Quietus of Baruch said: We who live by faith ought to obey with careful observance those things which before have been foretold for our instruction. For it is written in Solomon: “He that is baptized from the dead, (and again touches the dead,) what avails his washing?” which certainly speaks of those who are washed by heretics, and of those that wash them. For if those who are baptized among them obtain by remission of their sins life eternal, why do they come to the Church? But if from a dead person no salvation is received, and therefore, acknowledging their previous error, they return to the truth with penitence, they ought to be sanctified with the one vital baptism which is in the Catholic Church.
Castus of Sicca said: He who with contempt of the truth presumes to follow custom, is either envious and malignant in respect of his brethren to whom the truth is revealed, or is ungrateful in respect of God, by whose inspiration His Church is instructed.
Euchratius of Thenae said: God and our Lord Jesus Christ, teaching the apostles with His own mouth, has entirely completed our faith, and the grace of baptism, and the rule of the ecclesiastical law, saying: “Go and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost.” Thus the false and wicked baptism of heretics must be rejected by us, and refuted with all detestation, from whose month is expressed poison, not life, not celestial grace, but blasphemy of the Trinity. And therefore it is manifest that heretics who come to the Church ought to be baptized with the sound and Catholic baptism, in order that, being purified from the blasphemy of their presumption, they may be reformed by the grace of the Holy Spirit.
Libosus of Vaga said: In the Gospel the Lord says, “I am the truth.” He said not, I am the custom. Therefore the truth being manifest, let custom yield to truth; so that, although for the past any one was not in the habit of baptizing heretics in the Church, let him now begin to baptize them.
Lucius of Thebeste said: I determine that blasphemous and unrighteous heretics, who with various words tear asunder the holy and adorable words of the Scriptures, are to be accursed, and therefore that they must be exorcised and baptized.
Eugenius of Ammedera said: And I determine the same— that heretics must be baptized.
Also another Felix of Amaccora said: And I myself, following the authority of the divine Scriptures, judge that heretics must be baptized; and, moreover, those also who contend that they have been baptized among the schismatics. For if, according to Christ's warning, our font is private to us, let all the adversaries of our Church understand that it cannot be for another. Nor can He who is the Shepherd of the one flock give the saving water to two peoples. And therefore it is plain that neither heretics nor schismatics can receive anything heavenly, seeing that they dare to receive from men who are sinners, and from those who are external to the Church. When there is no place for the giver, assuredly there is no profit for the receiver.
Also another Januarius of Muzzuli said: I am surprised, since all confess that there is one baptism, that all do not perceive the unity of the same baptism. For the Church and heresy are two things, and different things. If heretics have baptism, we have it not; but if we have it, heretics cannot have it. But there is no doubt that the Church alone possesses the baptism of Christ, since she alone possesses both the grace and the truth of Christ.
Adelphius of Thasvalte said: Certain persons without reason impugn the truth by false and envious words, in saying that we rebaptize, when the Church does not rebaptize heretics, but baptizes them.
Demetrius of Leptiminus said: We maintain one baptism, because we demand for the Church Catholic alone her own property. But they who say that heretics truly and legitimately baptize, are themselves the people who make not one, but many baptisms. For since heresies are many, according to their number will be reckoned baptisms.
Vincentius of Thibaris said: We know that heretics are worse than Gentiles. If, therefore, being converted, they should wish to come to the Lord, we have assuredly the rule of truth which the Lord by His divine precept commanded to His apostles, saying, “Go, lay on hands in my name, expel demons.” And in another place: “Go and teach the nations, baptizing them in the name of the Father, of the Son, and of the Holy Ghost.” Therefore first of all by imposition of hands in exorcism, secondly by the regeneration of baptism, they may then come to the promise of Christ. Otherwise I think it ought not to be done.
Marcus of Mactaris said: It is not to be wondered at if heretics, enemies, and impugners of the truth claim to themselves a matter in the power and condescension of others. But it is to be wondered at, that some of us, prevaricators of the truth, support heretics and oppose themselves to Christians. Therefore we decree that heretics must be baptized.
Sattius of Sicilibba said: If to heretics in baptism their sins are remitted, they come to the Church without reason. For since, in the day of judgment, they are sins which are punished, there is nothing which the heretics can fear from Christ's judgment, if they have already obtained remission of their sins.
Victor of Gor said: Since sins are not remitted save in the baptism of the Church, he who admits a heretic to communion without baptism does two things against reason: he does not cleanse the heretics, and he befouls the Christians.
Aurelius of Utica said: Since the apostle says that we are not to communicate with other people's sins, what else does he do but communicate with other people's sins, who holds communion with heretics without the Church's baptism? And therefore I judge that heretics must be baptized, that they may receive forgiveness of their sins; and thus communion may be had with them.
Iambus of Germaniciana said: They who approve of the baptism of heretics, disapprove of ours, in denying that they who are, I will not say washed, but befouled, outside the Church, ought to be baptized in the Church.
Lucianus of Rucuma said: It is written, “And God saw the light, that it was good, and divided between the light and the darkness.” If there can be agreement between light and darkness, there may be something in common between us and heretics. Therefore I determine that heretics must be baptized.
Pelagianus of Luperciana said: It is written, “Either the Lord is God, or Baal is God.” Therefore in the present case also, either the Church is the Church, or heresy is the Church. On the other hand, if heresy is not the Church, how can the Church's baptism be among heretics?
Jader of Midila said: We know that there is but one baptism in the Catholic Church, and therefore we ought not to receive a heretic unless he has been baptized among us; lest he should think that he has been baptized out of the Catholic Church.
Also another Felix of Marazana said: There is one faith, one baptism, but of the Catholic Church, which alone has the right to baptize.
Paulus of Obba said: It does not disturb me if any man does not assert the faith and truth of the Church, since the apostle says, “For what if some of them have fallen away from the faith? Has their unbelief made the faith of God of no effect? By no means. For God is true, but every man a liar.” But if God is true, how can the truth of baptism be among the heretics, among whom God is not?
Pomponius of Dionysiana said: It is evident that heretics cannot baptize and give remission of sins, seeing that they have not power to be able to loose or to bind anything on earth.
Venantius of Timisa said: If a husband, going into foreign parts, had commended his wife to the guardianship of his friend, that friend would take care of her who was commended to him with all possible diligence, that her chastity and holiness should not be corrupted by any one. Christ the Lord and our God, going to His Father, has commended to us His bride. Shall we guard her incorrupt and inviolate, or shall we betray her integrity and chastity to adulterers and corrupters? For he who makes the Church's baptism common to heretics, betrays the spouse of Christ to adulterers.
Ahymnus of Ausvaga said: We have received one baptism, and that same we maintain and practise. But he who says that heretics also may lawfully baptize, makes two baptisms.
Source: The Seventh Council of Carthage (New Advent)