he 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.

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.

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 unde