o be related to another as the double of it, that quantity must be
twice as large as the other. In the same way, proceeding to Kant's
instances, we see that if we are to combine or relate a manifold into
a triangle, and therefore into a triangle of a particular size and
shape, the elements of the manifold must be lines, and lines of a
particular size. If we are to combine a manifold into a house, and
therefore into a house of a certain shape and size, the manifold must
consist of bodies of a suitable shape and size. If we are to relate a
manifold by way of necessary succession, the manifold must be such
that it can be so related; in other words, if we are to relate an
element X of the manifold with some other Y as the necessary
antecedent of X, there must be some definite element Y which is
connected with, and always occurs along with, X. To put the matter
generally, we may say that the manifold must be adapted to or 'fit'
the categories not only, as has been pointed out, in the sense that it
must be of the right kind, but also in the sense that its individual
elements must have that orderly character which enables them to be
related according to the categories.

Now it is plain from Kant's vindication of what he calls the affinity
of phenomena,[10] that he recognizes the existence of this
presupposition. But the question arises whether this vindication can
be successful. For since the manifold is originated by the thing in
itself, it seems prima facie impossible to prove that the elements of
the manifold must have affinity, and so be capable of being related
according to the categories. Before, however, we consider the chief
passage in which Kant tries to make good his position, we may notice a
defence which might naturally be offered on his behalf. It might be
said that he establishes the conformity of the manifold to the
categories at least hypothetically, i. e. upon the supposition that
the manifold is capable of entering into knowledge, and also upon the
supposition that we are capable of being conscious of our identity
with respect to it; for upon either supposition any element of the
manifold must be capable of being combined with all the rest into one
world of nature. Moreover, it might be added that these suppositions
are justified, for our experience is not a mere dream, but is
throughout the consciousness of a world, and we are self-conscious
throughout our experience; and therefore it is clear that the manif