You are perhaps thinking of the three persons as separate ontological entities.
They are not. There is only one ontological entity called God.
Does personhood “add something” to your humanity? Does it make you into two entities instead of one ontological human being? No. Personhood expresses your humanity in such a way as to make you a subject, capable of saying “I.”
“Adding” personhood to human nature does not create two human beings.
Neither does three persons in the one Godhead create three divine beings.
The problem is that this analogy leaves out an important detail of the trinity, namely, that each person is 100 percent God.
If my personhood is identical to my humanity, fine…but if I have two personhoods, each 100 percent my humanity, yet not identical to each other…then I have a serious contradiction to deal with. If my personhood is my humanity, and a second personhood is also my humanity…then the first personhood and the second personhood must be identical to each other. If they aren’t, then logically, they are either a) not both my humanity or b) not 100 percent my humanity (ie, there is something that makes the two not identical above and beyond the identical portion.)
So it’s not that logic requires that personhood add something, it’s that in order for there to be
distinctions between persons of the same substance, there must be something other than the substance that constitutes the distinction. Otherwise, you have the contradictory formula that follows:
- Person 1 is 100 percent God
- Person 2 is 100 percent God
- Person 2 is not Person 1
- There is only one God
The above is a textbook example of a contradiction. You can’t have identity in propositions 1 and 2, and still hold proposition three, given that there is only one God. A substitution (always possible, if in fact there is identity between the terms) will illustrate that:
Person 2-substitute for God (for example, the Father is God)
Person 1-substitute for God (for example, the Son is God)
Now, write proposition three with the substitutions, and you get:
[God] is not [God]
Do you see the problem now? There is no way to distinguish between the persons of the trinity without contradicting the claim that each person is 100 percent God. If it weren’t required that each person be identical to God, then it would be a different story, but that is required by the trinity.