The result of the analysis of the biblical testimony in the light of the tradition of the church is that the distinctions Father, Son and Spirit do not refer to persons in the modern sense [i.e., as separate centers of consciousness] or parts of God; each refers to the whole of the Godhead. They do not refer to aspects, qualities, or attributes of God, because all of these apply equally to each of the "persons." They do not refer to functions or types of activity of God, because each of the "persons" is involved in each activity of God. They are not simply ways in which God is revealed or ways in which we experience God but rather essential or immanent distinctions in the godhead. The names Father, Son and Holy Spirit refer to modes of being of God, distinctions in the way in which God is God, distinctions in the form, pattern, order, or structure of all of God's activities.
Quote taken from Thomas' work Introduction to Theology. Harrisburg, PA: Morehouse, 1994. Page 71.