Historically plausible: Atonement theology is an interpretation of events, not a recital of “bare facts,” which is impossible in any case. But that interpretation must make sense of the historical events, not by transcending phenomena into a noumenal realm of meaning, but by tracing and perhaps extrapolating the logic of the events. Successful atonement theology must, for instance, make sense of Jesus as a figure in the first-century Judaism dominated by Rome. A successful atonement theory has got to show how the death and resurrection of Jesus is the key to human history, which means that atonement theory has to provide and account of human history: It has to be a theory of everything.
Levitical: A successful atonement theology treats Jesus’ death (at least) as a sacrifice, and it must be able to show that Jesus’ sacrifice fulfills Levitical ritual in historical events.
Evangelical: Successful atonement theology must arise from within the Gospel narratives rather than be an imposition from outside (even a Pauline outside).
Pauline: Atonement theology must make sense of the actual words and sentences and arguments in Paul’s letters.
Inevitable: A successful atonement theology should leave the impression of inevitability: “Was it not necessary for the Christ to suffer these things and to enter into His glory?” (Lk. 24:26 NASB). Jesus should appear to be the obvious divine response to the human condition. Like the denouement of a well-constructed drama, the cross and the resurrection should emerge as the most fitting climax to the history of Israel among the nations, as the climax of the history of sacrifice.
Fruitful: A successful atonement theology must offer a framework for making sense not only of the history of Jesus but also of the subsequent history of the church and of the world. It must, for instance, not shrink from addressing the apparent failure of the atonement, the palpable fact that the world Jesus is said to have saved is self-evidently not saved. (19-20)
Rishmaway adds a couple more categories: Christological (” Leithart’s criteria for atonement theology are, for the most part, explicitly concerned with making sense of the plot. I’m saying, we also need to explicitly call for a careful account of the characters.,” he says) and Theological (“For a successful atonement theology, you need to be able to give something of a sketch of the kind of God who would and could become man and why.”)
I’m in agreement with both parties, but am more satisfied with the added Christological category than the broader ‘Theological’ one. Probably because it seems the second category could also be divided into various subsets and we just haven’t found the words yet to do it.