32 And if any one seek for divine authority in this matter, though what is held by the whole Church, and that not as instituted by Councils, but as a matter of invariable custom, is rightly held to have been handed down by authority, still we can form a true conjecture of the value of the sacrament of baptism in the case of infants, from the parallel of circumcision, which was received by God's earlier people, and before receiving which Abraham was justified, as Cornelius also was enriched with the gift of the Holy Spirit before he was baptized.
Yet the apostle says of Abraham himself, that "he received the sign of circumcision, a seal of the righteousness of the faith," having already believed in his heart, so that "it was counted unto him for righteousness." Why, therefore, was it commanded him that he should circumcise every male child in order on the eighth day, though it could not yet believe with the heart, that it should be counted unto it for righteousness, because the sacrament in itself was of great avail?
And this was made manifest by the message of an angel in the case of Moses' son; for when he was carried by his mother, being yet uncircumcised, it was required, by manifest present peril, that he should be circumcised, and when this was done, the danger of death was removed. As therefore in Abraham the justification of faith came first, and circumcision was added afterwards as the seal of faith; so in Cornelius the spiritual sanctification came first in the gift of the Holy Spirit, and the sacrament of regeneration was added afterwards in the laver of baptism.
And as in Isaac, who was circumcised on the eighth day after his birth, the seal of this righteousness of faith was given first, and afterwards, as he imitated the faith of his father, the righteousness itself followed as he grew up, of which the seal had been given before when he was an infant; so in infants, who are baptized, the sacrament of regeneration is given first, and if they maintain a Christian piety, conversion also in the heart will follow, of which the mysterious sign had gone before in the outward body.
And as in the thief the gracious goodness of the Almighty supplied what had been wanting in the sacrament of baptism, because it had been missing not from pride or contempt, but from want of opportunity; so in infants who die baptized, we must believe that the same grace of the Almighty supplies the want, that, not from perversity of will, but from insufficiency of age, they can neither believe with the heart unto righteousness, nor make confession with the mouth unto salvation.
Therefore, when others take the vows for them, that the celebration of the sacrament may be complete in their behalf, it is unquestionably of avail for their dedication to God, because they cannot answer for themselves. But if another were to answer for one who could answer for himself, it would not be of the same avail. In accordance with which rule, we find in the gospel what strikes every one as natural when he reads it, "He is of age, he shall speak for himself."
Source: On Baptism, Against the Donatists (New Advent)