Part 4: The Argument for a Single John
Some scholars argue that Papias spoke of the same John twice, thus removing any possibility that a second John, the Elder, was associated with the Johannine writings.
To review, here are Papias’s words:
And if by chance someone who had been a follower of the elders should come my way, I inquired about the words of the elders—what Andrew or Peter said, or Philip, or Thomas or James, or John or Matthew or any other of the Lord’s disciples, and whatever Aristion and the elder John, the Lord’s disciples, were saying.Fragment 3.4 = Eusebius, Hist. eccl. 3.39.4 [Holmes]
The view that Papias spoke of the same John twice is generally (if not exclusively) defended by those who hold to the view that the early Christians identified John the son of Zebedee with the Evangelist  (though as noted in Part 3, some holding the traditional view consider this interpretation of Papias to be indefensible).
The argument usually goes that when Papias spoke of the second John as “the Elder,” he was employing an anophric article, or article that refers back to someone or something previously mentioned in the context, thus identifying him as the aforementioned John.
This idea was first suggested by the German scholar Guericke in 1831. This is perhaps somewhat ironic, since those holding this view often point out that Eusebius was the first extant writer to differentiate Papias’s two Johns.
This reading of Papias as identifying the two Johns rests in turn upon a second questionable interpretation of Papias’s words, again first suggested by Guericke, namely that Papias was identifying the apostles whom Papias names as the very “elders” concerning whose words he made inquiries, rather than (as is generally held) as those who were reporting the words of the apostles.
I inquired about the words of the elders—what Andrew or Peter said, or Philip, or Thomas or James, or John or Matthew or any other of the Lord’s disciples, and whatever Aristion and the elder John, the Lord’s disciples, were saying.
Thus, D. A. Carson claimed that by speaking of the second John as “the Elder,” Papias was referring to him as “the (aforementioned) elder [i.e. apostle],” that is, as John the Apostle.
In my book I provide examples from ancient Greek to show why Papias was almost certainly differentiating the apostles and elders (as Irenaeus and Eusebius, two of his early readers, did). While the discussion is too detailed to enter into here, in the final part of this series attention will be drawn to other evidence that seems to rule out the possibility that Papias identified the two Johns.
 E.g. John R. W. Stott, The Letters of John: An Introduction and Commentary (TNTC; Downers Grove, Ill.: IVP, 1988) 38–43; Smalley, John, Evangelist and Interpreter, 81; Andreas J. Köstenberger and Stephen O. Stout, “ ‘The Disciple Jesus Loved’: Witness, Author, Apostle—A Response to Richard Bauckham’s Jesus and the Eyewitnesses,” BBR 18 (2008) 219; J. Ramsey Michaels, The Gospel of John (NICNT; Grand Rapids: Eerdmans, 2010); 10–12; Monte A. Shanks, Papias and the New Testament (Eugene: Wipf and Stock, 2013) 139–143 19–21.
 Heinrich Ernst Ferdinand Guericke, Die Hypothese von dem Presbyter Johannes als Verfasser der Offenbarung (Halle, 1831), 6–8.
 Leon Morris, Studies in the Fourth Gospel (Grand Rapids: Eerdmans, 1969), 279; Donald Guthrie, New Testament Introduction (4th rev. ed.; Downers Grove, Ill.: IVP, 1996), 280; Michaels, The Gospel of John, 12; Shanks, Papias, 19
 D. A. Carson, The Gospel According to John (PNTC; Grand Rapids: Eerdmans, 1991) 70.
A summary of my book’s discussion on this subject can be found here.