This is a chapter from Wayne A. Grudem’s Systematic Theology. An Introduction to Biblical Doctrine.
Grudem, editor of the ESV Study Bible, concludes that the New Testament canon is closed and correct. He does not give the criteria for canonicity in an enumerated list. However, he seems to include divine authorship, apostolic authorship, or apostolic desire for the writing to be preserved. On this basis he does not seem to require that the book of Hebrews be associated with an apostle because its divine authorship is apparent to a reader (and it likey had the endorsement of the apostles as well).
The development of the New Testament canon begins with the writings of the apostles.
[T]he New Testament consists of the writings of the apostles.
The apostles, then, have authority to write words that are God’s own words, equal in truth status and authority to the words of the Old Testament Scriptures. They do this to record, interpret, and apply to the lives of believers the great truths about the life, death, and resurrection of Christ.
Because the apostles, by virtue of their apostolic office, had authority to write words of Scripture, the authentic written teachings of the apostles were accepted by the early church as part of the canon of Scripture.
This brings us to the heart of the question of canonicity. For a book to belong in the canon, it is absolutely necessary that the book have divine authorship. If the words of the book are God’s words (through human authors), and if the early church, under the direction of the apostles, preserved the book as part of Scripture, then the book belongs in the canon.
A few New Testament books (Mark, Luke, Acts, Hebrews, and Jude) were not written by apostles but by others closely associated with them and apparently authorized by them…
(43 min read; 10,611 words)
The Canon of Scripture (Wayne Grudem) | Free online Bible classes | BiblicalTraining.org. (registration required)