The Vatican Council has defined as “a divinely revealed dogma” that “the Roman Pontiff, when he 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 – is, by reason of the Divine assistance promised to him in blessed Peter, possessed of that infallibility with which the Divine Redeemer wished His Church to be endowed in defining doctrines of faith and morals; and consequently that such definitions of the Roman Pontiff are irreformable of their own nature (ex sese) and not by reason of the Church’s consent” (Densinger no. 1839 – old no. 1680). For the correct understanding of this definition it is to be noted that:
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.
It should be observed in conclusion that papal infallibility is a personal and incommunicable charisma, which is not shared by any pontifical tribunal. It was promised directly to Peter, and to each of Peter’s successors in the primacy, but not as a prerogative the exercise of which could be delegated to others. Hence doctrinal decisions or instructions issued by the Roman congregations, even when approved by the pope in the ordinary way, have no claim to be considered infallible. To be infallible they must be issued by the pope himself in his own name according to the conditions already mentioned as requisite for ex cathedra teaching.
newadvent.org/cathen/07790a.htm