Does Vatican I disprove Sedevacantism?

The “Perpetual Successors” Objection

After the objection that “you guys are just a bunch of Protestants!!”, probably the most frequently-made argument against Sedevacantism is that our position contradicts the teaching of the First Vatican Council that St. Peter will have “perpetual successors”. If there hasn’t been a true Pope in decades, how then can we maintain that there is a perpetual succession of Popes?

We have addressed this argument on this site before, but a dedicated post on the issue is in order.

Our response will be twofold. We will demonstrate that (1) the objection from perpetual successors is actually based on a misunderstanding of the teaching of Vatican I; (2) even if the objection were not based on a misunderstanding, it would still not refute the sedevacantist position.