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Fortunately, the RCC and it's "Pope" had nothing to do with it.
The New Testament Canon
First Century:
1. The "heart of the Canon" is often regarded to be Paul's epistles. By the time 2 Peter was written (perhaps 70 AD), they seem to be regarding as normative and referred to as Scriptures (2 Peter 3:15-16). Many theologians - conservative and liberal - give great importance to Paul's works as perhaps the theological framework for that which was later added. So, by 70 AD, we have perhaps half of the NT books in some aspect of a Canon. A bit later, Clement and others also speak of "Paul's letters" in this way, indicating a canonical status.
2. The Synoptic Gospels (written between 45 - 65) also seem to have been quickly and nearly universally seen as canonical. They were "published" together - as a single tome - as early as 115 and were very common. They too are repeatedly spoken of as canonical.
By this point, we have a fairly solid canon of 18 of our 27 NT books. And the RCC had absolutely nothing whatsoever to do with it. In fact, there's zero evidence that it even existed at this time.
Second Century:
Many early writers not only reveal a knowledge of NT books, but refer to them specially - as Scripture. Clement points to Romans, 1 Corinthians, Ephesians and maybe Titus. The Shepherd of Hermas (140) quotes from Romans, 1 & 2 Corinthians, Ephesians, Hebrews, 1 & 2 Peter, Revelation and James. Ignatius (d.117) speaks of "all of Paul's epistles" authoritatively, he frequently uses normative quotes from Matthew, John and Acts as well. Tatian (c 170) writes that all Christians recognize that there are four Gospel books. Irenaeus also mentions that Christians accept only four Gospel books, he too speaks of "all Paul's epistles" and quotes from 1 Peter and 1 John. He speaks of these as a parallel of the Old Testament - having equal authority (ie being normative and canonical). Tertullian (d. 220) quotes authoritatively and normatively from all 4 Gospels, all the Pauline epistles, Acts, 1 Peter, 1 John, Jude and Revelation. All these reveal that much of the NT canon was in place by the end of the Second Century.
At this point, we have 20 of the books in place. And the Catholic Church had absolutely nothing whatsoever to do with it; in fact, there's no evidence it even existed.
Third Century:
At the beginning, we seem to have a rather solid Canon of 20 of the 27 books. They are the Pauline letters (13), the 4 Gospels, Acts, 1 Peter and 1 John. The great majority of the Canon is in place. But a few books - including those eventually being dismissed - were still not embraces with a solid consensus.
Cprian of Carthage (d. 258) says that all Christians accept 21 books: Paul's 13 (in all these lists, nearly always mentioned first), the 4 Gospels, Acts, First Peter, First John and revelation. They are referenced as normative and canonical.
Origin (d. 255) also reports on the status of the books as regarded by Christians. He places them into two groups: Homologoumena (all embrace) as 21 books - the same as Cyprian's list. Antilegomena (challenged) as 10 - they are Hebrews, 2 Peter, 2 & 3 John, James, Jude (all which would eventually be accepted) and also Barnabas, Hermas, Didache and the Gospel of the Hebrews (all of which would soon be rejected).
The NT Canon is now solid for 21 of the 27 books. And the Catholic Church had absolutely nothing whatsoever to do with it. Nothing at all.
Fourth Century:
By this time, there is clearly an embrace of 21 books - and has been for a long time. the only "debate" centers around 5- 6 that eventually were embraced, and a handfull soon to be dropped. The core of 21 is now very solid and unquestioned.
Eusebius (d. 340) wrote that Christians all accept 21 books. He lists 4 as ones accepted by most but not by all: James, Jude, 2 Peter, 2 & 3 John (all eventually embraced). And he lists some as "spurious" - Acts of Paul, Shepherd of Hermas, Apocalypse of Peter, the Didache. Most historians fully agree on this situation, although one of that solid 21 (Revelation) some historians think was more debated than Eusebius seems to indicate.
Cyril of Jerusalem (d. 350) does the same for us, listing the books that all Christians embrace as Holy Scripture. His list is the final Canon, except that Revelation was left out, giving us 26 (Matthew - Jude)
There now seems to be little debate at all, a consensus seem pretty solid - God's people settling on a pretty solid list. Although some historians believe that Revelation was still more disputed in the East.
Athanasius of Alexandria (d. 373) Once again, we have someone telling us what we want to know: What books were Christians embracing as Holy Scripture - the NT Canon? He lists them: It's our 27. He does mention the Didache and Hermas as "associated with" but clearly as inferior and below the 27.
Christians clearly had a canon of 27. And the RCC had NOTHING to do with.
Early Meetings:
Early meetings were usually not focused on stating a canon (such seems to have already been in place, with no need to state) but more with practical issues of the lectionary - what would be the Sunday readings.
The Council of Laodicea (363) Really just a regional synod, it says that "uncanonical books are not to be read in the churches." While it mentions none by name, clearly all knew what was and was not a "canonical book" since there was no need whatsoever to specify which were so regarded. The canon already existed - clearly - in everyone's mind.
The Council of Hippo (393) Actually, just a regional council, this is the first official meeting (rather than individual) specifically listing the approved lectionary books. It's our 27, the 27 that had been clearly embraced as such for several decades (and in most cases, since the First Century).
The Third Council of Carthage (397) This again listed the by now very well established NT Canon, already agreed upon by consensus by Christians. It's the now familiar 27.
Since then, hundreds upon hundreds of gatherings of various types have confirmed this consensus that Christians developed and which later these councils acknowledged. The RCC did this at the Council of Trent in the 16th Century.
Some words from St. Augustine regarding the Canon:
Augustine (352-430): "Let us treat scripture like scripture, like God speaking. It is not for nothing, you see, that the canon has been established for the Church. This is the function of the Holy Spirit." John E. Rotelle, O.S.A., ed., The Works of Saint Augustine, Newly Discovered Sermons, Part 3, Vol. 11, trans. Edmund Hill, O.P., Sermon 162C.15 (Hyde Park: New City Press, 1997), p. 176.
A note about the DEUTEROcanonical OT books:
"The New Catholic Encyclopedia states, "The Council of Trent definitively settled the matter of the Old Testament Canon. That this had not been done previously is apparent from the uncertainty that persisted up to the time of Trent"
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