On the author of 1 Peter and 2 Peter, this should come as no surprise, but "Peter" the apostle ("Simon Peter") doubtfully wrote either of them.
On 1 Peter:
Despite 1 Pet 1:1, the author is unlikely to have been the apostle Peter. The cultured Greek of the epistle makes it perhaps the most literary composition in the NT. The apostle Peter probably knew some Greek, but 1 Peter does not look like the product of an unlettered (Acts 4:13) Galilean fisherman. It employs a sophisticated vocabulary incorporating several NT hapax legomena, and its author appears to have some command of the techniques of Hellenistic rhetoric. He is also intimately acquainted with the OT in the LXX, whereas we should have expected the Galilean Peter to have been more familiar with an Aramaic Targum or the Hebrew." (The Oxford Bible Commentary, p. 1263)
And as W. G. Kümmel writes in his "Introduction to the New Testament":
I Pet presupposes the Pauline theology. This is true not only in the general sense that the Jewish-Christian readers, the 'people of God' (2:10), are no longer concerned about the problem of the fulfillment of the Law, but also in the special sense that, as in Paul, the death of Jesus has atoned for the sins of Christians and has accomplished justification (1:18 f; 2:24). Christians are to suffer with Christ (4:13; 5:1), obedience to the civil authorities is demanded (2:14 f), and the Pauline formula en xristw is encountered (3:16; 5:10, 14). The frequently advanced proposal that I Pet is literarily dependent on Rom (and Eph) is improbable because the linguistic contacts can be explained on the basis of a common catechetical tradition. But there can be no doubt that the author of I Pet stands in the line of succession of Pauline theology, and that is scarcely conceivable for Peter, who at the time of Gal 2:11 was able in only a very unsure way to follow the Pauline basic principle of freedom from the Law for Gentile Christians.
On 2 Peter, Kümmel offers numerous reasons why it is doubtfully a genuine letter of Simon Peter:
1. The literary dependence on Jude rules this out. II Pet 1 and 3 already have a number of contacts with Jude: cf. II Pet 1:5 with Jude 3; II Pet 1:12 with Jude 5; II Pet 3:2 f with Jude 17 f; II Pet 3:14 with Jude 24; II Pet 3:18 with Jude 25. The most striking agreements with Jude are shown in the portrayal of the false teachers in II Pet 2 and also in the illustrations based on the OT and the pictures drawn from nature, agreements in the exact wording and extensive agreements in sequence. The false teachers deny the Lord Christ and lead a dissolute life (II Pet 2:1 f = Jude 4), they despise and blaspheme the good angelic powers (II Pet 2:10 f = Jude 8 f), they speak in high-handed fashion (uperogka; II Pet 2:18 = Jude 16), they are blotches on the communal meal (spigoi suneuwcwmenoi; II Pet 2:13 = Jude 12), they are clouds tossed about by the wind, devoid of water, for whom the gloom of darkness is reserved (II Pet 2:17 = Jude 12 f), they are denounced for their fleshly corruption and their unrestrained mode of life (II Pet 2:10, 12 ff, 18 = Jude 7 f, 10, 12, 16). The sequence of examples of punishment from the OT in Jude 5 ff (Israel in the desert, fallen angels, Sodom and Gomorrah) is arranged in historical order in II Pet 2:4 ff and modified (fallen angels, Flood, Sodom and Gomorrah) because the author of II Pet needs the example of the Flood to combat the deniers of the parousia. The general statement in II Pet 2:11 makes sense only if note has been made of the concrete example mentioned in Jude 9. The image in Jude 12 f is more genuine and more plastic than the parallel in II Pet 2:17.
This material shows, therefore, that it is II Pet which is the dependent factor. It is further to be observed that the quotation from a noncanonical writing (Jude 14 f = the Apocalypse of Enoch 1:9; 60:8) is lacking in II Pet, and that by omitting certain essential features the allusions to the apocryphal writings have been somewhat obscured in Jude 6 (fallen angels) and 9 (the struggle between the archangel Michael and the Devil). From this it may be concluded that II Pet is already reluctant to use this literature whereas Jude has a naive attitude toward it. II Pet betrays a literary strategem in that the false teachers who are characterized by Jude as being in the present are depicted in II Pet as future and indeed predicted by Peter (2:1 ff, in the future; 3:3, 17 proginwskontes). But in spite of this they are also described in the present tense (2:10, 12 ff, 20), and indeed the past tense is used (2:15, 22). Consequently it is almost universally recognized today that II Pet is dependent on Jude and not the reverse. Then II Pet 3:3 ff portrays the libertines as the deniers of the parousia. In this way he representes a more developed stage, while a less developed stage is evident in Jude, who does not yet know that the false teachers against whom he directs his attention might have denied the parousia. Since Jude belongs in the postapostolic age, Peter cannot have written II Pet.
2.The conceptual world and the rhetorical language are so strongly influenced by Hellenism as to rule out Peter definitely, nor could it have been written by one of his helpers or pupils under instructions from Peter. Not even at some time after the death of the apostle. The Hellenistic concepts include: the areth of God (1:3), virtue in addition to faith (1:5); knowledge (1:2, 3, 6, 8; 2:20; 3:18); participation in the divine nature (qeias koinwnoi fusews) "in order that one might escape corruption that is present in the world because of lust" (1:4); the term epoptai comes from the language of the mysteries (1:16); placed side by side are a quotation from Proverbs and a trite saying from the Hellenistic tradition (2:22).
3. The letter has a keen interest in opposing the denial of the Christians' expectation of the parousia. 1:12 ff already deals with the hope of the parousia, which is based on the fact of the transfiguration of Jesus and the OT prophecy. In 3:3 ff there is a direct polemic against those who deny the parousia. These ask scornfully, "Where is the promise of the parousia of Christ?" and draw attention to the fact that since the fathers have fallen asleep everything remains as it has been from the beginning of creation (3:4). In I Clem 23:3 f and II Clem 11:2 ff too, there is adduced a writing which was obviously read in Christian circles, in which is laid down the challenge "We have already heard that in the days of our fathers, but look, we are become old and nothing of that has happened to us." I Clem was written ca. 95, and II Clem can hardly have been written earlier than 150. We have, therefore, historical evidence from the end of the first century onward for the disdainful skepticism which is expressed in II Pet 3:3 ff. But it is the Gnostics of the second century who have opposed the parousia and reinterpreted it along spiritualistic lines. It is probably also they who are meant by the proclaimers of the "clever myths" (1:16) and of "knowledge" (see point 2). Characteristic of them are the libertinism and the insolent disrespect for spirit powers (see point 1). II Pet is therefore aimed against a movement which bears the essential features of second-century gnosis. A more exact determination is not possible, however.
4. Also indicative of the second century is the appeal to a collection of Pauline letters from which "statements that are hard to understand" have been misinterpreted by the false teachers, and to further normative writings which inlcude not only the OT but also the developing NT (3:16). In view of the difficulty in understanding "scripture," and its ambiguity, II Pet offers the thesis that "no prophetic scripture allows an individual interpretation" because men have spoken under the power of the Holy Spirit (1:20 f). Since not every Christian has the Spirit, the explanation of Scripture is reserved for the ecclesiastical teaching office. Accordingly we find ourselves without doubt far beyond the time of Peter and into the epoch of "early Catholocism."
It is certain, therefore, that II Pet does not originate with Peter, and this is today widely acknowledged. This point of view can be confirmed through two further facts.
5. As in the case of the Pastorals, the pseudonymity in II Pet is carried through consistently by means of heavy stress on the Petrine authorship (see above, p. 430). The auther adduces his authority not only on the basis of the fiction of a "testament of Peter" but also by reference back to I Pet in 3:1 f, intending II Pet only to "recall" (1:12, 15; 3:1 f) what was said in I Pet to the extent that it corresponds to the interpretation which the author of II Pet wants to give to I Pet. This appeal to the apostolic authority of Peter and his letter is obviously occasioned by the sharpening of the Gnostic false teaching which is being combated in Jdue, as a result of a consistent denial of the parousia of the false teachers. In this way, the apostle has become the "guarantor of the tradition" (1:12 f), and as a consequence of the abandonment of the near expectation (3:8) the parousia is stripped of its christological character and functions as an anthropologically oriented doctrine of rewards. In its consistent quality the pseudonymity betrays the late origins of II Pet.
6. In spite of its heavy stress on Petrine authorship, II Pet is nowhwere mentioned in the second century. The apologists, Irenaeus, Tertullian, Cyprian, Clement of Alexandria, and the Muratorian Canon are completely silent about it. Its first attestation is in Origen, but according to him the letter is contested (amfiballetai). Eusebius lists it among the antilegomena. . . Even down to the fourth century II Pet was largely unknown or not recognized as canonical.
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