As to this phrase "Our Father," he notes that by inviting us to share this phrase, Jesus is signifying our adoption as children of God. But what does it mean for us to have this opportunity? Calvin writes:
Therefore God both calls himself our Father and would have us so address him. By the great sweetness of this name he frees us from all distrust, since no greater feeling of love can be found elsewhere than in the Father. Therefore he could not attest his own boundless love toward us with any surer proof than the fact that we are called "children of God" (1 John 3:1). But just as he surpasses all men in goodness and mercy, so is his love greater and more excellent than all our parents' love. Hence, though all earthly fathers should divest themselves of all feeling of fatherhood and forsake their children, he will never fail us (cf. Ps. 27:10; Isa. 63:16), since he cannot deny himself (2 Tim. 2:12). For we have his promise: "If you, although you are evil, know how to give good gifts to your children, how much more will your Father who is in heaven" (Matt. 7:11p.)? Similarly, in the prophet: Can a woman forget her . . . children? . . . Even if she forgets, yet I shall not forget you." (Isa. 49:15p.) But a son cannot give himself over to the safekeeping of a stranger and an alien without at the same time complaining either of his father's cruelty or want. Thus, if we are his sons, we cannot seek help anywhere else than from him without reproaching him for poverty, or want of means, or cruelty and excessive rigor. (John Calvin, Institutes of the Christian Religion, 3:20:36)
Although the idea of a child-like intimacy that was perhaps envisioned by Jeremias may not be present in the text, there remains a strong sense of intimacy here in any case. For as Calvin suggests, from whom can we expect greater love than from God our Father. Now, again, there is an issue that must be acknowledged. Addressing God as Father carries with it certain patriarchal nuances that we must acknowledge and wrestle with. Nonetheless, Calvin does remind us that we are children of God and that this status -- not of birth but of adoption is important.