Eusebius borrows Hegesippus to determine the list of bishops of Jerusalem from the destruction of the temple until 144 CE. He has - strangely - very little information about what happens next. There is the important statement in HE 4.5:
The chronology of the bishops of Jerusalem I have nowhere found preserved in writing; for tradition says that they were all short lived. But I have learned this much from writings, that until the siege of the Jews, which took place under Adrian, there were fifteen bishops in succession there, all of whom are said to have been of Hebrew descent, and to have received the knowledge of Christ in purity, so that they were approved by those who were able to judge of such matters, and were deemed worthy of the episcopate. For their whole church consisted then of believing Hebrews who continued from the days of the apostles until the siege which took place at this time; in which siege the Jews, having again rebelled against the Romans, were conquered after severe battles.
3. But since the bishops of the circumcision ceased at this time, it is proper to give here a list of their names from the beginning. The first, then, was James, the so-called brother of the Lord; the second, Symeon; the third, Justus; the fourth, Zacchæus; the fifth, Tobias; the sixth, Benjamin; the seventh, John; the eighth, Matthias; the ninth, Philip; the tenth, Seneca; the eleventh, Justus; the twelfth, Levi; the thirteenth, Ephres; the fourteenth, Joseph; and finally, the fifteenth, Judas. These are the bishops of Jerusalem that lived between the age of the apostles and the time referred to, all of them belonging to the circumcision.
The emboldened words clearly apply to the Church starting with Hadrian's reign. He uses Hegesippus's list - slightly reluctantly. But the words clearly also apply to the period immediately following the conquest by Hadrian. At the end of his discussion of Hadrian's reconquest he simply says:
And as the church there was now composed of Gentiles, the first one to assume the government of it after the bishops of the circumcision was Marcus. [HE 4.7]
There is nothing further said about this Marcus. Instead we hear about a bishop living two decades later:
At this time Narcissus was the bishop of the church at Jerusalem, and he is celebrated by many to this day. He was the fifteenth in succession from the siege of the Jews under Adrian. We have shown that from that time first the church in Jerusalem was composed of Gentiles, after those of the circumcision, and that Marcus was the first Gentile bishop that presided over them. After him the succession in the episcopate was: first Cassianus; after him Publius; then Maximus; following them Julian; then Gaius; after him Symmachus and another Gaius, and again another Julian; after these Capito and Valens and Dolichianus; and after all of them Narcissus, the thirtieth in regular succession from the apostles.[HE 4.12]
We have to go back and revisit the original statement earlier in the chapter (HE 4.5) that Eusebius could find no information about the succession of bishops in Jerusalem. It is an odd statement given that now he produces a list. The obvious question now is - where did this list come from? Probably Eusebius's own imagination.
It is safe to say that Narcissus is the first bishop of the 'Gentile Church' that Eusebius knows anything about. In the same way Demtrius is the first bishop of the 'official' Alexandrian Church that has been preserved. Not surprisingly the two are mentioned together the next time Narcissus is mentioned:
In the tenth year of the reign of Commodus, Victor succeeded Eleutherus, the latter having held the episcopate for thirteen years. In the same year, after Julian had completed his tenth year, Demetrius received the charge of the parishes at Alexandria. At this time the above-mentioned Serapion, the eighth from the apostles, was still well known as bishop of the church at Antioch. Theophilus presided at Cæsarea in Palestine; and Narcissus, whom we have mentioned before, still had charge of the church at Jerusalem. Bacchylus at the same time was bishop of Corinth in Greece, and Polycrates of the parish of Ephesus. And besides these a multitude of others, as is likely, were then prominent. But we have given the names of those alone, the soundness of whose faith has come down to us in writing. [HE 4.22]
A little later a synod in Rome is mentioned when Narcissus and Demetrius met with Victor:
There is still extant a writing of those who were then assembled in Palestine, over whom Theophilus, bishop of Cæsarea, and Narcissus, bishop of Jerusalem, presided. [HE 4.23]
He says again that Narcissus agreed with all the other bishops. But what evidence is there really that Narcissus ever set foot in Jerusalem? None. He may have been at this synod over the Easter controversy. But there is simply no reason to think that he ever held any position of prominence in Jerusalem.
More unusual still is the fact that both he and Alexander live to an extraordinary old age. Narcissus is alleged to have lived past 116. Alexander dies in 251 CE during the persecution of Decius. What proof is there that they weren't third century bishops projected back retroactively into the second because, as Eusebius confesses, he has no information about any actual Catholic bishops of Jerusalem?
Note that Alexander is suddenly introduced into the sixth chapter:
Severus, having held the government for eighteen years, was succeeded by his son, Antoninus. Among those who had endured courageously the persecution of that time, and had been preserved by the Providence of God through the conflicts of confession, was Alexander, of whom we have spoken already as bishop of the church in Jerusalem. On account of his pre-eminence in the confession of Christ he was thought worthy of that bishopric, while Narcissus, his predecessor, was still living.
Eusebius hasn't mentioned Alexander previously. We are now well into the third century. This Narcissus for whom we have no actual proof he was ever a bishop in Jerusalem. Just this odd section which introduces Alexanders almost forty year reign in Jerusalem:
The citizens of that parish (Jerusalem) mention many other miracles of Narcissus, on the tradition of the brethren who succeeded him; among which they relate the following wonder as performed by him. They say that the oil once failed while the deacons were watching through the night at the great paschal vigil. Thereupon the whole multitude being dismayed, Narcissus directed those who attended to the lights, to draw water and bring it to him. This being immediately done he prayed over the water, and with firm faith in the Lord, commanded them to pour it into the lamps. And when they had done so, contrary to all expectation by a wonderful and divine power, the nature of the water was changed into that of oil. A small portion of it has been preserved even to our day by many of the brethren there as a memento of the wonder. They tell many other things worthy to be noted of the life of this man, among which is this. Certain base men being unable to endure the strength and firmness of his life, and fearing punishment for the many evil deeds of which they were conscious, sought by plotting to anticipate him, and circulated a terrible slander against him. And to persuade those who heard of it, they confirmed their accusations with oaths: one invoked upon himself destruction by fire; another the wasting of his body by a foul disease; the third the loss of his eyes. But though they swore in this manner, they could not affect the mind of the believers; because the continence and virtuous life of Narcissus were well known to all.
But he could not in any wise endure the wickedness of these men; and as he had followed a philosophic life for a long time, he fled from the whole body of the Church, and hid himself in desert and secret places, and remained there many years. But the great eye of judgment was not unmoved by these things, but soon looked down upon these impious men, and brought on them the curses with which they had bound themselves. The residence of the first, from nothing but a little spark falling upon it, was entirely consumed by night, and he perished with all his family. The second was speedily covered with the disease which he had imprecated upon himself, from the sole of his feet to his head. But the third, perceiving what had happened to the others, and fearing the inevitable judgment of God, the ruler of all, confessed publicly what they had plotted together. And in his repentance he became so wasted by his great lamentations, and continued weeping to such an extent, that both his eyes were destroyed. Such were the punishments which these men received for their falsehood.
If you really look carefully at this section, Eusebius is openly admitting that he is drawing from word of mouth of Christian laypeople living in Jerusalem almost a century after the dates for this alleged bishop. What is the slander mentioned here by Eusebius? Could it be that it was that he never existed?
The point of course is that we have yet to land upon anything approaching actual history of a Catholic bishop of Jerusalem. Ambrose could well have been the bishop in this period. There is no history to speak of. Eusebius goes on to deal with the non-existence of his Narcissus by writing:
Narcissus having departed, and no one knowing where he was, those presiding over the neighboring churches thought it best to ordain another bishop. His name was Dius. He presided but a short time, and Germanio succeeded him. He was followed by Gordius, in whose time Narcissus appeared again, as if raised from the dead. And immediately the brethren besought him to take the episcopate, as all admired him the more on account of his retirement and philosophy, and especially because of the punishment with which God had avenged him.
But as on account of his great age Narcissus was no longer able to perform his official duties, the Providence of God called to the office with him, by a revelation given him in a night vision, the above-mentioned Alexander, who was then bishop of another parish. Thereupon, as by Divine direction, he journeyed from the land of Cappadocia, where he first held the episcopate, to Jerusalem, in consequence of a vow and for the sake of information in regard to its places. They received him there with great cordiality, and would not permit him to return, because of another revelation seen by them at night, which uttered the clearest message to the most zealous among them. For it made known that if they would go outside the gates, they would receive the bishop foreordained for them by God. And having done this, with the unanimous consent of the bishops of the neighboring churches, they constrained him to remain.
Alexander, himself, in private letters to the Antinoites, which are still preserved among us, mentions the joint episcopate of Narcissus and himself, writing in these words at the end of the epistle:
Narcissus salutes you, who held the episcopate here before me, and is now associated with me in prayers, being one hundred and sixteen years of age; and he exhorts you, as I do, to be of one mind.
These things took place in this manner. But, on the death of Serapion, Asclepiades, who had been himself distinguished among the confessors during the persecution, succeeded to the episcopate of the church at Antioch. Alexander alludes to his appointment, writing thus to the church at Antioch:
Alexander, a servant and prisoner of Jesus Christ, to the blessed church of Antioch, greeting in the Lord. The Lord has made my bonds during the time of my imprisonment light and easy, since I learned that, by the Divine Providence, Asclepiades, who in regard to the true faith is eminently qualified, has undertaken the bishopric of your holy church at Antioch.
He indicates that he sent this epistle by Clement, writing toward its close as follows:
My honored brethren, I have sent this letter to you by Clement, the blessed presbyter, a man virtuous and approved, whom you yourselves also know and will recognize. Being here, in the providence and oversight of the Master, he has strengthened and built up the Church of the Lord.
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If you really look at ALL the information which emerges from Eusebius we come up with:
1. Eusebius acknowledges he has no information about the existence of Catholic bishops of Jerusalem in the second century.
2. He makes up a list of names with no information about any of the bishops he makes up.
3. The first person he has anything to say about is Narcissus but he is little more than a phantom. He partook in the synod in Rome about Passover at the end of the second century and that is about it.
4. The next person he has anything to say about is Alexander in the first generation of the third century.
The fact that Alexander comes from another bishopric (which is odd in itself) is eclipsed by the fact that the history of the Catholic Jerusalem Church only begins in 211 CE. Alexander establishes a library of books - not just Christian books - which survived until Eusebius's time:
There flourished many learned men in the Church at that time, whose letters to each other have been preserved and are easily accessible. They have been kept until our time in the library at Ælia, which was established by Alexander, who at that time presided over that church. We have been able to gather from that library material for our present work.
“Finally, from so little sleeping and so much reading, his brain dried up and he went completely out of his mind.”
― Miguel de Cervantes Saavedra, Don Quixote