THE PROBLEMS OF PHILOSOPHY

By Bertrand Russell

Contents

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I have derived valuable assistance from unpublished writings of G. E.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 by 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 premisses 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 premisses; 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 premisses, 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 premisses 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 Cassio. We cannot
say that this belief consists in a relation to a single object,
‘Desdemona’s love for Cassio’, 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 Cassio’; but it is almost as difficult to
suppose that there is such an object as this, when Desdemona does not love
Cassio, as it was to suppose that there is ‘Desdemona’s love for Cassio’.
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
Cassio, he must not have before his mind a single object, ‘Desdemona’s
love for Cassio’, or ‘that Desdemona loves Cassio ‘, 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 Cassio must all be terms in the relation which subsists
when Othello believes that Desdemona loves Cassio. 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 Cassio. 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 Cassio, Othello is the subject, while
the objects are Desdemona and loving and Cassio. 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 Cassio loves Desdemona differs from
his judgement that Desdemona loves Cassio, 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
Cassio 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 Cassio, then there is a complex unity, ‘Desdemona’s
love for Cassio’, 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 premisses 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 beleagured
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: