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 i