Did this Pythagorean concept influence Tatian? Possibly. Just as Justin used the Platonic/Pythagorean concept of memoirs to the three Christian Gospels he had harmonized, Tatian might have selected the Platonic/Pythagorean term diatessaron to identify his new fitting together of the four sacred books "of the barbarian philosophy.[A History of the Synoptic Problem p. 41]I find this conception particularly intriguing because Clement in the Letter to Theodore identifies certain υπομνήματα associated with Mark and Peter which apparently harmonize together to make the 'secret gospel' associated with the evangelist.
I can't for the life of me though understand what Dungan means by a 'Platonic/Pythagorean' ἀπομνημονεύματα unless he means Xenophon's ἀπομνημονεύματα of things said by Socrates. It is interesting to note that Robbins in his preface to Xenophon's Memorabilia note that ἀπομνημονεύματα and υπομνήματα are viritually indistinguishable from one another as classical terminology:
ἀπομνημονεύματα from ἀπομνημονεύείν, things related from memory. It is not, however, restricted to that which fell under the author's own observation, but includes also particulars which he received from other witnesses. The Latin term Memorabilia, things memorable or worthy to be remembered, although it does not correspond precisely t: the Greek word, is a veiy good designation of the contents of these Books, and as such is very commonly used in English. We not unfrequently affix the termination ana to proper names to designate much the same thing; as Johnsoniana, the memorable sayings of Johnson. Aulus Gellius (NH XIV. 3.) called these books: Libras quos dictorum atque factorum Socratis commentarios composuit Xenophon. And some modern editors, as Kuhner, retain Commcntarii as the most fitting title of the work. Cicero de Nat. Deor. 1. 12, refers to Xenophon in iis, quae a Socrate dicta retulit
Instead of ἀπομνημονεύματα, two Mss. Victorii, have υπομνήματα; and one, Parisiensis F. has ὲκ τῶν τοῦ Ξενοφῶντος υπομνήμονεύματων, ie memoranda, things written written down in order not to forget them. This name does not seem to apply so well to the contents of a work which consists not merely of hasty sketches, but in many parts exhibits signs of elaboration; still the two words ἀπομνημονεύματα and υπομνήματα may have been used, even in ancient times, as nearly synonymous. Thus υπομνήματα seems to be used like ἀπομνημονεύματα in Polybius 1. 1. 1., 6. 32. 4 et al.[Xenophon Memorabilia, trans. R D C Robbins p. 173]
So we have established that the term Clement uses for Peter and Mark's 'notes' is the same as Justin's 'gospel.' Yet the same terminology is also used in Eusebius's description of the creation of the gospel of Mark:
And so greatly did the splendor of piety illumine the minds of Peter's hearers that they were not satisfied with hearing once only, and were not content with the unwritten teaching of the divine Gospel, but with all sorts of entreaties they besought Mark, a follower of Peter, and the one whose Gospel is extant, that he would leave them a written monument of the doctrine which had been orally communicated to them [καὶ διὰ γραφῆς ὑπόμνημα τῆς διὰ λόγου παραδοθείσης αὐτοῖς καταλείψοι διδασκαλίας]. Nor did they cease until they had prevailed with the man, and had thus become the occasion of the written Gospel which bears the name of Mark.[Eusebius Church History 2.15]
But what of Dungan's claim that this is somehow 'Platonic/Pythagorean'? Is this all a bit of stretch? Or does it just come down to an association or imitation of Socrates (and thus only indirectly 'Platonic')? I don't really know right now. This certainly requires more investigation. But it might begin with the clue Wikipedia provides for us in its entry for hypomnema:
Plato's theory of anamnesis recognized the new status of writing as a device of artificial memory, and he developed the hypomnesic principles for his students to follow in the Academy. The hypomnemata constituted a material memory of things read, heard, or thought, thus offering these as an accumulated treasure for rereading and later meditation. They also formed a raw material for the writing of more systematic treatises in which were given arguments and means by which to struggle against some defect (such as anger, envy, gossip, flattery) or to overcome some difficult circumstance (a mourning, an exile, downfall, disgrace).
Dungan's point seems to be that Justin's use of the terminology suggests not only a connection with Plato but the idea that the gospel that was being used 'openly' in the Church was a rough unfinished composition. Yet if there is a relationship between the 'rough notes' of Justin and the finished 'harmony' of Tatian, doesn't it necessarily presuppose the kind of gospel paradigm that the Letter to Theodore suggests existed between rough υπομνήματα and a later gospel text that was finished, polished or 'perfected' finally in an Alexandria and that the relation between the two texts was that of a 'diatessaron' - i.e. separated by a chasm or interval - owing to the relative completeness of the original composition?
I really can't see it in any other terms.
Scholarship has been too blindly influenced by Irenaeus and his obsession that all the gospels were perfect, all the truths contained in them immaculate. Yet even if we leave Clement's newly discovered letter to the side, what of Justin's use of the term 'ἀπομνημονεύματα' for the text associated with Peter? Is this really 'an immaculate' collection or something imperfect which could be polished and reworked into something sublime ('a diamond in the rough' as they say today). Similarly Eusebius also gets the idea that the gospel Mark wrote for the followers of Peter is a ὑπόμνημα strikes the same chord.
I just don't happen to believe that Clement's explanation seems 'forced' or 'faked' in any way. The publicly circulating gospel texts were by nature less than perfect, and perhaps even for Justin and Tatian the 'finished' text developed from these ἀπομνημονεύματα or υπομνήματα were deliberately kept from public viewing. What I am suggesting now of course is that Justin's use of the terminology necessarily assumes the existence of something 'more perfect' that he isn't mentioning, perhaps because it was meant to be kept secret.