How do paedobaptists address the argument that infants are incapable of doing what those of Cornelius' household did? Acts 10, the conversion of Cornelius' household, is often used as one of the prooftexts for infant baptism.

However, when reviewing Acts 10:44-46, I have two objections to its use as support for the doctrine: 


After receiving the Spirit the gentiles magnified/praised God. Infants can't verbally speak, let alone verbally praise God.
Acts 10:44 implies that those who heard the word could understand it. Infants can't understand the gospel message nor trust Christ as savior.


How do those who use Cornelius' conversion as support for infant baptism respond to these points? I know that other scripture is used to support infant baptism, but this question is specifically about Acts 10.
On a controversial issue like this, we need to be careful about the approach we take and the assumptions we bring to the discussion. As a person who supports infant baptism, I will do my best to lay out my understanding of how Acts 10 is read in this issue.

I'm going to start by looking at two issues:


What does the text itself tell us about who was present?
How does our answer to the first issue relate to the other more theological elements of the question?


The text has various markers indicating who may have been present.
In 10.1-2 we are introduced to Cornelius. We learn that he is head of an oikos, which is usually translated in English as either family or household. We don't know in this particular case the details of the household. But we do know that the piety of Cornelius is extended to the whole household.

In 10.3-8 Cornelius has the dream and in response he sends people to summon Peter. We learn from this section that the household includes at least two servants and a soldier/attendant (verse 7 NIV).

In 10.9-23 the focus is on Peter and his dream about the clean and unclean animals.

In 10.24-45 Peter arrives at Cornelius' home, gives his message and watches in amazement as the Spirit is poured out. Who is present? We know that Cornelius is present. We know that his relatives and close friends are present (verse 24). We don't know if his immediate household is present, but given the opening narrative and the focus on family throughout, it's a reasonable assumption.

We also know that Peter is present, and we find out in verse 45 that he has come as the leader of a group of circumcised believers. This is a detail not made clear till the final sentences of this long story. So it should alert us to the literary pattern of referring to Peter and Cornelius not just as individuals but as representatives of the two groups involved: circumcised believers and Gentiles. So we cannot assume that, at any point in the story where Peter or Cornelius alone are referred to, no one else is present.

So in summary this is a story where Cornelius and his family, household, friends and relatives are present. Peter and his fellow Jewish believers are also present. We do not and cannot know the precise make up of those two groups. All we can say is that children are quite possibly included in a household group such as this, but we don't know definitely one way or the other.

What then do we do with verses 44-46, and the statements about the Holy Spirit coming upon the Gentile group, who responded with praise and speaking in tongues. In my view a reasonable answer would be that to even ask the question is to read back into this text categories that don't apply. We have seen that the two key groups are the Jewish believers (headed by Peter) and the Gentiles (signified by Cornelius); and that we don't know the precise membership of the two groups. So the climax is not that the Spirit is poured out on adults. It's that the Spirit is poured out on Gentiles. To rule out children because children can't respond in intelligent faith is to miss the key theme of this text. It's also to make an assumption about the nature of faith which is irrelevant to the text. Why is adult faith required for those who are other than adults?

If this is a correct reading of the text, then there is another corollary. It is not a text that explicitly supports infant baptism. We can't use this text either way. We don't know conclusively if children were either present or absent. The best infant baptist view on this matter is a combination of two elements:
(1) Theological - such as the idea that baptism embraces the covenantal meaning of circumcision, and is therefore applicable to the same range of people.
(2) Historical - rather than look at one particular proof text such as Acts 10, the baptismal stories in the New Testament show a wide diversity of individuals (Paul and the Ethiopian eunuch), households (Cornelius and the Philippian jailer) and mass groups (Pentecost). This diversity is wide enough to embrace the faith of individual believers and the faith of parents and the church at large.