The non-technical use of the term "infallibility" in the sense of "when someone cannot err" seems to have become ubiquitous, but when interpreting historical documents like Pastor Aeternus on papal infallibility, it is essential to use the technical term. The technical term refers to situations when we are guaranteed by faith to know that doctrines are true based on the assurance of the God who neither deceives nor is deceived. The term "infallibility" is used to invoke the property of God as revealer who neither deceives nor is deceived; it is a formal assertion that the particular mode of teaching partakes of this assurance.
"Infallibility" in the non-technical sense is a synonym for "incapable of error." But if that is confused with the technical sense of "infallibility," the reasoning from the concept will be fallacious. Formally, inability to err is a consequence of infallibility in the technical sense. Thus, if P is "is infallible" and Q is "cannot possibly err," then P->Q. But if one were to reason from the lack of infallibility (~P) to infer that one could possibly err (~Q), this would be the fallacy of denying the antecedent. Only in the case that infallibility is used definitionally as "cannot err," so that P=Q (P⇄Q), would this conclusion be logically entailed.
That is the unfortunate reason that, following Pastor Aeternus, there has been a frequent assertion that only what is infallible is certain not to err. But this is definitely not the case; on the contrary, that assertion has been the most common avenue of dissent in the modern era of the Church by both progressives and traditionalists. Even before the First Vatican Council, Bl. Pio Nono warned against this tendency by the German bishops in his letter Tuas Libenter:
We address to the members of this Congress well-merited praise, because, rejecting, as We expected they would, this false distinction between the philosopher and the philosophy of which We have spoken in earlier letters, they have recognized and accepted that all Catholics are obliged in conscience in their writings to obey the dogmatic decrees of the Catholic Church, which is infallible. In giving them the praise which is their due for confessing a truth which flows necessarily from the obligation of the Catholic faith, We love to think that they have not intended to restrict this obligation of obedience, which is strictly binding on Catholic professors and writers, solely to the points defined by the infallible judgment of the Church as dogmas of faith which all men must believe. And We are persuaded that they have not intended to declare that this perfect adhesion to revealed truths, which they have recognized to be absolutely necessary to the true progress of science and the refutation of error, could be theirs if faith and obedience were only accorded to dogmas expressly defined by the Church. Even when it is only a question of the submission owed to divine faith, this cannot be limited merely to points defined by the express decrees of the Ecumenical Councils, or of the Roman Pontiffs and of this Apostolic See; this submission must also be extended to all that has been handed down as divinely revealed by the ordinary teaching authority of the entire Church spread over the whole world, and which, for this reason, Catholic theologians, with a universal and constant consent, regard as being of the faith. But, since it is a question of the submission obliging in conscience all those Catholic who are engaged in that study of the speculative sciences so as to procure for the Church new advantages by their writings, the members of the Congress must recognize that it is not sufficient for Catholic savants to accept and respect the dogmas of the Church which We have been speaking about: they must, besides, submit themselves, whether to doctrinal decisions stemming from pontifical congregations, or to points of doctrine which, with common and constant consent, are held in the Church as truths and as theological conclusions so certain that opposing opinions, though they may not be dubbed heretical, nonetheless, merit some other form of theological censure.
It is that last category "held in the Church as truths and as theological conclusions so certain that opposing opinions, though they may not be dubbed heretical, nonetheless, merit some other form of theological censure" in which Cardinal Franzelin finds "infallible security," which entails theological certainty that adherence to the opposite proposition will not err. In that case, because submission (obedience) is required of the indefectible universal Church, such submission cannot entail something objectively displeasing to God, such as heresy or other theological error. So both Bl. Pope Pius IX and Cardinal Franzelin, the two minds most clearly behind the declaration of papal infallibility, affirm three following categories that require either the submission of faith or the submission of obedience:
(1) Express decrees of the Ecumenical Councils, or of the Roman Pontiffs and of this Apostolic See, which are infallible (extraordinary Magisterium, infallibly true, submission of faith)
(2) All that has been handed down as divinely revealed by the ordinary teaching authority of the entire Church spread over the whole world, and which, for this reason, Catholic theologians, with a universal and constant consent, regard as being of the faith (ordinary and universal Magisterium, infallibly true, submission of faith).
(3) Doctrines that "are held in the Church as truths and theological conclusions so certain that opposing opinions, though they may not be dubbed heretical, nonetheless, merit some other form of theological censure" (authentic papal Magisterium or "universal ecclesial providence for the security of doctrine," infallibly safe, submission of obedience)
These correspond to three authoritative modes of exercise of the papal authority:
(1) The Pope can manifest the intention to definitively teach a doctrine ex cathedra.
(2) The Pope can manifest the intention to ratify the ordinary and universal Magisterium without teaching definitively.
(3) The Pope can manifest in a binding way through discipline that a truth or theological conclusion is so certain that it would be censurable to oppose it. (This also applies to liturgical discipline generally, such as canonization of Saints.)
What I like about Franzelin is that he restricts the term "religious submission" to what is required by obedience, as Bl. Pius IX does, rather than expanding it to the more general sense of reverence to bishops, which he correctly calls "respect." Unfortunately, Vatican II was not nearly so careful, calling the respect due to bishops "religious submission," which is true only in a much broader sense. Vatican II refers to the religious submission owed under (3) as religious submission "in a special way," but it would have been much clearer just to say that the "special way" just is religious submission and that what is owed to bishops is simply pious respect of superiors, not obedience in this strict sense. This sort of pious respect for the teaching of the Magisterium outside of obedience in the strict sense is what is described in Donum Veritatis. The use of the term "religious submission" to include these two very distinct concepts of obedience is similar to how the term "ordinary Magisterium" was used to encompass two completely different things: the ordinary exercise of authority of individual bishops (including the Pope) and the ordinary and universal Magisterium, the latter of which is an infallible mode of teaching by the bishops dispersed throughout the world in communion with the Pope. In a similar way, the ambiguity in these terms has led to a great deal of confusion regarding Magisterial authority.
If the Pope manifests none of the intentions in (1)-(3), such as when he renders advice or guidance on a particular subject or prudential matter, then he teaches only as an individual bishop. That is owed pious respect on account of the office but does not require the obedience to doctrine (religious submission properly speaking) commanded under (3), nor does it carry the associated infallible security. For example, Franzelin believed that Pope Honorius did not manifest any binding intent of (1)-(3) in his letters to Sergius, nor did Pope Paul V when he commanded silence on the subject of grace (this would presumably be the case of Vigilius's reversals as well). Franzelin also believed that Honorius's letters were not heretical, but in any case, his letters were the subject neither of infallibility nor or infallible security, since he did not authoritatively command or forbid adherence to any particular doctrine (other than Chalcedon, of course, which was already infallibly binding).
Because applying inerrancy only to infallible teaching has essentially been the preferred path for dissent in the last two hundred years, it is important to turn back to the guidance of Bl. Pio Nono and Cardinal Franzelin. We should not allow their work in Pastor Aeternus to be misused so as to deny the certain theological truth that there is no possibility of error in matters of universal ecclesial providence that demand obedience to the papal office.
