What does papal infallibility actually mean, and what does it not mean?

Papal infallibility means that when the pope meets four specific conditions laid down by Vatican I he is divinely protected from teaching error on faith or morals, and it does not mean he is sinless, inspired, always right, or infallible in anything he happens to say. Vatican I in 1870 put it in one sentence, and the whole doctrine lives or dies on its wording. The Roman Pontiff, when he speaks ex cathedra, that is, when carrying out the duty of the pastor and teacher of all Christians, in accord with his supreme apostolic authority, he explains a doctrine of faith or morals to be held by the universal Church, operates with that infallibility with which the divine Redeemer wished that his Church be instructed. And such definitions of the Roman Pontiff, of themselves and not from the consensus of the Church, are unalterable. That paragraph is traditionally distilled into four criteria. One, the pope intends to teach. Two, he teaches by virtue of his supreme apostolic authority. Three, he teaches on a matter of faith or morals. Four, he directs the teaching to the universal Church. All four have to be present. Miss one and you do not have an infallible definition. Now the negatives, because this is where most of the confusion lives. Infallibility is not impeccability. Our Lord never promised that the pope would live a holy life. If that is what you are looking for in the Catholic Church, you are in the wrong place. Read the Gospels on Peter himself: an impetuous man who spoke before he thought and acted before he knew the right thing to do, and even after Pentecost he had to be corrected. We have had popes the Church herself calls bad popes. The Borgias made a monopoly of the papacy. There have been a few rascals in the twentieth century too, some of them shielded by their popularity. The only thing Christ promised was that the Church would be protected in her doctrine. Heaven guarantees that you will be given the right teaching. What you do with it, with your free will and God's grace, is on you. Infallibility is not inspiration, and it does not produce new revelation. Public revelation closed with the death of the apostles. The pope guards the deposit; he does not add to it. Infallibility does not attach to everything a pope says or writes. Here I have to be blunt about something Catholics are rarely told: popes have taught error. The most famous case is Honorius I, who declared to the bishops of the east that Christ had only one will (Denzinger 251), and who was condemned posthumously by Pope Agatho, Pope Leo II, and the sixth, seventh and eighth ecumenical councils. There are roughly forty other instances of error in the teaching of Catholic popes. Far from undermining the doctrine, those very incidents are what pushed Vatican I to define papal infallibility with precision, so that the Church would say what it covered and what it did not. Then there is the practical difficulty, and I do not pretend it away. The words "infallible" and "irreformable" are not used in dogmatic proclamations. No pope prefaces a teaching with, "this statement fulfills all four criteria and is therefore irreformable." The Church has never published an official list of her dogmas, nor a list of which papal decrees were infallible and which were not. And the 1983 Code of Canon Law adds that no doctrine is understood as defined infallibly unless this is manifestly evident (canon 749.3), which repeats the 1917 Code (canon 1323). So you are frequently left to judge. The result is that good Catholics argue. Is Humanae Vitae on contraception formally infallible? Is Ordinatio Sacerdotalis on women's ordination? Neither document says so. Defenders often retreat to the ordinary universal magisterium or the constant teaching of the Church instead. That appeal is legitimate, but it carries its own problem, because it hands the determination to clerics and laymen operating at a much lower level of authority than the pope, which guarantees diverse opinions about which traditional teachings are infallible and which are not. As good as the doctrine of infallibility is, its self-imposed restrictions mean the whole process can turn into a quagmire of distinctions and counter-distinctions, tedious legalese that confuses more than it clarifies. Here is the part people get backwards. If a teaching is not formally infallible, that does not make it false, and it does not make it optional. A doctrine at a lower level of certainty still binds you to assent and obedience. What the lower level means is narrower than most assume: you cannot be condemned to eternal punishment for holding a mental reservation about it. The scriptural ground for the office is three texts the Fathers and the popes cite together. Matthew 16:18-19, where Christ builds the Church on Peter, gives him the keys of the kingdom, and gives him the power to bind and loose. Luke 22:32, where Christ says he has prayed for Peter that his faith may not fail, and tells him to strengthen his brethren. And John 21:15-17, feed my sheep. Pope Gregory the Great quoted all three to the Emperor Maurice in one breath. And Theodore Abuqurra, the Melkite bishop of Haran, made the decisive point about Luke 22:32: those words cannot have been meant for Peter's person alone, because the apostle who denied Christ was abandoned in the very moment, and no apostle ever fell so that Peter might strengthen him. It was after the apostles died that the heresiarchs agitated the Church. Christ was designating those who would take Peter's place at Rome.