Paragraph 34 stresses that there can be no objective principles of taste. Such a principle would make it possible to deduce by syllogism that something is beautiful. But Kant believes that to experience beauty I must immediately feel pleasure in the presentation of the object, and not be persuaded of its beauty by proof. Critics, as Hume says, may reason better than cooks, but they still cannot expect to establish the value of a work of art by way of proof. They can only expect their judgments to be based on reflection on the proper state of their immediate pleasure or pain in response to the object. Kant stresses that all precepts and rules need to be rejected here. (This may go against Hume, who does allow empirically grounded principles of taste.)
To be sure, reasoning can help critics perfect and extend their judgments of taste. But rather than finding a universal formula, critics, when acting according to their proper role, investigate the cognitive faculties and their practice of making judgments, as well as explaining, by examples, the form of purposiveness which "constitutes the beauty of the object." (The latter seems to be what we normally expect of critics, although to see the objects of criticism as simply examples seems to put it the wrong way around.)
The critique of taste, then, is "the art or science of reducing to rules the reciprocal relation between the understanding and the imagination in the given representation." This is a phenomenological point, a point about the structure of our experience of an aesthetic object. The representation in our mind, say of the Virginia State House by Thomas Jefferson, will exhibit in it this relation between understanding and imagination. The reference to "reducing to rules" is puzzling since we are supposed to reject objective principles, but see below. The reciprocity of the relation is also explained below.
The critique of taste will explain the accordance or discordance between the two faculties, imagination and understanding. It is an art if it only shows by examples; whereas it is a science if it derives this possibility from the nature of these faculties. Here, by “science,” Kant means the sort of thing he is doing is doing here. He calls this "Transcendental Critique." The Transcendental Critique derives the subjective principle of taste as an a priori principle. This is all Kant means by "reducing to rules." As art, the critique of taste applies physiological (psychological) rules concerning how taste actually proceeds. He also thinks it "criticizes the products of beautiful art..." although it is not clear how it could do this.
#35 The principle of taste is the subjective principle of judgment in general.
The subjective condition of all judgments is the faculty of judgment itself. For beauty to exist there has to be an accord of the two representative powers: the imagination and the understanding. And “because no concept of the object lies here at the basis of the judgment, it can only consist in the subsumption of the imagination itself…under the conditions that the understanding requires to pass from intuition to concepts.” Moreover, “because the freedom of the imagination consists in the fact that it schematizes without any concept, the judgment of taste must rest on a mere sensation of the reciprocal activity of the imagination in its freedom and the understanding with its conformity to law.” This is hard to parse out. The judgment of taste rests on a feeling in which we judge the object by the purposiveness of its representation in respect of the furtherance of the cognitive faculty in its free play. In taste there is subsumption not of intuitions under concepts but of the faculty of intuitions, that is, the imagination, under the faculty of concepts, the understanding. This is freedom harmonizing with conformity to law. To discover the ground of a deduction of taste we need to consider the form of this kind of judgment.
This all goes along with the tenor of the rest of the Critique of Judgment. Taste is a yin-yang thing: it involves both the imagination and the understanding, both freedom and law in a reciprocal relationship. Kant elsewhere talks about the need for academic training for the genius artist, a similar kind of balance.
Kant says "the judgment of taste is not determinable by concepts" for "it is based only on the subjective formal condition of a judgment in general." He further says "the subjective condition of all judgments is the faculty of judgment itself."
It is puzzling exactly what is going on here. I think that Kant is stressing that in judgments of taste there is a movement from intuition to concepts as we also find in objective reasoning, and yet the concepts at the end of the line are indeterminate and hence not true concepts of the understanding. Later, these will be referred to as aesthetic ideas.
What however should we make of the following sentence: "It [the judgment of taste] must therefore rest on a feeling, which makes us judge the object by the purposiveness of the representation (by which an object is given) in respect of the furtherance of the cognitive faculty in its free play." Kant seems to be saying that the judgment of taste rests on some fusion of the purposiveness in the object with the sense that free play furthers our cognitive powers, a fusion of something seemingly objective and something else seemingly subjective. It is also hard to know what it means to subsume the faculty of intuitions under the faculty of concepts so that the first "in its freedom harmonizes with the latter in its conformity to law" and how this relates to appropriate appreciation of an art object.
Well, as you can see, I have not fully understood these two chapters, but this is the best I can do for now.