Karen Kilby has been one of the more ardent critics of the social trinitarianism  of theologians like Jürgen Moltmann, Miroslav Volf, John Zizoulas, Catherine LaCugna, and Leonardo Boff. The core of her criticism is that social doctrines of the Trinity presume to know more than is possible about the inner life and relations among the persons of the Trinity. Ultimately, human social relations cannot be modeled on the Trinity, as proponents of social trinitarianism claim, because the nature of the relations among the persons of the Trinity is unknowable. What’s more, theological models that aim to elucidate our understanding of the immanent Trinity based on concepts such as relations, perichoresis, processions, etc., are just models, mere “technical ways of articulating our inability to know.” 
Perceiving that what attracts many to a social doctrine of the Trinity is it’s political appeal, Kilby makes the fascinating suggestion that the unknowability of the Trinity itself has significant social and political implications . While a properly apophatic  approach to the Trinity can’t provide us with a clear programme or vision upon which to model human social relations, the doctrine can serve to remind us that God is beyond our grasp. This should, according to Kilby, be grounds for a deep epistemic humility that might open up space for much more provisional, less absolute, approach to political theology (Though I’m uncertain whether this political apophaticism can offer anything more radical than the prescriptive tolerance that already characterizes liberal polity).
What I find intriguing about Kilby’s suggestion — why I’m writing about it here — is it’s possible implications for a political theology of other animals. It occurs to me that the mystery of the inner life of other animals is analogous to the mystery of the inner life of the triune God. Like the transcendence of God, the unknowability of other animal minds has the potential to unseat human pretensions. It can force us to acknowledge the limits of our own ability to know, and confront us with our own finitude and creatureliness. For Kilby, an apophatic approach to the Trinity serves as a corrective to the overconfidence represented in social doctrines of the trinity, steering us away from attempts to relate to God as an object of knowledge, and directing us instead toward contemplation and active participation in the life of the Trinity. Perhaps then such an apophatic approach can serve more generally to transform our basic orientation to all non-human otherness (whether that of God, or of other animals) from one of objectification to one of contemplation and participation. Perhaps the creaturely humility learned through such an apophatic approach can help us learn to see other animals no longer primarily as objects for human knowledge (whether as symbols on which to project our own meanings, or as literal objects in scientific experimentation), and see them instead as something like divine mysteries to be contemplated but never mastered, never subsumed fully in human thought. Perhaps we can even learn to respect these nonhuman others as co-participants in the economic life of the Trinity.
 “Social trinitarianism” refers primarily to a particular model of the unity of the Divine Persons of the Trinity (Father, Son and Spirit). In contrast to views typically associated with Western theology, which place a primary emphasis on the oneness of God and only subsequently speak of how this one God exists in three Persons, social trinitarianism begins with the three Persons and their relationship with one another in order to show how the three are one. Proponents of social trinitarianism often claim that their model of the trinity contains important egalitarian implications for human social and political relations.
 Kilby, Karen. “Is an Apophatic Trinitarianism Possible?” International Journal of Systematic Theology 12, no. 1 (2010): 65–77.
 Kilby, Karen. “The Trinity and Politics: An Apophatic Approach” Advancing Trinitarian Theology: Explorations in Constructive Dogmatics. Ed. Oliver Crisp and Fred Sanders. Grand Rapids: Zondervan, 2014. 75–93.
 Apophatic theology (from Ancient Greek: ἀπόφασις via ἀπόφημι apophēmi, meaning “to deny”), refers to a particular way of doing theology, or more generally, of speaking about God, that is based on the belief that God’s essence is unknowable or ineffable and that human language is inadequate to describe God (see, e.g., John 1:18; 1Tim 6:16; Rom 11:33-36). Kilby’s novel suggestion is that we should apply this approach, which is usually reserved for very general philosophical speculation about God’s nature, to the specific doctrine of the Trinity.