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According to Calvin the Papacy is totally invalid because in the New Testament there is no injunction given to Peter to find successors in a juridical sense. To keep the unity of the Church, Christ is all we need.
This is an excerpt from my forthcoming book, A Christian’s Pocket Guide to the Papacy (Fearn: Christian Focus Publications, 2015)
The Papacy has always had its critics throughout the centuries. It is fair to say, however, that it was the XVI century Protestant Reformation that developed the most comprehensive and massive argument against the Papacy pulling together Biblical, doctrinal, historical, moral, and institutional threads in order to do so. The Protestant critique reached its peak with the identification of the Pope as the Antichrist. According to the New Testament the Antichrist is someone who is against Christ and His church by wanting to take His place and destroy His work (e.g. 2 Thessalonians 2). For Christians the Antichrist is the enemy par excellence. This equation stirred the religious emotions more than many subtle theological arguments.
The Protestant Reformation was not the first movement that referred to the Pope as the Antichrist. There was a robust Medieval European tradition – from the Waldensians to Wycliffe, and down to the Hussites – that had denounced the Pope in such a radical way. This is why a recent Roman Catholic and Lutheran dialogue in the United States acknowledges this fact: “In calling the pope the ‘antichrist’ the early Lutherans stood in a tradition that reached back into the eleventh century. Not only dissidents and heretics but even saints had called the bishop of Rome the ‘antichrist’ when they wished to castigate his abuse of power”. Even in this case the Reformers were not necessarily innovative but relied on previous strands of thought well attested for in Church history. Here is how John Calvin argued his case against the Papacy.
The French Reformer John Calvin dealt with Roman Catholic representatives at various times and in different ways.  His major work, the Institutes of the Christian Religion (first edition: 1536) contains frequent interactions with Roman Catholic doctrines and practices. Here Calvin develops his argument that the Pope is the Antichrist (Institutes IV,7,25). The historical Pope that Calvin had in view was Paul III (1534-1549) but his critique never focuses on his person, but rather on the Papal institution.
After underlining the fact that the Antichrist sets his tyranny in opposition to the spiritual kingdom of Christ, Calvin writes that the Antichrist “abolishes not the name of either Christ or the Church, but rather uses the name of Christ as a pretext, and lurks under the name of Church as under a mask” by robbing God of his honor. This is, for him, a clear picture of the Pope and therefore he concludes by saying that “it is certain that the Roman Pontiff has impudently transferred to himself the most peculiar properties of God and Christ, there cannot be a doubt that he is the leader and standard-bearer of an impious and abominable kingdom”. Calvin is not speaking of a particular historical Pope, but he is referring to the Pope as representing the institution of the Papacy.
AN ANTIDOTE TO THE PAPACY
Calvin’s main critical analysis of the Papacy is found in two works in particular. In 1543 the theological faculty of the Sorbonne published twenty-five articles that candidates had to subscribe to as a kind of oath to remain faithful to the Catholic Church. The following year, Calvin wrote a refutation of this summary of Catholic doctrine in his Articuli a facultate sacrae theologiae parisiensi by quoting each article and providing a critical review, i.e. an “antidote”. Article XXIII treats the primacy of the See of Rome and rehearses Catholic proofs for it. In response, Calvin argues that while Scripture often speaks of Christ as the head of the Church, it never does so as far as the Pope is concerned.
The unity of the Church is based on one God, one faith and one baptism (Ephesians 4:4), but there is no mention of the necessity of the Pope in order for the Church to be the Church. Moreover, in listing the ministries and offices of the Church, Paul is silent about a present or future Papacy. Peter was Paul’s co-worker, not his pope-like leader. The universal Bishop of the Church is Christ alone. To this Biblical argument for the headship of Christ, Calvin adds a historical reference to some Patristic writings that support the same New Testament view. Even Cyprian of Carthage, who is often considered a Church Father who favored an early form of a Papacy, calls the bishop of Rome a “brother, fellow-Christian, and colleague in the episcopate”, thus showing that he did not have in view the kind of primacy that was later attributed to the Pope.
These kinds of Biblical and patristic arguments against the Papacy can be found in another giant of the Protestant Reformation of the XVI century, namely Peter Martyr Vermigli (1499-1562), especially in his 1542 Trattato della vera chiesa e della necessità di viver in essa (Treatise of the true church and the necessity to live in her). They appear to be standard controversial treatments of the magisterial Reformation.
WHAT IS WRONG WITH THE PAPACY?
Returning to Calvin, another of his works that deals with the Papacy was written in 1549. When Charles tried to find a compromise solution to the Augsbug Interim, Bucer and Bullinger urged Calvin to respond. He wrote the treatise Vera Christianae pacificationis et Ecclesiae reformandae ratio, in which he described the doctrines that should be upheld, including justification by faith. In expounding the doctrine of the Church, Calvin devotes a section to the Papacy. Here he criticizes the standard Catholic reading of John 21, a New Testament text that is considered to be one of the Biblical foundations of the Papal office. In commenting on the passage, Calvin notes that the threefold command to Peter to shepherd the sheep is to be related to the threefold denial of Jesus by Peter.
This office is not exclusive given the fact that Peter exhorts his fellow-elders to do the same (1 Peter 5:2). Furthermore, according to Calvin the Papacy is totally invalid because in the New Testament there is no injunction given to Peter to find successors in a juridical sense. To keep the unity of the Church, Christ is all we need. Calvin then comments on the choice of Rome as the chosen See for the Pope. “Why Rome,” Calvin asks. In writing to the Romans, Paul mentions many individual names, but Peter is not on the list. And even if Peter would later go to Rome, why was the city selected as the special and central place for future Popes? Why not Jerusalem? Or Antioch? Calvin, however, does not address the political and historical importance of Rome as reasons for locating the Papacy there.
Finally, Calvin once again accuses the Pope of being the Antichrist because of his “tyranny”, “destruction of the truth”, “corruption of the worship of God”, “breaking of His ordinances”, and the “dispersion of the order of His Church”. Here we see many similarities with Luther, with the exception that with Calvin the apocalyptic tone is not as strong and is less evident than that of the German reformer. Rather than passionate eschatological concerns, Calvin relies on lucid theological and Biblical arguments in his effort to grapple with the Papacy.
 “Differing Attitudes Towards Papal Primacy” (1973). The text can be accessed at http://www.usccb.org/beliefs-and-teachings/ecumenical-and-interreligious/ecumenical/lutheran/attitudes-papal-primacy.cfm and is a useful summary of the main controversial issues around the Papacy between present-day Lutherans and Roman Catholics.
 On Calvin’s views of Rome as they are presented in various writings, see M. Stolk, Calvin and Rome in H.J. Selderhuis (ed.), The Calvin Handbook (Grand Rapids, MI: Eerdmans, 2009) pp. 104-112.
 This word “antidote” would come back in Calvin’s refutations of the Acts of the Council of Trent. See his Acta synodi Tridentinae cum Antidoto (1547).
 See also Calvin’s Institutes IV,6-7.
 See my paper “Separazione e riforma della Chiesa ne ‘Il Trattato della vera Chiesa e della necessità di viver in essa’”, A. Oliveri and P. Bolognesi (edd.), Pietro Martire Vermigli (1499-1562). Umanista, Riformatore, Pastore (Rome: Herder, 2003) pp. 225-232.