Nobody is disputing St. Cyprian’s views on Peter. The question is whether he equated that authority of Peter with all bishops or with the pope alone. His defiance in the face of pope Stephen seems to indicate the former, especially in light of the quotations provided by Hesychios.
It depends on how you look at it. Sparring with the Pope over an unsettled doctrinal matter is not conclusive against the idea of a Papacy. As well, Cyprian clearly placed a higher view on the Petrine See as evidence in my citations above.
In the incident with Pope Stephen, Cyprian’s close ally on the matter was Firmillian. Cyprian and Firmillian did not accept (at the time) the validity of so-called “heretical baptism” and argued that those baptized in such circumstances would have to be baptized again. Stephen believed otherwise, that a baptism did not depend on the doctrinal prowess of the minister, but on the Spirit acting on the intent of the sacrament.
Firmillian wrote a letter to Cyprian. In that letter, is the following:
But what is the greatness of his error, and what the depth of his blindness, who says that remission of sins can be granted in the synagogues of heretics, and does not abide on the foundation of the one Church which was once based by Christ upon the rock, may be perceived from this, that Christ said to Peter alone, Whatsoever you shall bind on earth shall be bound in heaven…the power of remitting sins was given to the apostles, and to the churches which they, sent by Christ, established, and to the bishops who succeeded to them by vicarious ordination…I am justly indignant at this so open and manifest folly of Stephen, that he who so boasts of the place of his episcopate, and contends that he holds the succession from Peter*, on whom the foundations of the Church were laid**, should introduce many other rocks and establish new buildings of many churches; maintaining that there is baptism in them by his authority…Stephen, who announces that he holds by succession the throne of Peter, is stirred with no zeal against heretics…*There is no dispute from Firmilian that Stephen holds the place of Peter. Firmillian’s point is that Stephen is essentially disgracing the place of Peter by what he considers a departure from Peter “on whom the foundations of the Church were laid.”
When relating the decision of a local council,
Cyprian sent a letter to Stephen that read in part:*But the subject in regard to which we had chiefly to write to you, and
to confer with your gravity and wisdom, is one that more especially pertains both to the priestly authority and to the unity, as well as the dignity, of the Catholic Church, arising as these do from the ordination of the divine appointment; to wit, that those who have been dipped abroad outside the Church, and have been stained among heretics and schismatics with the taint of profane water, when they come to us and to the Church which is one, ought to be baptized … We have brought these things, dearest brother, to your knowledge, for the sake of our mutual honour and sincere affection;
believing that, according to the truth of your religion and faith, those things which are no less religious than true will be approved by you.*Cyprian is asking Stephen to approve their decision, a council’s decision.
According to Augustine’s historical account of the incident, Cyprian eventually conceded to Stephen’s view:*Seek counsel from the blessed Cyprian himself.
See how much he considered to depend upon the blessing of unity, from which he did not sever himself to avoid the communion of those who disagreed with him; how, though he considered that those who were baptized outside the communion of the Church had no true baptism, he was yet willing to believe that, by simple admission into the Church, they might, merely in virtue of the bond of unity, be admitted to a share in pardon. For thus he solved the question which he proposed to himself in writing as follows to Jubaianus: “But some will say, ‘What then will become of those who, in times past, coming to the Church from heresy, were admitted without baptism?’ The Lord is able of His mercy to grant pardon, and not to sever from the gifts of His Church those who, being out of simplicity admitted to the Church, have in the Church fallen asleep.” (Augustine,
On Baptism, II.18)*So according to the historical record, Cyprian submitted to Stephen’s view even though his position was otherwise. This, coupled with his letter regarding the council, seems to indicate that the Pope’s blessing was sought in order to certify the doctrine.