The Catholic Church does not teach that the pope is infallible in everything he says; official invocation of papal infallibility is – apart from canonizations of saints – extremely rare. And those are usually regarded as not of divine faith, as they depend on facts that post-date New Testament revelation.
Catholic theologians agree that both Pope Pius IX's 1854 definition of the dogma of the Immaculate Conception of Mary and Pope Pius XII's 1950 definition of the dogma of the Assumption of Mary are instances of papal infallibility, a fact confirmed by the Church's magisterium.[64] However, theologians disagree about what other documents qualify.
Regarding historical papal documents, Catholic theologian and church historian Klaus Schatz made a thorough study, published in 1985, that identified the following list of ex cathedra documents (see Creative Fidelity: Weighing and Interpreting Documents of the Magisterium, by Francis A. Sullivan, chapter 6):
Tome to Flavian, Pope Leo I, 449, on the two natures in Christ, received by the Council of Chalcedon;
Letter of Pope Agatho, 680, on the two wills of Christ, received by the Third Council of Constantinople;
Benedictus Deus, Pope Benedict XII, 1336, on the beatific vision of the just after death rather than only just prior to final judgment;[65]
Cum occasione, Pope Innocent X, 1653, condemning five propositions of Jansen as heretical;
Auctorem fidei, Pope Pius VI, 1794, condemning seven Jansenist propositions of the Synod of Pistoia as heretical;
Ineffabilis Deus, Pope Pius IX, 1854, defining the Immaculate Conception;
Munificentissimus Deus, Pope Pius XII, 1950, defining the Assumption of Mary.
There is no complete list of papal statements considered infallible. A 1998 commentary on Ad Tuendam Fidem issued by the Congregation for the Doctrine of the Faith published on L'Osservatore Romano in July 1998[66] listed a number of instances of infallible pronouncements by popes and by ecumenical councils, but explicitly stated (at no. 11) that this was not meant to be a complete list.
One of the documents mentioned is Pope John Paul II's apostolic letter Ordinatio Sacerdotalis on reserving priestly ordination to men alone,[67] which the Congregation earlier stated to be infallible, although not taught ex cathedra (i.e., although not a teaching of the extraordinary magisterium), clarifying that the content of this letter has been taught infallibly by the ordinary and universal magisterium.[68] This was confirmed in a commentary by the same Congregation[66] and in commentaries by Cardinals Joseph Ratzinger[69] and Tarcisio Bertone.[70] Many eminent theologians dispute that this is truly infallible, including Nicholas Lash, an ex-priest and Emeritus Professor of Divinity at the University of Cambridge.[71] The Catholic Theological Society of America in a report, "Tradition and the Ordination of Women", concluded that Ordinatio Sacerdotalis is mistaken with regard to its claims on the authority of this teaching and its grounds in Tradition.[72]
As well as popes, ecumenical councils have made pronouncements that the Church considers infallible.