Boethius defined persona as an “individual substance of a rational nature (natuae rationalis individua substantia). This definition is often cited as evidence that medieval Trinitarian theology, deeply influenced by Boethius, did not teach that the Trinitarian “Persons” are persons in the modern sense of the term - that is, not self-conscious centers of will, intention, and activity. For Boethius, “person” has a more (even merely) formal connotation. To say the Three are Persons means only that they are individual instances of a nature.
For instance, Stephen Holmes (Quest for the Trinity) says of the work of John Zizioulas: “By ‘personality' in the modern sense, I assume that we mean the possession of self-determination, and so volition, and of self-awareness, and so cognition.” Holmes doesn't think this is what the church fathers or medieval theologians meant by “person.” Earlier, he approvingly cites Barth, who “offers a lengthy genealogy of the use of ‘person' . . . in technical Trinitarian discourse, highlighting both the habit of offering precise philosophical definitions that have little or nothing to do with ‘personality' (so Boethius; Thomas Aquinas), and the regular expressions of hesitation about the term.”
Similarly, in a critique of social theories of the Trinity, Sarah Coakley cites Gregory of Nyssa's definition of hypostasis as “the conception which, by means of the specific notes it indicates, restricts and circumscribes in a particular thing what is general and uncircumscribed.” Coakley observes that “this ‘definition' is peculiarly devoid of any overtones of ‘personality,' let along of ‘consciousness.' A hypostasis is simply a distinct enough entity to bear some ‘particularizing marks' - the the case of the Trinity the distinctions of different causal relations within the Godhead” (essay in The Trinity, 133).
Advocates of a social doctrine often draw the same conclusion regarding Boethius, but to criticize the absence of “personality” in ancient and medieval notions of person.
No doubt concepts of “person” and “personality” have changed over time. But that doesn't close the question. Go back to Boethius: The nature of which persons are individual substances is rational nature. So the question is not merely, “What does persona mean?” but “What characterizes a rational nature? What capacities do beings possessing rational nature possess?”
For Boethius, rational nature at least have involves a capacity for intellection, for following premises to conclusions. Can we say more? Is an individual substance of rational nature, for example, self-conscious? Boethius would have thought so, since he considered reason to be immaterial and agreed with the philosophical consensus that immaterial thinkers were aware of their own thoughts, aware of themselves as thinkers. He believed that beings with rational natures possessed will; a rational being without volition would have been nonsensical. (Thanks to Prof John Marenbon for clarifying Boethius on these points in private communication. He is not responsible for the theological musings that follow.)
If the divine Persons are instances of rational nature, they must possess a divine capacity analogous to what humans experience as self-consciousness. Going beyond Boethius, we may ask: Of what are the divine Persons conscious when they are self-conscious? Is the Son conscious of being God, or also of being Son? Is the Son aware that He is Son? It would be exceedingly odd to say No. More than odd: Jesus knows that He's Son (cf. especially John's gospel), and the Person of the incarnate Son is the eternal Son, so the eternal Son must know that He is Son.
But then we must add: The Father is not aware of Himself as Son Son, nor is the Spirit. The Father and Spirit cannot be aware of themselves as Son, because they are not. The Father rather knows Himself as Father of the Son by the Spirit, the Spirit knows Himself as the Spirit of the Father and Son. As individual substances of rational nature, their self-consciousness is individuated, and the “contents” of self-consciousness must be to this extent distinct. Even on the Boethian definition of persona, then, we seem to verge toward “personality,” the “social Trinitarian” idea that each persona is a center of self-consciousness. It hardly seems like a verge at all; it seems to be implied in the definition of persons as instances of rational nature.
If the persons individual substances of rational nature, then they also will. But what do they will? Does the Son will Himself to be Son? I am not suggesting that the Son is Son by virtue of willing His Sonship, but surely the Son isn't unwillingly Himself. The will to be what one is would also seem to be an aspect of rational nature. Trees don't have the option to will to be what they are; I do, though I can also will to not-be. But then we must ask: Does the Father will Himself to be Son, or the Spirit. Surely not: The Father is willingly Father of the Son in the Spirit, the Spirit willingly Spirit of Father and Son. And that means, again, that the will of God is hypostatized, on Boethius's definition of persona as a individual substance of a rational nature.
Suppose rational nature includes also capacity for communication or language. Does rational nature imply capacity for some sort of relationship with other beings with like capacities? I don't know what Boethius would say, though having a logikos nature would seem to imply a capacity for logos.
Boethius is not a social Trinitarian, of course. And perhaps his definition of personhood isn't a good one. But italicizing the rational nature part of his definition is illuminating. It suggests that the gap between Boethius and recent Trinitarian theology is not as wide as both sides have sometimes thought.