synthesis
integration of two opposing representations into one new representation, with a view towards constructing a new level of the object's reality. Philosophy as Critique employs synthesis more than analysis. On the operation of synthesis in the first Critique, see imagination. (Cf. analysis.)
[A77/B103] An action necessary for experience, involving the combination of intuitions (from the faculty of sensibility), concepts (from the faculty of understanding) through an act of judgment (from the faculty of judgment). Referring to a manifold of "received representations of objects", i.e. a manifold of intuitions, Kant writes "if this manifold is to be known, the spontaneity of our thought [i.e., the faculty of understanding] requires that it be gone through in a certain way, taken up, and connected. This act I name synthesis". Again: "By synthesis, in its most general sense, I understand the act of putting different representations together, and of grasping what is manifold in them in one act of knowledge. Such a synthesis is pure, if the manifold is not empirical but is given a priori, as is the manifold of space and time [i.e., as forms of sensibility]". [A78/B103] Kant distinguishes "synthesis in general", which is "the mere result of the power of imagination..a blind but indispensable function of the soul" and synthesis involving concepts, which takes place through the understanding, "to bring synthesis to concepts is a function which belongs to the understanding, and it is through this function of this understanding that we first obtain knowledge properly so called". First, the "synthesis in general" synthesizes together intuitions, synthesizes the manifold of pure intuition. It is this "pure synthesis of intuitions", and not the "raw" given intuitions, which "we bring to concepts" for further synthesis. The synthesis of the manifold of intuition is by the imagination; its result, the pure synthesis of intuitions, which is synthesized together in the understanding; it is the product of this synthesis--of the manifold of pure intuitions "brought to concepts"--of which we are conscious when we have experience. The manifold is "brought to concepts" through two acts of synthesis: first it is synthesized, in the understanding, with the pure concepts of the understanding (the categories), and then, through an act of judgment, it is synthesized with empirical concepts. Somewhere in this process of synthesis of the manifold of intuition the synthesis of the unity of apperception is brought into play; most likely, this is not an separate synthesis, but part of either the pure synthesis of intuitions by the imagination or (more likely, because the unity of apperception is characterized as an act of spontaneity, in which case it is an act of the understanding) the pure synthesis with the categories. (In Kant's considered view, judgment really isn't a third function, but is part of the understanding: the understanding synthesizes--combines intuitions according to a rule--through acts of judgment.)
The categories are crucial to "giving unity" to the manifold of intuition after it has been acted upon by the imagination in the pure synthesis of intuitions. Namely, they give an "a priori synthetic unity" through a pure synthesis of the understanding. After the categories are thus applied, and the manifold of intuition is ordered in this "a priori synthetic unity", the manifold now meets the conditions necessary to be acted upon by the faculty of judgment. Finally, the manifold as it is now (i.e., after the pure synthesis of the imagination and the pure synthesis of the understanding) is synthesized empirically, with empirical concepts, through an act of judgment. In experience we are conscious of this triply-synthesized manifold. (In the Deduction in B, at B130, Kant says that all synthesis takes place through the understanding, including the pure synthesis of the manifold of intuition. The unity of apperception is the a priori synthetic unity after application of the categories.)