THE PROBLEMS OF PHILOSOPHY

THE PROBLEMS OF PHILOSOPHY

By Bertrand Russell

Contents

PREFACE

CHAPTER I. APPEARANCE AND REALITY

CHAPTER II. THE EXISTENCE OF MATTER

CHAPTER III. THE NATURE OF MATTER

CHAPTER IV. IDEALISM

CHAPTER V. KNOWLEDGE BY ACQUAINTANCE AND KNOWLEDGE BY

DESCRIPTION

CHAPTER VI. ON INDUCTION

CHAPTER VII. ON OUR KNOWLEDGE OF GENERAL PRINCIPLES

CHAPTER VIII. HOW /A PRIORI/ KNOWLEDGE IS POSSIBLE

CHAPTER IX. THE WORLD OF UNIVERSALS

CHAPTER X. ON OUR KNOWLEDGE OF UNIVERSALS

CHAPTER XI. ON INTUITIVE KNOWLEDGE

CHAPTER XII. TRUTH AND FALSEHOOD

CHAPTER XIII. KNOWLEDGE, ERROR, AND PROBABLE OPINION

CHAPTER XIV. THE LIMITS OF PHILOSOPHICAL KNOWLEDGE

CHAPTER XV. THE VALUE OF PHILOSOPHY

BIBLIOGRAPHICAL NOTE

PREFACE

In the following pages I have confined myself in the main to those

problems of philosophy in regard to which I thought it possible to say

something positive and constructive, since merely negative criticism

seemed out of place. For this reason, theory of knowledge occupies a

larger space than metaphysics in the present volume, and some topics

much discussed by philosophers are treated very briefly, if at all.

I have derived valuable assistance from unpublished writings of G. E.

Moore and J. M. Keynes: from the former, as regards the relations of

sense-data to physical objects, and from the latter as regards

probability and induction. I have also profited greatly by the

criticisms and suggestions of Professor Gilbert Murray.

1912

CHAPTER I. APPEARANCE AND REALITY

Is there any knowledge in the world which is so certain that no

reasonable man could doubt it? This question, which at first sight might

not seem difficult, is really one of the most difficult that can be

asked. When we have realized the obstacles in the way of a

straightforward and confident answer, we shall be well launched on the

study of philosophy?for philosophy is merely the attempt to answer such

ultimate questions, not carelessly and dogmatically, as we do in

ordinary life and even in the sciences, but critically, after exploring

all that makes such questions puzzling, and after realizing all the

vagueness and confusion that underlie our ordinary ideas.

In daily life, we assume as certain many things which, on a closer

scrutiny, are found to be so full of apparent contradictions that only a

great amount of thought enables us to know what it is that we really may

believe. In the search for certainty, it is natural to begin with our

present experiences, and in some sense, no doubt, knowledge is to be

derived from them. But any statement as to what it is that our immediate

experiences make us know is very likely to be wrong. It seems to me that

I am now sitting in a chair, at a table of a certain shape, on which I

see sheets of paper with writing or print. By turning my head I see out

of the window buildings and clouds and the sun. I believe that the sun

is about ninety-three million miles from the earth; that it is a hot

globe many times bigger than the earth; that, owing to the earth's

rotation, it rises every morning, and will continue to do so for an

indefinite time in the future. I believe that, if any other normal

person comes into my room, he will see the same chairs and tables and

books and papers as I see, and that the table which I see is the same as

the table which I feel pressing against my arm. All this seems to be so

evident as to be hardly worth stating, except in answer to a man who

doubts whether I know anything. Yet all this may be reasonably doubted,

and all of it requires much careful discussion before we can be sure

that we have stated it in a form that is wholly true.

To make our difficulties plain, let us concentrate attention on the

table. To the eye it is oblong, brown and shiny, to the touch it is

smooth and cool and hard; when I tap it, it gives out a wooden sound.

Any one else who sees and feels and hears the table will agree with this

description, so that it might seem as if no difficulty would arise; but

as soon as we try to be more precise our troubles begin. Although I

believe that the table is 'really' of the same colour all over, the

parts that reflect the light look much brighter than the other parts,

and some parts look white because of reflected light. I know that, if I

move, the parts that reflect the light will be different, so that the

apparent distribution of colours on the table will change. It follows

that if several people are looking at the table at the same moment, no

two of them will see exactly the same distribution of colours, because

no two can see it from exactly the same point of view, and any change in

the point of view makes some change in the way the light is reflected.

For most practical purposes these differences are unimportant, but to

the painter they are all-important: the painter has to unlearn the habit

of thinking that things seem to have the colour which common sense says

they 'really' have, and to learn the habit of seeing things as they

appear. Here we have already the beginning of one of the distinctions

that cause most trouble in philosophy?the distinction between

'appearance' and 'reality', between what things seem to be and what they

are. The painter wants to know what things seem to be, the practical man

and the philosopher want to know what they are; but the philosopher's

wish to know this is stronger than the practical man's, and is more

troubled by knowledge as to the difficulties of answering the question.

To return to the table. It is evident from what we have found, that

there is no colour which pre-eminently appears to be /the/ colour of the

table, or even of any one particular part of the table?it appears to be

of different colours from different points of view, and there is no

reason for regarding some of these as more really its colour than

others. And we know that even from a given point of view the colour will

seem different by artificial light, or to a colour-blind man, or to a

man wearing blue spectacles, while in the dark there will be no colour

at all, though to touch and hearing the table will be unchanged. This

colour is not something which is inherent in the table, but something

depending upon the table and the spectator and the way the light falls

on the table. When, in ordinary life, we speak of /the/ colour of the

table, we only mean the sort of colour which it will seem to have to a

normal spectator from an ordinary point of view under usual conditions

of light. But the other colours which appear under other conditions have

just as good a right to be considered real; and therefore, to avoid

favouritism, we are compelled to deny that, in itself, the table has any

one particular colour.

The same thing applies to the texture. With the naked eye one can see

the grain, but otherwise the table looks smooth and even. If we looked

at it through a microscope, we should see roughnesses and hills and

valleys, and all sorts of differences that are imperceptible to the

naked eye. Which of these is the 'real' table? We are naturally tempted

to say that what we see through the microscope is more real, but that in

turn would be changed by a still more powerful microscope. If, then, we

cannot trust what we see with the naked eye, why should we trust what we

see through a microscope? Thus, again, the confidence in our senses with

which we began deserts us.

The shape of the table is no better. We are all in the habit of judging

as to the 'real' shapes of things, and we do this so unreflectingly that

we come to think we actually see the real shapes. But, in fact, as we

all have to learn if we try to draw, a given thing looks different in

shape from every different point of view. If our table is 'really'

rectangular, it will look, from almost all points of view, as if it had

two acute angles and two obtuse angles. If opposite sides are parallel,

they will look as if they converged to a point away from the spectator;

if they are of equal length, they will look as if the nearer side were

longer. All these things are not commonly noticed in looking at a table,

because experience has taught us to construct the 'real' shape from the

apparent shape, and the 'real' shape is what interests us as practical

men. But the 'real' shape is not what we see; it is something inferred

from what we see. And what we see is constantly changing in shape as we

move about the room; so that here again the senses seem not to give us

the truth about the table itself, but only about the appearance of the

table.

Similar difficulties arise when we consider the sense of touch. It is

true that the table always gives us a sensation of hardness, and we feel

that it resists pressure. But the sensation we obtain depends upon how

hard we press the table and also upon what part of the body we press

with; thus the various sensations due to various pressures or various

parts of the body cannot be supposed to reveal /directly/ any definite

property of the table, but at most to be /signs/ of some property which

perhaps /causes/ all the sensations, but is not actually apparent in any

of them. And the same applies still more obviously to the sounds which

can be elicited by rapping the table.

Thus it becomes evident that the real table, if there is one, is not the

same as what we immediately experience by sight or touch or hearing. The

real table, if there is one, is not /immediately/ known to us at all,

but must be an inference from what is immediately known. Hence, two very

difficult questions at once arise; namely, (1) Is there a real table at

all? (2) If so, what sort of object can it be?

It will help us in considering these questions to have a few simple

terms of which the meaning is definite and clear. Let us give the name

of 'sense-data' to the things that are immediately known in sensation:

such things as colours, sounds, smells, hardnesses, roughnesses, and so

on. We shall give the name 'sensation' to the experience of being

immediately aware of these things. Thus, whenever we see a colour, we

have a sensation /of/ the colour, but the colour itself is a

sense-datum, not a sensation. The colour is that /of/ which we are

immediately aware, and the awareness itself is the sensation. It is

plain that if we are to know anything about the table, it must be by

means of the sense-data?brown colour, oblong shape, smoothness,

etc.?which we associate with the table; but, for the reasons which have

been given, we cannot say that the table is the sense-data, or even that

the sense-data are directly properties of the table. Thus a problem

arises as to the relation of the sense-data to the real table, supposing

there is such a thing.

The real table, if it exists, we will call a 'physical object'. Thus we

have to consider the relation of sense-data to physical objects. The

collection of all physical objects is called 'matter'. Thus our two

questions may be re-stated as follows: (1) Is there any such thing as

matter? (2) If so, what is its nature?

The philosopher who first brought prominently forward the reasons for

regarding the immediate objects of our senses as not existing

independently of us was Bishop Berkeley (1685-1753). His /Three

Dialogues between Hylas and Philonous, in Opposition to Sceptics and

Atheists/, undertake to prove that there is no such thing as matter at

all, and that the world consists of nothing but minds and their ideas.

Hylas has hitherto believed in matter, but he is no match for Philonous,

who mercilessly drives him into contradictions and paradoxes, and makes

his own denial of matter seem, in the end, as if it were almost common

sense. The arguments employed are of very different value: some are

important and sound, others are confused or quibbling. But Berkeley

retains the merit of having shown that the existence of matter is

capable of being denied without absurdity, and that if there are any

things that exist independently of us they cannot be the immediate

objects of our sensations.

There are two different questions involved when we ask whether matter

exists, and it is important to keep them clear. We commonly mean by

'matter' something which is opposed to 'mind', something which we think

of as occupying space and as radically incapable of any sort of thought

or consciousness. It is chiefly in this sense that Berkeley denies

matter; that is to say, he does not deny that the sense-data which we

commonly take as signs of the existence of the table are really signs of

the existence of /something/ independent of us, but he does deny that

this something is non-mental, that it is neither mind nor ideas

entertained by some mind. He admits that there must be something which

continues to exist when we go out of the room or shut our eyes, and that

what we call seeing the table does really give us reason for believing

in something which persists even when we are not seeing it. But he

thinks that this something cannot be radically different in nature from

what we see, and cannot be independent of seeing altogether, though it

must be independent of /our/ seeing. He is thus led to regard the 'real'

table as an idea in the mind of God. Such an idea has the required

permanence and independence of ourselves, without being?as matter would

otherwise be?something quite unknowable, in the sense that we can only

infer it, and can never be directly and immediately aware of it.

Other philosophers since Berkeley have also held that, although the

table does not depend for its existence upon being seen by me, it does

depend upon being seen (or otherwise apprehended in sensation) by /some/

mind?not necessarily the mind of God, but more often the whole

collective mind of the universe. This they hold, as Berkeley does,

chiefly because they think there can be nothing real?or at any rate

nothing known to be real except minds and their thoughts and feelings.

We might state the argument by which they support their view in some

such way as this: 'Whatever can be thought of is an idea in the mind of

the person thinking of it; therefore nothing can be thought of except

ideas in minds; therefore anything else is inconceivable, and what is

inconceivable cannot exist.'

Such an argument, in my opinion, is fallacious; and of course those who

advance it do not put it so shortly or so crudely. But whether valid or

not, the argument has been very widely advanced in one form or another;

and very many philosophers, perhaps a majority, have held that there is

nothing real except minds and their ideas. Such philosophers are called

'idealists'. When they come to explaining matter, they either say, like

Berkeley, that matter is really nothing but a collection of ideas, or

they say, like Leibniz (1646-1716), that what appears as matter is

really a collection of more or less rudimentary minds.

But these philosophers, though they deny matter as opposed to mind,

nevertheless, in another sense, admit matter. It will be remembered that

we asked two questions; namely, (1) Is there a real table at all? (2) If

so, what sort of object can it be? Now both Berkeley and Leibniz admit

that there is a real table, but Berkeley says it is certain ideas in the

mind of God, and Leibniz says it is a colony of souls. Thus both of them

answer our first question in the affirmative, and only diverge from the

views of ordinary mortals in their answer to our second question. In

fact, almost all philosophers seem to be agreed that there is a real

table: they almost all agree that, however much our sense-data?colour,

shape, smoothness, etc.?may depend upon us, yet their occurrence is a

sign of something existing independently of us, something differing,

perhaps, completely from our sense-data, and yet to be regarded as

causing those sense-data whenever we are in a suitable relation to the

real table.

Now obviously this point in which the philosophers are agreed?the view

that there /is/ a real table, whatever its nature may be?is vitally

important, and it will be worth while to consider what reasons there are

for accepting this view before we go on to the further question as to

the nature of the real table. Our next chapter, therefore, will be

concerned with the reasons for supposing that there is a real table at all.

Before we go farther it will be well to consider for a moment what it is

that we have discovered so far. It has appeared that, if we take any

common object of the sort that is supposed to be known by the senses,

what the senses /immediately/ tell us is not the truth about the object

as it is apart from us, but only the truth about certain sense-data

which, so far as we can see, depend upon the relations between us and

the object. Thus what we directly see and feel is merely 'appearance',

which we believe to be a sign of some 'reality' behind. But if the

reality is not what appears, have we any means of knowing whether there

is any reality at all? And if so, have we any means of finding out what

it is like?

Such questions are bewildering, and it is difficult to know that even

the strangest hypotheses may not be true. Thus our familiar table, which

has roused but the slightest thoughts in us hitherto, has become a

problem full of surprising possibilities. The one thing we know about it

is that it is not what it seems. Beyond this modest result, so far, we

have the most complete liberty of conjecture. Leibniz tells us it is a

community of souls: Berkeley tells us it is an idea in the mind of God;

sober science, scarcely less wonderful, tells us it is a vast collection

of electric charges in violent motion.

Among these surprising possibilities, doubt suggests that perhaps there

is no table at all. Philosophy, if it cannot /answer/ so many questions

as we could wish, has at least the power of /asking/ questions which

increase the interest of the world, and show the strangeness and wonder

lying just below the surface even in the commonest things of daily life.

CHAPTER II. THE EXISTENCE OF MATTER

In this chapter we have to ask ourselves whether, in any sense at all,

there is such a thing as matter. Is there a table which has a certain

intrinsic nature, and continues to exist when I am not looking, or is

the table merely a product of my imagination, a dream-table in a very

prolonged dream? This question is of the greatest importance. For if we

cannot be sure of the independent existence of objects, we cannot be

sure of the independent existence of other people's bodies, and

therefore still less of other people's minds, since we have no grounds

for believing in their minds except such as are derived from observing

their bodies. Thus if we cannot be sure of the independent existence of

objects, we shall be left alone in a desert?it may be that the whole

outer world is nothing but a dream, and that we alone exist. This is an

uncomfortable possibility; but although it cannot be strictly proved to

be false, there is not the slightest reason to suppose that it is true.

In this chapter we have to see why this is the case.

Before we embark upon doubtful matters, let us try to find some more or

less fixed point from which to start. Although we are doubting the

physical existence of the table, we are not doubting the existence of

the sense-data which made us think there was a table; we are not

doubting that, while we look, a certain colour and shape appear to us,

and while we press, a certain sensation of hardness is experienced by

us. All this, which is psychological, we are not calling in question. In

fact, whatever else may be doubtful, some at least of our immediate

experiences seem absolutely certain.

Descartes (1596-1650), the founder of modern philosophy, invented a

method which may still be used with profit?the method of systematic

doubt. He determined that he would believe nothing which he did not see

quite clearly and distinctly to be true. Whatever he could bring himself

to doubt, he would doubt, until he saw reason for not doubting it. By

applying this method he gradually became convinced that the only

existence of which he could be /quite/ certain was his own. He imagined

a deceitful demon, who presented unreal things to his senses in a

perpetual phantasmagoria; it might be very improbable that such a demon

existed, but still it was possible, and therefore doubt concerning

things perceived by the senses was possible.

But doubt concerning his own existence was not possible, for if he did

not exist, no demon could deceive him. If he doubted, he must exist; if

he had any experiences whatever, he must exist. Thus his own existence

was an absolute certainty to him. 'I think, therefore I am,' he said

(/Cogito, ergo sum/); and on the basis of this certainty he set to work

to build up again the world of knowledge which his doubt had laid in

ruins. By inventing the method of doubt, and by showing that subjective

things are the most certain, Descartes performed a great service to

philosophy, and one which makes him still useful to all students of the

subject.

But some care is needed in using Descartes' argument. 'I think,

therefore I am' says rather more than is strictly certain. It might seem

as though we were quite sure of being the same person to-day as we were

yesterday, and this is no doubt true in some sense. But the real Self is

as hard to arrive at as the real table, and does not seem to have that

absolute, convincing certainty that belongs to particular experiences.

When I look at my table and see a certain brown colour, what is quite

certain at once is not '/I/ am seeing a brown colour', but rather, 'a

brown colour is being seen'. This of course involves something (or

somebody) which (or who) sees the brown colour; but it does not of

itself involve that more or less permanent person whom we call 'I'. So

far as immediate certainty goes, it might be that the something which

sees the brown colour is quite momentary, and not the same as the

something which has some different experience the next moment.

Thus it is our particular thoughts and feelings that have primitive

certainty. And this applies to dreams and hallucinations as well as to

normal perceptions: when we dream or see a ghost, we certainly do have

the sensations we think we have, but for various reasons it is held that

no physical object corresponds to these sensations. Thus the certainty

of our knowledge of our own experiences does not have to be limited in

any way to allow for exceptional cases. Here, therefore, we have, for

what it is worth, a solid basis from which to begin our pursuit of

knowledge.

The problem we have to consider is this: Granted that we are certain of

our own sense-data, have we any reason for regarding them as signs of

the existence of something else, which we can call the physical object?

When we have enumerated all the sense-data which we should naturally

regard as connected with the table, have we said all there is to say

about the table, or is there still something else?something not a

sense-datum, something which persists when we go out of the room? Common

sense unhesitatingly answers that there is. What can be bought and sold

and pushed about and have a cloth laid on it, and so on, cannot be a

/mere/ collection of sense-data. If the cloth completely hides the

table, we shall derive no sense-data from the table, and therefore, if

the table were merely sense-data, it would have ceased to exist, and the

cloth would be suspended in empty air, resting, by a miracle, in the

place where the table formerly was. This seems plainly absurd; but

whoever wishes to become a philosopher must learn not to be frightened

by absurdities.

One great reason why it is felt that we must secure a physical object in

addition to the sense-data, is that we want the same object for

different people. When ten people are sitting round a dinner-table, it

seems preposterous to maintain that they are not seeing the same

tablecloth, the same knives and forks and spoons and glasses. But the

sense-data are private to each separate person; what is immediately

present to the sight of one is not immediately present to the sight of

another: they all see things from slightly different points of view, and

therefore see them slightly differently. Thus, if there are to be public

neutral objects, which can be in some sense known to many different

people, there must be something over and above the private and

particular sense-data which appear to various people. What reason, then,

have we for believing that there are such public neutral objects?

The first answer that naturally occurs to one is that, although

different people may see the table slightly differently, still they all

see more or less similar things when they look at the table, and the

variations in what they see follow the laws of perspective and

reflection of light, so that it is easy to arrive at a permanent object

underlying all the different people's sense-data. I bought my table from

the former occupant of my room; I could not buy /his/ sense-data, which

died when he went away, but I could and did buy the confident

expectation of more or less similar sense-data. Thus it is the fact that

different people have similar sense-data, and that one person in a given

place at different times has similar sense-data, which makes us suppose

that over and above the sense-data there is a permanent public object

which underlies or causes the sense-data of various people at various

times.

Now in so far as the above considerations depend upon supposing that

there are other people besides ourselves, they beg the very question at

issue. Other people are represented to me by certain sense-data, such as

the sight of them or the sound of their voices, and if I had no reason

to believe that there were physical objects independent of my

sense-data, I should have no reason to believe that other people exist

except as part of my dream. Thus, when we are trying to show that there

must be objects independent of our own sense-data, we cannot appeal to

the testimony of other people, since this testimony itself consists of

sense-data, and does not reveal other people's experiences unless our

own sense-data are signs of things existing independently of us. We must

therefore, if possible, find, in our own purely private experiences,

characteristics which show, or tend to show, that there are in the world

things other than ourselves and our private experiences.

In one sense it must be admitted that we can never prove the existence

of things other than ourselves and our experiences. No logical absurdity

results from the hypothesis that the world consists of myself and my

thoughts and feelings and sensations, and that everything else is mere

fancy. In dreams a very complicated world may seem to be present, and

yet on waking we find it was a delusion; that is to say, we find that

the sense-data in the dream do not appear to have corresponded with such

physical objects as we should naturally infer from our sense-data. (It

is true that, when the physical world is assumed, it is possible to find

physical causes for the sense-data in dreams: a door banging, for

instance, may cause us to dream of a naval engagement. But although, in

this case, there is a physical cause for the sense-data, there is not a

physical object corresponding to the sense-data in the way in which an

actual naval battle would correspond.) There is no logical impossibility

in the supposition that the whole of life is a dream, in which we

ourselves create all the objects that come before us. But although this

is not logically impossible, there is no reason whatever to suppose that

it is true; and it is, in fact, a less simple hypothesis, viewed as a

means of accounting for the facts of our own life, than the common-sense

hypothesis that there really are objects independent of us, whose action

on us causes our sensations.

The way in which simplicity comes in from supposing that there really

are physical objects is easily seen. If the cat appears at one moment in

one part of the room, and at another in another part, it is natural to

suppose that it has moved from the one to the other, passing over a

series of intermediate positions. But if it is merely a set of

sense-data, it cannot have ever been in any place where I did not see

it; thus we shall have to suppose that it did not exist at all while I

was not looking, but suddenly sprang into being in a new place. If the

cat exists whether I see it or not, we can understand from our own

experience how it gets hungry between one meal and the next; but if it

does not exist when I am not seeing it, it seems odd that appetite

should grow during non-existence as fast as during existence. And if the

cat consists only of sense-data, it cannot be hungry, since no hunger

but my own can be a sense-datum to me. Thus the behaviour of the

sense-data which represent the cat to me, though it seems quite natural

when regarded as an expression of hunger, becomes utterly inexplicable

when regarded as mere movements and changes of patches of colour, which

are as incapable of hunger as a triangle is of playing football.

But the difficulty in the case of the cat is nothing compared to the

difficulty in the case of human beings. When human beings speak?that is,

when we hear certain noises which we associate with ideas, and

simultaneously see certain motions of lips and expressions of face?it is

very difficult to suppose that what we hear is not the expression of a

thought, as we know it would be if we emitted the same sounds. Of course

similar things happen in dreams, where we are mistaken as to the

existence of other people. But dreams are more or less suggested by what

we call waking life, and are capable of being more or less accounted for

on scientific principles if we assume that there really is a physical

world. Thus every principle of simplicity urges us to adopt the natural

view, that there really are objects other than ourselves and our

sense-data which have an existence not dependent upon our perceiving them.

Of course it is not by argument that we originally come by our belief in

an independent external world. We find this belief ready in ourselves as

soon as we begin to reflect: it is what may be called an /instinctive/

belief. We should never have been led to question this belief but for

the fact that, at any rate in the case of sight, it seems as if the

sense-datum itself were instinctively believed to be the independent

object, whereas argument shows that the object cannot be identical with

the sense-datum. This discovery, however?which is not at all paradoxical

in the case of taste and smell and sound, and only slightly so in the

case of touch?leaves undiminished our instinctive belief that there

/are/ objects /corresponding/ to our sense-data. Since this belief does

not lead to any difficulties, but on the contrary tends to simplify and

systematize our account of our experiences, there seems no good reason

for rejecting it. We may therefore admit?though with a slight doubt

derived from dreams?that the external world does really exist, and is

not wholly dependent for its existence upon our continuing to perceive it.

The argument which has led us to this conclusion is doubtless less

strong than we could wish, but it is typical of many philosophical

arguments, and it is therefore worth while to consider briefly its

general character and validity. All knowledge, we find, must be built up

upon our instinctive beliefs, and if these are rejected, nothing is

left. But among our instinctive beliefs some are much stronger than

others, while many have, by habit and association, become entangled with

other beliefs, not really instinctive, but falsely supposed to be part

of what is believed instinctively.

Philosophy should show us the hierarchy of our instinctive beliefs,

beginning with those we hold most strongly, and presenting each as much

isolated and as free from irrelevant additions as possible. It should

take care to show that, in the form in which they are finally set forth,

our instinctive beliefs do not clash, but form a harmonious system.

There can never be any reason for rejecting one instinctive belief

except that it clashes with others; thus, if they are found to

harmonize, the whole system becomes worthy of acceptance.

It is of course /possible/ that all or any of our beliefs may be

mistaken, and therefore all ought to be held with at least some slight

element of doubt. But we cannot have /reason/ to reject a belief except

on the ground of some other belief. Hence, by organizing our instinctive

beliefs and their consequences, by considering which among them is most

possible, if necessary, to modify or abandon, we can arrive, on the

basis of accepting as our sole data what we instinctively believe, at an

orderly systematic organization of our knowledge, in which, though the

/possibility/ of error remains, its likelihood is diminished by the

interrelation of the parts and by the critical scrutiny which has

preceded acquiescence.

This function, at least, philosophy can perform. Most philosophers,

rightly or wrongly, believe that philosophy can do much more than

this?that it can give us knowledge, not otherwise attainable, concerning

the universe as a whole, and concerning the nature of ultimate reality.

Whether this be the case or not, the more modest function we have spoken

of can certainly be performed by philosophy, and certainly suffices, for

those who have once begun to doubt the adequacy of common sense, to

justify the arduous and difficult labours that philosophical problems

involve.

CHAPTER III. THE NATURE OF MATTER

In the preceding chapter we agreed, though without being able to find

demonstrative reasons, that it is rational to believe that our

sense-data?for example, those which we regard as associated with my

table?are really signs of the existence of something independent of us

and our perceptions. That is to say, over and above the sensations of

colour, hardness, noise, and so on, which make up the appearance of the

table to me, I assume that there is something else, of which these

things are appearances. The colour ceases to exist if I shut my eyes,

the sensation of hardness ceases to exist if I remove my arm from

contact with the table, the sound ceases to exist if I cease to rap the

table with my knuckles. But I do not believe that when all these things

cease the table ceases. On the contrary, I believe that it is because

the table exists continuously that all these sense-data will reappear

when I open my eyes, replace my arm, and begin again to rap with my

knuckles. The question we have to consider in this chapter is: What is

the nature of this real table, which persists independently of my

perception of it?

To this question physical science gives an answer, somewhat incomplete

it is true, and in part still very hypothetical, but yet deserving of

respect so far as it goes. Physical science, more or less unconsciously,

has drifted into the view that all natural phenomena ought to be reduced

to motions. Light and heat and sound are all due to wave-motions, which

travel from the body emitting them to the person who sees light or feels

heat or hears sound. That which has the wave-motion is either aether or

'gross matter', but in either case is what the philosopher would call

matter. The only properties which science assigns to it are position in

space, and the power of motion according to the laws of motion. Science

does not deny that it /may/ have other properties; but if so, such other

properties are not useful to the man of science, and in no way assist

him in explaining the phenomena.

It is sometimes said that 'light /is/ a form of wave-motion', but this

is misleading, for the light which we immediately see, which we know

directly by means of our senses, is /not/ a form of wave-motion, but

something quite different?something which we all know if we are not

blind, though we cannot describe it so as to convey our knowledge to a

man who is blind. A wave-motion, on the contrary, could quite well be

described to a blind man, since he can acquire a knowledge of space by

the sense of touch; and he can experience a wave-motion by a sea voyage

almost as well as we can. But this, which a blind man can understand, is

not what we mean by /light/: we mean by /light/ just that which a blind

man can never understand, and which we can never describe to him.

Now this something, which all of us who are not blind know, is not,

according to science, really to be found in the outer world: it is

something caused by the action of certain waves upon the eyes and nerves

and brain of the person who sees the light. When it is said that light

/is/ waves, what is really meant is that waves are the physical cause of

our sensations of light. But light itself, the thing which seeing people

experience and blind people do not, is not supposed by science to form

any part of the world that is independent of us and our senses. And very

similar remarks would apply to other kinds of sensations.

It is not only colours and sounds and so on that are absent from the

scientific world of matter, but also /space/ as we get it through sight

or touch. It is essential to science that its matter should be in /a/

space, but the space in which it is cannot be exactly the space we see

or feel. To begin with, space as we see it is not the same as space as

we get it by the sense of touch; it is only by experience in infancy

that we learn how to touch things we see, or how to get a sight of

things which we feel touching us. But the space of science is neutral as

between touch and sight; thus it cannot be either the space of touch or

the space of sight.

Again, different people see the same object as of different shapes,

according to their point of view. A circular coin, for example, though

we should always /judge/ it to be circular, will /look/ oval unless we

are straight in front of it. When we judge that it /is/ circular, we are

judging that it has a real shape which is not its apparent shape, but

belongs to it intrinsically apart from its appearance. But this real

shape, which is what concerns science, must be in a real space, not the

same as anybody's /apparent/ space. The real space is public, the

apparent space is private to the percipient. In different people's

/private/ spaces the same object seems to have different shapes; thus

the real space, in which it has its real shape, must be different from

the private spaces. The space of science, therefore, though /connected/

with the spaces we see and feel, is not identical with them, and the

manner of its connexion requires investigation.

We agreed provisionally that physical objects cannot be quite like our

sense-data, but may be regarded as /causing/ our sensations. These

physical objects are in the space of science, which we may call

'physical' space. It is important to notice that, if our sensations are

to be caused by physical objects, there must be a physical space

containing these objects and our sense-organs and nerves and brain. We

get a sensation of touch from an object when we are in contact with it;

that is to say, when some part of our body occupies a place in physical

space quite close to the space occupied by the object. We see an object

(roughly speaking) when no opaque body is between the object and our

eyes in physical space. Similarly, we only hear or smell or taste an

object when we are sufficiently near to it, or when it touches the

tongue, or has some suitable position in physical space relatively to

our body. We cannot begin to state what different sensations we shall

derive from a given object under different circumstances unless we

regard the object and our body as both in one physical space, for it is

mainly the relative positions of the object and our body that determine

what sensations we shall derive from the object.

Now our sense-data are situated in our private spaces, either the space

of sight or the space of touch or such vaguer spaces as other senses may

give us. If, as science and common sense assume, there is one public

all-embracing physical space in which physical objects are, the relative

positions of physical objects in physical space must more or less

correspond to the relative positions of sense-data in our private

spaces. There is no difficulty in supposing this to be the case. If we

see on a road one house nearer to us than another, our other senses will

bear out the view that it is nearer; for example, it will be reached

sooner if we walk along the road. Other people will agree that the house

which looks nearer to us is nearer; the ordnance map will take the same

view; and thus everything points to a spatial relation between the

houses corresponding to the relation between the sense-data which we see

when we look at the houses. Thus we may assume that there is a physical

space in which physical objects have spatial relations corresponding to

those which the corresponding sense-data have in our private spaces. It

is this physical space which is dealt with in geometry and assumed in

physics and astronomy.

Assuming that there is physical space, and that it does thus correspond

to private spaces, what can we know about it? We can know /only/ what is

required in order to secure the correspondence. That is to say, we can

know nothing of what it is like in itself, but we can know the sort of

arrangement of physical objects which results from their spatial

relations. We can know, for example, that the earth and moon and sun are

in one straight line during an eclipse, though we cannot know what a

physical straight line is in itself, as we know the look of a straight

line in our visual space. Thus we come to know much more about the

/relations/ of distances in physical space than about the distances

themselves; we may know that one distance is greater than another, or

that it is along the same straight line as the other, but we cannot have

that immediate acquaintance with physical distances that we have with

distances in our private spaces, or with colours or sounds or other

sense-data. We can know all those things about physical space which a

man born blind might know through other people about the space of sight;

but the kind of things which a man born blind could never know about the

space of sight we also cannot know about physical space. We can know the

properties of the relations required to preserve the correspondence with

sense-data, but we cannot know the nature of the terms between which the

relations hold.

With regard to time, our /feeling/ of duration or of the lapse of time

is notoriously an unsafe guide as to the time that has elapsed by the

clock. Times when we are bored or suffering pain pass slowly, times when

we are agreeably occupied pass quickly, and times when we are sleeping

pass almost as if they did not exist. Thus, in so far as time is

constituted by duration, there is the same necessity for distinguishing

a public and a private time as there was in the case of space. But in so

far as time consists in an /order/ of before and after, there is no need

to make such a distinction; the time-order which events seem to have is,

so far as we can see, the same as the time-order which they do have. At

any rate no reason can be given for supposing that the two orders are

not the same. The same is usually true of space: if a regiment of men

are marching along a road, the shape of the regiment will look different

from different points of view, but the men will appear arranged in the

same order from all points of view. Hence we regard the order as true

also in physical space, whereas the shape is only supposed to correspond

to the physical space so far as is required for the preservation of the

order.

In saying that the time-order which events seem to have is the same as

the time-order which they really have, it is necessary to guard against

a possible misunderstanding. It must not be supposed that the various

states of different physical objects have the same time-order as the

sense-data which constitute the perceptions of those objects. Considered

as physical objects, the thunder and lightning are simultaneous; that is

to say, the lightning is simultaneous with the disturbance of the air in

the place where the disturbance begins, namely, where the lightning is.

But the sense-datum which we call hearing the thunder does not take

place until the disturbance of the air has travelled as far as to where

we are. Similarly, it takes about eight minutes for the sun's light to

reach us; thus, when we see the sun we are seeing the sun of eight

minutes ago. So far as our sense-data afford evidence as to the physical

sun they afford evidence as to the physical sun of eight minutes ago; if

the physical sun had ceased to exist within the last eight minutes, that

would make no difference to the sense-data which we call 'seeing the

sun'. This affords a fresh illustration of the necessity of

distinguishing between sense-data and physical objects.

What we have found as regards space is much the same as what we find in

relation to the correspondence of the sense-data with their physical

counterparts. If one object looks blue and another red, we may

reasonably presume that there is some corresponding difference between

the physical objects; if two objects both look blue, we may presume a

corresponding similarity. But we cannot hope to be acquainted directly

with the quality in the physical object which makes it look blue or red.

Science tells us that this quality is a certain sort of wave-motion, and

this sounds familiar, because we think of wave-motions in the space we

see. But the wave-motions must really be in physical space, with which

we have no direct acquaintance; thus the real wave-motions have not that

familiarity which we might have supposed them to have. And what holds

for colours is closely similar to what holds for other sense-data. Thus

we find that, although the /relations/ of physical objects have all

sorts of knowable properties, derived from their correspondence with the

relations of sense-data, the physical objects themselves remain unknown

in their intrinsic nature, so far at least as can be discovered by means

of the senses. The question remains whether there is any other method of

discovering the intrinsic nature of physical objects.

The most natural, though not ultimately the most defensible, hypothesis

to adopt in the first instance, at any rate as regards visual

sense-data, would be that, though physical objects cannot, for the

reasons we have been considering, be /exactly/ like sense-data, yet they

may be more or less like. According to this view, physical objects will,

for example, really have colours, and we might, by good luck, see an

object as of the colour it really is. The colour which an object seems

to have at any given moment will in general be very similar, though not

quite the same, from many different points of view; we might thus

suppose the 'real' colour to be a sort of medium colour, intermediate

between the various shades which appear from the different points of view.

Such a theory is perhaps not capable of being definitely refuted, but it

can be shown to be groundless. To begin with, it is plain that the

colour we see depends only upon the nature of the light-waves that

strike the eye, and is therefore modified by the medium intervening

between us and the object, as well as by the manner in which light is

reflected from the object in the direction of the eye. The intervening

air alters colours unless it is perfectly clear, and any strong

reflection will alter them completely. Thus the colour we see is a

result of the ray as it reaches the eye, and not simply a property of

the object from which the ray comes. Hence, also, provided certain waves

reach the eye, we shall see a certain colour, whether the object from

which the waves start has any colour or not. Thus it is quite gratuitous

to suppose that physical objects have colours, and therefore there is no

justification for making such a supposition. Exactly similar arguments

will apply to other sense-data.

It remains to ask whether there are any general philosophical arguments

enabling us to say that, if matter is real, it must be of such and such

a nature. As explained above, very many philosophers, perhaps most, have

held that whatever is real must be in some sense mental, or at any rate

that whatever we can know anything about must be in some sense mental.

Such philosophers are called 'idealists'. Idealists tell us that what

appears as matter is really something mental; namely, either (as Leibniz

held) more or less rudimentary minds, or (as Berkeley contended) ideas

in the minds which, as we should commonly say, 'perceive' the matter.

Thus idealists deny the existence of matter as something intrinsically

different from mind, though they do not deny that our sense-data are

signs of something which exists independently of our private sensations.

In the following chapter we shall consider briefly the reasons?in my

opinion fallacious?which idealists advance in favour of their theory.

CHAPTER IV. IDEALISM

The word 'idealism' is used by different philosophers in somewhat

different senses. We shall understand by it the doctrine that whatever

exists, or at any rate whatever can be known to exist, must be in some

sense mental. This doctrine, which is very widely held among

philosophers, has several forms, and is advocated on several different

grounds. The doctrine is so widely held, and so interesting in itself,

that even the briefest survey of philosophy must give some account of it.

Those who are unaccustomed to philosophical speculation may be inclined

to dismiss such a doctrine as obviously absurd. There is no doubt that

common sense regards tables and chairs and the sun and moon and material

objects generally as something radically different from minds and the

contents of minds, and as having an existence which might continue if

minds ceased. We think of matter as having existed long before there

were any minds, and it is hard to think of it as a mere product of

mental activity. But whether true or false, idealism is not to be

dismissed as obviously absurd.

We have seen that, even if physical objects do have an independent

existence, they must differ very widely from sense-data, and can only

have a /correspondence/ with sense-data, in the same sort of way in

which a catalogue has a correspondence with the things catalogued. Hence

common sense leaves us completely in the dark as to the true intrinsic

nature of physical objects, and if there were good reason to regard them

as mental, we could not legitimately reject this opinion merely because

it strikes us as strange. The truth about physical objects /must/ be

strange. It may be unattainable, but if any philosopher believes that he

has attained it, the fact that what he offers as the truth is strange

ought not to be made a ground of objection to his opinion.

The grounds on which idealism is advocated are generally grounds derived

from the theory of knowledge, that is to say, from a discussion of the

conditions which things must satisfy in order that we may be able to

know them. The first serious attempt to establish idealism on such

grounds was that of Bishop Berkeley. He proved first, by arguments which

were largely valid, that our sense-data cannot be supposed to have an

existence independent of us, but must be, in part at least, 'in' the

mind, in the sense that their existence would not continue if there were

no seeing or hearing or touching or smelling or tasting. So far, his

contention was almost certainly valid, even if some of his arguments

were not so. But he went on to argue that sense-data were the only

things of whose existence our perceptions could assure us; and that to

be known is to be 'in' a mind, and therefore to be mental. Hence he

concluded that nothing can ever be known except what is in some mind,

and that whatever is known without being in my mind must be in some

other mind.

In order to understand his argument, it is necessary to understand his

use of the word 'idea'. He gives the name 'idea' to anything which is

/immediately/ known, as, for example, sense-data are known. Thus a

particular colour which we see is an idea; so is a voice which we hear,

and so on. But the term is not wholly confined to sense-data. There will

also be things remembered or imagined, for with such things also we have

immediate acquaintance at the moment of remembering or imagining. All

such immediate data he calls 'ideas'.

He then proceeds to consider common objects, such as a tree, for

instance. He shows that all we know immediately when we 'perceive' the

tree consists of ideas in his sense of the word, and he argues that

there is not the slightest ground for supposing that there is anything

real about the tree except what is perceived. Its being, he says,

consists in being perceived: in the Latin of the schoolmen its '/esse/'

is '/percipi/'. He fully admits that the tree must continue to exist

even when we shut our eyes or when no human being is near it. But this

continued existence, he says, is due to the fact that God continues to

perceive it; the 'real' tree, which corresponds to what we called the

physical object, consists of ideas in the mind of God, ideas more or

less like those we have when we see the tree, but differing in the fact

that they are permanent in God's mind so long as the tree continues to

exist. All our perceptions, according to him, consist in a partial

participation in God's perceptions, and it is because of this

participation that different people see more or less the same tree. Thus

apart from minds and their ideas there is nothing in the world, nor is

it possible that anything else should ever be known, since whatever is

known is necessarily an idea.

There are in this argument a good many fallacies which have been

important in the history of philosophy, and which it will be as well to

bring to light. In the first place, there is a confusion engendered by

the use of the word 'idea'. We think of an idea as essentially something

in somebody's mind, and thus when we are told that a tree consists

entirely of ideas, it is natural to suppose that, if so, the tree must

be entirely in minds. But the notion of being 'in' the mind is

ambiguous. We speak of bearing a person in mind, not meaning that the

person is in our minds, but that a thought of him is in our minds. When

a man says that some business he had to arrange went clean out of his

mind, he does not mean to imply that the business itself was ever in his

mind, but only that a thought of the business was formerly in his mind,

but afterwards ceased to be in his mind. And so when Berkeley says that

the tree must be in our minds if we can know it, all that he really has

a right to say is that a thought of the tree must be in our minds. To

argue that the tree itself must be in our minds is like arguing that a

person whom we bear in mind is himself in our minds. This confusion may

seem too gross to have been really committed by any competent

philosopher, but various attendant circumstances rendered it possible.

In order to see how it was possible, we must go more deeply into the

question as to the nature of ideas.

Before taking up the general question of the nature of ideas, we must

disentangle two entirely separate questions which arise concerning

sense-data and physical objects. We saw that, for various reasons of

detail, Berkeley was right in treating the sense-data which constitute

our perception of the tree as more or less subjective, in the sense that

they depend upon us as much as upon the tree, and would not exist if the

tree were not being perceived. But this is an entirely different point

from the one by which Berkeley seeks to prove that whatever can be

immediately known must be in a mind. For this purpose arguments of

detail as to the dependence of sense-data upon us are useless. It is

necessary to prove, generally, that by being known, things are shown to

be mental. This is what Berkeley believes himself to have done. It is

this question, and not our previous question as to the difference

between sense-data and the physical object, that must now concern us.

Taking the word 'idea' in Berkeley's sense, there are two quite distinct

things to be considered whenever an idea is before the mind. There is on

the one hand the thing of which we are aware?say the colour of my

table?and on the other hand the actual awareness itself, the mental act

of apprehending the thing. The mental act is undoubtedly mental, but is

there any reason to suppose that the thing apprehended is in any sense

mental? Our previous arguments concerning the colour did not prove it to

be mental; they only proved that its existence depends upon the relation

of our sense organs to the physical object?in our case, the table. That

is to say, they proved that a certain colour will exist, in a certain

light, if a normal eye is placed at a certain point relatively to the

table. They did not prove that the colour is in the mind of the percipient.

Berkeley's view, that obviously the colour must be in the mind, seems to

depend for its plausibility upon confusing the thing apprehended with

the act of apprehension. Either of these might be called an 'idea';

probably either would have been called an idea by Berkeley. The act is

undoubtedly in the mind; hence, when we are thinking of the act, we

readily assent to the view that ideas must be in the mind. Then,

forgetting that this was only true when ideas were taken as acts of

apprehension, we transfer the proposition that 'ideas are in the mind'

to ideas in the other sense, i.e. to the things apprehended by our acts

of apprehension. Thus, by an unconscious equivocation, we arrive at the

conclusion that whatever we can apprehend must be in our minds. This

seems to be the true analysis of Berkeley's argument, and the ultimate

fallacy upon which it rests.

This question of the distinction between act and object in our

apprehending of things is vitally important, since our whole power of

acquiring knowledge is bound up with it. The faculty of being acquainted

with things other than itself is the main characteristic of a mind.

Acquaintance with objects essentially consists in a relation between the

mind and something other than the mind; it is this that constitutes the

mind's power of knowing things. If we say that the things known must be

in the mind, we are either unduly limiting the mind's power of knowing,

or we are uttering a mere tautology. We are uttering a mere tautology if

we mean by '/in/ the mind' the same as by '/before/ the mind', i.e. if

we mean merely being apprehended by the mind. But if we mean this, we

shall have to admit that what, /in this sense/, is in the mind, may

nevertheless be not mental. Thus when we realize the nature of

knowledge, Berkeley's argument is seen to be wrong in substance as well

as in form, and his grounds for supposing that 'ideas'?i.e. the objects

apprehended?must be mental, are found to have no validity whatever.

Hence his grounds in favour of idealism may be dismissed. It remains to

see whether there are any other grounds.

It is often said, as though it were a self-evident truism, that we

cannot know that anything exists which we do not know. It is inferred

that whatever can in any way be relevant to our experience must be at

least capable of being known by us; whence it follows that if matter

were essentially something with which we could not become acquainted,

matter would be something which we could not know to exist, and which

could have for us no importance whatever. It is generally also implied,

for reasons which remain obscure, that what can have no importance for

us cannot be real, and that therefore matter, if it is not composed of

minds or of mental ideas, is impossible and a mere chimaera.

To go into this argument fully at our present stage would be impossible,

since it raises points requiring a considerable preliminary discussion;

but certain reasons for rejecting the argument may be noticed at once.

To begin at the end: there is no reason why what cannot have any

/practical/ importance for us should not be real. It is true that, if

/theoretical/ importance is included, everything real is of /some/

importance to us, since, as persons desirous of knowing the truth about

the universe, we have some interest in everything that the universe

contains. But if this sort of interest is included, it is not the case

that matter has no importance for us, provided it exists even if we

cannot know that it exists. We can, obviously, suspect that it may

exist, and wonder whether it does; hence it is connected with our desire

for knowledge, and has the importance of either satisfying or thwarting

this desire.

Again, it is by no means a truism, and is in fact false, that we cannot

know that anything exists which we do not know. The word 'know' is here

used in two different senses. (1) In its first use it is applicable to

the sort of knowledge which is opposed to error, the sense in which what

we know is /true/, the sense which applies to our beliefs and

convictions, i.e. to what are called /judgements/. In this sense of the

word we know /that/ something is the case. This sort of knowledge may be

described as knowledge of /truths/. (2) In the second use of the word

'know' above, the word applies to our knowledge of /things/, which we

may call /acquaintance/. This is the sense in which we know sense-data.

(The distinction involved is roughly that between /savoir/ and

/connaître/ in French, or between /wissen/ and /kennen/ in German.)

Thus the statement which seemed like a truism becomes, when re-stated,

the following: 'We can never truly judge that something with which we

are not acquainted exists.' This is by no means a truism, but on the

contrary a palpable falsehood. I have not the honour to be acquainted

with the Emperor of China, but I truly judge that he exists. It may be

said, of course, that I judge this because of other people's

acquaintance with him. This, however, would be an irrelevant retort,

since, if the principle were true, I could not know that any one else is

acquainted with him. But further: there is no reason why I should not

know of the existence of something with which nobody is acquainted. This

point is important, and demands elucidation.

If I am acquainted with a thing which exists, my acquaintance gives me

the knowledge that it exists. But it is not true that, conversely,

whenever I can know that a thing of a certain sort exists, I or some one

else must be acquainted with the thing. What happens, in cases where I

have true judgement without acquaintance, is that the thing is known to

me by /description/, and that, in virtue of some general principle, the

existence of a thing answering to this description can be inferred from

the existence of something with which I am acquainted. In order to

understand this point fully, it will be well first to deal with the

difference between knowledge by acquaintance and knowledge by

description, and then to consider what knowledge of general principles,

if any, has the same kind of certainty as our knowledge of the existence

of our own experiences. These subjects will be dealt with in the

following chapters.

CHAPTER V. KNOWLEDGE BY ACQUAINTANCE AND KNOWLEDGE BY DESCRIPTION

In the preceding chapter we saw that there are two sorts of knowledge:

knowledge of things, and knowledge of truths. In this chapter we shall

be concerned exclusively with knowledge of things, of which in turn we

shall have to distinguish two kinds. Knowledge of things, when it is of

the kind we call knowledge by /acquaintance/, is essentially simpler

than any knowledge of truths, and logically independent of knowledge of

truths, though it would be rash to assume that human beings ever, in

fact, have acquaintance with things without at the same time knowing

some truth about them. Knowledge of things by /description/, on the

contrary, always involves, as we shall find in the course of the present

chapter, some knowledge of truths as its source and ground. But first of

all we must make clear what we mean by 'acquaintance' and what we mean

by 'description'.

We shall say that we have /acquaintance/ with anything of which we are

directly aware, without the intermediary of any process of inference or

any knowledge of truths. Thus in the presence of my table I am

acquainted with the sense-data that make up the appearance of my

table?its colour, shape, hardness, smoothness, etc.; all these are

things of which I am immediately conscious when I am seeing and touching

my table. The particular shade of colour that I am seeing may have many

things said about it?I may say that it is brown, that it is rather dark,

and so on. But such statements, though they make me know truths about

the colour, do not make me know the colour itself any better than I did

before so far as concerns knowledge of the colour itself, as opposed to

knowledge of truths about it, I know the colour perfectly and completely

when I see it, and no further knowledge of it itself is even

theoretically possible. Thus the sense-data which make up the appearance

of my table are things with which I have acquaintance, things

immediately known to me just as they are.

My knowledge of the table as a physical object, on the contrary, is not

direct knowledge. Such as it is, it is obtained through acquaintance

with the sense-data that make up the appearance of the table. We have

seen that it is possible, without absurdity, to doubt whether there is a

table at all, whereas it is not possible to doubt the sense-data. My

knowledge of the table is of the kind which we shall call 'knowledge by

description'. The table is 'the physical object which causes

such-and-such sense-data'. This describes the table by means of the

sense-data. In order to know anything at all about the table, we must

know truths connecting it with things with which we have acquaintance:

we must know that 'such-and-such sense-data are caused by a physical

object'. There is no state of mind in which we are directly aware of the

table; all our knowledge of the table is really knowledge of truths, and

the actual thing which is the table is not, strictly speaking, known to

us at all. We know a description, and we know that there is just one

object to which this description applies, though the object itself is

not directly known to us. In such a case, we say that our knowledge of

the object is knowledge by description.

All our knowledge, both knowledge of things and knowledge of truths,

rests upon acquaintance as its foundation. It is therefore important to

consider what kinds of things there are with which we have acquaintance.

Sense-data, as we have already seen, are among the things with which we

are acquainted; in fact, they supply the most obvious and striking

example of knowledge by acquaintance. But if they were the sole example,

our knowledge would be very much more restricted than it is. We should

only know what is now present to our senses: we could not know anything

about the past?not even that there was a past?nor could we know any

truths about our sense-data, for all knowledge of truths, as we shall

show, demands acquaintance with things which are of an essentially

different character from sense-data, the things which are sometimes

called 'abstract ideas', but which we shall call 'universals'. We have

therefore to consider acquaintance with other things besides sense-data

if we are to obtain any tolerably adequate analysis of our knowledge.

The first extension beyond sense-data to be considered is acquaintance

by /memory/. It is obvious that we often remember what we have seen or

heard or had otherwise present to our senses, and that in such cases we

are still immediately aware of what we remember, in spite of the fact

that it appears as past and not as present. This immediate knowledge by

memory is the source of all our knowledge concerning the past: without

it, there could be no knowledge of the past by inference, since we

should never know that there was anything past to be inferred.

The next extension to be considered is acquaintance by /introspection/.

We are not only aware of things, but we are often aware of being aware

of them. When I see the sun, I am often aware of my seeing the sun; thus

'my seeing the sun' is an object with which I have acquaintance. When I

desire food, I may be aware of my desire for food; thus 'my desiring

food' is an object with which I am acquainted. Similarly we may be aware

of our feeling pleasure or pain, and generally of the events which

happen in our minds. This kind of acquaintance, which may be called

self-consciousness, is the source of all our knowledge of mental things.

It is obvious that it is only what goes on in our own minds that can be

thus known immediately. What goes on in the minds of others is known to

us through our perception of their bodies, that is, through the

sense-data in us which are associated with their bodies. But for our

acquaintance with the contents of our own minds, we should be unable to

imagine the minds of others, and therefore we could never arrive at the

knowledge that they have minds. It seems natural to suppose that

self-consciousness is one of the things that distinguish men from

animals: animals, we may suppose, though they have acquaintance with

sense-data, never become aware of this acquaintance. I do not mean that

they /doubt/ whether they exist, but that they have never become

conscious of the fact that they have sensations and feelings, nor

therefore of the fact that they, the subjects of their sensations and

feelings, exist.

We have spoken of acquaintance with the contents of our minds as

/self/-consciousness, but it is not, of course, consciousness of our

/self/: it is consciousness of particular thoughts and feelings. The

question whether we are also acquainted with our bare selves, as opposed

to particular thoughts and feelings, is a very difficult one, upon which

it would be rash to speak positively. When we try to look into ourselves

we always seem to come upon some particular thought or feeling, and not

upon the 'I' which has the thought or feeling. Nevertheless there are

some reasons for thinking that we are acquainted with the 'I', though

the acquaintance is hard to disentangle from other things. To make clear

what sort of reason there is, let us consider for a moment what our

acquaintance with particular thoughts really involves.

When I am acquainted with 'my seeing the sun', it seems plain that I am

acquainted with two different things in relation to each other. On the

one hand there is the sense-datum which represents the sun to me, on the

other hand there is that which sees this sense-datum. All acquaintance,

such as my acquaintance with the sense-datum which represents the sun,

seems obviously a relation between the person acquainted and the object

with which the person is acquainted. When a case of acquaintance is one

with which I can be acquainted (as I am acquainted with my acquaintance

with the sense-datum representing the sun), it is plain that the person

acquainted is myself. Thus, when I am acquainted with my seeing the sun,

the whole fact with which I am acquainted is

'Self-acquainted-with-sense-datum'.

Further, we know the truth 'I am acquainted with this sense-datum'. It

is hard to see how we could know this truth, or even understand what is

meant by it, unless we were acquainted with something which we call 'I'.

It does not seem necessary to suppose that we are acquainted with a more

or less permanent person, the same to-day as yesterday, but it does seem

as though we must be acquainted with that thing, whatever its nature,

which sees the sun and has acquaintance with sense-data. Thus, in some

sense it would seem we must be acquainted with our Selves as opposed to

our particular experiences. But the question is difficult, and

complicated arguments can be adduced on either side. Hence, although

acquaintance with ourselves seems /probably/ to occur, it is not wise to

assert that it undoubtedly does occur.

We may therefore sum up as follows what has been said concerning

acquaintance with things that exist. We have acquaintance in sensation

with the data of the outer senses, and in introspection with the data of

what may be called the inner sense?thoughts, feelings, desires, etc.; we

have acquaintance in memory with things which have been data either of

the outer senses or of the inner sense. Further, it is probable, though

not certain, that we have acquaintance with Self, as that which is aware

of things or has desires towards things.

In addition to our acquaintance with particular existing things, we also

have acquaintance with what we shall call /universals/, that is to say,

general ideas, such as /whiteness/, /diversity/, /brotherhood/, and so

on. Every complete sentence must contain at least one word which stands

for a universal, since all verbs have a meaning which is universal. We

shall return to universals later on, in Chapter IX; for the present, it

is only necessary to guard against the supposition that whatever we can

be acquainted with must be something particular and existent. Awareness

of universals is called /conceiving/, and a universal of which we are

aware is called a /concept/.

It will be seen that among the objects with which we are acquainted are

not included physical objects (as opposed to sense-data), nor other

people's minds. These things are known to us by what I call 'knowledge

by description', which we must now consider.

By a 'description' I mean any phrase of the form 'a so-and-so' or 'the

so-and-so'. A phrase of the form 'a so-and-so' I shall call an

'ambiguous' description; a phrase of the form 'the so-and-so' (in the

singular) I shall call a 'definite' description. Thus 'a man' is an

ambiguous description, and 'the man with the iron mask' is a definite

description. There are various problems connected with ambiguous

descriptions, but I pass them by, since they do not directly concern the

matter we are discussing, which is the nature of our knowledge

concerning objects in cases where we know that there is an object

answering to a definite description, though we are not acquainted with

any such object. This is a matter which is concerned exclusively with

definite descriptions. I shall therefore, in the sequel, speak simply of

'descriptions' when I mean 'definite descriptions'. Thus a description

will mean any phrase of the form 'the so-and-so' in the singular.

We shall say that an object is 'known by description' when we know that

it is 'the so-and-so', i.e. when we know that there is one object, and

no more, having a certain property; and it will generally be implied

that we do not have knowledge of the same object by acquaintance. We

know that the man with the iron mask existed, and many propositions are

known about him; but we do not know who he was. We know that the

candidate who gets the most votes will be elected, and in this case we

are very likely also acquainted (in the only sense in which one can be

acquainted with some one else) with the man who is, in fact, the

candidate who will get most votes; but we do not know which of the

candidates he is, i.e. we do not know any proposition of the form 'A is

the candidate who will get most votes' where A is one of the candidates

by name. We shall say that we have 'merely descriptive knowledge' of the

so-and-so when, although we know that the so-and-so exists, and although

we may possibly be acquainted with the object which is, in fact, the

so-and-so, yet we do not know any proposition '/a/ is the so-and-so',

where /a/ is something with which we are acquainted.

When we say 'the so-and-so exists', we mean that there is just one

object which is the so-and-so. The proposition '/a/ is the so-and-so'

means that /a/ has the property so-and-so, and nothing else has. 'Mr. A.

is the Unionist candidate for this constituency' means 'Mr. A. is a

Unionist candidate for this constituency, and no one else is'. 'The

Unionist candidate for this constituency exists' means 'some one is a

Unionist candidate for this constituency, and no one else is'. Thus,

when we are acquainted with an object which is the so-and-so, we know

that the so-and-so exists; but we may know that the so-and-so exists

when we are not acquainted with any object which we know to be the

so-and-so, and even when we are not acquainted with any object which, in

fact, is the so-and-so.

Common words, even proper names, are usually really descriptions. That

is to say, the thought in the mind of a person using a proper name

correctly can generally only be expressed explicitly if we replace the

proper name by a description. Moreover, the description required to

express the thought will vary for different people, or for the same

person at different times. The only thing constant (so long as the name

is rightly used) is the object to which the name applies. But so long as

this remains constant, the particular description involved usually makes

no difference to the truth or falsehood of the proposition in which the

name appears.

Let us take some illustrations. Suppose some statement made about

Bismarck. Assuming that there is such a thing as direct acquaintance

with oneself, Bismarck himself might have used his name directly to

designate the particular person with whom he was acquainted. In this

case, if he made a judgement about himself, he himself might be a

constituent of the judgement. Here the proper name has the direct use

which it always wishes to have, as simply standing for a certain object,

and not for a description of the object. But if a person who knew

Bismarck made a judgement about him, the case is different. What this

person was acquainted with were certain sense-data which he connected

(rightly, we will suppose) with Bismarck's body. His body, as a physical

object, and still more his mind, were only known as the body and the

mind connected with these sense-data. That is, they were known by

description. It is, of course, very much a matter af chance which

characteristics of a man's appearance will come into a friend's mind

when he thinks of him; thus the description actually in the friend's

mind is accidental. The essential point is that he knows that the

various descriptions all apply to the same entity, in spite of not being

acquainted with the entity in question.

When we, who did not know Bismarck, make a judgement about him, the

description in our minds will probably be some more or less vague mass

of historical knowledge?far more, in most cases, than is required to

identify him. But, for the sake of illustration, let us assume that we

think of him as 'the first Chancellor of the German Empire'. Here all

the words are abstract except 'German'. The word 'German' will, again,

have different meanings for different people. To some it will recall

travels in Germany, to some the look of Germany on the map, and so on.

But if we are to obtain a description which we know to be applicable, we

shall be compelled, at some point, to bring in a reference to a

particular with which we are acquainted. Such reference is involved in

any mention of past, present, and future (as opposed to definite dates),

or of here and there, or of what others have told us. Thus it would seem

that, in some way or other, a description known to be applicable to a

particular must involve some reference to a particular with which we are

acquainted, if our knowledge about the thing described is not to be

merely what follows /logically/ from the description. For example, 'the

most long-lived of men' is a description involving only universals,

which must apply to some man, but we can make no judgements concerning

this man which involve knowledge about him beyond what the description

gives. If, however, we say, 'The first Chancellor of the German Empire

was an astute diplomatist', we can only be assured of the truth of our

judgement in virtue of something with which we are acquainted?usually a

testimony heard or read. Apart from the information we convey to others,

apart from the fact about the actual Bismarck, which gives importance to

our judgement, the thought we really have contains the one or more

particulars involved, and otherwise consists wholly of concepts.

All names of places?London, England, Europe, the Earth, the Solar

System?similarly involve, when used, descriptions which start from some

one or more particulars with which we are acquainted. I suspect that

even the Universe, as considered by metaphysics, involves such a

connexion with particulars. In logic, on the contrary, where we are

concerned not merely with what does exist, but with whatever might or

could exist or be, no reference to actual particulars is involved.

It would seem that, when we make a statement about something only known

by description, we often /intend/ to make our statement, not in the form

involving the description, but about the actual thing described. That is

to say, when we say anything about Bismarck, we should like, if we

could, to make the judgement which Bismarck alone can make, namely, the

judgement of which he himself is a constituent. In this we are

necessarily defeated, since the actual Bismarck is unknown to us. But we

know that there is an object B, called Bismarck, and that B was an

astute diplomatist. We can thus /describe/ the proposition we should

like to affirm, namely, 'B was an astute diplomatist', where B is the

object which was Bismarck. If we are describing Bismarck as 'the first

Chancellor of the German Empire', the proposition we should like to

affirm may be described as 'the proposition asserting, concerning the

actual object which was the first Chancellor of the German Empire, that

this object was an astute diplomatist'. What enables us to communicate

in spite of the varying descriptions we employ is that we know there is

a true proposition concerning the actual Bismarck, and that however we

may vary the description (so long as the description is correct) the

proposition described is still the same. This proposition, which is

described and is known to be true, is what interests us; but we are not

acquainted with the proposition itself, and do not know it, though we

know it is true.

It will be seen that there are various stages in the removal from

acquaintance with particulars: there is Bismarck to people who knew him;

Bismarck to those who only know of him through history; the man with the

iron mask; the longest-lived of men. These are progressively further

removed from acquaintance with particulars; the first comes as near to

acquaintance as is possible in regard to another person; in the second,

we shall still be said to know 'who Bismarck was'; in the third, we do

not know who was the man with the iron mask, though we can know many

propositions about him which are not logically deducible from the fact

that he wore an iron mask; in the fourth, finally, we know nothing

beyond what is logically deducible from the definition of the man. There

is a similar hierarchy in the region of universals. Many universals,

like many particulars, are only known to us by description. But here, as

in the case of particulars, knowledge concerning what is known by

description is ultimately reducible to knowledge concerning what is

known by acquaintance.

The fundamental principle in the analysis of propositions containing

descriptions is this: /Every proposition which we can understand must be

composed wholly of constituents with which we are acquainted/.

We shall not at this stage attempt to answer all the objections which

may be urged against this fundamental principle. For the present, we

shall merely point out that, in some way or other, it must be possible

to meet these objections, for it is scarcely conceivable that we can

make a judgement or entertain a supposition without knowing what it is

that we are judging or supposing about. We must attach /some/ meaning to

the words we use, if we are to speak significantly and not utter mere

noise; and the meaning we attach to our words must be something with

which we are acquainted. Thus when, for example, we make a statement

about Julius Caesar, it is plain that Julius Caesar himself is not

before our minds, since we are not acquainted with him. We have in mind

some description of Julius Caesar: 'the man who was assassinated on the

Ides of March', 'the founder of the Roman Empire', or, perhaps, merely

'the man whose name was /Julius Caesar/'. (In this last description,

/Julius Caesar/ is a noise or shape with which we are acquainted.) Thus

our statement does not mean quite what it seems to mean, but means

something involving, instead of Julius Caesar, some description of him

which is composed wholly of particulars and universals with which we are

acquainted.

The chief importance of knowledge by description is that it enables us

to pass beyond the limits of our private experience. In spite of the

fact that we can only know truths which are wholly composed of terms

which we have experienced in acquaintance, we can yet have knowledge by

description of things which we have never experienced. In view of the

very narrow range of our immediate experience, this result is vital, and

until it is understood, much of our knowledge must remain mysterious and

therefore doubtful.

CHAPTER VI. ON INDUCTION

In almost all our previous discussions we have been concerned in the

attempt to get clear as to our data in the way of knowledge of

existence. What things are there in the universe whose existence is

known to us owing to our being acquainted with them? So far, our answer

has been that we are acquainted with our sense-data, and, probably, with

ourselves. These we know to exist. And past sense-data which are

remembered are known to have existed in the past. This knowledge

supplies our data.

But if we are to be able to draw inferences from these data?if we are to

know of the existence of matter, of other people, of the past before our

individual memory begins, or of the future, we must know general

principles of some kind by means of which such inferences can be drawn.

It must be known to us that the existence of some one sort of thing, A,

is a sign of the existence of some other sort of thing, B, either at the

same time as A or at some earlier or later time, as, for example,

thunder is a sign of the earlier existence of lightning. If this were

not known to us, we could never extend our knowledge beyond the sphere

of our private experience; and this sphere, as we have seen, is

exceedingly limited. The question we have now to consider is whether

such an extension is possible, and if so, how it is effected.

Let us take as an illustration a matter about which none of us, in fact,

feel the slightest doubt. We are all convinced that the sun will rise

to-morrow. Why? Is this belief a mere blind outcome of past experience,

or can it be justified as a reasonable belief? It is not easy to find a

test by which to judge whether a belief of this kind is reasonable or

not, but we can at least ascertain what sort of general beliefs would

suffice, if true, to justify the judgement that the sun will rise

to-morrow, and the many other similar judgements upon which our actions

are based.

It is obvious that if we are asked why we believe that the sun will rise

to-morrow, we shall naturally answer 'Because it always has risen every

day'. We have a firm belief that it will rise in the future, because it

has risen in the past. If we are challenged as to why we believe that it

will continue to rise as heretofore, we may appeal to the laws of

motion: the earth, we shall say, is a freely rotating body, and such

bodies do not cease to rotate unless something interferes from outside,

and there is nothing outside to interfere with the earth between now and

to-morrow. Of course it might be doubted whether we are quite certain

that there is nothing outside to interfere, but this is not the

interesting doubt. The interesting doubt is as to whether the laws of

motion will remain in operation until to-morrow. If this doubt is

raised, we find ourselves in the same position as when the doubt about

the sunrise was first raised.

The /only/ reason for believing that the laws of motion will remain in

operation is that they have operated hitherto, so far as our knowledge

of the past enables us to judge. It is true that we have a greater body

of evidence from the past in favour of the laws of motion than we have

in favour of the sunrise, because the sunrise is merely a particular

case of fulfilment of the laws of motion, and there are countless other

particular cases. But the real question is: Do /any/ number of cases of

a law being fulfilled in the past afford evidence that it will be

fulfilled in the future? If not, it becomes plain that we have no ground

whatever for expecting the sun to rise to-morrow, or for expecting the

bread we shall eat at our next meal not to poison us, or for any of the

other scarcely conscious expectations that control our daily lives. It

is to be observed that all such expectations are only /probable/; thus

we have not to seek for a proof that they /must/ be fulfilled, but only

for some reason in favour of the view that they are /likely/ to be

fulfilled.

Now in dealing with this question we must, to begin with, make an

important distinction, without which we should soon become involved in

hopeless confusions. Experience has shown us that, hitherto, the

frequent repetition of some uniform succession or coexistence has been a

/cause/ of our expecting the same succession or coexistence on the next

occasion. Food that has a certain appearance generally has a certain

taste, and it is a severe shock to our expectations when the familiar

appearance is found to be associated with an unusual taste. Things which

we see become associated, by habit, with certain tactile sensations

which we expect if we touch them; one of the horrors of a ghost (in many

ghost-stories) is that it fails to give us any sensations of touch.

Uneducated people who go abroad for the first time are so surprised as

to be incredulous when they find their native language not understood.

And this kind of association is not confined to men; in animals also it

is very strong. A horse which has been often driven along a certain road

resists the attempt to drive him in a different direction. Domestic

animals expect food when they see the person who usually feeds them. We

know that all these rather crude expectations of uniformity are liable

to be misleading. The man who has fed the chicken every day throughout

its life at last wrings its neck instead, showing that more refined

views as to the uniformity of nature would have been useful to the chicken.

But in spite of the misleadingness of such expectations, they

nevertheless exist. The mere fact that something has happened a certain

number of times causes animals and men to expect that it will happen

again. Thus our instincts certainly cause us to believe that the sun

will rise to-morrow, but we may be in no better a position than the

chicken which unexpectedly has its neck wrung. We have therefore to

distinguish the fact that past uniformities /cause/ expectations as to

the future, from the question whether there is any reasonable ground for

giving weight to such expectations after the question of their validity

has been raised.

The problem we have to discuss is whether there is any reason for

believing in what is called 'the uniformity of nature'. The belief in

the uniformity of nature is the belief that everything that has happened

or will happen is an instance of some general law to which there are no

exceptions. The crude expectations which we have been considering are

all subject to exceptions, and therefore liable to disappoint those who

entertain them. But science habitually assumes, at least as a working

hypothesis, that general rules which have exceptions can be replaced by

general rules which have no exceptions. 'Unsupported bodies in air fall'

is a general rule to which balloons and aeroplanes are exceptions. But

the laws of motion and the law of gravitation, which account for the

fact that most bodies fall, also account for the fact that balloons and

aeroplanes can rise; thus the laws of motion and the law of gravitation

are not subject to these exceptions.

The belief that the sun will rise to-morrow might be falsified if the

earth came suddenly into contact with a large body which destroyed its

rotation; but the laws of motion and the law of gravitation would not be

infringed by such an event. The business of science is to find

uniformities, such as the laws of motion and the law of gravitation, to

which, so far as our experience extends, there are no exceptions. In

this search science has been remarkably successful, and it may be

conceded that such uniformities have held hitherto. This brings us back

to the question: Have we any reason, assuming that they have always held

in the past, to suppose that they will hold in the future?

It has been argued that we have reason to know that the future will

resemble the past, because what was the future has constantly become the

past, and has always been found to resemble the past, so that we really

have experience of the future, namely of times which were formerly

future, which we may call past futures. But such an argument really begs

the very question at issue. We have experience of past futures, but not

of future futures, and the question is: Will future futures resemble

past futures? This question is not to be answered by an argument which

starts from past futures alone. We have therefore still to seek for some

principle which shall enable us to know that the future will follow the

same laws as the past.

The reference to the future in this question is not essential. The same

question arises when we apply the laws that work in our experience to

past things of which we have no experience?as, for example, in geology,

or in theories as to the origin of the Solar System. The question we

really have to ask is: 'When two things have been found to be often

associated, and no instance is known of the one occurring without the

other, does the occurrence of one of the two, in a fresh instance, give

any good ground for expecting the other?' On our answer to this question

must depend the validity of the whole of our expectations as to the

future, the whole of the results obtained by induction, and in fact

practically all the beliefs upon which our daily life is based.

It must be conceded, to begin with, that the fact that two things have

been found often together and never apart does not, by itself, suffice

to /prove/ demonstratively that they will be found together in the next

case we examine. The most we can hope is that the oftener things are

found together, the more probable it becomes that they will be found

together another time, and that, if they have been found together often

enough, the probability will amount /almost/ to certainty. It can never

quite reach certainty, because we know that in spite of frequent

repetitions there sometimes is a failure at the last, as in the case of

the chicken whose neck is wrung. Thus probability is all we ought to seek.

It might be urged, as against the view we are advocating, that we know

all natural phenomena to be subject to the reign of law, and that

sometimes, on the basis of observation, we can see that only one law can

possibly fit the facts of the case. Now to this view there are two

answers. The first is that, even if /some/ law which has no exceptions

applies to our case, we can never, in practice, be sure that we have

discovered that law and not one to which there are exceptions. The

second is that the reign of law would seem to be itself only probable,

and that our belief that it will hold in the future, or in unexamined

cases in the past, is itself based upon the very principle we are

examining.

The principle we are examining may be called the /principle of

induction/, and its two parts may be stated as follows:

(a) When a thing of a certain sort A has been found to be associated

with a thing of a certain other sort B, and has never been found

dissociated from a thing of the sort B, the greater the number of cases

in which A and B have been associated, the greater is the probability

that they will be associated in a fresh case in which one of them is

known to be present;

(b) Under the same circumstances, a sufficient number of cases of

association will make the probability of a fresh association nearly a

certainty, and will make it approach certainty without limit.

As just stated, the principle applies only to the verification of our

expectation in a single fresh instance. But we want also to know that

there is a probability in favour of the general law that things of the

sort A are /always/ associated with things of the sort B, provided a

sufficient number of cases of association are known, and no cases of

failure of association are known. The probability of the general law is

obviously less than the probability of the particular case, since if the

general law is true, the particular case must also be true, whereas the

particular case may be true without the general law being true.

Nevertheless the probability of the general law is increased by

repetitions, just as the probability of the particular case is. We may

therefore repeat the two parts of our principle as regards the general

law, thus:

(a) The greater the number of cases in which a thing of the sort A has

been found associated with a thing of the sort B, the more probable it

is (if no cases of failure of association are known) that A is always

associated with B;

b) Under the same circumstances, a sufficient number of cases of the

association of A with B will make it nearly certain that A is always

associated with B, and will make this general law approach certainty

without limit.

It should be noted that probability is always relative to certain data.

In our case, the data are merely the known cases of coexistence of A and

B. There may be other data, which /might/ be taken into account, which

would gravely alter the probability. For example, a man who had seen a

great many white swans might argue, by our principle, that on the data

it was /probable/ that all swans were white, and this might be a

perfectly sound argument. The argument is not disproved ny the fact that

some swans are black, because a thing may very well happen in spite of

the fact that some data render it improbable. In the case of the swans,

a man might know that colour is a very variable characteristic in many

species of animals, and that, therefore, an induction as to colour is

peculiarly liable to error. But this knowledge would be a fresh datum,

by no means proving that the probability relatively to our previous data

had been wrongly estimated. The fact, therefore, that things often fail

to fulfil our expectations is no evidence that our expectations will not

/probably/ be fulfilled in a given case or a given class of cases. Thus

our inductive principle is at any rate not capable of being /disproved/

by an appeal to experience.

The inductive principle, however, is equally incapable of being /proved/

by an appeal to experience. Experience might conceivably confirm the

inductive principle as regards the cases that have been already

examined; but as regards unexamined cases, it is the inductive principle

alone that can justify any inference from what has been examined to what

has not been examined. All arguments which, on the basis of experience,

argue as to the future or the unexperienced parts of the past or

present, assume the inductive principle; hence we can never use

experience to prove the inductive principle without begging the

question. Thus we must either accept the inductive principle on the

ground of its intrinsic evidence, or forgo all justification of our

expectations about the future. If the principle is unsound, we have no

reason to expect the sun to rise to-morrow, to expect bread to be more

nourishing than a stone, or to expect that if we throw ourselves off the

roof we shall fall. When we see what looks like our best friend

approaching us, we shall have no reason to suppose that his body is not

inhabited by the mind of our worst enemy or of some total stranger. All

our conduct is based upon associations which have worked in the past,

and which we therefore regard as likely to work in the future; and this

likelihood is dependent for its validity upon the inductive principle.

The general principles of science, such as the belief in the reign of

law, and the belief that every event must have a cause, are as

completely dependent upon the inductive principle as are the beliefs of

daily life All such general principles are believed because mankind have

found innumerable instances of their truth and no instances of their

falsehood. But this affords no evidence for their truth in the future,

unless the inductive principle is assumed.

Thus all knowledge which, on a basis of experience tells us something

about what is not experienced, is based upon a belief which experience

can neither confirm nor confute, yet which, at least in its more

concrete applications, appears to be as firmly rooted in us as many of

the facts of experience. The existence and justification of such

beliefs?for the inductive principle, as we shall see, is not the only

example?raises some of the most difficult and most debated problems of

philosophy. We will, in the next chapter, consider briefly what may be

said to account for such knowledge, and what is its scope and its degree

of certainty.

CHAPTER VII. ON OUR KNOWLEDGE OF GENERAL PRINCIPLES

We saw in the preceding chapter that the principle of induction, while

necessary to the validity of all arguments based on experience, is

itself not capable of being proved by experience, and yet is

unhesitatingly believed by every one, at least in all its concrete

applications. In these characteristics the principle of induction does

not stand alone. There are a number of other principles which cannot be

proved or disproved by experience, but are used in arguments which start

from what is experienced.

Some of these principles have even greater evidence than the principle

of induction, and the knowledge of them has the same degree of certainty

as the knowledge of the existence of sense-data. They constitute the

means of drawing inferences from what is given in sensation; and if what

we infer is to be true, it is just as necessary that our principles of

inference should be true as it is that our data should be true. The

principles of inference are apt to be overlooked because of their very

obviousness?the assumption involved is assented to without our realizing

that it is an assumption. But it is very important to realize the use of

principles of inference, if a correct theory of knowledge is to be

obtained; for our knowledge of them raises interesting and difficult

questions.

In all our knowledge of general principles, what actually happens is

that first of all we realize some particular application of the

principle, and then we realize that the particularity is irrelevant, and

that there is a generality which may equally truly be affirmed. This is

of course familiar in such matters as teaching arithmetic: 'two and two

are four' is first learnt in the case of some particular pair of

couples, and then in some other particular case, and so on, until at

last it becomes possible to see that it is true of any pair of couples.

The same thing happens with logical principles. Suppose two men are

discussing what day of the month it is. One of them says, 'At least you

will admit that /if/ yesterday was the 15th to-day must be the 16th.'

'Yes', says the other, 'I admit that.' 'And you know', the first

continues, 'that yesterday was the 15th, because you dined with Jones,

and your diary will tell you that was on the 15th.' 'Yes', says the

second; 'therefore to-day /is/ the 16th.'

Now such an argument is not hard to follow; and if it is granted that

its premisses are true in fact, no one will deny that the conclusion

must also be true. But it depends for its truth upon an instance of a

general logical principle. The logical principle is as follows: 'Suppose

it known that /if/ this is true, then that is true. Suppose it also

known that this /is/ true, then it follows that that is true.' When it

is the case that if this is true, that is true, we shall say that this

'implies' that, and that that 'follows from' this. Thus our principle

states that if this implies that, and this is true, then that is true.

In other words, 'anything implied by a true proposition is true', or

'whatever follows from a true proposition is true'.

This principle is really involved?at least, concrete instances of it are

involved?in all demonstrations. Whenever one thing which we believe is

used to prove something else, which we consequently believe, this

principle is relevant. If any one asks: 'Why should I accept the results

of valid arguments based on true premisses?' we can only answer by

appealing to our principle. In fact, the truth of the principle is

impossible to doubt, and its obviousness is so great that at first sight

it seems almost trivial. Such principles, however, are not trivial to

the philosopher, for they show that we may have indubitable knowledge

which is in no way derived from objects of sense.

The above principle is merely one of a certain number of self-evident

logical principles. Some at least of these principles must be granted

before any argument or proof becomes possible. When some of them have

been granted, others can be proved, though these others, so long as they

are simple, are just as obvious as the principles taken for granted. For

no very good reason, three of these principles have been singled out by

tradition under the name of 'Laws of Thought'.

They are as follows:

(1) /The law of identity/: 'Whatever is, is.'

(2) /The law of contradiction/: 'Nothing can both be and not be.'

(3) /The law of excluded middle/: 'Everything must either be or not be.'

These three laws are samples of self-evident logical principles, but are

not really more fundamental or more self-evident than various other

similar principles: for instance, the one we considered just now, which

states that what follows from a true premiss is true. The name 'laws of

thought' is also misleading, for what is important is not the fact that

we think in accordance with these laws, but the fact that things behave

in accordance with them; in other words, the fact that when we think in

accordance with them we think /truly/. But this is a large question, to

which we must return at a later stage.

In addition to the logical principles which enable us to prove from a

given premiss that something is /certainly/ true, there are other

logical principles which enable us to prove, from a given premiss, that

there is a greater or less probability that something is true. An

example of such principles perhaps the most important example is the

inductive principle, which we considered in the preceding chapter.

One of the great historic controversies in philosophy is the controversy

between the two schools called respectively 'empiricists' and

'rationalists'. The empiricists who are best represented by the British

philosophers, Locke, Berkeley, and Hume maintained that all our

knowledge is derived from experience; the rationalists who are

represented by the Continental philosophers of the seventeenth century,

especially Descartes and Leibniz maintained that, in addition to what we

know by experience, there are certain 'innate ideas' and 'innate

principles', which we know independently of experience. It has now

become possible to decide with some confidence as to the truth or

falsehood of these opposing schools. It must be admitted, for the

reasons already stated, that logical principles are known to us, and

cannot be themselves proved by experience, since all proof presupposes

them. In this, therefore, which was the most important point of the

controversy, the rationalists were in the right.

On the other hand, even that part of our knowledge which is /logically/

independent of experience (in the sense that experience cannot prove it)

is yet elicited and caused by experience. It is on occasion of

particular experiences that we become aware of the general laws which

their connexions exemplify. It would certainly be absurd to suppose that

there are innate principles in the sense that babies are born with a

knowledge of everything which men know and which cannot be deduced from

what is experienced. For this reason, the word 'innate' would not now be

employed to describe our knowledge of logical principles. The phrase '/a

priori/' is less objectionable, and is more usual in modern writers.

Thus, while admitting that all knowledge is elicited and caused by

experience, we shall nevertheless hold that some knowledge is /a

priori/, in the sense that the experience which makes us think of it

does not suffice to prove it, but merely so directs our attention that

we see its truth without requiring any proof from experience.

There is another point of great importance, in which the empiricists

were in the right as against the rationalists. Nothing can be known to

/exist/ except by the help of experience. That is to say, if we wish to

prove that something of which we have no direct experience exists, we

must have among our premises the existence of one or more things of

which we have direct experience. Our belief that the Emperor of China

exists, for example, rests upon testimony, and testimony consists, in

the last analysis, of sense-data seen or heard in reading or being

spoken to. Rationalists believed that, from general consideration as to

what must be, they could deduce the existence of this or that in the

actual world. In this belief they seem to have been mistaken. All the

knowledge that we can acquire /a priori/ concerning existence seems to

be hypothetical: it tells us that if one thing exists, another must

exist, or, more generally, that if one proposition is true, another must

be true. This is exemplified by the principles we have already dealt

with, such as '/if/ this is true, and this implies that, then that is

true', or '/if/ this and that have been repeatedly found connected, they

will probably be connected in the next instance in which one of them is

found'. Thus the scope and power of /a priori/ principles is strictly

limited. All knowledge that something exists must be in part dependent

on experience. When anything is known immediately, its existence is

known by experience alone; when anything is proved to exist, without

being known immediately, both experience and /a priori/ principles must

be required in the proof. Knowledge is called /empirical/ when it rests

wholly or partly upon experience. Thus all knowledge which asserts

existence is empirical, and the only /a priori/ knowledge concerning

existence is hypothetical, giving connexions among things that exist or

may exist, but not giving actual existence.

/A priori/ knowledge is not all of the logical kind we have been

hitherto considering. Perhaps the most important example of non-logical

/a priori/ knowledge is knowledge as to ethical value. I am not speaking

of judgements as to what is useful or as to what is virtuous, for such

judgements do require empirical premises; I am speaking of judgements

as to the intrinsic desirability of things. If something is useful, it

must be useful because it secures some end; the end must, if we have

gone far enough, be valuable on its own account, and not merely because

it is useful for some further end. Thus all judgements as to what is

useful depend upon judgements as to what has value on its own account.

We judge, for example, that happiness is more desirable than misery,

knowledge than ignorance, goodwill than hatred, and so on. Such

judgements must, in part at least, be immediate and /a priori/. Like our

previous /a priori/ judgements, they may be elicited by experience, and

indeed they must be; for it seems not possible to judge whether anything

is intrinsically valuable unless we have experienced something of the

same kind. But it is fairly obvious that they cannot be proved by

experience; for the fact that a thing exists or does not exist cannot

prove either that it is good that it should exist or that it is bad. The

pursuit of this subject belongs to ethics, where the impossibility of

deducing what ought to be from what is has to be established. In the

present connexion, it is only important to realize that knowledge as to

what is intrinsically of value is /a priori/ in the same sense in which

logic is /a priori/, namely in the sense that the truth of such

knowledge can be neither proved nor disproved by experience.

All pure mathematics is /a priori/, like logic. This was strenuously

denied by the empirical philosophers, who maintained that experience was

as much the source of our knowledge of arithmetic as of our knowledge of

geography. They maintained that by the repeated experience of seeing two

things and two other things, and finding that altogether they made four

things, we were led by induction to the conclusion that two things and

two other things would /always/ make four things altogether. If,

however, this were the source of our knowledge that two and two are

four, we should proceed differently, in persuading ourselves of its

truth, from the way in which we do actually proceed. In fact, a certain

number of instances are needed to make us think of two abstractly,

rather than of two coins or two books or two people, or two of any other

specified kind. But as soon as we are able to divest our thoughts of

irrelevant particularity, we become able to see the general principle

that two and two are four; any one instance is seen to be /typical/, and

the examination of other instances becomes unnecessary.(1)

(1) Cf. A. N. Whitehead, /Introduction to Mathematics/ (Home University

Library).

The same thing is exemplified in geometry. If we want to prove some

property of /all/ triangles, we draw some one triangle and reason about

it; but we can avoid making use of any property which it does not share

with all other triangles, and thus, from our particular case, we obtain

a general result. We do not, in fact, feel our certainty that two and

two are four increased by fresh instances, because, as soon as we have

seen the truth of this proposition, our certainty becomes so great as to

be incapable of growing greater. Moreover, we feel some quality of

necessity about the proposition 'two and two are four', which is absent

from even the best attested empirical generalizations. Such

generalizations always remain mere facts: we feel that there might be a

world in which they were false, though in the actual world they happen

to be true. In any possible world, on the contrary, we feel that two and

two would be four: this is not a mere fact, but a necessity to which

everything actual and possible must conform.

The case may be made clearer by considering a genuinely-empirical

generalization, such as 'All men are mortal.' It is plain that we

believe this proposition, in the first place, because there is no known

instance of men living beyond a certain age, and in the second place

because there seem to be physiological grounds for thinking that an

organism such as a man's body must sooner or later wear out. Neglecting

the second ground, and considering merely our experience of men's

mortality, it is plain that we should not be content with one quite

clearly understood instance of a man dying, whereas, in the case of 'two

and two are four', one instance does suffice, when carefully considered,

to persuade us that the same must happen in any other instance. Also we

can be forced to admit, on reflection, that there may be some doubt,

however slight, as to whether /all/ men are mortal. This may be made

plain by the attempt to imagine two different worlds, in one of which

there are men who are not mortal, while in the other two and two make

five. When Swift invites us to consider the race of Struldbugs who never

die, we are able to acquiesce in imagination. But a world where two and

two make five seems quite on a different level. We feel that such a

world, if there were one, would upset the whole fabric of our knowledge

and reduce us to utter doubt.

The fact is that, in simple mathematical judgements such as 'two and two

are four', and also in many judgements of logic, we can know the general

proposition without inferring it from instances, although some instance

is usually necessary to make clear to us what the general proposition

means. This is why there is real utility in the process of /deduction/,

which goes from the general to the general, or from the general to the

particular, as well as in the process of /induction/, which goes from

the particular to the particular, or from the particular to the general.

It is an old debate among philosophers whether deduction ever gives

/new/ knowledge. We can now see that in certain cases, at least, it does

do so. If we already know that two and two always make four, and we know

that Brown and Jones are two, and so are Robinson and Smith, we can

deduce that Brown and Jones and Robinson and Smith are four. This is new

knowledge, not contained in our premises, because the general

proposition, 'two and two are four', never told us there were such

people as Brown and Jones and Robinson and Smith, and the particular

premises do not tell us that there were four of them, whereas the

particular proposition deduced does tell us both these things.

But the newness of the knowledge is much less certain if we take the

stock instance of deduction that is always given in books on logic,

namely, 'All men are mortal; Socrates is a man, therefore Socrates is

mortal.' In this case, what we really know beyond reasonable doubt is

that certain men, A, B, C, were mortal, since, in fact, they have died.

If Socrates is one of these men, it is foolish to go the roundabout way

through 'all men are mortal' to arrive at the conclusion that /probably/

Socrates is mortal. If Socrates is not one of the men on whom our

induction is based, we shall still do better to argue straight from our

A, B, C, to Socrates, than to go round by the general proposition, 'all

men are mortal'. For the probability that Socrates is mortal is greater,

on our data, than the probability that all men are mortal. (This is

obvious, because if all men are mortal, so is Socrates; but if Socrates

is mortal, it does not follow that all men are mortal.) Hence we shall

reach the conclusion that Socrates is mortal with a greater approach to

certainty if we make our argument purely inductive than if we go by way

of 'all men are mortal' and then use deduction.

This illustrates the difference between general propositions known /a

priori/ such as 'two and two are four', and empirical generalizations

such as 'all men are mortal'. In regard to the former, deduction is the

right mode of argument, whereas in regard to the latter, induction is

always theoretically preferable, and warrants a greater confidence in

the truth of our conclusion, because all empirical generalizations are

more uncertain than the instances of them.

We have now seen that there are propositions known /a priori/, and that

among them are the propositions of logic and pure mathematics, as well

as the fundamental propositions of ethics. The question which must next

occupy us is this: How is it possible that there should be such

knowledge? And more particularly, how can there be knowledge of general

propositions in cases where we have not examined all the instances, and

indeed never can examine them all, because their number is infinite?

These questions, which were first brought prominently forward by the

German philosopher Kant (1724-1804), are very difficult, and

historically very important.

CHAPTER VIII. HOW /A PRIORI/ KNOWLEDGE IS POSSIBLE

Immanuel Kant is generally regarded as the greatest of the modern

philosophers. Though he lived through the Seven Years War and the French

Revolution, he never interrupted his teaching of philosophy at

Königsberg in East Prussia. His most distinctive contribution was the

invention of what he called the 'critical' philosophy, which, assuming

as a datum that there is knowledge of various kinds, inquired how such

knowledge comes to be possible, and deduced, from the answer to this

inquiry, many metaphysical results as to the nature of the world.

Whether these results were valid may well be doubted. But Kant

undoubtedly deserves credit for two things: first, for having perceived

that we have /a priori/ knowledge which is not purely 'analytic', i.e.

such that the opposite would be self-contradictory, and secondly, for

having made evident the philosophical importance of the theory of

knowledge.

Before the time of Kant, it was generally held that whatever knowledge

was /a priori/ must be 'analytic'. What this word means will be best

illustrated by examples. If I say, 'A bald man is a man', 'A plane

figure is a figure', 'A bad poet is a poet', I make a purely analytic

judgement: the subject spoken about is given as having at least two

properties, of which one is singled out to be asserted of it. Such

propositions as the above are trivial, and would never be enunciated in

real life except by an orator preparing the way for a piece of

sophistry. They are called 'analytic' because the predicate is obtained

by merely analysing the subject. Before the time of Kant it was thought

that all judgements of which we could be certain /a priori/ were of this

kind: that in all of them there was a predicate which was only part of

the subject of which it was asserted. If this were so, we should be

involved in a definite contradiction if we attempted to deny anything

that could be known /a priori/. 'A bald man is not bald' would assert

and deny baldness of the same man, and would therefore contradict

itself. Thus according to the philosophers before Kant, the law of

contradiction, which asserts that nothing can at the same time have and

not have a certain property, sufficed to establish the truth of all /a

priori/ knowledge.

Hume (1711-76), who preceded Kant, accepting the usual view as to what

makes knowledge /a priori/, discovered that, in many cases which had

previously been supposed analytic, and notably in the case of cause and

effect, the connexion was really synthetic. Before Hume, rationalists at

least had supposed that the effect could be logically deduced from the

cause, if only we had sufficient knowledge. Hume argued?correctly, as

would now be generally admitted?that this could not be done. Hence he

inferred the far more doubtful proposition that nothing could be known

/a priori/ about the connexion of cause and effect. Kant, who had been

educated in the rationalist tradition, was much perturbed by Hume's

scepticism, and endeavoured to find an answer to it. He perceived that

not only the connexion of cause and effect, but all the propositions of

arithmetic and geometry, are 'synthetic', i.e. not analytic: in all

these propositions, no analysis of the subject will reveal the

predicate. His stock instance was the proposition 7 + 5 = 12. He pointed

out, quite truly, that 7 and 5 have to be put together to give 12: the

idea of 12 is not contained in them, nor even in the idea of adding them

together. Thus he was led to the conclusion that all pure mathematics,

though /a priori/, is synthetic; and this conclusion raised a new

problem of which he endeavoured to find the solution.

The question which Kant put at the beginning of his philosophy, namely

'How is pure mathematics possible?' is an interesting and difficult one,

to which every philosophy which is not purely sceptical must find some

answer. The answer of the pure empiricists, that our mathematical

knowledge is derived by induction from particular instances, we have

already seen to be inadequate, for two reasons: first, that the validity

of the inductive principle itself cannot be proved by induction;

secondly, that the general propositions of mathematics, such as 'two and

two always make four', can obviously be known with certainty by

consideration of a single instance, and gain nothing by enumeration of

other cases in which they have been found to be true. Thus our knowledge

of the general propositions of mathematics (and the same applies to

logic) must be accounted for otherwise than our (merely probable)

knowledge of empirical generalizations such as 'all men are mortal'.

The problem arises through the fact that such knowledge is general,

whereas all experience is particular. It seems strange that we should

apparently be able to know some truths in advance about particular

things of which we have as yet no experience; but it cannot easily be

doubted that logic and arithmetic will apply to such things. We do not

know who will be the inhabitants of London a hundred years hence; but we

know that any two of them and any other two of them will make four of

them. This apparent power of anticipating facts about things of which we

have no experience is certainly surprising. Kant's solution of the

problem, though not valid in my opinion, is interesting. It is, however,

very difficult, and is differently understood by different philosophers.

We can, therefore, only give the merest outline of it, and even that

will be thought misleading by many exponents of Kant's system.

What Kant maintained was that in all our experience there are two

elements to be distinguished, the one due to the object (i.e. to what we

have called the 'physical object'), the other due to our own nature. We

saw, in discussing matter and sense-data, that the physical object is

different from the associated sense-data, and that the sense-data are to

be regarded as resulting from an interaction between the physical object

and ourselves. So far, we are in agreement with Kant. But what is

distinctive of Kant is the way in which he apportions the shares of

ourselves and the physical object respectively. He considers that the

crude material given in sensation?the colour, hardness, etc.?is due to

the object, and that what we supply is the arrangement in space and

time, and all the relations between sense-data which result from

comparison or from considering one as the cause of the other or in any

other way. His chief reason in favour of this view is that we seem to

have /a priori/ knowledge as to space and time and causality and

comparison, but not as to the actual crude material of sensation. We can

be sure, he says, that anything we shall ever experience must show the

characteristics affirmed of it in our /a priori/ knowledge, because

these characteristics are due to our own nature, and therefore nothing

can ever come into our experience without acquiring these characteristics.

The physical object, which he calls the 'thing in itself',(1) he regards

as essentially unknowable; what can be known is the object as we have it

in experience, which he calls the 'phenomenon'. The phenomenon, being a

joint product of us and the thing in itself, is sure to have those

characteristics which are due to us, and is therefore sure to conform to

our /a priori/ knowledge. Hence this knowledge, though true of all

actual and possible experience, must not be supposed to apply outside

experience. Thus in spite of the existence of /a priori/ knowledge, we

cannot know anything about the thing in itself or about what is not an

actual or possible object of experience. In this way he tries to

reconcile and harmonize the contentions of the rationalists with the

arguments of the empiricists.

(1) Kant's 'thing in itself' is identical in /definition/ with the

physical object, namely, it is the cause of sensations. In the

properties deduced from the definition it is not identical, since Kant

held (in spite of some inconsistency as regards cause) that we can know

that none of the categories are applicable to the 'thing in itself'.

Apart from minor grounds on which Kant's philosophy may be criticized,

there is one main objection which seems fatal to any attempt to deal

with the problem of /a priori/ knowledge by his method. The thing to be

accounted for is our certainty that the facts must always conform to

logic and arithmetic. To say that logic and arithmetic are contributed

by us does not account for this. Our nature is as much a fact of the

existing world as anything, and there can be no certainty that it will

remain constant. It might happen, if Kant is right, that to-morrow our

nature would so change as to make two and two become five. This

possibility seems never to have occurred to him, yet it is one which

utterly destroys the certainty and universality which he is anxious to

vindicate for arithmetical propositions. It is true that this

possibility, formally, is inconsistent with the Kantian view that time

itself is a form imposed by the subject upon phenomena, so that our real

Self is not in time and has no to-morrow. But he will still have to

suppose that the time-order of phenomena is determined by

characteristics of what is behind phenomena, and this suffices for the

substance of our argument.

Reflection, moreover, seems to make it clear that, if there is any truth

in our arithmetical beliefs, they must apply to things equally whether

we think of them or not. Two physical objects and two other physical

objects must make four physical objects, even if physical objects cannot

be experienced. To assert this is certainly within the scope of what we

mean when we state that two and two are four. Its truth is just as

indubitable as the truth of the assertion that two phenomena and two

other phenomena make four phenomena. Thus Kant's solution unduly limits

the scope of /a priori/ propositions, in addition to failing in the

attempt at explaining their certainty.

Apart from the special doctrines advocated by Kant, it is very common

among philosophers to regard what is /a priori/ as in some sense mental,

as concerned rather with the way we must think than with any fact of the

outer world. We noted in the preceding chapter the three principles

commonly called 'laws of thought'. The view which led to their being so

named is a natural one, but there are strong reasons for thinking that

it is erroneous. Let us take as an illustration the law of

contradiction. This is commonly stated in the form 'Nothing can both be

and not be', which is intended to express the fact that nothing can at

once have and not have a given quality. Thus, for example, if a tree is

a beech it cannot also be not a beech; if my table is rectangular it

cannot also be not rectangular, and so on.

Now what makes it natural to call this principle a law of /thought/ is

that it is by thought rather than by outward observation that we

persuade ourselves of its necessary truth. When we have seen that a tree

is a beech, we do not need to look again in order to ascertain whether

it is also not a beech; thought alone makes us know that this is

impossible. But the conclusion that the law of contradiction is a law of

/thought/ is nevertheless erroneous. What we believe, when we believe

the law of contradiction, is not that the mind is so made that it must

believe the law of contradiction. /This/ belief is a subsequent result

of psychological reflection, which presupposes the belief in the law of

contradiction. The belief in the law of contradiction is a belief about

things, not only about thoughts. It is not, e.g., the belief that if we

/think/ a certain tree is a beech, we cannot at the same time /think/

that it is not a beech; it is the belief that if the tree /is/ a beech,

it cannot at the same time /be/ not a beech. Thus the law of

contradiction is about things, and not merely about thoughts; and

although belief in the law of contradiction is a thought, the law of

contradiction itself is not a thought, but a fact concerning the things

in the world. If this, which we believe when we believe the law of

contradiction, were not true of the things in the world, the fact that

we were compelled to /think/ it true would not save the law of

contradiction from being false; and this shows that the law is not a law

of /thought/.

A similar argument applies to any other /a priori/ judgement. When we

judge that two and two are four, we are not making a judgement about our

thoughts, but about all actual or possible couples. The fact that our

minds are so constituted as to believe that two and two are four, though

it is true, is emphatically not what we assert when we assert that two

and two are four. And no fact about the constitution of our minds could

make it /true/ that two and two are four. Thus our /a priori/ knowledge,

if it is not erroneous, is not merely knowledge about the constitution

of our minds, but is applicable to whatever the world may contain, both

what is mental and what is non-mental.

The fact seems to be that all our /a priori/ knowledge is concerned with

entities which do not, properly speaking, /exist/, either in the mental

or in the physical world. These entities are such as can be named by

parts of speech which are not substantives; they are such entities as

qualities and relations. Suppose, for instance, that I am in my room. I

exist, and my room exists; but does 'in' exist? Yet obviously the word

'in' has a meaning; it denotes a relation which holds between me and my

room. This relation is something, although we cannot say that it exists

/in the same sense/ in which I and my room exist. The relation 'in' is

something which we can think about and understand, for, if we could not

understand it, we could not understand the sentence 'I am in my room'.

Many philosophers, following Kant, have maintained that relations are

the work of the mind, that things in themselves have no relations, but

that the mind brings them together in one act of thought and thus

produces the relations which it judges them to have.

This view, however, seems open to objections similar to those which we

urged before against Kant. It seems plain that it is not thought which

produces the truth of the proposition 'I am in my room'. It may be true

that an earwig is in my room, even if neither I nor the earwig nor any

one else is aware of this truth; for this truth concerns only the earwig

and the room, and does not depend upon anything else. Thus relations, as

we shall see more fully in the next chapter, must be placed in a world

which is neither mental nor physical. This world is of great importance

to philosophy, and in particular to the problems of /a priori/

knowledge. In the next chapter we shall proceed to develop its nature

and its bearing upon the questions with which we have been dealing.

CHAPTER IX. THE WORLD OF UNIVERSALS

At the end of the preceding chapter we saw that such entities as

relations appear to have a being which is in some way different from

that of physical objects, and also different from that of minds and from

that of sense-data. In the present chapter we have to consider what is

the nature of this kind of being, and also what objects there are that

have this kind of being. We will begin with the latter question.

The problem with which we are now concerned is a very old one, since it

was brought into philosophy by Plato. Plato's 'theory of ideas' is an

attempt to solve this very problem, and in my opinion it is one of the

most successful attempts hitherto made. The theory to be advocated in

what follows is largely Plato's, with merely such modifications as time

has shown to be necessary.

The way the problem arose for Plato was more or less as follows. Let us

consider, say, such a notion as /justice/. If we ask ourselves what

justice is, it is natural to proceed by considering this, that, and the

other just act, with a view to discovering what they have in common.

They must all, in some sense, partake of a common nature, which will be

found in whatever is just and in nothing else. This common nature, in

virtue of which they are all just, will be justice itself, the pure

essence the admixture of which with facts of ordinary life produces the

multiplicity of just acts. Similarly with any other word which may be

applicable to common facts, such as 'whiteness' for example. The word

will be applicable to a number of particular things because they all

participate in a common nature or essence. This pure essence is what

Plato calls an 'idea' or 'form'. (It must not be supposed that 'ideas',

in his sense, exist in minds, though they may be apprehended by minds.)

The 'idea' /justice/ is not identical with anything that is just: it is

something other than particular things, which particular things partake

of. Not being particular, it cannot itself exist in the world of sense.

Moreover it is not fleeting or changeable like the things of sense: it

is eternally itself, immutable and indestructible.

Thus Plato is led to a supra-sensible world, more real than the common

world of sense, the unchangeable world of ideas, which alone gives to

the world of sense whatever pale reflection of reality may belong to it.

The truly real world, for Plato, is the world of ideas; for whatever we

may attempt to say about things in the world of sense, we can only

succeed in saying that they participate in such and such ideas, which,

therefore, constitute all their character. Hence it is easy to pass on

into a mysticism. We may hope, in a mystic illumination, to see the

ideas as we see objects of sense; and we may imagine that the ideas

exist in heaven. These mystical developments are very natural, but the

basis of the theory is in logic, and it is as based in logic that we

have to consider it.

The word 'idea' has acquired, in the course of time, many associations

which are quite misleading when applied to Plato's 'ideas'. We shall

therefore use the word 'universal' instead of the word 'idea', to

describe what Plato meant. The essence of the sort of entity that Plato

meant is that it is opposed to the particular things that are given in

sensation. We speak of whatever is given in sensation, or is of the same

nature as things given in sensation, as a /particular/; by opposition to

this, a /universal/ will be anything which may be shared by many

particulars, and has those characteristics which, as we saw, distinguish

justice and whiteness from just acts and white things.

When we examine common words, we find that, broadly speaking, proper

names stand for particulars, while other substantives, adjectives,

prepositions, and verbs stand for universals. Pronouns stand for

particulars, but are ambiguous: it is only by the context or the

circumstances that we know what particulars they stand for. The word

'now' stands for a particular, namely the present moment; but like

pronouns, it stands for an ambiguous particular, because the present is

always changing.

It will be seen that no sentence can be made up without at least one

word which denotes a universal. The nearest approach would be some such

statement as 'I like this'. But even here the word 'like' denotes a

universal, for I may like other things, and other people may like

things. Thus all truths involve universals, and all knowledge of truths

involves acquaintance with universals.

Seeing that nearly all the words to be found in the dictionary stand for

universals, it is strange that hardly anybody except students of

philosophy ever realizes that there are such entities as universals. We

do not naturally dwell upon those words in a sentence which do not stand

for particulars; and if we are forced to dwell upon a word which stands

for a universal, we naturally think of it as standing for some one of

the particulars that come under the universal. When, for example, we

hear the sentence, 'Charles I's head was cut off', we may naturally

enough think of Charles I, of Charles I's head, and of the operation of

cutting off /his/ head, which are all particulars; but we do not

naturally dwell upon what is meant by the word 'head' or the word 'cut',

which is a universal: We feel such words to be incomplete and

insubstantial; they seem to demand a context before anything can be done

with them. Hence we succeed in avoiding all notice of universals as

such, until the study of philosophy forces them upon our attention.

Even among philosophers, we may say, broadly, that only those universals

which are named by adjectives or substantives have been much or often

recognized, while those named by verbs and prepositions have been

usually overlooked. This omission has had a very great effect upon

philosophy; it is hardly too much to say that most metaphysics, since

Spinoza, has been largely determined by it. The way this has occurred

is, in outline, as follows: Speaking generally, adjectives and common

nouns express qualities or properties of single things, whereas

prepositions and verbs tend to express relations between two or more

things. Thus the neglect of prepositions and verbs led to the belief

that every proposition can be regarded as attributing a property to a

single thing, rather than as expressing a relation between two or more

things. Hence it was supposed that, ultimately, there can be no such

entities as relations between things. Hence either there can be only one

thing in the universe, or, if there are many things, they cannot

possibly interact in any way, since any interaction would be a relation,

and relations are impossible.

The first of these views, advocated by Spinoza and held in our own day

by Bradley and many other philosophers, is called /monism/; the second,

advocated by Leibniz but not very common nowadays, is called /monadism/,

because each of the isolated things is called a /monad/. Both these

opposing philosophies, interesting as they are, result, in my opinion,

from an undue attention to one sort of universals, namely the sort

represented by adjectives and substantives rather than by verbs and

prepositions.

As a matter of fact, if any one were anxious to deny altogether that

there are such things as universals, we should find that we cannot

strictly prove that there are such entities as /qualities/, i.e. the

universals represented by adjectives and substantives, whereas we can

prove that there must be /relations/, i.e. the sort of universals

generally represented by verbs and prepositions. Let us take in

illustration the universal /whiteness/. If we believe that there is such

a universal, we shall say that things are white because they have the

quality of whiteness. This view, however, was strenuously denied by

Berkeley and Hume, who have been followed in this by later empiricists.

The form which their denial took was to deny that there are such things

as 'abstract ideas '. When we want to think of whiteness, they said, we

form an image of some particular white thing, and reason concerning this

particular, taking care not to deduce anything concerning it which we

cannot see to be equally true of any other white thing. As an account of

our actual mental processes, this is no doubt largely true. In geometry,

for example, when we wish to prove something about all triangles, we

draw a particular triangle and reason about it, taking care not to use

any characteristic which it does not share with other triangles. The

beginner, in order to avoid error, often finds it useful to draw several

triangles, as unlike each other as possible, in order to make sure that

his reasoning is equally applicable to all of them. But a difficulty

emerges as soon as we ask ourselves how we know that a thing is white or

a triangle. If we wish to avoid the universals /whiteness/ and

/triangularity/, we shall choose some particular patch of white or some

particular triangle, and say that anything is white or a triangle if it

has the right sort of resemblance to our chosen particular. But then the

resemblance required will have to be a universal. Since there are many

white things, the resemblance must hold between many pairs of particular

white things; and this is the characteristic of a universal. It will be

useless to say that there is a different resemblance for each pair, for

then we shall have to say that these resemblances resemble each other,

and thus at last we shall be forced to admit resemblance as a universal.

The relation of resemblance, therefore, must be a true universal. And

having been forced to admit this universal, we find that it is no longer

worth while to invent difficult and unplausible theories to avoid the

admission of such universals as whiteness and triangularity.

Berkeley and Hume failed to perceive this refutation of their rejection

of 'abstract ideas', because, like their adversaries, they only thought

of /qualities/, and altogether ignored /relations/ as universals. We

have therefore here another respect in which the rationalists appear to

have been in the right as against the empiricists, although, owing to

the neglect or denial of relations, the deductions made by rationalists

were, if anything, more apt to be mistaken than those made by empiricists.

Having now seen that there must be such entities as universals, the next

point to be proved is that their being is not merely mental. By this is

meant that whatever being belongs to them is independent of their being

thought of or in any way apprehended by minds. We have already touched

on this subject at the end of the preceding chapter, but we must now

consider more fully what sort of being it is that belongs to universals.

Consider such a proposition as 'Edinburgh is north of London'. Here we

have a relation between two places, and it seems plain that the relation

subsists independently of our knowledge of it. When we come to know that

Edinburgh is north of London, we come to know something which has to do

only with Edinburgh and London: we do not cause the truth of the

proposition by coming to know it, on the contrary we merely apprehend a

fact which was there before we knew it. The part of the earth's surface

where Edinburgh stands would be north of the part where London stands,

even if there were no human being to know about north and south, and

even if there were no minds at all in the universe. This is, of course,

denied by many philosophers, either for Berkeley's reasons or for

Kant's. But we have already considered these reasons, and decided that

they are inadequate. We may therefore now assume it to be true that

nothing mental is presupposed in the fact that Edinburgh is north of

London. But this fact involves the relation 'north of', which is a

universal; and it would be impossible for the whole fact to involve

nothing mental if the relation 'north of', which is a constituent part

of the fact, did involve anything mental. Hence we must admit that the

relation, like the terms it relates, is not dependent upon thought, but

belongs to the independent world which thought apprehends but does not

create.

This conclusion, however, is met by the difficulty that the relation

'north of' does not seem to /exist/ in the same sense in which Edinburgh

and London exist. If we ask 'Where and when does this relation exist?'

the answer must be 'Nowhere and nowhen'. There is no place or time where

we can find the relation 'north of'. It does not exist in Edinburgh any

more than in London, for it relates the two and is neutral as between

them. Nor can we say that it exists at any particular time. Now

everything that can be apprehended by the senses or by introspection

exists at some particular time. Hence the relation 'north of' is

radically different from such things. It is neither in space nor in

time, neither material nor mental; yet it is something.

It is largely the very peculiar kind of being that belongs to universals

which has led many people to suppose that they are really mental. We can

think /of/ a universal, and our thinking then exists in a perfectly

ordinary sense, like any other mental act. Suppose, for example, that we

are thinking of whiteness. Then /in one sense/ it may be said that

whiteness is 'in our mind'. We have here the same ambiguity as we noted

in discussing Berkeley in Chapter IV. In the strict sense, it is not

whiteness that is in our mind, but the act of thinking of whiteness. The

connected ambiguity in the word 'idea', which we noted at the same time,

also causes confusion here. In one sense of this word, namely the sense

in which it denotes the /object/ of an act of thought, whiteness is an

'idea'. Hence, if the ambiguity is not guarded against, we may come to

think that whiteness is an 'idea' in the other sense, i.e. an act of

thought; and thus we come to think that whiteness is mental. But in so

thinking, we rob it of its essential quality of universality. One man's

act of thought is necessarily a different thing from another man's; one

man's act of thought at one time is necessarily a different thing from

the same man's act of thought at another time. Hence, if whiteness were

the thought as opposed to its object, no two different men could think

of it, and no one man could think of it twice. That which many different

thoughts of whiteness have in common is their /object/, and this object

is different from all of them. Thus universals are not thoughts, though

when known they are the objects of thoughts.

We shall find it convenient only to speak of things /existing/ when they

are in time, that is to say, when we can point to some time at which

they exist (not excluding the possibility of their existing at all

times). Thus thoughts and feelings, minds and physical objects exist.

But universals do not exist in this sense; we shall say that they

/subsist/ or /have being/, where 'being' is opposed to 'existence' as

being timeless. The world of universals, therefore, may also be

described as the world of being. The world of being is unchangeable,

rigid, exact, delightful to the mathematician, the logician, the builder

of metaphysical systems, and all who love perfection more than life. The

world of existence is fleeting, vague, without sharp boundaries, without

any clear plan or arrangement, but it contains all thoughts and

feelings, all the data of sense, and all physical objects, everything

that can do either good or harm, everything that makes any difference to

the value of life and the world. According to our temperaments, we shall

prefer the contemplation of the one or of the other. The one we do not

prefer will probably seem to us a pale shadow of the one we prefer, and

hardly worthy to be regarded as in any sense real. But the truth is that

both have the same claim on our impartial attention, both are real, and

both are important to the metaphysician. Indeed no sooner have we

distinguished the two worlds than it becomes necessary to consider their

relations.

But first of all we must examine our knowledge of universals. This

consideration will occupy us in the following chapter, where we shall

find that it solves the problem of /a priori/ knowledge, from which we

were first led to consider universals.

CHAPTER X. ON OUR KNOWLEDGE OF UNIVERSALS

In regard to one man's knowledge at a given time, universals, like

particulars, may be divided into those known by acquaintance, those

known only by description, and those not known either by acquaintance or

by description.

Let us consider first the knowledge of universals by acquaintance. It is

obvious, to begin with, that we are acquainted with such universals as

white, red, black, sweet, sour, loud, hard, etc., i.e. with qualities

which are exemplified in sense-data. When we see a white patch, we are

acquainted, in the first instance, with the particular patch; but by

seeing many white patches, we easily learn to abstract the whiteness

which they all have in common, and in learning to do this we are

learning to be acquainted with whiteness. A similar process will make us

acquainted with any other universal of the same sort. Universals of this

sort may be called 'sensible qualities'. They can be apprehended with

less effort of abstraction than any others, and they seem less removed

from particulars than other universals are.

We come next to relations. The easiest relations to apprehend are those

which hold between the different parts of a single complex sense-datum.

For example, I can see at a glance the whole of the page on which I am

writing; thus the whole page is included in one sense-datum. But I

perceive that some parts of the page are to the left of other parts, and

some parts are above other parts. The process of abstraction in this

case seems to proceed somewhat as follows: I see successively a number

of sense-data in which one part is to the left of another; I perceive,

as in the case of different white patches, that all these sense-data

have something in common, and by abstraction I find that what they have

in common is a certain relation between their parts, namely the relation

which I call 'being to the left of'. In this way I become acquainted

with the universal relation.

In like manner I become aware of the relation of before and after in

time. Suppose I hear a chime of bells: when the last bell of the chime

sounds, I can retain the whole chime before my mind, and I can perceive

that the earlier bells came before the later ones. Also in memory I

perceive that what I am remembering came before the present time. From

either of these sources I can abstract the universal relation of before

and after, just as I abstracted the universal relation 'being to the

left of'. Thus time-relations, like space-relations, are among those

with which we are acquainted.

Another relation with which we become acquainted in much the same way is

resemblance. If I see simultaneously two shades of green, I can see that

they resemble each other; if I also see a shade of red: at the same

time, I can see that the two greens have more resemblance to each other

than either has to the red. In this way I become acquainted with the

universal /resemblance/ or /similarity/.

Between universals, as between particulars, there are relations of which

we may be immediately aware. We have just seen that we can perceive that

the resemblance between two shades of green is greater than the

resemblance between a shade of red and a shade of green. Here we are

dealing with a relation, namely 'greater than', between two relations.

Our knowledge of such relations, though it requires more power of

abstraction than is required for perceiving the qualities of sense-data,

appears to be equally immediate, and (at least in some cases) equally

indubitable. Thus there is immediate knowledge concerning universals as

well as concerning sense-data.

Returning now to the problem of /a priori/ knowledge, which we left

unsolved when we began the consideration of universals, we find

ourselves in a position to deal with it in a much more satisfactory

manner than was possible before. Let us revert to the proposition 'two

and two are four'. It is fairly obvious, in view of what has been said,

that this proposition states a relation between the universal 'two' and

the universal 'four'. This suggests a proposition which we shall now

endeavour to establish: namely, /All /a priori/knowledge deals

exclusively with the relations of universals/. This proposition is of

great importance, and goes a long way towards solving our previous

difficulties concerning /a priori/ knowledge.

The only case in which it might seem, at first sight, as if our

proposition were untrue, is the case in which an /a priori/ proposition

states that /all/ of one class of particulars belong to some other

class, or (what comes to the same thing) that /all/ particulars having

some one property also have some other. In this case it might seem as

though we were dealing with the particulars that have the property

rather than with the property. The proposition 'two and two are four' is

really a case in point, for this may be stated in the form 'any two and

any other two are four', or 'any collection formed of two twos is a

collection of four'. If we can show that such statements as this really

deal only with universals, our proposition may be regarded as proved.

One way of discovering what a proposition deals with is to ask ourselves

what words we must understand?in other words, what objects we must be

acquainted with?in order to see what the proposition means. As soon as

we see what the proposition means, even if we do not yet know whether it

is true or false, it is evident that we must have acquaintance with

whatever is really dealt with by the proposition. By applying this test,

it appears that many propositions which might seem to be concerned with

particulars are really concerned only with universals. In the special

case of 'two and two are four', even when we interpret it as meaning

'any collection formed of two twos is a collection of four', it is plain

that we can understand the proposition, i.e. we can see what it is that

it asserts, as soon as we know what is meant by 'collection' and 'two'

and 'four'. It is quite unnecessary to know all the couples in the

world: if it were necessary, obviously we could never understand the

proposition, since the couples are infinitely numerous and therefore

cannot all be known to us. Thus although our general statement /implies/

statements about particular couples, /as soon as we know that there are

such particular couples/, yet it does not itself assert or imply that

there are such particular couples, and thus fails to make any statement

whatever about any actual particular couple. The statement made is about

'couple', the universal, and not about this or that couple.

Thus the statement 'two and two are four' deals exclusively with

universals, and therefore may be known by anybody who is acquainted with

the universals concerned and can perceive the relation between them

which the statement asserts. It must be taken as a fact, discovered by

reflecting upon our knowledge, that we have the power of sometimes

perceiving such relations between universals, and therefore of sometimes

knowing general /a priori/ propositions such as those of arithmetic and

logic. The thing that seemed mysterious, when we formerly considered

such knowledge, was that it seemed to anticipate and control experience.

This, however, we can now see to have been an error. /No/ fact

concerning anything capable of being experienced can be known

independently of experience. We know /a priori/ that two things and two

other things together make four things, but we do /not/ know /a priori/

that if Brown and Jones are two, and Robinson and Smith are two, then

Brown and Jones and Robinson and Smith are four. The reason is that this

proposition cannot be understood at all unless we know that there are

such people as Brown and Jones and Robinson and Smith, and this we can

only know by experience. Hence, although our general proposition is /a

priori/, all its applications to actual particulars involve experience

and therefore contain an empirical element. In this way what seemed

mysterious in our /a priori/ knowledge is seen to have been based upon

an error.

It will serve to make the point clearer if we contrast our genuine /a

priori/ judgement with an empirical generalization, such as 'all men are

mortals'. Here as before, we can /understand/ what the proposition means

as soon as we understand the universals involved, namely /man/ and

/mortal/. It is obviously unnecessary to have an individual acquaintance

with the whole human race in order to understand what our proposition

means. Thus the difference between an /a priori/ general proposition and

an empirical generalization does not come in the /meaning/ of the

proposition; it comes in the nature of the /evidence/ for it. In the

empirical case, the evidence consists in the particular instances. We

believe that all men are mortal because we know that there are

innumerable instances of men dying, and no instances of their living

beyond a certain age. We do not believe it because we see a connexion

between the universal /man/ and the universal /mortal/. It is true that

if physiology can prove, assuming the general laws that govern living

bodies, that no living organism can last for ever, that gives a

connexion between /man/ and /mortality/ which would enable us to assert

our proposition without appealing to the special evidence of /men/

dying. But that only means that our generalization has been subsumed

under a wider generalization, for which the evidence is still of the

same kind, though more extensive. The progress of science is constantly

producing such subsumptions, and therefore giving a constantly wider

inductive basis for scientific generalizations. But although this gives

a greater /degree/ of certainty, it does not give a different /kind/:

the ultimate ground remains inductive, i.e. derived from instances, and

not an /a priori/ connexion of universals such as we have in logic and

arithmetic.

Two opposite points are to be observed concerning /a priori/ general

propositions. The first is that, if many particular instances are known,

our general proposition may be arrived at in the first instance by

induction, and the connexion of universals may be only subsequently

perceived. For example, it is known that if we draw perpendiculars to

the sides of a triangle from the opposite angles, all three

perpendiculars meet in a point. It would be quite possible to be first

led to this proposition by actually drawing perpendiculars in many

cases, and finding that they always met in a point; this experience

might lead us to look for the general proof and find it. Such cases are

common in the experience of every mathematician.

The other point is more interesting, and of more philosophical

importance. It is, that we may sometimes know a general proposition in

cases where we do not know a single instance of it. Take such a case as

the following: We know that any two numbers can be multiplied together,

and will give a third called their /product/. We know that all pairs of

integers the product of which is less than 100 have been actually

multiplied together, and the value of the product recorded in the

multiplication table. But we also know that the number of integers is

infinite, and that only a finite number of pairs of integers ever have

been or ever will be thought of by human beings. Hence it follows that

there are pairs of integers which never have been and never will be

thought of by human beings, and that all of them deal with integers the

product of which is over 100. Hence we arrive at the proposition: 'All

products of two integers, which never have been and never will be

thought of by any human being, are over 100.' Here is a general

proposition of which the truth is undeniable, and yet, from the very

nature of the case, we can never give an instance; because any two

numbers we may think of are excluded by the terms of the proposition.

This possibility, of knowledge of general propositions of which no

instance can be given, is often denied, because it is not perceived that

the knowledge of such propositions only requires a knowledge of the

relations of universals, and does not require any knowledge of instances

of the universals in question. Yet the knowledge of such general

propositions is quite vital to a great deal of what is generally

admitted to be known. For example, we saw, in our early chapters, that

knowledge of physical objects, as opposed to sense-data, is only

obtained by an inference, and that they are not things with which we are

acquainted. Hence we can never know any proposition of the form 'this is

a physical object', where 'this' is something immediately known. It

follows that all our knowledge concerning physical objects is such that

no actual instance can be given. We can give instances of the associated

sense-data, but we cannot give instances of the actual physical objects.

Hence our knowledge as to physical objects depends throughout upon this

possibility of general knowledge where no instance can be given. And the

same applies to our knowledge of other people's minds, or of any other

class of things of which no instance is known to us by acquaintance.

We may now take a survey of the sources of our knowledge, as they have

appeared in the course of our analysis. We have first to distinguish

knowledge of things and knowledge of truths. In each there are two

kinds, one immediate and one derivative. Our immediate knowledge of

things, which we called /acquaintance/, consists of two sorts, according

as the things known are particulars or universals. Among particulars, we

have acquaintance with sense-data and (probably) with ourselves. Among

universals, there seems to be no principle by which we can decide which

can be known by acquaintance, but it is clear that among those that can

be so known are sensible qualities, relations of space and time,

similarity, and certain abstract logical universals. Our derivative

knowledge of things, which we call knowledge by /description/, always

involves both acquaintance with something and knowledge of truths. Our

immediate knowledge of /truths/ may be called /intuitive/ knowledge, and

the truths so known may be called /self-evident/ truths. Among such

truths are included those which merely state what is given in sense, and

also certain abstract logical and arithmetical principles, and (though

with less certainty) some ethical propositions. Our /derivative/

knowledge of truths consists of everything that we can deduce from

self-evident truths by the use of self-evident principles of deduction.

If the above account is correct, all our knowledge of truths depends

upon our intuitive knowledge. It therefore becomes important to consider

the nature and scope of intuitive knowledge, in much the same way as, at

an earlier stage, we considered the nature and scope of knowledge by

acquaintance. But knowledge of truths raises a further problem, which

does not arise in regard to knowledge of things, namely the problem of

/error/. Some of our beliefs turn out to be erroneous, and therefore it

becomes necessary to consider how, if at all, we can distinguish

knowledge from error. This problem does not arise with regard to

knowledge by acquaintance, for, whatever may be the object of

acquaintance, even in dreams and hallucinations, there is no error

involved so long as we do not go beyond the immediate object: error can

only arise when we regard the immediate object, i.e. the sense-datum, as

the mark of some physical object. Thus the problems connected with

knowledge of truths are more difficult than those connected with

knowledge of things. As the first of the problems connected with

knowledge of truths, let us examine the nature and scope of our

intuitive judgements.

CHAPTER XI. ON INTUITIVE KNOWLEDGE

There is a common impression that everything that we believe ought to be

capable of proof, or at least of being shown to be highly probable. It

is felt by many that a belief for which no reason can be given is an

unreasonable belief. In the main, this view is just. Almost all our

common beliefs are either inferred, or capable of being inferred, from

other beliefs which may be regarded as giving the reason for them. As a

rule, the reason has been forgotten, or has even never been consciously

present to our minds. Few of us ever ask ourselves, for example, what

reason there is to suppose the food we are just going to eat will not

turn out to be poison. Yet we feel, when challenged, that a perfectly

good reason could be found, even if we are not ready with it at the

moment. And in this belief we are usually justified.

But let us imagine some insistent Socrates, who, whatever reason we give

him, continues to demand a reason for the reason. We must sooner or

later, and probably before very long, be driven to a point where we

cannot find any further reason, and where it becomes almost certain that

no further reason is even theoretically discoverable. Starting with the

common beliefs of daily life, we can be driven back from point to point,

until we come to some general principle, or some instance of a general

principle, which seems luminously evident, and is not itself capable of

being deduced from anything more evident. In most questions of daily

life, such as whether our food is likely to be nourishing and not

poisonous, we shall be driven back to the inductive principle, which we

discussed in Chapter VI. But beyond that, there seems to be no further

regress. The principle itself is constantly used in our reasoning,

sometimes consciously, sometimes unconsciously; but there is no

reasoning which, starting from some simpler self-evident principle,

leads us to the principle of induction as its conclusion. And the same

holds for other logical principles. Their truth is evident to us, and we

employ them in constructing demonstrations; but they themselves, or at

least some of them, are incapable of demonstration.

Self-evidence, however, is not confined to those among general

principles which are incapable of proof. When a certain number of

logical principles have been admitted, the rest can be deduced from

them; but the propositions deduced are often just as self-evident as

those that were assumed without proof. All arithmetic, moreover, can be

deduced from the general principles of logic, yet the simple

propositions of arithmetic, such as 'two and two are four', are just as

self-evident as the principles of logic.

It would seem, also, though this is more disputable, that there are some

self-evident ethical principles, such as 'we ought to pursue what is good'.

It should be observed that, in all cases of general principles,

particular instances, dealing with familiar things, are more evident

than the general principle. For example, the law of contradiction states

that nothing can both have a certain property and not have it. This is

evident as soon as it is understood, but it is not so evident as that a

particular rose which we see cannot be both red and not red. (It is of

course possible that parts of the rose may be red and parts not red, or

that the rose may be of a shade of pink which we hardly know whether to

call red or not; but in the former case it is plain that the rose as a

whole is not red, while in the latter case the answer is theoretically

definite as soon as we have decided on a precise definition of 'red'.)

It is usually through particular instances that we come to be able to

see the general principle. Only those who are practised in dealing with

abstractions can readily grasp a general principle without the help of

instances.

In addition to general principles, the other kind of self-evident truths

are those immediately derived from sensation. We will call such truths

'truths of perception', and the judgements expressing them we will call

'judgements of perception'. But here a certain amount of care is

required in getting at the precise nature of the truths that are

self-evident. The actual sense-data are neither true nor false. A

particular patch of colour which I see, for example, simply exists: it

is not the sort of thing that is true or false. It is true that there is

such a patch, true that it has a certain shape and degree of brightness,

true that it is surrounded by certain other colours. But the patch

itself, like everything else in the world of sense, is of a radically

different kind from the things that are true or false, and therefore

cannot properly be said to be /true/. Thus whatever self-evident truths

may be obtained from our senses must be different from the sense-data

from which they are obtained.

It would seem that there are two kinds of self-evident truths of

perception, though perhaps in the last analysis the two kinds may

coalesce. First, there is the kind which simply asserts the /existence/

of the sense-datum, without in any way analysing it. We see a patch of

red, and we judge 'there is such-and-such a patch of red', or more

strictly 'there is that'; this is one kind of intuitive judgement of

perception. The other kind arises when the object of sense is complex,

and we subject it to some degree of analysis. If, for instance, we see a

/round/ patch of red, we may judge 'that patch of red is round'. This is

again a judgement of perception, but it differs from our previous kind.

In our present kind we have a single sense-datum which has both colour

and shape: the colour is red and the shape is round. Our judgement

analyses the datum into colour and shape, and then recombines them by

stating that the red colour is round in shape. Another example of this

kind of judgement is 'this is to the right of that', where 'this' and

'that' are seen simultaneously. In this kind of judgement the

sense-datum contains constituents which have some relation to each

other, and the judgement asserts that these constituents have this

relation.

Another class of intuitive judgements, analogous to those of sense and

yet quite distinct from them, are judgements of /memory/. There is some

danger of confusion as to the nature of memory, owing to the fact that

memory of an object is apt to be accompanied by an image of the object,

and yet the image cannot be what constitutes memory. This is easily seen

by merely noticing that the image is in the present, whereas what is

remembered is known to be in the past. Moreover, we are certainly able

to some extent to compare our image with the object remembered, so that

we often know, within somewhat wide limits, how far our image is

accurate; but this would be impossible, unless the object, as opposed to

the image, were in some way before the mind. Thus the essence of memory

is not constituted by the image, but by having immediately before the

mind an object which is recognized as past. But for the fact of memory

in this sense, we should not know that there ever was a past at all, nor

should we be able to understand the word 'past', any more than a man

born blind can understand the word 'light'. Thus there must be intuitive

judgements of memory, and it is upon them, ultimately, that all our

knowledge of the past depends.

The case of memory, however, raises a difficulty, for it is notoriously

fallacious, and thus throws doubt on the trustworthiness of intuitive

judgements in general. This difficulty is no light one. But let us first

narrow its scope as far as possible. Broadly speaking, memory is

trustworthy in proportion to the vividness of the experience and to its

nearness in time. If the house next door was struck by lightning half a

minute ago, my memory of what I saw and heard will be so reliable that

it would be preposterous to doubt whether there had been a flash at all.

And the same applies to less vivid experiences, so long as they are

recent. I am absolutely certain that half a minute ago I was sitting in

the same chair in which I am sitting now. Going backward over the day, I

find things of which I am quite certain, other things of which I am

almost certain, other things of which I can become certain by thought

and by calling up attendant circumstances, and some things of which I am

by no means certain. I am quite certain that I ate my breakfast this

morning, but if I were as indifferent to my breakfast as a philosopher

should be, I should be doubtful. As to the conversation at breakfast, I

can recall some of it easily, some with an effort, some only with a

large element of doubt, and some not at all. Thus there is a continual

gradation in the degree of self-evidence of what I remember, and a

corresponding gradation in the trustworthiness of my memory.

Thus the first answer to the difficulty of fallacious memory is to say

that memory has degrees of self-evidence, and that these correspond to

the degrees of its trustworthiness, reaching a limit of perfect

self-evidence and perfect trustworthiness in our memory of events which

are recent and vivid.

It would seem, however, that there are cases of very firm belief in a

memory which is wholly false. It is probable that, in these cases, what

is really remembered, in the sense of being immediately before the mind,

is something other than what is falsely believed in, though something

generally associated with it. George IV is said to have at last believed

that he was at the battle of Waterloo, because he had so often said that

he was. In this case, what was immediately remembered was his repeated

assertion; the belief in what he was asserting (if it existed) would be

produced by association with the remembered assertion, and would

therefore not be a genuine case of memory. It would seem that cases of

fallacious memory can probably all be dealt with in this way, i.e. they

can be shown to be not cases of memory in the strict sense at all.

One important point about self-evidence is made clear by the case of

memory, and that is, that self-evidence has degrees: it is not a quality

which is simply present or absent, but a quality which may be more or

less present, in gradations ranging from absolute certainty down to an

almost imperceptible faintness. Truths of perception and some of the

principles of logic have the very highest degree of self-evidence;

truths of immediate memory have an almost equally high degree. The

inductive principle has less self-evidence than some of the other

principles of logic, such as 'what follows from a true premiss must be

true'. Memories have a diminishing self-evidence as they become remoter

and fainter; the truths of logic and mathematics have (broadly speaking)

less self-evidence as they become more complicated. Judgements of

intrinsic ethical or aesthetic value are apt to have some self-evidence,

but not much.

Degrees of self-evidence are important in the theory of knowledge,

since, if propositions may (as seems likely) have some degree of

self-evidence without being true, it will not be necessary to abandon

all connexion between self-evidence and truth, but merely to say that,

where there is a conflict, the more self-evident proposition is to be

retained and the less self-evident rejected.

It seems, however, highly probable that two different notions are

combined in 'self-evidence' as above explained; that one of them, which

corresponds to the highest degree of self-evidence, is really an

infallible guarantee of truth, while the other, which corresponds to all

the other degrees, does not give an infallible guarantee, but only a

greater or less presumption. This, however, is only a suggestion, which

we cannot as yet develop further. After we have dealt with the nature of

truth, we shall return to the subject of self-evidence, in connexion

with the distinction between knowledge and error.

CHAPTER XII. TRUTH AND FALSEHOOD

Our knowledge of truths, unlike our knowledge of things, has an

opposite, namely /error/. So far as things are concerned, we may know

them or not know them, but there is no positive state of mind which can

be described as erroneous knowledge of things, so long, at any rate, as

we confine ourselves to knowledge by acquaintance. Whatever we are

acquainted with must be something; we may draw wrong inferences from our

acquaintance, but the acquaintance itself cannot be deceptive. Thus

there is no dualism as regards acquaintance. But as regards knowledge of

truths, there is a dualism. We may believe what is false as well as what

is true. We know that on very many subjects different people hold

different and incompatible opinions: hence some beliefs must be

erroneous. Since erroneous beliefs are often held just as strongly as

true beliefs, it becomes a difficult question how they are to be

distinguished from true beliefs. How are we to know, in a given case,

that our belief is not erroneous? This is a question of the very

greatest difficulty, to which no completely satisfactory answer is

possible. There is, however, a preliminary question which is rather less

difficult, and that is: What do we /mean/ by truth and falsehood? It is

this preliminary question which is to be considered in this chapter. In

this chapter we are not asking how we can know whether a belief is true

or false: we are asking what is meant by the question whether a belief

is true or false. It is to be hoped that a clear answer to this question

may help us to obtain an answer to the question what beliefs are true,

but for the present we ask only 'What is truth?' and 'What is

falsehood?' not 'What beliefs are true?' and 'What beliefs are false?'

It is very important to keep these different questions entirely

separate, since any confusion between them is sure to produce an answer

which is not really applicable to either.

There are three points to observe in the attempt to discover the nature

of truth, three requisites which any theory must fulfil.

(1) Our theory of truth must be such as to admit of its opposite,

falsehood. A good many philosophers have failed adequately to satisfy

this condition: they have constructed theories according to which all

our thinking ought to have been true, and have then had the greatest

difficulty in finding a place for falsehood. In this respect our theory

of belief must differ from our theory of acquaintance, since in the case

of acquaintance it was not necessary to take account of any opposite.

(2) It seems fairly evident that if there were no beliefs there could be

no falsehood, and no truth either, in the sense in which truth is

correlative to falsehood. If we imagine a world of mere matter, there

would be no room for falsehood in such a world, and although it would

contain what may be called 'facts', it would not contain any truths, in

the sense in which truths are things of the same kind as falsehoods. In

fact, truth and falsehood are properties of beliefs and statements:

hence a world of mere matter, since it would contain no beliefs or

statements, would also contain no truth or falsehood.

(3) But, as against what we have just said, it is to be observed that

the truth or falsehood of a belief always depends upon something which

lies outside the belief itself. If I believe that Charles I died on the

scaffold, I believe truly, not because of any intrinsic quality of my

belief, which could be discovered by merely examining the belief, but

because of an historical event which happened two and a half centuries

ago. If I believe that Charles I died in his bed, I believe falsely: no

degree of vividness in my belief, or of care in arriving at it, prevents

it from being false, again because of what happened long ago, and not

because of any intrinsic property of my belief. Hence, although truth

and falsehood are properties of beliefs, they are properties dependent

upon the relations of the beliefs to other things, not upon any internal

quality of the beliefs.

The third of the above requisites leads us to adopt the view which has

on the whole been commonest among philosophers that truth consists in

some form of correspondence between belief and fact. It is, however, by

no means an easy matter to discover a form of correspondence to which

there are no irrefutable objections. By this partly and partly by the

feeling that, if truth consists in a correspondence of thought with

something outside thought, thought can never know when truth has been

attained?many philosophers have been led to try to find some definition

of truth which shall not consist in relation to something wholly outside

belief. The most important attempt at a definition of this sort is the

theory that truth consists in /coherence/. It is said that the mark of

falsehood is failure to cohere in the body of our beliefs, and that it

is the essence of a truth to form part of the completely rounded system

which is The Truth.

There is, however, a great difficulty in this view, or rather two great

difficulties. The first is that there is no reason to suppose that only

/one/ coherent body of beliefs is possible. It may be that, with

sufficient imagination, a novelist might invent a past for the world

that would perfectly fit on to what we know, and yet be quite different

from the real past. In more scientific matters, it is certain that there

are often two or more hypotheses which account for all the known facts

on some subject, and although, in such cases, men of science endeavour

to find facts which will rule out all the hypotheses except one, there

is no reason why they should always succeed.

In philosophy, again, it seems not uncommon for two rival hypotheses to

be both able to account for all the facts. Thus, for example, it is

possible that life is one long dream, and that the outer world has only

that degree of reality that the objects of dreams have; but although

such a view does not seem inconsistent with known facts, there is no

reason to prefer it to the common-sense view, according to which other

people and things do really exist. Thus coherence as the definition of

truth fails because there is no proof that there can be only one

coherent system.

The other objection to this definition of truth is that it assumes the

meaning of 'coherence' known, whereas, in fact, 'coherence' presupposes

the truth of the laws of logic. Two propositions are coherent when both

may be true, and are incoherent when one at least must be false. Now in

order to know whether two propositions can both be true, we must know

such truths as the law of contradiction. For example, the two

propositions, 'this tree is a beech' and 'this tree is not a beech', are

not coherent, because of the law of contradiction. But if the law of

contradiction itself were subjected to the test of coherence, we should

find that, if we choose to suppose it false, nothing will any longer be

incoherent with anything else. Thus the laws of logic supply the

skeleton or framework within which the test of coherence applies, and

they themselves cannot be established by this test.

For the above two reasons, coherence cannot be accepted as giving the

/meaning/ of truth, though it is often a most important /test/ of truth

after a certain amount of truth has become known.

Hence we are driven back to /correspondence with fact/ as constituting

the nature of truth. It remains to define precisely what we mean by

'fact', and what is the nature of the correspondence which must subsist

between belief and fact, in order that belief may be true.

In accordance with our three requisites, we have to seek a theory of

truth which (1) allows truth to have an opposite, namely falsehood, (2)

makes truth a property of beliefs, but (3) makes it a property wholly

dependent upon the relation of the beliefs to outside things.

The necessity of allowing for falsehood makes it impossible to regard

belief as a relation of the mind to a single object, which could be said

to be what is believed. If belief were so regarded, we should find that,

like acquaintance, it would not admit of the opposition of truth and

falsehood, but would have to be always true. This may be made clear by

examples. Othello believes falsely that Desdemona loves Casio. We

cannot say that this belief consists in a relation to a single object,

'Desdemona's love for Casio', for if there were such an object, the

belief would be true. There is in fact no such object, and therefore

Othello cannot have any relation to such an object. Hence his belief

cannot possibly consist in a relation to this object.

It might be said that his belief is a relation to a different object,

namely 'that Desdemona loves Casio'; but it is almost as difficult to

suppose that there is such an object as this, when Desdemona does not

love Casio, as it was to suppose that there is 'Desdemona's love for

Casio'. Hence it will be better to seek for a theory of belief which

does not make it consist in a relation of the mind to a single object.

It is common to think of relations as though they always held between

two terms, but in fact this is not always the case. Some relations

demand three terms, some four, and so on. Take, for instance, the

relation 'between'. So long as only two terms come in, the relation

'between' is impossible: three terms are the smallest number that render

it possible. York is between London and Edinburgh; but if London and

Edinburgh were the only places in the world, there could be nothing

which was between one place and another. Similarly /jealousy/ requires

three people: there can be no such relation that does not involve three

at least. Such a proposition as 'A wishes B to promote C's marriage with

D' involves a relation of four terms; that is to say, A and B and C and

D all come in, and the relation involved cannot be expressed otherwise

than in a form involving all four. Instances might be multiplied

indefinitely, but enough has been said to show that there are relations

which require more than two terms before they can occur.

The relation involved in /judging/ or /believing/ must, if falsehood is

to be duly allowed for, be taken to be a relation between several terms,

not between two. When Othello believes that Desdemona loves Casio, he

must not have before his mind a single object, 'Desdemona's love for

Cassio', or 'that Desdemona loves Casio ', for that would require that

there should be objective falsehoods, which subsist independently of any

minds; and this, though not logically refutable, is a theory to be

avoided if possible. Thus it is easier to account for falsehood if we

take judgement to be a relation in which the mind and the various

objects concerned all occur severally; that is to say, Desdemona and

loving and Casio must all be terms in the relation which subsists when

Othello believes that Desdemona loves Casio. This relation, therefore,

is a relation of four terms, since Othello also is one of the terms of

the relation. When we say that it is a relation of four terms, we do not

mean that Othello has a certain relation to Desdemona, and has the same

relation to loving and also to Casio. This may be true of some other

relation than believing; but believing, plainly, is not a relation which

Othello has to /each/ of the three terms concerned, but to /all/ of them

together: there is only one example of the relation of believing

involved, but this one example knits together four terms. Thus the

actual occurrence, at the moment when Othello is entertaining his

belief, is that the relation called 'believing' is knitting together

into one complex whole the four terms Othello, Desdemona, loving, and

Cassio. What is called belief or judgement is nothing but this relation

of believing or judging, which relates a mind to several things other

than itself. An /act/ of belief or of judgement is the occurrence

between certain terms at some particular time, of the relation of

believing or judging.

We are now in a position to understand what it is that distinguishes a

true judgement from a false one. For this purpose we will adopt certain

definitions. In every act of judgement there is a mind which judges, and

there are terms concerning which it judges. We will call the mind the

/subject/ in the judgement, and the remaining terms the /objects/. Thus,

when Othello judges that Desdemona loves Casio, Othello is the subject,

while the objects are Desdemona and loving and Casio. The subject and

the objects together are called the /constituents/ of the judgement. It

will be observed that the relation of judging has what is called a

'sense' or 'direction'. We may say, metaphorically, that it puts its

objects in a certain /order/, which we may indicate by means of the

order of the words in the sentence. (In an inflected language, the same

thing will be indicated by inflections, e.g. by the difference between

nominative and accusative.) Othello's judgement that Casio loves

Desdemona differs from his judgement that Desdemona loves Casio, in

spite of the fact that it consists of the same constituents, because the

relation of judging places the constituents in a different order in the

two cases. Similarly, if Casio judges that Desdemona loves Othello, the

constituents of the judgement are still the same, but their order is

different. This property of having a 'sense' or 'direction' is one which

the relation of judging shares with all other relations. The 'sense' of

relations is the ultimate source of order and series and a host of

mathematical concepts; but we need not concern ourselves further with

this aspect.

We spoke of the relation called 'judging' or 'believing' as knitting

together into one complex whole the subject and the objects. In this

respect, judging is exactly like every other relation. Whenever a

relation holds between two or more terms, it unites the terms into a

complex whole. If Othello loves Desdemona, there is such a complex whole

as 'Othello's love for Desdemona'. The terms united by the relation may

be themselves complex, or may be simple, but the whole which results

from their being united must be complex. Wherever there is a relation

which relates certain terms, there is a complex object formed of the

union of those terms; and conversely, wherever there is a complex

object, there is a relation which relates its constituents. When an act

of believing occurs, there is a complex, in which 'believing' is the

uniting relation, and subject and objects are arranged in a certain

order by the 'sense' of the relation of believing. Among the objects, as

we saw in considering 'Othello believes that Desdemona loves Cassio',

one must be a relation?in this instance, the relation 'loving'. But this

relation, as it occurs in the act of believing, is not the relation

which creates the unity of the complex whole consisting of the subject

and the objects. The relation 'loving', as it occurs in the act of

believing, is one of the objects it is a brick in the structure, not the

cement. The cement is the relation 'believing'. When the belief is

/true/, there is another complex unity, in which the relation which was

one of the objects of the belief relates the other objects. Thus, e.g.,

if Othello believes /truly/ that Desdemona loves Casio, then there is a

complex unity, 'Desdemona's love for Casio', which is composed

exclusively of the /objects/ of the belief, in the same order as they

had in the belief, with the relation which was one of the objects

occurring now as the cement that binds together the other objects of the

belief. On the other hand, when a belief is /false/, there is no such

complex unity composed only of the objects of the belief. If Othello

believes /falsely/ that Desdemona loves Cassio, then there is no such

complex unity as 'Desdemona's love for Cassio'.

Thus a belief is /true/ when it /corresponds/ to a certain associated

complex, and /false/ when it does not. Assuming, for the sake of

definiteness, that the objects of the belief are two terms and a

relation, the terms being put in a certain order by the 'sense' of the

believing, then if the two terms in that order are united by the

relation into a complex, the belief is true; if not, it is false. This

constitutes the definition of truth and falsehood that we were in search

of. Judging or believing is a certain complex unity of which a mind is a

constituent; if the remaining constituents, taken in the order which

they have in the belief, form a complex unity, then the belief is true;

if not, it is false.

Thus although truth and falsehood are properties of beliefs, yet they

are in a sense extrinsic properties, for the condition of the truth of a

belief is something not involving beliefs, or (in general) any mind at

all, but only the /objects/ of the belief. A mind, which believes,

believes truly when there is a /corresponding/ complex not involving the

mind, but only its objects. This correspondence ensures truth, and its

absence entails falsehood. Hence we account simultaneously for the two

facts that beliefs (a) depend on minds for their /existence/, (b) do not

depend on minds for their /truth/.

We may restate our theory as follows: If we take such a belief as

'Othello believes that Desdemona loves Cassio', we will call Desdemona

and Cassio the /object-terms/, and loving the /object-relation/. If

there is a complex unity 'Desdemona's love for Cassio', consisting of

the object-terms related by the object-relation in the same order as

they have in the belief, then this complex unity is called the /fact

corresponding to the belief/. Thus a belief is true when there is a

corresponding fact, and is false when there is no corresponding fact.

It will be seen that minds do not /create/ truth or falsehood. They

create beliefs, but when once the beliefs are created, the mind cannot

make them true or false, except in the special case where they concern

future things which are within the power of the person believing, such

as catching trains. What makes a belief true is a /fact/, and this fact

does not (except in exceptional cases) in any way involve the mind of

the person who has the belief.

Having now decided what we /mean/ by truth and falsehood, we have next

to consider what ways there are of knowing whether this or that belief

is true or false. This consideration will occupy the next chapter.

CHAPTER XIII. KNOWLEDGE, ERROR, AND PROBABLE OPINION

The question as to what we mean by truth and falsehood, which we

considered in the preceding chapter, is of much less interest than the

question as to how we can know what is true and what is false. This

question will occupy us in the present chapter. There can be no doubt

that /some/ of our beliefs are erroneous; thus we are led to inquire

what certainty we can ever have that such and such a belief is not

erroneous. In other words, can we ever /know/ anything at all, or do we

merely sometimes by good luck believe what is true? Before we can attack

this question, we must, however, first decide what we mean by 'knowing',

and this question is not so easy as might be supposed.

At first sight we might imagine that knowledge could be defined as 'true

belief'. When what we believe is true, it might be supposed that we had

achieved a knowledge of what we believe. But this would not accord with

the way in which the word is commonly used. To take a very trivial

instance: If a man believes that the late Prime Minister's last name

began with a B, he believes what is true, since the late Prime Minister

was Sir Henry Campbell Bannerman. But if he believes that Mr. Balfour

was the late Prime Minister, he will still believe that the late Prime

Minister's last name began with a B, yet this belief, though true, would

not be thought to constitute knowledge. If a newspaper, by an

intelligent anticipation, announces the result of a battle before any

telegram giving the result has been received, it may by good fortune

announce what afterwards turns out to be the right result, and it may

produce belief in some of its less experienced readers. But in spite of

the truth of their belief, they cannot be said to have knowledge. Thus

it is clear that a true belief is not knowledge when it is deduced from

a false belief.

In like manner, a true belief cannot be called knowledge when it is

deduced by a fallacious process of reasoning, even if the premises from

which it is deduced are true. If I know that all Greeks are men and that

Socrates was a man, and I infer that Socrates was a Greek, I cannot be

said to /know/ that Socrates was a Greek, because, although my premisses

and my conclusion are true, the conclusion does not follow from the

premisses.

But are we to say that nothing is knowledge except what is validly

deduced from true premisses? Obviously we cannot say this. Such a

definition is at once too wide and too narrow. In the first place, it is

too wide, because it is not enough that our premisses should be /true/,

they must also be /known/. The man who believes that Mr. Balfour was the

late Prime Minister may proceed to draw valid deductions from the true

premiss that the late Prime Minister's name began with a B, but he

cannot be said to /know/ the conclusions reached by these deductions.

Thus we shall have to amend our definition by saying that knowledge is

what is validly deduced from /known/ premisses. This, however, is a

circular definition: it assumes that we already know what is meant by

'known premisses'. It can, therefore, at best define one sort of

knowledge, the sort we call derivative, as opposed to intuitive

knowledge. We may say: '/Derivative/ knowledge is what is validly

deduced from premisses known intuitively'. In this statement there is no

formal defect, but it leaves the definition of /intuitive/ knowledge

still to seek.

Leaving on one side, for the moment, the question of intuitive

knowledge, let us consider the above suggested definition of derivative

knowledge. The chief objection to it is that it unduly limits knowledge.

It constantly happens that people entertain a true belief, which has

grown up in them because of some piece of intuitive knowledge from which

it is capable of being validly inferred, but from which it has not, as a

matter of fact, been inferred by any logical process.

Take, for example, the beliefs produced by reading. If the newspapers

announce the death of the King, we are fairly well justified in

believing that the King is dead, since this is the sort of announcement

which would not be made if it were false. And we are quite amply

justified in believing that the newspaper asserts that the King is dead.

But here the intuitive knowledge upon which our belief is based is

knowledge of the existence of sense-data derived from looking at the

print which gives the news. This knowledge scarcely rises into

consciousness, except in a person who cannot read easily. A child may be

aware of the shapes of the letters, and pass gradually and painfully to

a realization of their meaning. But anybody accustomed to reading passes

at once to what the letters mean, and is not aware, except on

reflection, that he has derived this knowledge from the sense-data

called seeing the printed letters. Thus although a valid inference from

the-letters to their meaning is possible, and /could/ be performed by

the reader, it is not in fact performed, since he does not in fact

perform any operation which can be called logical inference. Yet it

would be absurd to say that the reader does not /know/ that the

newspaper announces the King's death.

We must, therefore, admit as derivative knowledge whatever is the result

of intuitive knowledge even if by mere association, provided there /is/

a valid logical connexion, and the person in question could become aware

of this connexion by reflection. There are in fact many ways, besides

logical inference, by which we pass from one belief to another: the

passage from the print to its meaning illustrates these ways. These ways

may be called 'psychological inference'. We shall, then, admit such

psychological inference as a means of obtaining derivative knowledge,

provided there is a discoverable logical inference which runs parallel

to the psychological inference. This renders our definition of

derivative knowledge less precise than we could wish, since the word

'discoverable' is vague: it does not tell us how much reflection may be

needed in order to make the discovery. But in fact 'knowledge' is not a

precise conception: it merges into 'probable opinion', as we shall see

more fully in the course of the present chapter. A very precise

definition, therefore, should not be sought, since any such definition

must be more or less misleading.

The chief difficulty in regard to knowledge, however, does not arise

over derivative knowledge, but over intuitive knowledge. So long as we

are dealing with derivative knowledge, we have the test of intuitive

knowledge to fall back upon. But in regard to intuitive beliefs, it is

by no means easy to discover any criterion by which to distinguish some

as true and others as erroneous. In this question it is scarcely

possible to reach any very precise result: all our knowledge of truths

is infected with some degree of doubt, and a theory which ignored this

fact would be plainly wrong. Something may be done, however, to mitigate

the difficulties of the question.

Our theory of truth, to begin with, supplies the possibility of

distinguishing certain truths as /self-evident/ in a sense which ensures

infallibility. When a belief is true, we said, there is a corresponding

fact, in which the several objects of the belief form a single complex.

The belief is said to constitute /knowledge/ of this fact, provided it

fulfils those further somewhat vague conditions which we have been

considering in the present chapter. But in regard to any fact, besides

the knowledge constituted by belief, we may also have the kind of

knowledge constituted by /perception/ (taking this word in its widest

possible sense). For example, if you know the hour of the sunset, you

can at that hour know the fact that the sun is setting: this is

knowledge of the fact by way of knowledge of /truths/; but you can also,

if the weather is fine, look to the west and actually see the setting

sun: you then know the same fact by the way of knowledge of /things/.

Thus in regard to any complex fact, there are, theoretically, two ways

in which it may be known: (1) by means of a judgement, in which its

several parts are judged to be related as they are in fact related; (2)

by means of /acquaintance/ with the complex fact itself, which may (in a

large sense) be called perception, though it is by no means confined to

objects of the senses. Now it will be observed that the second way of

knowing a complex fact, the way of acquaintance, is only possible when

there really is such a fact, while the first way, like all judgement, is

liable to error. The second way gives us the complex whole, and is

therefore only possible when its parts do actually have that relation

which makes them combine to form such a complex. The first way, on the

contrary, gives us the parts and the relation severally, and demands

only the reality of the parts and the relation: the relation may not

relate those parts in that way, and yet the judgement may occur.

It will be remembered that at the end of Chapter XI we suggested that

there might be two kinds of self-evidence, one giving an absolute

guarantee of truth, the other only a partial guarantee. These two kinds

can now be distinguished.

We may say that a truth is self-evident, in the first and most absolute

sense, when we have acquaintance with the fact which corresponds to the

truth. When Othello believes that Desdemona loves Cassio, the

corresponding fact, if his belief were true, would be 'Desdemona's love

for Cassio'. This would be a fact with which no one could have

acquaintance except Desdemona; hence in the sense of self-evidence that

we are considering, the truth that Desdemona loves Cassio (if it were a

truth) could only be self-evident to Desdemona. All mental facts, and

all facts concerning sense-data, have this same privacy: there is only

one person to whom they can be self-evident in our present sense, since

there is only one person who can be acquainted with the mental things or

the sense-data concerned. Thus no fact about any particular existing

thing can be self-evident to more than one person. On the other hand,

facts about universals do not have this privacy. Many minds may be

acquainted with the same universals; hence a relation between universals

may be known by acquaintance to many different people. In all cases

where we know by acquaintance a complex fact consisting of certain terms

in a certain relation, we say that the truth that these terms are so

related has the first or absolute kind of self-evidence, and in these

cases the judgement that the terms are so related /must/ be true. Thus

this sort of self-evidence is an absolute guarantee of truth.

But although this sort of self-evidence is an absolute guarantee of

truth, it does not enable us to be /absolutely/ certain, in the case of

any given judgement, that the judgement in question is true. Suppose we

first perceive the sun shining, which is a complex fact, and thence

proceed to make the judgement 'the sun is shining'. In passing from the

perception to the judgement, it is necessary to analyse the given

complex fact: we have to separate out 'the sun' and 'shining' as

constituents of the fact. In this process it is possible to commit an

error; hence even where a /fact/ has the first or absolute kind of

self-evidence, a judgement believed to correspond to the fact is not

absolutely infallible, because it may not really correspond to the fact.

But if it does correspond (in the sense explained in the preceding

chapter), then it /must/ be true.

The second sort of self-evidence will be that which belongs to

judgements in the first instance, and is not derived from direct

perception of a fact as a single complex whole. This second kind of

self-evidence will have degrees, from the very highest degree down to a

bare inclination in favour of the belief. Take, for example, the case of

a horse trotting away from us along a hard road. At first our certainty

that we hear the hoofs is complete; gradually, if we listen intently,

there comes a moment when we think perhaps it was imagination or the

blind upstairs or our own heartbeats; at last we become doubtful whether

there was any noise at all; then we /think/ we no longer hear anything,

and at last we /know/ we no longer hear anything. In this process, there

is a continual gradation of self-evidence, from the highest degree to

the least, not in the sense-data themselves, but in the judgements based

on them.

Or again: Suppose we are comparing two shades of colour, one blue and

one green. We can be quite sure they are different shades of colour; but

if the green colour is gradually altered to be more and more like the

blue, becoming first a blue-green, then a greeny-blue, then blue, there

will come a moment when we are doubtful whether we can see any

difference, and then a moment when we know that we cannot see any

difference. The same thing happens in tuning a musical instrument, or in

any other case where there is a continuous gradation. Thus self-evidence

of this sort is a matter of degree; and it seems plain that the higher

degrees are more to be trusted than the lower degrees.

In derivative knowledge our ultimate premisses must have some degree of

self-evidence, and so must their connexion with the conclusions deduced

from them. Take for example a piece of reasoning in geometry. It is not

enough that the axioms from which we start should be self-evident: it is

necessary also that, at each step in the reasoning, the connexion of

premiss and conclusion should be self-evident. In difficult reasoning,

this connexion has often only a very small degree of self-evidence;

hence errors of reasoning are not improbable where the difficulty is great.

From what has been said it is evident that, both as regards intuitive

knowledge and as regards derivative knowledge, if we assume that

intuitive knowledge is trustworthy in proportion to the degree of its

self-evidence, there will be a gradation in trustworthiness, from the

existence of noteworthy sense-data and the simpler truths of logic and

arithmetic, which may be taken as quite certain, down to judgements

which seem only just more probable than their opposites. What we firmly

believe, if it is true, is called /knowledge/, provided it is either

intuitive or inferred (logically or psychologically) from intuitive

knowledge from which it follows logically. What we firmly believe, if it

is not true, is called /error/. What we firmly believe, if it is neither

knowledge nor error, and also what we believe hesitatingly, because it

is, or is derived from, something which has not the highest degree of

self-evidence, may be called /probable opinion/. Thus the greater part

of what would commonly pass as knowledge is more or less probable opinion.

In regard to probable opinion, we can derive great assistance from

/coherence/, which we rejected as the /definition/ of truth, but may

often use as a /criterion/. A body of individually probable opinions, if

they are mutually coherent, become more probable than any one of them

would be individually. It is in this way that many scientific hypotheses

acquire their probability. They fit into a coherent system of probable

opinions, and thus become more probable than they would be in isolation.

The same thing applies to general philosophical hypotheses. Often in a

single case such hypotheses may seem highly doubtful, while yet, when we

consider the order and coherence which they introduce into a mass of

probable opinion, they become pretty nearly certain. This applies, in

particular, to such matters as the distinction between dreams and waking

life. If our dreams, night after night, were as coherent one with

another as our days, we should hardly know whether to believe the dreams

or the waking life. As it is, the test of coherence condemns the dreams

and confirms the waking life. But this test, though it increases

probability where it is successful, never gives absolute certainty,

unless there is certainty already at some point in the coherent system.

Thus the mere organization of probable opinion will never, by itself,

transform it into indubitable knowledge.

CHAPTER XIV. THE LIMITS OF PHILOSOPHICAL KNOWLEDGE

In all that we have said hitherto concerning philosophy, we have

scarcely touched on many matters that occupy a great space in the

writings of most philosophers. Most philosophers?or, at any rate, very

many?profess to be able to prove, by /a priori/ metaphysical reasoning,

such things as the fundamental dogmas of religion, the essential

rationality of the universe, the illusoriness of matter, the unreality

of all evil, and so on. There can be no doubt that the hope of finding

reason to believe such theses as these has been the chief inspiration of

many life-long students of philosophy. This hope, I believe, is vain. It

would seem that knowledge concerning the universe as a whole is not to

be obtained by metaphysics, and that the proposed proofs that, in virtue

of the laws of logic such and such things /must/ exist and such and such

others cannot, are not capable of surviving a critical scrutiny. In this

chapter we shall briefly consider the kind of way in which such

reasoning is attempted, with a view to discovering whether we can hope

that it may be valid.

The great representative, in modern times, of the kind of view which we

wish to examine, was Hegel (1770-1831). Hegel's philosophy is very

difficult, and commentators differ as to the true interpretation of it.

According to the interpretation I shall adopt, which is that of many, if

not most, of the commentators and has the merit of giving an interesting

and important type of philosophy, his main thesis is that everything

short of the Whole is obviously fragmentary, and obviously incapable of

existing without the complement supplied by the rest of the world. Just

as a comparative anatomist, from a single bone, sees what kind of animal

the whole must have been, so the metaphysician, according to Hegel,

sees, from any one piece of reality, what the whole of reality must

be?at least in its large outlines. Every apparently separate piece of

reality has, as it were, hooks which grapple it to the next piece; the

next piece, in turn, has fresh hooks, and so on, until the whole

universe is reconstructed. This essential incompleteness appears,

according to Hegel, equally in the world of thought and in the world of

things. In the world of thought, if we take any idea which is abstract

or incomplete, we find, on examination, that if we forget its

incompleteness, we become involved in contradictions; these

contradictions turn the idea in question into its opposite, or

antithesis; and in order to escape, we have to find a new, less

incomplete idea, which is the synthesis of our original idea and its

antithesis. This new idea, though less incomplete than the idea we

started with, will be found, nevertheless, to be still not wholly

complete, but to pass into its antithesis, with which it must be

combined in a new synthesis. In this way Hegel advances until he reaches

the 'Absolute Idea', which, according to him, has no incompleteness, no

opposite, and no need of further development. The Absolute Idea,

therefore, is adequate to describe Absolute Reality; but all lower ideas

only describe reality as it appears to a partial view, not as it is to

one who simultaneously surveys the Whole. Thus Hegel reaches the

conclusion that Absolute Reality forms one single harmonious system, not

in space or time, not in any degree evil, wholly rational, and wholly

spiritual. Any appearance to the contrary, in the world we know, can be

proved logically so he believes to be entirely due to our fragmentary

piecemeal view of the universe. If we saw the universe whole, as we may

suppose God sees it, space and time and matter and evil and all striving

and struggling would disappear, and we should see instead an eternal

perfect unchanging spiritual unity.

In this conception, there is undeniably something sublime, something to

which we could wish to yield assent. Nevertheless, when the arguments in

support of it are carefully examined, they appear to involve much

confusion and many unwarrantable assumptions. The fundamental tenet upon

which the system is built up is that what is incomplete must be not

self-subsistent, but must need the support of other things before it can

exist. It is held that whatever has relations to things outside itself

must contain some reference to those outside things in its own nature,

and could not, therefore, be what it is if those outside things did not

exist. A man's nature, for example, is constituted by his memories and

the rest of his knowledge, by his loves and hatreds, and so on; thus,

but for the objects which he knows or loves or hates, he could not be

what he is. He is essentially and obviously a fragment: taken as the

sum-total of reality he would be self-contradictory.

This whole point of view, however, turns upon the notion of the 'nature'

of a thing, which seems to mean 'all the truths about the thing'. It is

of course the case that a truth which connects one thing with another

thing could not subsist if the other thing did not subsist. But a truth

about a thing is not part of the thing itself, although it must,

according to the above usage, be part of the 'nature' of the thing. If

we mean by a thing's 'nature' all the truths about the thing, then

plainly we cannot know a thing's 'nature' unless we know all the thing's

relations to all the other things in the universe. But if the word

'nature' is used in this sense, we shall have to hold that the thing may

be known when its 'nature' is not known, or at any rate is not known

completely. There is a confusion, when this use of the word 'nature' is

employed, between knowledge of things and knowledge of truths. We may

have knowledge of a thing by acquaintance even if we know very few

propositions about it theoretically we need not know any propositions

about it. Thus, acquaintance with a thing does not involve knowledge of

its 'nature' in the above sense. And although acquaintance with a thing

is involved in our knowing any one proposition about a thing, knowledge

of its 'nature', in the above sense, is not involved. Hence, (1)

acquaintance with a thing does not logically involve a knowledge of its

relations, and (2) a knowledge of some of its relations does not involve

a knowledge of all of its relations nor a knowledge of its 'nature' in

the above sense. I may be acquainted, for example, with my toothache,

and this knowledge may be as complete as knowledge by acquaintance ever

can be, without knowing all that the dentist (who is not acquainted with

it) can tell me about its cause, and without therefore knowing its

'nature' in the above sense. Thus the fact that a thing has relations

does not prove that its relations are logically necessary. That is to

say, from the mere fact that it is the thing it is we cannot deduce that

it must have the various relations which in fact it has. This only

/seems/ to follow because we know it already.

It follows that we cannot prove that the universe as a whole forms a

single harmonious system such as Hegel believes that it forms. And if we

cannot prove this, we also cannot prove the unreality of space and time

and matter and evil, for this is deduced by Hegel from the fragmentary

and relational character of these things. Thus we are left to the

piecemeal investigation of the world, and are unable to know the

characters of those parts of the universe that are remote from our

experience. This result, disappointing as it is to those whose hopes

have been raised by the systems of philosophers, is in harmony with the

inductive and scientific temper of our age, and is borne out by the

whole examination of human knowledge which has occupied our previous

chapters.

Most of the great ambitious attempts of metaphysicians have proceeded by

the attempt to prove that such and such apparent features of the actual

world were self-contradictory, and therefore could not be real. The

whole tendency of modern thought, however, is more and more in the

direction of showing that the supposed contradictions were illusory, and

that very little can be proved /a priori/ from considerations of what

/must/ be. A good illustration of this is afforded by space and time.

Space and time appear to be infinite in extent, and infinitely

divisible. If we travel along a straight line in either direction, it is

difficult to believe that we shall finally reach a last point, beyond

which there is nothing, not even empty space. Similarly, if in

imagination we travel backwards or forwards in time, it is difficult to

believe that we shall reach a first or last time, with not even empty

time beyond it. Thus space and time appear to be infinite in extent.

Again, if we take any two points on a line, it seems evident that there

must be other points between them however small the distance between

them may be: every distance can be halved, and the halves can be halved

again, and so on /ad infinitum/. In time, similarly, however little time

may elapse between two moments, it seems evident that there will be

other moments between them. Thus space and time appear to be infinitely

divisible. But as against these apparent facts infinite extent and

infinite divisibility philosophers have advanced arguments tending to

show that there could be no infinite collections of things, and that

therefore the number of points in space, or of instants in time, must be

finite. Thus a contradiction emerged between the apparent nature of

space and time and the supposed impossibility of infinite collections.

Kant, who first emphasized this contradiction, deduced the impossibility

of space and time, which he declared to be merely subjective; and since

his time very many philosophers have believed that space and time are

mere appearance, not characteristic of the world as it really is. Now,

however, owing to the labours of the mathematicians, notably Georg

Cantor, it has appeared that the impossibility of infinite collections

was a mistake. They are not in fact self-contradictory, but only

contradictory of certain rather obstinate mental prejudices. Hence the

reasons for regarding space and time as unreal have become inoperative,

and one of the great sources of metaphysical constructions is dried up.

The mathematicians, however, have not been content with showing that

space as it is commonly supposed to be is possible; they have shown also

that many other forms of space are equally possible, so far as logic can

show. Some of Euclid's axioms, which appear to common sense to be

necessary, and were formerly supposed to be necessary by philosophers,

are now known to derive their appearance of necessity from our mere

familiarity with actual space, and not from any /a priori/ logical

foundation. By imagining worlds in which these axioms are false, the

mathematicians have used logic to loosen the prejudices of common sense,

and to show the possibility of spaces differing some more, some

less from that in which we live. And some of these spaces differ so

little from Euclidean space, where distances such as we can measure are

concerned, that it is impossible to discover by observation whether our

actual space is strictly Euclidean or of one of these other kinds. Thus

the position is completely reversed. Formerly it appeared that

experience left only one kind of space to logic, and logic showed this

one kind to be impossible. Now, logic presents many kinds of space as

possible apart from experience, and experience only partially decides

between them. Thus, while our knowledge of what is has become less than

it was formerly supposed to be, our knowledge of what may be is

enormously increased. Instead of being shut in within narrow walls, of

which every nook and cranny could be explored, we find ourselves in an

open world of free possibilities, where much remains unknown because

there is so much to know.

What has happened in the case of space and time has happened, to some

extent, in other directions as well. The attempt to prescribe to the

universe by means of /a priori/ principles has broken down; logic,

instead of being, as formerly, the bar to possibilities, has become the

great liberator of the imagination, presenting innumerable alternatives

which are closed to unreflective common sense, and leaving to experience

the task of deciding, where decision is possible, between the many

worlds which logic offers for our choice. Thus knowledge as to what

exists becomes limited to what we can learn from experience not to what

we can actually experience, for, as we have seen, there is much

knowledge by description concerning things of which we have no direct

experience. But in all cases of knowledge by description, we need some

connexion of universals, enabling us, from such and such a datum, to

infer an object of a certain sort as implied by our datum. Thus in

regard to physical objects, for example, the principle that sense-data

are signs of physical objects is itself a connexion of universals; and

it is only in virtue of this principle that experience enables us to

acquire knowledge concerning physical objects. The same applies to the

law of causality, or, to descend to what is less general, to such

principles as the law of gravitation.

Principles such as the law of gravitation are proved, or rather are

rendered highly probable, by a combination of experience with some

wholly /a priori/ principle, such as the principle of induction. Thus

our intuitive knowledge, which is the source of all our other knowledge

of truths, is of two sorts: pure empirical knowledge, which tells us of

the existence and some of the properties of particular things with which

we are acquainted, and pure /a priori/ knowledge, which gives us

connexions between universals, and enables us to draw inferences from

the particular facts given in empirical knowledge. Our derivative

knowledge always depends upon some pure /a priori/ knowledge and usually

also depends upon some pure empirical knowledge.

Philosophical knowledge, if what has been said above is true, does not

differ essentially from scientific knowledge; there is no special source

of wisdom which is open to philosophy but not to science, and the

results obtained by philosophy are not radically different from those

obtained from science. The essential characteristic of philosophy, which

makes it a study distinct from science, is criticism. It examines

critically the principles employed in science and in daily life; it

searches out any inconsistencies there may be in these principles, and

it only accepts them when, as the result of a critical inquiry, no

reason for rejecting them has appeared. If, as many philosophers have

believed, the principles underlying the sciences were capable, when

disengaged from irrelevant detail, of giving us knowledge concerning the

universe as a whole, such knowledge would have the same claim on our

belief as scientific knowledge has; but our inquiry has not revealed any

such knowledge, and therefore, as regards the special doctrines of the

bolder metaphysicians, has had a mainly negative result. But as regards

what would be commonly accepted as knowledge, our result is in the main

positive: we have seldom found reason to reject such knowledge as the

result of our criticism, and we have seen no reason to suppose man

incapable of the kind of knowledge which he is generally believed to

possess.

When, however, we speak of philosophy as a /criticism/ of knowledge, it

is necessary to impose a certain limitation. If we adopt the attitude of

the complete sceptic, placing ourselves wholly outside all knowledge,

and asking, from this outside position, to be compelled to return within

the circle of knowledge, we are demanding what is impossible, and our

scepticism can never be refuted. For all refutation must begin with some

piece of knowledge which the disputants share; from blank doubt, no

argument can begin. Hence the criticism of knowledge which philosophy

employs must not be of this destructive kind, if any result is to be

achieved. Against this absolute scepticism, no /logical/ argument can be

advanced. But it is not difficult to see that scepticism of this kind is

unreasonable. Descartes' 'methodical doubt', with which modern

philosophy began, is not of this kind, but is rather the kind of

criticism which we are asserting to be the essence of philosophy. His

'methodical doubt' consisted in doubting whatever seemed doubtful; in

pausing, with each apparent piece of knowledge, to ask himself whether,

on reflection, he could feel certain that he really knew it. This is the

kind of criticism which constitutes philosophy. Some knowledge, such as

knowledge of the existence of our sense-data, appears quite indubitable,

however calmly and thoroughly we reflect upon it. In regard to such

knowledge, philosophical criticism does not require that we should

abstain from belief. But there are beliefs such, for example, as the

belief that physical objects exactly resemble our sense-data which are

entertained until we begin to reflect, but are found to melt away when

subjected to a close inquiry. Such beliefs philosophy will bid us

reject, unless some new line of argument is found to support them. But

to reject the beliefs which do not appear open to any objections,

however closely we examine them, is not reasonable, and is not what

philosophy advocates.

The criticism aimed at, in a word, is not that which, without reason,

determines to reject, but that which considers each piece of apparent

knowledge on its merits, and retains whatever still appears to be

knowledge when this consideration is completed. That some risk of error

remains must be admitted, since human beings are fallible. Philosophy

may claim justly that it diminishes the risk of error, and that in some

cases it renders the risk so small as to be practically negligible. To

do more than this is not possible in a world where mistakes must occur;

and more than this no prudent advocate of philosophy would claim to have

performed.

CHAPTER XV. THE VALUE OF PHILOSOPHY

Having now come to the end of our brief and very incomplete review of

the problems of philosophy, it will be well to consider, in conclusion,

what is the value of philosophy and why it ought to be studied. It is

the more necessary to consider this question, in view of the fact that

many men, under the influence of science or of practical affairs, are

inclined to doubt whether philosophy is anything better than innocent

but useless trifling, hair-splitting distinctions, and controversies on

matters concerning which knowledge is impossible.

This view of philosophy appears to result, partly from a wrong

conception of the ends of life, partly from a wrong conception of the

kind of goods which philosophy strives to achieve. Physical science,

through the medium of inventions, is useful to innumerable people who

are wholly ignorant of it; thus the study of physical science is to be

recommended, not only, or primarily, because of the effect on the

student, but rather because of the effect on mankind in general. Thus

utility does not belong to philosophy. If the study of philosophy has

any value at all for others than students of philosophy, it must be only

indirectly, through its effects upon the lives of those who study it. It

is in these effects, therefore, if anywhere, that the value of

philosophy must be primarily sought.

But further, if we are not to fail in our endeavour to determine the

value of philosophy, we must first free our minds from the prejudices of

what are wrongly called 'practical' men. The 'practical' man, as this

word is often used, is one who recognizes only material needs, who

realizes that men must have food for the body, but is oblivious of the

necessity of providing food for the mind. If all men were well off, if

poverty and disease had been reduced to their lowest possible point,

there would still remain much to be done to produce a valuable society;

and even in the existing world the goods of the mind are at least as

important as the goods of the body. It is exclusively among the goods of

the mind that the value of philosophy is to be found; and only those who

are not indifferent to these goods can be persuaded that the study of

philosophy is not a waste of time.

Philosophy, like all other studies, aims primarily at knowledge. The

knowledge it aims at is the kind of knowledge which gives unity and

system to the body of the sciences, and the kind which results from a

critical examination of the grounds of our convictions, prejudices, and

beliefs. But it cannot be maintained that philosophy has had any very

great measure of success in its attempts to provide definite answers to

its questions. If you ask a mathematician, a mineralogist, a historian,

or any other man of learning, what definite body of truths has been

ascertained by his science, his answer will last as long as you are

willing to listen. But if you put the same question to a philosopher, he

will, if he is candid, have to confess that his study has not achieved

positive results such as have been achieved by other sciences. It is

true that this is partly accounted for by the fact that, as soon as

definite knowledge concerning any subject becomes possible, this subject

ceases to be called philosophy, and becomes a separate science. The

whole study of the heavens, which now belongs to astronomy, was once

included in philosophy; Newton's great work was called 'the mathematical

principles of natural philosophy'. Similarly, the study of the human

mind, which was a part of philosophy, has now been separated from

philosophy and has become the science of psychology. Thus, to a great

extent, the uncertainty of philosophy is more apparent than real: those

questions which are already capable of definite answers are placed in

the sciences, while those only to which, at present, no definite answer

can be given, remain to form the residue which is called philosophy.

This is, however, only a part of the truth concerning the uncertainty of

philosophy. There are many questions and among them those that are of

the profoundest interest to our spiritual life which, so far as we can

see, must remain insoluble to the human intellect unless its powers

become of quite a different order from what they are now. Has the

universe any unity of plan or purpose, or is it a fortuitous concourse

of atoms? Is consciousness a permanent part of the universe, giving hope

of indefinite growth in wisdom, or is it a transitory accident on a

small planet on which life must ultimately become impossible? Are good

and evil of importance to the universe or only to man? Such questions

are asked by philosophy, and variously answered by various philosophers.

But it would seem that, whether answers be otherwise discoverable or

not, the answers suggested by philosophy are none of them demonstrably

true. Yet, however slight may be the hope of discovering an answer, it

is part of the business of philosophy to continue the consideration of

such questions, to make us aware of their importance, to examine all the

approaches to them, and to keep alive that speculative interest in the

universe which is apt to be killed by confining ourselves to definitely

ascertainable knowledge.

Many philosophers, it is true, have held that philosophy could establish

the truth of certain answers to such fundamental questions. They have

supposed that what is of most importance in religious beliefs could be

proved by strict demonstration to be true. In order to judge of such

attempts, it is necessary to take a survey of human knowledge, and to

form an opinion as to its methods and its limitations. On such a subject

it would be unwise to pronounce dogmatically; but if the investigations

of our previous chapters have not led us astray, we shall be compelled

to renounce the hope of finding philosophical proofs of religious

beliefs. We cannot, therefore, include as part of the value of

philosophy any definite set of answers to such questions. Hence, once

more, the value of philosophy must not depend upon any supposed body of

definitely ascertainable knowledge to be acquired by those who study it.

The value of philosophy is, in fact, to be sought largely in its very

uncertainty. The man who has no tincture of philosophy goes through life

imprisoned in the prejudices derived from common sense, from the

habitual beliefs of his age or his nation, and from convictions which

have grown up in his mind without the co-operation or consent of his

deliberate reason. To such a man the world tends to become definite,

finite, obvious; common objects rouse no questions, and unfamiliar

possibilities are contemptuously rejected. As soon as we begin to

philosophize, on the contrary, we find, as we saw in our opening

chapters, that even the most everyday things lead to problems to which

only very incomplete answers can be given. Philosophy, though unable to

tell us with certainty what is the true answer to the doubts which it

raises, is able to suggest many possibilities which enlarge our thoughts

and free them from the tyranny of custom. Thus, while diminishing our

feeling of certainty as to what things are, it greatly increases our

knowledge as to what they may be; it removes the somewhat arrogant

dogmatism of those who have never travelled into the region of

liberating doubt, and it keeps alive our sense of wonder by showing

familiar things in an unfamiliar aspect.

Apart from its utility in showing unsuspected possibilities, philosophy

has a value perhaps its chief value?through the greatness of the objects

which it contemplates, and the freedom from narrow and personal aims

resulting from this contemplation. The life of the instinctive man is

shut up within the circle of his private interests: family and friends

may be included, but the outer world is not regarded except as it may

help or hinder what comes within the circle of instinctive wishes. In

such a life there is something feverish and confined, in comparison with

which the philosophic life is calm and free. The private world of

instinctive interests is a small one, set in the midst of a great and

powerful world which must, sooner or later, lay our private world in

ruins. Unless we can so enlarge our interests as to include the whole

outer world, we remain like a garrison in a beleaguered fortress, knowing

that the enemy prevents escape and that ultimate surrender is

inevitable. In such a life there is no peace, but a constant strife

between the insistence of desire and the powerlessness of will. In one

way or another, if our life is to be great and free, we must escape this

prison and this strife.

One way of escape is by philosophic contemplation. Philosophic

contemplation does not, in its widest survey, divide the universe into

two hostile camps friends and foes, helpful and hostile, good and bad?it

views the whole impartially. Philosophic contemplation, when it is

unalloyed, does not aim at proving that the rest of the universe is akin

to man. All acquisition of knowledge is an enlargement of the Self, but

this enlargement is best attained when it is not directly sought. It is

obtained when the desire for knowledge is alone operative, by a study

which does not wish in advance that its objects should have this or that

character, but adapts the Self to the characters which it finds in its

objects. This enlargement of Self is not obtained when, taking the Self

as it is, we try to show that the world is so similar to this Self that

knowledge of it is possible without any admission of what seems alien.

The desire to prove this is a form of self-assertion and, like all

self-assertion, it is an obstacle to the growth of Self which it

desires, and of which the Self knows that it is capable. Self-assertion,

in philosophic speculation as elsewhere, views the world as a means to

its own ends; thus it makes the world of less account than Self, and the

Self sets bounds to the greatness of its goods. In contemplation, on the

contrary, we start from the not-Self, and through its greatness the

boundaries of Self are enlarged; through the infinity of the universe

the mind which contemplates it achieves some share in infinity.

For this reason greatness of soul is not fostered by those philosophies

which assimilate the universe to Man. Knowledge is a form of union of

Self and not-Self; like all union, it is impaired by dominion, and

therefore by any attempt to force the universe into conformity with what

we find in ourselves. There is a widespread philosophical tendency

towards the view which tells us that Man is the measure of all things,

that truth is man-made, that space and time and the world of universals

are properties of the mind, and that, if there be anything not created

by the mind, it is unknowable and of no account for us. This view, if

our previous discussions were correct, is untrue; but in addition to

being untrue, it has the effect of robbing philosophic contemplation of

all that gives it value, since it fetters contemplation to Self. What it

calls knowledge is not a union with the not-Self, but a set of

prejudices, habits, and desires, making an impenetrable veil between us

and the world beyond. The man who finds pleasure in such a theory of

knowledge is like the man who never leaves the domestic circle for fear

his word might not be law.

The true philosophic contemplation, on the contrary, finds its

satisfaction in every enlargement of the not-Self, in everything that

magnifies the objects contemplated, and thereby the subject

contemplating. Everything, in contemplation, that is personal or

private, everything that depends upon habit, self-interest, or desire,

distorts the object, and hence impairs the union which the intellect

seeks. By thus making a barrier between subject and object, such

personal and private things become a prison to the intellect. The free

intellect will see as God might see, without a /here/ and /now/, without

hopes and fears, without the trammels of customary beliefs and

traditional prejudices, calmly, dispassionately, in the sole and

exclusive desire of knowledge knowledge as impersonal, as purely

contemplative, as it is possible for man to attain. Hence also the free

intellect will value more the abstract and universal knowledge into

which the accidents of private history do not enter, than the knowledge

brought by the senses, and dependent, as such knowledge must be, upon an

exclusive and personal point of view and a body whose sense-organs

distort as much as they reveal.

The mind which has become accustomed to the freedom and impartiality of

philosophic contemplation will preserve something of the same freedom

and impartiality in the world of action and emotion. It will view its

purposes and desires as parts of the whole, with the absence of

insistence that results from seeing them as infinitesimal fragments in a

world of which all the rest is unaffected by any one man's deeds. The

impartiality which, in contemplation, is the unalloyed desire for truth,

is the very same quality of mind which, in action, is justice, and in

emotion is that universal love which can be given to all, and not only

to those who are judged useful or admirable. Thus contemplation enlarges

not only the objects of our thoughts, but also the objects of our

actions and our affections: it makes us citizens of the universe, not

only of one walled city at war with all the rest. In this citizenship of

the universe consists man's true freedom, and his liberation from the

thraldom of narrow hopes and fears.

Thus, to sum up our discussion of the value of philosophy; Philosophy is

to be studied, not for the sake of any definite answers to its

questions, since no definite answers can, as a rule, be known to be

true, but rather for the sake of the questions themselves; because these

questions enlarge our conception of what is possible, enrich our

intellectual imagination and diminish the dogmatic assurance which

closes the mind against speculation; but above all because, through the

greatness of the universe which philosophy contemplates, the mind also

is rendered great, and becomes capable of that union with the universe

which constitutes its highest good.

BIBLIOGRAPHICAL NOTE

The student who wishes to acquire an elementary knowledge of philosophy

will find it both easier and more profitable to read some of the works

of the great philosophers than to attempt to derive an all-round view

from handbooks. The following are specially recommended:

Plato: /Republic/, especially Books VI and VII.

Descartes: /Meditations/.

Spinoza: /Ethics/.

Leibniz: /The Monadology/.

Berkeley: /Three Dialogues between Hylas and Philonous/.

Hume: /Enquiry concerning Human Understanding/.

Kant: /Prolegomena to any Future Metaphysic/.