Bishop Williamson is saying that the Conciliar Church is not the Catholic Church.
How can he then inisist, as he so frequesntly does, that the Conciliar popes are Catholic popes?
According to Bishop Williamson's argument, if "Conciliar Rome is occupying the structures of Catholic Rome", then the Conciliar popes are the 'popes' of that occupying force. How, then, can they be Catholic popes, especially if "Conciliarism is heresy" as the Bishop maintains.
Sedevacantism is the only logical conclusion of Bishop Williamson's own argument, because if the Conciliar Church is not the Catholic Church, then the Conciliar popes cannot possibly be Catholic popes. They are only 'popes' of the heretical Conciliar Church, meaning that the Catholic Church at present has no pope. Therefore the Seat is vacant.
Bp. Williamson has explained this in the following way:
We can think of an apple partially rotten: one part is still good while the other is not, but both parts are the apple. The conciliar church would be the rotten part while the Catholic Church would be the good part, but the pope is the pope of the whole thing: pope of the conciliar church and pope of the Catholic Church.
I disagree with the bishop, but when he has been asked about this matter, that is what he has answered.
The rotten apple analogy and the cuckoo occupying the nightingale's nest analogy are quite different. In this EC, +W is separating the Conciliar Church and the Catholic Church entirely. Has his thinking changed here? If so, then his conclusions about the pope question must also change..
If the Conciliar Church is a separate entity from the true Catholic Church, then the men at the head of the Conciliar Church - the Conciliar popes - cannot also be Popes of the true Catholic Church.