2nd Peter

Here's basically the arguments people make:

(1) The letter has a literary relationship with the epistle of Jude (which is itself dated to the late 1st-early 2nd century); there are huge similarities between the two in the language and some of the themes. The similarities are especially prominent in the portrayal of the false teachers in chapter 2. What scholars who don't accept 2 Peter is authentically Peter's say is that it's more likely that 2 Peter is dependent on Jude, due to a number of factors, rather than the other way around.

(2) The letter is quite unique among all the other NT books in that it makes very heavy use of Greek rhetoric and Atticisms, more at home with the elevated language and rhetoric of 2nd century Christian writings than those of the 1st. (For example, the phrase "partakers of the divine nature" in 1:4; this is a phrase not found elsewhere in the NT but has a long history in Greek philosophy.) This is one of the reasons why even some scholars who even consider 1 Peter to have a possibility of being authentic can be a bit more reserved about 2 Peter: it's so 'Greek', even the style of Greek it uses is very complicated and elaborate. (1 Peter by contrast is still simple in its language.)

For example, in chapter 2 the fall of the angels is sort of described in the language of the fall of the Titans in Greek mythology: "For if God did not spare angels when they sinned, but cast them into Tartarus and committed them to chains of gloomy darkness to be kept until the judgment ..." (But then again, some Jewish writers at the time - usually Hellenistic ones - did already make the fallen angels = Titans connection.)

(3) This passage from chapter 3:

And count the patience of our Lord as salvation, just as our beloved brother Paul also wrote to you according to the wisdom given him, as he does in all his letters when he speaks in them of these matters. There are some things in them that are hard to understand, which the ignorant and unstable twist to their own destruction, as they do the other Scriptures.

The argument runs basically that it's quite difficult to imagine that St. Paul's letters would have already been collected, considered as Scripture, and widely disseminated as the letter seems to imply at so early a date (remember, Peter is supposed to have died in the mid-60s, so if he's the one writing this, this would have been somewhere around that time - when according to the consensus, a good deal of the non-Pauline books of the NT were not even written yet). The idea is, the letters of Paul - or the books of the New Testament in general, for that matter - are thought to be not definitively compiled together or achieved a 'scriptural' status among early Christians until the post-Apostolic age.

(4) The context of the letter - the rise of false prophets and "destructive heresies" (gnostics?), the persecution of believers, the skepticism among some that the second coming will ever happen - seems to fit more the situation of the late 1st-early 2nd century than the mid-1st century. While Paul stated that Peter's ministry was mainly to Jews (Galatians 2:8), 2 Peter seems to be written to former gentiles dealing with their gentile neighbors. Even then, the author's tone is still different from Paul's, who is himself writing to gentiles: the Christology is cosmic that the writer doesn't even dwell much on the historical Jesus; there is apparently also no interest in Israel, the Law or the covenant (as we would have expected a writer of Jewish origins - like Paul - to deal with).

(5) Then there's also the silence towards the letter among the Apostolic Fathers and other earlier Christian authors (Irenaeus, Tertullian, Cyprian, Clement of Alexandria). The Muratorian canonalso doesn't include it or 1 Peter (it only makes reference to the Apocalypse of Peter, "though some amongst us will not have this latter read in the Church"). Our first attestation of it is in Origen, but even according to him the letter in his time is contested (αμφιβαλλεται). Eusebius lists it among the antilegomena, but by his time he was in the minority - the majority already supported the text. It was by the time of St. Jerome that the letter was mostly accepted as canonical.

That's pretty much how the ideas run.

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