Abraham Prefigures Paul's Gospel of Faith
Early in the letter (1:2) Paul asserted that his gospel had been pre-proclaimed in the Old Testament. Later he pronounced the same (3:21). To this point, however, he has never shown any evidence for his claim. But now, having just claimed that his gospel of faith is manifested 'apart from the law', he must. So, in chapter 4 he preaches to prove his point from the life of Abraham (as well as David). And as a result, we learn that getting right with God has always been by faith, and not only that, but that from the beginning this good news was intended for all people.