Today, the question as to whether the children of believers should be baptized divides the visible church. Yet, this was not so for the magisterial Reformers. The Lutherans, the Reformed, and the Anglicans during the Reformation did not have identical theologies of baptism, but they all agreed that baptism is rightly administered both to those who profess faith and to their children.
In contrast to even those Baptists who affirm the five points of Calvinism, the historic Reformed position is that the children of believers should be baptized as well as those who profess faith. Why? First, if there is no necessary time relationship between regeneration and its visible sign and seal, as we saw with Abraham (regenerated before the sign) and Isaac (regenerated after the sign), then baptism can occur before evidence of regeneration is present.
That does not mean we go about administering the sign to all people. In Scripture, the sign of regeneration is given only to members of the visible covenant community. We see this in today’s passage, where Abraham and his descendants are commanded to give the old covenant sign and seal of regeneration—circumcision—to everyone in his household and not to the pagans (Gen. 17). This is particularly notable when we consider that believers in Christ are the children of Abraham (Gal. 3). If Abraham was to give the sacrament of regeneration to his children, and his children were to give it to their children, then we who follow Christ should give the sacrament of regeneration to our children. In fact, the New Testament tells us that God’s new covenant promises are as much for our children as the old covenant promises were for the children of old covenant believers (Acts 2:39).
However, one might object, the New Testament does not tell us explicitly to baptize children. That is true enough, although in some cases entire households, some of which probably had children, were baptized (Acts 16:15). More importantly, the objection assumes a large degree of discontinuity between the old and new covenants, that something from the old covenant must be explicitly commanded or repeated in the new covenant for it to remain in force. But that is not how Jesus read the Bible (Matt. 5:17–20). Following Jesus’ example, the Reformed way to interpret the Scriptures is to assume continuity, to follow Old Testament prescriptions unless we are told otherwise. The New Testament never tells us to stop applying the sacrament of regeneration to the children of believers.