{5} That is, They which are the children of the {k} flesh, these are not the children of God: but the children of the {l} promise are counted for the seed.

(5) A general application of the former proof or example.

(k) Who are born of Abraham by the course of nature.

(l) Who are born by virtue of the promise.

People's New Testament

9:8 That is, They which are the children of the flesh, etc. Since Ishmael, born according to natural laws, was not of the chosen race, but Isaac, the child of promise, born contrary to natural law, because the chosen people, it follows that the children of God are not the children of the flesh, the mere fleshly descendants of Abraham, but the children of the promise; those who are of the seed according to the conditions of the promise. This argument is a reply to those who based all upon their fleshly relation to Abraham: We have Abraham to our Father (Mt 3:9). In order to show this more fully Paul recalls the incidents recorded in Ge 18:10-14.

Wesley's Notes

9:8 That is, Not the children, and c. - As if he had said, This is a clear type of things to come; showing us, that in all succeeding generations, not the children of the flesh, the lineal descendants of Abraham, but the children of the promise, they to whom the promise is made, that is, believers, are the children of God. Gen 21:12

Matthew Henry's Concise Commentary

9:6-13 The rejection of the Jews by the gospel dispensation, did not break God's promise to the patriarchs. The promises and threatenings shall be fulfilled. Grace does not run in the blood; nor are saving benefits always found with outward church privileges. Not only some of Abraham's seed were chosen, and others not, but God therein wrought according to the counsel of his own will. God foresaw both Esau and Jacob as born in sin, by nature children of wrath even as others. If left to themselves they would have continued in sin through life; but for wise and holy reasons, not made known to us, he purposed to change Jacob's heart, and to leave Esau to his perverseness. This instance of Esau and Jacob throws light upon the Divine conduct to the fallen race of man. The whole Scripture shows the difference between the professed Christian and the real believer. Outward privileges are bestowed on many who are not the children of God. There is, however, full encouragement to diligent use of the means of grace which God has appointed.