Benjamin B. Warfield sums up the argument in favor of infant baptism as follows:
“The argument in a nutshell is simply this: God established his Church in the days of Abraham and put children into it. They must remain there until He puts them out. He has nowhere put them out. They are still then members of His church and as such entitled to its ordinances. Among these ordinances is baptism, which standing in similar place in the New Dispensation to circumcision in the Old, is like it to be given to children.” (The Works of Benjamin B. Warfield, Vol. IX, p.408)
The first thing that Warfield points out is that “God has established his church in the days of Abraham and put children into it.” And so the starting point and key to understanding his argument is a right understanding of the church and the covenant of grace.
In his book, Christ & Covenant Theology, Cornelius Venema includes an entire chapter dealing with Covenant Theology and the practice in infant baptism. In this chapter, he interacts with Warfield’s treatment of the subject (citing the statement quoted above), providing a brief overview of Covenant theology, and then showing how this view applies to infant baptism. There he writes,
“The Reformed practice of baptizing believers and their children, as Warfield rightly maintained, is largely based upon an understanding of the biblical doctrine of the covenant of grace. In the principal writings of the Reformers of the sixteenth century, and in the great confessional symbols of the Reformed tradition, the one argument for paedobaptism that repeatedly stands out is the covenant argument. Children, like adult believers, are to be baptized because they belong to the covenant community in Christ.” (p.258).
Venema then goes on to flesh out the covenant argument in what he himself calls “a series of steps, moving from the more general and basic elements of covenant theology to its specific implications regarding the proper recipients of Christian baptism” (Ibid).
He points out that one of the most important elements of Reformed covenant theology is that there is “one covenant of grace throughout redemptive history” (p.270), the same in substance, but differing in how it is administered. The Westminster Confession of Faith puts it this way:
“This covenant was differently administered in the time of the law, and in the time of the gospel: under the law, it was administered by promises, prophecies, sacrifices, circumcision, the paschal lamb, and other types and ordinances delivered to the people of the Jews, all foresignifying Christ to come; which were, for that time, sufficient and efficacious, through the operation of the Spirit, to instruct and build up the elect in faith in the promised Messiah, by whom they had full remission of sins, and eternal salvation; and is called the old testament.” (16.5)
Another way of saying this would be to say that there has always been one way of salvation, whether in the Old Testament or in the New. In Galatians 3:7-9, Paul writes,
“Know then that it is those of faith who are the sons of Abraham. And the Scripture, foreseeing that God would justify the Gentiles by faith, preached the gospel beforehand to Abraham, saying, “In you shall all the nations be blessed.” So then, those who are of faith are blessed along with Abraham, the man of faith.” (ESV)
Those who are “of faith” (i.e. those who trust in Christ alone for salvation) “are the sons of Abraham” (v.7). All of the Old Testament saints were saved by grace through faith in Christ alone (Ephesians 2:8-9), just as we are today. Their faith looked forward to the Christ who was yet to come; while our faith looks back to the Christ who has already come.
And God’s covenant with Abraham included even his infant offspring, who were also to receive the sign and seal of that administration of the covenant of grace, that is, the sacrament of circumcision. Genesis 17:9-12 says,
“And God said to Abraham, “As for you, you shall keep my covenant, you and your offspring after you throughout their generations. This is my covenant, which you shall keep, between me and you and your offspring after you: Every male among you shall be circumcised. You shall be circumcised in the flesh of your foreskins, and it shall be a sign of the covenant between me and you. He who is eight days old among you shall be circumcised. . . .” (ESV)
When you consider the fact that the sign and seal of the covenant (i.e. circumcision) was explicitly commanded by the Lord to be applied to infants (8-day-old male children!) in the Old Testament, many of the arguments against infant baptism begin to crumble under their own weight. As Calvin puts it, “For what will they [i.e. critics of infant baptism] bring forward to impugn infant baptism that may not be turned back against circumcision?” (Institutes of the Christian Religion, 4.16.9).
That is why John Murray writes the following:
“If infants are excluded now, it cannot be too strongly emphasised [sic] that this change implies a complete reversal of the earlier divinely instituted practice. So we must ask: do we find any hint or intimation of such reversal in either the Old or the New Testament? More pointedly, does the New Testament revoke or does it provide any intimation of revoking so expressly authorised [sic] a principle as that of the inclusion of infants in the covenant and their participation in the covenant sign and seal?” (Christian Baptism, p.49)
Do we find any hint of such a reversal? No, we do not. And so Murray concludes by saying,
“In the absence of such evidence of repeal we conclude that the administering of the sign and seal of the covenant to the infant seed of believers is still in operation and has perpetual divine warrant. In other words, the command to administer the sign to infants has not been revoked: therefore it is still in force.” (Christian Baptism, p.50)
In other words, the burden of proof actually rests upon those who reject infant baptism, not on those who affirm it. There would actually need to be an explicit prohibition in Scripture forbidding us from baptizing infants, rather than an explicit command telling us to do so.