Thus, even when the Chair of Peter is not occupied, the visible, hierarchical nature of the Church is maintained. Thus the situation during such an interregnum cannot be compared to the situation that the Church would be in if Pope John Paul II is not the legitimately reigning pontiff as there would be no visible source of authority capable of convoking a conclave to elect a new pope.
The theological weakness of sedevacantism is an inadequate concept of the nature of the Church. Without realizing it, they believe in a Church which can fail - and such a Church is not the Church founded by Our Lord Jesus Christ. The Church that He founded cannot fail, for it is indefectible (i.e. it cannot fail). It will continue to exist until the Second Coming as a visible, hierarchically governed body, teaching the truth and sanctifying its members with indubitably valid sacraments. To state that we have no pope is to claim that the Church is no longer visible and hierarchically governed, which, in effect, means that it has ceased to exist. Catholic theologians accept that a pope could lose his office through heresy, but it would have to be such notorious heresy that no doubt concerning the matter could exist in the minds of the faithful, and a statement that the Pope had deposed himself would need to come from a high level in the Church, most probably a general Council. Archbishop Marcel Lefebvre warned in 1979.
The visibility of the Church is too necessary to its existence for it to be possible that God would allow that visibility to disappear for decades. The reasoning of those who deny that we have a pope puts the Church into an inextricable situation. Who will tell us who the future pope is to be? How, as there are no cardinals, is he to be chosen? The spirit is a schismatical one. [...] And so, far from refusing to pray for the Pope, we redouble our prayers and supplications that the Holy Ghost will grant him the light and strength in his affirmations and defense of the Faith.
The question of whether the Holy See is vacant must be considered from three aspects, that is: whether a pope could become an heretic and forfeit his office; what constitutes heresy; and whether any of the conciliar popes can be considered to be heretics within the context of this definition.
1. Can a pope forfeit his office through heresy?
The problem which would face the Church if a legitimately reigning pope became an heretic has been discussed in numerous standard works of reference. The solution is provided in the 1913 edition of The Catholic Encyclopedia:
The Pope himself, if notoriously guilty of heresy, would cease to be pope because he would cease to be a member of the Church.
Many theologians have discussed the possibility of a pope falling into heresy, and the consensus of their opinion concurs with that of The Catholic Encyclopedia. The Pope must evidently be a Catholic, and if he ceased to be a Catholic he could hardly remain the Vicar of Christ, the head of the Mystical Body. St. Robert Bellarmine taught:
The manifestly heretical pope ceases per se to be pope and head as he ceases per se to be a Christian and member of the Church, and therefore he can be judged and punished by the Church. This is the teaching of all the early Fathers.
Saint Robert was, of course, discussing a theoretical possibility, and believed that a pope could not become an heretic and thus could not be deposed, but he also acknowledged that the more common opinion was that the pope could become an heretic, and he was thus willing to discuss what would need to be done if, per impossible, this should happen:
This opinion (that the Pope could not become an heretic) is probable and easily defended. [...] Nonetheless, in view of the fact that this is not certain, and that the common opinion is the opposite one, it is useful to examine the solution to this question, within the hypothesis that the Pope can be an heretic.
The great Jesuit theologian, Francisco de Suarez (1548-1617) was also sure that God’s "sweet providence" would never allow the one who could not teach error to fall into error, and that this was guaranteed by the promise Ego autem rogavi pro te ... (Luke 22: 32). But, like Bellarmine, Suarez was willing to consider the possibility of an heretical pope as an hypothesis, particularly in view of the fact, he claimed, that several "general councils had admitted the hypothesis in question." Saint Alphonsus Liguori (1696-1787) did not believe that God would ever permit a Roman Pontiff to become a public or an occult heretic, even as a private person:
We ought rightly to presume as Cardinal Bellarmine declares, that God will never let it happen that a Roman Pontiff, even as a private person, becomes a public heretic or an occult heretic.
If, per impossible, a pope became a formal heretic through pertinaciously denying a de fide doctrine, how would the faithful know that he had forfeited his office as he had ceased to be a Catholic? It must be remembered that no one in the Church, including a General Council, has the authority to judge the Popes. Reputable authorities teach that if a pope did pertinaciously deny a truth which must be believed by divine and Catholic faith, after this had been brought to his attention by responsible members of the hierarchy (just as St. Paul reproved St. Peter to his face), a General Council could announce to the Church that the Pope, as a notorious heretic, had ceased to be a Catholic and hence had ceased to be Pope. It is important to note that the Council would neither be judging nor deposing the Pope, since it would not possess the authority for such an act. It would simply be making a declaratory sentence, i.e. declaring to the Church what had already become manifest from the Pope’s own actions. This is the view taken in the classic manual on Canon Law by Father F.X. Wernz, Rector of the Gregorian University and Jesuit General from 1906 to 1914. This work was revised by Father P. Vidal and was last republished in 1952. It states clearly that an heretical Pope is not deposed in virtue of the sentence of the Council, but "the General Council declares the fact of the crime by which the heretical pope has separated himself from the Church and deprived himself of his dignity." Other authorities believe that such a declaration could come from the College of Cardinals or from a representative group of bishop, while others maintain that such a declaration would not be necessary. What all those who accept the hypothesis of an heretical pope are agreed upon is that for such a pope to forfeit the papacy his heresy would have to be "manifest", as Saint Robert Bellarmine expressed it, that is notorious and public (notorium et palam divulgata). A notorious offence can be defined as one for which the evidence is so certain that it can in no way be either hidden or excused. A pope who, while not being guilty of formal heresy in the strict sense, has allowed heresy to undermine the Church through compromise, weakness, ambiguous or even gravely imprudent teaching remains Pope, but can be judged by his successors, and condemned as was the case with Honorius I.
2. What is heresy?
There has never been a case of a pope who was undoubtedly a formal heretic, and it is unlikely in the extreme that there ever will be one. This will become evident if some consideration is given to examining precisely what constitutes formal heresy. The Code of Canon Law defines an heretic as one who after baptism, while remaining nominally a Catholic, pertinaciously doubts or denies one of the truths which must be believed by divine and Catholic faith. It teaches us that by divine and Catholic faith must be believed all that is contained in the written word of God or in tradition, that is, the one deposit of faith entrusted to the Church and proposed as divinely revealed either by the solemn Magisterium of the Church or by its Ordinary Universal Magisterium. No teaching is to be considered as dogmatically defined unless this is evidently proved.
A doctrine is de fide divina et catholica only when it has been infallibly declared by the Church to be revealed by God. Hence this term does not apply to doctrines which one knows to have been revealed by God, but which have not been declared by the Church to have been so revealed (de fide divina); nor to those which the Church has infallibly declared, but which she does not present formally as having been revealed (de fide ecclesiastica); nor to those which the Church teaches without exercising her infallible authority upon them. If a doctrine is not de fide divina et catholica, a person is not an heretic for denying or doubting it, though such a denial or doubt may be grave sin.
3. The conciliar Popes
It should now be apparent that there is no case whatsoever for claiming that any of the conciliar popes have lost their office as a result of heresy. Anyone wishing to dispute this assertion would need to state the doctrines de fide divina et catholica which any of these popes are alleged to have rejected pertinaciously. There is not one instance which comes remotely within this category. The nearest one can come to a formal contradiction between preconciliar and post-conciliar teaching is the subject of religious liberty. It has yet to be shown how they can be reconciled. It is possible that the Magisterium will eventually have to present either a correction or at least a clarification of the teaching of Vatican II on this subject. Neither the pre-conciliar teaching nor that of the Council on religious liberty comes within the category of de fide divina et catholica, and so the question of formal heresy does not arise.
 Catholic Encyclopedia (New York, 1917), vol. III, p. 217.
 CE, vol. VII, p. 261.
 Saint Robert Bellarmine, De Romano Pontifice (Milan, 1857), vol. II, chap. 30, p. 420.
 Ibid., p. 418.
 F. Suarez, De legibus (Paris, 1856), vol. IV, chap. 7, no. 10, p. 361.
 Dogmatic Works of St. Alphonsus Maria de Ligouri (Turin, 1848), vol. VIII, p. 720.
 Wernz-Vidal, Jus Canonicum (Rome, 1942), vol II, p. 518.
 Ibid., p. 433.
 Op. cit., note 92, Wernz-Vidal, (Rome, 1937), vol VII, pp. 46-47.
 Code of Canon Law: Old Code, Canon 1325; New Code, Canon 751.
 Denzinger, 1792; CCL: Old Code, Canon 1323; New Code, Canon 750.
 CCL, Old Code, 1323, §3; New Code, 749, §3.
 T. Bouscaren & A. Ellis, Canon Law, A Text & Commentary (Milwaukee, 1958), p. 724.
 M. Davies, The Second Vatican Council and Religious Liberty (The Neumann Press, Minnesota, 1992).