A nice, straightforward Pauline case for infant baptism
This argument contains no Abrahams or covenants or foreskins or anything like that. You don’t have to leave the New Testament for this one. In fact, you don’t even need to venture beyond the Pauline epistles.
I think that simply by considering what Paul says about baptism together with his exhortations to children in Ephesians and Colossians, you can make the inference that Paul presumed that the children hearing the reading of his epistles were baptised.
(I can imagine some possible objections to the argument as presented, but I omit responding to them for the sake of brevity. Perhaps another day.)
The argument goes like this:
Firstly, Paul says in his epistles that his hearers are in union with Christ by their baptisms.
Secondly, Paul exhorts his hearers to spiritual obedience on the basis of their being in union with Christ by their baptisms.
Thirdly, amongst other Christians in the church, Paul exhorts children to this same kind of spiritual obedience.
Therefore, I conclude that the children to whom Paul gives these exhortations have been baptised into union with Christ.
Baptised into Christ
For as many of you as have been baptised into Christ have put on Christ. (Gal. 3:27)
Firstly, Paul says in his epistles that his hearers are in union with Christ by their baptisms.
The rite of baptism, in some way or other, closely relates to union with Christ, so that Paul can use “baptised”, “in Christ” and “in the Lord” more or less interchangeably. Paul tells the Colossians that they have put off the body of the sins of the flesh because they were buried with Christ in baptism (Col. 2:11-12). Similarly, he tells the Romans that those baptised into Christ have been baptised into his death, so that the body of sin might be destroyed (Rom. 6:3). He tells the Galatians that those that have been baptised into Christ have put on Christ (Gal. 3:27).
My argument does not depend on a particular view of how baptism is related to union with Christ. For my purposes here, it suffices to show that Paul everywhere describes baptised people as people who are thereby united to Christ as members of his body.
Spiritual obedience
Therefore we are buried with him by baptism into death: that like as Christ was raised up from the dead by the glory of the Father, even so we also should walk in newness of life. (Rom. 6:4)
Secondly, Paul exhorts his hearers to spiritual obedience on the basis of their being in union with Christ by their baptisms.
Having told the Colossians that by their baptisms they have been buried with Christ and put off the body of sin, Paul goes on throughout the rest of the epistle to exhort to his hearers to certain acts of obedience on that basis. For example, Paul commands the Colossians not to lie to each other, and the basis for this is that they have “put off the old man with his deeds; and have put on the new man” (Col. 3:9-10). Later, he commands wives to submit to their husbands “as it is fit in the Lord” (Col. 3:18).
Similarly in Romans, burial with Christ in baptism means union with Christ in his death and resurrection, and this fact leads naturally to Paul’s ethical exhortation that “we too might walk in newness of life” (Rom. 6:1-4). Again, baptism is the basis of the exhortation.
When I say “spiritual obedience”, I mean something stronger than mere outward compliance with ethical principles, which anyone in the flesh might be able to do. I mean the kind of obedience from the heart which is the fruit of the Spirit, that comes from union with Christ and is truly pleasing to God. As Paul teaches, those that are in the flesh cannot please God. But he presumes that his readers are different: they are baptised into Christ's death, so that the body of sin has been destroyed. They are made ready by the Spirit of God for fruitful spiritual obedience which pleases the Lord:
So then they that are in the flesh cannot please God. But ye are not in the flesh, but in the Spirit, if so be that the Spirit of God dwell in you. Now if any man have not the Spirit of Christ, he is none of his… (Rom. 8:8-9)
Children “in the Lord”
Children, obey your parents in the Lord: for this is right. (Eph. 6:1)
Children, obey your parents in all things: for this is well pleasing unto the Lord. (Col: 3:20)
Thirdly, amongst other Christians in the church, Paul exhorts children to this same kind of spiritual obedience.
Not only are husbands, wives, fathers, masters and slaves exhorted to the spiritual obedience discussed above, but so are children. It seems to go without saying for Paul that children can appropriately be addressed on the same footing as these other Christians, without any further qualifications.
Paul instructs the children in Ephesus to obey their parents “in the Lord: for this is right” (Eph. 6:1). Quite obviously, this is an exhortation to spiritual obedience that assumes union with Christ.
Paul gives us another angle on this same commandment in Colossians, where he exhorts children to obey their parents “for this is well pleasing unto the Lord” (Col. 3:20). Recalling what Paul says about pleasing the Lord in Romans 8:8-9, we should note that Paul assumes that these children are not in the flesh, but rather in the Spirit–that is, they are in Christ and the Spirit of Christ dwells in them.
In both these cases where Paul addresses children, he assumes that they are in union with Christ, and he gives them exhortations that only make sense with that assumption.
Conclusion: these children were baptised
Therefore, I conclude that the children to whom Paul gives these exhortations have been baptised into union with Christ.
If we accept that baptism is so closely related to union with Christ that Paul speaks of them interchangeably, and we accept that Paul makes exhortations that assume union with Christ to children, then we must conclude that these children addressed in Ephesians and Colossians were baptised.
If we must be as modest as possible, we can at least say that Paul expected that children born to Christian parents could be presumed to be baptised. I think we have enough here to show what Paul believed to be the norm.
However, if Paul didn’t assume as a norm that Christian parents would have their children baptised, then it should strike us as exceedingly strange that Paul doesn’t have anything whatsoever to say about such children who are not baptised into Christ. This is an argument from silence, yes–but this is exactly the kind of silence one would expect if the baptism of children were the expected and normal practice in these churches. If Christian churches in the apostolic era entertained many children who were not baptised into Christ, we should marvel that we don't see a single mention of such children in the New Testament