into knowledge. All
synthetic knowledge, whether empirical or _a priori_, requires the
realization of three conditions. In the first place, there must be a
manifold given in perception. In the second place, this manifold must
be 'gone through, taken up, and combined'. In other words, if
synthesis be defined as 'the act of joining different representations
to one another and of including their multiplicity in one knowledge',
the manifold must be subjected to an act of synthesis. This is
effected by the imagination. In the third place, this synthesis
produced by the imagination must be brought to a conception, i. e.
brought under a conception which will constitute the synthesis a
unity. This is the work of the understanding. The realization of _a
priori_ knowledge, therefore, will require the realization of the
three conditions in a manner appropriate to its _a priori_ character.
There must be a pure or _a priori_ manifold; this is to be found in
individual spaces and individual times. There must be an act of pure
synthesis of this manifold; this is effected by the pure imagination.
Finally, this pure synthesis must be brought under a conception. This
is effected by the pure understanding by means of its pure or a priori
conceptions, i. e. the categories. This, then, is the process by which
_a priori_ knowledge is originated. The activity of thought or
understanding, however, which unites two conceptions in a judgement by
analysis of them--this being the act studied by Formal Logic--is the
same as that which gives unity to the synthesis of the pure manifold
of perception--this being the act studied by Transcendental Logic.
Consequently, 'the same understanding, and indeed by the same
activities whereby in dealing with conceptions it unifies them in a
judgement by an act of analysis, introduces by means of the
synthetical unity which it produces in the pure manifold of perception
a content into its own conceptions, in consequence of which these
conceptions are called pure conceptions of the understanding,'[4] and
we are entitled to say _a priori_ that these conceptions apply to
objects because they are involved in the process by which we acquire
_a priori_ knowledge of objects.'

[4] An interpretation of B. 105 init., M. 63 fin.

A discussion of the various difficulties raised by the general drift
of this passage, as well as by its details,[5] is unnecessary, and
would anticipate discussion of the _Transcendental Ded