Proving an unbroken chain of succession in the Roman Catholic Church is, by the strict definition, impossible. But the strict definition is pretty useless for most things, so I don’t see much reason to use it to defend Protestantism on the issues of teaching authority and succession. If Roman Catholics can make a credible case that there was an unbroken succession of bishops in Rome, then we should grant that point and move on to argue about other things.

Of course, that is an argument for church historians to make and for us to read about when we have time.  I haven’t read Luther on the “Babylonian Captivity of the Church” nor any replies.

But I have read Clement’s letter to the Corinthians, and that ends the issue as far as I’m concerned.

Clement did not know he was the Pope and did not act like the Pope.  I’ve seen some point out how much weight Clement gives his own authority, but that just seals the deal. He doesn’t give himself anything like Papal authority nor does he show any sign that he holds an office instituted by Christ to have authority over the Corinthian church.  His belief in the relative importance of his own church, in comparison to the Corinthians, if that is what he believed, only proves that we are seeing early in the development of the myth of the Papacy.

If the Papal office was instituted by Christ, then Roman Catholics must believe that there was a Great Fall from the pristine doctrine and practice of Peter and maybe Linus, and only afterward did the Church recover the fullness of the truth in the third and fourth centuries.

And, just to be clear, you can use a developmental argument for the Papacy or you can argue that it was instituted by Christ in Matthew 18. You can’t do both. They contradict one another.