How do Kants metaphysical and transcendental deductions differ?
What’s “metaphysical” about the metaphysical deduction of the categories can be understood by reference to the Aristotelian definition of metaphysics — the study of being as being. Kant, I believe, was trying to understand what kinds of concepts are used in our thinking about what exists, and how we use these concepts to make judgments. What’s “transcendental” about the transcendental deduction is that Kant is trying to show that these concepts are a priori, and thus transcend all of our thinking, and are used by all thinkers.
Nitpicking: I think that thinking of transcendental concepts as “transcending” tends to confuse my thinking about them. I grasp the thought more clearly when I think of them as the prior and necessary conditions for all possible experience—which necessity, I take it, is the source of their universal and a priori status and thus of their “transcendence,” such as it is. (I know your question was about why they are transcendent; this is just my two pfennigs on the terminology.) Transcendental concepts also refer to what exists; they just refer to it before any experience. Metaphysical concepts concern the further determination of an empirically given object—which is to say that though they are also a priori, they concern objects that are not given a priori. Thus, there is both a transcendental and a metaphysical concept of, say, change as it affects a body, and it is not enough of a distinction to say that transcendental principles are a priori, or that the metaphysical is concerned with
Can’t beat jayder for a concise, precise answer there. It helps to remember that the term “transcendental” got taken up after Kant to have all its current New Age connotations. (Actually, the same thing kind of happened to “metaphysical,” I guess.) It might help to remember that it’s all a distinction about representations (thoughts) and what transcends particular representations and particular representers by appearing in every possible version of them. So it’s not an appeal to some additional realm beyond thought.
