From his famous and classic Confessions, Bk. 13, Ch. 11, St. Augustine writes:
I speak of these three: to be, to know, and to will. For I am, and I know, and I will: I am a knowing and a willing being, and I know that I am and that I will, and I will to be and to know. Therefore, in these three, let him who can do so perceive how inseparable a life there is, one life and one mind and one essence, and finally how inseparable a distinction there is, and yet there is a distinction. Surely a man stands face to face with himself. Let him take heed of himself, and look there, and tell me. But when he has discovered any of these and is ready to speak, let him not think that he has found that immutable being which is above all these, which is immutably, and knows immutably, and wills immutably....
These “three” do not “equal” one if we are trying to say 3=1 mathematically. These three are distinct realities, relationally speaking, just as my own being, knowing, and willing are three distinct realities in me. Yet, in both God and man these three relationally distinct realities subsist in one being.
As St. Augustine points out, we can never know God or understand God completely through this or any analogy, but it can help us to understand how you can have relational distinctions within one being. And we can see this is reasonable.
The weakness inherent here—there are weaknesses in all analogies with reference to God—is that our knowing, being, and willing are not each infinite and co-extensive as the persons of God are. They subsist in one being in us, but they are not persons.
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The Catechism of the Catholic Church gives us another analogy wherein we can see the reasonableness of the Trinity by helping us to see the possibility of distinct persons who possess the same nature. CCC 2205 provides:
The Christian family is a communion of persons, a sign and image of the communion of the Father and the Son in the Holy Spirit.
When we think of a family, we can see how a father, mother, and child can be distinct persons and yet possess the same nature (human), just as the Father, Son, and Holy Spirit are three distinct persons who each possess the same nature (divine).
The weakness, of course, is that in God each person possesses the one infinite and immutable divine nature, and is therefore, one being. Our analogous family consists of three beings. Again, no analogy is perfect.
But in the end, if we combine our two analogies, we can at least see both how there can be three relationally distinct realities subsisting within one being in the anthropological analogy, and how there can be three relationally distinct persons who share the same nature in the analogy of the family.
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