Acts 2 (specifically part of verse 39) is a favorite of paedobaptists to bring up in support of their position. I think this is very ironic however, as the passage very clearly teaches credobaptism. In Acts 2 Peter preaches his first sermon after the Spirit is poured out on him (Acts 2:4-5). This causes some of the crowd to become convicted of their sins and repent. After this, the apostles begin baptizing the new converts:
41 Then they that gladly received his word were baptized: and the same day there were added unto them about three thousand souls.Acts 2:41 (KJV)
Whatever our interpretation of the rest of Acts 2, it must be consistent with this fact, that all those who gladly received the word, that is they who believed in the Apostle’s message, are the ones who were baptized. It does not say all that believed with their children were baptized, even though there would indeed have been children there as Deuteronomy 16:11 commands sons and daughters to be brought to the feast. Nor does it say that all the Jews were baptized as if being a Jew automatically meant that they were to be given the sign of baptism. It is only those whom the apostles saw had received the word that were baptized. Now on to the contested verses:
37 Now when they heard this, they were pricked in their heart, and said unto Peter and to the rest of the apostles, Men and brethren, what shall we do? 38 Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost. 39 For the promise is unto you, and to your children, and to all that are afar off, even as many as the Lord our God shall call. 40 And with many other words did he testify and exhort, saying, Save yourselves from this untoward generation.Acts 2:37–40 (KJV)
As you’ll note verse 39 does indeed say the promise is “to your children”. Before we conclude that this means all believer’s children should be baptized, we should first ask what promise this is. Because Peter has been talking about the Holy Spirit, it is most likely the promise of the pouring out of the Holy Spirit. So the promise of the Spirit is to “you, and to your children, and to all that are afar off, even as many as the Lord our God shall call.” Now as we’ve already seen not all the Jews were baptized so clearly the “you” must be conditional in some way. Additionally, no one thinks that “all that are far off”, a reference to the Jews that were dispersed from Israel out into the world and to gentiles, were all going to receive the Holy Spirit. These groups are conditioned by the phrase at the end, “even as many as the Lord our God shall call”. This it those who are called by God who have this promise. Thus is not to everyone who has the word preached to them, but those who receive what is called the inward call of God (see Romans 8:28-30 and John 6:43-48). So if the “You” and the “those far off” are conditioned upon the call of God, should we expect that the “your children” is not also conditioned by this phrase? The promise of the Holy Spirit is to those who are called by God, not merely any children of believers. And this interpretation fits in perfectly with what we see in Acts 2:41, that only believers were baptized.
To attack the pedobaptist interpretation from another angle, why is it that the children of those far off are not explicitly included in the promise? Why is it only the children of the Jews that are mentioned? If we search the scripture there is a connection to what the crowd of Jews said when Pilate was attempting to get them to choose Jesus for release:
25 Then answered all the people, and said, His blood be on us, and on our children.Matthew 27:25 (KJV)
We know from verses 23 and 36 of Acts 2 that many people (if not all) to whom Peter was preaching were the same ones who shouted this on that day. Peter says they participated in the crucifixion of Jesus, and the only way that could be true is if they were part of the crowd that asked for Jesus’ execution. So in telling the Jews that their children were included in the promise, he gives them assurance that just because they invoked a curse upon their children, doesn’t mean they were doomed forever. (As a brief aside here, is our God not wonderful that despite such a rebellious act where they desired to be cursed, that God did not give them what they asked but pardoned their sins? What mercy He has.) If Peter’s statement about the children is to reassure the Jews, it explains why the children of those far of were not included in the statement, as they were not under any particular curse. Thus, this isn’t some universal promise to the children of believers anywhere, but rather a recognition that there is no category of person (Jew, Gentile, whatever), that the Lord is not willing to call to himself.
A final point I want to make is that repentance is a precondition for receiving the Holy Spirit (v38). Although it does not explicitly say that repentance must precede baptism, many pedobaptists (although not all), would say that baptism of infants mean they automatically receive the Holy Spirit at that time. This, however, runs contrary to Acts 2. Those who would receive the Holy Spirit must repent. Baptism alone will not do this, and to teach our children that they have received the Holy Spirit when they have not is a terrible thing that may lead to a false assurance. Our children should be urged to examine themselves and repent, not told immediately they are Christians when God has not promised any such thing.
So after looking at this passage in Acts 2, who is it that we are to baptize? Just like the apostles, we should baptize those that receive the word, that is those who repent and believe. This includes any of our children who are believers. We do this when we have reason to think that someone has received the word, not immediately upon birth when we don’t know if they have received the word. The hope that someday they might receive the word is not grounds to baptize them either. We need to follow the apostolic pattern for whom baptism is to be administered.