This goes to the very heart of the problem of “Francis” who has been such a HOT HOT HOT HOT topic in the last couple of years, no?
The solution is going to come down to one thing in many ways: That to remain a strong Catholic one ought to be capable of identifying a false pope if one arises in his lifetime.
In light of testimony given by Archbishop John Purcell (1800-1883) that the Fathers of the First Vatican Council said that a heretical pope is impossible, that leaves only that the heresy being daily demonstrated by the man in white in Rome is being demonstrated by an imposter, by one rejected not so much by Sedevacantists, but by God Himself!:
Read the words of the attendee of the First Vatican Council below, those of aforementioned Archbishop John Purcell:
The question was also raised by a Cardinal, “What is to be done with the Pope if he becomes a heretic?” It was answered that there has never been such a case; the Council of Bishops could depose him for heresy, for from the moment he becomes a heretic he is not the head or even a member of the Church. The Church would not be, for a moment, obliged to listen to him when he begins to teach a doctrine the Church knows to be a false doctrine, and he would cease to be Pope, being deposed by God Himself.
If the Pope, for instance, were to say that the belief in God is false, you would not be obliged to believe him, or if he were to deny the rest of the creed, “I believe in Christ,” etc. The supposition is injurious to the Holy Father in the very idea, but serves to show you the fullness with which the subject has been considered and the ample thought given to every possibility. If he denies any dogma of the Church held by every true believer, he is no more Pope than either you or I; and so in this respect the dogma of infallibility amounts to nothing as an article of temporal government or cover for heresy.
(Abp. John B. Purcell, quoted in Rev. James J. McGovern, Life and Life Work of Pope Leo XIII [Chicago, IL: Allied Printing, 1903], p. 241)
Serious questions:
Does this only apply when the Pope is speaking "ex cathedra" or for all things said by the Pope?