4:5 to redeem. The concept of redemption comes from the institution of slavery. In both the Jewish and Greco-Roman worlds, a slave could buy his freedom (or someone else could buy it for him) by paying a redemption price to his owners. The price of our redemption was paid by the Father in the blood of His Son (1 Pet. 1:17, 18), and by the Son in giving His life a ransom for many (Matt. 20:28).
those . . . under the law. Not only Jews, circumcised under the law of Moses, but also Gentiles, for both are under the curse of the law (3:13, 14).
adoption as sons. Paul has been speaking of God’s people under the law as children (Ex. 4:23; Is. 1:2). He now describes the only way in which the children become full members of the household, no longer minors. God seals our adoption by giving us the Spirit of His Son (Rom. 8:9–17). See theological note “Adoption.”