Books: The Problems of Philosophy

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[1] Kant's 'thing in itself' is identical in _definition_ with the
physical object, namely, it is the cause of sensations. In the
properties deduced from the definition it is not identical, since Kant
held (in spite of some inconsistency as regards cause) that we can
know that none of the categories are applicable to the 'thing in
itself'.

Apart from minor grounds on which Kant's philosophy may be criticized,
there is one main objection which seems fatal to any attempt to deal
with the problem of _a priori_ knowledge by his method. The thing to
be accounted for is our certainty that the facts must always conform
to logic and arithmetic. To say that logic and arithmetic are
contributed by us does not account for this. Our nature is as much a
fact of the existing world as anything, and there can be no certainty
that it will remain constant. It might happen, if Kant is right, that
to-morrow our nature would so change as to make two and two become
five. This possibility seems never to have occurred to him, yet it is
one which utterly destroys the certainty and universality which he is
anxious to vindicate for arithmetical propositions. It is true that
this possibility, formally, is inconsistent with the Kantian view that
time itself is a form imposed by the subject upon phenomena, so that
our real Self is not in time and has no to-morrow. But he will still
have to suppose that the time-order of phenomena is determined by
characteristics of what is behind phenomena, and this suffices for the
substance of our argument.

Reflection, moreover, seems to make it clear that, if there is any
truth in our arithmetical beliefs, they must apply to things equally
whether we think of them or not. Two physical objects and two other
physical objects must make four physical objects, even if physical
objects cannot be experienced. To assert this is certainly within the
scope of what we mean when we state that two and two are four. Its
truth is just as indubitable as the truth of the assertion that two
phenomena and two other phenomena make four phenomena. Thus Kant's
solution unduly limits the scope of _a priori_ propositions, in
addition to failing in the attempt at explaining their certainty.

Apart from the special doctrines advocated by Kant, it is very common
among philosophers to regard what is _a priori_ as in some sense
mental, as concerned rather with the way we must think than with any
fact of the outer world. We noted in the preceding chapter the three
principles commonly called 'laws of thought'. The view which led to
their being so named is a natural one, but there are strong reasons
for thinking that it is erroneous. Let us take as an illustration the
law of contradiction. This is commonly stated in the form 'Nothing
can both be and not be', which is intended to express the fact that
nothing can at once have and not have a given quality. Thus, for
example, if a tree is a beech it cannot also be not a beech; if my
table is rectangular it cannot also be not rectangular, and so on.

Now what makes it natural to call this principle a law of _thought_ is
that it is by thought rather than by outward observation that we
persuade ourselves of its necessary truth. When we have seen that a
tree is a beech, we do not need to look again in order to ascertain
whether it is also not a beech; thought alone makes us know that this
is impossible. But the conclusion that the law of contradiction is a
law of _thought_ is nevertheless erroneous. What we believe, when we
believe the law of contradiction, is not that the mind is so made that
it must believe the law of contradiction. _This_ belief is a
subsequent result of psychological reflection, which presupposes the
belief in the law of contradiction. The belief in the law of
contradiction is a belief about things, not only about thoughts. It
is not, e.g., the belief that if we _think_ a certain tree is a beech,
we cannot at the same time _think_ that it is not a beech; it is the
belief that if the tree _is_ a beech, it cannot at the same time _be_
not a beech. Thus the law of contradiction is about things, and not
merely about thoughts; and although belief in the law of contradiction
is a thought, the law of contradiction itself is not a thought, but a
fact concerning the things in the world. If this, which we believe
when we believe the law of contradiction, were not true of the things
in the world, the fact that we were compelled to _think_ it true would
not save the law of contradiction from being false; and this shows
that the iaw is not a law of _thought_.

A similar argument applies to any other _a priori_ judgement. When we
judge that two and two are four, we are not making a judgement about
our thoughts, but about all actual or possible couples. The fact that
our minds are so constituted as to believe that two and two are four,
though it is true, is emphatically not what we assert when we assert
that two and two are four. And no fact about the constitution of our
minds could make it _true_ that two and two are four. Thus our _a
priori_ knowledge, if it is not erroneous, is not merely knowledge
about the constitution of our minds, but is applicable to whatever the
world may contain, both what is mental and what is non-mental.

The fact seems to be that all our _a priori_ knowledge is concerned
with entities which do not, properly speaking, _exist_, either in the
mental or in the physical world. These entities are such as can be
named by parts of speech which are not substantives; they are such
entities as qualities and relations. Suppose, for instance, that I am
in my room. I exist, and my room exists; but does 'in' exist? Yet
obviously the word 'in' has a meaning; it denotes a relation which
holds between me and my room. This relation is something, although we
cannot say that it exists _in the same sense_ in which I and my room
exist. The relation 'in' is something which we can think about and
understand, for, if we could not understand it, we could not
understand the sentence 'I am in my room'. Many philosophers,
following Kant, have maintained that relations are the work of the
mind, that things in themselves have no relations, but that the mind
brings them together in one act of thought and thus produces the
relations which it judges them to have.

This view, however, seems open to objections similar to those which we
urged before against Kant. It seems plain that it is not thought
which produces the truth of the proposition 'I am in my room'. It may
be true that an earwig is in my room, even if neither I nor the earwig
nor any one else is aware of this truth; for this truth concerns only
the earwig and the room, and does not depend upon anything else. Thus
relations, as we shall see more fully in the next chapter, must be
placed in a world which is neither mental nor physical. This world is
of great importance to philosophy, and in particular to the problems
of _a priori_ knowledge. In the next chapter we shall proceed to
develop its nature and its bearing upon the questions with which we
have been dealing.

CHAPTER IX
THE WORLD OF UNIVERSALS

At the end of the preceding chapter we saw that such entities as
relations appear to have a being which is in some way different from
that of physical objects, and also different from that of minds and
from that of sense-data. In the present chapter we have to consider
what is the nature of this kind of being, and also what objects there
are that have this kind of being. We will begin with the latter
question.

The problem with which we are now concerned is a very old one, since
it was brought into philosophy by Plato. Plato's 'theory of ideas' is
an attempt to solve this very problem, and in my opinion it is one of
the most successful attempts hitherto made. The theory to be
advocated in what follows is largely Plato's, with merely such
modifications as time has shown to be necessary.

The way the problem arose for Plato was more or less as follows. Let
us consider, say, such a notion as _justice_. If we ask ourselves
what justice is, it is natural to proceed by considering this, that,
and the other just act, with a view to discovering what they have in
common. They must all, in some sense, partake of a common nature,
which will be found in whatever is just and in nothing else. This
common nature, in virtue of which they are all just, will be justice
itself, the pure essence the admixture of which with facts of ordinary
life produces the multiplicity of just acts. Similarly with any other
word which may be applicable to common facts, such as 'whiteness' for
example. The word will be applicable to a number of particular things
because they all participate in a common nature or essence. This pure
essence is what Plato calls an 'idea' or 'form'. (It must not be
supposed that 'ideas', in his sense, exist in minds, though they may
be apprehended by minds.) The 'idea' _justice_ is not identical with
anything that is just: it is something other than particular things,
which particular things partake of. Not being particular, it cannot
itself exist in the world of sense. Moreover it is not fleeting or
changeable like the things of sense: it is eternally itself, immutable
and indestructible.

Thus Plato is led to a supra-sensible world, more real than the common
world of sense, the unchangeable world of ideas, which alone gives to
the world of sense whatever pale reflection of reality may belong to
it. The truly real world, for Plato, is the world of ideas; for
whatever we may attempt to say about things in the world of sense, we
can only succeed in saying that they participate in such and such
ideas, which, therefore, constitute all their character. Hence it is
easy to pass on into a mysticism. We may hope, in a mystic
illumination, to see the ideas as we see objects of sense; and we may
imagine that the ideas exist in heaven. These mystical developments
are very natural, but the basis of the theory is in logic, and it is
as based in logic that we have to consider it.

The word 'idea' has acquired, in the course of time, many associations
which are quite misleading when applied to Plato's 'ideas'. We shall
therefore use the word 'universal' instead of the word 'idea', to
describe what Plato meant. The essence of the sort of entity that
Plato meant is that it is opposed to the particular things that are
given in sensation. We speak of whatever is given in sensation, or is
of the same nature as things given in sensation, as a _particular_; by
opposition to this, a _universal_ will be anything which may be shared
by many particulars, and has those characteristics which, as we saw,
distinguish justice and whiteness from just acts and white things.

When we examine common words, we find that, broadly speaking, proper
names stand for particulars, while other substantives, adjectives,
prepositions, and verbs stand for universals. Pronouns stand for
particulars, but are ambiguous: it is only by the context or the
circumstances that we know what particulars they stand for. The word
'now' stands for a particular, namely the present moment; but like
pronouns, it stands for an ambiguous particular, because the present
is always changing.

It will be seen that no sentence can be made up without at least one
word which denotes a universal. The nearest approach would be some
such statement as 'I like this'. But even here the word 'like'
denotes a universal, for I may like other things, and other people may
like things. Thus all truths involve universals, and all knowledge of
truths involves acquaintance with universals.

Seeing that nearly all the words to be found in the dictionary stand
for universals, it is strange that hardly anybody except students of
philosophy ever realizes that there are such entities as universals.
We do not naturally dwell upon those words in a sentence which do not
stand for particulars; and if we are forced to dwell upon a word which
stands for a universal, we naturally think of it as standing for some
one of the particulars that come under the universal. When, for
example, we hear the sentence, 'Charles I's head was cut off', we may
naturally enough think of Charles I, of Charles I's head, and of the
operation of cutting off _his_ head, which are all particulars; but we
do not naturally dwell upon what is meant by the word 'head' or the
word 'cut', which is a universal: We feel such words to be incomplete
and insubstantial; they seem to demand a context before anything can
be done with them. Hence we succeed in avoiding all notice of
universals as such, until the study of philosophy forces them upon our
attention.

Even among philosophers, we may say, broadly, that only those
universals which are named by adjectives or substantives have been
much or often recognized, while those named by verbs and prepositions
have been usually overlooked. This omission has had a very great
effect upon philosophy; it is hardly too much to say that most
metaphysics, since Spinoza, has been largely determined by it. The
way this has occurred is, in outline, as follows: Speaking generally,
adjectives and common nouns express qualities or properties of single
things, whereas prepositions and verbs tend to express relations
between two or more things. Thus the neglect of prepositions and
verbs led to the belief that every proposition can be regarded as
attributing a property to a single thing, rather than as expressing a
relation between two or more things. Hence it was supposed that,
ultimately, there can be no such entities as relations between things.
Hence either there can be only one thing in the universe, or, if there
are many things, they cannot possibly interact in any way, since any
interaction would be a relation, and relations are impossible.

The first of these views, advocated by Spinoza and held in our own day
by Bradley and many other philosophers, is called _monism_; the
second, advocated by Leibniz but not very common nowadays, is called
_monadism_, because each of the isolated things is called a _monad_.
Both these opposing philosophies, interesting as they are, result, in
my opinion, from an undue attention to one sort of universals, namely
the sort represented by adjectives and substantives rather than by
verbs and prepositions.

As a matter of fact, if any one were anxious to deny altogether that
there are such things as universals, we should find that we cannot
strictly prove that there are such entities as _qualities_, i.e. the
universals represented by adjectives and substantives, whereas we can
prove that there must be _relations_, i.e. the sort of universals
generally represented by verbs and prepositions. Let us take in
illustration the universal _whiteness_. If we believe that there is
such a universal, we shall say that things are white because they have
the quality of whiteness. This view, however, was strenuously denied
by Berkeley and Hume, who have been followed in this by later
empiricists. The form which their denial took was to deny that there
are such things as 'abstract ideas '. When we want to think of
whiteness, they said, we form an image of some particular white thing,
and reason concerning this particular, taking care not to deduce
anything concerning it which we cannot see to be equally true of any
other white thing. As an account of our actual mental processes, this
is no doubt largely true. In geometry, for example, when we wish to
prove something about all triangles, we draw a particular triangle and
reason about it, taking care not to use any characteristic which it
does not share with other triangles. The beginner, in order to avoid
error, often finds it useful to draw several triangles, as unlike each
other as possible, in order to make sure that his reasoning is equally
applicable to all of them. But a difficulty emerges as soon as we ask
ourselves how we know that a thing is white or a triangle. If we wish
to avoid the universals _whiteness_ and _triangularity_, we shall
choose some particular patch of white or some particular triangle, and
say that anything is white or a triangle if it has the right sort of
resemblance to our chosen particular. But then the resemblance
required will have to be a universal. Since there are many white
things, the resemblance must hold between many pairs of particular
white things; and this is the characteristic of a universal. It will
be useless to say that there is a different resemblance for each pair,
for then we shall have to say that these resemblances resemble each
other, and thus at last we shall be forced to admit resemblance as a
universal. The relation of resemblance, therefore, must be a true
universal. And having been forced to admit this universal, we find
that it is no longer worth while to invent difficult and unplausible
theories to avoid the admission of such universals as whiteness and
triangularity.

Berkeley and Hume failed to perceive this refutation of their
rejection of 'abstract ideas', because, like their adversaries, they
only thought of _qualities_, and altogether ignored _relations_ as
universals. We have therefore here another respect in which the
rationalists appear to have been in the right as against the
empiricists, although, owing to the neglect or denial of relations,
the deductions made by rationalists were, if anything, more apt to be
mistaken than those made by empiricists.

Having now seen that there must be such entities as universals, the
next point to be proved is that their being is not merely mental. By
this is meant that whatever being belongs to them is independent of
their being thought of or in any way apprehended by minds. We have
already touched on this subject at the end of the preceding chapter,
but we must now consider more fully what sort of being it is that
belongs to universals.

Consider such a proposition as 'Edinburgh is north of London'. Here
we have a relation between two places, and it seems plain that the
relation subsists independently of our knowledge of it. When we come
to know that Edinburgh is north of London, we come to know something
which has to do only with Edinburgh and London: we do not cause the
truth of the proposition by coming to know it, on the contrary we
merely apprehend a fact which was there before we knew it. The part
of the earth's surface where Edinburgh stands would be north of the
part where London stands, even if there were no human being to know
about north and south, and even if there were no minds at all in the
universe. This is, of course, denied by many philosophers, either for
Berkeley's reasons or for Kant's. But we have already considered
these reasons, and decided that they are inadequate. We may therefore
now assume it to be true that nothing mental is presupposed in the
fact that Edinburgh is north of London. But this fact involves the
relation 'north of', which is a universal; and it would be impossible
for the whole fact to involve nothing mental if the relation 'north
of', which is a constituent part of the fact, did involve anything
mental. Hence we must admit that the relation, like the terms it
relates, is not dependent upon thought, but belongs to the independent
world which thought apprehends but does not create.

This conclusion, however, is met by the difficulty that the relation
'north of' does not seem to _exist_ in the same sense in which
Edinburgh and London exist. If we ask 'Where and when does this
relation exist?' the answer must be 'Nowhere and nowhen'. There is no
place or time where we can find the relation 'north of'. It does not
exist in Edinburgh any more than in London, for it relates the two and
is neutral as between them. Nor can we say that it exists at any
particular time. Now everything that can be apprehended by the senses
or by introspection exists at some particular time. Hence the
relation 'north of' is radically different from such things. It is
neither in space nor in time, neither material nor mental; yet it is
something.

It is largely the very peculiar kind of being that belongs to
universals which has led many people to suppose that they are really
mental. We can think _of_ a universal, and our thinking then exists
in a perfectly ordinary sense, like any other mental act. Suppose,
for example, that we are thinking of whiteness. Then _in one sense_
it may be said that whiteness is 'in our mind'. We have here the same
ambiguity as we noted in discussing Berkeley in Chapter IV. In the
strict sense, it is not whiteness that is in our mind, but the act of
thinking of whiteness. The connected ambiguity in the word 'idea',
which we noted at the same time, also causes confusion here. In one
sense of this word, namely the sense in which it denotes the _object_
of an act of thought, whiteness is an 'idea'. Hence, if the ambiguity
is not guarded against, we may come to think that whiteness is an
'idea' in the other sense, i.e. an act of thought; and thus we come
to think that whiteness is mental. But in so thinking, we rob it of
its essential quality of universality. One man's act of thought is
necessarily a different thing from another man's; one man's act of
thought at one time is necessarily a different thing from the same
man's act of thought at another time. Hence, if whiteness were the
thought as opposed to its object, no two different men could think of
it, and no one man could think of it twice. That which many different
thoughts of whiteness have in common is their _object_, and this
object is different from all of them. Thus universals are not
thoughts, though when known they are the objects of thoughts.

We shall find it convenient only to speak of things _existing_ when
they are in time, that is to say, when we can point to some time at
which they exist (not excluding the possibility of their existing at
all times). Thus thoughts and feelings, minds and physical objects
exist. But universals do not exist in this sense; we shall say that
they _subsist_ or _have being_, where 'being' is opposed to
'existence' as being timeless. The world of universals, therefore,
may also be described as the world of being. The world of being is
unchangeable, rigid, exact, delightful to the mathematician, the
logician, the builder of metaphysical systems, and all who love
perfection more than life. The world of existence is fleeting, vague,
without sharp boundaries, without any clear plan or arrangement, but
it contains all thoughts and feelings, all the data of sense, and all
physical objects, everything that can do either good or harm,
everything that makes any difference to the value of life and the
world. According to our temperaments, we shall prefer the
contemplation of the one or of the other. The one we do not prefer
will probably seem to us a pale shadow of the one we prefer, and
hardly worthy to be regarded as in any sense real. But the truth is
that both have the same claim on our impartial attention, both are
real, and both are important to the metaphysician. Indeed no sooner
have we distinguished the two worlds than it becomes necessary to
consider their relations.

But first of all we must examine our knowledge of universals. This
consideration will occupy us in the following chapter, where we shall
find that it solves the problem of _a priori_ knowledge, from which we
were first led to consider universals.

CHAPTER X
ON OUR KNOWLEDGE OF UNIVERSALS

In regard to one man's knowledge at a given time, universals, like
particulars, may be divided into those known by acquaintance, those
known only by description, and those not known either by acquaintance
or by description.

Let us consider first the knowledge of universals by acquaintance. It
is obvious, to begin with, that we are acquainted with such universals
as white, red, black, sweet, sour, loud, hard, etc., i.e. with
qualities which are exemplified in sense-data. When we see a white
patch, we are acquainted, in the first instance, with the particular
patch; but by seeing many white patches, we easily learn to abstract
the whiteness which they all have in common, and in learning to do
this we are learning to be acquainted with whiteness. A similar
process will make us acquainted with any other universal of the same
sort. Universals of this sort may be called 'sensible qualities'.
They can be apprehended with less effort of abstraction than any
others, and they seem less removed from particulars than other
universals are.

We come next to relations. The easiest relations to apprehend are
those which hold between the different parts of a single complex
sense-datum. For example, I can see at a glance the whole of the page
on which I am writing; thus the whole page is included in one
sense-datum. But I perceive that some parts of the page are to the
left of other parts, and some parts are above other parts. The
process of abstraction in this case seems to proceed somewhat as
follows: I see successively a number of sense-data in which one part
is to the left of another; I perceive, as in the case of different
white patches, that all these sense-data have something in common, and
by abstraction I find that what they have in common is a certain
relation between their parts, namely the relation which I call 'being
to the left of'. In this way I become acquainted with the universal
relation.

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