Paul here starts to apply the allegory specifically to his readers, at the same time bringing to their attention the two sons of Abraham, whose mothers have so far been the focus of Paul’s discourse. Now at the beginning of the verse is clearly continuative rather than temporal. The closest equivalent in some languages is “on the basis of this comparison,” or simply “hence” or “therefore.”
Some translations adopt the reading “we” instead of “you,” but the latter seems to be the better reading, both from external and internal evidences. Paul once again addresses his readers with the more or less formal my brothers, which he has used twice before. As in many similar contexts, this may be rendered as “my fellow believers” or “you who trust Christ along with me.”
They are God’s children as a result of his promise (literally, “are children of promise”). The clue to the meaning of the expression is found in the last part of the verse: just as Isaac was. Just as Isaac was conceived, not through natural means, but through the fulfillment of God’s promise, so the Galatians also have become God’s children, not through their own efforts, much less through natural and physical descent, but exclusively as a fulfillment of what God promised to Abraham.
As a result of his promise may be rendered as “because that was the way in which God had promised it would happen,” or “because God had made a promise.”
The final clause, just as Isaac was, may require certain expansion because of the rather severe ellipsis, for example, “in the same way Isaac became Abraham’s son because of what God had promised,” or “in the same way Abraham had a son, Isaac, because of what God had promised,” or “… because God had promised Abraham that such would happen.”
Quoted with permission from Arichea, Daniel C. and Nida, Eugene A. A Handbook on Paul’s Letter to the Galatians. (UBS Handbook Series). New York: UBS, 1976. For this and other handbooks for translators see here .
