rstand the
proposition, since the couples are infinitely numerous and therefore
cannot all be known to us. Thus although our general statement _implies_
statements about particular couples, _as soon as we know that there are
such particular couples_, yet it does not itself assert or imply that
there are such particular couples, and thus fails to make any statement
whatever about any actual particular couple. The statement made is about
'couple', the universal, and not about this or that couple.

Thus the statement 'two and two are four' deals exclusively with
universals, and therefore may be known by anybody who is acquainted
with the universals concerned and can perceive the relation between them
which the statement asserts. It must be taken as a fact, discovered
by reflecting upon our knowledge, that we have the power of sometimes
perceiving such relations between universals, and therefore of sometimes
knowing general _a priori_ propositions such as those of arithmetic and
logic. The thing that seemed mysterious, when we formerly considered
such knowledge, was that it seemed to anticipate and control experience.
This, however, we can now see to have been an error. _No_ fact
concerning anything capable of being experienced can be known
independently of experience. We know _a priori_ that two things and two
other things together make four things, but we do _not_ know _a priori_
that if Brown and Jones are two, and Robinson and Smith are two, then
Brown and Jones and Robinson and Smith are four. The reason is that this
proposition cannot be understood at all unless we know that there are
such people as Brown and Jones and Robinson and Smith, and this we can
only know by experience. Hence, although our general proposition is _a
priori_, all its applications to actual particulars involve experience
and therefore contain an empirical element. In this way what seemed
mysterious in our _a priori_ knowledge is seen to have been based upon
an error.

It will serve to make the point clearer if we contrast our genuine _a
priori_ judgement with an empirical generalization, such as 'all men are
mortals'. Here as before, we can _understand_ what the proposition
means as soon as we understand the universals involved, namely _man_ and
_mortal_. It is obviously unnecessary to have an individual acquaintance
with the whole human race in order to understand what our proposition
means. Thus the difference between an _a priori_ general pr