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 ask 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 three, which was to put the foundations of physics on a

satisfactory basis.

Just a small task. And that was for mathematicians.

That was for mathematicians, not for physicists. The ideas--

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 to you. 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 that science was finding out more and more about this matter, and its

structure, and its motion by a method which you just characterized-- the scientific method.

And the idea was that, if we went on long enough, we'd simply-- as you said we do a

crossword puzzle metaphor-- we'd find out everything there was to fine 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.

Today, I think-- 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 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. You know--

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. It'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 we 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?