The doctrine of infant baptism is central to the truth of the Scripture because baptism is the mark of God's covenant of grace; the truth of God's covenant is central to all the doctrines of God's Word. Many Reformed churches, while holding formally to infant baptism, nevertheless do not consider the doctrine in connection with and as related to the truth of God's covenant. Or, if they do, an erroneous and basically Arminian view of God's covenant vitiates the doctrine of infant baptism as well as other doctrines and makes a solid biblical apologetic all but impossible. (excerpt from the Preface to the Second Edition, xi)
A crucial issue between those who hold to infant baptism and those who do not is whether God saves his church in the line of continued generations. It is clear that all the children of the Israelites were circumcised in infancy. The Reformed maintain that this was commanded because God saves his church in the line of continued generations.
Our conclusion is that the law addresses children because they are redeemed in the blood of Christ. The slavery to which the people of Israel were subjected was, in the dispensation of types and shadows, a picture of the slavery of sin in which man finds himself by virtue of his birth from his parents. Deliverance from Egypt was typical of God's salvation of his people through Christ. While in the old dispensation this work of salvation was performed for God's people on the basis of God's promise to send Christ, the work today is essentially the same. God's people in every age are saved through Christ's cross so that the power of his perfect work results in the regeneration, conversion, faith, justification, sanctification and glorification of all the elect. This is all implied in Israel's deliverance from "the land of Egypt, out of the house of bondage." In that work, children are included. "Children, you who are also brought out of Egypt and are redeemed, honor your parents."...
The introduction of the law is inseparably related to the law as part of it. That there is no one commandment specifically referring to children proves that that introduction also refers to children of believers. If God is the God of believers' children, if the children are also redeemed from the bondage of sin, then they must bear the sign of such redemption as well. (excerpt from Chapter 6: The Covenant with Believers and Their Seed)
The principle of the salvation of believers and their seed is a principle that pervades the whole of scripture, both in the Old and New Testaments. Thus, Scripture teaches that children of believers as well as believers themselves are incorporated into God's everlasting covenant of Grace. The Heidelberg Catechism is completely correct in Question and Answer 74:
Q: Are infants also to be baptized:
A: Yes; for since they, as well as their parents, belong to the covenant and people of God, and both redemption from sin and the Holy Ghost, who works faith, and through the blood of Christ promised to them no less than to their parents, they are also by Baptism, as a sign of the covenant, to be ingrafted into the Christian Church, and distinguished from the children of unbelievers, as was done in the Old Testament by Circumcision, in place of which in the New Testament Baptism is appointed. (excerpt from Chapter 7: The Organism of the Covenant)