How would you address the following, as it pertains to the question of a broken apostolic sucession?
If this is supposed to mean that the Pope is paramount because his authority descends from Peter, there's a little problem. The problem is that the link was broken in the 13th century by Philip Le Bel and Guillaume de Nogart who kidnapped and killed one Pope, assassinated another and then stole the Papacy and moved it, lock stock and Earthly power, to France. Thus began the Avignon captivity. (don't bother to damn the French - they already are)
I believe that there have been truly holy men who have occupied the Papacy since it was returned to Rome. There have also been great sinners. Regardless, I believe the link to Peter has been irrevocably broken.
That was the point that the Cathars had in mind.
The reason I ask is that I think this is quite an important point, and IMO has not been successfully defended against in this thread.
I'm not capable of defending against it because I don't know enough, but from reading your posts, and having confidence in Tantumergo I thought you guys might be able to.
"How would you address the following, as it pertains to the question of a broken apostolic sucession?"
This whole argument misunderstands the concept of Apostolic succession. There is no tactile succession from one Pope to the next for the simple reason that the previous Pope is generally rather dead before the next one is elected!!! ;)
Whoever is elected the bishop of Rome by the Church of Rome, or later the College of Cardinals, is by definition the Pope - no matter what sort of person he is (as long as he's male!) and no matter where he is. Does JPII cease to be Pope when he's not in Rome?
Each Pope receives his place in the apostolic succession by being consecrated as a bishop by other bishops who are in the Apostolic succession. If he is a bishop before he is elected Pope, then the mere fact of his election and coronation means that he is the Bishop of Rome or Pope. If he is not a bishop at his election (such as the Deacon Gregory who became Gregory the Great) then he is ordained as priest and bishop by bishops in the Apostolic succession before his Papal coronation.
Every time a Pope dies we have a situation of sede vacante, until the next one is elected. But there has never been a time when there has been a "broken apostolic succession" in Rome, because Rome has existed for the entire Christian era and it has always had a bishop even if he has not been resident there for good or bad reasons.
The only way that you could have a "broken succession" in a particular Pope is if someone who was elected Pope did not have valid orders received from bishops in the Apostolic succession. Should such a situation ever arise (extremely unlikely as the Cardinals would never elect a man who they knew to have invalid orders) then it would be rectified when the next Pope with valid orders was elected.
This is why a terrorist attack against the Pope would be a pointless waste of time - if someone killed him we'd just elect another one. And as long as there is a single Catholic bishop left alive in the world, we will always have a Pope.
Remember the Pope doesn't receive the Keys from the previous Pope - he receives them from Christ.