Discussion of the Trinity can easily collapse into either modalism (there is a single God and the “persons” are mere masks) or tri-theism (there are three gods rather than the one God). Owen opens chapter 3 with a series of distinctions and limitations to explain how it is that one can hold communion with the Father, Son and Holy Spirit distinctly and yet hold to the unity of God.
This section of his work does not summarize easily, in that it relies on technical language and precise distinctions. Any attempt to summarize and restate will necessarily miss some of Owen’s nuance and precision.
That being said, the pastoral intent of Owen is to make sure that one holds to the unity of God while considering communion with the persons of the Trinity. The nature of the Triune God is such that while we may speak of “peculiarly” communing with the Father we must remember that we are “secondarily” in communion with the other persons. Moreover, no action of the Trinity outside the Trinity takes place as the sole working of a single person: When any person of the Trinity acts, all persons are involved. Owen provides this example:
As suppose it to be the act of faith: — It is bestowed on us by the Father: “It is not of yourselves: it is the gift of God,” Ephesians 2:8. It is the Father that revealeth the gospel, and Christ therein, Matthew 11:25. And it is purchased for us by the Son: “Unto you it is given in the behalf of Christ, to believe on him,” Philippians 1:29. In him are we “blessed with spiritual blessings,” Ephesians 1:3. He bestows on us, and increaseth faith in us, Luke 17:5. And it is wrought in us by the Spirit; he administers that “exceeding greatness of his power,” which he exerciseth towards them who believe, “according to the working of his mighty power, which he wrought in Christ, when he raised him from the dead,” Ephesians 1:19,20; Romans 8:11
Moreover, we must not think that in personal communion with the Father, say, that we should exclude the point that we also have communion with God as unity.