Pathetic.
St. Robert Bellarmine refutes the sedevacantist.
He said the Church had to be involved in the process, whereas sedes pay him lip service dishonestly (kind of like the liberals do to Cardinal Newman), in order to associate a name to their invention, then cast him aside and declare the see empty (forever) without any recourse to the Church.
Who can take these nuts seriously?
The expression "had to be involved" in English has several significantly different meanings, and I believe this ambiguity has created a difficulty in discussing St. Robert Bellarmine's teaching on sedevacantism (no, that is not an anachronism, as he taught the principles of sedevacantism that would not need to be applied until the 20th century).
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In general, the expression "has to" can mean either:
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1. What is being discussed is a sine qua non condition for something else. For example: you have to have your car key to start your car, or
2. What "has to" be is a simple obligation. For example: You have to pay your debts.
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You are claiming St. Robert is using the expression in both senses, and sedevacantists say he used it only in the second sense. Of course the Church (the Cardinals) must remove a pope who falls into heresy, at least in the second sense. I think we'd both agree on that part. But you are essentially claiming that a heretical pope retains office until the Church deprives it of him. St. Robert actually states this position is not only false, but indefensible:
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From St. Robert Bellarmine (source here):
The fourth opinion is that of Cajetan, for whom (de auctor. papae et con., cap. 20 et 21) the manifestly heretical Pope is not ipso facto deposed, but can and must be deposed by the Church. To my judgment, this opinion cannot be defended. For, in the first place, etc."
Not only does Bellarmine not think the Church had to be involved before the pope was actually deposed (in terms of chronological order), but even rejected it with strong language. His words "can and must be deposed by the Church" look the same as your statement that "the Church has to be involved." Do I understand your position correctly?
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He gives his position as follows (emphasis mine, and my comments are in
blue):
Therefore, the true opinion is the fifth, according to which the Pope who is manifestly a heretic [such as Bergoglio] ceases by himself to be Pope and head, in the same way as he ceases to be a Christian [as Bergoglio has] and a member of the body of the Church; and for this reason he can be judged and punished by the Church [which he still must be, "must be" in the second sense I gave above, but it's clear above that the pope ceases to be pope first, and is judged and punished afterwards, chronologically speaking. You are arguing that the two events are simultaneous, but that is not the sense given here.]. This is the opinion of all the ancient Fathers, who teach that manifest heretics immediately [!!] lose all jurisdiction, and outstandingly that of St. Cyprian (lib. 4, epist. 2) who speaks as follows of Novatian, who was Pope [i.e. antipope] in the schism which occurred during the pontificate of St. Cornelius: 'He would not be able to retain the episcopate [i.e. of Rome], and, if he was made bishop before, he separated himself from the body of those who were, like him, bishops, and from the unity of the Church.'
According to what St. Cyprian affirms in this passage, even had Novatian been the true and legitimate Pope, he would have automatically fallen from the pontificate, if he separated himself from the Church.
"This is the opinion of great recent doctors, as John Driedo (lib. 4 de Script. et dogmat. Eccles., cap. 2, par. 2, sent. 2), who teaches that only they separate themselves from the Church who are expelled, like the excommunicated, and those who depart by themselves from her or oppose her, as heretics and schismatics. [Note the distinction between 1) being expelled or excommunicated, and 2) departing by themselves. If, as you say, someone who professes heresy retains the papacy until he is expelled, then what is the meaning of this distinction? It can only mean anything if someone professes heresy and is not expelled, such as Bergoglio. Bellarmine is saying here that such a person has "absolutely no spiritual power over those who are in the Church"] And in his seventh affirmation, he maintains that in those who turn away from the Church, there remains absolutely no spiritual power over those who are in the Church.