What is the thrust of the argument in Romans 4? Is Paul mainly concerned to present Abraham as an example of individual belief and trust in God? Or is the argument mainly about Abraham as father of both Jews and Gentiles? Is Abraham’s faith presented as the means by which he receives right standing with God, and so will be saved at the final judgment? Or is his faith presented as the means by which he becomes the father of nations?
Paul does deal with Abraham’s individual belief and forgiveness of sin, especially in verses 3-8. He quotes Genesis 15:7, to the effect that “Abraham believed God and it was reckoned to him as righteousness” (v. 3). The following verses reflect on that verb “reckon” (logizomai). Reckoning implies that something is given as favor or grace (kata charin) rather than as due (kata opheilema). The fact that Abraham receives righteousness as something “reckoned” means that he didn’t receive it as a wage due to him for his work. If Abraham earned righteousness, Paul would not have spoke of “reckoning.” David’s statement in Psalm 32:1-2 (quoted, vv. 7-8) supports this, for David speaks of a blessing to those whose anomia is forgiven, sins covered, and whose wrongs are not reckoned (logizomai). He writes of those who “follow in the steps of the faith of our father Abraham” (v. 12), again citing Abraham as example.
Paul’s appeal to Abraham in verses 3-8 at this point accomplishes pretty much what Protestant interpreters have said it does. Paul claims to have Scriptural support for denying that Abraham attained his status by his just works. If he had done so, why would Genesis have spoken of “reckoning” righteousness? Why not “achieved” righteousness? The fact that God reckons righteousness demonstrates that Abraham’s reward is given kata charin and not kata opheilema.
Paul is contesting standard Jewish beliefs about Abraham’s righteousness. From at least the books of the Maccabees on, Abraham’s righteousness was dislodged from Genesis 15 and “predicated upon Abraham’s entire life of obedience which culminates in Gen. 22” (Joshua Jipp, “Rereading the Story of Abraham, Isaac, and ‘Us’ in Romans 4,” JSNT 32:2  222-3). Thus, for many Jews, Abraham was considered righteous because he lived a life of righteousness, especially exemplified in his offering of Isaac. Paul rejects this reading by highlighting the fact that Abraham is reckoned righteous before he was circumcised, and before he fathered or offered Isaac.
But Paul’s argument doesn’t make sense if Paul is merely presenting Abraham as an example of faith, an illustration of an ordo salutis. As Jipp points out, the language of “reckoning” drops out after verse 10, reappearing at the end of the chapter with a more focused significance (v. 22). Why did Paul write verses 9-25 if he only wanted to present Abraham as an exemplar of faith? Jipp suggests that Paul is answering a series of questions in the chapter. I think it better to see the chapter as a single coherent argument, of which Paul’s comments about reckoning providing important deck-clearing premises. Verses 3-9 clarify what it means for God to reckon someone righteous. What it means for Abraham to believe, and what the gift of righteousness is like—these issues are still unexplained.
Here’s the spoiler: Though he presents Abraham as an example of faith, Paul is also, equally, perhaps more concerned with presenting the faithful man Abraham as a father, and explaining how he becomes father. By becoming father by faith, Abraham is a type of the Faithful One who fulfills the promise to Abraham by His faith. As Abraham becomes a father of nations by faith, so Jesus is the head of a new humanity by His faith.
We can come at this in more exegetical detail by examining what role “boasting” plays in Paul’s argument in Romans. Abraham has nothing to boast of before God. He might boast of his own righteous works, but Paul has dispensed with that possibility by focusing attention on the import of the verb “reckon.” Earlier in Romans, Paul has not been concerned with the boasting in individual achievement; he’s concerned with the boasting of Jews, whose pride is in the possession of the law (2:17, 23). That sort of boasting is excluded (3:27) by what Paul provocatively calls “the law of faith” (3:27).
The question Paul deals with in the remainder of the chapter is implicitly posed at the beginning: Isn’t Abraham our forefather according to flesh? Paul denies what appears to be obvious. Abraham is indeed father, but his fatherhood is not by flesh or the law, but by faith. In 4:9-15, Paul shows that Abraham cannot boast in either circumcision or law. He is not righteous by virtue of circumcision, since he was reckoned righteous before he was circumcised (4:10-12). He was not righteous by the law because that is not the work that Torah does. It can only bring wrath (4:15). Inheritance cannot come through law because Abraham was designated as heir before the law; if inheritance comes through law, Abraham’s faith is voided (4:13-14). Abraham believed Yahweh’s promise about becoming the father of nations, and because he trusted God’s promise, the promise came to fulfillment.
Circumcision plays into Romans 4 and Galatians 4 in similar ways. In the latter, circumcision isn’t mentioned, but it’s the unstated difference between Abraham fathering Ishmael, a child of flesh, and his fathering Isaac, the child of the Spirit. Only after the removal of flesh, and confidence in flesh, is Abraham capable of being the father of the miracle child of the covenant. That is the same point Paul makes in Romans 4:16-22. Yahweh promises Abraham fatherhood to many nations, but his own body and Sarah’s womb are dead (v. 19). Abraham trusts Yahweh’s promises regardless, hoping against hope. Boasting in circumcision is worse than idle; circumcision renounces boasting in flesh, and implies total reliance on the power of the God who calls things that are not into being, the God who raises the dead. Abraham became a father by faith, not according to flesh.
By the time Paul re-quotes to Genesis 15 in verse 22, he has moved through Abraham’s circumcision and the birth of Isaac. As Jipp says, God’s reckoning Abraham as righteous is not a bare declaration but takes public form in the birth of Isaac. It’s not as if Abraham believed in some generic goodness of God and received an invisible gift of righteousness; he believed specific promises—“a father of many nations have I made you”; “so shall your seed be”—in circumstances that made them seem impossible (age, barrenness, death). The gift fulfilled the promise and matched Abraham’s faith. The gift of righteousness took the form of the fulfillment of these specific promises. Which is to say: The gift of righteousness took the form of a son risen from the dead body of Abraham and the dead womb of Sarah. Abraham’s own fortunes rose from the dead with the resurrection-birth of Isaac, and so Abraham and his faith were vindicated by the fulfillment of the promise.
This is how Abraham becomes father: Not by flesh but by the overcoming of fleshly weakness; not by flesh but by faith. The overall thrust of Paul’s argument is about this becoming-father. Abraham’s faith is once-for-all, a founding faith, the faith of a father, faith in the life-giving power of the living God that becomes an agent for the fulfillment of God’s promise. Because of his faith, Abraham became a father to Isaac, and, beyond Isaac, a father to a stream of descendants. Trusting that promise of resurrection, Abraham became a means by which resurrection life was born. Abraham is example, but he’s an example in the way fathers are examples. Abraham-as-example is incorporated into Abraham-as-father: He is the father of circumcision and uncircumcison, all who “walk in the steps of the faith of our father Abraham” (v. 12). Imitate the faith of Abraham is a specification of the exhortation to “live like your Daddy.”
All this smooths out the transition from Abraham’s faith to Jesus. Abraham as father isn’t merely an example for believers. He’s an example because he is a type of another “father,” another founder, who also trusts God to raise Him from the dead and who receives this gift of righteousness in being delivered from the grave (“justified in the Spirit,” as Paul puts it in 1 Timothy 3:16). The story of Abraham was written “for our sake also” because it shows us how the promises to Abraham are fulfilled—in the resurrection of the Son, in whose resurrection we who believe have life from the dead.