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== Introduction ==
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The Problems of Philosophy, one of Russell's defining writings, offers a brief and accessible guide to the problems of philosophy. Focusing on problems he believes will provoke positive and constructive discussion, Russell concentrates on knowledge rather than metaphysics, steering the reader through his famous 1910 distinction between "knowledge by acquaintance and knowledge by description," and introducing important theories of Descartes, Kant, Hegel, Hume, Locke, Plato, and others to lay the foundation for philosophical inquiry by general readers and scholars alike. The edition on the PhilosophyArchive.com servers is the Project Gutenberg 2002 edition.
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<b>Title: </b>The Problems of Philosophy
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<br><hr></small><h3>
The Problems of Philosophy<br>
Bertrand Russell</h3>
<br><a name="preface"></a><h4>
PREFACE</h4>
<br>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.
<br>I have derived valuable assistance from unpublished writings of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.
<br>1912
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== CHAPTER I ==
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APPEARANCE AND REALITY
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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?
<br>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.
<br>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?
<br>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.
<br>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.
<br>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.'
<br>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.
<br>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.
<br>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.
<br>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?
<br>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.
<br>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.
<br>

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== CHAPTER II ==
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THE EXISTENCE OF MATTER</h4>
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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?
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
</html>
== CHAPTER III ==
<html>
THE NATURE OF MATTER
<br>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?
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
</html>
== CHAPTER IV ==
<html>
IDEALISM

<br>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.
<br>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.
<br>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.
<br>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.
<br>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'.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.)
<br>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.
<br>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.
</html>
== CHAPTER V ==
<html>
KNOWLEDGE BY ACQUAINTANCE AND KNOWLEDGE BY DESCRIPTION
<br>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'.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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'.
<br>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.
<br>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.
<br>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_.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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_.
<br>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.
<br>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.
</html>
== CHAPTER VI ==
<html>
ON INDUCTION
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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?
<br>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.
<br>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.
<br>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.
<br>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.
<br>The principle we are examining may be called the _principle of
induction_, and its two parts may be stated as follows:
<br>(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;
<br>(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.
<br>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:
<br>(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;
<br>(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.
<br>It should be noted that probability is always relative to certain
data.  In our case, the data are merely the known cases of coexistence
of A and B.  There may be other data, which _might_ be taken into
account, which would gravely alter the probability.  For example, a
man who had seen a great many white swans might argue, by our
principle, that on the data it was _probable_ that all swans were
white, and this might be a perfectly sound argument.  The argument is
not disproved ny the fact that some swans are black, because a thing
may very well happen in spite of the fact that some data render it
improbable.  In the case of the swans, a man might know that colour is
a very variable characteristic in many species of animals, and that,
therefore, an induction as to colour is peculiarly liable to error.
But this knowledge would be a fresh datum, by no means proving that
the probability relatively to our previous data had been wrongly
estimated.  The fact, therefore, that things often fail to fulfil our
expectations is no evidence that our expectations will not _probably_
be fulfilled in a given case or a given class of cases.  Thus our
inductive principle is at any rate not capable of being _disproved_ by
an appeal to experience.
<br>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.
<br>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.
<br>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.
</html>
== CHAPTER VII ==
<html>
ON OUR KNOWLEDGE OF GENERAL PRINCIPLES</h4>
<br>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.
<br>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.
<br>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.'
<br>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'.
<br>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.
<br>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'.
<br>They are as follows:
<br>(1) _The law of identity_: 'Whatever is, is.'
<br>(2) _The law of contradiction_: 'Nothing can both be and not be.'
<br>(3) _The law of excluded middle_: 'Everything must either be or not
be.'
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>_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.
<br>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.
<br>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]
<br>[1] Cf.  A.  N.  Whitehead, _Introduction to Mathematics_ (Home
University Library).
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
</html>
== CHAPTER VIII ==
<html>
HOW A PRIORI KNOWLEDGE IS POSSIBLE
<br>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.
<br>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.
<br>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.
<br>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'.
<br>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.
<br>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.
<br>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.
<br>[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'.
<br>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.
<br>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.
<br>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.
<br>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 iaw is not a law of _thought_.
<br>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.
<br>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.
<br>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.
</html>
== CHAPTER IX ==
<html>
THE WORLD OF UNIVERSALS
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
</html>
== CHAPTER X ==
<html>
ON OUR KNOWLEDGE OF UNIVERSALS</h4>
<br>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.
<br>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.
<br>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.
<br>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.
<br>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_.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>
</html>
== CHAPTER XI ==
<html>
ON INTUITIVE KNOWLEDGE
<br>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.
<br>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.
<br>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.
<br>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'.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>
</html>
== CHAPTER XII ==
TRUTH AND FALSEHOOD
<html>
<br>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.
<br>There are three points to observe in the attempt to discover the
nature of truth, three requisites which any theory must fulfil.
<br>(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.
<br>(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.
<br>(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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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'.
<br>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.
<br>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_.
<br>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.
<br>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.
<br>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.
</html>
== CHAPTER XIII ==
<html>
KNOWLEDGE, ERROR, AND PROBABLE OPINION</h4>
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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_.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>
</html>
== CHAPTER XIV ==
<html>
THE LIMITS OF PHILOSOPHICAL KNOWLEDGE</h4>
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>
<html>
== CHAPTER XV ==
</html>
THE VALUE OF PHILOSOPHY
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>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.
<br>

<a name="bio"></a>
<h4>BIBLIOGRAPHICAL NOTE</h4>
<br>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:
<br>Plato: Republic, especially Books VI and VII.
Descartes: Meditations.
Spinoza: Ethics.
Leibniz: The Monadology.
Berkeley: Three Dialogues between Hylas and Philonous.
Hume: Enquiry concerning Human Understanding.
Kant: _Prolegomena to any Future Metaphysic.
<br><br>
<br>
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[[Category:Bertrand Russell Primary Sources]]
[[Category:Primary_Sources]]