The pope can exercise his papal infallibility in two ways. One is called the Extraordinary Magisterium, and the other is called Ordinary Magisterium. The word magisterium is from the Latin word magister meaning teacher, so the Magisterium is the teaching authority of the Church, which is manifested by the pope alone and or the pope along with the bishops all over the world.
The Extraordinary Magisterium
Extraordinary means just that, out of the ordinary. When an Ecumenical (General) Council is convened, presided over, and approved by the pope, and he issues definitive decrees, they’re considered infallible because they come from the Extraordinary Magisterium.
The Catholic Church has held an all-time total of only 21 councils. These are gatherings of the world’s bishops and cardinals. Sometimes priests, deacons, and laity are invited to observe, but only bishops and the pope can discuss and vote. The culmination of these councils is a written letter that explains the faith, interprets Scripture, or settles disputed topics of faith and morals.
They never contradict the Bible but apply biblical truths to contemporary concerns and problems, as well as giving more understanding to essential core beliefs.
The Ecumenical Councils have defined doctrines such as the divinity of Christ (Nicea); the title of Mary as the Mother of God (Ephesus); the two natures of Christ, human and divine, being united in the one divine person (Chalcedon); transubstantiation to describe how the bread and wine are changed at Mass into the Body and Blood of Christ (Lateran IV); the seven sacraments, Sacred Scripture and Sacred Tradition, and other responses to the Reformation (Trent); and papal infallibility (Vatican I).
These conciliar decrees and ex cathedra papal pronouncements form the Extraordinary Magisterium.
Ex cathedra (Latin for from the chair) pronouncements from the pope are considered infallible teachings. The only two ex cathedra pronouncements in 2,000 years have been the dogmas of the Immaculate Conception (1854) and the Assumption (1950). When the pope teaches ex cathedra, he’s exercising his universal authority as Supreme Teacher of a doctrine on faith or morals, and he’s incapable of error.
Catholics consider the Assumption of Mary and the Immaculate Conception infallible teachings because they involve the solemn, full, and universal papal authority.
The word cathedral comes from the Latin cathedra because it’s the church where the bishop’s chair (cathedra) resides. The chair is symbolic of authority going back to Roman days when Caesar or his governors sat on a chair and made public decisions, pronouncements, or judgments. When the pope teaches ex cathedra, he’s not physically sitting on a particular chair but exercising his universal authority as Supreme Teacher.
Unlike governments that separate their executive, legislative, and judicial branches, in the Catholic Church, the pope is all three rolled into one. He’s the chief judge, the chief lawmaker, and the commander in chief all at the same time.
That’s why the triple crown (also known as a tiara or triregnum) was used in papal coronations — to symbolize his three-fold authority and that he’s higher in dignity and authority than a king (one crown) or even an emperor (double crown). (Pope Paul VI was the last pope to wear the tiara. It’s a matter of personal choice and preference now.)
The Ordinary Magisterium
The second way that an infallible teaching is taught to Catholics is through the Ordinary Magisterium, which is the more common and typical manner, hence the reason why it’s called ordinary. This teaching of the popes is consistent, constant, and universal through their various documents, letters, papal encyclicals, decrees, and so on.
It’s never a new doctrine but rather one that has been taught ubique, semper et ab omnibus (Latin for everywhere, always and by all). In other words, when the pope reinforces, reiterates, or restates the consistent teaching of his predecessors and of the bishops united with him around the world, that’s considered the Ordinary Magisterium and should be treated as infallible doctrine.
When popes write papal documents (anything authored by a pope), the title they use to refer to themselves the most is Servant of the Servants of God (Servus Servorum Dei in Latin). St. Gregory the Great (590–604) was the first pope to use this title. Check out the different types of papal documents from the most solemn on down:
Papal Bulls
Papal Encyclicals
Papal Briefs
Apostolic Exhortations
Apostolic Constitutions
Apostolic Letters
Motu Proprios
Prior to the Second Vatican Council (1962–65), more commonly known as Vatican II, the type of papal document the pope chose determined how much authority he intended to exercise. The preceding list indicates the order of authority that various papal documents traditionally had.
For example, the lowest level was the Motu Proprio, which is a Latin phrase meaning of his own initiative. Somewhat like an international memo, it’s a short papal letter granting a dispensation or making a modification applying to the whole world but on a disciplinary matter only, such as an issue that has nothing to do with doctrine.
An example of Motu Proprio was when John Paul II granted permission to celebrate the Tridentine Mass (the order and structure of the Mass as it was celebrated between the Council of Trent and Vatican II). On the other hand, Papal Bulls were considered the highest authority.
Since Vatican II, however, the content and context of the document determine the degree of authority and not just the type of papal document. If the pope intends to definitively teach the universal Church on a matter of faith or morals, then he is expressing his supreme authority as head of the Church.
When John Paul II issued his Apostolic Letter Ordinatio Sacerdotalis in 1994, he officially declared that the Catholic Church has no power to ordain women. Ordinatio Sacerdotalis was not an ex cathedra papal statement, but it’s part of the Ordinary Magisterium, and thus, according to the Prefect for the Sacred Congregation for the Doctrine of the Faith, the teaching is infallible.
The Cardinal Prefect is the pope’s watchdog to investigate all suspected cases of heresy (false teaching) and to explain official church dogma.
Papal encyclicals are letters addressed to the world on contemporary issues and concerns. Encyclical comes from the Latin word for circular, because these documents are meant to circulate around the world. The name of each letter consists of the first two words of the letter in Latin, because every official document coming from the Vatican is still written in Latin. Encyclicals aren’t ex cathedra pronouncements.
Encyclicals are the routine, day-to-day, consistent teaching of the Ordinary Magisterium, which is equally infallible when it concerns faith and morals and reiterates the constant, consistent, and universal teaching of the popes and bishops. Their content requires religious submission of mind and will of faithful Catholics around the world.
So-called dissent from papal teaching in encyclicals isn’t part of Catholic belief. The Catholic faithful willfully conform to papal teaching and don’t dispute it.