Papal infallibility is a dogma of the Catholic Church which states that, in virtue of the promise of Jesus to Peter, the pope when he speaks ex cathedra is preserved from the possibility of error on doctrine "initially given to the apostolic Church and handed down in Scripture and tradition".This doctrine, defined dogmatically at the First Vatican Council of 18691870 in the document Pastor aeternus, is claimed to have existed in medieval theology and to have been the majority opinion at the time of the Counter-Reformation.The doctrine of infallibility relies on one of the cornerstones of Catholic dogma, that of papal supremacy, whereby the authority of the pope is the ruling agent as to what are accepted as formal beliefs in the Catholic Church. The use of this power is referred to as speaking ex cathedra. "Any doctrine 'of faith or morals' issued by the pope in his capacity as successor to St. Peter, speaking as pastor and teacher of the Church Universal [Ecclesia Catolica], from the seat of his episcopal authority in Rome, and meant to be believed 'by the universal church,' has the special status of an ex cathedra statement. Vatican Council I in 1870 declared that any such ex cathedra doctrines have the character of infallibility (session 4, Constitution on the Church 4)." The doctrine of the Immaculate Conception proclaimed by Ineffabilis Deus in 1854 is "generally accepted" as being an ex cathedra statement. Since the declaration of papal infallibility by Vatican I (1870), the only example of an ex cathedra statement thereafter took place in 1950, when Pope Pius XII defined the Assumption of Mary as an article of faith. In Ineffabilis Deus and Pius XII's cases, the popes consulted with Catholic bishops before making their declaration.When he was prefect of the Congregation for the Doctrine of the Faith, Cardinal Ratzinger (later Pope Benedict XVI), under John Paul II's authority, stated in a formal response (responsum) to an inquiry (dubium) that John Paul II's decision on the ordination of women into the Catholic priesthood in his apostolic letter Ordinatio sacerdotalis was part of the "ordinary and infallible" magisterial teaching of the Catholic Church. Prof. Frank K. Flinn claims that Pope John Paul II's statement on the inadmissibility of women to the priesthood was not infallible; Flinn considers that Cardinal Ratzinger's later responsa to the dubium on the subject was therefore erroneous. Pope Francis stated in an interview that John Paul II's decision was "[t]he final word" on women ordination.

The First Vatican Council (Latin: Concilium Vaticanum Primum) was convoked by Pope Pius IX on 29 June 1868, after a period of planning and preparation that began on 6 December 1864. This, the twentieth ecumenical council of the Catholic Church, held three centuries after the Council of Trent, opened on 8 December 1869 and adjourned on 20 October 1870 after the revolutionary Capture of Rome. Unlike the five earlier general councils held in Rome, which met in the Lateran Basilica and are known as Lateran councils, it met in Saint Peter's Basilica in the Vatican, hence its name. Its best-known decision is its definition of papal infallibility.The council was convoked to deal with the contemporary "problems" of the rising influence of rationalism, anarchism, communism, socialism, liberalism, and materialism. Its purpose was, besides this, to define the Catholic doctrine concerning the Church of Christ. There was discussion and approval of only two constitutions: the Dogmatic Constitution on the Catholic Faith (Dei Filius) and the First Dogmatic Constitution on the Church of Christ (Pastor aeternus), the latter dealing with the primacy and infallibility of the Bishop of Rome. The first matter brought up for debate was the dogmatic draft of Catholic doctrine against the manifold errors due to rationalism. The Council condemned rationalism, secularism, liberalism, naturalism, modernism, materialism and pantheism. The Catholic Church was on the defensive against the main ideology of the 19th century. Another main goal of the council was to definitively define the powers and role of the pope.