When was Luke Written?
The Gospel according to Luke was written neither after the persecution by Emperor Nero and his execution of Peter and Paul nor after the fall of the Temple in Jerusalem in the Jewish-Roman War.
The Gospel According to Luke, also called the Gospel of Luke, or simply Luke, is the third of the four canonical Gospels. It tells of the origins, birth, ministry, death, resurrection, and ascension of Jesus Christ.There is no fear of the large-scale persecution of early Christians in Rome in Luke. If Luke had experienced Nero's persecution, he should have not stressed his denial of the worldly authority. Luke's assertion in his Gospel could invoke a kind of anger from the Roman authority, although he clearly stated the standpoint of early Christianity. Luke took such a risk to preach or explain the Gospel to the Roman authority with a hope that he might get some followers among Roman elites. It was reasonable if Luke had written it before the trail for which Paul was sent to Rome.
Luke needed to define the position of Christians in relation to two political and social entities, the Roman Empire and Judaism. Regarding the Empire Luke makes clear that, while Christians are not a threat to the established order, the rulers of this world hold their power from Satan, and the essential loyalty of Christ's followers is to God and this world will be the kingdom of God, ruled by Christ the King. Regarding the Jews, Luke emphasises the fact that Jesus and all his earliest followers were Jews, although by his time the majority of Christ-followers were gentiles; nevertheless, the Jews had rejected and killed the Messiah, and the Christian mission now lay with the gentiles.
Luke also emphasized the possibility that early Christianity was going to be separated from Judaism. But if Luke had experienced Nero's persecution, he should have emphasized the tie of early Christianity to Judaism so that the Roman authority would not regard early Christianity as a new dangerous religion separated from Judaism.
From these points of view, it is naturally thought that the Gospel according to Luke was written even before the trial of Paul.
On the other hand, the Gospel according to Mathew emphasizes the tie between early Christianity and Judaism as if in order to avoid further persecution of early Christians in Rome after Nero's persecution. Mathew must have been written between Nero's persecution and the Jewish-Roman War. But Luke was written before this period of crises to early Christians. So, Luke was written rather in a bold manner of advertising early Christianity to Romans.
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Luk 3:9 And now also the axe is laid unto the root of the trees: every tree therefore which bringeth not forth good fruit is hewn down, and cast into the fire.