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The Collaborative International Dictionary
Papal infallibility

Infallibility \In*fal`li*bil"i*ty\, n. [Cf. F. infaillibilit['e].] The quality or state of being infallible, or exempt from error; inerrability.

Infallibility is the highest perfection of the knowing faculty.
--Tillotson.

Papal infallibility (R. C. Ch.), the dogma that the pope can not, when acting in his official character of supreme pontiff, err in defining a doctrine of Christian faith or rule of morals, to be held by the church. This was decreed by the Ecumenical Council at the Vatican, July 18, 1870.

Wiktionary
papal infallibility

n. (context Roman Catholicism English) The concept that the Pope, under certain circumstance (when making a statement on faith or morals, etc.) is protected by the Holy Spirit from being able to make a mistake.

Wikipedia
Papal infallibility

Papal infallibility is a dogma of the Catholic Church that states that, in virtue of the promise of Jesus to Peter, the Pope is preserved from the possibility of error "when, in the exercise of his office as shepherd and teacher of all Christians, in virtue of his supreme apostolic authority, he defines a doctrine concerning faith or morals to be held by the whole Church."

This doctrine was defined dogmatically in the First Vatican Council of 1869–1870, but had been defended before that, existing already in medieval theology and being the majority opinion at the time of the Counter-Reformation.

According to Catholic theology, there are several concepts important to the understanding of infallible, divine revelation: Sacred Scripture, Sacred Tradition, and the Sacred Magisterium. The infallible teachings of the Pope are part of the Sacred Magisterium, which also consists of ecumenical councils and the "ordinary and universal magisterium." In Catholic theology, papal infallibility is one of the channels of the infallibility of the Church. The infallible teachings of the Pope must be based on, or at least not contradict, Sacred Tradition or Sacred Scripture.

The doctrine of infallibility relies on one of the cornerstones of Catholic dogma: that of petrine supremacy of the pope, and his authority as the ruling agent who decides what is accepted as formal beliefs in the Roman Catholic Church. The use of this power is referred to as speaking ex cathedra. The solemn declaration of papal infallibility by Vatican I took place on 18 July 1870. Since that time, the clearest example of an ex cathedra decree (not the only such decree) took place in 1950, when Pope Pius XII defined the Assumption of Mary as an article of faith. Prior to the solemn definition of 1870, there were other ex cathedra decrees, for example, Pope Boniface VIII in the bull Unam Sanctam of 1302, and Pope Pius IX in the Papal constitution Ineffabilis Deus of 1854.