Honestly, you’re going to be hard-pressed to find such a list. As one example, the following is an infallible statement:
I believe in one God, the Father almighty, maker of heaven and earth, of all things visible and invisible. I believe in one Lord Jesus Christ, the Only Begotten Son of God, born of the Father before all ages. God from God, Light from Light, true God from true God, begotten, not made, consubstantial with the Father; Through him all things were made. For us men and for our salvation he came down from heaven, and by the Holy Spirit was incarnate of the Virgin Mary, and became man. For our sake he was crucified under Pontius Pilate, he suffered death and was buried, and rose again on the third day in accordance with the Scriptures. He ascended into heaven and is seated at the right hand of the Father. He will come again in glory to judge the living and the dead and his kingdom will have no end. I believe in the Holy Spirit, the Lord, the giver of life, who proceeds from the Father and the Son, who with the Father and the Son is adored and glorified, who has spoken through the prophets. I believe in one, holy, catholic, and apostolic Church. I confess one baptism for the forgiveness of sins and I look forward to the resurrection of the dead and the life of the world to come. Amen.
But which Pope “said” it? Most of them. It’s the Niceno-Constantinopolitan Creed, first adopted by the Councils of Nicea and Constantinople in 325 and 381 and restated throughout the centuries since.
Now, how many times has any Pope said “God is three Persons in one God” or “Jesus existed from before creation began” or “The Holy Spirit is divine” or “Jesus had two natures: one human, one divine” or “Jesus laid down His life for us, so that all might have eternal life”?
Every time a Pope says that sort of thing, it’s correct. But the charism of infallibility is more subtle than that. Papal infallibility is a short-hand term for the following doctrine: Jesus sent the Holy Spirit to watch over the Church and to prevent it from leading the flock astray. Accordingly, when the Pope speaks definitively on an issue of faith or morals, the Holy Spirit prevents him from doing so inaccurately.
The universe of definitive statements of faith and morals issued by Popes throughout history is fairly small. It’s also fairly basic; one might even say that most (not all) Protestants agree with most (not all) infallible declarations by Popes (e.g., the Creed). So there really isn’t a lot out there that would fall under this doctrine.
On the other hand, if you want to quibble, in theory the charism of papal infallibility is at work literally
all the time. Is the Pope right now issuing a definitive statement that Jesus was just a man and not divine? Nope; because he can’t – the Holy Spirit would prevent him from doing so.
As for figuring out which statements are covered by the charism, the Catholic Encyclopedia has a useful article on the subject. In brief, there are basically two ways for infallible dogma to be proclaimed: by ecumenical councils and by the Pope himself. Ecumenical councils require permission of the Pope for the council itself and papal approval afterward of the conciliar decrees. Papal infallibility occurs when the Pope speaks “ex cathedra — that is, when in the exercise of his office as pastor and teacher of all Christians he defines, by virtue of his supreme Apostolic authority, a doctrine of faith or morals to be held by the whole Church.”
The article makes the following points about papal infallibility:
•what is claimed for the pope is infallibility merely, not impeccability or inspiration (see above under I).
•the infallibility claimed for the pope is the same in its nature, scope, and extent as that which the Church as a whole possesses; his ex cathedra teaching does not have to be ratified by the Church’s in order to be infallible.
•infallibility is not attributed to every doctrinal act of the pope, but only to his ex cathedra teaching; and the conditions required for ex cathedra teaching are mentioned in the Vatican decree:
◦The pontiff must teach in his public and official capacity as pastor and doctor of all Christians, not merely in his private capacity as a theologian, preacher or allocutionist, nor in his capacity as a temporal prince or as a mere ordinary of the Diocese of Rome. It must be clear that he speaks as spiritual head of the Church universal.
◦Then it is only when, in this capacity, he teaches some doctrine of faith or morals that he is infallible (see below, IV).
◦Further it must be sufficiently evident that he intends to teach with all the fullness and finality of his supreme Apostolic authority, in other words that he wishes to determine some point of doctrine in an absolutely final and irrevocable way, or to define it in the technical sense (see DEFINITION). These are well-recognized formulas by means of which the defining intention may be manifested.
◦Finally for an ex cathedra decision it must be clear that the pope intends to bind the whole Church. To demand internal assent from all the faithful to his teaching under pain of incurring spiritual shipwreck (naufragium fidei) according to the expression used by Pius IX in defining the Immaculate Conception of the Blessed Virgin. Theoretically, this intention might be made sufficiently clear in a papal decision which is addressed only to a particular Church; but in present day conditions, when it is so easy to communicate with the most distant parts of the earth and to secure a literally universal promulgation of papal acts, the presumption is that unless the pope formally addresses the whole Church in the recognized official way, he does not intend his doctrinal teaching to be held by all the faithful as ex cathedra and infallible.
newadvent.org/cathen/07790a.htm
Hope this helps.
