2 Timothy is one of the three epistles known collectively as the pastorals (1 Timothy, 2 Timothy, and Titus). They were not included in Marcion's canon of ten epistles assembled c. 140 CE. Against Wallace, there is no certain quotation of these epistles before Irenaeus c. 170 CE.
Norman Perrin summarises four reasons that have lead critical scholarship to regard the pastorals as inauthentic (The New Testament: An Introduction, pp. 264-5):
Vocabulary. While statistics are not always as meaningful as they may seem, of 848 words (excluding proper names) found in the Pastorals, 306 are not in the remainder of the Pauline corpus, even including the deutero-Pauline 2 Thessalonians, Colossians, and Ephesians. Of these 306 words, 175 do not occur elsewhere in the New Testament, while 211 are part of the general vocabulary of Christian writers of the second century. Indeed, the vocabulary of the Pastorals is closer to that of popular Hellenistic philosophy than it is to the vocabulary of Paul or the deutero-Pauline letters. Furthermore, the Pastorals use Pauline words ina non-Pauline sense: dikaios in Paul means "righteous" and here means "upright"; pistis, "faith," has become "the body of Christian faith"; and so on.
Literary style. Paul writes a characteristically dynamic Greek, with dramatic arguments, emotional outbursts, and the introduction of real or imaginary opponents and partners in dialogue. The Pastorals are in a quiet meditative style, far more characteristic of Hebrews or 1 Peter, or even of literary Hellenistic Greek in general, than of the Corinthian correspondence or of Romans, to say nothing of Galatians.
The situation of the apostle implied in the letters. Paul's situation as envisaged in the Pastorals can in no way be fitted into any reconstruction of Paul's life and work as we know it from the other letters or can deduce it from the Acts of the Apostles. If Paul wrote these letters, then he must have been released from his first Roman imprisonment and have traveled in the West. But such meager tradition as we have seems to be more a deduction of what must have happened from his plans as detailed in Romans than a reflection of known historical reality.
The letters as reflecting the characteristics of emergent Catholocism. The arguments presented above are forceful, but a last consideration is overwhelming, namely that, together with 2 Peter, the Pastorals are of all the texts in the New Testament the most distinctive representatives of the emphases of emergent Catholocism. The apostle Paul could no more have written the Pastorals than the apostle Peter could have written 2 Peter.
The arguments that establish the inauthenticity of the pastoral epistles are expounded by Kummel in his Introduction to the New Testament, pp. 371-84. In addition to providing more detail to the arguments stated by Perrin, Kummel adds a few more considerations.
Concerning the struggle against the false teachers, Kummel writes (op. cit., pp. 379-80):
. . . in addition to the predictions concerning the appearance of the false teachers 'in the last days' (I Tim 4:1 ff; II Tim 3:1 ff, 13; 4:3 f), there are references to the present activity of the false teachers and instructions about combating them (I Tim 1:3 ff, 19 f; 6:20 f; II Tim 2:16 ff; 3:8; Tit 1:10 ff; 3:9 ff), so that there is no perceptible distinction between the teaching of the predicted false teachers and the present ones. But since nowhere in the Pastorals is there to be found any consciousness of living 'in the last days,' in the prediction of the End-time which evidently describes present phenomena it is clear that we are dealing only with a traditional literary motif (vaticinium ex eventu) which is now being employed by 'Paul.' Still more striking, however, is the matter of how the false teachers are opposed. Completely otherwise than in Col, the viewpoints of the false teachers are not contradicted by being confronted with the preaching about Christ, but they are countered simply by reference to the traditional teaching, from which the false teachers have erred and which is to be held fast (I Tim 4:1; 6:20; II Tim 1:14; 2:2 Tit 3:10 f). The lack of any substantive debate cannot be explained on the ground that Paul did not regard the prattle of false teachers as being worth contradicting and assumed that Timothy and Titus themselves knew what should be said in refutation of the false teachers. In that case there would be no necessity to make those addressed aware of the dangers of the false teaching in detail. This lack is much more readily explained by the fact that Paul is not writing these letters.
In the pastorals, there is an emphasis on the preservation of tradition, and the community situation seems to be that of the sub-apostolic age. The pastorals evince a level of church organization that most likely would not have existed in the lifetime of Paul. The requirements particular to bishops and deacons are spelled out clearly (I Tim 3:1-13). Kummel writes (op. cit., pp. 381-2):
The actual task of Timothy and Titus consists rather in preserving the correct teaching which they received from Paul and passing it on to their pupils (I Tim 1:11; 6:20; II Tim 1:14; 2:2). Though there is no chain of succession constructed from Paul via his apostolic disciples to the holders of office in the congregations - not even in II Tim 2:2, the chain of tradition is strongly stressed, whose beginning lies with the apostle (II Tim 2:2, 8). The presupposition of this central role of the tradition is a community which, in contrast to Paul's expectation of a near end of the age, is already making provision for the time after the death of the bearers of tradition appointed by the apostolic disciples (II Tim 2:1 f). Although Paul certainly did not know of the task of preserving the tradition through ordanted presbyters (presbuteros is not meant in Paul as an indication of an office), the ecclesiastical office of the widows (I Tim 5:3 ff) whose essential task is continual prayer in connection with sexual abstinence is totally foreign to Paul. Though it is questionable whether the Pastorals presuppose a distinction between clergy and laity, still there is no longer any indication of active cooperation and responsibility on the part of the community.
And Kummel goes on to amass further evidence that the theological expressions used are incompatible with Pauline authorship (op. cit., pp. 382-84). All these arguments establish that the pastoral epistles are second century products.
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