You are too kind.
As for your lines of questioning here, the only answer that I think can be given is "the Holy Spirit". You seem to be focusing on the human side of this infallible charism - but this infallible charism is not something that results from the Pope's own nature as man, but rather comes entirely from the Holy Spirit. See again that paragraph from Vatican I, specifically:
"he possesses, by the divine assistance promised to him in blessed Peter, that infallibility which the divine Redeemer willed his Church to enjoy in defining doctrine concerning faith or morals."
It is not by virtue of the merely human (or private) nature that this infallibility is obtained; it comes from God, from the Holy Spirit. And because this is so, I do not think it is entirely possible for me to explain how a man, like Francis for example, could even in theory go from sympathizing with homosexual "civic unions" to condemning them when speaking ex cathedra; in other words, since this very charism is accomplished by the Holy Spirit, how can I, or anyone, be expected to explain its mysteries? I know this may sound like a cop-out to skeptics, but when we appreciate what is actually being argued here, I think this defence follows naturally.
It is as Pope John Paul II said in 1993:
“Infallibility is not given to the Roman Pontiff as a private person, but inasmuch as he fulfils the office of pastor and teacher of all Christians. He also does not exercise it as having authority in himself and by himself, but ‘by his supreme apostolic authority’ and ‘by the divine assistance promised to him in Blessed Peter.’ Finally, he does not possess it as if he could dispose of it or count on it in every circumstance, but only ‘when he speaks from the chair,’ and only in a doctrinal field limited to the truths of faith and morals and those closely connected with them (...) the Pope must act as ‘pastor and doctor of all Christians,’ pronouncing on truths concerning ‘faith and morals,’ in terms which clearly express his intention to define a certain truth and to demand the definitive adherence to it by all Christians.
And while I believe I already cited this example, I will remind you that it was Pope Paul VI who wrote Humanae Vitae, a modern Church document that, despite following the era of Vatican II, affirmed the immorality of contraception, even when "the spirit of the world" was so desperately beseeching him to declare otherwise: J. D. Rockefeller III flew to the Vatican and tried to convince the pope to support contraception, and even offered to write the encyclical for him (Libido Dominandi, pg. 434-435). Pope Paul VI, widely regarded as a "liberal pope" just like Pope Jon XXIII (and like Francis today), who was the one who closed Vatican II, just as Pope John XXIII opened it, nonetheless declared magisterially against birth control. Now, this isn't an example of ex cathedra infallibility, but it is the Magisterium, and the Holy Spirit guides all the Magisterium, and even though I'm not aware of Pope Paul VI campaigning for contraception at any point, even in casual conversation, I think this still serves as an example of how the kind of pope who would be most inclined to do such a thing, nonetheless does not when operating at a level of the Magisterium higher than casual conversation. And if this holds at a lower (non-infallible) level of the pope's teaching authority, would it not hold all the more when considering ex cathedra statements?
One rebuttal to this is the writings of Pope Francis himself, contrary to my example above, do seem to contradict traditional Church teaching, and the existing Magisterium itself - so where is the Holy Spirit here? I can only begin by pointing out how profoundly unique and complex the nuances are of Francis' pontificate - it is in a sense a consummation of the "weaponized ambiguity" that the drafters of Vatican II documents instilled with the intention of later exploiting. The point in the case of the Vatican II documents - miraculous in its own right - is how, upon analysis, even these V2 documents are preserved from error, given the known nefarious intentions of those who drafted them. The Holy Spirit was clearly at work there, since, as an ecumenical council, this clearly constituted the Magisterium.
The writings of Francis are less clear. Mere papal encyclicals occupy a lower level of the Magisterium than Council documents, so the "need" for preservation from error is less pronounced - as I said before, with reference to ecological sin, if a teaching is novel with no clear basis in tradition, than very little assent is owed to it, until it is picked up by later popes. Secondly, Francis' tendency to address not the Church, but vague groups or the world itself, calls the magisterial authority of his documents into question. Thirdly, since papal encyclicals are typically part of the ordinary Magisterium, not extraordinary / sacred Magisterium (unless the encyclical meets the criteria of ex cathedra), then they are non-infallible by definition - which does not mean they can be dismissed, but it does mean their legitimacy is not self-justifying, but rather depends on reference to the rest of the Church's Magisterium. Notably, Francis has a habit of quoting himself more than any other source in his writings. These are all details that do have to be kept in mind; I think the most important thing for people having trouble digesting the papacy / papal infallibility etc. is to understand the nature of the Church's Magisterium. I highly recommend Fr. Ripperger's very short work, Magisterial Authority to help with this.
Is it pretty widely held that Vatican II did not contradict the core magisterium?
Traditionalists cite its many concerning anomalies as justification for rejecting it outright - the fact that working documents were scrapped, the (weaponized) ambiguity in the texts, the fact that Pope John XXIII when opening the council stated they did not intend to exercise the Church's extraordinary (infallible) magisterium through the Council, and Pope Paul VI echoed the same sentiment upon closing the council, etc. Then of course the liturgical reforms that were carried out in the spirit if Vatican II. It was undoubtedly a unique council, and undoubtedly exploited to the detriment of the faithful.
And to answer your question, it is widely viewed as representing a break with Tradition. The majority of naive liberal laypeople see it this way, and welcome it - despite the drop in numbers among young people attending Mass, among priestly and religious vocations, etc. And many trads see it this way also, and so reject it on these grounds.
The facts are these: indeed, the extraordinary Magisterium was not exercised (no heresies were anathematized, no dogmas were pronounced, as badly as this was needed in the 60s). Therefore the possibility of error does exist. However, as I said above, the weight of ordinary Magisterium must be understood by comparing it in terms of previous Tradition and previous Magisterium. Because ambiguity was written into the documents, there is room for interpretation. This is where Pope Benedict XVI has stressed the need to apply a hermeneutic of continuity rather than one of rupture to the Council documents- and this can be done. The fact that it has to be done should compel the Church to call another Council, but that is a separate point. What matters is that, as things stand, the faithful are obliged to understand these documents in continuity with the previous Tradition and Magisterium, and in fact, because the documents are only ordinary Magisterium, then if this is not done they do not carry the same weight (or any weight) at all. So the modernist bishops who have employed a hermeneuric of rupture to justify the liturgical reforms in the spirit of Vatican II etc., and the naive liberal Catholics who have welcomed this, are acting on grounds lacking sufficient Magisterial authority.
The Syllabus of Errors, promulgated by Pope Pius X (I think it was him), condemns modernism as the synthesis of all heresies; that's why trads like to cite from that document so much. But in paragraph 22 of that very document, the pope anathematizes those who think they only have to assent to extraordinary Magisterium because it alone is infallible. "Religious assent", even if this is not the full assent of faith, must be given to the ordinary Magisterium (again remembering from what the ordinary Magisterium receives it weight and must be understood), and it certainly cannot be rejected outright.
And so even though we know there was malicious intent, and that this was exploited, the faithful are obliged to see the documents in both a charitable and traditional light, and cannot justify just applying a hermeneutic of rupture to support their own narrative - whether this be by the left or the right. But yes, most people do apply such an hermeneutic, without justification.
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