There’s two common misconceptions about papal infalliblity–1) that everything the Pope says in his capacity as Pope is infallible, 2) and more common today, only twice in history has a papal proclamation of doctrine been infallible.
1)The first is easily avoidable by recourse to the definition of the First Vatican Council and its repetition by the Second. The Pope must be acting as supreme teacher, his act must be a definitive binding on the whole Church, and it must be a truth of faith or morals revealed by God (“to be believed”) or a truth of faith or morals connected to revelation by logical necessity (“to be held” or sententia definitive tenenda).
As St. Francis de Sales explained it, he must be definitively laying down the universal law of faith (either divine or ecclesiastical faith).
Bl. Urban II is offering an indulgence (or absolution, depending on the differing accounts) to some soldiers who die in battle. I don’t see how this can be confused with a universal and definitive judgment about some truth or error.
- The idea that this has happened only twice seems common, but I don’t know why. It would mean that Saints and theologians for centuries and centuries defended this truth for merely hypothetical reasons–and that heretics went out of their way to deny it for hypothetical reasons. It means an ecumenical Council was convened to re-affirm this truth when it had only happened once. It doesn’t pass the common sense test.
In fact, at the First Vatican Council, some bishops wanted to make the Pope follow a particular procedure or use a particular formula when proclaiming something infallibly and the official relator, Bishop Gasser, explained to them that this was impossible as “thousands and thousands” of such proclamations had already been issued (he was speaking somewhat hyperbolically, but the point is valid).
I think a main point of confusion is that Popes have defintively proclaimed the truths of the of faith, not just through positive formulations of doctrine (although there are even more than two of these), but also more commonly (as the Councils have also done more commonly) through the definitive condemnation of heresy and error.
So where’s a list, one might ask? Denzinger is a good source, although it is neither exhaustive nor restricted to only such things. But, really, to ask for a list goes against the Church’s praxis. Books and copies of papal decrees may be lost and destroyed, etc., etc. We rely on the ordinary and universal Magisterium ordinarily–the constant teaching of the true faith by Popes and bishops in their words, letters, catechisms; the belief and handing on of the faith by the faithful in all times and places; in the Church’s worship and traditions, etc. Our faith is not just a list of papal definitions–the Pope’s ability to define the faith is called an extraordinary exercise of the Magisterium for this reason. When the clarity of a truth is cast into doubt (not in the sense that people know what the Church teaches but don’t believe it, but rather in the sense that what the Church actually teaches becomes uncertain) and the ordinary means fail to bring this clarity and unity of faith, it is the duty of the Pope to definitively settle the matter and call all to the unity and clarity of faith, so these truths once again can be handed on by the ordinary means throughout the world for ever and ever.