Infallibility: The state of being incapable of error. The requirements presumed for this are usually infinite wisdom and infinite knowledge. However, infallibility can, according to some, be temporarily bestowed upon a human being by ►God.
According to the conclusion of the First Vatican Council of July 18, 1870 under Pope Pius IX, a pope is infallible whenever he states a formal (ex cathedra) doctrine of faith. The wording of the statement is as follows:
"Faithfully adhering, therefore, to the tradition inherited from the beginning of the Christian Faith, we, with the approbation of the sacred council, for the glory of God our Savior, for the exaltation of the Catholic religion, and the salvation of Christian peoples, teach and define, as a Divinely revealed dogma, that the Roman pontiff, when he speaks ex cathedra, that is, when he, in the exercise of his office as shepherd and teacher of all Christians, by virtue of his supreme Apostolic authority, decides that a doctrine concerning faith or morals is to be held by the entire Church he possesses, in consequence of the Divine aid promised him in St. Peter, that infallibility with which the Divine Savior wished to have His Church furnished for the definition of doctrine concerning faith or morals; and that such definitions of the Roman pontiff are of themselves, and not in consequence of the Church's consent, irreformable."*
Pius IX showed already signs of mental confusion at the time of the council, and attributed himself not only infallibility but also miraculous healing forces. Still, since this statement on papal infallibility is itself conveyed as an infallible doctrine, no non-pope was allowed to contradict it. Indeed, some bishops who rejected the Council's decree were immediately excommunicated. The question of what would happen if a pope ex cathedra should declare the infallible doctrines of an earlier pope to be false was not discussed by the Council.
* Council decree Pastor aeternus, 07/18/1870. This English translation from"Vatican Council" in The Catholic Encyclopedia (online).