"Just as Jannes and Jambres opposed Moses, so these men also oppose the truth, men of depraved mind, rejected in regard to the faith. But they will not make further progress; for their folly will be obvious to all, just as Jannes' and Jambres' folly was also" (2 Timothy 3:8-9, performed miracles before Pharaoh equal to those of Moses and Aaron?". Their appearance in 2 Timothy 3:8-9) needlessly cites the Holy Spirit as Paul's source of the names as he wants to avoid any reference to tradition as a source. He is in an argument with Catholic and Orthodox believers who hold reverence for the Bible and oral tradition. Rudd is a sola scriptura man but doesn't need to rely on inspiration when there was such wide-ranging evidence for these two magicians' names.
The Book of Jannes and Jambres and legends about their names, since the Old Testament does not supply their identities, clearly predate all those that cite them, i.e., OrigenF1, Cyprian, EusebiusF2 , ApuleiusF3, Numenius, PlinyF4 and Paul writing to Timothy in the first century. It is reasonably regarded as having been composed in Egypt, probably by a Jewish writer. In the 3rd century some church fathers doubted the authenticity of 2 Timothy partly because of its citing of this apocryphal book.
Details of the four surviving fragmentary texts that we have can be found online at http://www.chass.utoronto.ca/%7Epietersm/jandj.html where various solutions to the lost ending or sequel are put forward. The text includes the story of Jannes' consignment to Hades for his sins and his appeal to his brother Jambres not to follow in his footsteps. It may be that the legend was taken over by Jews and/or early Christians to create a cautionary tale encouraging repentance. The Penitence of Cyprian says that the brothers, in spite of acknowledging God, did not obtain forgiveness.
Although Pliny the Elder, born A.D. 23 was a contemporary of Paul, his reference to Moses and Jannes in his Natural History in the chapter dealing with magic was not published until A.D. 77. So we must look elsewhere for any written source predating Paul. Another contemporary of Paul was Jonathan ben Uzziel, a promising student of Rabbi Hillel, and contemporary of Jesus. He is regarded as the oral author of the Targum of Jonathan, not finally circulated in written form much before the 5th century. On Exodus 7:11 this Aramaic paraphrase of the biblical text has:
"and Pharaoh called the wise men and the magicians; and Janis and Jambres, the magicians of the Egyptians, did so by the enchantments of their divinations." (Targum of Jonathan to Exodus 7:11; cf. similarly on 1:15)
Other Jewish traditions regard these men as being the source of Pharaoh's warning about the birth of Moses (Babylonian Talmud, Sotah 11a; Sanhedrin 106a, cf. Menachot 85a). Furthermore a later Midrash (Yelammedenu, Ki Tissa, Exodus 32) relates that they came out of Egypt with Moses but fell away and were part of the making of the golden calf.
Thus, there are plenty of oral and written sources for Paul to have found their names. The use of an apocryphal book is not wrong in itself, some may contain 1%-99% truth or facts. Jude quotes from the book of Enoch verbatim. Paul's use of Jannes and Jambres is illustrational not doctrinal and the true or apocryphal story serves to illustrate his point, not to establish the veracity of the tale, one way or another.
F1: Commentary on Matthew 27:9; Against Celsus
F2: Præparatio Evangelica, 9.8
F3: Apuleius in his Apologia mentions Moses and Jannes as amongst the world's great magicians at his 2nd century A.D. trial for magical practices.
F4: Historia Naturalis, 30.1
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