Ishmael was born after the flesh (by human effort) and Isaac was born according to the promise when Abraham and Sarah were beyond the age of bearing children. Ishmael was a descendant of Abraham as was Isaac, but Isaac was the child of promise.

Isaac had two sons, Esau and Jacob.

Esau was Isaac’s firstborn son, yet he did not esteem his birthright as the first born which would have made him the heir to the blessing. Instead, he sold his birthright to Jacob for a bowl of pottage (stew) ~ Genesis 25:29. Jacob bargained with Esau for his birthright because he desired the blessing. Through a series of events Jacob inherited and possessed the blessing which originally belonged to Esau.

Esau was a descendant of Abraham as was Jacob, but God loved Jacob and hated Esau because Jacob desired the blessing and Esau despised it.

As it was with Ishmael and Isaac, and Esau and Jacob, so it was with the nation of Israel. Within Israel, there were those who were Abraham’s descendants according to the flesh only. They were not heirs according to the promise, they are not the true children of Abraham.

In John 8, Jesus was opposed by some antagonistic Jews who boasted that they were the children of Abraham as they expressed their opposition to Jesus.

If the Son therefore shall make you free, ye shall be free indeed. I know that ye are Abraham’s seed; but ye seek to kill me, because my word hath no place in you. I speak that which I have seen with my Father: and ye do that which ye have seen with your father.
They answered and said unto him, Abraham is our father. Jesus saith unto them, If ye were Abraham’s children, ye would do the works of Abraham. ~ John 8:36-39 KJV

Jesus goes on to tell them that not only were they not Abraham’s children, but they were actually the children of the devil even though they were physical descendants of Abraham.

The family God promised to Abraham is a household of faith – a spiritual family. In his confrontation with the antagonistic Jews in John 8 (referenced above), Jesus identified the true spiritual father of these physical descendants of Abraham.

But now ye seek to kill me, a man that hath told you the truth, which I have heard of God: this did not Abraham. Ye do the deeds of your father. Then said they to him, We be not born of fornication; we have one Father, even God. Jesus said unto them, If God were your Father, ye would love me: for I proceeded forth and came from God; neither came I of myself, but he sent me. Why do ye not understand my speech? even because ye cannot hear my word. Ye are of your father the devil, and the lusts of your father ye will do. He was a murderer from the beginning, and abode not in the truth, because there is no truth in him. When he speaketh a lie, he speaketh of his own: for he is a liar, and the father of it. ~ John 8:40-44 KJV

In this confrontation, Jesus does not dispute the physical descendancy of these Jews. In fact he affirms it,“I know you are Abraham’s seed” ~ (v 37).  However, this physical descendancy did not mean they were God’s children, “For they are not all Israel, which are of Israel: Neither, because they are the seed of Abraham, are they all children: but, In Isaac shall thy seed be called.” ~ Romans 9:6-7

Jesus did not define “Abraham’s children” by their physical descent only. Neither did John the Baptist, who warned those who did not repent and follow Jesus that they would be cut off as the people of God.

And think not to say within yourselves, we have Abraham to our father: for I say unto you, that God is able of these stones to raise up children unto Abraham. And now also the axe is laid unto the root of the trees: therefore every tree which bringeth not forth good fruit is hewn down, and cast into the fire. I indeed baptize you with water unto repentance. but he that cometh after me is mightier than I, whose shoes I am not worthy to bear: he shall baptize you with the Holy Ghost, and with fire: ~ Matthew 3:9-11

The baptism with the Holy Ghost and fire is not a reference to the same blessing, but rather, a contrast between blessing and judgment. Those who would repent would receive the baptism of the Holy Ghost. Those who would not repent, would receive the baptism of fire, which is God’s wrath.

In the very next verse, after the baptism of fire is mentioned, John says, “Whose fan is in his hand, and he will thoroughly purge his floor, and gather his wheat into the garner; but he will burn up the chaff with unquenchable fire.” ~ Matthew 3:12

The ministry of Jesus and his fore runner John the Baptist, reveal that only those who responded to the gospel from among the Jews, were truly Abraham’s children.

Consider Paul’s words from Romans 9:7-8 again: Neither, because they are the seed of Abraham, are they all children: but, In Isaac shall thy seed be called. That is, they which are the children of the flesh, these are not the children of God: but the children of the promise are counted for the seed.

We can see from these words of Paul that not all in Israel were the children of the promise, and therefore were not considered “the true seed of Abraham” in the eyes of God. This is consistent with the words of Jesus and John the Baptist.

Only those who were children of the promise were counted as the seed. Who then are the children of promise? They are those who are the children of Abraham by faith according to the truth of the gospel.

For  the promise, that he should be the heir of the world, was not to Abraham, or to his seed, through the law, but through the righteousness of faith. ~ Romans 4:13

Notice first that Abraham was promised to be the “heir of the world.” Abraham’s children were to be from “all nations” ~ Galatians 3:8. Secondly, notice that he says that the promise was not made to Abraham or his seed “through the law.” 

The Law was given to Israel through Moses, and served as ethnic Israel’s covenant with God. The Law bound the Jews with the curse if they did not circumcise their hearts to obey God, and serve him only. The Law made a distinction between ethnic Israel and the Gentile nations. It was the rule of law and constitution for the Jewish people. It was the “wall of separation” of which Paul speaks in Ephesians 2, which made a distinction between the people of Israel (who were God’s covenant people) and the nations.

Israel did not obey the Law, and consequently broke the covenant.

When Paul says the promise was not made to Abraham or his seed “through the Law,” he is referring to Israel’s national identity as a covenant nation  before God.  It was the Law which separated Israel from all other nations, for the law was Israel’s covenant with God. The promise was not given to Abraham or his seed because of DNA, or ethnic status. Thus Paul makes the following argument:

Cometh this blessedness then upon the circumcision (Jews) only, or upon the uncircumcision (Gentiles) also? for we say that faith was reckoned to Abraham for righteousness. How was it then reckoned? when he was in circumcision, or in uncircumcision? Not in circumcision, but in uncircumcision. And he received the sign of circumcision, a seal of the righteousness of the faith which he had yet being uncircumcised: that he might be the father of all them that believe, though they be not circumcised; that righteousness might be imputed unto them also: And the father of circumcision to them who are not of the circumcision only, but who also walk in the steps of that faith of our father Abraham, which he had being yet uncircumcised. ~ Romans 4:9-12

The promise was spiritual and pertained to those who would follow Abraham’s faith!

For if they which are of the law be heirs, faith is made void, and the promise made of none effect: Because the law worketh wrath: for where no law is, there is no transgression.  Therefore it is of faith, that it might be by grace; to the end the promise might be sure to all the seed; not to that only which is of the law, but to that also which is of the faith of Abraham; who is the father of us all, (As it is written, I have made thee a father of many nations,) before him whom he believed, even God, who quickeneth the dead, and calleth those things which be not as though they were. ~ Romans 4:13-17

The promise which God made to Abraham was that he would be the father of many nations. Abraham believed this promise and was declared righteous in the sight of God.

According to Galatians 3:8, when God made this promise to Abraham, he preached the gospel to him. In the fullest sense of the word, Abraham believed the gospel when he believed God’s promise to make him the father of many nations and was declared righteous!

Christ is the promised seed of Abraham (Galatians 3:16) through whom the blessing promised to Abraham comes to fruition, for it is only in and through Jesus Christ that a person can be justified in the sight of God. Abraham was justified by God because he believed the promise God made “in Christ”  (Galatians 3:17).

Being an heir to the promise God made to Abraham comes only through faith in Jesus. This applies to Jews and Gentiles alike. Being a descendant of Abraham “after the flesh” is not the same as being “an heir to the promise.”

For ye are all the children of God by faith in Christ Jesus. For as many of you as have been baptized into Christ have put on Christ. There is neither Jew nor Greek, there is neither bond nor free, there is neither male nor female: for ye are all one in Christ Jesus. And if ye be Christ’s, then are ye Abraham’s seed, and heirs according to the promise. ~ Galatians 3:26-29