EWTN's chatter before the emergence of a new pope today (or, as EWTN kept saying, "a new Holy Father"; as I've said before, the use of "a Holy Father" as a common noun that way is a huge pet peeve of mine) was discussing the count of popes. Is Francis number 265, 266, 267?
This raised the issue of counting popes in general, which is something I've spent quite a bit of time thinking about in my life, and one of the few things I've actually edited wikipedia to clarify. But, long story short, I'd count him as 266th pope, the 265th successor to St. Peter, and the 264th separate man to hold the office (the 263rd individual man to succeed St. Peter).
The Vatican's official list of popes in the Annuario Pontificio currently includes 265 popes from Peter to Benedict XVI. Francis will be the 266th on this list. (Though, it is to be noted, this list does not perfectly correspond to the portraits of popes in St. Paul's Outside the Walls, for example).
However, I would not accept the current Vatican list simply. There are many points of historical dispute over whom should be counted as a Pope during various points in the Middle Ages, especially the horrible saeculum obscurum in the 10th century. Who was a Pope and who was an antipope? Who was validly elected? Who acquiesced to their depositions (and thus can be considered valid resignations) and who refused to renounce their claims in spite of imprisonment or being chased out militarily?
Generally, the Vatican list seems pretty good and based on sound scholarship and principles. For example, in the early 20th century Christopher was identified as an antipope though he was previously included as legitimate on lists of popes. This exclusion makes sense. Christopher threw Leo V into prison in September 903, and it seems Leo did not acquiesce to this deposition, so Leo would still have been Pope in spite of Christopher's claim. Eventually, early the next year, both Leo and Christopher died in short order. It's possible they were both assassinated by the next claimant, Pope Sergius III who began his papacy late that January. Some argue that Christopher may have killed Leo shortly before Sergius had Christopher himself killed, and that Christopher can thus be considered valid pope between Leo's death and his own, but without any record of a new election this does not seem to follow given that his own election was originally invalid on account of Leo still being alive, and given that Sergius came in and was actually elected so soon after.
Furthermore, I'd generally agree with the idea that Benedict IX reigned and resigned three times. That he had at least two terms is indisputable; no one questions his second resignation in favor of his uncle (Gregory VI). Whether or not the brief reign of Sylvester III during Benedict's being driven out of Rome from September 1044 to April 1045 should be considered valid...is a trickier question. It's not clear Benedict acquiesced to this deposition, given that he fought to return so soon after. Nevertheless, Sylvester was not elected until January 1045, so his election and Benedict being driven out were not one in the same event (as one would expect in a true case of attempted usurpation) and the people of Rome must have had reason to believe that Benedict, being absent, was no longer Pope. Either way, the fact that Benedict had non-consecutive reigns (at least two, if not three) means that the count of individual men who were pope will always be lower than the number of papacies, the ordinal count (Grover Cleveland's two non-consecutive terms have a similar effect on the count of U.S. Presidents).
Another interesting case, in which I also agree with the Vatican's order, is that of John XII, Benedict V, and Leo VIII. Leo has the interesting distinction of having been both pope and antipope, seemingly. He was installed by force when John XII was still pope (having refused to relinquish his claim after Emperor Otto tried to depose him), and so was an antipope. And when John XII died, it seems clear Benedict V was his legitimate successor. But when Otto got Leo installed again, Benedict unambiguously acquiesced to his deposition, gave up his claims to the papacy, and it seems that from that point forward Leo VIII was accepted finally and can be considered valid pope.
There are two cases in which I disagree with the Vatican list, however. However, in one case I believe they include someone who shouldn't be, and in the other I believe they didn't include someone who should be, and so the total count remains the same.
Specifically, I believe that Pope-elect Adrian V should not be included on the list. He was elected pope, but never consecrated bishop, and it is now agreed that since the papacy derives first and foremost from being Bishop of Rome, a non-bishop is not pope until he is consecrated. Somewhat bafflingly, the Vatican recognizes this, and so for this same reason does not include Pope-elect Stephen [II], who likewise was never consecrated bishop (more on regnal numbering later). Actually, the debate on EWTN which started this post seemed to center their discussion about the numbering question around whether Pope-elect Stephen is included, but that's actually something of a red herring, I think; modern lists do not now include him, nor do the oldest lists contemporary to him. He was only included later (and incorrectly) before being removed again.
However, on the other hand, I believe that "antipope" Boniface VII was actually probably a valid pope during his second reign. Certainly, the next (valid) pope Boniface seemed to recognize this, as he took the name Pope Boniface VIII (though, the inclusion of antipopes has misleadingly advanced the regnal numbering of certain popes, so it would not be unprecedented). Boniface first tried to seize the papacy in June 974, imprisoning and then murdering Benedict VI. However, he was driven out of Rome less than six weeks later by imperial representative Count Sicco, and replaced by Benedict VII. It might be possible that Boniface VII was a valid pope during those six weeks after Benedict VI's death, but from what I can tell, any "election" happened when Benedict was still alive in prison (and thus invalidly), and Boniface only had him killed upon hearing of the approach of Sicco. Still, if he were Pope during those six weeks, then some might suggest he remained Pope during the entire next decade during his "exile" in Constantinople, but I think a ten-year absence makes that unlikely. However, when Boniface returned a second time, in 984, again seizing the papacy by murder (this time from John XIV), he remained in power eleven months, with no competing claimants, and another election was then held only after he died. To me, being in power eleven months without anyone questioning it and having a new election only at his death...suggests to me that Boniface VII was accepted as valid pope during this time, and should be counted as such.
So that's my historical opinion on the count of popes. In my next post I'll discuss regnal numbers.