Boethius famously defined a person as:
An Individual Substance of a Rational Nature
This definition was intended to include angelic beings. I have always wondered, however, how he squared this definition with the Trinity. I think, in reading Boethius’ De Trinitate and thinking it over, the solution is obvious.
A person is an individual Substance of a rational nature, but not such that for any one person there exists one and only one Substance AND for any one such Substance there exists one and only one person. In fact, the latter half of that conjunction represents precisely the assumption which Trinitarianism calls into question – that one individual substance of a rational nature cannot be more-than-one person. In other words, though it is the case that for every person P there is one and only one individual substance of a rational nature, it is not the case that for every individual substance of a rational nature there is one and only one individual person. Instead we must say that for every individual substance of a rational nature there is at least one person P.
The Trinitarian maintains, therefore, that it is logically possible for one individual substance of a rational nature to be more than one person. I can think of no way to demonstrate any logical absurdity from this, anymore than I can think of a way to demonstrate the logical absurdity of bi-location; just because it runs against (or seems to run against) certain intuitions does not mean that it cannot or should not be accepted, so long as it is both logically possible and plausible (and here all the reasons one has for thinking Christianity true will act to increase the plausibility of there being at least one substance of a rational nature which consists in three persons). As a Trinitarian I would challenge anyone who thinks the Trinity impossible or implausible to provide any good reason to think it is either impossible or implausible.
Interestingly we can follow this thought up by anticipating an objection concerning the grammatical place of substance in any intelligible sentence. One might think that a person is always one individual subject. A subject, as opposed to a predicate, is that of which other things are said, and which is never said of other things. However, since any person P is exactly one subject S, any personal subject S should be exactly one person P. God, then would be three subjects, one for each person of the God-head. However, a substance is just a bearer of predicates, and therefore is that of which things are said, and which is never said of other things. Therefore, it seems, no substance can be more than one person.
The principle mistake isn’t, I think, the assumption that a substance in metaphysics cannot be distinguished in any relevant sense from a subject in grammar ( though that is clearly a mistake; I think we can refer linguistically to each of the individual persons of the Trinity as subjects, but that isn’t yet to have admitted three substances). The principle mistake is thinking that there is no sense in which one individual subject can be more than one person – but that’s just an analogous mistake to the former mistake of thinking that an individual substance cannot be more than one person.