Most translations (NASB, ESV, NIV, NRSV) also have Cainan in Luke 3:36. The apparent problem is that Cainan does not appear in the genealogy in Genesis, Chronicles, or in other Jewish histories. Only some late manuscripts of the Septuagint have Cainan as the son of Arphaxad in Genesis 11. Thus, the charge is that “Cainan” was an addition in Luke 3:36 based on these tampered texts of the Septuagint. Critics allege that “Cainan” appeared first in a text of the Septuagint and then made its way into Luke 3:36. However, it is just as logical that an authentic Luke 3:36 had “Cainan” and a later editor of the Septuagint inserted “Cainan” into Genesis 11 in order to harmonize Genesis with Luke. The Septuagint is known for trying to harmonize the New Testament with the Old Testament. For example, the Septuagint inserts Romans 3:13-18 into Psalm 14:3. The Sinaiticus, Vaticanus, and Alexandrinus have “Cainan” at Luke 3:36. P75 and Bezae omit “Cainan.” But P75 also omits Luke 23:34, Luke 22:43-44 and Bezae also omits Luke 23:34, Luke 24:6, Luke 24:12, Luke 24:36, Luke 24:40, and Luke 24:51. These two manuscripts were heavily edited. They could have omitted “Cainan” in Luke 3:36 to harmonize the New Testament genealogy with that of the Old Testament.
With respect to the argument that the same name "Cainan" appears twice in Luke 3:36 and Luke 3:37, this is typical of the pre-flood genealogy. Two individuals were named "Enoch" (Genesis 4:17, 5:19) and two individuals were named "Lamech" (Genesis 4:18, 5:25) only a few generations apart.
It is perfectly understandable why the genealogy of Luke includes a name that never appeared in any Jewish genealogy, including Genesis, Chronicles and Josephus. Previous Jewish genealogies focused on biological sonship. However, the genealogy of Luke clearly focuses on sonship by adoption. Luke 3:23 says that Jesus was “the son of Joseph” despite Joseph having no biological connection to Jesus. Jesus was the adopted son of Joseph. Luke 3:23 also says that Joseph "was the son of Heli” (literally "was of Heli") despite Joseph being the biological son of Jacob (Matthew 1:16). Heli was actually the father of Mary, Joseph’s wife. Thus, Joseph was the adopted son (son in law) of Heli. If this pattern continues in the genealogy, it would not be surprising to find an adopted son who had previously been omitted from biological genealogies. We can reasonably accept that Cainan was the adopted son of Arphaxad, and that Cainan raised Sala, who was the biological son of Arphaxad. The Masoretic text is not in error because its genealogies in Genesis and Chronicles focus on biological sonship.
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Also read: Masoretic Readings Defended