Franke’s Character of Theology, which I began here, turns in the second chapter to the Subject of Theology. The book is written for seminary students and academics.
A Brief of the second chapter
In essence (no pun here), the Subject of theology is the Trinitarian God who is Truth and who makes himself known truly in Christ and Spirit.(Incidentally, some in the emerging movement are “playing” with the doctrine of the Trinity, and this would be a good chapter for them to read.)

More particulars
Franke surveys the historical development of Trinity: its substantive orientation (person, substance, essence) and its relational and historical orientation (relation among persons of Trinity, manifestation in creation, role of redemptive plan in Trinity). Put differently, the internal history and the external history of God.
For those who don’t know the debates and names and issues, this chp would be a good introduction to the topic. The doctrine has worked around two nodes: either rooting one’s discussion in God’s immutable nature or in God’s interpersonal/creative relations. [I think Franke could do more with Eastern Orthodoxy here, but he focuses on the post-Augustinian issues and the interplay of substantive and relational nodes.] A singular development is the 20th Century’s ability to relate Trinity to the historical process of God’s redemptive work, and this is undoubtedly at work (for instance) in the work of many, including Vanhoozer’s The Drama of Doctrine.
Ultimately, he comes to the view that the dominant view today is the relational view of the Trinity (Social God), and that God is missional in nature. Uses Guder at this point to anchor mission in God’s trinitarian being.
This leads Franke to what he has been perhaps aiming at since the beginning of this chapter: a postconservative, evangelical understanding of revelation. It begins with a careful consideration of Chalcedonian christology as the framework for revelation: both human and divine (two persons, one nature), but not mixed or separated. This leads to a genuine incarnation, a genuinely human and limited human named Jesus. Revelation is therefore possible, and Franke appeals here to the wondrously dynamic but always slightly confusing language of Barth in “indirect revelation.” If you like this sort of dialexis, here’s one for you: “God unveils (reveals) himself in and through creaturely veils and that these veils, although they may be used by God for the purposes of unveiling himself, remain veils” (76). Theologians, bless their hearts, do their best to be poetic, but E.B. White would ask them for simpler, clearer expressions.
Here he sounds notes shaping the emerging movement’s theology: human nature is fallen, all theology is shaped by linguistic context, theology is therefore limited, Truth is found in God, but that “God is truly revealed through the appointed creaturely medium” (75). [His view of revelation could get a boost from considering Eucharist and even the historical Jesus question, but he’s already doing enough in this chapter.]
Theology is also nonfoundational, except in the sense that the trinitarian God made known in Christ is the foundation of Truth. Theology is therefore limited, an ongoing conversation, and public.