I think you're simultaneously over-stating your position and making mine broader than it is.
This discussion began with an utterly stupid claim that the NT being written in Greek precludes apostolic authorship. I think most are satisfied that this can just be ignored.
It quickly spiraled off into the usual bad arguments about how we can't know anything because of an unfathomable ~100 year gap between writing and attestation of authorship, which is an arbitrary standard that literally no work of antiquity can meet. The last time this discussion happened I noted that, for example, Herodotus while alluded to and referenced in other works is not explicitly identified as the author of his Histories until Roman Imperial era Greek writers such as Plutarch. And if we take this as an analogy, we must include the allusions and references of the NT itself back to the gospels as seriously as Sophocles or Euripides allusions to Herodotus. In the end, the facts on the ground remain that we have no other actual historical evidence, not one, of the gospels being attributed to anyone else.
Then we moved onto the related question of order, which touches on the question of authorship.
Here my claims are simple:
- The gospels namesake are the source for their attributed gospel. Matthew is the source of Matthew, much as Paul is the source for all Pauline writing. But what this means can have a huge range. Using the Pauline literature as an example we have everything from a letter written by Paul alone through an amanuensis (e.g., Romans and Tertius or likely Ephesians and Tychicus) to a work explicitly co-authored by a probable amanuensis (e.g., 1 Cor and Sosthenes or 2 Cor and Timothy) yet seemingly still close to dictation at least in some points (1 Cor 1:16), to multiple authors (e.g., 1 and 2 Thess written by Paul, Silvanus, and Timothy) to possibly a sermon written down and possibly edited by a third party (Hebrews, perhaps by Luke). Yet all are "Paul" and none are "Paul" depending on how specific you are being. Just like Baruch is Jeremiah, even though it isn't.
- We don't know the order of the four Greek gospels we have. There are a couple of varying theories in the fathers, usually pertaining to the swapping of Luke and Mark in second place, but the fathers are clear on Matthew writing first, but not clear or silent that the Greek gospel they use was published before Mark's.
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If the early church is only claiming that matthew originally wrote first in hebrew why must we pretend to be confident he's the author or primary source of the greek?
this is the interesting question - to rephrase it, the question would be multifold:
- to what extent is the gospel of Matthew we have written by Matthew
- to what extent is does it draw on the unknown / lost Aramaic gospel written by Matthew
- when was it published and by whom
there's a huge range of "reasonable" arguments associated with this, which is why the Synoptic problem remains unsolved.