Indeed there are as noted earlier no shortage of ‘source criticism’ theories with respect to Book Four. Bousset, Loofs, Quispell and many others have for instance argued that the section 4.36 – 41 derives from the writings of Theophilus of Antioch. Yet the CEF (4.26 – 31) certainly belong with Adversus Haereses 3.3.1 – 3.4.1. Indeed, as noted above, it was Hill who first notes that:
Behr merely repeats Hill’s original suggestion but Hartog adds the important observation that Irenaeus used the phrases 'as I have shown' (4.26.2) and 'as I have pointed out' (4.32.1) to point the reader back to the discussions in Book Three concerning the presbyters and apostles (see also the back—referencing in 4.32.2).[16]the string of presbyterial references in book 4 with which we are concerned occurs where Irenaeus is stressing the importance of obeying 'the presbyters who are in the church … who ... possess the succession from the apostles” who "have received the certain gift of truth" (4.26.2). Very probably he already expected his reader to make the connection with the men he had described in this way, and named, back in 3.3-4, “have in mind men he had described in this way, and named, back in 3.3, that is, Linus, Anacletus, and Clement in Rome, and Polycarp in Smyrna.”[15]
The point here is that Hill ultimately uses the connection between the two sections of text to further his thesis that Polycarp should be identified as the elder. Nevertheless a careful consideration of the context for the section at the beginning of Book Three will ultimately make a better case for John – especially considering the fact that Irenaeus is drawing from Papias' elder and his statement regarding the relationship between the gospel of Mark and the logia of Matthew. Irenaeus expands the reference to make it seem that Matthew’s gospel was written at the time ‘Peter and Paul preaching in Rome.’[17] Yet as Watson notes “Irenaeus constructs a fourfold gospel out of passages in Papias which intend no such thing.”[18]
The underlying question then necessarily comes down to whether we should understand the CEF to be connected to the beginning of Book Three by way of John or Polycarp? The fact that the entire discussion of ‘apostolic tradition’ that follows is grounded in a statement of Papias’s ‘elder’ should settle the issue once and for all. In other words, Irenaeus uses Papias, the hearer of John the elder, disciple of the Lord as a witness to the existence of a set of apostolic gospels. Included in this set is the gospel attributed to John. But Papias is unlike to have used anything resembling a narrative gospel. This
15. C E Hill p. 23
16. J Behr Irenaeus of Lyons Identifying Christianity (Oxford University Press 2013) p. 62; P Hartog Polycarp's Epistle to the Philippians and the Martyrdom of Polycarp (Oxford University 2013) p. 19
17. Adversus Haereses 3.3.1.
18. F Watson Gospel Writing: A Canonical Perspective (Grand Rapids: Eerdmans, 2013) p. 258