This plea in their defense he would not have subjoined had he not believed it to be perfectly just, and one which would be of service to these infants at the bar of divine judgment. For if it is said by them with truth, We have done nothing, then the soul that sins, it shall die; and in the just dispensation of judgment by God, those shall not be doomed to perish whose souls their parents did, so far at least as concerns their own guilt in the transaction, bring to ruin.
...
The presentation of the little ones to receive the spiritual grace is the act not so much of those by whose hands they are borne up (although it is theirs also in part, if they themselves are good believers) as of the whole society of saints and believers. For it is proper to regard the infants as presented by all who take pleasure in their baptism, and through whose holy and perfectly-united love they are assisted in receiving the communion of the Holy Spirit. Therefore this is done by the whole mother Church, which is in the saints, because the whole Church is the parent of all the saints, and the whole Church is the parent of each one of them. For if the sacrament of Christian baptism, being always one and the same, is of value even when administered by heretics, and though not in that case sufficing to secure to the baptized person participation in eternal life, does suffice to seal his consecration to God; and if this consecration makes him who, having the mark of the Lord, remains outside of the Lord's flock, guilty as a heretic, but reminds us at the same time that he is to be corrected by sound doctrine, but not to be a second time consecrated by repetition of the ordinance — if this be the case even in the baptism of heretics, how much more credible is it that within the Catholic Church that which is only straw should be of service in bearing the grain to the floor in which it is to be winnowed, and by means of which it is to be prepared for being added to the heap of good grain!
6. I would, moreover, wish you not to remain under the mistake of supposing that the bond of guilt which is inherited from Adam cannot be cancelled in any other way than by the parents themselves presenting their little ones to receive the grace of Christ; for you write: As the parents have been the authors of the life which makes them liable to condemnation, the children should receive justification through the same channel, through the faith of the same parents; whereas you see that many are not presented by parents, but also by any strangers whatever, as sometimes the infant children of slaves are presented by their masters. Sometimes also, when their parents are deceased, little orphans are baptized, being presented by those who had it in their power to manifest their compassion in this way. Again, sometimes foundlings which heartless parents have exposed in order to their being cared for by any passer-by, are picked up by holy virgins, and are presented for baptism by these persons, who neither have nor desire to have children of their own: and in this you behold precisely what was done in the case mentioned in the Gospel of the man wounded by thieves, and left half dead on the way, regarding whom the Lord asked who was neighbour to him, and received for answer: He that showed mercy on him. Luke 10:37
https://www.newadvent.org/fathers/1102098.htm
...
The presentation of the little ones to receive the spiritual grace is the act not so much of those by whose hands they are borne up (although it is theirs also in part, if they themselves are good believers) as of the whole society of saints and believers. For it is proper to regard the infants as presented by all who take pleasure in their baptism, and through whose holy and perfectly-united love they are assisted in receiving the communion of the Holy Spirit. Therefore this is done by the whole mother Church, which is in the saints, because the whole Church is the parent of all the saints, and the whole Church is the parent of each one of them. For if the sacrament of Christian baptism, being always one and the same, is of value even when administered by heretics, and though not in that case sufficing to secure to the baptized person participation in eternal life, does suffice to seal his consecration to God; and if this consecration makes him who, having the mark of the Lord, remains outside of the Lord's flock, guilty as a heretic, but reminds us at the same time that he is to be corrected by sound doctrine, but not to be a second time consecrated by repetition of the ordinance — if this be the case even in the baptism of heretics, how much more credible is it that within the Catholic Church that which is only straw should be of service in bearing the grain to the floor in which it is to be winnowed, and by means of which it is to be prepared for being added to the heap of good grain!
6. I would, moreover, wish you not to remain under the mistake of supposing that the bond of guilt which is inherited from Adam cannot be cancelled in any other way than by the parents themselves presenting their little ones to receive the grace of Christ; for you write: As the parents have been the authors of the life which makes them liable to condemnation, the children should receive justification through the same channel, through the faith of the same parents; whereas you see that many are not presented by parents, but also by any strangers whatever, as sometimes the infant children of slaves are presented by their masters. Sometimes also, when their parents are deceased, little orphans are baptized, being presented by those who had it in their power to manifest their compassion in this way. Again, sometimes foundlings which heartless parents have exposed in order to their being cared for by any passer-by, are picked up by holy virgins, and are presented for baptism by these persons, who neither have nor desire to have children of their own: and in this you behold precisely what was done in the case mentioned in the Gospel of the man wounded by thieves, and left half dead on the way, regarding whom the Lord asked who was neighbour to him, and received for answer: He that showed mercy on him. Luke 10:37
https://www.newadvent.org/fathers/1102098.htm