Papal Infallibility was defined by the First Vatican Council of 1870 as the dogma that the Pope, when he solemnly defines a matter of faith and morals ex cathedra (that is, officially and as Supreme Pastor of the Universal Church), does not have the possibility of error.

Vatican Council, Sess. IV, Const. de Ecclesiâ Christi, c. iv, holds:

We teach and define that it is a dogma Divinely revealed that the Roman pontiff when he speaks ex cathedra, that is when in discharge of the office of pastor and doctor of all Christians, by virtue of his supreme Apostolic authority, he defines a doctrine regarding faith or morals to be held by the universal Church, by the Divine assistance promised to him in Blessed Peter, is possessed of that infallibility with which the Divine Redeemer willed that his Church should be endowed in defining doctrine regarding faith or morals, and that therefore such definitions of the Roman pontiff are of themselves and not from the consent of the Church irreformable.

The conditions required for ex cathedra teaching are mentioned in the Vatican decree:

Ex cathedra solemn definitions made as above (or by a Council convened and confirmed by a Pope) are said to be an exercise of the "Extraordinary Magisterium" (also called the "Solemn Magisterium").

The only other statements of the Pope that are infallible are statements that simply reiterate what has been handed down by the apostles and has always been taught by the Church. These infallible statements are said to exercise the "Universal Magisterium" (also called the "Constant Magisterium").

Statements that exercise neither the Universal Magisterium nor the Extraordinary Magisterium (i.e., statements that do not simply reiterate what has always been taught or which are not solemn definitions expressed ex cathedra) are not infallible, and are said to be an exercise of the merely authentic Magisterium (i.e., "authoritative" Magisterium). Such teaching is also to be obeyed as long as it does not contradict infallible Magisterium and does not harm the faith or lead to sin.

Invocations of the Pope's Solemn (or "Extraordinary") Magisterium are rare. Since 1870 only one statement exercising the Solemn Magisterium has been made, Pope Pius XII's dogma on the "Assumption of the Virgin Mary into Heaven" in 1950.

Following the first Vatican Council, 1870, dissent, mostly among German, Austrian and Swiss Catholics, arose over the definition of Papal Infallibility. The dissenters, holding the General Councils of the Church infallible, were unwilling to accept the dogma of Papal Infallibility. Many of these Catholics formed independent communities which became known as the Old Catholic Church.

In reality very few doctrines have been proclaimed as infallible in Roman Catholicism. Among the issues not proclaimed as infallible are teachings on sexuality (notably Pope Paul VI's Humanæ Vitæ, which neither he nor his successors chose to proclaim ex-cathedra), the decisions of either of the Vatican Councils and the Church's stance on the celibacy and gender of its clergy.

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