This is a significant departure from the Church's historic doctrine of the Trinity, within which the language of 'person' functions rather differently and does not carry the meaning that it does in popular parlance. The 'persons' of the Trinity are not three distinct centres of consciousness or agencies--which would suggest something resembling tritheism and undermine the oneness (and the simplicity) of God. The persons, or hypostases, are three instantiations of the one divine nature. However, most of the things that we would associate with personhood--knowledge, will, love, wisdom, mind, etc.--are grounded, not in the three hypostases, but in the one divine nature. In this respect, if we were working in terms of our modern usage of the term 'person', in some respects God might be more aptly spoken of as one 'person' with three self-relations, rather than as one being in three persons. This language still falls far short, though. - See more at: http://www.reformation21.org/blog/2016/07/the-eternal-subordination-of-t-2.php#sthash.clr3cPau.dpuf
That's a very flawed formulation:
i) I'm struck by how so many theologians think it's more important to guard agains the appearance of tritheism than unitarianism. Do they think unitarianism is less heretical then tritheism?
ii) Alastair's formulation works within a Platonic paradigm in which the divine nature is like an abstract universal which members of the godhead exemplify, as property instances of the divine nature. They participate in the psychological properties of the divine nature. Knowledge, love, will, wisdom, mind, &c. primarily inhere in the nature, and only derivatively in the Father, Son, and Spirit.
iii) Does his formulation do justice to Biblical revelation? For instance, in the Fourth Gospel, doesn't the Son have a first-person viewpoint distinct from the Father's first-person viewpoint? Doesn't that dovetail with the modern connotation of a "person"?
Doesn't the Fourth Gospel project that back into the preexistent relationship between Father and Son? In other words, when the Son comes into the world, that's a carryover from his antemundane existence and status.
Likewise, take Paul's analogy in 1 Cor 2:10-11. Doesn't that define the personality (as well as divinity) of the Spirit in "modern" psychological terms? By contrast, I find Alastair's formulation strikingly modalistic.