Terminological Background
The traditional tripartite view of human nature, or the trichotomy of human persons, refers to the distinguishing of soul and spirit in humans (the body of course being the third part). In Christian theology, this is usually associated with the idea that in regeneration, the spirit is made new but not the soul. Thus "the tension between soul and spirit accounts for many of the struggles of the life of faith" (Richard Gamble, The Whole Counsel of God, Vol I, 247). The bipartite view of human nature (which Gamble argues for), or the dichotomy of human persons, is the view that there is no difference between soul and spirit. In Christian theology, this is often accompanied by interpreting πνευματικός in most of its occurrences in the New Testament as referring to the Holy Spirit of God rather than the spirit of man. I am more familiar with the bi- than the tri- view.
Question
Reading The Sickness Unto Death, I am trying to get my mind around Kierkegaard's understanding of human nature. It seems fairly clear that he does not equate soul and spirit; for example, on the (in)famous first page he says:
The human being is spirit. But what is spirit? Spirit is the self. But what is the self? The self is a relation which relates to itself... In a relation between two things the relation is the third term in the form of a negative unity, and the two relate to the relation, and in the relation to that relation; this is what it is from the point of view of soul for soul and body to be in relation.
Here is another thick quote (page 55 in the Penguin Classics edition):
As soon as man ceases to be regarded under the aspect of spirit (and unless he is regarded in that way, neither can there be any question of despair), but merely as a synthesis of soul and body, then health becomes an immediate characteristic, and it is only in the soul's or the body's sickness that the dialectical arises.
Nevertheless, it also seems to me that this is significantly different than the traditional tripartite view of man; he does not seem to conceptualize spirit as one of three components of man, but the relation of the two components. How does Kierkegaard's position compare to standard bipartite and tripartite views of human nature?