The first step is to offer a brief characterisation of contemporary social theories of the Trinity. Most basically, social theorists propose that Christians should not imagine God on the model of some individual person or thing which has three sides, aspects, dimensions or modes of being; God is instead to be thought of as a collective, a group, or a society, bound together by the mutual love, accord and self-giving of its members.
God is presented as having a wonderful and wonderfully attractive inner life. I already mentioned Moltmann’s notion of “the most perfect and intense empathy” existing between the persons. Another proponent of the social doctrine, Cornelius Plantinga, in what is in general a very carefully constructed and restrained presentation, writes of the Trinity as “a zestful, wondrous community of divine light, love, joy, mutuality and verve”, where there is “no isolation, no insulation, no secretiveness, no fear of being transparent to another”. So the interrelatedness of the Trinity, the divine perichoresis, makes God intrinsically attractive.
God’s inner life is [then] presented as having positive implications for that which is not God...In the hands of these thinkers, then, the claim that God though three is yet one becomes a source of metaphysical insight and a resource for combating individualism, patriarchy and oppressive forms of political and ecclesiastical organization. No wonder the enthusiasm: the very thing [i.e., the doctrine of the Trinity] which in the past has been viewed as the embarrassment has become the chief point upon which to commend the Christian doctrine of God: not an intellectual difficulty but a source of insight, not a philosophical stumbling block but something with which to transform the world.
In short, then, I am suggesting we have here something like a three stage process. First, a concept, perichoresis, is used to name what is not understood, to name whatever it is that makes the three Persons one. Secondly, the concept is filled out rather suggestively with notions borrowed from our own experience of relationships and relatedness. And then, finally, it is presented as an exciting resource Christian theology has to offer the wider world in its reflections upon relationships and relatedness.
Projection, then, is particularly problematic in at least some social theories of the Trinity because what is projected onto God is immediately reflected back onto the world, and this reverse projection is said to be what is in fact important about the doctrine.
Theologians are of course free to speculate about social or any other kind of analogies to the Trinity. But they should not, on the view I am proposing, claim for their speculations the authority that the doctrine carries within the Christian tradition, nor should they use the doctrine as a pretext for claiming such an insight into the inner nature of God that they can use it to promote social, political or ecclesiastical regimes.