CHAPTER VIII

KNOWLEDGE BEHAVIOURISTICALLY CONSIDERED

The word “knowledge”, like the word “memory”, is avoided by the

behaviourist. Nevertheless there is a phenomenon commonly called

“knowledge”, which is tested behaviouristically in examinations. I want

to consider this phenomenon in this chapter, with a view to deciding

whether there is anything in it that the behaviourist cannot deal with

adequately.

It will be remembered that, in Chapter II, we were led to the view that

knowledge is a characteristic of the complete process from stimulus to

reaction, or even, in the cases of sight and hearing, from an external

object to a reaction, the external object being connected with the

stimulus by a chain of physical causation in the outer world. Let us,

for the moment, leave on one side such cases as sight and hearing, and

confine ourselves, for the sake of definiteness, to knowledge derived

from touch.

We can observe touch producing reactions in quite humble animals, such

as worms and sea anemones. Are we to say that they have “knowledge”

of what they touch? In some sense, yes. Knowledge is a matter of

degree. When it is regarded in a purely behaviouristic manner, we

shall have to concede that it exists, in some degree, wherever there

is a characteristic reaction to a stimulus of a certain kind, and this

reaction does not occur in the absence of the right kind of stimulus.

In this sense, “knowledge” is indistinguishable from “sensitivity”,

which we considered in connection with perception. We might say that

a thermometer “knows” the temperature, and that a compass “knows” the

direction of the magnetic north. This is the only sense in which, on

grounds of observation, we can attribute knowledge to animals that

are low in the scale. Many animals, for example, hide themselves when

exposed to light, but as a rule not otherwise. In this, however, they

do not differ from a radiometer. No doubt the mechanism is different,

but the observed molar motion has similar characteristics. Wherever

there is a reflex, an animal may be said, in a sense, to “know” the

stimulus. This is, no doubt, not the usual sense of “knowledge”, but it

is the germ out of which knowledge in the usual sense has grown, and

without which no knowledge would be possible.

Knowledge in any more advanced sense is only possible as a result of

learning, in the sense considered in Chapter III. The rat that has

learned the maze “knows” the way out of it; the boy who has learned

certain verbal reactions “knows” the multiplication table. Between

these two cases there is no important difference. In both cases, we

say that the subject “knows” something because he reacts in a manner

advantageous to himself, in which he could not react before he had had

certain experiences. I do not think, however, that we ought to use such

a notion as “advantageous” in connection with knowledge. What we can

observe, for instance, with the rat in the maze, is violent activity

until the food is reached, followed by eating when it is reached; also

a gradual elimination of acts which do not lead to the food. Where this

sort of behaviour is observed, we may say that it is directed towards

the food, and that the animal “knows” the way to the food when he gets

to it by the shortest possible route.

But if this view is right, we cannot define any knowledge acquired

by learning except with reference to circumstances toward which an

animal’s activity is directed. We should say, popularly, that the

animal “desires” such circumstances. “Desire”, like “knowledge”,

is capable of a behaviouristic definition, and it would seem that

the two are correlative. Let us, then, spend a little time on the

behaviouristic treatment of “desire”.

The best example of desire, from this point of view, is hunger. The

stimulus to hunger is a certain well-ascertained bodily condition.

When in this condition, an animal moves restlessly; if he sees or

smells food, he moves in a manner which, in conditions to which he is

accustomed, would bring him to the food; if he reaches it, he eats it,

and if the quantity is sufficient he then becomes quiescent. This kind

of behaviour may be summarised by saying that a hungry animal “desires”

food. It is behaviour which is in various ways different from that of

inanimate matter, because restless movements persist until a certain

condition is realised. These movements may or may not be the best

adapted to realising the condition in question. Every one knows about

the pike that was put on one side of a glass partition, with minnows

on the other side. He continually bumped his nose on the glass, and

after six weeks gave up the attempt to catch them. When, after this,

the partition was removed, he still refrained from pursuing them. I do

not know whether the experiment was tried of leaving a possibility of

getting to the minnows by a roundabout route. To have learned to take a

roundabout route would perhaps have required a degree of intelligence

beyond the capacity of fishes; this is a matter, however, which offers

little difficulty to dogs or monkeys.

What applies to hunger applies equally to other forms of “desire”.

Every animal has a certain congenital apparatus of “desires”; that

is to say, in certain bodily conditions he is stimulated to restless

activities which tend towards the performance of some reflex, and

if a given situation is often repeated the animal arrives more and

more quickly at the performance of the reflex. This last, however, is

only true of the higher animals; in the lower, the whole process from

beginning to end is reflex, and can therefore only succeed in normal

circumstances. The higher animals, and more especially men, have a

larger proportion of learning and a smaller proportion of reflexes in

their behaviour, and are therefore better able to adapt themselves

to new circumstances. The helplessness of infants is a necessary

condition for the adaptability of adults; infants have fewer useful

reflexes than the young of animals, but have far more power of forming

useful habits, which can be adapted to circumstances and are not

fatally fixed from birth. This fact is intimately connected with the

superiority of the human intelligence above that of the brutes.

Desire is extremely subject to “conditioning”. If A is a primitive

desire and B has on many occasions been a means to A, B comes to be

desired in the same sense in which A was previously desired. It may

even happen, as in misers, that the desire for B completely displaces

the desire for A, so that B, when attained, is no longer used as a

means to A. This, however, is more or less exceptional. In general, the

desire for A persists, although the desire for B has a more or less

independent life.

The “conditioning” of primitive desires in human beings is the source

of much that distinguishes our life from that of animals. Most animals

only seek food when they are hungry; they may, then, die of starvation

before they find it. Men, on the contrary, must have early acquired

pleasure in hunting as an art, and must have set out on hunting

expeditions before they were actually hungry. A further stage in the

conditioning of hunger came with domestic animals; a still further

stage with agriculture. Nowadays, when a man sets to work to earn his

living, his activity is still connected, though not very directly,

with hunger and the other primitive desires that can be gratified by

means of money. These primitive desires are still, so to speak, the

power station, though their energy is widely distributed to all sorts

of undertakings that seem, at first sight, to have no connection with

them. Consider “freedom” and the political activities it inspires; this

is derivable, by “conditioning”, from the emotion of rage which Dr.

Watson observed in infants whose limbs are not “free”. Again we speak

of the “fall” of empires and of “fallen” women; this is connected with

the fear which infants display when left without support.

After this excursion into the realm of desire, we can now return to

“knowledge”, which, as we saw, is a term correlative to “desire”, and

applicable to another feature of the same kind of activity. We may say,

broadly, that a response to a stimulus of the kind involving desire

in the above sense shows “knowledge” if it leads by the quickest or

easiest route to the state of affairs which, in the above sense, is

behaviouristically the object of desire. Knowledge is thus a matter

of degree: the rat, during its progressive improvements in the maze,

is gradually acquiring more and more knowledge. Its “intelligence

quotient”, so far as that particular task is concerned, will be the

ratio of the time it took on the first trial to the time it takes now

to get out of the maze. Another point, if our definition of knowledge

is accepted, is, that there is no such thing as purely contemplative

knowledge: knowledge exists only in relation to the satisfaction of

desire, or, as we say, in the capacity to choose the right means to

achieve our ends.

But can such a definition as the above really stand? Does it represent

at all the sort of thing that would commonly be called knowledge? I

think it does in the main, but there is need of some discussion to make

this clear.

In some cases, the definition is obviously applicable. These are the

cases that are analogous to the rat in the maze, the consideration of

which led us to our definition. Do you “know” the way from Trafalgar

Square to St. Pancras? Yes, if you can walk it without taking any wrong

turnings. In practice, you can give verbal proof of such knowledge,

without actually having to walk the distance; but that depends upon

the correlation of names with streets, and is part of the process of

substituting words for things. There may, it is true, come doubtful

cases. I was once on a bus in Whitehall, and my neighbour asked “What

street is this?” I answered him, not without surprise at his ignorance.

He then said, “What building is that?” and I replied “The Foreign

Office”. To this he retorted, “but I thought the Foreign Office was in

Downing Street”. This time, it was his knowledge that surprised me.

Should we say that he knew where the Foreign Office is? The answer is

yes or no according to his purpose. From the point of view of sending a

letter to it, he knew; from the point of view of walking to it, he did

not know. He had, in fact, been a British Consul in South America, and

was in London for the first time.

But now let us come to cases less obviously within the scope of our

definition. The reader “knows” that Columbus crossed the ocean in

1492. What do we mean by saying that he “knows” this? We mean, no

doubt, primarily that writing down this statement is the way to pass

examinations, which is just as useful to us as getting out of the

maze is to the rat. But we do not mean only this. There is historical

evidence of the fact, at least I suppose there is. The historical

evidence consists of printed books and manuscripts. Certain rules have

been developed by historians as to the conditions in which statements

in books or manuscripts may be accepted as true, and the evidence in

our case is (I presume) in accordance with these rules. Historical

facts often have importance in the present; for example, wills, or

laws not yet repealed. The rules for weighing historical evidence

are such as will, in general bring out self-consistent results. Two

results are self-consistent when, in relation to a desire to which both

are relevant, they enjoin the same action, or actions which can form

part of the one movement towards the goal. At Coton, near Cambridge,

there is (or was in my time) a signpost with two arms pointing in

diametrically opposite directions, and each arm said “To Cambridge”.

This was a perfect example of self-contradiction, since the two arms

made statements representing exactly opposite actions. And this case

illustrates why self-contradiction is to be avoided. But the avoidance

of self-contradiction makes great demands upon us; Hegel and Bradley

imagined that we could know the nature of the universe by means of

this principle alone. In this they were pretty certainly mistaken,

but nevertheless a great deal of our “knowledge” depends upon this

principle to a greater or less extent.

Most of our knowledge is like that in a cookery book, maxims to be

followed when occasion arises, but not useful at every moment of every

day. Since knowledge may be useful at any time, we get gradually,

through conditioning, a general desire for knowledge. The learned man

who is helpless in practical affairs is analogous to the miser, in that

he has become absorbed in a means. It should be observed, also, that

knowledge is neutral as among different purposes. If you know that

arsenic is a poison, that enables you equally to avoid it if you wish

to remain in health, and to take it if you wish to commit suicide. You

cannot judge from a man’s conduct in relation to arsenic whether he

knows that it is a poison or not, unless you know his desires. He may

be tired of life, but avoid arsenic because he has been told that it

is a good medicine; in this case, his avoidance of it is evidence of

_lack_ of knowledge.

But to return to Columbus: surely, the reader will say, Columbus really

did cross the Atlantic in 1492, and that is why we call this statement

“knowledge”. This is the definition of “truth” as “correspondence with

fact”. I think there is an important element of correctness in this

definition, but it is an element to be elicited at a later stage,

after we have discussed the physical world. And it has the defect--as

pragmatists have urged--that there seems no way of getting at “facts”

and comparing them with our beliefs: all that we ever reach consists of

other beliefs. I do not offer our present behaviouristic and pragmatic

definition of “knowledge” as the only possible one, but I offer it as

the one to which we are led if we wish to regard knowledge as something

causally important, to be exemplified in our reactions to stimuli. This

is the appropriate point of view when we are studying man from without,

as we have been doing hitherto.

There is, however, within the behaviourist philosophy, one important

addition to be made to our definition. We began this chapter with

sensitivity, but we went on to the consideration of learned reactions,

where the learning depended upon association. But there is another

sort of learning--at least it is _prima facie_ another sort--which

consists of increase of sensitivity. All sensitivity in animals and

human beings must count as a sort of knowledge; that is to say, if an

animal behaves, in the presence of a stimulus of a certain kind, as it

would not behave in the absence of that stimulus then, in an important

sense, it has “knowledge” as regards the stimulus. Now it appears that

practice--_e.g._ in music--very greatly increases sensitivity. We

learn to react differently to stimuli which only differ sightly; what

is more, we learn to react to differences. A violin-player can react

with great precision to an interval of a fifth; if the interval is very

slightly greater or less, his behaviour in tuning is influenced by the

difference from a fifth. And as we have already had occasion to notice,

we become, through practice, increasingly sensitive to form. All this

increased sensitivity must count as increase of knowledge.

But in saying this we are not saying anything inconsistent with our

earlier definition of knowledge. Sensitivity is essential to choosing

the right reaction in many cases. To take the cookery-book again; when

it says “take a pinch of salt”, a good cook knows how much to take,

which is an instance of sensitivity. Accurate scientific observation,

which is of great practical importance, depends upon sensitivity. And

so do many of our practical dealings with other people: if we cannot

“feel” their moods, we shall be always getting at cross purposes.

The extent to which sensitivity is improved by practice is astonishing.

Town-bred people do not know whether the weather is warm or cold until

they read the weather reports in the paper. An entomologist perceives

vastly more beetles in the course of a country walk than other people

do. The subtlety with which connoisseurs can distinguish among wines

and cigars is the despair of youths who wish to become men of the

world. Whether this increase of sensitivity can be accounted for by

the law of association, I do not know. In many cases, probably, it can,

but I think sensitiveness to form, which is the essential element in

the more difficult forms of abstract thought as well as in many other

matters, cannot be regarded as derivative from the law of association,

but is more analogous to the development of a new sense. I should

therefore include improvement in sensitivity as an independent element

in the advancement of knowledge. But I do so with some hesitation.

The above discussion does not pretend to cover the whole of the ground

that has to be covered in discussing the definition of “knowledge”.

There are other points of view, which are also necessary to a complete

consideration of the question. But these must wait until, after

considering the physical world, we come to the discussion of man as

viewed from within.

PART II

THE PHYSICAL WORLD

CHAPTER IX

THE STRUCTURE OF THE ATOM

In all that we have said hitherto on the subject of man from without,

we have taken a common-sense view of the material world. We have not

asked ourselves: what _is_ matter? Is there such a thing, or is the

outside world composed of stuff of a different kind? And what light

does a correct theory of the physical world throw upon the process of

perception? These are questions which we must attempt to answer in the

following chapters. And in doing so the science upon which we must

depend is physics. Modern physics, however, is very abstract, and by

no means easy to explain in simple language. I shall do my best, but

the reader must not blame me too severely if, here and there, he finds

some slight difficulty or obscurity. The physical world, both through

the theory of relativity and through the most recent doctrines as to

the structure of the atom, has become very different from the world

of everyday life, and also from that of scientific materialism of the

eighteenth-century variety. No philosophy can ignore the revolutionary

changes in our physical ideas that the men of science have found

necessary; indeed it may be said that all traditional philosophies have

to be discarded, and we have to start afresh with as little respect

as possible for the systems of the past. Our age has penetrated more

deeply into the nature of things than any earlier age, and it would be

a false modesty to over-estimate what can still be learned from the

metaphysicians of the seventeenth, eighteenth and nineteenth centuries.

What physics has to say about matter, and the physical world generally,

from the standpoint of the philosopher, comes under two main heads:

first, the structure of the atom; secondly, the theory of relativity.

The former was, until recently, the less revolutionary philosophically,

though the more revolutionary in physics. Until 1925, theories of the

structure of the atom were based upon the old conception of matter as

indestructible substance, although this was already regarded as no

more than a convenience. Now, owing chiefly to two German physicists,

Heisenberg and Schrödinger, the last vestiges of the old solid atom

have melted away, and matter has become as ghostly as anything in

a spiritualist seance. But before tackling these newer views, it

is necessary to understand the much simpler theory which they have

displaced. This theory does not, except here and there, take account

of the new doctrines on fundamentals that have been introduced by

Einstein, and it is much easier to understand than relativity. It

explains so much of the facts that, whatever may happen, it must remain

a stepping-stone to a complete theory of the structure of the atom;

indeed, the newer theories have grown directly out of it, and could

hardly have arisen in any other way. We must therefore spend a little

time in giving a bare outline, which is the less to be regretted as the

theory is in itself fascinating.

The theory that matter consists of “atoms”, _i.e._ of little bits

that cannot be divided, is due to the Greeks, but with them it was

only a speculation. The evidence for what is called the atomic

theory was derived from chemistry, and the theory itself, in its

nineteenth-century form, was mainly due to Dalton. It was found that

there were a number of “elements”, and that other substances were

compounds of these elements. Compound substances were found to be

composed of “molecules”, each molecule being composed of “atoms” of one

substance combined with “atoms” of another or of the same. A molecule

of water consists of two atoms of hydrogen and one atom of oxygen; they

can be separated by electrolysis. It was supposed, until radio-activity

was discovered, that atoms were indestructible and unchangeable.

Substances which were not compounds were called “elements”. The

Russian chemist Mendeleev discovered that the elements can be arranged

in a series by means of progressive changes in their properties; in his

time, there were gaps in this series, but most of them have since been

filled by the discovery of new elements. If all the gaps were filled,

there would be 92 elements; actually the number known is 87, or,

including three about which there is still some doubt, 90. The place of

an element in this series is called its “atomic number”. Hydrogen is

the first, and has the atomic number 1; helium is the second, and has

the atomic number 2; uranium is the last, and has the atomic number 92.

Perhaps in the stars there are elements with higher atomic numbers, but

so far none has been actually observed.

The discovery of radio-activity necessitated new views as to “atoms”.

It was found that an atom of one radio-active element can break up into

an atom of another element and an atom of helium, and that there is

also another way in which it can change. It was found also that there

can be different elements having the same place in the series; these

are called “isotopes”. For example, when radium disintegrates it gives

rise, in the end, to a kind of lead, but this is somewhat different

from the lead found in lead-mines. A great many “elements” have been

shown by Dr. F. W. Aston to be really mixtures of isotopes, which can

be sorted out by ingenious methods. All this, but more especially the

transmutation of elements in radio-activity, led to the conclusion that

what had been called “atoms” were really complex structures, which

could change into atoms of a different sort by losing a part. After

various attempts to imagine the structure of an atom, physicists were

led to accept the view of Sir Ernest Rutherford, which was further

developed by Niels Bohr.

In this theory, which, in spite of recent developments, remains

substantially correct, all matter is composed of two sorts of units,

electrons and protons. All electrons are exactly alike, and all protons

are exactly alike. All protons carry a certain amount of positive

electricity, and all electrons carry an equal amount of negative

electricity. But the mass of a proton is about 1835 times that of an

electron: it takes 1835 electrons to weigh as much as one proton.

Protons repel each other, and electrons repel each other, but an

electron and a proton attract each other. Every atom is a structure

consisting of electrons and protons. The hydrogen atom, which is the

simplest, consists of one proton with one electron going round it as

a planet goes round the sun. The electron may be lost, and the proton

left alone; the atom is then positively electrified. But when it has

its electron, it is, as a whole, electrically neutral, since the

positive electricity of the proton is exactly balanced by the negative

electricity of the electron.

The second element, helium, has already a much more complicated

structure. It has a nucleus, consisting of four protons, and two

electrons very close together, and in its normal state it has two

planetary electrons going round the nucleus. But it may lose either or

both of these, and it is then positively electrified.

All the latter elements consist, like helium, of a nucleus composed of

protons and electrons, and a number of planetary electrons going round

the nucleus. There are more protons than electrons in the nucleus,

but the excess is balanced by the planetary electrons when the atom

is unelectrified. The number of protons in the nucleus gives the

“atomic weight” of the element: the excess of protons over electrons

in the nucleus gives the “atomic number”, which is also the number of

planetary electrons when the atom is unelectrified. Uranium, the last

element, has 238 protons and 146 electrons in the nucleus, and when

unelectrified it has 92 planetary electrons. The arrangement of the

planetary electrons in atoms other than hydrogen is not accurately

known, but it is clear that, in some sense, they form different rings,

those in the outer rings being more easily lost than those nearer the

nucleus.

I come now to what Bohr added to the theory of atoms as developed

by Rutherford. This was a most curious discovery, introducing, in a

new field, a certain type of discontinuity which was already known

to be exhibited by some other natural processes. No adage had seemed

more respectable in philosophy than “natura non facit saltum”, Nature

makes no jumps. But if there is one thing more than another that the

experience of a long life has taught me, it is that Latin tags always

express falsehoods; and so it has proved in this case. Apparently

Nature does make jumps, not only now and then, but whenever a body

emits light, as well as on certain other occasions. The German

physicist Planck was the first to demonstrate the necessity of jumps.

He was considering how bodies radiate heat when they are warmer

than their surroundings. Heat, as has long been known, consists of

vibrations, which are distinguished by their “frequency”, _i.e._ by the

number of vibrations per second. Planck showed that, for vibrations

having a given frequency, not all amounts of energy are possible, but

only those having to the frequency a ratio which is a certain quantity

_h_ multiplied by 1 or 2 or 3 or some other whole number, in practice

always a small whole number. The quantity _h_ is known as “Planck’s

constant”; it has turned out to be involved practically everywhere

where measurement is delicate enough to know whether it is involved or

not. It is such a small quantity that, except where measurement can

reach a very high degree of accuracy, the departure from continuity is

not appreciable.[7]

[7] The dimensions of _h_ are those of “action”, _i.e._

energy multiplied by time, or moment of momentum, or

mass multiplied by length multiplied by velocity. Its

magnitude is about 6.55 × 10.27 erg secs.

Bohr’s great discovery was that this same quantity _h_ is involved

in the orbits of the planetary electrons in atoms, and that it

limits the possible orbits in ways for which nothing in Newtonian

dynamics had prepared us, and for which so far, there is nothing in

relativity-dynamics to account. According to Newtonian principles, an

electron ought to be able to go round the nucleus in any circle with

the nucleus in the centre, or in any ellipse with the nucleus in a

focus; among possible orbits, it would select one or another according

to its direction and velocity. But in fact only certain out of all

these orbits occur. Those that occur are among those that are possible

on Newtonian principles, but are only an infinitesimal selection from

among these. It will simplify the explanation if we confine ourselves,

as Bohr did at first, to circular orbits; moreover we will consider

only the hydrogen atom, which has one planetary electron and a nucleus

consisting of one proton. To define the circular orbits that are

found to be possible, we proceed as follows: multiply the mass of the

electron by the circumference of its orbit, and this again by the

velocity of the electron; the result will always be _h_ or 2_h_, or

3_h_, or some other small exact multiple of _h_, where _h_, as before,

is “Planck’s constant”. There is thus a smallest possible orbit, in

which the above product is _h_; the radius of the next orbit, in which

the above produce is 2_h_, will have a length four times this minimum;

the next, nine times; the next, sixteen times; and so on through the

“square numbers” (_i.e._ those got by multiplying a number by itself).

Apparently no other circular orbits than these are possible in the

hydrogen atom. Elliptic orbits are possible, and these again introduce

exact multiples of _h_: but we need not, for our purposes, concern

ourselves with them.

When a hydrogen atom is left to itself, if the electron is in the

minimum orbit it will continue to rotate in that orbit so long as

nothing from outside disturbs it; but if the electron is in any of

the larger possible orbits, it may sooner or later jump suddenly to a

smaller orbit, either the minimum or one of the intermediate possible

orbits. So long as the electron does not change its orbit, the atom

does not radiate energy, but when the electron jumps to a smaller

orbit, the atom loses energy, which is radiated out in the form of a

light-wave. This light-wave is always such that its energy divided by

its frequency is exactly _h_. The atom may absorb energy from without,

and it does so by the electron jumping to a larger orbit. It may then

afterwards, when the external source of energy is removed, jump back to

the smaller orbit; this is the cause of fluorescence, since, in doing

so, the atom gives out energy in the form of light.

The same principles, with greater mathematical complications, apply

to the other elements. There is, however, with some of the latest

elements, a phenomenon which cannot have any analogue in hydrogen, and

that is radio-activity. When an atom is radio-active, it emits rays of

three kinds, called respectively α-rays, β-rays, and γ-rays. Of these,

the γ-rays are analogous to light, but of much higher frequencies,

or shorter wave-lengths; we need not further concern ourselves with

them. The α-rays and β-rays, on the contrary, are important as our

chief source of knowledge concerning the nuclei of atoms. It is found

that the α-rays consist of helium nuclei, while the β-rays consist

of electrons. Both come out of the nucleus, since the atom after

radio-activity disruption is a different element from what it was

before. But no one knows just why the nucleus disintegrates when it

does, nor why, in a piece of radium, for example, some atoms break down

while others do not.

The three principal sources of our knowledge concerning atoms have been

the light they emit, X-rays and radio-activity. As everyone knows,

when the light emitted by a glowing gas is passed through a prism, it

is found to consist of well-defined lines of different colours, which

are characteristic for each element, and constitute what is called its

“spectrum”. The spectrum extends beyond the range of visible light,

both into the infra-red and into the ultra-violet. In the latter

direction, it extends right into the region of X-rays, which are only

ultra-ultra-violet light. By means of crystals, it has been found

possible to study X-ray spectra as exactly as those of ordinary light.

The great merit of Bohr’s theory was that it explained why elements

have the spectra they do have, which had, before, been a complete

mystery. In the cases of hydrogen and positively electrified helium,

the explanation, particularly as extended by the German physicist

Sommerfeld, gave the most minute numerical agreement between theory

and observation; in other cases, mathematical difficulties made

this completeness impossible, but there was every reason to think

that the same principles were adequate. This was the main reason for

accepting Bohr’s theory; and certainly it was a very strong one. It

was found that visible light enabled us to study the outer rings of

planetary electrons, X-rays enabled us to study the inner rings,

and radio-activity enabled us to study the nucleus. For the latter

purpose, there are also other methods, more particularly Rutherford’s

“bombardment”, which aims at breaking up nuclei by firing projectiles

at them, and sometimes succeeds in making a hit in spite of the

smallness of the target.

The theory of atomic structure that has just been outlined, like

everything in theoretical physics, is capable of expression in

mathematical formulæ; but like many things in theoretical physics, it

is also capable of expression in the form of an imaginative picture.

But here, as always, it is necessary to distinguish sharply between

the mathematical symbols and the pictorial words. The symbols are

pretty sure to be right, or nearly so; the imaginative picture, on

the other hand, should not be taken too seriously. When we consider

the nature of the evidence upon which the above theory of the atom is

based, we can see that the attempt to make a picture of what goes on

has led us to be far more concrete than we have any right to be. If

we want to assert only what we have good reason to believe, we shall

have to abandon the attempt to be concrete about what goes on in the

atom, and say merely something like this: An atom with its electrons

is a system characterised by certain integers, all small, and all

capable of changing independently. These integers are the multiples of

_h_ involved. When any of them changes to a smaller integer, energy

of a definite amount is emitted, and its frequency will be obtained

by dividing the energy of _h_. When any of the integers concerned

changes to a larger integer, energy is absorbed, and again the amount

absorbed is definite. But we cannot know what goes on when the atom is

neither absorbing nor radiating energy, since then it has no effects in

surrounding regions; consequently all evidence as to atoms is as to

their changes, not as to their steady states.

The point is not that the facts do not fit with the hypothesis of

the atom as a planetary system. There are, it is true, certain

difficulties which afford empirical grounds for the newer theory which

has superseded Bohr’s, and which we shall shortly consider. But even

if no such grounds existed, it would be obvious that Bohr’s theory

states more than we have a right to infer from what we can observe. Of

theories that state so much, there must be an infinite number that are

compatible with what is known, and it is only what all of these have in

common that we are really entitled to assert. Suppose your knowledge

of Great Britain were entirely confined to observing the people and

goods that enter and leave the ports; you could, in that case, invent

many theories as to the interior of Great Britain, all of which would

agree with all known facts. This is an exact analogy. If you delimit

in the physical universe any region, large or small, not containing a

scientific observer, all scientific observers will have exactly the

same experiences whatever happens inside this region, provided it

does not affect the flow of energy across the boundary of the region.

And so, if the region contains one atom, any two theories which give

the same results as to the energy that the atom radiates or absorbs

are empirically indistinguishable, and there can be no reason except

simplicity for preferring one of them to the other. On this ground,

even if on no other, prudence compels us to seek a more abstract theory

of the atom than that which we owe to Rutherford and Bohr.

The newer theory has been put forward mainly by two physicists already

mentioned, Heisenberg and Schrödinger, in forms which look different,

but are in fact mathematically equivalent. It is as yet an impossible

task to describe this theory in simple language, but something can be

said to show its philosophical bearing. Broadly speaking, it describes

the atom by means of the radiations that come out of it. In Bohr’s

theory, the planetary electrons are supposed to describe orbits over

and over again while the atom is not radiating; in the newer theory,

we say nothing at all as to what happens at these times. The aim

is to confine the theory to what is empirically verifiable, namely

radiations; as to what there is where the radiations come from, we

cannot tell, and it is scientifically unnecessary to speculate. The

theory requires modifications in our conception of space, of a sort not

yet quite clear. It also has the consequence that we cannot identify an

electron at one time with an electron at another, if in the interval,

the atom has radiated energy. The electron ceases altogether to have

the properties of a “thing” as conceived by common sense; it is merely

a region from which energy may radiate.

On the subject of discontinuity, there is disagreement between

Schrödinger and other physicists. Most of them maintain that quantum

changes--_i.e._ the changes that occur in an atom when it radiates or

absorbs energy--must be discontinuous. Schrödinger thinks otherwise.

This is a matter in debate among experts, as to which it would be rash

to venture an opinion. Probably it will be decided one way or other

before very long.

The main point for the philosopher in the modern theory is the

disappearance of matter as a “thing”. It has been replaced by

emanations from a locality--the sort of influences that characterise

haunted rooms in ghost stories. As we shall see in the next chapter,

the theory of relativity leads to a similar destruction of the solidity

of matter, by a different line of argument. All sorts of events happen

in the physical world, but tables and chairs, the sun and moon,

and even our daily bread, have become pale abstractions, mere laws

exhibited in the successions of events which radiate from certain

regions.

CHAPTER X

RELATIVITY

We have seen that the world of the atom is a world of revolution rather

than evolution: the electron which has been moving in one orbit hops

quite suddenly into another, so that the motion is what is called

“discontinuous”, that is to say, the electron is first in one place and

then in another, without having passed over any intermediate places.

This sounds like magic, and there may be some way of avoiding such a

disconcerting hypothesis. At any rate, nothing of the sort seems to

happen in the regions where there are no electrons and protons. In

these regions, so far as we can discover, there is continuity, that

is to say, everything goes by gradual transitions, not by jumps. The

regions in which there are no electrons and protons may be called

“æther” or “empty space” as you prefer: the difference is only verbal.

The theory of relativity is especially concerned with what goes on in

these regions, as opposed to what goes on where there are electrons

and protons. Apart from the theory of relativity, what we know about

these regions is that waves travel across them, and that these waves,

when they are waves of light or electromagnetism (which are identical),

behave in a certain fashion set forth by Maxwell in certain formulæ

called “Maxwell’s equations”. When I say we “know” this, I am saying

more than is strictly correct, because all we know is what happens

when the waves reach our bodies. It is as if we could not see the sea,

but could only see the people disembarking at Dover, and inferred the

waves from the fact that the people looked green. It is obvious, in any

case, that we can only know so much about the waves as is involved in

their having such-and-such causes at one end and such-and-such effects

at the other. What can be inferred in this way will be, at best,

something wholly expressible in terms of mathematical structure. We

must not think of the waves as being necessarily “in” the æther or “in”

anything else; they are to be thought of merely as progressive periodic

processes, whose laws are more or less known, but whose intrinsic

character is not known and never can be.

The theory of relativity has arisen from the study of what goes on in

the regions where there are no electrons and protons. While the study

of the atom has led us to discontinuities, relativity has produced

a completely continuous theory of the intervening medium--far more

continuous than any theory formerly imagined. At the moment, these

two points of view stand more or less opposed to each other, but no

doubt before long they will be reconciled. There is not, even now, any

logical contradiction between them; there is only a fairly complete

lack of connection.

For philosophy, far the most important thing about the theory of

relativity is the abolition of the one cosmic time and the one

persistent space, and the substitution of space-time in place of both.

This is a change of quite enormous importance, because it alters

fundamentally our notion of the structure of the physical world, and

has, I think, repercussions in psychology. It would be useless, in our

day, to talk about philosophy without explaining this matter. Therefore

I shall make the attempt, in spite of some difficulty.

Common-sense and pre-relativity physicists believed that, if two events

happen in different places, there must always be a definite answer, in

theory, to the question whether they were simultaneous. This is found

to be a mistake. Let us suppose two persons A and B a long way apart,

each provided with a mirror and means of sending out light-signals. The

events that happen to A still have a perfectly definite time-order, and

so have those that happen to B; the difficulty comes in connecting A’s

time with B’s. Suppose A sends a flash to B, B’s mirror reflects it,

and it returns to A after a certain time. If A is on the earth and B

on the sun, the time will be about sixteen minutes. We shall naturally

say that the time when B received the light-signal is half way between

the times when A sent it out and received it back. But this definition

turns out to be not unambiguous; it will depend upon how A and B are

moving relatively to each other. The more this difficulty is examined,

the more insuperable it is seen to be. Anything that happens to A after

he sends out the flash and before he gets it back is neither definitely

before nor definitely after nor definitely simultaneous with the

arrival of the flash at B. To this extent, there is no unambiguous way

of correlating times in different places.

The notion of a “place” is also quite vague. Is London a “place”? But

the earth is rotating. Is the earth a “place”? But it is going round

the sun. Is the sun a “place”? But it is moving relatively to the

stars. At best you could talk of a place at a given time; but then it

is ambiguous what is a given time, unless you confine yourself to one

place. So the notion of “place” evaporates.

We naturally think of the universe as being in one state at one time

and in another at another. This is a mistake. There is no cosmic time,

and so we cannot speak of the state of the universe at a given time.

And similarly we cannot speak unambiguously of the distance between

two bodies at a given time. If we take the time appropriate to one of

the two bodies, we shall get one estimate; if the time of the other,

another. This makes the Newtonian law of gravitation ambiguous, and

shows that it needs restatement, independently of empirical evidence.

Geometry also goes wrong. A straight line, for example, is supposed to

be a certain track in space whose parts all exist simultaneously. We

shall now find that what is a straight line for one observer is not a

straight line for another. Therefore geometry ceases to be separable

from physics.

The “observer” need not be a mind, but may be a photographic plate.

The peculiarities of the “observer” in this region belong to physics,

not to psychology.

So long as we continue to think in terms of bodies moving, and try to

adjust this way of thinking to the new ideas by successive corrections,

we shall only get more and more confused. The only way to get clear is

to make a fresh start, with _events_ instead of bodies. In physics, an

“event” is anything which, according to the old notions, would be said

to have both a date and a place. An explosion, a flash of lightning,

the starting of a light-wave from an atom, the arrival of the

light-wave at some other body, any of these would be an “event”. Some

strings of events make up what we regard as the history of one body;

some make up the course of one light-wave; and so on. The unity of a

body is a unity of history--it is like the unity of a tune, which takes

time to play, and does not exist whole in any one moment. What exists

at any one moment is only what we call an “event”. It may be that the

word “event”, as used in physics, cannot be quite identified with the

same word as used in psychology; for the present we are concerned

with “events” as the constituents of physical processes, and need not

trouble ourselves about “events” in psychology.

The events in the physical world have relations to each other which

are of the sort that have led to the notions of space and time. They

have relations of order, so that we can say that one event is nearer

to a second than to a third. In this way we can arrive at the notion

of the “neighbourhood” of an event: it will consist roughly speaking

of all the events that are very near the given event. When we say that

neighbouring events have a certain relation, we shall mean that the

nearer two events are to each other, the more nearly they have this

relation, and that they approximate to having it without limit as they

are taken nearer and nearer together.

Two neighbouring events have a measurable quantitative relation

called “interval”, which is sometimes analogous to distance in space,

sometimes to lapse of time. In the former case it is called space-like,

in the latter time-like. The interval between two events is time-like

when one body might be present at both--for example, when both are

parts of the history of your body. The interval is space-like in the

contrary case. In the marginal case between the two, the interval is

zero; this happens when both are parts of one light-ray.

The interval between two neighbouring events is something objective,

in the sense that any two careful observers will arrive at the same

estimate of it. They will not arrive at the same estimate for the

distance in space or the lapse of time between the two events, but the

interval is a genuine physical fact, the same for all. If a body can

travel freely from one event to the other, the interval between the two

events will be the same as the time between them as measured by a clock

travelling with the body. If such a journey is physically impossible,

the interval will be the same as the distance as estimated by an

observer to whom the two events are simultaneous. But the interval is

only definite when the two events are very near together; otherwise

the interval depends upon the route chosen for travelling from the one

event to the other.

Four numbers are needed to fix the position of an event in the world;

these correspond to the time and the three dimensions of space in the

old reckoning. These four numbers are called the co-ordinates of the

event. They may be assigned on any principle which gives neighbouring

co-ordinates to neighbouring events; subject to this condition, they

are merely conventional. For example, suppose an aeroplane has had an

accident. You can fix the position of the accident by four numbers:

latitude, longitude, altitude above sea-level, and Greenwich Mean Time.

But you cannot fix the position of the explosion in space-time by means

of less than four numbers.

Everything in relativity-theory goes (in a sense) from next to

next; there are no direct relations between distant events, such as

distance in time or space. And of course there are no forces acting

at a distance; in fact, except as a convenient fiction, there are

no “forces” at all. Bodies take the course which is easiest at each

moment, according to the character of space-time in the particular

region where they are; this course is called a _geodesic_.

Now it will be observed that I have been speaking freely of bodies and

motion, although I said that bodies were merely certain strings of

events. That being so, it is of course necessary to say what strings of

events constitute bodies, since not all continuous strings of events

do so, not even all geodesics. Until we have defined the sort of thing

that makes a body, we cannot legitimately speak of motion, since this

involves the presence of one body on different occasions. We must

therefore set to work to define what we mean by the persistence of a

body, and how a string of events constituting a body differs from one

which does not. This topic will occupy the next chapter.

But it may be useful, as a preliminary, to teach our imagination to

work in accordance with the new ideas. We must give up what Whitehead

admirably calls the “pushiness” of matter. We naturally think of an

atom as being like a billiard-ball; we should do better to think of it

as like a ghost, which has no “pushiness” and yet can make you fly. We

have to change our notions both of substance and of cause. To say that

an atom persists is like saying that a tune persists. If a tune takes

five minutes to play, we do not conceive of it as a single thing which

exists throughout that time, but as a series of notes, so related as

to form a unity. In the case of the tune, the unity is æsthetic; in

the case of the atom, it is causal. But when I say “causal” I do not

mean exactly what the word naturally conveys. There must be no idea of

compulsion or “force”, neither the force of contact which we imagine

we see between billiard-balls nor the action at a distance which

was formerly supposed to constitute gravitation. There is merely an

observed law of succession from next to next. An event at one moment

is succeeded by an event at a neighbouring moment, which, to the first

order of small quantities, can be calculated from the earlier event.

This enables us to construct a string of events, each, approximately,

growing out of a slightly earlier event according to an intrinsic law.

Outside influences only affect the second order of small quantities. A

string of events connected, in this way, by an approximate intrinsic

law of development is called one piece of matter. This is what I mean

by saying that the unity of a piece of matter is causal. I shall

explain this notion more fully in later chapters.

CHAPTER XI

CAUSAL LAWS IN PHYSICS

In the last chapter we spoke about the substitution of space-time for

space and time, and the effect which this has had in substituting

strings of events for “things” conceived as substances. In this chapter

we will deal with cause and effect as they appear in the light of

modern science. It is at least as difficult to purge our imagination

of irrelevances in this matter as in regard to substance. The

old-fashioned notion of cause appeared in dynamics as “force”. We still

speak of forces just as we still speak of the sunrise, but we recognise

that this is nothing but a convenient way of speaking, in the one case

as in the other.

Causation is deeply embedded in language and common sense. We say that

people build houses or make roads: to “build” and to “make” are both

notions involving causality. We say that a man is “powerful”, meaning

that his volitions are causes over a wide range. Some examples of

causation seem to us quite natural, others less so. It seems natural

that our muscles should obey our will, and only reflection makes us

perceive the necessity of finding an explanation of this phenomenon. It

seems natural that when you hit a billiard-ball with a cue it moves.

When we see a horse pulling a cart, or a heavy object being dragged by

a rope, we _feel_ as if we understood all about it. It is events of

this sort that have given rise to the common-sense belief in causes and

forces.

But as a matter of fact the world is incredibly more complicated than

it seems to common sense. When we think we understand a process--I mean

by “we” the non-reflective part in each of us--what really happens

is that there is some sequence of events so familiar through past

experience that at each stage we expect the next stage. The whole

process seems to us peculiarly intelligible when human desires enter

in, for example, in watching a game: what the ball does and what the

players do seem “natural”, and we feel as if we quite understood how

the stages succeed each other. We thus arrive at the notion of what is

called “necessary” sequence. The text-books say that A is the cause of

B if A is “necessarily” followed by B. This notion of “necessity” seems

to be purely anthropomorphic, and not based upon anything that is a

discoverable feature of the world. Things happen according to certain

rules; the rules can be generalised, but in the end remain brute facts.

Unless the rules are concealed conventions or definitions, no reason

can be given why they should not be completely different.

To say that A is “necessarily” followed by B is thus to say no more

than that there is some general rule, exemplified in a very large

number of observed instances, and falsified in none, according to which

events such as A are followed by events such as B. We must not have any

notion of “compulsion”, as if the cause _forced_ the effect to happen.

A good test for the imagination in this respect is the reversibility

of causal laws. We can just as often infer backwards as forwards.

When you get a letter, you are justified in inferring that somebody

wrote it, but you do not feel that your receiving it _compelled_

the sender to write it. The notion of compulsion is just as little

applicable to effects as to causes. To say that causes compel effects

is as misleading as to say that effects compel causes. Compulsion is

anthropomorphic: a man is compelled to do something when he wishes to

do the opposite, but except where human or animal wishes come in the

notion of compulsion is inapplicable. Science is concerned merely with

what happens, not with what _must_ happen.

When we look for invariable rules of sequence in nature, we find that

they are not such as common sense sets up. Common sense says: thunder

follows lightning, waves at sea follow wind, and so on. Rules of

this sort are indispensable in practical life, but in science they

are all only approximate. If there is any finite interval of time,

however short, between the cause and the effect, something may happen

to prevent the effect from occurring. Scientific laws can only be

expressed in differential equations. This means that, although you

cannot tell what may happen after a finite time, you can say that, if

you make the time shorter and shorter, what will happen will be more

and more nearly according to such-and-such a rule. To take a very

simple case: I am now in this room; you cannot tell where I shall be

in another second, because a bomb may explode and blow me sky-high,

but if you take any two small fragments of my body which are now very

close together, you can be sure that, after _some_ very short finite

time, they will still be very close together. If a second is not short

enough, you must take a shorter time; you cannot tell in advance how

short a time you may have to take, but you may feel fairly certain that

there is a short enough time.

The laws of sequence in physics, apart from quantum phenomena, are of

two sorts, which appeared in traditional dynamics as laws of velocity

and laws of acceleration. In a very short time, the velocity of a

body alters very little, and if the time is taken short enough, the

change of velocity diminishes without limit. This is what, in the last

chapter, we called an “intrinsic” causal law. Then there is the effect

of the outer world, as it appeared in traditional dynamics, which

is shown in acceleration. The small change which does occur in the

velocity in a short time is attributed to surrounding bodies, because

it is found to vary as they vary, and to vary according to ascertained

laws. Thus we think of surrounding bodies as exerting an influence,

which we call “force”, though this remains as mysterious as the

influence of the stars in astrology.

Einstein’s theory of gravitation has done away with this conception in

so far as gravitational forces are concerned. In this theory, a planet

moving round the sun is moving in the nearest approach to a straight

line that the neighbourhood permits. The neighbourhood is supposed to

be non-Euclidean, that is to say, to contain no straight lines such

as Euclid imagined. If a body is moving freely, as the planets do, it

observes a certain rule. Perhaps the simplest way to state this rule

is as follows: Suppose you take any two events which happen on the

earth, and you measure the time between them by ideally accurate clocks

which move with the earth. Suppose some traveller on a magic carpet had

meanwhile cruised about the universe, leaving the earth at the time of

the first event and returning at the time of the second. By his clocks

the period elapsed will be less than by the terrestial clocks. This is

what is meant by saying that the earth moves in a “geodesic”, which

is the nearest approach to a straight line to be found in the region

in which we live. All this is, so to speak, geometrical, and involves

no “forces”. It is not the sun that makes the earth go round, but the

nature of space-time where the earth is.

Even this is not quite correct. Space-time does not make the earth go

round the sun; it makes us _say_ the earth goes round the sun. That is

to say, it makes this the shortest way of describing what occurs. We

could describe it in other language, which would be equally correct,

but less convenient.

The abolition of “force” in astronomy is perhaps connected with the

fact that astronomy depends only upon the sense of sight. On the

earth, we push and pull, we touch things, and we experience muscular

strains. This all gives us a notion of “force”, but this notion is

anthropomorphic. To imagine the laws of motion of heavenly bodies,

think of the motions of objects in a mirror; they may move very fast,

although in the mirror world there are no forces.

What we really have to substitute for force is laws of correlation.

Events can be collected in groups by their correlations. This is

all that is true in the old notion of causality. And this is not a

“postulate” or “category”, but an observed fact--lucky, not necessary.

As we suggested before, it is these correlations of events that lead

to the definition of permanent “things”. There is no essential

difference, as regards substantiality, between an electron and a

light-ray. Each is really a string of events or of sets of events. In

the case of the light-ray, we have no temptation to think otherwise.

But in the case of the electron, we think of it as a single persistent

entity. There _may_ be such an entity, but we can have no evidence that

there is. What we can discover is (_a_) a group of events spreading

outwards from a centre--say, for definiteness, the events constituting

a wave of light--and attributed, hypothetically, to a “cause” in that

centre; (_b_) more or less similar groups of events at other times,

connected with the first group according to the laws of physics, and

therefore attributed to the same hypothetical cause at other times. But

all that we ought to assume is series of groups of events, connected by

discoverable laws. These series we may _define_ as “matter”. Whether

there is matter in any other sense, no one can tell.

What is true in the old notion of causality is the fact that events at

different times are connected by laws (differential equations). When

there is a law connecting an event A with an event B, the two have a

definite unambiguous time-order. But if the events are such that a ray

of light starting from A would arrive at any body which was present at

B after B had occurred, and _vice versa_, then there is no definite

true order, and no possible causal law connecting A and B. A and B must

then be regarded as separate facts of geography.

Perhaps the scope and purpose of this and the foregoing chapters may

be made clearer by showing their bearing upon certain popular beliefs

which may seem self-evident but are really in my opinion either false

or likely to lead to falsehood. I shall confine myself to objections

which have actually been made to me when trying to explain the

philosophical outcome of modern physics.[8]

[8] These objections are quoted (with kind permission) from a

letter written to me by a well-known engineer, Mr. Percy

Griffith, who is also a writer on philosophical subjects.

“We cannot conceive of movement apart from some _thing_ as moving.”

This is, in a sense, a truism; but in the sense in which it is usually

meant, it is a falsehood. We speak of the “movement” of a drama or

piece of music, although we do not conceive either as a “thing” which

exists complete at every moment of the performance. This is the sort of

picture we must have in our minds when we try to conceive the physical

world. We must think of a string of events, connected together by

certain causal connections, and having enough unity to deserve a single

name. We then begin to imagine that the single name denotes a single

“thing”, and if the events concerned are not all in the same place, we

say the “thing” has “moved.” But this is only a convenient shorthand.

In the cinema, we seem to see a man falling off a skyscraper, catching

hold of the telegraph wires, and reaching the ground none the worse.

We know that, in fact, there are a number of different photographs,

and the appearance of a single “thing” moving is deceptive. In this

respect, the real world resembles the cinema.

In connection with motion one needs to emphasise the very difficult

distinction between _experience_ and _prejudice_. Experience, roughly,

is what you see, and prejudice is what you only think you see.

Prejudice tells you that you see the _same_ table on two different

occasions; you _think_ that experience tells you this. If it really

were experience, you could not be mistaken; yet a similar table may be

substituted without altering the experience. If you look at a table

on two different occasions, you have very similar sensations, and

memory tells you that they are similar; but there is nothing to show

that one identical entity causes the two sensations. If the table is

in a cinema, you know that there is not such an entity, even though

you can watch it changing with apparent continuity. The experience is

just like that with a “real” table; so in the case of a “real” table

also, there is nothing in the actual experience to show whether there

is a persistent entity or not. I say, therefore: I do not know whether

there is a persistent entity, but I do know that my experiences can be

explained without assuming that there is. Therefore it can be no part

of legitimate science to assert or deny the persistent entity; if it

does either, it goes beyond the warrant of experience.

The following is a verbally cited passage in the letter referred to

objecting to what was said above about “force”:

“The concept of Force is not of physical but of psychological origin.

Rightly or wrongly it arises in the most impersonal contemplation of

the Stellar Universe, where we observe an infinite number of spherical

bodies revolving on their own axes and gyrating in orbits round each

other. Rightly or wrongly, we naturally conceive of these as having

been so constituted and so maintained by some Force or Forces.”

We do not, in fact, “observe” what it is here said that we observe; all

this is _inferred_. What we observe, in astronomy, is a two-dimensional

pattern of points of light, with a few bright surfaces of measurable

size when seen through the telescope (the planets), and of course

the larger bright surfaces that we call the sun and moon. Most of

this pattern (the fixed stars) rotates round the earth once in every

twenty-three hours and fifty-six minutes. The sun rotates in varying

periods, which average twenty-four hours and never departs very far

from the average. The moon and planets have apparent motions which are

more irregular. These are the _observed_ facts. There is no logical

impossibility about the formulæ doctrine of spheres rotating round the

earth, one for each planet and one for the stars. The modern doctrines

are simpler, but not one whit more in accordance with observed facts;

it is our passion for _simple_ laws that has made us adopt them.

The last sentence of the above quotation raises some further points of

interest. “Rightly or wrongly”, the writer says, “we naturally conceive

of these as having been so constituted and so maintained by some Force

or Forces.” I do not deny this. It is “natural”, and it is “right or

wrong”--more specifically, it is wrong. “Force” is part of our love of

explanations. Everyone knows about the Hindu who thought that the world

does not fall because it is supported by an elephant, and the elephant

does not fall because it is supported by a tortoise. When his European

interlocutor said “But how about the tortoise?” he replied that he was

tired of metaphysics and wanted to change the subject. “Force”, as an

explanation, is no better than the elephant and the tortoise. It is

an attempt to get at the “why” of natural processes, not only at the

“how”. What we observe, to a limited extent, is what happens, and we

can arrive at laws according to which observable things happen, but

we cannot arrive at a reason for the laws. If we invent a reason, it

needs a reason in its turn, and so on. “Force” is a rationalising of

natural processes, but a fruitless one since “force” would have to be

rationalised also.

When it is said, as it often is, that “force” belongs to the world of

experience, we must be careful to understand what can be meant. In

the first place, it may be meant that calculations which employ the

notion of force work out right in practice. This, broadly speaking,

is admitted: no one would suggest that the engineer should alter his

methods, or should give up working out stresses and strains. But that

does not prove that there are stresses and strains. A British medical

man renders his accounts in guineas, although they have long since

ceased to exist except as a name; he obtains a real payment, though he

employs a fictitious coin. Similarly, the engineer is concerned with

the question whether his bridge will stand: the fact of experience is

that it stands (or does not stand), and the stresses and strains are

only a way of explaining what sort of bridge will stand. They are as

useful as guineas, but equally imaginary.

But when it is said that force is a fact of experience, there is

something quite different that may be meant. It may be meant that we

experience force when we experience such things as pressure or muscular

exertion. We cannot discuss this contention adequately without going

into the relation of physics to psychology, which is a topic we shall

consider at length at a later stage. But we may say this much: if

you press your finger-tip upon a hard object, you have an experience

which you attribute to your finger-tip, but there is a long chain of

intermediate causes in nerves and brain. If your finger were amputated

you could still have the same experience by a suitable operation on

the nerves that formerly connected the finger with the brain, so that

the force between the finger-tip and the hard object, as a fact of

experience, may exist when there is no finger-tip. This shows that

force, in this sense, cannot be what concerns physics.

As the above example illustrates, we do not, in fact, experience

many things that we think we experience. This makes it necessary to

ask, without too much assurance, in what sense physics can be based

upon experience, and what must be the nature of its entities and its

inferences if it is to make good its claim to be empirically grounded.

We shall begin this inquiry in the next chapter.

CHAPTER XII

PHYSICS AND PERCEPTION

It will be remembered that we regarded perception, in Chapter V, as

a species of “sensitivity”. Sensitivity to a given feature of the

environment we defined as consisting in some characteristic reaction

which is exhibited whenever that feature is present, but not otherwise;

this property is possessed more perfectly, in given directions, by

scientific instruments than by living bodies, though scientific

instruments are more selective as to the stimuli to which they will

respond. We decided that what, from the standpoint of an external

observer, distinguishes perception from other forms of sensitivity is

the law of association or conditioned reflexes. But we also found that

this purely external treatment of perception presupposes our knowledge

of the physical world as a going concern. We have now to investigate

this presupposition, and to consider how we come to know about physics,

and how much we really do know.

According to the theory of Chapter V, it is possible to perceive things

that are not in a spatial contact with the body. There must be a

reaction to a feature of the environment, but that feature may be at a

greater or less distance from the body of the percipient; we can even

perceive the sun and stars, within the limits of the definition. All

that is necessary is that our reaction should depend upon the spatial

relation between our body and the feature of the environment. When our

back is towards the sun, we do not see it; when our face is towards it,

we do.

When we consider perception--visual or auditory--of an external event,

there are three different matters to be examined. There is first the

process in the outside world, from the event to the percipient’s body;

there is next the process in his body, in so far as this can be known

by an outside observer; lastly, there is the question, which must be

faced sooner or later, whether the percipient can perceive something of

the process in his body which no other observer could perceive. We will

take these points in order.

If it is to be possible to “perceive” an event not in the percipient’s

body, there must be a physical process in the outer world such that,

when a certain event occurs, it produces a stimulus of a certain kind

at the surface of the percipient’s body. Suppose, for example, that

pictures of different animals are exhibited on a magic lantern to a

class of children, and all the children are asked to say the name of

each animal in turn. We may assume that the children are sufficiently

familiar with animals to say “cat”, “dog”, “giraffe”, “hippopotamus”,

etc., at the right moments. We must then suppose--taking the physical

world for granted--that some process travels from each picture to the

eyes of the various children, retaining throughout these journeys such

peculiarities that, when the process reaches their eyes, it can in one

case stimulate the word “cat” and in another the word “dog”. All this

the physical theory of light provides for. But there is one interesting

point about language that should be noticed in this connection. If the

usual physical theory of light is correct, the various children will

receive stimuli which differ greatly according to their distance and

direction from the picture, and according to the way the light falls.

There are also differences in their reactions, for, though they all

utter the word “cat”, some say it loud, others soft, some in a soprano

voice, some in a contralto. But the differences in their reactions are

much less than the differences in the stimuli. This is still more the

case if we consider various different pictures of cats, to all of which

they respond with the word “cat”. Thus language is a means of producing

responses which differ less than the stimuli do, in cases where the

resemblances between the stimuli are more important to us than the

differences. This fact makes us apt to overlook the differences

between stimuli which produce nearly identical responses.

As appears from the above, when a number of people simultaneously

perceive a picture of a cat, there are differences between the stimuli

to their various perceptions, and these differences must obviously

involve differences in their reactions. The _verbal_ responses may

differ very little, but even the verbal responses could be made to

differ by putting more complicated questions than merely “What animal

is that?” One could ask: “Can the picture be covered by your thumb-nail

held at arm’s length?” Then the answer would be different according

as the percipient was near the picture or far off. But the normal

percipient, if left to himself, will not notice such differences,

that is to say, his verbal response will be the same in spite of the

differences in the stimuli.

The fact that it is possible for a number of people to perceive the

same noise or the same coloured pattern obviously depends upon the fact

that a physical process can travel outward from a centre and retain

certain of its characteristics unchanged, or very little changed. The

most notable of such characteristics is frequency in a wave-motion.

That, no doubt, affords a biological reason for the fact that our most

delicate senses, sight and hearing, are sensitive to frequencies, which

determine colour in what we see and pitch in what we hear. If there

were not, in the physical world, processes spreading out from centres

and retaining certain characters practically unchanged, it would be

impossible for different percipients to perceive the same object from

different points of view, and we should not have been able to discover

that we all live in a common world.

We come now to the process in the percipient’s body, in so far as

this can be perceived by an outside observer. This raises no new

philosophical problems, because we are still concerned, as before, with

the perception of events outside the observer’s body. The observer,

now, is supposed to be a physiologist, observing, say, what goes on

in the eye when light falls upon it. His means of knowing are, in

principle, exactly the same as in the observation of dead matter.

An event in an eye upon which light is falling causes light-waves

to travel in a certain manner until they reach the eye of the

physiologist. They there cause a process in the physiologist’s eye

and optic nerve and brain, which ends in what he calls “seeing what

happens in the eye he is observing”. But this event, which happens in

the physiologist, is not what happened in the eye he was observing;

it is only connected with this by a complicated causal chain. Thus

our knowledge of physiology is no more direct or intimate than our

knowledge of processes in dead matter; we do not know any more about

our eyes than about the trees and fields and clouds that we see by

means of them. The event which happens when a physiologist observes an

eye is an event in him, not on the eye that he is observing.

We come now at last to the question of self-observation, which we have

hitherto avoided. I say “self-observation” rather than “introspection”,

because the latter word has controversial associations that I wish to

avoid. I mean by “self-observation” anything that a man can perceive

about himself but that others, however situated, cannot perceive about

him. What follows is only preliminary, since the subject will be

discussed at length in Chapter XVI.

No one can deny that we know things about ourselves which others

cannot know unless we tell them. We know when we have toothache, when

we feel thirsty, what we were dreaming when we woke up, and so on.

Dr. Watson might say that the dentist can know we have toothache by

observing a cavity in a tooth. I will not reply that the dentist is

often mistaken; this may be merely because the art of dentistry has not

been sufficiently perfected. I will concede as possible, in the future,

a state of odontology in which the dentist could always know whether

I am feeling toothache. But even then his knowledge has a different

character from mine. His knowledge is an inference, based upon the

inducive law that people with such-and-such cavities suffer pain of

a certain kind. But this law cannot be established by observation of

cavities alone; it requires that, where these are observed, the people

who have them should tell us that they feel toothache. And, more than

that, they must be speaking the truth. Purely external observation can

discover that people with cavities _say_ they have toothache, but not

that they have it. Saying one has toothache is a different thing from

having it; if not we could cure toothache by not talking about it, and

so save our dentists’ bills. I am sure the expert opinion of dentists

will agree with me that this is impossible.

To this argument, however, it might be replied that having toothache is

a state of the body, and that knowing I have toothache is a response to

this bodily stimulus. It will be said that, theoretically, the state

of my body when I have toothache can be observed by an outsider, who

can then also know that I have toothache. This answer, however, does

not really meet the point. When the outside observer knows that I have

toothache, not only is his knowledge based upon an inductive inference,

as we have already seen, but his knowledge of the inferred term,

“toothache”, must be based upon personal experience. No knowledge of

dentistry could enable a man to know what toothache is if he had never

felt it. If, then, toothache is really a state of the body--which, at

the moment, I neither affirm nor deny--it is a state of the body which

only the man himself can perceive. In a word, whoever has experienced

toothache and can remember it has knowledge that cannot be possessed by

a man who has never experienced toothache.

Take next our knowledge of our own dreams. Dr. Watson has not, so far

as I know, ever discussed dreams, but I imagine he would say something

like this: In dreams, there are probably small laryngeal movements

such as, if they were greater, would lead to speech; indeed, people

do sometimes cry out in dreams. There may also be stimulations of the

sense-organs, which produce unusual reactions owing to the peculiar

physiological condition of the brain during sleep: but all these

reactions must consist of small movements, which could theoretically be

seen from outside, say by some elaboration of X-ray apparatus. This is

all very well, but meantime it is hypothetical, and the dreamer himself

knows his dreams without all this elaborate inference. Can we say that

he really knows these hypothetical small bodily movements, although

he thinks he knows something else? That would presumably be Dr.

Watson’s position, and it must be admitted that, with a definition of

“knowledge” such as we considered in Chapter VIII, such a view is not

to be dismissed offhand as obviously impossible. Moreover, if we are to

say the perception gives knowledge of the physical world, we shall have

to admit that what we are perceiving may be quite different from what

it seems to be. A table does not look like a vast number of electrons

and protons, nor like trains of waves meeting and clashing. Yet this

is the sort of thing a table is said to be by modern physicists. If,

then, what seems to us to be just a table such as may be seen any day

is really this odd sort of thing, it is possible that what seems to us

to be a dream is really a number of movements in the brain.

This again is all very well, but there is one point which it fails to

explain, namely, what is meant by “seeming”. If a dream or a table

“seems” to be one sort of thing while it is “really” another, we shall

have to admit that it _really_ seems, and that what it seems to be has

a reality of its own. Nay more, we only arrive at what it “really” is

by an inference, valid or invalid, from what it seems to be. If we are

wrong about the seeming, we must be doubly wrong about the reality,

since the sole ground for asserting the table composed of electrons and

protons is the table that we see, _i.e._ the “seeming” table. We must

therefore treat “seeming” with respect.

Let us consider Dr. Watson watching a rat in a maze. He means to be

quite objective, and report only what really goes on. Can he succeed?

In one sense he can. He can use words about what he sees which are

the same as any other scientifically trained observer will use if he

watches the same rat at the same time. But Dr. Watson’s objectivity

emphatically does not consist in using the same words as other people

use; his vocabulary is very different from that of most psychologists.

He cannot take as the sole test of truth the consensus of mankind.

“Securus judicat orbis terrarum” is another example of a Latin tag

which is false, and which certainly Dr. Watson would not consider

true. It has happened again and again in human history that a man who

said something that had never been said before turned out to be right,

while the people who repeated the wise saws of their forefathers were

talking nonsense. Therefore, when Dr. Watson endeavours to eliminate

subjectivity in observing rats, he does not mean that he says what

everybody else says. He means that he refrains from inferring anything

about the rat beyond its bodily movements. This is all to the good,

but I think he fails to realise that almost as long and difficult

an inference is required to give us knowledge of the rat’s bodily

movements as to give us knowledge of its “mind”. And what is more,

the data from which we must start in order to get to know the rat’s

bodily movements are data of just the sort that Dr. Watson wishes to

avoid, namely private data patent to self-observation but not patent to

anyone except the observer. This is the point at which, in my opinion,

behaviourism _as a final philosophy_ breaks down.

When several people simultaneously watch a rat in a maze, or any other

example of what we should naturally regard as matter in motion, there

is by no means complete identity between the physical events which

happen at the surface of their eyes and constitute the stimuli to

their perceptions. There are differences of perspective, of light and

shade, of apparent size, and so on, all of which will be reproduced

in photographs taken from the places where the eyes of the several

observers are. These differences produce differences in the reactions

of the observers--differences which a quite unthinking person may

overlook, but which are familiar to every artist. Now it is contrary

to all scientific canons to suppose that the object perceived, in

addition to affecting us in the way of stimulus and reaction, also

affects us directly by some mystical epiphany; certainly it is not what

any behaviourist would care to assert. Our knowledge of the physical

world, therefore, must be contained in our reaction to the stimulus

which reaches us across the intervening medium; and it seems hardly

possible that our reaction should have a more intimate relation to the

object than the stimulus has. Since the stimulus differs for different

observers, the reaction also differs; consequently, in all our

perceptions of physical processes there is an element of subjectivity.

If, therefore, physics is true in its broad outlines (as the above

argument supposes), what we call “perceiving” a physical process is

something private and subjective, at least in part, and is yet the only

possible starting-point for our knowledge of the physical world.

There is an objection to the above argument which might naturally be

made, but it would be in fact invalid. It may be said that we do not in

fact proceed to _infer_ the physical world from our perceptions, but

that we begin at once with a rough-and-ready knowledge of the physical

world, and only at a late stage of sophistication compel ourselves to

regard our knowledge of the physical world as an inference. What is

valid in this statement is the fact that our knowledge of the physical

world is not at first inferential, but that is only because we take our

percepts to _be_ the physical world. Sophistication and philosophy come

in at the stage at which we realise that the physical world cannot be

identified with our percepts. When my boy was three years old, I showed

him Jupiter, and told him that Jupiter was larger than the earth. He

insisted that I must be speaking of some other Jupiter, because, as he

patiently explained, the one he was seeing was obviously quite small.

After some efforts, I had to give it up and leave him unconvinced. In

the case of the heavenly bodies, adults have got used to the idea that

what is really there can only be _inferred_ from what they see; but

where rats in mazes are concerned, they still tend to think that they

are seeing what is happening in the physical world. The difference,

however, is only one of degree, and naive realism is as untenable in

the one case as in the other. There are differences in the perceptions

of two persons observing the same process; there are sometimes no

discoverable differences between two perceptions of the same persons

observing different processes, _e.g._ pure water and water full of

bacilli. The subjectivity of our perceptions is thus of practical as

well as theoretical importance.

I am not maintaining that what we primarily know is our own

perceptions. This is largely a verbal question; but with the definition

of knowledge given in Chapter VIII, it will be correct to say that

from the first we know external objects, the question is not as to

what are the objects we know, but rather as to how accurately we

know them. Our non-inferential knowledge of an object cannot be more

accurate than our reaction to it, since it is part of that reaction.

And our reaction cannot be more accurate than the stimulus. But what

on earth can you mean by the “accuracy” of a stimulus? I may be

asked. I mean just the same as by the accuracy of a map or a set of

statistics. I mean a certain kind of correspondence. One pattern is

an accurate representation of another if every element of the one can

be taken as the representative of just one element of the other, and

the relations that make the one set into a pattern correspond with

relations making the other set into a pattern. In this sense, writing

can represent speech with a certain degree of accuracy; to every spoken

word a written word corresponds, and to the time-order of the spoken

words the space-order of the written words corresponds. But there are

inflexions and tones of voice that cannot be represented in writing,

except, to some extent, by musical notation. A gramophone record is

a much more accurate representation of vocal sounds than any writing

can be; but even the best gramophone record fails to be completely

accurate. The impression made upon an observer is very analogous to

a gramophone record or a photograph, but usually less accurate owing

to the influence of the law of association, and the lack of delicacy

in our senses. And whatever limitations there are to the accuracy of

our impressions are limitations to the accuracy of our non-inferential

knowledge of the external world.

Another point: If we accept the definition of knowledge given

in Chapter VIII, which was framed so far as to be as favourable

as possible to behaviourism, a given reaction may be regarded as

knowledge of various different occurrences. When we see Jupiter, we

have, according to the definition, knowledge of Jupiter, but we also

have knowledge of the stimulus at the surface of the eye, and even

of the process in the optic nerve. For it is arbitrary at what point

we start in the process leading to a certain event in the brain:

this event, and the consequent bodily action, may be regarded as a

reaction to a process starting at any earlier point. And the nearer

our starting-point is to the brain, the more accurate becomes the

knowledge displayed in our reaction. A lamp at the top of a tall

building might produce the same visual stimulus as Jupiter, or at any

rate one practically indistinguishable from that produced by Jupiter.

A blow on the nose might make us “see stars”. Theoretically, it should

be possible to apply a stimulus direct to the optic nerve, which

should give us a visual sensation. Thus when we think we see Jupiter,

we may be mistaken. We are less likely to be mistaken if we say that

the surface of the eye is being stimulated in a certain way, and still

less likely to be mistaken if we say that the optic nerve is being

stimulated in a certain way. We do not eliminate the risk of error

completely unless we confine ourselves to saying that an event of a

certain sort is happening in the brain; this statement may still be

true if we see Jupiter in a dream.

But, I shall be asked, what do you know about what is happening in the

brain? Surely nothing. Not so, I reply. I know about what is happening

in the brain exactly what naive realism thinks it knows about what is

happening in the outside world. But this needs explaining, and there

are other matters that must be explained first.

When the light from a fixed star reaches me, I see the star if it is

night and I am looking in the right direction. The light started years

ago, probably many years ago, but my reaction is primarily to something

that is happening _now_. When my eyes are open, I see the star; when

they are shut, I do not. Children discover at a fairly early age

that they see nothing when their eyes are shut. They are aware of the

difference between seeing and not seeing, and also of the difference

between eyes open and eyes shut; gradually they discover that these

two differences are correlated--I mean that they have expectations of

which this is the intellectualist transcription. Again, children learn

to name the colours, and to state correctly whether a thing is blue

or red or yellow or what-not. They ought not to be sure that light of

the appropriate wave-length started from the object. The sun looks red

in a London fog, grass looks blue through blue spectacles, everything

looks yellow to a person suffering from jaundice. But suppose you ask:

What colour are you seeing? The person who answers, in these cases,

red for the sun, blue for the grass, and yellow for the sick-room of

the jaundiced patient, is answering quite truly. And in each of these

cases he is stating something that he _knows_. What he knows in such

cases is what I call a “percept”. I shall contend later that, from the

standpoint of physics, a percept is in the brain; for the present, I am

only concerned to say that a percept is what is most indubitable in our

knowledge of the world.

To behaviourism as a metaphysic one may put the following dilemma.

Either physics is valid in its main lines, or it is not. If it is

not, we know nothing about the movements of matter; for physics is

the result of the most serious and careful study of which the human

intelligence has hitherto been capable. If, on the other hand, physics

is valid in its main lines, any physical process starting either inside

or outside the body will, if it reaches the brain, be different if

the intervening medium is different; moreover two persons, initially

very different, may become indistinguishable as they spread and grow

fainter. On both grounds, what happens in the brain is not connected

quite accurately with what happens elsewhere, and our perceptions

are therefore infected with subjectivity on purely physical grounds.

Even, therefore, when we assume the truth of physics, what we know

most indubitably through perception is not the movements of matter,

but certain events in ourselves which are connected, in a manner not

quite invariable, with the movements of matter. To be specific, when

Dr. Watson watches rats in mazes, what he knows, apart from difficult

inferences, are certain events in himself. The behaviour of the rats

can only be inferred by the help of physics, and is by no means to be

accepted as something accurately knowable by direct observation.

I do not in fact entertain any doubts that physics is true in its main

lines. The interpretation of physical formulæ is a matter as to which

a considerable degree of uncertainty is possible; but we cannot well

doubt that there is an interpretation which is true roughly and in

the main. I shall come to the question of interpretation later; for

the present, I shall assume that we may accept physics in its broad

outlines, without troubling to consider how it is to be interpreted.

On this basis, the above remarks on perception seem undeniable. We

are often misled as to what is happening, either by peculiarities of

the medium between the object and our bodies, or by unusual states of

our bodies, or by a temporary or permanent abnormality in the brain.

But in all these cases _something_ is really happening, as to which,

if we turn our attention to it, we can obtain knowledge that is not

misleading. At one time when, owing to illness, I had been taking a

great deal of quinine, I became hypersensitive to noise, so that when

the nurse rustled the newspaper I thought she was spilling a scuttle

of coals on the floor. The interpretation was mistaken, but it was

quite true that I heard a loud noise. It is a commonplace that a man

whose leg has been amputated can still feel pains in it; here again,

he does really feel the pains, and is only mistaken in his belief that

they come from his leg. A percept is an observable event, but its

interpretation as knowledge of this or that event in the physical world

is liable to be mistaken, for reasons which physics and physiology can

make fairly clear.

The subjectivity of percepts is a matter of degree. They are more

subjective when people are drunk or asleep than when they are sober

and awake. They are more subjective in regard to distant objects than

in regard to such as are near. They may acquire various peculiar kinds

of subjectivity through injuries to the brain or to the nerves. When

I speak of a percept as “subjective” I mean that the physiological

inferences to which it gives rise are mistaken or vague. This is

always the case to some extent, but much more so in some circumstances

than in others. And the sort of defect that leads to mistakes must be

distinguished from the sort that leads to vagueness. If you see a man a

quarter of a mile away, you can see that it is a man if you have normal

eyesight, but you probably cannot tell who it is, even if in fact

it is some one you know well. This is vagueness in the percept: the

inferences you draw are correct so far as they go, but they do not go

very far. On the other hand, if you are seeing double and think there

are two men, you have a case of mistake. Vagueness, to a greater or

less extent, is universal and inevitable; mistakes, on the other hand,

can usually be avoided by taking trouble and by not always trusting

to physiological inference. Anybody can see double on purpose, by

focussing on a distant object and noticing a near one; but this will

not cause mistakes, since the man is aware of the subjective element in

his double vision. Similarly we are not deceived by after-images, and

only dogs are deceived by gramophones.

From what has been said in this chapter, it is clear that our knowledge

of the physical world, if it is to be made as reliable as possible,

must start from percepts, and must scrutinize the physiological

inferences by which percepts are accompanied. Physiological inference

is inference in the sense that it sometimes leads to error and physics

gives reason to expect that percepts will, in certain circumstances,

be more or less deceptive if taken as signs of something outside the

brain. It is these facts that give a subjective cast to the philosophy

of physics, at any rate in its beginnings. We cannot start cheerfully

with a world of matter in motion, as to which any two sane and sober

observers must agree. To some extent, each man dreams his own dream,

and the disentangling of the dream element in our percepts is no easy

matter. This is, indeed, the work that scientific physics undertakes to

do.

CHAPTER XIII

PHYSICAL AND PERCEPTUAL SPACE

Perhaps there is nothing so difficult for the imagination as to teach

it to feel about space as modern science compels us to think. This is

the task which must be attempted in the present chapter.

We said in Chapter XII that we know about what is happening in the

brain exactly what naive realism thinks it knows about what is

happening in the world. This remark may have seemed cryptic; it must

now be expanded and expounded.

The gist of the matter is that percepts, which we spoke about at the

end of last chapter, are in our heads; that percepts are what we can

know with most certainty; and that percepts contain what naive realism

thinks it knows about the world.

But when I say that my percepts are in my head, I am saying something

which is ambiguous until the different kinds of space have been

explained, for the statement is only true in connection with _physical_

space. There is also a space in our percepts, and of this space

the statement would not be true. When I say that there is space

in our percepts, I mean nothing at all difficult to understand. I

mean--to take the sense of sight, which is the most important in this

connection--that in what we see at one time there is up and down, right

and left, inside and outside. If we see, say, a circle on a blackboard,

all these relations exist within what we see. The circle has a top half

and a bottom half, a right-hand half and a left-hand half, an inside

and an outside. Those relations alone are enough to make up a space

of sorts. But the space of everyday life is filled out with what we

derive from touch and movement--how a thing feels when we touch it,

and what movements are necessary in order to grasp it. Other elements

also come into the genesis of the space in which everybody believes

who has not been troubled by philosophy; but it is unnecessary for

our purposes to go into this question any more deeply. The point that

concerns us is that a man’s percepts are private to himself: what I

see, no one else sees; what I hear, no one else hears; what I touch,

no one else touches; and so on. True, others hear and see something

very like what I hear and see, if they are suitably placed; but there

are always differences. Sounds are less loud at a distance; objects

change their visual appearance according to the laws of perspective.

Therefore it is impossible for two persons at the same time to have

exactly identical percepts. It follows that the space of percepts, like

the percepts, must be private; there are as many perceptual spaces as

there are percipients. My percept of a table is outside my percept of

my head, in my perceptual space; but it does not follow that it is

outside my head as a physical object in physical space. Physical space

is neutral and public: in this space, all my percepts are in my head,

even the most distant star _as I see it_. Physical and perceptual space

have relations, but they are not identical, and failure to grasp the

difference between them is a potent source of confusion.

To say that you see a star when you see the light that has come from it

is no more correct than to say that you see New Zealand when you see

a New Zealander in London. Your perception when (as we say) you see a

star is causally connected, in the first instance, with what happens

in the brain, the optic nerve, and the eye, then with a light-wave

which, according to physics, can be traced back to the star as its

source. Your sensations will be closely similar if the light comes from

a lamp at the top of a mast. The physical space in which you believe

the “real” star to be is an elaborate inference; what is given is the

private space in which the speck of light you see is situated. It is

still an open question whether the space of sight has depth, or is

merely a surface, as Berkeley contended. This does not matter for

our purposes. Even if we admit that sight alone shows a difference

between an object a few inches from the eyes and an object several feet

distant, yet you certainly cannot, by sight alone, see that a cloud

is less distant than a fixed star, though you may _infer_ that it is,

because it can hide the star. The world of astronomy, from the point of

view of sight, is a surface. If you were put in a dark room with little

holes cut in the ceiling in the pattern of the stars letting light come

through, there would be nothing in your immediate visual data to show

that you were not “seeing the stars”. This illustrates what I mean by

saying that what you see is _not_ “out there” in the sense of physics.

We learn in infancy that we can sometimes touch objects we see, and

sometimes not. When we cannot touch them at once, we can sometimes do

so by walking to them. That is to say, we learn to correlate sensations

of sight with sensations of touch, and sometimes with sensations of

movement followed by sensations of touch. In this way we locate our

sensations in a three-dimensional world. Those which involve sight

alone we think of as “external”, but there is no justification for this

view. What you see when you see a star is just as internal as what you

feel when you feel a headache. That is to say, it is internal from the

standpoint of _physical_ space. It is distant in your private space,

because it is not associated with sensations of touch, and cannot be

associated with them by means of any journey you can perform.

Your own body, as known to you through direct experience, is quite

different from your own body as considered in physics. You know more

about your own body than about any other through direct experience,

because your own body can give you a number of sensations that no other

body can, for instance all kinds of bodily pains. But you still know

it only through sensations; apart from inference, it _is_ a bundle of

sensations, and therefore quite different, _prima facie_, from what

physics calls a body.

Most of the things you see are outside what you see when (as one says)

you see your own body. That is to say: you see certain other patches of

colour, differently situated in visual space, and say you are seeing

things outside your body. But from the point of view of physics, all

that you see must count as inside your body; what goes on elsewhere

can only be inferred. Thus the whole space of your sensible world with

all its percepts counts as one tiny region from the point of view of

physics.

There is no direct spatial relation between what one person sees and

what another sees, because no two ever see exactly the same object.

Each person carries about a private space of his own, which can be

located in physical space by indirect methods, but which contains no

place in common with another person’s private space. This shows how

entirely physical space is a matter of inference and construction.

To make the matter definite, let us suppose that a physiologist is

observing a living brain--no longer an impossible supposition, as

it would have been formerly. It is natural to suppose that what the

physiologist sees is in the brain he is observing. But if we are

speaking of physical space, what the physiologist sees is in his

own brain. It is in no sense in the brain that he is observing,

though it is in the percept of that brain, which occupies part of

the physiologist’s perceptual space. Causal continuity makes the

matter perfectly evident: light-waves travel from the brain that is

being observed to the eye of the physiologist, at which they only

arrive after an interval of time, which is finite though short. The

physiologist sees what he is observing only after the light-waves have

reached his eye; therefore the event which constitutes his seeing comes

at the end of a series of events which travel from the observed brain

into the brain of the physiologist. We cannot, without a preposterous

kind of discontinuity, suppose that the physiologist’s percept,

which comes at the end of this series, is anywhere else but in the

physiologist’s head.

This question is very important, and must be understood if metaphysics

is ever to be got straight. The traditional dualism of mind and

matter, which I regard as mistaken, is intimately connected with

confusions on this point. So long as we adhere to the conventional

notions of mind and matter, we are condemned to a view of perception

which is miraculous. We suppose that a physical process starts from a

visible object, travels to the eye, there changes into another physical

process, causes yet another physical process in the optic nerve,

finally produces some effect in the brain, simultaneously with which

we see the object from which the process started, the seeing being

something “mental”, totally different in character from the physical

processes which precede and accompany it. This view is so queer

that metaphysicians have invented all sorts of theories designed to

substitute something less incredible. But nobody noticed an elementary

confusion.

To return to the physiologist observing another man’s brain: what the

physiologist sees is by no means identical with what happens in the

brain he is observing, but is a somewhat remote effect. From what he

sees, therefore, he cannot judge whether what is happening in the brain

he is observing is, or is not, the sort of event that he would call

“mental”. When he says that certain physical events in the brain are

accompanied by mental events, he is thinking of physical events as if

they were what he sees. He does not see a mental event in the brain he

is observing, and therefore supposes there is in that brain a physical

process which he can observe and a mental process which he cannot.

This is a complete mistake. In the strict sense, he cannot observe

anything in the other brain, but only the percepts which he himself has

when he is suitably related to that brain (eye to microscope, etc.).

We first identify physical processes with our percepts, and then,

since our percepts are not other people’s thoughts, we argue that the

physical processes in their brains are something quite different from

their thoughts. In fact, everything that we can directly observe of

the physical world happens inside our heads, and consists of “mental”

events in at least one sense of the word “mental”. It also consists

of events which form part of the physical world. The development of

this point of view will lead us to the conclusion that the distinction

between mind and matter is illusory. The stuff of the world may be

called physical or mental or both or neither, as we please; in fact,

the words serve no purpose. There is only one definition of the words

that is unobjectionable: “physical” is what is dealt with by physics,

and “mental” is what is dealt with by psychology. When, accordingly, I

speak of “physical” space, I mean the space that occurs in physics.

It is extraordinarily difficult to divest ourselves of the belief that

the physical world is the world we perceive by sight and touch; even

if, in our philosophic moments, we are aware that this is an error,

we nevertheless fall into it again as soon as we are off our guard.

The notion that what we see is “out there” in physical space is one

which cannot survive while we are grasping the difference between what

physics supposes to be really happening, and what our senses show us

as happening; but it is sure to return and plague us when we begin to

forget the argument. Only long reflection can make a radically new

point of view familiar and easy.

Our illustrations hitherto have been taken from the sense of sight;

let us now take one from the sense of touch. Suppose that, with your

eyes shut, you let your finger-tip press against a hard table. What

is really happening? The physicist says that your finger-tip and the

table consist, roughly speaking, of vast numbers of electrons and

protons; more correctly, each electron and proton is to be thought of

as a collection of processes of radiation, but we can ignore this for

our present purposes. Although you think you are touching the table,

no electron or proton in your finger ever really touches an electron

or proton in the table, because this would develop an infinite force.

When you press, repulsions are set up between parts of your finger and

parts of the table. If you try to press upon a liquid or a gas, there

is room in it for the parts that are repelled to get away. But if you

press a hard solid, the electrons and protons that try to get away,

because electrical forces from your finger repel them, are unable to

do so, because they are crowded close to others which elbow them back

to more or less their original position, like people in a dense crowd.

Therefore the more you press the more they repel your finger. The

repulsion consists of electrical forces, which set up in the nerves a

current whose nature is not very definitely known. This current runs

into the brain, and there has effects which, so far as the physiologist

is concerned, are almost wholly conjectural. But there is one effect

which is not conjectural, and that is the sensation of touch. This

effect, owing to physiological inference or perhaps to a reflex, is

associated by us with the finger-tip. But the sensation is the same

if, by artificial means, the parts of the nerve nearer the brain are

suitably stimulated--_e.g._ if your hand has been amputated and the

right nerves are skilfully manipulated. Thus our confidence that touch

affords evidence of the existence of bodies at the place which we think

is being touched is quite misplaced. As a rule we are right, but we can

be wrong; there is nothing of the nature of an infallible revelation

about the matter. And even in the most favorable case, the perception

of touch is something very different from the mad dance of electrons

and protons trying to jazz out of each other’s way, which is what

physics maintains is really taking place at your finger-tip. Or, at

least, it _seems_ very different. But as we shall see, the knowledge

we derive from physics is so abstract that we are not warranted

in saying that what goes on in the physical world is, or is not,

intrinsically very different from the events that we know through our

own experiences.

CHAPTER XIV

PERCEPTION AND PHYSICAL CAUSAL LAWS

In an earlier chapter we saw the inadequacy of the traditional notion

of cause, without adequately explaining the causal laws which are a

substitute in the practice of science. The time has now come when it

is possible to remedy this defect, and, in so doing, to fit perception

into its place in the chain of physical causation and recapitulate the

main points of previous arguments.

The old view was that an event A will always be followed by a certain

event B, and that the problem of discovering causal laws is the

problem, given an event B, of finding that event A which is its

invariable antecedent or _vice versa_. At an early stage of a science

this point of view is useful; it gives laws which are true usually,

though probably not always, and it affords the basis for more exact

laws. But it has no philosophical validity, and is superseded in

science as soon as we arrive at genuine laws. Genuine laws, in advanced

sciences, are practically always quantitative laws of _tendency_. I

will try to illustrate by taking the simplest possible case in physics.

Imagine a hydrogen atom, in which the electron is revolving not in

the minimum orbit, but in the next, which has four times the minimum

radius. So long as this state continues, the atom has no external

effects, apart from its infinitesimal gravitational action; we cannot,

therefore, obtain any evidence of its existence except when it changes

its state. In fact, our knowledge of atoms is like that which a ticket

collector has of the population of his town: he knows nothing of those

who stay quietly at home. Now at some moment, according to laws of

which we have only statistical knowledge, the electron in our atom

jumps to a smaller orbit, and the energy lost to the atom travels

outward in a light-wave. We know no causal law as to when the electron

will jump, though we know how far it will jump and exactly what will

happen in the neighbourhood when it does. At least, when I say we

know exactly what will happen, I ought to say that we know exactly

the mathematical laws of what will happen. A series of events, having

quantitative characteristics which obey certain equations, will travel

outward in all directions from the electron, and will proceed quite

regularly, like ripples on a pool, until other matter is encountered.

We have here one important and apparently fundamental kind of causal

law, the kind regulating the propagation of light _in vacuo_. This is

summed up in Maxwell’s equations, which enable us to calculate the

diffusion of an electro-magnetic disturbance starting from a source. So

long as two such disturbances do not meet, the matter is exceedingly

simple; but the equations also tell us what happens when they do

meet. We then have, as always in traditional physics, two separate

tendencies, which have a resultant compounded according to mathematical

laws, of which the parallelogram law is the oldest and simplest. That

is to say, each previous circumstance in the space-time neighbourhood

contributes a tendency, and the resulting event is obtained by

compounding these tendencies according to a mathematical law.

So far, we have been considering only electro-magnetic phenomena in

empty space. We have another set of facts about empty space, namely

those upon which gravitation depends. These have to do with the

structure of space-time, and show that this structure has singularities

in the regions where there is matter, which spread with diminishing

intensity as we get away from these regions. You may conceive the

structure of space-time on the analogy of a pond with a fountain

playing in it, so that wherever a spray falls from the fountain there

is a little hill of water which flattens quickly as you get away from

the spot where the spray falls. Here again the same sort of thing

applies: to infer the structure in a small region of space-time from

that in the neighbourhood, it will be necessary to superpose a number

of tendencies according to mathematical rules. Thus philosophically

this introduces no novelty.

But now consider what happens when the wave of light which started

from our hydrogen atom comes in contact with matter. Various things

may happen. The matter may absorb all or some of the energy of the

light-ray; this is the interesting case from our point of view. The

absorption may take the form of causing the electrons to move in larger

orbits, in which case, later, when they return to their previous

orbits, we get the phenomenon of fluorescence. Or the body may become

heated; or it may visibly move, like a radiometer. The effects upon

bodies depend upon the bodies as well as the light. Some of them can be

individually predicted, others can only be calculated in statistical

averages; this depends upon whether quantum considerations come in

or not. Where they do, we can enumerate possibilities, and state the

relative frequencies with which they will be realised, but we cannot

tell which will be realised in any given case.

So far, we have considered the radiation of energy from matter into

empty space, its propagation in empty space and its impact on matter

from empty space. We have not considered the history of a given piece

of matter, or the distinction between matter and empty space.

The essence of matter appears to be this: We can distinguish series of

events in space-time which have a certain kind of close resemblance

to each other, such that common sense regards them as manifestations

of one “thing”. But when we look closely at the question, it turns

out that what physics offers is something more abstract than this.

Take, _e. g._ the continued existence of a certain electron. This

means to say that events in a certain neighbourhood will be such as

can be calculated on the assumption that there is an electric charge

of a certain standard magnitude in the middle of that neighbourhood;

and that the neighbourhoods of which this is true form a tube in

space-time.

So long as we stick to the standpoint of pure physics there is a

certain air of taking in each other’s washing about the whole business.

Events in empty space are only known as regards their abstract

mathematical characteristics; matter is only an abstract mathematical

characteristic of events in empty space. This seems rather a cold

world. But as a matter of fact we know some things that are a little

more concrete. We know, _e.g._ what it feels like when we see things.

From the point of view of physics, when our light-wave starts out

through empty space, if it presently reaches our eye we know one link

in the causal chain, namely the visual sensation, otherwise than as a

term in an abstract mathematical formula. And it is this one term which

forms the basis for our belief in all the rest. Seeing is believing.