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Kant and Transcendental Deductions

The key to the first and most compelling parts of the CPR is the deduction of the categories of the understanding.
By "deduction" K does not mean something one does with one's taxes, or the sale price of shampoo. Nor does he mean the process that Sherlock H uses to solve cases. His use refers to a juridical environment, to law courts, in which, when an argument is presented, one can offer either a de facto or a de juris defense or prosecution. The boundary is of course permeable but the idea is clear enough. Sometimes attorneys ask by what right someone did something. We use the concept in a familiar way: what right did the neighbor have to buy a goat and pen it in his back yard, where it bleats the day away while I am trying to complete my Kant midterm? There is no question of fact here - I can look over the fence and see the goat and I can definitely hear it. The question is justification. Does my neighbor have a legal right, a warrant, for keeping a goat? And here the question is one of law. Is my property zoned for agricultural uses, and does keeping a goat count as such a use?
Think of the question of how, by what right, do concepts, or the twelve a priori categories, which K thinks are given as necessary parts of human reason, apply to the manifold of sensation, to order it into experience and then into propositional knowledge? First the categories get applied to make experience possible in the first place: "This is a creepy, sticky chair I am sitting in", then they allow us to make more general judgments: "Plastic chairs in small town bus stations tend to have unpleasant surfaces", and then even more general judgments: "Inexpensive plastic materials used for chair seats and backs tend to retain viscous liquids and semi-liquids, for the following chemical/physical reasons ... " (there follows an unintelligible but accurate scientific account of the composition of the chair plastic). 
K's question is this: how come these concepts, which in themselves have nothing in common with sense manifolds, get to apply to them? 
There are really three answers.
First, and this is in a sense one K did not write about but assumed -- we do make such applications all the time and they work quite nicely. In fact, as human history moves on, we seem to be able to make such judgments even more accurately, and to predict and control what happens to us in the world on the basis of that knowledge. 
Second, and this is one that K covers, we are justified because we are able, by a mysterious process K cannot exactly explain rationally (that is, by using the very concepts he is trying to justify), to schematize the sense manifold, that is, we are able to create, via the faculty of imagination (our mental power to produce visual, tactile, olfactory images), general templates that are part concept and part sensory detail, which we use as halfway houses between sense material and pure concepts. These templates, which have a priori elements -- the conceptual rules -- are ultimately empirical, because they develop over time. It must be true, of course, that we develop purely a priori schemata(plural of 'schema') around our thinking of the pure a priori forms of intuition. These are the ideal images (circle, square, polyhedron. etc.) that we use in geometry, and K might even see numbers in this way, as general images of different quantities. 
Third, we are justified because all of the categories are unified into a single system, of which we are always aware, by what he calls the transcendental unity of apperception, or an a priori "I think" that he says accompanies all our judgments and experience. K postulates that there must be this persisting "I think" to make experience itself possible, because, of course, to have experience as an object of thought, to be able to say things about our experiences, there must be a unifying second-order awareness that we are having experiences. 
Thus we know that we know, we think that we are experiencing, we are always already aware-that. If we did not have this then we would not be justified in saying that the categories apply to sense material because we would not even be aware that they did or did not. What really justifies us in saying that we can apply the categories is our reflexive awareness that we do so. So, the "justification" is not really about the fittingness of the categories but of the fact that we must be unified and unifying subjects in order to have human experience.
The real point here is to argue that self-consciousness, of a highly formal rather than a psychological sort, is required for human experience and knowledge to be possible.
Major point: for K, this "I think" transcends direct experience. We know that it must be operating or we would not be making judgments but it lies, as do the things-in-themselves, outside of our direct experience. We know that we are such subjects because we make the judgments but we never, ever directly live that formal subject-hood. 
This is really what 'transcendental' means in the final analysis. Things that we know must be there to make experience possible, but that we cannot ever touch directly, like things in themselves and the 'I think', are transcendental conditions that make experience possible and thinkable. But the conditions can never become direct parts of the game. They are shadowy presences behind, or at the edges, of the scene, never quite able to be grasped as themselves and therefore, for some, as the American philosopher Stanley Cavell speculates, causes for despair. The despair is born from the fact that both the world and the self, my two anchors, are always only represented to me-as-consciousness. Thus I am always doubly alienated, and assailed by the idea that there might ultimately not be anything behind me or appearances, that this is all a terrible dream.  

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