This is a subsidiary post of Apostolicity and the New Testament.
R. L. Harris (1911-2008) says:
“[T]he canonicity of a book of the Bible depends upon its authorship…”
He goes on to say:
“It is freely recognized that other views of the principle of canonicity have been held and that there are some problems connected with our thesis. The chief problem is that we cannot name with certainty all the authors of the Old Testament books and that the apostolic authorship of some of the New Testament books may be questioned… the authorship of the major parts of both Testaments is clear… and for the remaining portions where the authorship is less certain there is not positive evidence against, indeed, there is some evidence for, the authorship by prophets and apostles.” (Pg. 284)
We also find this on page 278 of that book (emphasis added):
It may be true that apostolicity was not so important an item by A.D. 400 when the consensus of the church was rather well established and when the information about the early authorities had somewhat faded. But in the earlier times, when the books were new and decisions had to be made, the evidence shows that apostolicity was the main criterion in the church’s decisions.
[F. F.] Bruce [1910-1990] himself admits, “In the early church as a whole the predominant criterion appears to have been apostolic authority, if not apostolic authorship.” [B. F.] Westcott [1825-1903] comes to the same conclusion, “Step by step the books which were stamped with Apostolic authority were separated from the mass of other works which contained the traditions or opinions of less authoritative teachers.”