Bellarmine here clearly specifies the material / formal distinctive elements of a pontificate:

Notice matter / form:

"... the cardinals, when they create a Pontiff, exercise their authority, not on the pope as such, since he is not yet such, but on the matter, that is to say, on the person which they
dispose in some way by the election in order that he might receive from God the form of the pontificate."

~ St. Robert Bellarmine, "De Romano Pontifice," I, II, c.30.

On the distinction in the Papacy between a material aspect and a formal aspect:

Archbishop St. Antoninus of Florence (writing in the 1470's):

“Such power remains in the Church and in the College with respect to that which is material in the Papacy, since after the death of the Pope the College is able, through election, to determine a person to the Papacy, that it be such or such a one”; “if by the term ‘Papacy’ one means the election and the determination of the person, this is what constitutes in the Papacy the material element”; “(…) as to the election and the determination of the person, this is like to the material element.”

http://mostholytrinityseminary.org/wp-content/uploads/2019/01/Fr.-Ricossas-article-Pope-Papacy-and-the-Vacant-See.pdf

@Ladislaus: Maybe my situation isn't the norm, but I still wanna at least throw this out there for discussion.

My average experience with Catholics are admittedly mostly converts.  Most of them were Protestant when I met them, when we were freshmen in college, and converted sometime in the past few years.

Except for me, none of them have any doubts about the Pope (I get looked at a bit nutty when I even give some thought to Sedevacantism, I've considered it at times both before, during, and after my conversion) and they don't seem as bugged by Vatican II or the apparent discontinuity on ecuмenism as I am (I think they either just aren't devoting as much thought to it, or else accept that its a change in discipline rather than a change in doctrine.) Yet, they hold to every doctrine of the Catholic Church, at least to their best understanding of it.  They might put more qualifications on extra ecclesiam than you'd be comfortable with, but they'd definitely hold to it, they'd explain to you what they think Florence means, they wouldn't deny it.  They'd hold to transubstantaition, the immaculate conception, the immorality of contraception, etc. etc. etc.  

Having talked to a few people from my local diocesan Latin Mass, they also seem like the kind of people who believe every dogma of the faith, and they're a bit more conservative/having serious problems with Vatican II, but Sedevacantism is instantly dismissed and doesn't seriously seem to be considered/doubted by those people.

Do you really believe the kind of Catholic I describe above is less common than those who have doubts about the legitimacy of the current Pope?

To be clear, if your argument is that multiple bishops have doubted the legitimacy of the current pontificate so its not just some whacko with an internet connection somewhere, I can accept that.  If that's all you're arguing, I have no real quarrel (at the least, *I* am certainly not qualified to question the Catholicity of someone like Lefebvre because he had doubts about this.)  But if your argument is that the *majority* of Catholics who believe in the basic dogmas of the faith (and all the dogmas they are aware of) are doubting the legitimacy of the Conciliar Popes, at least in my experience that doesn't seem to be true.  Do you think my experience is a major anomaly?

When Ladislaus says that "most catholics doubt the legitimacy of the v2 popes" he's only talking about Traditional Catholics (i.e. no one in communion with new-rome).

OK no offense, but this seems like kind of a self-serving definition (and I mean that objectively, not subjectively.)  "Most people who aren't in communion with current Rome have doubts about the validity of the V2 Popes."  I'd really, really hope so.  I mean, if Francis is the pope, you'd be obligated (objectively) to be in communion with him.  Now I could see a case being made that authority is limited and thus particular perameters have to be placed on being in communion with him, but it wouldn't make sense for someone who thought Francis was the Pope to want to reject communion with him and his Church outright.

Of course, I asked Ladislaus earlier, and he said he would *not* say that someone who accepts Vatican II is automatically not Catholic, rather he was saying most Novus Ordo Catholics aren't Catholic because they overtly deny some dogma of the faith (transubstantiation, papal infallibility, etc.)  
And if you define a real Catholic *that* way (ie. someone who accepts every dogma of the Church they're aware of, and would on principle submit their judgment to that of the Church were they to be shown that one or more of their beliefs were not compatible with it) it seems most likely that more real Catholics than not do *not* doubt the legitimacy of the post Vatican II popes.

But yeah, if you define it as just people who aren't in communion with New Rome... would that even include the current SSPX? (as opposed to the SSPX Resistance.)  Even if so, yeah, I would probably suspect that a good chunk of people in SSPX chapels at least have some amount of doubt about this.  

And again, to be clear, I'm not necessarily arguing that the doubt isn't justified.  I'm purposely not arguing for any particular opinion, but trying to understand the logic of the various opinions and how they reconcile with reality.  Thanks for engaging.

I don't want to speak for Ladislaus, because he is usually never self-serving, but I agree, my definition came across that way.

Yeah.  Just to be clear, I have no reason to think any forum posters here are self-serving.  I just thought that the particular definition you proposed (and I'm not sure if that was even the definition Ladislaus was using or not) seemed that way.

Right, I agree, most novus ordo catholics don't have a reason to reject the V2 popes.  They may disagree with some things but on the whole, they accept the conciliar church.  However, let me point out that the phrase "in communion with" is modernistic and has only been around since the V2 days, so what does this even mean?  You're either in schism or you're not, right?  New-rome wants to argue that Trads are not in schism but are not in "full communion".  To me, this is modernist mumbo-jumbo and they invented a term to describe those Trads who aren't in schism (i.e. they are orthodox) but they are not "in communion with" the "new" interpretation of orthodoxy (i.e. V2).

Is it modernist to ask whether someone is in communion with the Pope or not?  I'm sincerely asking, there is no sarcasm here at all.

I agree.  But the dogma of EENS is the most denied dogma of our day; most people believe (for sentimental reasons) that "good people" go to heaven, no matter their faith.  Denying this dogma is just as heretical as denying transubstantiation or infallibility.

That would be the loosest interpretation, with the strictest possible interpretation being that of Fr. Feeney or the Dimond Brothers.  But there's a spectrum of opinion between "Good people automatically get in" and "all who are visibly outside the Catholic Church are damned" (And what I'm saying here is true even if feeney was right.)  Lefebvre and the Baltimore Catechism, for better or worse, both disagreed with both of those opinions.  I don't think St Justin Martyr (to be fair he was really early, so you could argue he was before extra ecclesiam was explicitly formulated) would've said all good people make it.  Augustine thought that some of the Donatists weren't formal heretics.  Even Vatican II says that those who know the Catholic Church is the true Church and reject it are damned.  That's a bit vague but even Vatican II would rule out the Pelagian "all good people make it" view.

Ok, that's true (from a certain perspective).  But...as soon as you were to show these "good willed" catholics their errors and how they are not 100% orthodox, then they would see the contradiction of their old ways (i.e. V2) vs the true way (i.e. pre-V2).  Ergo, they would immediately see the modernism/heresies of the V2 popes, and a doubt about their legitimacy would arise.

I think that assumes a lot about the way people's logic tend to be wired, but TBH I'm not arguing that they're of good will or not.  I'm using people who don't deny any dogma, whether they're of good will or not.  I think its fair definitionally to say that someone who says "I know the Church teaches Transubstantiation, but I reject it anyway" is not a Catholic.  I think its fair to say someone who says "I know the Church teaches that Mary never sinned, but I just don't buy it" isn't Catholic.  But I don't think you can say that about someone who says "You know what, I realize pre Vatican II doctrine says X, and Vatican II doctrine says Y, and I don't know how they can be reconciled, but I accept on faith that both have to be true and have to be reconciled somehow" is "not Catholic."  Nor do I think you can say that about someone who (rightly or wrongly) attempts to provide a reconciliation for the apparent contradictions.  Maybe they're wrong, maybe they're even of bad will, but to say they're "not Catholic" and thus don't count when it comes to establishing whether widespread doubt exists or does not exist is what I was getting at when I was talking about the self-serving definition.  If you limit "real Catholic" to anyone who accepts all dogmas he is aware of, and is on principle willing to submit to whatever the Church teaches on any issue, I think most people who fall under that category probably don't have any doubt that Francis is the Pope, though I grant that most people in the Novus Ordo probably don't even meet this standard.  But if you define "real Catholic" in a way that's stricter than that, I think that's just kinda skewing the definitions to get the result you want, if that makes sense.  If someone were a dogmatic Sedevacantist, such that they thought non Sedes weren't really Catholic, they could then say that every single "real Catholic" knows there's no pope, and based on their definition they wouldn't be wrong.  

To be clear, I'm not suggesting that anyone is doing this on purpose, and I'm not certain it matters to the argument Ladislaus is making either.  As I said, if his point is just that its doubted by multiple quite sane bishops around the world, and its not just a random quack somewhere, than I can agree that seems to be the case today, and as far as I know wasn't the case in 1958, say.  I was raising my question on the assumption that he was arguing that the majority of "real Catholics" have doubt.

For the record, I disagree with the argument that a lack of orthodoxy on the part of the pope leads to doubt about his papacy because I believe that it's possible for a pope to lose his faith, become a heretic and still retain the papacy (until the Church removes him).  Many theologians have argued this is possible, including +Bellarmine.  Most Trads, due to the sede influence, think that an unorthodox pope loses his chair immediately, or automatically.  Thus their "doubts" are more easily aroused and since, in their theory, they don't have to wait for a formal process to happen, then their rejection of a papacy is fairly hasty.  I reject this thought process as leading to chaos and private interpretation, which is not at all consistent with the monarchical foundation of the Church.

Fair enough.  I don't know enough about this subject to comment on it.

I think if more people were to remember that the papacy has a human element to it, instead of just concentrating on the spiritual element (i.e. orthodoxy), then they would see that the vast majority of theologians did not have a problem with the idea of a pope becoming a heretic and that this does NOT lead to doubts about his papacy, it only leads to doubts about his personal salvation.  God gives us bad leaders as a punishment for sin.  No amount of bad popes will change the Truth of His Church, so it is unnecessary to doubt the legitimacy of a bad pope.  A bad pope or no pope - practically it's the same result.

Honestly that seems a bit strange to me that it wouldn't matter, you'd think having bad authority would be different than having none, but I again am outside my current competence to comment on it.  

Cantarella, thank you for the citation. That's interesting. Did either Cardinal St. Robert or Cardinal Cajetan say that a Pope who falls into heresy loses the form of the Papacy? If I recall the argument correctly, Cardinal Cajetan had argued that as the Cardinal electors unite the Pontificate to the Person elected, they can also disjoin the Pontificate from that person later on, and in this case, they do not exercise authority over the Papacy, but only over the link that unites the man to the papacy. Cardinal St. Bellarmine rejects this opinion saying, in the case of election, the Pope doesn't yet exist, but if they exercised authority against the Pope after his election, they would necessarily be exercising it over the Papacy itself. And also that as when the Pope deposes Bishops, we deduce the Pope is superior to Bishops; so, if Cardinals could depose the Pope, then it would seem to follow the Church is superior to the Pope. I do not know what Cardinal Cajetan would have said; but St. Robert's opinion on this hypothetical case seems to be that the Pope would lose everything.

Do you think that a Pope, after having become a public and formal heretic, can still appoint Bishops to episcopal sees, and incardinate Cardinals or Roman Clergy, such that these latter would have full authority? I think he would lose the authority to be able to do that.

It's an interesting speculation. My person view is that a Pope can never be a formal and notorious heretic, though he may err or make mistakes. The Lord prayed the faith of St. Peter would not fail, and while Vatican I did not formally define anything on whether a Pope would or would not become a heretic, it did seem to endorse the theological opinion that a Pope would not become a heretic as at least a probable one, saying, "This gift of truth and never-failing faith was therefore divinely conferred on Peter and his Successors", now faith does not fail if a man falls into lesser errors, or even more serious and grave ones without pertinacity; but faith does fail if a man becomes a heretic. Therefore, it seems likely that as St. Peter was weak during the Passion of Christ, the Popes will also be weak during this Passion of the Church; until the Triumph of the Church, through the Collegial Consecration of Russia to the Immaculate Heart by the Pope and the Bishops, comes. But as St. Peter according to the Saints and Doctors did not actually lose faith on the night of the Passion when he denied Our Lord, but only was negligent in outwardly professing it, so also imho it is more likely than not that the Popes will never be heretics. Would you disagree? Let us pray the Pope and the Bishops do God's Will.

I hold the belief, as most theologians do, that the Pope cannot ever become a heretic, let alone teach heresy to the whole Church. It is impossible. I also think that the Pope cannot lose His Faith personally. Whereas it is within the realm of possibility that he commits a mistake here and there as an individual, he will never lose his Faith and he will never err doctrinally. Christ has prayed for that intention.

Having said that, I do believe it possible that a true conspirator may usurp the Seat of Peter, in which case, he was never Pope; but a political infiltrator. That situation would explain what has occurred in the Vatican (as of today, I really think it is the ONLY possible explanation). What is the alternative? Admit that the Church of Christ has defected, making a mockery of the promises of Our Lord?

It is necessary to completely dissociate any blemish of error from the Holy See and the Chair of Peter.

From Vatican I Council:

So the fathers of the Fourth Council of Constantinople, following the footsteps of their predecessors, published this solemn profession of faith:

The first condition of salvation is to maintain the rule of the true faith. And since that saying of our lord Jesus Christ, You are Peter, and upon this rock I will build my church, CANNOT fail of its effect, the words spoken are confirmed by their consequences. For in the Apostolic See the catholic religion has always been preserved unblemished, and sacred doctrine been held in honour. Since it is our earnest desire to be in no way separated from this faith and doctrine, we hope that we may deserve to remain in that one communion which the apostolic see preaches, for in it is the whole and true strength of the christian religion

What is more, with the approval of the Second Council of Lyons, the Greeks made the following profession:

“The holy Roman church possesses the supreme and full primacy and principality over the whole catholic church. She truly and humbly acknowledges that she received this from the Lord himself in blessed Peter, the prince and chief of the apostles, whose successor the Roman pontiff is, together with the fullness of power. And since before all others she has the duty of defending the truth of the faith, so if any questions arise concerning the faith, it is by her judgment that they must be settled.”

Then there is the definition of the Council of Florence:

“The Roman pontiff is the true vicar of Christ, the head of the whole church and the father and teacher of all Christians; and to him was committed in blessed Peter, by our lord Jesus Christ, the full power of tending, ruling and governing the whole church.”

I hold the belief, as most theologians do, that the Pope cannot ever become a heretic, let alone teach heresy to the whole Church. It is impossible. I also think that the Pope cannot lose His Faith personally. Whereas it is within the realm of possibility that he commits a mistake here and there as an individual, he will never lose his Faith and he will never err doctrinally. Christ has prayed for that intention.

If you actually do believe this, then you necessarily must hold the belief that all popes are impeccable (incapable of ever sinning), as such, you are bound by this belief to be Novus Ordo.

Having said that, I do believe it possible that a true conspirator may usurp the Seat of Peter, in which case, he was never Pope; but a political infiltrator. That situation would explain what has occurred in the Vatican (as of today, I really think it is the ONLY possible explanation). What is the alternative? Admit that the Church of Christ has defected, making a mockery of the promises of Our Lord?

If such a thing were possible, it would, at the very least, reduce the papal election laws, ceremonies and procedures, both before and after the election, which laws btw, have themselves been established by popes, to nothing more than ceremonies used as instruments designed to deceive the whole world - if such a thing as electing a usurper to the Seat of Peter were even possible.

If such a thing as that were possible, it would mean that by design, nobody in the world could ever have any certainty whatsoever regarding the legitimacy of any pope.

The alternative is reality. The reality that popes can do what the conciliar popes have done - of course believing reality will altogether contradict all the various ideas it takes to arrive at the various different conspiracy theories.