PaxChristi2 says: 《The word Bellarmine usually uses is "convicted," or "legitimately judged."》
Bellarmine only uses the words "convicted" or "legitimately judged" in reference to opinion no. 2, i.e. an occult heretic's loss of office.
He used convicted and legitimately judged for a heretical Pope who had not openly separated himself from the Church. Here’s how Bellarmine said the process would take place if a Pope were accused of infidelity:
Bellarmine: “Marcellinus was accused of an act of infidelity, in which case a Council can discuss the case of the Pope, and if they were to discover that he really was an infidel [discretionary judgment], the Council can declare him outside the Church and thus condemn him.” (On Councils).
Listen to Bellarmine's commentary on the case of Liberius:
Bellarmine: “Then two years later came the lapse of Liberius, of which we have spoken above. Then indeed the Roman clergy, stripping Liberius of his pontifical dignity (abrogata Liberio Pontificia dignitate), went over to Felix, whom they knew to be a Catholic. From that time, Felix began to be the true Pontiff. For although Liberius was not a heretic, nevertheless he was considered one, on account of the peace he made with the Arians, and by that presumption the pontificate could rightly be taken from him. for men are not bound, or able to read hearts; but when they see that someone is a heretic by his external works, they judge him to be a heretic pure and simple, and condemn him as a heretic.” (De Romano Pontifice, bk IV)
Even though Bellarmine did not believe Liberius was a heretic, he says the clergy of Rome could strip him of his pontifical dignity, since they judged him to be a heretic. There was no ipso facto loss of office for heresy before they judged him. It is certain that Bellarmine didn’t believe there was, since he explicitly stated that he did not believe Marcellinus’ lost his office when he committed the public act of apostasy by offering incense to the idols, and he also said Marcellinus’ sin against the faith was worse than that of Liberius. “Liberius neither taught heresy, nor was a heretic, but only sinned by external act, as did St. Marcellinus, and unless I am mistaken, sinned less than St. Marcellinus" (Bellarmine). If he did not believe Marcellinus lost his office (without human judgment) for his sin against the faith, he obviously did not believe Liberius lost his without human judgment for a lesser sin.In De Concilii, Bellarmine says the bishops can “deposed” a Pope (“abrogate his pontificate,” as he said about Liberius), if they can convict him of heresy: Bellarmine: “… the oath [of fidelity] does not take away the freedom of the Bishops, which is necessary in Councils: for they promise to be obedient to the supreme Pontiff, which is understood as long as he is Pope, and provided he commands those things which, according to God and the sacred canons, he can command; but they do not swear that they are not going to say what they think in the Council, or that they are not going to depose him, if they were to clearly prove (convincant) that he is a heretic. (…) inferiors ought not be free from the obedience owed to their superiors, unless first he were legitimately deposed (legitimate deponatur) or declared not to be a superior (vel declaretur non esse superior) ... (De Concilli).
In the same chapter, he says a Pope retains the right to call a council and preside over it until he has been legitimately judged and convicted, and hence is no longer the Pope:Bellarmine: “the Roman Pontiff cannot be deprived of the right to summon a Council, and preside over it – a right he has possessed for 1500 years – unless he were first legitimately judged and convicted [discretionary judgment], and is not the Supreme Pontiff. (…) the Pope is not the only judged in a Council, but has many colleagues, that is, all the Bishops who, if they could convict him of heresy [discretionary judgment], could judge and depose him [coercive judgment] against his will.” (De Concilii).
Here’s what Bellarmine said in response to a Sedevacantist Protestant of his day, who said the Catholic bishop defected from the faith, lost their office, and could be replaced:Bellarmine: “I respond to this argument of Brenz (…): Catholic bishops, who for centuries have possessed their sees peacefully, cannot be deprived unless they are legitimately judged and condemned; for in every controversy, the condition of the one possessing is better. Moreover, it is certain that the Catholic bishops were not condemned by any legitimate judgment; for who condemned them apart from the Lutherans? But they are accusers, not judges. Who made them our judges? (Bellarmine, On the Marks of the Church, cap. vii)
Must be legitimately judged, and that includes the Pope.In his book On Clerics, he says the faithful are not to listen to heretical bishops, but they cannot depose them, which is no different than “declaring” them deposed based on private judgment: Bellarmine: “Moreover, it should be observed that, on the one hand, the people, by the rule which we have laid down, can indeed discern a true prophet from a false one; but, on the other hand, they cannot, for all that, depose the false prophet, if he be a bishop, and substitute another in his place. For the Lord and the Apostle command only that the people not hear false prophets, and not that they depose them [or declare them deposed]. And certainly the practice of the Church has always been thus, that heretical bishops be deposed by bishops’ councils or by the supreme pontiffs. (On Clerics, bk.1, ch.7).
Obviously, Bellarmine is referring to heretical bishops who were teaching heresy, since if their heresy remained entirely hidden there would be no need to avoid listening to them.
What it boils down to is this: If a heretical bishop or Pope remains in possession of his see, he has to be “legitimately judged” and “convicted” before he will lose his office, even if he is judged to be a “manifest heretic” beforehand by private judgment.
I would also note that when there is a doubt of fact or law, the Church supplies jurisdiction for the governance of the Church in both the internal and external forums:
Doubts of fact or law:
Can. 143 §1. Ordinary power ceases by loss of the office to which it is connected.
§2. Unless the law provides otherwise, ordinary power is suspended if, legitimately, an appeal is made or a recourse is lodged against privation of or removal from office.
Can. 144 §1. In factual or legal common error and in positive and probable doubt of law or of fact, the Church supplies executive power of governance for both the external and internal forum.
Here’s what Woywood said about the “Popes” during the time of the Great Western Schism:
“Yet is must be maintained according to Catholic teaching and Church history (see any standard Catholic Apologetics text book) that although there was during this period of confusion, two or even three claimants to the papacy, yet in actual fact there was only one Legitimate Pope, the others being antipopes. In such cases of common error, no matter how they are created, the Church supplies the jurisdiction for the benefit of the people (Canon 209. Practical Commentary of the Code, Law. Woywod. Vol. 1. p. 80.)
Other theologians have said that if all the Popes during the Great Western Schism were false Popes, Christ Himself would have supplied the jurisdiction (since the Church cannot supply papal jurisdiction if there is no true Pope).
Along the same lines, Bellarmine’s fellow Jesuit, the renowned canonist Fr. Paul Laymann, teaches that even the Pope is notoriously heretical, as long as he is publicly recognized as Pope by the Church, he will retain his jurisdiction:
Fr. Laymann, S.J.: “It is more probable that the Supreme Pontiff, as concerns his own person, could fall into heresy, even a notorious one, by reason of which he would deserve to be deposed by the Church, or rather declared to be separated from her. … The proof of this assertion is that neither Sacred Scripture nor the tradition of the Fathers indicates that such a privilege [i.e., being preserved from heresy when not defining a doctrine] was granted by Christ to the Supreme Pontiff: therefore the privilege is not to be asserted.
The first part of the proof is shown from the fact that the promises made by Christ to St. Peter cannot be transferred to the other Supreme Pontiffs insofar as they are private persons, but only as the successor of Peter in the pastoral power of teaching, etc. The latter part is proven from the fact that it is rather the contrary that one finds in the writings of the Fathers and in decrees: not indeed as if the Roman Pontiffs were at any time heretics de facto (for one could hardly show that); but it was the persuasion that it could happen that they fall into heresy and that, therefore, if such a thing should seem to have happened, it would pertain to the other bishops to examine and give a judgment on the matter; as one can see in the Sixth Synod, Act 13; the Seventh Synod, last Act; the eight Synod, Act 7 in the epistle of [Pope] Hadrian; and in the fifth Roman Council under Pope Symmachus: ‘By many of those who came before us it was declared and ratified in Synod, that the sheep should not reprehend their Pastor, unless they presume that he has departed from the Faith’. And in Si Papa d. 40, it is reported from Archbishop Boniface: ‘He who is to judge all men is to be judged by none, unless he be found by chance to be deviating from the Faith’. And Bellarmine himself, book 2, ch. 30, writes: ‘We cannot deny that [Pope] Hadrian with the Roman Council, and the entire 8th General Synod was of the belief that, in the case of heresy, the Roman Pontiff could be judged,’ as one can see in Melchior Cano, bk. 6, De Locis Theologicis, last chapter.
But note that, although we affirm that the Supreme Pontiff, as a private person, might become a heretic … nevertheless, for as long as he is tolerated by the Church, and is publicly recognized as the universal pastor, he is still endowed, in fact, with the pontifical power, in such a way that all his decrees have no less force and authority than they would if he were a truly faithful, as Dominic Barnes notes well (q.1, a. 10, doubt 2, ad. 3) Suarez bk 4, on laws, ch. 7. The reason is: because it is conducive to the governing of the Church, even as, in any other well-constituted commonwealth, that the acts of a public magistrate are in force as long as he remains in office and is publicly tolerated.” (Laymann, Theol. Mor., bk. 2, tract 1, ch. 7, p. 153).