Father Larry Rice explains papal infallibility and how it works.
“Papal infallibility is a recent thing in the history of the Church, because it was not even thoroughly defined until the first Vatican Council in the middle of the 19th century. It had always been kind of presumed that the pope had this authority, but it was not until Vatican I that this was thoroughly defined.”
“For something to be an infallible papal pronouncement, there are some conditions that have to be met. First, it has to be a decree on matters of faith or morals. So the Pope cannot infallibly declare that the earth revolves around the moon or that hydrogen atoms have four electrons and not one. [Second,] the declaration is binding on the whole church, but it has to happen in union with the whole Church. So, it has to be pronounced in union with the bishops and in continuity with what the Church has always taught. It can’t be something that’s completely new and out of left field. This is a way of pinning down something that the Church believes, not creating something new. And the Pope has to be speaking with the full authority of the papacy and not in a personal capacity. That means he has to say, ‘I am intending to pronounce this infallibly with the full authority of the chair of St. Peter.’ You can’t make an infallible statement by accident.”
Father Larry points out that there have only been two formal infallible statements or declarations a pope has made since the first Vatican Council: The dogma of the Immaculate Conception and the Assumption of the Blessed Virgin Mary.