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2. Fr. Boulet proceeds to provide a brief “Exposition of the Sedevacantist thesis,” as follows:

“Let me first quote from a Sedevacantist author: ‘Sedevacantism is the theological position of those traditional Catholics who most certainly believe in the papacy, papal infallibility and the primacy of the Roman Pontiff, and yet do not recognize John Paul II as a legitimate successor of Peter in the primacy. In other words, they do not recognize John Paul II as a true Pope. The word Sedevacantism is a compound of two Latin words which together mean the Chair is vacant.’ (Bishop Pivarunas). Sedevacantism appears then to be a theological position or a theory kept by some traditional Catholics who think that the most recent Popes, the Popes of the Vatican II council, lost their pontifical authority on account of the grave heresies they have been promoting, and the crisis that came along.”

Fr. Boulet is imprecise. Bishop Pivarunas has in these words defined the sedevacantist thesis as the denial of the claim of John Paul II to the papacy. And that is all. It is a very narrow definition, in keeping with the spirit I have mentioned above that demands a humble minimalism. Fr. Boulet, for reasons not apparent, proceeds to interpret Bishop Pivarunas’ statement to mean that sedevacantists believe that “the Popes of the Vatican II council, lost their pontifical authority on account of the grave heresies they have been promoting,...” But that inference is unjustified. Indeed, there are many sedevacantists who are content to follow St. Robert Bellarmine and the more common opinion of theologians, which is that Popes cannot lose the Faith, so that if the Vatican II Popes were not true Popes, then they must never have been Popes. The notion that sedevacantists believe that the Conciliar Popes lost their authority by public heresy is entirely absent from Bishop Pivarunas’ words, as quoted by Fr. Boulet.

---From LoT

I believe it is more likely for a purported Pope never to have had the authority in the first place.  I do believe it is quite plausible that John 23 and Paul 6 were material Popes until Paul 6 aprroved Lumen Gentium in November of 1964.  This is when he resigned from the Catholic Church and became the head of something broader.  This occuring when he redefined the Church of Christ to that which is a mish mash of the Catholic and heretical religions that are attached to the Catholic Church by his definition.  "The Catholic Church Subsists in the Church of Christ".  It is difficult to find blatent "official" heresies (they are only official if a valid Pope promulgates them) before that docuмent was approved but not after.    

   While I have previously said that John Lane is the most eloquent of the sedevacantist authors, this does not mean he is correct in his position.

   Truth can be poorly argued.

   Error can be eloquently argued.

   But here is where Mr. Lane stumbles, in my opinion:

1) There has never been a case in the history of the Church where a false "Pope" has ruled with universal consent;

2) And without a counter-claimant;

3) Or for such a long duration;

4) Which makes all the sedevacantist writings merely speculative, not practical.

5) Their having no reference point in the history of the Church.

6) And finally, I am not satisfied with Mr Lane's solution to the problems for the visibility of the Church that the sedevacantist thesis creates (i.e., He says there are a sufficient number of validly consecrated traditional bishopss from which the visibility of the Church could be restored).

7) What this solution overlooks is that none of them, even if there were a thousand of them, would have ordinary jurisdiction, and so the official heirarchy would still be dead.

8) Which is impossible

LoT,

As you have pointed out, this part of Fr Boulet’s argument is disingenuous. In effect, he is applying the straw-man fallacy.

On your other point:

Whether a true pope can fall into error in his teaching on matters of faith and morals.

In the Gospel according to Saint Luke, we read in chapter 22:

(31) Ait autem Dominus Simon Simon ecce Satanas expetivit vos ut cribraret sicut triticuм:
(32) ego autem rogavi pro te ut non deficiat fides tua et tu aliquando conversus confirma fratres tuos
[Vulgate]

(31) And the Lord said: Simon, Simon, behold Satan hath desired to have you, that he may sift you as wheat:
(32) But I have prayed for thee, that thy faith fail not: and thou, being once converted, confirm thy brethren.
[Douay-Rheims]

It is to be noticed that in verse 31, the personal pronoun (vos) is plural, referring to all of the Apostles; whereas in verse 32 the personal pronoun (te) is singular, referring to Simon Peter as the head of the Apostles. Thus, in these words Our Lord,  just before His Passion, warned the Apostles that they would all be attacked by Satan, but also advised that, in advance of the attack, He had especially prayed for the endurance of Peter’s faith, even then knowing that Peter’s courage would temporarily fail him. But having recovered, it would be Peter’s duty to confirm the others in the faith. With the birth of the Church at Pentecost, we see Peter boldly fulfilling this mandate.

From this, I deduce that the divine protection of the faith in Peter and in his successors is guaranteed by Christ. If it were not so, then the Church would be without an infallible final court of appeal, and each of us would be left to his own devices to divide truth from error.

Therefore, I am drawn to the conclusion that, being under a special form of divine protection for the good of the faithful, a true pope cannot fall into error in his teaching on matters of faith and morals -- as in fact the Church teaches.
 
On the other hand, when a purported pope, either by his words or by his deeds, gives public expression to errors of this class, it must follow that he lacks the divine protection proper to a true pope, and that, lacking this protection, he was never a true pope from the outset. If it were not so, then, in principle, it would be left to the faithful, each to become a mini-pope sifting out the errors from the public expressions of the maxi-pope -- which is absurd, and a formula for every flavour of Protestantism, for quis custodiet ipsos custodies?

To put this another way, it is inimical to my way of thinking that a genuine pope should ever fall into error in his teaching on matters of faith and morals. -- A point of view, which I think you share.

A Pope cannot fall into error when teaching Ex Cathedra, his personal opinions as a theologian are not infallible. People attempt to deify the Pope and that is the opposite extreme of the anti-infalliblists. Neither extreme is true, they both are against Church teaching. Pope John XXII taught error in his sermons and repented before his death. What he taught was against an undefined dogma. But it was still a dogma and proxima fidei(So intrinsic to other matters of Dogma that to deny it is to deny other beliefs of the Church). Wherein he preached that noone received the beatific vision until the final judgement.

Now the people were not stupid, they knew that if this were true, then it was impossible to pray to the Saints and the Blessed Virgin Mary, since none of them would be WITH God until the final judgement. HERESY they said. Rightfully so, it was not formal heresy, he taught what he thought the church taught but he was wrong. He didn't preach it Ex Cathedra. He agreed to allow a theological commision at one of the universities look into it, and they came back and told him he was wrong. On his deathbed he repented. His successor condemned the error but not the person.

Clearly Pope's are not infallible when they speak as private persons, they are not gods. They are mortal men such as we, God will prevent them from teaching error, when the 4 conditions are met as defined in the first(and imo only) Vatican Council.