http://strobertbellarmine.net/books/Concerning_A_SSPX_Dossier_on_Sedevacantism.pdf

6.  Returning then, to Fr. Boulet’s text.

2nd  Opinion: “As he falls into heresy, even only internal, the Pope would ipso facto lose his pontificate”.  Such opinion is now abandoned by theologians.  Because the Church is Visible, it is necessary that its government be visible, and not depends on internal acts.

3rd Opinion: “Even if he falls into notorious heresy, the Pope will never lose his pontificate.” Xavier de Silveira comments: “among the 136 authors we have consulted (for the book LNM), Bouix is the only one to defend such opinion” 6 [6 St Robert Bellarmine, De Romano Pontifice, lib. II, cap. 30. ] We could say like St. Robert Bellarmine that such opinion is very improbable, because it goes against the unanimous consent of the Tradition of the Church.

4th  Opinion: “The heretical Pope would lose effectively his pontificate only upon an official declaration of heresy.”  It is clear that such declaration cannot be judicial one, for the Pope doesn’t have any superior on earth, capable to judge him.  It would be only a non-judicial act by which Jesus-Christ would Himself  dismiss  the  Pope.   Even  though  such  opinion  is defended by serious theologians, like Cajetan and Suarez, it is not admitted by St. Robert Bellarmine.  I can see two dangers that can rise from such opinion - to fall into the heresy of Conciliarism, which was condemned by the Church - or at least, to fall into subjectivism. What can tell us, for sure, that a declaration of heresy coming from a group of bishops is not an attempt to make an act of deposition?

a)  Obviously the 2nd and 3rd opinions require no further comment.

b)  In relation to Fr. Boulet’s comment on the 4th opinion, I am reluctant to follow him in discussing the danger that might arise from the doctrine expressed.  Either the doctrine is true or it is false.  It may well be true and still be occasion for some danger.  But I do not think it is true, and in fact St. Robert Bellarmine refuted it in his usual masterful manner.  It would be a shame to consider this erroneous opinion without reading the refutation of St. Robert Bellarmine, so here it is.


This principle is most certain. The non-Christian cannot in any way be Pope, as Cajetan himself admits (ib. c. 26). The reason for this is that he cannot be head of what he is not a member; now he who is not a Christian is not a member of the Church, and a manifest heretic is not a Christian, as is clearly taught by St. Cyprian (lib. 4, epist. 2), St. Athanasius (Scr. 2 cont. Arian.), St. Augustine (lib. de great. Christ. cap. 20), St. Jerome (contra Lucifer.) and others; therefore the manifest heretic cannot be Pope.


To this Cajetan responds (in Apol. pro tract. praedicto cap. 25 et in ipso tract. cap. 22) that the heretic is not a Christian "simpliciter" [i.e. without qualification, or absolutely], but is one "secundum quid" [i.e. in a qualified or relative sense]. For, granted that two things constitute the Christian - the faith and the [baptismal] character - the heretic, having lost the faith, is still in some way united to the Church and is capable of jurisdiction; therefore, he is also
Pope, but ought to be removed, since he is disposed, with ultimate disposition, to cease to be Pope: as the man who is still not dead but is "in extremis" [at the point of death].


Against this: in the first place, if the heretic remained, "in actu" [actually], united to the Church in virtue of the character, he would never be able to be cut or separated from her "in actu", for the character is indelible. But there is no one who denies that some people may be separated "in actu" from the Church. Therefore, the character does not make the heretic be "in actu" in the Church, but is only a sign that he was in the Church and that he must return to her. Analogously, when a sheep wanders lost in the mountains, the mark impressed on it does not make it be in the fold, but indicates from which fold it had fled and to which fold it ought to be brought back. This truth has a confirmation in St. Thomas who says (Summ. Theol. III, q. 8, a. 3) that those who do not have the faith are not united "in actu" to Christ, but only potentially - and St. Thomas here refers to the internal union, and not to the external which is produced by the confession of faith and visible signs. Therefore, as the character is something internal, and not external, according to St. Thomas the character alone does not unite a man, "in actu," to Christ.


Further against the argument of Cajetan: either faith is a disposition necessary "simpliciter" for someone to be Pope, or it is only necessary for someone to be a good Pope ["ad bene esse," to exist well, to be good, as opposed to simply existing]. In the first hypothesis, in case this disposition be eliminated by the contrary disposition, which is heresy, the Pope immediately ceases to be Pope: for the form cannot maintain itself without the necessary dispositions. In the second hypothesis, the Pope cannot be deposed by reason of heresy, for otherwise he would also have to be deposed for ignorance, immorality, and other similar causes, which impede the knowledge, the morality, and the other dispositions necessary for him to be a good Pope ("ad bene esse papae"). In addition to this, Cajetan recognises (tract. praed., ca. 26) that the Pope cannot be deposed for the lack of dispositions necessary, not "simpliciter", but only "ad bene esse."


To this, Cajetan responds that faith is a disposition necessary "simpliciter", but partial, and not total; and that, therefore, even if his faith disappears he can still continue being Pope, by reason of the other part of the disposition, the character, which still endures.


Against this argument: either the total disposition, constituted by the character and by faith, is necessary "simpliciter," or it is not, the partial disposition then being sufficient. In the first hypothesis, the faith disappearing there no longer remains the disposition "simpliciter" necessary, for the disposition "simpliciter" necessary was the total, and the total no longer exists. In the second hypothesis, the faith is only necessary "ad bene esse", and therefore its absence does not justify the deposition of the Pope. In addition to this, what finds itself in the ultimate disposition to death, immediately thereafter ceases to exist, without the intervention of any other external force, as is obvious; therefore, also the Pope heretic ceases to be Pope by himself, without any deposition.5 [ St Robert Bellarmine, De Romano Pontifice, lib. II, cap. 30. Emphasis added.]

Thus we see why the 4th opinion decreased rapidly in theological respectability from the time of St. Robert Bellarmine.  It had been completely demolished as only the greatest master of apologetics and polemics could do.   It is worth noting once more that the argument put forth by St. Robert applies equally to a heretic who claims the papacy and to a Pope who disappears into heresy – in either case, the heretic cannot be Pope – that is, a heretic cannot become or remain Pope.  In St. Robert’s pithy words, “This principle is most certain. The non-Christian cannot in any way be Pope.”

I'll start the responses off.  John Lane and Saint Robert Bellarmine were obviously correct on this point