What is papal infallibility, and how often has a pope used it?

Papal infallibility is a dogma of the Catholic Church. It states that, by virtue of Jesus's promise to Peter, the pope when he speaks ex cathedra is preserved from the possibility of error on doctrine. It does not mean that the pope cannot sin or otherwise err. "Ex cathedra" means "from the chair", and in 1870 Pius IX proclaimed what it covers: when, in the exercise of his office as shepherd and teacher of all Christians, in virtue of his supreme apostolic authority, the Bishop of Rome defines a doctrine concerning faith or morals to be held by the whole Church.

So it is narrow. Not all Catholic teaching is infallible, and Pastor aeternus, the document that defined the dogma, does not allow any infallibility for new doctrines. How often has it been used? Scholars count it differently, and there is no complete list of papal statements considered infallible. According to Professor Frank K. Flinn, the 1854 definition of the Immaculate Conception is generally accepted as an ex cathedra statement, and since 1870 the only example took place in 1950, when Pius XII defined the Assumption of Mary. In both cases, the popes consulted Catholic bishops first.

The dogma was defined by the First Vatican Council. Pope Pius IX convoked it on 29 June 1868, under the rising threat of the Kingdom of Italy encroaching on the Papal States. It opened on 8 December 1869, and was adjourned on 20 September 1870 after the Italian capture of Rome. In a first vote on 13 July 1870, of 601 voters, 451 were affirmative, 62 conditionally affirmative and 88 negative. In the final vote on 18 July, 433 voted yes and only two voted no.

Not everyone was convinced. John Henry Newman, personally convinced of papal infallibility, opposed defining it as dogma, fearing that it might be expressed in over-broad terms. And after the council, dissent arose among some Catholics, almost exclusively German, Austrian and Swiss.