Like many Protestants, I was baptized as an infant in the Roman Catholic Church; but when I became a Christian later on, I came to believe that only believer's baptism was valid. The churches I attended were all churches that believed only in believer's baptism. We always looked at those people who baptized their children as something next to the dark, Medieval institution of Rome, or even as cultic. After all, baptize your children? They can't even believe, and faith is the requirement for salvation. Of course, it absolutely is. The problem was that the radical individualism that we had adopted from our Enlightenment-oriented worldview made infants/little children separate individuals from their parents. And this is where it all went wrong. When I came to understand that most of the entire Church before me baptized children, and that the Bible seemed to say things that reflected that children of believers were saved, it brought me to think about the issue again. When I understood what I'm going to argue below, it pushed me to believe that the Holy Spirit had, in fact, taught His Church to do this, and it was not merely some corrupt tradition that crept in while others were asleep.
I stated in the last post that both the Fall and the gospel are to be understood along the ancient Near Eastern line of thought through which they have been communicated; and that worldview sees what one owns as a part of him, not as something separate from him.
Satan acquired the world because he acquired the man who owned it. He acquired all the children of that man because all the man owns is identified with him. They are damned because the devil is damned, and every possession goes to its master's fate, being one with him. Likewise, Christ acquired back those who are in Him because of these same ownership issues. They are saved because He is saved. As I've said before, Christ is the only one who is saved. We are saved because we are identified with Him. This is how His righteousness can transfer to us, not because the righteousness of one man transfers to others who are separate from Him, but because they are identified as Christ, precisely because they are owned by Him. They are not separate individuals. Christ is identified with whatever He owns, so if He is saved, all that He owns is saved with Him.
Now, if this principle is to be understood as just, then we can no longer make the argument that it would be unjust to save the children of a believer, even if that child himself has not believed. We can understand, then, that a child is owned by his parent, and therefore, the child is bound to that parent's fate. He is not a separate individual, but one who is identified as one with the parent to whom he is in submission, to whom he truly belongs.
We cannot merely say that this principle is true for Adam, Satan, and Christ, but suddenly not true for us. For one, it's unbiblical to divorce just principles as one set for certain people and another set of principles for another. For another, it is unbiblical because God clearly works in judgment and salvation this way with children in the Bible.
The children of unbelievers are destroyed in judgment, not merely as a byproduct of God's judgment, but as a direct object of His judgment. The herem judgment in war contexts clearly seeks to destroy a wicked person from the face of the earth. It seeks to kill all of him, not just some of him, so it demands that he and all that he owns be destroyed or reconditioned for sacred use. Hence, the Canaanite children are destroyed because they are one and the same persons as their Canaanite parents. They are not seen as distinct from them, as a person is identified with his possessions, and children are considered possessions of the parents who function as their familial lords while they remain within their households.
Hence, Achan and his whole family, along with all that he owns, is destroyed for having disregarded the command of the Lord in rebellion; but Rahab and her whole household is saved through her act of faith and obedience toward the Lord. This is why Joshua can say that he and his household will serve the Lord rather than just speaking for himself. This is why David is punished directly through his infant son for his own personal sin. This is why the entire household is saved through the Passover meal when it is the head of the household who is directing that the meal take place in obedience to the command. This is why the obedience or disobedience of the kings of Israel or Judah end up bringing upon the entire nation judgment or deliverance. This is why Paul says to the Philippian Jailer that he is to believe on the Lord Jesus Christ "and you and your household will be saved" (Acts 16:31). It's why Cornelius is told that Peter will tell him words through which he and his entire household will be saved (Acts 11:13-15). It's why Paul states in 1 Corinthians 7:14 that the believing parent, being one with the unbelieving parent, sanctifies that individual in that way, and thus, makes his or her children holy to the Lord. Children are saved or damned through their parents, precisely because those parents belong themselves to either the devil who is damned or to Christ who is saved. Hence, all that they own, their entire households, are either damned or saved with them.
Now, of course, there are numerous questions one might bring up.
"Doesn't Ezekiel say that sons and fathers are judged for their own sins?"
Yes, but it is clear in the context that these are sons who are grown up adults and either pursue righteousness or wickedness on their own. In other words, they have separated from their parents at this point. Hence, they are judged separately as individuals. It is only the children within the household, under the rule and in submission to the head of the household, who are identified with the parent.
"But what about those who later reject Christ once they have grown? How were they saved when they were children and not saved now? Does that imply that one can lose his salvation?"
No, it only implies that the elect will remain saved, either through their own faith or through their parent's, and those who are not really saved will apostasize. But this is true for those who are baptized as adults too. They seem to meet the requirements of one who is saved, but then later turn away. The only sure thing is that the elect will remain and persevere in the faith.
"But doesn't this make people think they're saved and lead parents not teaching their children to follow the Lord on their own?"
No, Reformed children seem to be taught even more than children within other groups, and this is right, since the biblical pattern is that the entire household be taught the Word of God as individuals as well (see Acts 16:32, where the jailer's household is taught the Word of God too). You would not say that an adult believer should be neglected, since teaching him to follow the Lord teaches him to glorify God now by his own profession and persevere in the future. The same goes for children as they grow into understanding the faith.
"But I thought that each person needs to exercise faith for his own salvation?"
He does, and it is through Christ alone that one can be saved (remember, only He is saved, so all must be in Him). This is why children can be saved through their parent's faith. They are one with their parents. They are not separate individuals until adulthood, and it is then that their election will manifest itself in their choices. But if a child dies under the parent, his election is known by the belief or lack thereof of the parent.
Otherwise, we end up arguing that people are saved apart from exercising faith in Christ, or we argue that all infants/little children are damned regardless because they cannot exercise faith on their own. Both of these are unbiblical. Making a conscious decision to follow the Lord Jesus Christ is the only way to be saved, so either the child or mentally disabled who cannot do that are all damned, or they are one with those under whom they have been placed, and the faith of their parent covers all that parent owns, including them. They, therefore, are saved as a person's appendage is saved, not because the appendage can exercise faith, but because the person to whom the appendage is attached can.
And if all of this is true, then one ought to consider baptizing his children, since they have been saved through faith. This is why the Holy Spirit has led His Church to this conclusion for ages past. Those who would have their children saved must be saved as well. Those who believe should be baptized as a declaration of their decision to repent and follow Christ, both that person and his household.
A woman named Lydia, from the city of Thyatira, a seller of purple fabrics, a worshiper of God, was listening; and the Lord opened her heart to respond to the things spoken by Paul. And when she and her household had been baptized, she urged us, saying, "If you have judged me to be faithful to the Lord, come into my house and stay." And she prevailed upon us. (Acts 16:14-15)
But Jesus said, "Let the children come to me. Don't stop them! For the Kingdom of Heaven belongs to those who are like these children." (Matt 19:14)