The apostolic fathers

Catholic apologists appeal to the apostolic fathers. The inference is that since the apostolic fathers were disciples of the apostles, their theology replicates the theology of the apostles. I'm not a patrologist, so I could be mistaken in what I'm about to say, but most Catholic apologists have no professional expertise in patristics, either. I'll make some general observations before commenting on specific figures:

1. The "apostolic fathers" are an academic construct. The list is somewhat arbitrary. 

2. There were some reliable historical traditions floating around the early church. Conversely, there were legends floating around the early church. So sifting is required. 

3. There's a big difference between an apostolic father attributing his information to an apostle and a Catholic apologist attributing his information to an apostle just because he was (allegedly) a disciple of one or more apostles. 

4. You can know someone but have little knowledge or recollection of what they believe. How many of us remember what the pastor said in his sermon last Sunday? Or the sermon a month ago? Or the sermon a year ago? How many of you remember what the pastor said when you were a teenager?

Take public school, K-12. In elementary school, I had the same teacher for a full school year. In junior high and high school, I had particular teachers for particular courses. That still meant listening the same teacher 5 days a week for a semester. And sometimes I had the same teacher for multiple courses.

Despite that extensive and intensive exposure, I only remember a few things my teachers said over the years. Most of what they said is forgotten. 

There are degrees of familiarity, from a passing acquaintance to saturation exposure. Likewise, comprehension and recollection depends on the age at which we knew someone. 

5. We need to distinguish:

i) An eyewitness of Jesus

ii) An eyewitness of an eyewitness of Jesus

iii) An eyewitness of an eyewitness of an eyewitness of Jesus

The evidentiary chain-of-custody thins out. 

I. Clement of Rome

According to Irenaeus: 

He had seen the blessed apostles, and had been conversant with them.

Given his presumed DOB (c. 35) and his location in the Roman capital, it's plausible that Clement was an eyewitness to one or more apostles. But does that mean, for instance, that his appeal to the Phoenix reflects apostolic tradition? 

II. Ignatius of Antioch

Although Catholic apologists routinely make the unsourced claim he was a disciple of John, I haven't seen the documentation. What's the earliest Christian writing that makes that claim? 

III. Papias

1. Irenaeus says:

These things are borne witness to in writing by Papias, the hearer of John, and a companion of Polycarp. 

Eusebius says:

Irenæus makes mention of these as the only works written by him, in the following words: “These things are attested by Papias, an ancient man who was a hearer of John and a companion of Polycarp, in his fourth book. For five books have been written by him.” These are the words of Irenæus.

But Papias himself in the preface to his discourses by no means declares that he was himself a hearer and eyewitness of the holy apostles, but he shows by the words which he uses that he received the doctrines of the faith from those who were their friends.

So Eusebius says Irenaeus claims more for Papias than Papias claims for himself. Perhaps Eusebius is right. Or it may be open to interpretation. Or perhaps Irenaeus draws on personal knowledge of Papias. 

2. The DOB for Papias is generally estimated to be around 70 AD. And Papias would have to be old enough to understand and remember what he heard. So that narrows the window of opportunity to the 80s at the earliest. But that might still give Papias time to be an eyewitness to John, if John died in the 90s.  

3. Eusebius goes on to say:   

That Philip the apostle dwelt at Hierapolis with his daughters has been already stated. But it must be noted here that Papias, their contemporary, says that he heard a wonderful tale from the daughters of Philip. 

If true, Philip was well-connected. Knew several apostles. Probably knew other eyewitnesses to Jesus. May have been an eyewitness to Jesus in his own right. And his daughters became custodians of family lore. Nevertheless, knowing the daughters of Philip is a step removed from being an eyewitness of one or more apostles. At best, that's knowing someone who knew someone who knew Jesus. 

IV. Polycarp

According to Irenaeus:

Polycarp also was not only instructed by apostles, and conversed with many who had seen Christ, but was also, by apostles in Asia.

From what I've read, the estimated DOB for Polycarp is around 69-70. And he'd have to be old enough to understand and remember what he heard. How many apostles were still alive by the 80s? Were there any surviving candidates other than John? 

According to Tertullian:

For this is the manner in which the apostolic churches transmit their registers: as the church of Smyrna, which records that Polycarp was placed therein by John. 

Tertullian is referring to a local tradition. That could be true, although there's the danger of a self-serving legend, inasmuch as that's a prestigious claim for a church to make about itself. 

V. The Didache

Hard to date. Raymond Brown think its polity is pre-Ignatian–which is self-defeating for a Catholic apologist.

VI. The Epistle of Barnabas 

2C. Unknown author. Allegorical. Jewish influence. 

VII. The Shepherd of Hermas

Mid-2C by former slave and visionary.