Whenever we discuss the Trinity we should start with the humility to recognize that we are finite creatures trying to grasp something, or Someone, way beyond us. Yet we must also recognize that the Trinity is fundamental for Christian orthodoxy – so we ought to try!
In the Eastern branch of Christianity, the Trinity is generally spoken of as three persons (they begin with the threeness of God) and then these three are shown to be one. That is called the “social model” of the Trinity. The Western branch has generally spoken of the unity of God’s essense and then how there is a threeness within this unity. That is called the “psychological model” because it goes back originally to Augustine (and to Anselm of Canterbury) who sought to find the threeness of God in the human psyche – soul, mind, and will.
Jonathan Edwards, following Augustine and the psychological model, said in an unpublished essay, that God’s perfect idea of himself is Jesus, who Scripture calls “the Word” or “Wisdom” of God. Wow! That sounds so strange, and yet, it so remarkably biblical (John 1:1, Proverbs 8:22-30, Hebrews 1:3). So we have duplicity in God – God and God’s idea of himself.
Then between God and Jesus, his idea of himself, emerges the Holy Spirit, who is the “bond of love,” that is, God’s own love for his idea of himself. To reach this conclusion Edwards simply points out some biblical passages that push us in this direction; Scripture says “God is love” (1 John 4:8) and it says “God is Spirit” (John 4:24). Perhaps there is a divine reality behind this? Indeed, the Spirit descended on Jesus like a dove as the Father said “This is my beloved son” (Matthew 3:16-17). There are certainly many passages of Scripture that connect the Holy Spirit in us with our love for one another (2 Cor 6:6; Rom 15:30; Col 1:8; Rom 5:5; Gal 5:13-16). So perhaps there is a biblical foundation to view the Spirit as the “bond of love”?
Now I am not sure how these three “modes of being” really are different persons. That is the difficulty of this psychological model, which is ultimately an analogy, and all analogies have shortcomings. But at any rate, I still find it helpful.
Also, here is a YouTube discussion on Jonathan Edwards and the psychological model between Joe Rigney (from Bethlehem Baptist Seminary) and Douglas Wilson (from Christ Church Idaho). I recommend the whole thing but the discussion of the psychological model starts around the 6:17 mark.