Gillis Harp has written a masterful essay explaining the difficulties and contradictions inherent in the “Three Streams, One River” approach to Anglicanism that seems to have become embedded in the ACNA as an almost creedal doctrine. Be sure to read the entire thing:
But in looking at the new “three streams” typology, one meets with at least four difficulties. First, it takes a possibly helpful (but over-simplified) descriptive model of the Western church during the middle part of the twentieth century and turns it into a prescriptive theological ideal. Newbigin’s original description may be an easy way to conceptualize some of the different traditions within Christianity in the effort to facilitate ecumenical discussion, understanding and cooperation. But using it to create a kind of doctrinal synthesis is, however, an entirely different matter. The differences between the three streams (at least as commonly identified by champions of the model) are not all simple differences of emphasis; some actually constitute opposed positions based upon very different readings of the Bible.
Two of the three streams, for instance, reject the classical Pentecostal teaching about a post-conversion baptism of the Holy Spirit or the normative practice of Glossolalia and prophecy. Two of the three have historically repudiated the Roman Catholic understanding of the ordained ministry as sacerdotal, and would have a very different view of the nature and number of the sacraments. And, despite measured progress in ecumenical dialogue since the 1950s, one of the three does not understand justification as primarily the gracious imputation of Christ’s righteousness to individual believers received through faith alone. These are not peripheral matters. Wishful thinking about a tidy Hegelian historical synthesis of the three streams will not erase the contradictions. As Philip E. Hughes once wrote about dialogue between Roman Catholics and Anglicans during the early 1970s, “to resort to fine-sounding but ambivalent terminology is to paper over the cracks and then to call attention to the attractiveness of the wallpaper.”...more