Mike,
First of all, some things need to be cleared up here. During this era of the early Church, Rome was still the capital of the empire, and indeed the pre-eminent Church in the empire.
None of the early sources say that Rome held primacy because it was the capital of the Empire. While this is clearly why St. Peter (along with St. Paul) based himself in Rome (where "all roads led" ...making the management of a universal Covenant far easier), the church of Rome (like all other city-churches) was an illegal, underground society that was being persecuted by the Roman government. So, early Roman primacy did not come from its associations with the imperial capital, but from its Petrine succession. This is what all the early fathers say. It was only the 5th Century Byzantines (who were trying to promote their "one-Church, one Empire" agenda and create a political theocracy) who first made the claim that Rome held primacy because it was the original capital of the Empire -- the implication being that Constantinople should hold a similar primacy, because it was the "New Rome." But, even at the time, this silly and untenable argument was rejected by Rome and the other Apostolic patriarchates of Alexandria and Antioch, along with the rest of the Church.
Antioch's influence extended from Syria to Mesopotamia, Persia and even India, and Alexandria's influence was over Africa (excepting North Africa, which was traditionally Roman),
Well...not quite...
Alexandria's regional jurisdiction ended at the border between Roman Africa and Libya, as even canon 6 of the Council of Nicaea says. Alexandria did not oversee N. Africa. Rather, Carthage was pat of the patriarchate of Rome. And, as canon 6 of Nicaea also tells us, the regional authority of Alexandria and Antioch was recognized by the Church BECAUSE the Bishop of Rome recognized the regional authority of these patriarchs in these places. In other words, Alexandria and Antioch were under the ultimate jurisdiction of Rome, and the only reason they were regional patriarchates at all was because of their ties of Petrine discipleship to Petrine Rome. As Pope Damasus I in 382 says, responding to the Council of Constantinople I, and rejecting the church of Constantinople's first aborted attempted to make itself the primate in the East in place of Alexandria (the Traditional and Apostolic Eastern primate):
"Although all the Catholic churches spread abroad throughout the world comprise but one bridal chamber of Christ, nevertheless, the holy Roman church has been placed at the forefront not by the conciliar decisions of the churches, but has received the primacy by the evangelic voice of our Lord and Savior, Who says: "You are Peter ...(Matt 16:18-19)." In addition to this, there is also the companionship of the vessel of election, the most blessed Apostle Paul who, along with Peter in the city of Rome in the time of Caesar Nero, equally consecrated the above-mentioned holy Roman Church to Christ the Lord; and by their own presence and by their venerable triumph, they set it at the forefront over the others of all the cities of the world. The first see, therefore, is that of Peter the Apostle, that of the Roman church, which has neither stain nor blemish, nor anything like that. The second see is that of Alexandria, consecrated on behalf of the blessed Peter by Mark, his disciple and an Evangelist, who was sent to Egypt by the Apostle Peter, where he preached the word of truth and finished his glorious martyrdom. The third see is that of Antioch, which belonged to the most blessed Peter, where first he dwelled before he came to Rome, and where the name "Christians" was first applied, as to a new people." (Decree of Damasus # 3, 382 A.D.)
So, it was by St. Peter's design that Alexandria manage East Africa (along with Arabia and part of India), and that Antioch manage Asia, down into Mesopotamia and India; but they only did this as "satellites" of the Petrine authority of Rome, which remained the final court of appeal for the universal Church. This is undeniable for anyone who consults the historical record.
...and Alexandria also had tremendous theological influence.
As did Antioch. But that's just theology, not Church authority. Alexandria and Antioch were the centers of the two principal theology schools of the early Church. This was both a benefit and a curse, since most of the early heresy battles (e.g. Arianism, Nestorianism, Monophysism, etc.) were initiated because of theological competitions between "scholars" from these two rival schools. In this, Rome had to consistently play the "referee."
Jerusalem was very troubled at the time (several Jewish revolts), and thus it's geographical influence wasn't very great,
Sorry but this is also historically incorrect. Jerusalem did not become a patriarchate until the council of Chalcedon in A.D. 451. Before that time, it was not even a metropolitanate, but was under the metropolitan of Caesarea. When the city of Jerusalem was destroyed in A.D. 70, the original church of Jerusalem was reduced to a tiny community of Jewish Christians; and after the second Jewish revolt in A.D. 130, when the Emperor Hadrian re-named the city "Aelia Capitolina" and forbad any Jew (or even Jewish Christian) from entering the city, the tiny church of Jerusalem became an entirely Gentile church, with no connection to the original Jewish church at all. It was only during the reign of Constantine that Jerusalem was given some importance again; and this was only because Constantine and his mother St. Helena began to built beautiful basilicas over the traditional Christian holy sites, and this inspired a new wave of pilgrimate to Jerusalem (or "Aelia," as it was called). Indeed, canon 7 of the council of Nicaea clearly says that the bishop of Aelia (Jerusalem) should be honored, but should be denied the rights of a metropolitan. Rather, Jerusalem remained under the authority of Caesara, and this continued to be the case under St. Cyril of Jerusalem, who had to stand trial before the (Arian) metropolitan of Caesarea when he was falsely accused by his Arian enemies, and thereafter deposed. It was Bishop Juvernal of Jerusalem (a scheming politician) who called in a lot of political favors at the Council of Chalcedon (451) and succeeded in getting the council to recognize Jerusalem's independence from the patriarchate of Antioch, and have it declared a patriarchate in its own right. Jerusalem was not a patriarchate (or even a metropolitanate) before this time. Rather, the three Apostolic patriarchates were Rome, Alexandria, and Antioch - in THAT order of primacy. The other two patriarchates of Constantinople and Jerusalem are not Apostolic, and were later inventions of the Byzantine imperial court. Most modern Eastern Orthodox seem to be unaware of this historical reality.
...and Constantinople of course didn't exist yet.
That depends on which Eastern Orthodox you ask. LOL. In the 7th Century, the Byzantines adopted the historical fairy tale that the church of Byzantium (later "Constantinople") was established by the Apostle Andrew, and was thus an Apostolic church because of that, supposedly drawing its authority from that Apostle. The reality, however, is that, before Constantine adopted and re-named the city after himself, Byzantium was a minor church that was answerable to the metropolitan of Herculea in Thrace. The first recorded bishop of Byzantium was Metrophanes I (306-314) or (315-327). All of the supposedly earlier bishops popularized by medieval Byzantine succession lists (stretching back to St. Andrew) are completely apocryphal.
Many of the letters you use as 'proof' of the Papacy, were written by churches which were indeed under Roman influence at the time (Greece and Asia Minor, though considered Eastern today, were under Rome's influence at the time). This still doesn't prove a universal jurisdiction.
First of all, the churches of Asia Minor were under the immediate jurisdiction of Antioch, not Rome. Secondly, one of the early fathers referenced was Ignatius of Antioch, who was a patriarch in his own right, but who directly says that Rome "presides in the chief place" and speaks of Rome's teaching of all other churches, including his own. Thirdly, when we look at the rest of the patristic record, we find numerous cases of both Alexandria and Antioch appealing to Rome for decisions and clarifications (but
never vise-versa). For example, in about 255, Patriarch St. Dionysius of Alexandria writes to Pope Sixtus II of Rome and asks if it is permissible to re-Baptize a man who was Baptized in a heretical sect and who now maintains that the Baptism was perfomed improperly. This request was based upon Alexandria's earlier acceptance of the recent universal decree issued by Pope Stephen which mandated that heretics should not be re-Baptized on pain of excommunication. This decree of Stephen would later be reaffirmed in the Nicene Creed with the phrase "we believe in
one Baptism for the remission of sins." And, about a decade later, this same Patriarch Dionysius of Alexandria stood corrected by Pope Dionysius of Rome (they had the same name) when the Alexandrian Dionysius outraged his flock by teaching that the Son is subordinate to the Father within the Trinity. As St. Athanasius recounts the story, the outraged Alexandrians appealed to Pope Dionysius of Rome, who immediately condemned the teaching, forcing Dionysius of Alexandria to recant; and St. Athanasius (the later, great champion against Arianism, and Patriarch of Alexandria himself) says that Rome therefore condemned the Arian error long before the error seriously raised its head. Likewise, in the early 200's, Patriarch Demetrius of Alexandria appealed to Rome to uphold his condemnation of Origin, who had been ordained a priest without his permission (Origin was a deacon under Patriarch Demetrius of Alexandria) by the metropolitan of Caesarea in Palestine. Origin's illegal ordination created a huge controversy in the Eastern church (because Origin was an intellectual "superstar" at the time), with the Greeks, Syrians, and Cappadocians siding with Origen against the Patriarch of Alexandria, and both sides appealing to Rome for a solution to the matter. Pope Pontian of Rome, however, stood fast with Alexandria (its Petrine satellite in the East), and Origin's ordination was declared null and void - a decision that Origen himself accepted. Likewise, the patriarchate of Antioch also frequently recognized the primacy of Rome, as in the 270's, when the heretical Patriarch of Antioch, Paul of Samosata, was deposed by a local Antiochian council, and the council fathers appealed to Rome to ratify their decision, and Pope Felix I rejected a similar appeal by Paul of Samosata and pronounced him deposed. So, there are MANY examples of Rome's true and jurisdictional primacy in the early Church.
Also, Rome for a long time indeed was an 'authority' - not because of a unique office, but because of the importance of the city, and the succession of Saintly Popes (it's no coincidence that almost all the early Popes were Saints, and almost none of the Popes leading up to the Schism were).
Well...be careful not to fall into the trap of the Dontatist heresy (the belief that ecclesial authority is based on personal sanctity ...which is an error condemned repeatedly by the early Church). You also need to appreciate historical reality, in that the Pope that Photius initially rebelled against, SAINT Nicholas I (858-67), is recognized as a saint in both the Catholic and the Eastern Orthodox Tradition, as is Pope St. Stephen V [VI] (885-91), who also opposed Photius ...as is St. Ignatius of Constantinople, who was the patriarch that Photius unlawfully deposed to usurp his bishopric, which started the whole controversy (Photius attacking the Filioque was merely an attempt to distract from his unlawful appointment at Patriarch in St. Ignatius' place). This period of course set the stage for the Schism, which would take place in 1054, a century later. And, speaking of 1054, the Pope at the time of the actual Schism was SAINT Leo IX (1049-54).
Plus, you must not overlook the fact that NONE of the Patriarchs of Constantinople during a century before OR after the Schism were saints. ...Michael Cerularius was certainty no saint.
Here's the succession, fyi:
Stephanos I (886-893) --younger brother of Emperor Leo VI
Anthony II Kaleas (893-895) --restored communion with Rome.
Nicholas I Mystikos (895-906; 911-925)
Euthymios I (906-911)
Stephanos II (911-928)
Tryphon (928-931)
Theophylaktos (931-956)
Polyeuktos (956-970)
Basil I Skamandrenos (970-974)
Anthony II Studites (974-980)
[Throne Vacant (980-984)]
Nicholas B Chrysoberges (984-995)
Sissinios II (995-998?)
Sergios II Manuelites (998-1019)
Eustathios (1019-l025)
Alexios Studites (1025-1043)
Michael I Cerularios (1043-1057) --schismatic anti-Latin.
Constantine III Leichudes (1057-1064)
John VIII Xiphilinos (1064-1075)
Cosmas I Hierosolymites (1075-1081)
Eustratios Garidas (1081-l084)
Nicholas III Kyrdiniates (1084-1111)
John IX Agapetos (1111-1134)
Leo Styppes (1034-1143)
Michael II Kurkouas (1143-1146)
Kosmas II Attikos (1146-1147)
Nicholas IV Muzalon (1147-1151)
Theodotos II (1151-1153)
Neophytos 1 (1153)
Constantine IV Chliarinos (1154-1156)
Luke Chrysoberges (1156-1169)
Michael III (1169-1177)
Chariton (1177-1178)
Theodosios 1 (1178-1183)
Basil II Kamateros (1183-1187)
Niketas II (l187-1190)
Leontios (1190-1191)
Dositheos (Theodosios?) (1191-1192) ---offered unconditional absolution to any Greek killing a Wester Crusader.
Indeed, the last two patriarchs of Constantinople to be recognized as saints by the Eastern Orthodox Church were Ignatius (846-858; 867-878), who was deposed by Photus and then reinstated by Rome, and Photius himself (858-867; 878-886), who is not recognized as a saint by the West. After this, there is a great shortage of "saintliness" in the see of Constantinople. So, you would do well to look to your own house before criticizing ours. The Pope at the time of the Schism was a saint, the Patriarch of Constantinople was not.
There's still no proof that this authority and reputation couldn't expire, nor that Rome couldn't fall into heresy.
The proof comes from Jesus Christ and from the consistent testimony of the fathers (INCLUDING the Eastern fathers) who associated the promise of Matt 16:18-19 with the See of Rome. Also, if Rome is in heresy, by what authority do you declare it to be so? It's a fair question.
God's Peace,
NewMan