Q. Since there is only one God, why do you speak of three persons, Father, Son, and Holy Spirit?
A. Because God has so revealed Himself in His Word that these three distinct persons are the one, true, eternal God.

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Theological: This doctrine is, at once, one of the most intriguing and also one of the most foundational doctrines of the Christian faith. At the very heart of our faith stands the great mystery that is God. He’s not just personally mysterious, but he’s even numerically mysterious! While I’m happy to embrace mystery, I’m absolutely unwilling to affirm that Christianity includes contradiction. Not being able fully to comprehend something is one thing, but affirming a contradiction is something else altogether. Follow me, here: We affirm that God is one and three, right? But not one and three in the same way. We affirm one being (essence/substance) existing in three distinct persons. Being and persons are NOT the same thing. Therefore, Christianity has NEVER been so foolish as to assert that God is one and three in being. Neither has it been so foolish as to assert that God is one and three in persons. Christianity embraces the great mystery that God is one in being and three in persons. Christianity is full of mystery and even paradox (sometimes called antinome), but never affirms strict contradiction. At the center of the Christian faith stands the incomprehensible triune God. He blows our minds. This is as it should be.
Practical: We should be blowing people’s minds as we preach. The Bible, the story and teachings of the Christian faith are so rich, so profound, so full of magic and wonder, that we should routinely leave people in a state of wonder as they encounter the God of the Bible in his Christ. Preachers: study the triunity of God and end up getting lost in that wonder. Make sure that wonder works its way into your sermons. Part of the beauty of God is that he’s unspeakably majestic. The doctrine of the Holy Trinity is pretty good jumping-off point into that high majesty. We minister for a wonderful God, so let’s make sure our sermons have a distinct element of wonder in them. Let us marvel at God himself and at his unthinkable grace in Christ, and so let us leave our people in glorious wonder as we instruct them in the things of God.
“Antinomies” is not a good word for it: it implies contradiction. “Paradox” at least means APPEARS contradictory, but is merely beyond us. Barth and Heidegger ruined the word, but nevertheless the best choice remains “dialectic”.
I always need a diagram/picture to truly grok something, so I think of J. Edwards’ unpublished essay in Venn diagram form. Have you read that article and do you agree with it?http://www.ccel.org/e/edwards/trinity/trinity.html
Our British brethren use this word, but don’t mean contradiction. Packer’s a good example.
He gets it from “Rabbi” Duncan. It need not always mean contradictory, but it generally does. http://en.wikipedia.org/wiki/Antinomy Dialectic is better.
The Trinity is the resolution to the ancient paradox between the one and the many, between anarchy and fascism, between chaos and fate, between the individual and the state. All of these lead to violence. The Trinity is the only way to peace and is necessary to make sense out of the whole created order. Trinity is balance.