This limited view is relatively novel. At the First Vatican Council, when some bishops wanted to condition papal infallibility on the Pope following some procedure or using some verbal formula, the relator for the Commissio de fide (charged with providing official doctrinal explanations of Council documents to the Council Fathers) said this was impossible, because there were already so many instances with various procedures or even none at all:
But, most eminent and reverend fathers, this proposal simply cannot be accepted because we are not dealing with something new here. Already thousands and thousands of dogmatic judgments have gone forth from the Apostolic See; where is the law which prescribed the form to be observed in such judgments?
“Thousands and thousands” might be a bit hyperbolic, but the point remains–it has been more than two! I assume where a document contains a long list of definitively judged propositions, each one is considered a single judgment (e.g. e.g. Coelestis Pastor of Bl. Innocent XI, Ex Omnibus Afflictionibus of St. Pius V, Unigenitus of Clement VI, etc.). Also included would be definitive judgments the Pope makes in his own name in the context of a partial or even ecumenical synod.
The First Vatican Council itself notes the variety of ways such definitions have come about:
The Roman pontiffs, too, as the circumstances of the time or the state of affairs suggested, sometimes by summoning ecumenical councils or consulting the opinion of the Churches scattered throughout the world, sometimes by special synods, sometimes by taking advantage of other useful means afforded by divine providence, defined as doctrines to be held those things which, by God’s help, they knew to be in keeping with Sacred Scripture and the apostolic traditions.
Unfortunately, likely due to a false irenicism (condemned by Vatican II), the dogma of papal infallibility has been unduly minimized. The unusual ceremonial attached to the two famous instances involving Marian dogmas (and their unusual circumstances, where rather than settling a controversy, they were a kind of capstone on a settled point) have also minimized the other instances. The fact is, Popes have intervened to provide definitive/irreformable judgments binding the whole Church many, many, many times.
This dogma is best thought of in its relation to the indefectibility of the whole Church, the indefectibility of the Church of Rome in particular (a consequence of the primacy being fixed there) and the Bishop of Rome’s relationship to each. He is infallible where, if he were to err, profession of such an error would become a necessary condition for the whole Church to have full communion with the Apostolic See.
It should also be noted, the infallibility of the Church (and Pope) is not limited to dogma (truths to be believed with divine faith), but also those necessarily connected truths “to be definitively held” (which is why Vatican I used “held” specifically).
