John 16:2?
And John 9:22, John 12:42.
rfgdxm has the synagogue verses.
I am not a historian, so anyone who actually knows, feel free to correct me. But I seem to recall reading somewhere that in Ye Olde Days it was common practice for historical writers to put speeches in the mouths of the historic figures they were writing about, and that such speeches were not intended to be taken as word-for-word quotations, but as a summary or an amalgam of what that person might have said, or device used by the writer to display that person’s thoughts, beliefs, and character. It wasn’t a matter of forgery or deception; nobody expected a literal transcription of the person’s actual words.
On the other hand, I’ve also read that, because books were less readily available and there was less opportunity to write things down, people were more prone to memorization and had better memories. So it’s not inconceivable that one of Jesus’s close associates (John?) might have been able to remember at least the gist of some of his longer or more private sayings.
The stuff that is more likely to come from oral tradition is that which is bite sized, memorable and formulaic in some way.
It’s easy, for instance, to remember a parable. Most people can tell the parable of the Good Samaritan without looking it up. They might not get it word-for-word the same but they’ll get the story pretty close and they’ll retain the point of the story.
Another formula for oral transmission is repetition, the use of the same phrasing over and over again. The Sermon on the Mount shows this characteristic in the Beatitudes (with its repetition of “Blessed are the…”) as well as the “You have heard…but I say…” formulation.
The rest of the Sermon also contains easily remembered little nuggets rather than the long-winded discourses in John.
This doesn’t even mean that the Sermon on the Mount is a literal transcript of a single sermon but could very well be a compilation of memorable lines and quotations from numerous sermons- a sort of “highlight reel” if you will. It’s also not out of the question (in fact it’s more likely than not) that a peripatetic preacher going from town to town would give more or less the same sermon everywhere he went and that those who followed him closely would get it pretty well drilled into their heads.
Some of the anecdotes in the gospels also share the quality of being short and snappy, easy to remember with a bit a “punchline.” In fact the parables and anecdotal pericopes in Mark and Q are memorable for the same reason that jokes are memorable. They have pretty much the same sort of construction, short little stories with a memorable tagline.
The discourse in John do not show any of the characteristics of oral transmission. They are long and complex, they are not formulaic or memorable and they are distinctly different in tone and style from the synoptics.
If someone had actually transcribed some live speeches on paper then no Christian ever wrote about it or seemed to be aware of it before John’s Gospel and there are also the elements which I mentioned earlier in this thread that mitigate against apostolic authorship (albeit with some possibility of embedded fragments of genuine memory but those fragments are buried under fictional aspects).
That’s interesting. I hadn’t heard that before, but I have been told that Plato did this “for” Socrates.
The "beloved disciple’ was indeed- John. Of that there is very little doubt. John moved later to Ephesus, where he had a circle of his own disciples- and where he seems to have reached a long life- long enough to have been involved in the origins of the Gospel of John. My guess (and this is the theory also backed by the “Oxford Companion to the Bible”) is that the Gospel of John was written by the disciples of John at Ephesus. It would seem likely the first draft was John’s deathbed rememberances. The book was later edited and likely material added by his disciples. If John was around 90, this also explains a few inconsistancies. Having John narrate it, but others take his dictation and edit it- with later notes- explains nigh all inconsistancies.
It also appears that all 4 Gospels had as part of their source a small amount of the actual sayings of Jesus- which were likely written down while He was still alive. This is the “Q” (for Quelle= source" hypothesis. Whether or not the original Q Hypothesis is correct, or if later versions and combinations are more correct, we don’t know- but few argue there was some written record of the sayings of Jesus that was more or less contemporary.
There is no evidence whatsoever that Mary Magdalene was directly involved in any writing, although she certainly support the “movement” and was close to “the Man”.
What is your evidence that John was the Beloved Disciple?
Yep. Considering that at the time of his ministry some following Jesus may have seen him as Very Important, hardly inconceivable that someone would transcribe his sermons onto paper. If not immediately, perhaps a few loyal followers with very good memories later in the day would get together and compare notes they had to come up with the best possible reconstruction. However, if this was the case whoever wrote/edited the 3 synoptic gospels apparently were unaware, or had no access to, these transcriptions. And it is generally thought the synoptics predate John. John doesn’t look anything like a gospel that is characteristic of being based on oral transmission. If John isn’t a pious fiction, whoever wrote it had access to transcriptions the other early Christian writers didn’t.
Do you claim otherwise? 
I have seriously studied ancient Greek philosophy, as in getting a degree in college about that. With an emphasis on Socrates/Plato. The big difference is that Plato never thought that Socrates was divinely inspired and had to get thing word for word straight or such. Plato’s “Apology” (also known as the Defense of Socrates) is such an example. Getting the general gist of how the trial of Socrates for corrupting the youth of Athens, and that he also allegedly believed in false gods and was ALSO an atheist was enough. Just pointing out the absurdity of an alleged atheist believing in false gods was sufficient. And that Plato records that a greater number of citizens of Athens voted for the death penalty for Socrates than who voted to find him guilty of the charges is telling. Obviously Socrates must have said something Plato never recorded that that would motivate people who thought he was innocent to condemn him is telling. (Most likely that Socrates proposed a sentence of a small fine, rather than a large fine others had agreed to pay on his behalf is why.) However, that Plato considered Socrates a mere mortal he respected explains a lot. A summary is OK if the words aren’t thought to be divinely inspired.
Or, put another way, what is your evidence the Beloved Disciple was not John? If John was the Beloved Disciple, why would John not say so?
I’m claiming that the identity of said disciple is completely unknown. There is no more reason within the text to think it’s John than to think it’s Andrew or Peter or any other disciple. I’m not saying it can’t be John, but your staement that "The “beloved disciple’ was indeed- John. Of that there is very little doubt” is not exactly the consensus of scholarship.
There is also nothing in the text which says the Beloved Disciple is the author of the Gospel.
Well, the beloved disciple can’t be Peter, because he’s mentioned with Peter at one point, and he can’t be Judas, for obvious reasons, and he’s probably not Andrew, Philip, Nathaniel, Thomas, or the other Judas, because they’re all identified in the text, seperately.
And, there is something in the text which says the beloved disciple is the author of the Gospel, btw. John 21:24, which says,
John 21 is a later interpolation, not part of the original text.
Just because a disciple is identified by name doesn’t mean it can’t be the beloved disciple and John isn’t the only name not mentioned.
I know John 21 is a later interpolation. And you’re right, because a disciple is identified by name doesn’t mean he can’t be the beloved disciple. However, you had said,
And, I just was saying that, within the text, TBD can’t be Peter, because at various points, Peter is mentioned as interacting with TBD.
Good point. You got me.
The way I see it, I have to take what victories I can get. 
Do you know why, traditionally, John the Apostle was viewed as TBD, and the gospel author?
Third hand Patristic tradition- Eusebius quoting Irenaeus citing Papias.
As sort of a related question, do you know where the traditions that the other three gospels were written by the apostle Matthew, Peter’s follower Mark, and Luke the physician come from?