Absolutely not: "This gift, then, of truth and never-failing faith was conferred by Heaven upon Peter and his successors in this Chair, that they might perform their high office for the salvation of all; that the flock of Christ, kept away by them from the poisonous food of error, might be nourished with the pasture of heavenly doctrine..”
I believe you are over-reading the passage to include the preface to the definition within the definition of infallibility itself. This is an error that Newman pointed out when dealing with the problem of the "new Ultramontanists" of his day.
But the language itself using the term "gift" and not "tools" or "helps" as supplied by God to the Church. A gift by its very nature can be accepted or rejected. Also the use of the word "might" instead of "will" indicates that the preface to the definition is not a guarantee of the efficacy of the gift when under the stewardship of the Pope.
If the Pope could wither away into formal heresy, then the anti-Christ could rule the Church - for his “rejection” of the faith, if possible, need not be public.
The Pope being a human being is given a free will to either reject or accept the faith. He is not trapped in the faith by God and the papacy does not cost him his free will. Nor is God dependent on the quality of the Pope for the survival of His Church.
Formal heresy would be public, material heresy would not necessarily be public.
Even if the anti-Christ were to be sitting on the chair of Peter, the Holy Ghost would protect the Church from him one way or another, but He would not interfere with the free will of the AntiChrist. And since God permits evil so he can pull more Good from it, I wouldn't put it past him to specifically allow it one day in order to demonstrate his overwhelming goodness.
This Church is protected by the Holy Ghost from this very destruction. The Church cannot fail, which means Peter must have a never-failing faith.
Think about it.
I have thought about it and I don't subscribe to an exaggerated ultramontanism. The Church is protected by the Holy Ghost. Period. The Church is indefectible. Period. The quality or fidelity of the Pope is not the determining factor of the survival of the Church. If necessary, the Holy Ghost will protect the Church from the Pope at a certain point known only to Him.
No, true obedience means we do not judge the pope or sift his acts of Sovereign Primacy. There is no such thing as “false obedience” when submitting the mind and the will to the will of the Supreme Legislator as manifested in the promulgation of the Church's laws and disciplines.
Again, you are saying that the Pope can order an evil and by virtue of his being Pope, it is not evil. That is utter madness. I keep using the example of the trial of Formosus because it is so self-evident. The Supreme Legislator determines that the previous occupant was "unworthy" and "invalid." By your definition he cannot be judged in his decision. False obedience is certainly providing answers for the corpse of a Pope at the trial of that corpse.
No, the case is not “an example of Popes exercising their full power for the purpose of making formal judgments” because nowhere in the divine constitution of the Church is there a basis for one Pope having the power or right to judge another.
By your own position, the Pope has Supreme Authority, if he says he has that ability, his judgement is not subject to appeal. And it absolutely is an example of a Pope exercising his full power. Only a Pope can pass judgement on another Pope or declare someone an anti-Pope.
A couple of them have tried - and each attempt ended in disaster, as your example shows.
No. You're avoiding the reality of the history. It wasn't merely an attempt. It was done. The Pope did make a judgement on his predecessor and then another Pope ruled against Stephen and then another rule in favor of Stephen. They weren't attempts to make jugements. They were actual judgements brought to completion.
So you are right to say the Holy Ghost does not protect the Pope when he exceeds his authority by judging another pope - because he simply does not have the authority to do so.
He certainly does have the authority. They have done it. What he doesn't have is the protection of the Holy Ghost from error in those judgements.
He can amend or abrogate previous acts and even determine the extent of innocent error; but he cannot judge any of his predecessors - for the pope has no judge but God alone.
The condemnation of Honorius sure looks like a judgement to me. From the CE:
The new pope, Leo II, had naturally no difficulty in giving to the decrees of the council the formal confirmation which the council asked from him, according to custom. The words about Honorius in his letter of confirmation, by which the council gets its ecumenical rank, are necessarily more important than the decree of the council itself: "We anathematize the inventors of the new error, that is, Theodore, Sergius, ...and also Honorius, who did not attempt to sanctify this Apostolic Church with the teaching of Apostolic tradition, but by profane treachery permitted its purity to be polluted." This appears to express exactly the mind of the council, only that the council avoided suggesting that Honorius disgraced the Roman Church.
There is another moral to this story and that is that the Church ruled that Pope Formosa was indeed a valid pope; and it is also true that not one of these popes lost the Faith.
You can't have it both ways. The Supreme Legislator ruled that Pope Formosus was invalid. Then another Pope as Supreme Legislator ruled that Pope Stephen was wrong as Supreme Legislator and that Formosus was valid. Then another Pope Sergius III as Supreme Legislator ruled that Stephen was actually correct and Formosus was invalid. No further Popes have ruled on them, but theologians have argued the matter that Formosus was valid. The Popes have pretty much dropped it, but the last judgement was that Formosus was invalid.
But the reality is, no one believes it. A papal judgment has been for all practical purposes tossed in the garbage. And the Popes have been content to let it stay there.
Two Hundred and Sixty Five men have sat in the Chair of Peter. Some were scoundrels; many were unworthy of the honor. Many more have been Saints. Some are most certainly in hell. But none of them ever lost the faith.
To believe otherwise is to embrace objective heresy.
The only part of that statement that is not debatable is the number 265. I tend to agree with what you state but I don't understand how you can say it and maintain your beliefs. You say no one may judge a Pope but then you have a certainty that you not permitted to have that some are in Hell. How can someone who has "never-failing faith" go to Hell?