8. Children of the flesh. These are the merely physical descendants, who are born in the natural course of events, as was Ishmael (see Gal. 4:23). But spiritual blessings are not inherited by natural descent.
Children of God. This refers historically to the descendants of Abraham through Isaac. They were the ones who stood in covenant relation with God, inherited the promises, and received the privileges of the chosen people. From this distinction made between Isaac and Ishmael, Paul is drawing the principle that to be true sons of Abraham, and true sons of God, does not depend on physical descent alone. This was hard doctrine for the Jews, for their most cherished belief was that merely being a Jew constituted one a child of God. But how encouraging this message must have been to the Gentiles!
Children of the promise. The case of Isaac is doubtless referred to. Isaac was born when Abraham and Sarah had passed the time of life when they could naturally expect to have a child. But the promise of God and their acceptance of it by faith made it possible for them to become the parents of Isaac (see on 4:18-21). Likewise, as Paul explains in Gal. 4:21-31, it is by supernatural rebirth that Gentiles may become children of Abraham, children of the promise ( 28).