to Professor Papert’s very brilliant lecture today, is by saying that you can always say at any given point in time that the current programs written in artificial intelligence are really just tricks. It’s just a bag of tricks. But if you come back ten years later, you’ll always find that the machines have gotten smarter.

Yeah, that does. I think one feels a pull in that argument. Another way Professor Minsky has put the same point, again, I think it’s very closely related to what Papert told us, is that artificial intelligence is one damn thing after another.

The, th-this is really the same point is the simplicity of mental life point. What it says is, don’t expect that there’ll be the genius program, you know, which will finally give the machine intelligence. You write this program, you write this program, you write this program, gradually the machines get smarter.

Now, that’s a theory about the structure of our mental life. It’s a theory that fundamentally, um, what we have is a series of programs, an interlocking series of programs. Of course, that may be true.

Program is as general a word as functional organization. So– but we have to say more specifically, what we are is a structure, concatenated structure of programs, somewhat like the programs so– today being written.

I see no reason to believe that, and I don’t think I’m mystifying here. I can give you a couple of reasons why I disbelieve it. One is Charniak’s program, to which Professor Papert alluded.

I mean, Charniak’s project was to write a program to enable a machine to understand the story. Now, there are two things about this. Janet and Jane, and Janet having a, uh, something and, you know, trading dogs and for lollipops or whatever.

One is this, that Charniak didn’t write a program. Uh, he, he wrote a huge scheme. I mean, he said it got too complicated.

He couldn’t write the program. What Charniak does is to give you a description of a scheme by which one could, had one but world enough and time, produce a program to understand children’s stories. The other more important thing, that’s by itself neither here nor there.

The other more important thing is that at the end of a lecture, you know, Charniak will explain that of course the machine has to know that, you know, people have dogs, that you give people presents, that when you take something back to a store, that means they refund your money, you know, et cetera, et cetera, et cetera. At the end of the description, someone I remember asked Charniak, \”And if you had this program, would it, uh, the machine be able to understand any other story?\” The answer is no.

Now, I have done some work in artificial intelligence myself, at least in theorem proving by machine, and I’m still doing some work in that. And it is very easy to play this game of impressing people. I mean, I could say quite truthfully that la-last year’s, uh, Putnam Prize exam, the similarity in the name is a coincidence, uh, included a question which could be solved using seven lines of hand computation by a program written by myself and Martin Davis and McIlroy.

That’s true. Um, and in fact, that our program is good enough to do any quantification theory problem you’re likely to come across in a quantification theory course. And that’s true, and one can make that sound very impressive, right?

But I am struck by the following fact that, first of all, I doubt that our program could prove as simple a number theoretic theorem as Wilson’s Theorem. Wilson’s Theorem is a very nice little theorem in pure number theory. It says that a number p is a prime just in case p divides p minus one factorial plus one.

It’s a surprising fact, right? Because being a, being a prime is being not divisible itself. And that this number should divide this number, if and only if this number has no divisors, seems very remarkable.

It would be considered an easy theorem or a beginning theorem in number theory. Now, first of all, I, I, I’m pretty convinced that it’s almost certainly beyond the capacity of any known program to prove that theorem, although I would be delighted if my algorithm would. But even if, let’s say, next year we run our algorithm on some system of axioms, get out a proof of Wilson’s theorem, I think it’ll be fairly clear that that’s in no way a model of how human beings do it.

Because it is important that the machine programs exploit a capacity that human beings pretty clearly don’t have, the capacity to perform enormous numbers of computations. I mean, the way a machine would get a proof of Wilson’s theorem by present methods, if it would, would be to generate a very special kind of proof, a so-called normal form proof, not by breaking up the problem into smaller problems and solving those. And I agree with Papert’s remark that the latter way is the way that all science has proceeded.

Let me put it another way. The thing that’s characteristic of artificial intelligence programs is that they’re special purpose, that they have an extremely restricted solution space. And that although artificial intelligence and Chomsky’s view that we have an innate problem-solving capacity are often counterposed, I have the same objections to both.

I mean, the problem with Chomsky’s view is that even if it explains our capacity to learn English, it doesn’t explain our capacity to learn differential equations. I mean, Chomsky might say, well, the capacity to learn English is innate, and that’s somewhat plausible because when human evolution was completed, and it was comple-completed at least thirty thousand years ago, people already had full mastery of natural languages. But the striking thing about human intelligence, as distinct from all animal intelligence, is this, that human intelligence is constantly used to solve problems, not in exceptional or laboratory situations, but in daily life, constantly to use to solve problems which were not present or relevant in the environment when that capacity was evolved.

I mean, the, the, the environment of thirty thousand years ago, for God’s sake, I mean, the main problem was how to manipulate a piece of rock so it coincided with the head of a deer, you know, and how to start a fire. Those were the problems. The environment did not challenge one to solve any differential equations, to produce the theory of Lie groups, to paint paintings, to write literary criticism, to invent, uh, Heidegger’s philosophy or any of that.

Yet the capacity to do that was already present. You could have taken a smart Cro-Magnon boy thirty thousand years ago, sent him to a good university, and he would have undoubtedly been able to do that. I mean, no, I’m quite serious, right?

You have to see that these– some programs which were fantastically general purpose do exist in the real world. Now, if one looks at artificial intelligence, it seems to me that today it avoids precisely the areas where one might expect general purpose programs. The simplest regularizable situation which calls for a general purpose program is inductive logic.

Take the simplest, uh, space you like, red and black balls coming from an urn in some sequence. Consider the problem of devising a program for extrapolating the sequence. There’s almost nothing done on that, as I say, and what is done on, what is done on deductive logic avoids entirely proof from lemmas.

Right, bringing in the unpredictable, in effect. Whereas even in a science as remote from experience, apparently, as mathematics, it’s just this, the bringing in of what you don’t expect from the s- from the statement of the problem, that is constantly the, the surprising and main feature of every mathematical subject. I mean, you’re surprised by this theorem.

You might even be more surprised by the fact that its proof needs the fact that a quadratic equation c-can have at most two solutions in any field. Which doesn’t seem obviously the thing to think about when you see that statement. So that I know I’m falling into what the way of thinking that Professor Papert cautioned us against and argued we shouldn’t think.

And as I say, I’m not sure I’m right. I think when he is– I feel the pull of his argument, of Minsky’s argument, that the machines are getting smarter. But I will simply say that at this point, it seems to me that all of the programs written are too special purpose, that the solution spaces are too specific, that I do not see any serious.

He may say we have no serious reason to doubt or to disbelieve that just the accumulation of such programs will reach critical mass. I would reply that we have no serious reason to believe it either. We have no serious reason to believe that general intelligence is simply the accumulation of a large number of programs which have such restricted solution spaces.

In any case, even if AI did succeed, there would still be the very s– important question of whether the structure of these intelligent machines was our structure. So what is the importance of machines? I think machines have both a positive and a negative importance in the philosophy of mind.

I think the positive importance of machines was that it was by thinking about machines, and computing machines in particular, that this notion of functional organization first appeared. That machines forced us to distinguish between an abstract structure and its concrete realization. Not that that distinction, you know, came into the world for the first time with machines.

But in the case of computing machines, it— we could not avoid rubbing our noses in the fact that what we had to count as to all intents and purposes the same structure could be realized in a bewildering variety of different ways, that the important properties were just not physical-chemical. So that I think this fact that the machines made us catch on to the idea of functional organization is extremely important. The negative, however, importance of machines, at least if my skepticism about artificial intelligence is warranted, the negative importance of machines, in my view, is that they tempt us to oversimplification.

The notion of, of functional organization became clear to us through systems with a very restricted, very specific functional organization. So the temptation will always be present, you know, to assume that we must have that restricted and specific kind of functional organization. Now, I want to close too with an example.

An example which also may seem remote from what we’ve been talking about, but which may help. This is not an example about– from philosophy of mind at all, again. Consider the following fact.

The Earth does not go around the Sun in a circle, as was once believed. It goes around the Sun in an ellipse, with the Sun at one of the foci, foci, not even in the center of the ellipse. Yet, one statement which would hold true if the orbit was a circle and the Sun was at the center, still holds true, surprisingly.

That’s the following statement. If you draw a line from, say, the center of the Sun to the center of the Earth, so-called radius vector, and watch it trace out an area as the Earth moves around the Sun, that area– the area swept out is the same in equal times. The radius vector from the Sun to the Earth sweeps out equal areas in equal times.

Now, see, if it were a circle and the s-Earth were moving with a constant velocity, that would be trivial, right? Obviously. But this isn’t a circle.

Also, the velocity isn’t even constant. When the Earth is farthest away from the Sun, it’s going most slowly. When it’s closest to the Sun, it’s going fastest.

The Earth is speeding up and slowing down. These chunks do not have the same shape. Some are long cones, some are short, fat cones.

But I still say that in any given hour or day, the Earth’s radius vector will sweep out equal ar-areas at equal times. That’s one of Kepler’s laws. Newton, you know, deduced that law in Principia, and his deduction shows the surprising fact that the only thing on which that law depends is that the force acting on the Earth is in the direction of the Sun.

It’s absolutely the only statement you need to deduce that law. Mathematically, it’s equivalent to that law. And Newton needed hard arguments.

Today, one gives that, you know, as a three-minute theorem in a vector analysis course now. Now, that’s all well and good. One, your gravitational law is that every body attracts every other body according to an inverse square law.

Because then you say, “Well, so according to that law, the Earth is all– the Sun is always attracting the Earth. There’s always a force on the Earth in that direction.” If we assume that we can neglect all the other bodies, their influence is slight, then that’s all you need.

Then you use Newton’s proof or the, a more modern, simpler proof. But today, we have very complicated laws of gravitation. It’s so complicated you wouldn’t believe it.

You can say, first of all, force schmorce. I mean, what’s really going on is that the world lines of all the freely falling bodies in four-space are geodesics. And the four-geometry is determined by the mass-energy tensor, and the ankle bone is connected to the hip bone, and so forth.

So you might ask, how would a modern Relativity theorist, explain Kepler’s law? Well, he explained it very simply. Kepler’s laws are true because Newton’s laws are approximately true.

(laughter)

And in fact, an attempt to replace that by a deduction of Kepler’s laws from the field equations would be regarded as almost as ridiculous, not quite, as, you know, trying to deduce that the peg will go through one hole and not the other from the positions and velocities of the individual atoms. Now let me sharpen that. I want to draw the philosophical conclusions that Newton’s laws have a kind of reality in our world, even though they’re not true.

The point is that in a way, it will always be necessary to appeal to Newton’s laws in order to explain Kepler’s laws. In fact, methodologically, I can make that argument at least plausible. Of course, I can’t prove it on– I’m– it’s an empirical claim.

I’ll make that plausible by making a couple of remarks. One remark, I wish I remembered which of my friends made this remark because he deserves credit, but I don’t, is that a good explanation is invariant under small perturbations of the assumptions.

(laughter)

One trouble with deducing, uh, Kepler’s laws from the gravitational field equations, is, you know, e-even if you could do it, is that tomorrow the gravitational field equations are likely to be different. Whereas the explanation that consists in showing whichever equation you have, that it applies Newton’s equation to a first approximation, and of course, when you have a central force, you have Kepler’s laws, is invariant under even moderate perturbations, quite big perturbations of the assumptions. Which is what, as, uh, French mathematician Thom has put it, every explanation of Kepler’s laws passes through Newton’s laws.

Now, this brings me– Let me come back to the philosophy of mind now. If we assume a thorough atomic structure of matter, quantization, and so forth, then, at first blush, it looks as if continuities cannot be relevant to our mental, to our brain functioning. Mustn’t it all be discrete?

Physics says that at the deepest level it’s discrete. Well, there are two problems with that argument. One is that there are continuities even in quantum mechanics as well as discontinuities.

But ignore that. Suppose it were a thoroughly discretized theory. The other is that if that were a good argument, it would be an argument against the utilizability of the model of a continuous liquid, you know, or which is, you know, the main model on which, uh, aeroplane wings are constructed, at least if they’re to fly at anything less than supersonic speeds.

The point is that… There are two points really. One is that a dis- a con- a discontinuous structure, a discrete structure can approximate a continuous structure.

The discontinuities may be irrelevant, just as in the case of the peg and the board. The fact that the peg and the board are not continuous solids is irrelevant. You’d say that the peg and the board only approximate perfectly rigid, continuous solids.

But if the error in the approximation is irrelevant to that level of description, so what?

(cough)

It’s not just that discrete systems can approximate continuous systems. The fact is that the system may behave the way it does because a continuous system would behave in such and such a way, and it approximates a continuous system. There’s not a Newtonian world.

Tough. Kepler’s law comes out true because the Earth, the Sun-Earth system approximates a Newtonian system, and that’s the way a Newtonian system has to behave. And the error in the approximation is quite irrelevant at that level.

It’s not a perfect analogy because you are, you know, interested in, in laws to which the error in the approximation is relevant. Now, it seems to me in the psychological case, the point is even better, that it may well be, notwithstanding whatever the ultimate structure of the brain is, it may well be that, for example, continuous models like Hull’s model for rote learning, which uses a continuous potential. That such continuous models could perfectly well be correct, whatever the ultimate structure of the brain is.

We cannot deduce from the fact that ultimately there are neurons that a digital model has to be the correct model. That there’s no such valid argument. The brain may work the way it does because it approximates some system whose laws are best conceptualized in terms of continuous mathematics.

What’s more, the errors in that approximation may be irrelevant at the level of psychology. Now, what I’ve said for continuity goes as well for many other things. You see, let’s come back to our first question of the, the soul people and the brain people, and the isomorphism between the souls in the one world and the brains in the other.

See, one objection was if there is a functional isomorphism between souls and brains, wouldn’t the souls have to be rather simple?

(cough)

And the answer is no. Because brains can be essentially infinitely complex. A system with as many degrees of freedom as the brain can imitate to within the accuracy relevant to psychological theory, just about any structure you can mathematicize.

It might be, so to speak, that the ultimate physics of the souls would be quite different from the ultimate physics of the brain. But at the level that we are interested in, the level of functional organization, the same description might go for both. And also that that description might be formally incompatible with the actual physics of the brain, in the way that the description of the air flowing around an airplane wing as a continuous, uncompressible liquid is formally incompatible with the actual structure of the air.

So let me then see, since this is a talk which is attempting to speak to what I take it are real worries of real people, you know, let me close by saying that I think what these examples support is the idea that our substance, what we’re made of, places almost no, I think no, first order restrictions, you know, on our form. But what we’re really interested in, as Aristotle saw, is form and not matter here. What is our intellectual form is the question, not what the matter is.

And whatever our form may be, soul stuff or matter or Swiss cheese, it’s not going to place any interesting restrictions on the answer to the question of what our form is. It may, of course, place interesting higher order restrictions. Small effects may have to be explained, you know, in terms of the actual physics of the brain.

But when we’re not even at the level of an idealized description of the functional organization of the brain to talk about the importance of small perturbations seems decidedly premature. We’re not there yet. So again, I would emphasize that my conclusion is that we have what we always wanted, an autonomous mental life.

And we need no mysteries, no emergence, no élan vital to have it. Thank you.

(applause and cheering)