Second, my problem with Turcescu’s definition lies in the bolded part: “[A person is] an indivisible, unique and therefore non-replicable unity in human existence.”

Again, as I recall, his definition is seeking to define personhood in such a way that takes into consideration the triune persons who share a common essence but have true personal properties nonetheless. I imagine that indivisible, unique and non-replicable unity are ways to try and achieve a common ground with trinitarian thought that could have meaningful import into anthropology. Doing so might seem odd, even arbitrary, but it is certainly not imprecise simply because it isn’t intuitive.

And I fail to see how “an indivisible, unique and therefore non-replicable unity” is more open to communion.

To begin, Turcescu offers a broad definition of a person: “A person is ‘an indivisible, unique and therefore non-replicable unity in human existence.’”

I find that this definition narrows it down to much. It is true that ‘an indivisible, unique and therefore non-replicable unity in human existence’ is a person. But it’s not true that a person necessarily is ‘an indivisible, unique and therefore non-replicable unity in human existence.’ That would leave out divine and angelic persons. (And eventually rational ‘alien’ persons.)

It seems to me that it’s better to use Boethius’ definition, found in chapter 4 of his treatise against Eutyches and Nestorius. There he considers the two greek terms οὐσία (ousia, ‘nature’) and ὑποστασις (hypostasis, ‘person’). He defines οὐσία as “the specific property of any substance” and ὑποστασις as “the individual substance of a rational nature.” A person would then be a substance with a particular/specific rational nature. Which, it seems to me, would include God and the Angels. (And eventually rational ‘aliens.’)

I can’t think of anything on this. What I said about persons is my own attempt to apply some of this stuff to persons. Of course, Aquinas has a nice discussion of the doctrine of analogy in ST. prima pars Q13.

On the Aristotelian model (as I understand or better as I incorporate it) the notion of analogy or homonymy plays an important role. The paradigmatic example here is health. It makes sense to say that John is healthy, that the dinner is healthy and that John’s urine is healthy. But the last two uses of health are related to the first and the first is what allows or the last two to make any sense. The primary meaning or role of health has to do with properly functioning organisms. A dinner is health to the degree that it contributes to an organism’s health and urine is healthy to the degree that it reveal the health of the organism. So, the last two uses of health are derivative. The first use (John is healthy) is primary or fundamental. Because of this the following inference is invalid:
John is healthy.
The meal is healthy.
Hence, John and the meal are healthy.

It’s invalid because healthy does not have the same sense in each of the premises. No doubt all of this is so far familar. But notice that the same is likely true with respect to the following inference:

God is wise
John is wise
Hence, God and John are wise.

Just as the first inference is invalid so is this one and for similar reasons. God is wisdom, but John is not. Whenever we attribute a feature that we are familar with to God, we are almost always (I’d say always) guaranteed to run into the above kind of invalid inference. On a Platonic construal every feature has a paradigm that it is an instance of. So, the above inferences will turn out valid. But on the Aristotelian picture it’s a mistake to think that when we predicate F of a human and F of some other kind of substance, F is idential throughout. The substance of the thing transforms the Fness of that thing. For example, while it is true that humans are animals we are not animals in the same sense as cows or dogs are. Our animality is radically transformed by our rationality and our sociality. We might put it like this: our animality is saturated with our rationality in such a way that the same practices that all animals typically engage in are radically tranformed in the life of a rational animal. For example, sex and eating are comman activities animals engage in. But humans can engage in these activities in a rational way whereas bees or dogs cannot. Thus the activities themselves are different depending on the nature of the substance that engages in them.

Here’s another way to think of all of this (and this relates to something you gesture towards in your most recent post): For the Aristotelian, various activities or features or parts of an organism must be analysed or understood in light of an understanding or apprehension of the the nature of the organism. In this way the whole preceeds the part or the activity or feature.

Now getting to the theological stuff we have to be careful when we attempt to attribute features to God that are also features of His creatures. His nature transforms these features in such a way that they do not have the same sort of application to Him that they do to the creature. I suspect being a person is one such example. God is the paradigmatic person (or to avoid heresy God is paradigmatically personal) and all other persons are analogically related to Him.

I hope this helps. If it doesn’t please say so. this has been helpful for me too.

Here are some random, and perhaps not too relevant thoughts:

I too am not comfortable with property talk in this context. One problem with such talk is that it seems to suggest that the divine persons are persons just like you and me but have some really neat properties added to them to turn them into divine persons.

One way to think about this is in terms of Platonic and Aristotelian conceptions of things and properties. On a Platonic conceptions the above picture may make some sense. Person is univocal. If S is a person and S* is a person, then S and S* are persons. That is, it does not matter what kind of person S or S* is. Being a person is the same for all persons.

On an Aristotelian conception the above conditional is not necessary true (i.e. if S is a person and S* is a person, then S and S* are persons is not necessarily true). The reason is that person is not, in general, univocal, and so it may (slightly) change meaning within the conditional statement. That is, being a divine person and being a human person are not different species in the same genus of persons (genus–persons; species–divine or human or angelic or …). Instead a divine person is only analogically related to a human person. It is simply impossible to add properties to a generic person and somehow wind up with a divine person.

So, on the Aristotelian conception the property talk is misleading since its the individual (or kind) that determines which properties the thing can have in the first place. And since the kind (if I may so call it) divine person is not the same kind as human person there is no chance of the properties of the former kind have much to do with the properties of the latter kind (if it even makes literal sense to talk of divine persons having properties at all).