Is it possible for someone to be an antipope even though the majority of cardinals claim he is pope? The case of Antipope Anacletus II proves that it is possible for a majority of cardinals to claim a man is pope while he, in reality, is an antipope. In 1130, a majority of cardinals voted for Cardinal Peter Pierleone to be pope. He called himself Anacletus II. He was proclaimed pope and ruled Rome for eight years by vote and consent of a absolute majority of the cardinals despite the fact he was a antipope. In 1130, just prior to the election of antipope Anacletus, a small minority of cardinals elected the real pope: Pope Innocent II. How is this possible? St. Bernard said "the 'sanior pars' (the wiser portion)... declared in favor of Innocent II. By this he probably meant a majority of the cardinal-bishops." (St. Bernard of Clairvaux by Leon Christiani, Page 72) Again, how is this possible when the absolute majority of cardinals voted for A...
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In Article 38 it says: the Holy Spirit incorporated into the Church instituted in her the means of salvation through the bonds of "profession of faith, of the sacraments, of ecclesiastical government and of communion" through this structure which the document affirms to be visible, but "through the Supreme Pontiff and the Bishops."
Later, in Article 39, we can delve into this: the communion of the Church in the Eucharist is fundamental to communion with the Bishop and with the Roman Pontiff. The document condemns anyone who goes against this teaching because it is an "incongruity" to this unity. Because the Pope, as the successor of Peter, is "the perpetual and visible foundation of the unity not only of the Bishops, but also of the multitude of the faithful." And it becomes an "intrinsic requirement" to maintain a legitimate unity in the Catholic Church.
This Encyclical Letter shows us that the celebration of Mass is valid only when it expresses this communion with Peter, a legitimately elected Supreme Pontiff, and other legitimate Bishops in communion with him.