Infallibility belongs in a special way to the pope as head of the bishops (Matt. 16:17–19; John 21:15–17). As Vatican II remarked, it is a charism the pope "enjoys in virtue of his office, when, as the supreme shepherd and teacher of all the faithful, who confirms his brethren in their faith (Luke 22:32), he proclaims by a definitive act some doctrine of faith or morals. Therefore his definitions, of themselves, and not from the consent of the Church, are justly held irreformable, for they are pronounced with the assistance of the Holy Spirit, an assistance promised to him in blessed Peter." http://www.catholic.com/tracts/papal-infallibility Pope Alexander IV is a great study int his subject. One of my favorites. RCC apologists will say that the above doctrine does not protect the pope from personal sin. But this pope did his deeds in the name of the church. Even New Advent says, about him... An impartial appreciation of the career of this extraordinary person must at once distinguish between the man and the office. "An imperfect setting", says Dr. Pastor (op. cit., III, 475), "does not affect the intrinsic worth of the jewel, nor does the golden coin lose its value when it passes through impure hands. In so far as the priest is a public officer of a holy Church, a blameless life is expected from him, both because he is by his office the model of virtue to whom the laity look up, and because his life, when virtuous, inspires in onlookers respect for the society of which he is an ornament. But the treasures of the Church, her Divine character, her holiness, Divine revelation, the grace of God, spiritual authority, it is well known, are not dependent on the moral character of the agents and officers of the Church. The foremost of her priests cannot diminish by an iota the intrinsic value of the spiritual treasures confided to him." There have been at all times wicked men in the ecclesiastical ranks. Our Lord foretold, as one of its severest trials, the presence in His Church not only of false brethren, but of rulers who would offend, by various forms of selfishness, both the children of the household and "those who are without". Similarly, Ho compared His beloved spouse, the Church, to a threshing floor, on which fall both chaff and grain until the time of separation. The most severe arraignments of Alexander, because in a sense official, are those of his Catholic contemporaries, Pope Julius II (Gregorovius, VII, 494) and the Augustinian cardinal and reformer, Aegidius of Viterbo, in his manuscript "Historia XX Saeculorum", preserved at Rome in the Bibliotheca Angelica. The Oratorian Raynaldus (d. 1677), who continued the semi-official Annals of Baronius, gave to the world at Rome (ad an. 1460, no. 41) the above-mentioned paternal but severe reproof of the youthful Cardinal by Pius II, and stated elsewhere (ad an. 1495, no. 26) that it was in his time the opinion of historians that Alexander had obtained the papacy partly through money and partly through promises and the persuasion that ho would not interfere with the lives of his electors. Mansi, the scholarly Archbishop of Lucca editor and annotator of Raynaldus, says (XI, 4155) that it is easier to keep silence than to write write moderation about this Pope. The severe judgment of the late Cardinal Hergenröther, in his "Kirchengeschichte", or Manual of Church History (4th. ed., Freiburg, 1904, II, 982-983) is too well known to need more than mention. How does a church protected by God himself, from error, put a guy like this at the head of it ?