re 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 fro