 The
Problems of Philosophy
Bertrand Russell
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 of 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 Leibniz but
not very common nowadays, is called monadism, because
each of the isolated things is cd 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
universals.
Consider such a proposition as 'Edinburgh is north 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.
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