The connection between philosophy
and the mathematical sciences has always been very close. Plato had written
over the door of his academy the words, "Let no one enter here who is ignorant of
geometry." It was Aristotle who codified the basic sciences into the categories and
gave them the names that we use to this day. Some of the greatest philosophers have been
themselves great mathematicians who invented new branches of mathematics. Descartes is an
obvious example, and so is Leibniz and Pascal. In fact, most of the great philosophers, not all
but most, came to philosophy from mathematics or the sciences. And this tendency is
continued into our present century. Bertrand Russell was trained
first as a mathematician, Wittgenstein was trained first as an engineer. The reason for this persisting
connection is, I think, obvious. And that is that the basic urge, which has
driven most of the greatest philosophers, has been the urge to deepen our understanding
of the world and of its structure. And this is also what
creative scientists are doing. For most of the past, too, people thought that
mathematics was the most indubitable knowledge, as well as being utterly precise and clear, that
human beings possessed. So there have always been plenty of philosophers examining mathematics to
try and find out what was so special about it, and whether this was something that could be applied
to the acquisition of other sorts of knowledge. Ditto with the sciences, which were also
thought to yield a very specially safe and certain kind of knowledge. What was it about science that
made its results so reliable, people asked themselves. And could its methods,
whatever these were, be used in other fields? These investigations into the concepts, and
methods, and procedures, and models that are involved in mathematics and in science have come
to be known as the philosophy of mathematics and the philosophy of science. And it's with these
that we're going to be concerned in this program. Chiefly with the philosophy of science,
though, in fact, we have someone taking part who is expert in both -- Professor
Hilary Putnam of Harvard University. Professor Putnam, I'd like to start our discussion
from a standpoint which I think a very large number of our viewers occupy anyway. And it's
really this. Since the 17th century, I suppose, there's been a spectacular decline in religious
belief, especially in the West, and especially among educated people. And for millions, the
role that used to be taken in life by a world view based on religion has been increasingly
supplanting by a world view based on science or, at least, purporting to be derived from science,
anyway. And this is still enormously powerful, and the hold that it has on people's minds
throughout the West probably affects all of us. So I think I'd like to start this
discussion by getting you to pin down that scientific world outlook which
is so influential in the modern world and which will be underlying a lot of
what we're going to have to talk about. Let me dodge the question a little bit by talking
not about what scientists think now but what many scientists thought 100
years ago, or 75 years ago. Think of doing a crossword puzzle. You might
have to change a few things as you go along. But towards the end everything fits, and
things get added on one step at a time. That's the way the progress of
science looked for 300 years. In 1900, a famous mathematician, David Hilbert,
gave a list of 50 mathematical problems to a world congress of mathematicians, which are still very
famous. And it's very interesting that he included one problem which we would not call a
mathematical problem, very early in the list. I think it's problem 3, which was to put the
foundations of physics on a satisfactory basis. Just a small task. And that was for
mathematicians. Not for physicists. To tidy it up. That's right. The ideas is, Newton,
Maxwell, Dalton, and so on had all put in all the parts of the story, and now it was
just for mathematicians to, basically, clean up the logic, as it were. I think, in a conversation
we had a couple of days ago, you described this as a treasure chest view and I like that picture.
Here's this big chest that we're just filling up. It's an accumulation, and you don't have to
subtract, you don't have to take out. Occasionally you make a little mistake, but basically
the idea is, when you shift the metaphor, like building a pyramid. You put down the ground
floor, then the next floor, then the next floor. It just goes up. That's part of it. The view
of knowledge as growing by accumulation. The other part of it is the idea that the special
success of the sciences -- and obviously what we're impressed by is success. This culture values
success and science is a successful institution. But there is the idea that science owes
its success to using a special method. And that comes probably from history of science,
from the fact that Newton, for example, lived after Bacon, was influenced by Bacon. And the idea
that empirical science has grown up together with something called inductive logic. And this idea
that there's a method, the inductive method, and that the sciences can be characterized by
the fact that they use this method and use it explicitly and consciously as it were
-- not, unconsciously as maybe someone who's learning cooking might be using it,
but pretty deliberately and explicitly. So I think that these two things -- the idea of
knowledge as growing by accumulation and growing by the use of a special method, the inductive
method, are the key elements of the old view. Yes, and if I were going to put the same thing,
I suppose, slightly differently I think I'd say this. For 200 or 300 years, educated Western man
thought of the universe, and everything in it as consisting of matter in motion. And that was all
there was, whether from the outermost galaxies of the stars into ourselves, and our bodies,
and the cells of which we made up, and so on. And science was finding out more and more about
this matter, and its structure, and its motion, by a method which you just
characterized as the scientific method. And the idea was that, if we went on long
enough, we'd simply -- as you said with the crossword puzzle metaphor -- we'd find out
everything there was to find out. We could, eventually, by scientific methods
completely explain and understand the world. Now, that has been abandoned by scientists,
hasn't it, though in fact this hasn't got through yet to the non-scientists. There are still large
numbers of non-scientists who go on thinking that that's how scientists think.
But of course they no longer do, do they? I mean, this is starting to break down. I think it's started to break down. I think
it started to break down with Einstein. If I can drag in a bit of history of philosophy,
screaming, by the hair, Kant did something in philosophy which I think has begun to happen now
in science. He challenged a certain view of truth. Before Kant, no philosopher really doubted
that truth was simply correspondence to reality. I mean, there are different words, some
philosophers spoke of agreement. But the idea is a mirror theory of knowledge. Well, Kant said
it isn't so simple. There's a contribution of the thinking mind. Sure, it isn't made up by
the mind. Kant was no idealist. It isn't all a fiction. It isn't something we make up. But it
isn't just a copy, either. What we call truth depends both on what there is, on the way things
are, and on the contribution of the thinker, the mind. I think that today scientists have come to
a somewhat similar view. That since the beginning of the 20th century, the idea that there's
a human contribution, a mental contribution, to what we call truth, that theories aren't
simply dictated to us by the facts, as it were. I'd like to ask you to unpack that a little
because I think that some of our viewers will find idea a little puzzling. How can it be, some
people will ask themselves, that what is and is not true can depend not only on what the facts
are, but on the human mind? How can that be? Well, let me use an analogy with vision. We tend
to think that's what we see just depends on what's out there. But the more one studies vision, either
as a scientist or as a painter, one discovers that what's called vision involves an enormous amount
of interpretation. The color we see as red is not the same color, in terms of wavelengths, at
different times of the day. So that even in what we think of as our simplest transaction with the
world, just looking at it, we are interpreting. In other words we bring a whole number
of things to the world that we're not directly conscious of, usually, unless
we turn inwards and start examining them. That's right. I think the world must've looked
different in the Middle Ages to someone who looked up and thought of the stars as up and us at the
bottom, for example. Today, when we look out into space, I think we have a different experience
than somebody with the medieval world view. And what you're saying is that
the very categories in which we see the world and interpret
our experience, and the ideas within which we organize our observations
and the facts around us and such, are provided by us. So that the world as conceived by science
is partly contributed by external facts but also partly contributed by categories and ways of
seeing things which come from the human observer. That's right. And an example of that
in science -- I'll oversimplify, but it's not basically falsified -- is
this wave/particle business. It's not that there's something, an electron,
which is somehow half a wave and half a particle -- that would be meaningless --
but that there are many experiments which can be described two ways. You can either think
of the electron as a wave, or you can think of it as a particle. And both descriptions
are, in some crazy way, true and adequate. They're alternative ways of describing the
same fact, and both descriptions are accurate? That's right. Philosophies have started
talking of equivalent descriptions. That's a term used in philosophy of science. But now, for a couple of hundred years after
Newton, educated Weston man thought that what Newton had produced was objective fact, that he
had discovered laws which governed the workings of the world and the workings of the universe.
And this was just objectively true independently of us. That Newton and other scientists had read
these facts off of nature by observing it, and looking at it, and so on. And these statements,
which made up science, were simply true. Now, there came, didn't there, a period in the
development of science, beginning in the late 19th century, when people began to realize that
these statements were not entirely true, that this wasn't just a body of objective fact which had
been read off from the world. In other words, that science was corrigible, scientific theories
could be wrong. And that raises some very profound questions. I mean, if science isn't just
an objectively true description of the way things are, what is it? And if we don't get it from
observing the world, where do we get it from? Well, I don't want to say we don't get
it from observing the world at all. Obviously, part of this Kantian image is that
there is a contribution which is not us. There's something out there. But that also there's a
contribution from us. And even Kant, by the way, thought that Newtonian science was indubitable. in
fact he thought we contributed its indubitability. The step beyond Kant is the idea that not only is
reality partly mind dependent, but that there are alternatives, and that the concepts we impose on
the world may not be the right ones, and we may have to change them. That there's an interaction
between what we contribute and what we find out. Now, what was it that made people begin to
realize that this basic conception of science as objective truth was wrong, that science
was corrigible, that science was fallible? I think it's that the older science
turned out to be wrong where no one expected it to be wrong, not in
detail, but in the big picture. It's not that we find out that, say, the sun
isn't 93 million miles from the earth but only 20 million miles from the earth. That's not going to
happen. I mean, sometimes one makes blunders even about things like that. But that's like making a
blunder about whether there's a chair in the room. Wholesale skepticism about whether numerical
values are right in science would be as unjustified as wholesale
skepticism about anything. But where the newer theories don't agree with
Newton is not over the approximate truth of the mathematical expressions in Newton's theory.
Those are still perfectly good for calculation. It's over the big picture. We've replaced the
picture of an absolute space and an absolute time by the picture of a four dimensional space
time. We replaced a picture of a Euclidean world by a picture of a world which obeys a
geometry Euclid never dreamed of. We've swung back to the picture of the word as having
a beginning in time, which is really a shocker. It's not even that things once
refuted stay refuted forever. So it means, really, that a whole conception of
science has been superseded. Instead of thinking of science as a body of knowledge which is being
added to all the time by further scientific work, that whole conception of science has in dispensed
with, really, hasn't it? And we now think of it as a set of theories which are themselves
constantly being replaced by better theories, by more accurate theories, by richer, more
explanatory theories. And even the theories we now have, like those of Einstein and
his successors, will probably be replaced, in the course of time, by other, better theories
by scientists yet unknown. Isn't that so? That's exactly right. In fact scientists
themselves make this prediction, that is, that the main theories of the 20th century
-- relativity and quantum mechanics -- will give way to some other theory which will
interpret both of them, and so on forever. Now, this raises a very fundamental question,
namely, the question, what is truth? I mean, when we say that this or that scientific
statement is true, or this or that scientific theory is true, what, in these newly understood
circumstances of ours, can we mean by truth? There's still two views that have been since Kant.
One is that this old correspondence view still has its adherents. But I think the view that's
coming in more and more is that one cannot make a total separation between what's true
and what our standards of assertibility are. That the way in which -- what I call
using the Kantian picture -- the mind-dependence of truth comes in is the
fact that what's true and what's false is in part a function of what our
standards of truth and falsity are. And that depends on our interests, which,
again, change over time, of course. That's right. I'd like you to say a little more about
this question of truth because this again, I think, is puzzling to the layman. I
think that people who are not trained in science or philosophy are apt to think
that there are a certain set of facts, and a true statement is a statement
that accurately describes those facts. I'd like to talk a little about some of the
difficulties that are actually involved in this. I think the biggest difficulty in science
itself comes from the fact that, even within one scientific theory, you often find different
accounts can be given the so-called facts. This came in with the special theory of relativity,
when it turned out that facts about simultaneity, where the two things happen at the same
time, could be described differently by different observers. One could say "Boy Scout
A fired a starter's pistol before Boy Scout B," the other could say, "No, Boy Scout B fired a
starter's pistol before Boy Scout A," and if the distance is sufficiently large, so that a light
signal can't travel from one to the other without exceeding the speed of light, then it may be both
descriptions are correct. Both are admissible. Of course, this leads to profound
conceptual difficulties in understanding some modern scientific theories.
And this prompts the thought that a scientific theory can be useful, and
meaningful, and can work even if nobody really quite understands what it means. And this is the
case with quantum mechanics, isn't it? I mean, nobody is really sure what quantum
mechanics actually means, and yet it works. That's right. And, again, I want to say, one
shouldn't push that too far, because I think we don't want to give up our standards
of intelligibility altogether. We want to say -- quantum mechanics works, and the very
fact that it works means that there's something fundamentally right about it. And with respect
to its intelligibility, we're willing to say, in part, that may be that we have the wrong standards
of intelligibility, that we have to change our intuitions. But in part, there are real paradoxes
in the theory. And I think that's more work has to be done to really get a satisfactory resolution
of these paradoxes. Things are very ticklish now. Yes, I think somebody hearing our discussion to
whom, perhaps, some of these ideas are new might find himself thinking -- well, if all this is
so, how is it that science works? If traditional scientific theories are breaking down, if science
is turning out not to be a body of reliable, permanent, firm, objective knowledge, if a
significant portion of every scientific theory is subjective anyway, in the sense that
it's contributed by the human mind, by the observed by the scientists, how is it,
in these circumstances, that we can actually build bridges, fly airplanes, make rockets
go to the moon, and actually make all this soft fuzzy changing partly subjective body
of theory work for us. It must fit the world, in some very basic way, in spite of
everything that we've been saying. That's true, but I think the contrast between
being subjective and fitting the world isn't altogether right. I'm not saying that scientific
knowledge is subjective, or that anything goes. I'm saying we're in the difficult position that
we often are in in life of thinking there is a difference between good and bad reasoning, but we
don't have a mechanical rule. In everyday life, we use interest-loaded terms. We wouldn't
say that there's a policeman on the corner if we didn't have a whole network of social
institutions. Somebody coming from a primitive tribe which didn't have policemen might say
there's a man in blue on the corner. But the fact that the notion of a policeman is shaped
by our interests doesn't mean that it can't be objectively true that there's a policeman
on the corner. Also, I think science works precisely because of this corrigibility, in
large part, as Professor Poppers pointed out. The difference between science and previous ways
of trying to find out truth is in large part that scientists are willing to test their ideas
because they don't regard them as infallible, in a way, that was known at the beginning,
and then in the success of Newtonian science, somewhat forgotten. And we've had to be reminded
again of what Bacon knew -- that you have to put questions to nature and be willing to
change your ideas if they don't work. In some respects, the traditional opposition
between science and religion -- the two parties have crossed places, haven't they? I mean,
many religious people now believe they have certain knowledge about the world, that
it was created by called a god, that he made us in his own image, gave us immortal souls
which will survive out there, and so on. Certain very fundamental propositions which they hold
with absolute certainty. And it's the scientist who believes that everything is fallible, that
the world is a mysterious place that we'll never get to the end of the mystery of, and so on
and so forth. Isn't there something in that? Maybe. You say it maybe? I'm not sure. You're not sure. Well, let's not pursue that. But one point I do want to take up with
you, leaving even religion aside, is that now science is seen in this entirely
different way that you've been describing, by virtually all scientists, doesn't it mean that
the difference between science and non-science isn't what it was always thought of as being.
In other words, since science is so subjective, indefinite, changing, and so on, it's no longer a
clearly-cut and different kind of human activity, and kind of human knowledge, from other sorts of
human knowledge and other sorts of human activity. I think that's both true and culturally
very important. I think the harm that the old picture of science does is that
if there is this realm of absolute fact that scientists are gradually accumulating
then everything else appears, somehow, as non-knowledge, something to which even
words like true and false can't properly apply. I think that the so-called fact-value dichotomy
is a very good example of this. It's hard to have a discussion, on politics for example, without
someone very quickly say, at least in my country: "is that a fact or a value judgment?" As though
it can't be a fact that Hitler was a bad man, for example, or a factory that Farah
Fawcett Majors is a beautiful woman. And do you think that it is a
fact that Hitler was a bad man? Oh yes, I do. I do too. But then, if this is so, if we're abandoning
so many of these comfortable, clear-cut, distinctions of the past, what's the
point of continuing to use the category, or the notion or the term "science" anyway?
I mean, does it any longer clearly demarcate something differentiable from everything else. I don't think it does. I think that if you're
going to distinguish science from non-science, that makes a lot of sense if you still have this
old view that there's this inductive method. What make something science is that it uses it and uses
it pretty consciously and pretty deliberately. And that what makes something non-science
is, either it uses it entirety unconsciously, as in learning how to cook -- you're not
consciously thinking about inductive logic, or perhaps doesn't use it at all, as metaphysics
was alleged not to use it all, I think unfairly. But when you both say that there's a sharp line
between, say, practical knowledge and science. And to say that the method which is
supposed to draw this line is rather fuzzy, something that we can state exactly -- and
attempts to state it, by the way, have been very much a failure, still.
Inductive logic cannot be, say, programmed on a computer the way deductive
logic can be programmed on a computer. And I think the development of deductive logic
in the last 100 years and the development of the computer have really brought very dramatically
just what a different state we are in with respect to proof in the mathematical
sciences, which we can state rigorous canons for, and proof in what used to be called the inductive
sciences, where we can state general maxims, but you really have to use intuition,
general know-how, and so on in applying them. One of the two categories that you described the
old-fashioned way of looking at science in terms of was that there was a particular scientific
method, that you observed the facts, and, on the basis of these observed instances, you
generalized to form scientific theories which you then verified by experiment,
and so on. That was the old view. Now that that has been abandoned, is
there any longer any single method which is thought of as being scientific method? I don't think they should be. People talk of
scientific method as a sort of fiction. But I think that, even in physics where you do get
experiments and tests which pretty much fit the textbooks, there's a great deal that doesn't and
a great deal that shouldn't. And I think, in fact, in the culture I don't really believe there's
an agreement on what a science and what isn't. Any university will tell you in its
catalog that there are things called social sciences and that sociology is as
science, and that economics is a science. I bet if you ask anyone in the physics department
whether sociology is a science, he'll say no. And why will he say no? That's interesting. I think the real reason is not that the
sociologists don't use the inductive method. They probably use it more conscientiously, poor things, than the physicists do. I think
it's because they're not as successful. So in other words, science has become almost
a name for successful pursuit of knowledge? That's right. Well now, I think you've given a very, very good
description of the way in which these age-old view of what science was has broken down in our century
and been replaced by something much more fluid and perhaps much more difficult to get hold of. But
you have, I think, described it very clearly. Can we now come, against, this background
to what philosophers of science are actually doing. You are a philosopher of science.
What do you and your colleagues do? Well, part of what we do which I won't
try to describe on this broadcast is fairly technical investigation
of specific scientific theories. We look at quantum mechanics very closely, both to
learn what lessons we can from it for philosophy and to see what contributions we can make as
philosophers to clarifying its foundations. We look at relativity theory very closely.
We look at Darwinian evolution very closely, and so on. This is the part of philosophy of
science which provides the data for the rest. But much philosophy of sciences
shades over into general philosophy. And I think that the best way to
describe it is in terms of what we've been talking about. That is, each
of the issues we've been talking about divides philosophers of science. There
are philosophers of science who have a correspondence view of truth and try to
show that this can be made precise, that the objections can be overcome, you can
still view science, somehow, in the old way. And there are others who try to sketch
what another view of truth would come to. There are philosophers who still think there
is an inductive method that can be rigorously stated and who work on inductive logic. And by
the way, I think it's important there should be because we won't make progress to trying to
state the inductive method if there aren't. And that there are others who view
the development of science more culturally, more historically, and then people
like myself who are have a sort of in-between position, that there's something to the notion
of a scientific method, there are clear examples, but that it's more or less a continuum.
You mustn't think of it as a kind of mechanical rule, an algorithm, that you
can apply to get scientific knowledge. So that I'd say each of these issues -- the nature
of truth, the nature of the scientific method, whether there's any necessary truth in science,
any conceptual contribution which is permanent and can't be subject to
revision is a big question. And who are you, plural, doing all this work
for? I don't ask that in an irreverent way, but what I have in mind is this. I've myself
taken part in attempts to bring scientists and philosophers together for discussions of precisely
the issues that you've raised. And these attempts have usually failed and failed to the same reason,
namely, that the scientists lose interest. They go back to their laboratories and get on with doing
more science. And the great bulk of scientists, it seems to me, don't, in fact, take very much
of an interest in the issues that you've been talking about. I think it's conspicuous that the
greatest of all scientists are exceptions. I mean, the really block-busting, the path-breaking
scientists who've actually made the revolution in this century that you've been talking about--
people like Einstein, Max Planck, Neils Bohr, Max Born, Schrodinger, de Broglie, these people
were enormously interested in the conceptual questions that's you've raised. But these were
the pioneering geniuses. And the great mass of thousands of scientists, who follow on behind them
and put their work to its practical application, they don't seem to care so who is listening to
you, who is reading the stuff that you publish? Well, I'd say, first of all, I
think we are basically writing for the philosophically-interested
layman, for the reader of philosophy. I don't view philosophy of science as giving
direct advice to scientists, just as I think more philosophers are ill-advised to think
that they're giving, at least, immediately current contemporary advice on how to live
your life or what bills to pass in parliament. On the other hand, I do think it's scientists tend
to know the philosophy of science of 50 years ago. And perhaps this isn't a bad
thing. That is, perhaps this time lag, this culture lag has some value in
weeding out what they shouldn't pay attention to. It's annoying to a philosopher to encounter a scientist who's both sure that
he needn't listen to any philosophy of science, and then who produces verbatim ideas which you can
recognize as coming from what was popular in 1928. Is there a direct parallel here between
what you're saying about scientists and the economist Keynes' famous remark that
nearly all businessman who thought they were indifferent to airy-fairy
economic theory were in fact the slaves of the economic theorists of
yesterday, of a previous generation? That's exactly true. I suppose another parallel one
could make would be to say that the account that ordinary language-users give
of language, and their use of language, would be extremely unsophisticated simply because
they take it for granted and have never thought about it. That too would probably apply to
the account that most scientists would give of what they were doing when
they were doing their science. That's right. That is, it's a mistake
to think that merely because one practices an activity one can give a theory of it. One criticism that's often been made about
philosopher of science is that although they talk of science in this general way, what
they're nearly always referring to, in fact, is one science namely physics. Now, it's true, isn't it, that the science
in which the most exciting developments have probably taken place in the last 20 years,
anyway, has been not physics but biology. Are philosophers of science open,
genuinely open, to the criticism of being too physics-based in their view of
science and having ignored biology too much? I think I would defend us against that on
the grounds that I don't-- although the theories in biology are of
great scientific importance-- Darwin's theory of evolution, Crick/Watson
on DNA, and so on they don't, by and large, pose big methodological problems of a
kind of don't arise in physical science. I mean, I'm not sure whether
you're going to agree with that. Well, I mean, you mentioned evolution
just now. And it seems to me that here is a concept which originated in one of
the sciences, namely biology, and which, over a comparatively short period of time, has
spread throughout the whole of our culture. So the way almost everybody think is influenced
by the notion of evolution. Not only about the origins of man but about institutions, or
the arts, all kinds of other things. I mean, evolution has become a dimension of Western man's
thinking about almost anything. Is that not so? That's right and perhaps there has not been enough
attention to this theory. Though what strikes me as interesting is that the possibility of
explanations of what we think of as the biological kind -- explanations in terms of function,
rather than in terms of physics and chemistry, what you're made have come under more attention,
recently, as a result of computer science. Now, this does raise something
I'm particularly interested in when you talk of computer Science And that is the
interaction between our technology, in the case of computers, and philosophy. Not just science
and philosophy, but technology and philosophy. I mean, computers were originally constructed
on the basis of a self-conscious analogy with the human mind. But as they became more
and more sophisticated we began to learn things from them about the human mind. So
our construction of computers and what they, then, tell us about ourselves seems to actually
proceed by interactive growth. Isn't that so? That's right, and today this is one are,
by the way, in which philosophers are in close contact with scientists. That is, the
fields of linguistics, cognitive psychology, computer science, philosophy of language, today,
interact constantly. People send papers to one another -- not because someone tells them to.
There are conferences at which specialists needs to meet together -- again, not because someone
decided there should be some cross-fertilization. The interesting thing about the computer
case, if I can stick with it for a moment, is, one might have thought that the rise of the
computer would encourage a certain kind of vulgar materialism. That is, "so, after all, we
are machines. So, after all, everything about us can be explained in terms of physics and
chemistry." Paradoxically the real effect of the computer on psychology on philosophy of mind
has been a decrease in that kind of reductionism. See, the thing about the computer is
that when you work with computers you very rarely have to think about
their physics and chemistry. There's a distinction that people draw between
their software -- meaning their program, their instructions, their rules, the way they do things
-- and their hardware. And generally, you ignore their hardware. You talk about computers at the
software level. And you wouldn't really be able to explain what they do, in a way that would be if
any use to anyone, in terms at the hardware level. There is a kind of emergence here, although
it's not a mystical kind of emergence, it's not that they're violating the laws of
physics. It's just that the level of organization, that higher-level facts about organization
have a kind of autonomy. You'd say this, the fact that it's following this program explains
why does this, and I don't need to know how it's built. I only need to know it can be built
in such a way that will follow this program. If you apply this to the mind, it
suggests a return to view of mind that I associate with Aristotle. It's the
view that we are not ghosts in a machine, not spirits which only temporarily in
bodies, but that the relation between the mind in the body is a relation of
function to what has that function. Aristotle said, "if you use the word soul in
connection with an axe-- and of course," he said, "you don't-- you'd say the soul of
an axe is cutting." And he said, "the soul of the eye is seeing." And he
thought of man as "a thing that thinks." You're talking now of the alternative
to materialism and, say, a religious view that this gives us puts me in mind,
instantly, of the most significant of all the materialist philosophers in the modern
world, namely Marxism, which, after all, is the official state philosophy of about
a third of mankind as we sit here discussing this. Marxism claims to be scientific,
and this is a very important thing about it. Is there a significant Marxist
contribution to the philosophy of science? I don't think there's a significant Marxist
contribution. But I don't think that the Marxist were all wrong either. I think Engles was one
of the most scientifically learned men of his century. He got a number of things wrong. But
he had an immense general scientific knowledge. And Anti-Duhring, his big book on philosophy
of science -- although it contains some rather strange ideas, some of which he gets from Hegel,
by the way -- is, on the whole, a sensible book on philosophy of science, among other things. On
the other hand, it's not specifically Marxist. I'd say that Engles views on philosophy of
science are, in large part, influenced by the standard philosophy of science of the time.
They're a fairly sophisticated inductive account. And what about subsequent
Marxist thinkers who also had some pretension to be
philosophers, like Lenin, for example? Well, I think they're uneven.
Lenin, I think, is one of the worst. He says, for example, that theories are copies
of motion. And there you have the copy theory, of science just copying off the
reality, in its crudest view. Mao is more sophisticated. Mao
is very influenced by John Dewey, who was widely read in China in the 1920s. Do you think it's actually made contribution
to the subject as it is today, or not really? I think that it anticipated -- it
perhaps might have made a contribution if people have been less ideologically divided,
because I think non-Marx's could have learned: the Marxists were among the first people to try
to, somehow, combine a realist view with a stress on practice, with the stress on corrigibility.
And they were very hostile to the notion a priori truth. And today many mainline philosophers
of science are very hostile to a priori truth. As it is, they play some of the role in philosophy
of science, I think, that Keynes said they play in economics. He described Marx as one of
his, sort of, underground predecessors. When I was introducing this program I mentioned
not only the philosophy of science but also the philosophy of mathematics. And before we close, I
would like us to say something about that anyway. I suppose one can really say that the central
problem in the philosophy of mathematics is a direct parallel to the central problem
in the philosophy of science, namely, how long does it fit the world?
With science it's how does science fit the world? In mathematics it's how does
mathematics fit the world. is that right? That's right. And it's even worse,
because if you're trying to defend a copy view, a correspondence of view of
truth in empirical science, you can answer the question- - well how do we build up this
picture in such a way that it corresponds -- by saying we have sense organs. As I mentioned
before that's not a total answer because there's a tremendous amount of interpretation
involved in simple seeing and simple hearing. But if you are talking about numbers and sets, and somebody says, okay, if mathematical knowledge
is simply some kind of a copy of the way numbers are, and the way sets are, and the way other
abstract objects that mathematicians study are, the question then, what sense
enables us to see how they? Yes, what is a number? A deeply problematic
question, but still an important one. That's right. And on the other hand, I don't
want to say that the anti-correspondence has it very easy either. It seems to me that
mathematical knowledge is a real puzzle. And I think that philosophers should concentrate
more on philosophy of mathematics than they do now because it seems to be an area
where no theory works very well. Isn't there another very important parallel
between mathematics and science? I mean, throughout the history of science one of the
conflicts has been between one camp who thought that it was all about objects in the world
which existed independent of human experience and another camp which thought, no, it's
human beings and observers who actually contribute most of this. And as you
pointed out much earlier discussion, the truth is almost certainly
a combination of both. There is a longstanding dispute in mathematics,
isn't there, between one body of people who think that mathematical knowledge is something
that's, so to speak, inherent in the structure of the world, and we derive it from the world by
experience and observation, and another body of mathematical thought that says-- no, no, no,
mathematics is a creation of the human mind which we then try to impose on reality like a
grid, as it was, on a landscape. Isn't that so? That's right. The latter story's attractive
because of the sense organ problem, but it doesn't seem to work either because it seems
that we're not free to impose any mathematics or any logic we want. Almost anyone would admit
that, at least, you have to be consistent. And what's consistent and what isn't isn't
somehow something we can just make up or decide. When we try to stress conventionalist accounts, subjective accounts, we come up against the
objectivity of mathematics. When we try to stress the objectivity of mathematics we
come up against another set of problems. I think we can learn a lot more than
we now know about human knowledge and about scientific knowledge by
going further into this area. Talking of where we're going from where
we are, so to speak, I think the most interesting way in which you could end this
discussion, Professor Putnam, would be by talking about what you regard as the most
interesting problem areas of the moment, and therefore, I take it, the most-likely growth
area for the immediate future in both of the subjects we've been discussing -- philosophy
of science and philosophy of mathematics. OK, I think that if I'm allowed to confine my
prediction to the immediate future -- because we know that long-run predictions are always
false. But in the immediate future, I would expect philosophy of mathematics to be a growth area, and
philosophy of logic. I would expect philosophy of physics, I think, to decline somewhat from
its central place in philosophy of science. Although I think that part of it touches
philosophy of logic. The astounding suggestion has actually come forward in connection with quantum
mechanics that we may have to change our logic, our view of what the true logical laws are in
order to really understand how the world can be quantum mechanical. I think this side a philosophy
of quantum mechanics that touches philosophy of logic will be a hot discussion area. But more
generally, I think areas which we almost don't think of this philosophy of science, that become
philosophy of language and philosophy of mind, like these questions about computer models
of the mind, computer models of language, and these more general questions about
theories of truth, the nature of truth, the nature of verification, how science can be
objective even though there's not a rigorous scientific method -- I think these questions
will continue to be the staples of the field. One thing that worries me about this whole area
is its relationship to the educated layman which, in a sense, is the person our discussion has been
for. After all, it's not over the 70 years since the 25-year-old Einstein published the theory of
relativity. And I'm sure you agree with me that it's true to say now that the great majority
of educating people with higher education, university degrees and so on, still have
scarcely any idea of what this is all about. And it's done very little to actually
influence their view of the world. Isn't there a danger that now science and
mathematics are simply racing ahead, and the whole new range and world of insight that it's giving
us into the universe in which we live simply isn't filtering through to the non-specialist or
not filtering through anything like fast enough? That is a danger, but it's one
that something can be done about. There's now, for example, a text of special
relativity, called space time physics, which is designed for the first month of the first
freshman college physics course. And the authors say, at the beginning, that they look forward to
the time when it will be taught in high schools. And do think that time will,
in fact, come, and quite soon? Oh, I'm sure of it. Yes, well, I think you're right.
And indeed, I hope you are. Thank you very much Professor Putnam.
