Is Luke 3 the genealogy of Joseph?
That Matthew's Gospel gives an account of Joseph's genealogy is clear:
And Jacob begot Joseph the husband of Mary, of whom was born Jesus who is called Christ (Matthew 1:16).
Now if both Matthew and Luke give a genealogy through Joseph then there is no evidence presented in Scripture that Jesus was actually a biological descendant of David.
The Old Testament tells us that the Messiah will be a biological descendant of David:
I will set up your seed after you, who will come from your body, and I will establish his kingdom. (2 Samuel 7:12).
Twice in one verse it is asserted the Messiah will be literally a descendant of David.
For other Scriptures see Psalm 132.11, Luke 18.38, Acts 2.30, Romans 1.3, Revelation 5.5.
In the Gospel of Luke, then, it must be the genealogy of Mary. Only through Mary can there be a literal fulfilment of 2 Samuel 7:12.
It would seriously damage Christ's claim to be the Messiah of the seed of David, if this could not be proven; so Luke gives the proof.
If Jesus is only related to David through his adoptive father then Mary's magnificat statement in Luke 1:32, "... shall give unto him the throne of his father David", has little meaning (see also Luke 1:69).
Some claim that Mary cannot be of the tribe of Judah, and hence a descendant of David, because she has a relative of the tribe of Levi (Luke 1:36 & 1:5). But she could easily have been of the tribe of Judah. The priesthood were only required to marry a virgin woman of their own people (Levitcus 21:13,14), a fellow Israelite.
An ancestor or relative of Elizabeth of the tribe of Levi could have married into the tribe of Judah.
Matthew's Gospel establishes Jesus as the King of Israel in the earthly sense. When Joseph died Jesus became King according to Davidic descent, being the eldest son of Joseph.
So the chief verse in Luke's Gospel is Luke 3.23
And Jesus began to be about thirty years of age, being (as was supposed) the son of Joseph, which was of Heli, (Luke 3:23).
It is likely Luke and Matthew both went to Jerusalem and examined the genealogy of Jesus from the public records office. Public records were kept in many towns in ancient times. The public records in Jerusalem are mentioned by Josephus when he gives his own genealogy. (From Josephus account it is fairly clear these public records were not destroyed in the first Jewish-Roman War, 66-70 AD). (And have you ever wondered how Paul could prove his Roman citizenship? The legal proof would have been stored at the public records in Tarsus.)
It was convention of the Jews that the mothers were not recorded in these public records. The records partly existed for the purposes of inheritance, and for the Levites they existed for the purpose of determining if a man had the right to serve in the Temple.
It is important further to remember that Luke writes his genealogy thus:
"which was of Heli, which was of Matthat, which was of Levi," etc. Luke does not specify the relationship between Heli and Mattat and Levi.. they could be son to father or son to grandfather or great grandfather, etc.
Luke 3:23 is telling us then that Jesus's grandfather was Heli who was the nearest to an actual human father of Jesus, being the father of Mary.
William Hendriksen in his Commentary re-words verses 23 and 24 to give:-
Now Jesus himself, supposedly Joseph's son, was about thirty years of age when he began (his ministry), being a son of Heli, son of Matthat, son of Levi, son of Melchi, son of Jannai, ... (Luke 3:23-24)
It is not saying that Joseph was the son of Heli but rather that Jesus was the son (or grandson) of Heli. And Heli was Mary's father, the nearest equivalent to a human father for our Lord Jesus Christ.
Matthew Henry in his Commentary published around 1721 writes:
but Luke, designing to show that Christ was the seed of the woman, that should break the serpent's head, traces his pedigree upward as high as Adam, and begins it with Eli, or Heli, who was the father, not of Joseph, but of the virgin Mary.
Matthew draws the pedigree from Solomon, whose natural line ending in Jechonias, the legal right was transferred to Salathiel, who was of the house of Nathan, another son of David, which line Luke here pursues, and so leaves out all the kings of Judah.
The evangelists are not supposed to have written these genealogies either of their own knowledge or by divine inspiration, but to have copied them out of the authentic records of the genealogies among the Jews, the heralds' books, which therefore they were obliged to follow; and in them they found the pedigree of Jacob, the father of Joseph, to be as set down in Matthew; and the pedigree of Heli, the father of Mary, to be as set down here in Luke. And this is the meaning of the words "as it was supposed": they do not refer only to Joseph, but they refer to what is written into the books, as we find it upon the record. [In other words, it was written in the records that Joseph was the father of Jesus because that was "supposed" by the recorders of those records.]
And so it is that on both his father and his mother's side, that Jesus was the Son of David according to their own records, which anyone might at that time have liberty to examine and compare with the original, and any further the evangelists did not need to go. Had the evangelists varied from the original records they would have not gained their point. The fact that the genealogies in both Matthew and Luke were not contradicted at that time is satisfaction enough to us now that these are true copies, and it is further worthy of observation, that, when those records of the Jewish genealogies had continued thirty or forty years after these extracts out of them, long enough to justify the evangelists therein, they were all lost and destroyed with the Jewish state and nation; for now there was no more occasion for them.
It is a wonderful fact that these public records no longer exist. Presumably they were destroyed in the second Jewish-Roman War about 130 AD. [I believe the genealogical records existed in Jerusalem until about 130 AD, and were not destroyed in the first Jewish Rebellin 66-70 AD because Josephus said anyone could check the records for his own genealogy, and certainly he was writing after 70 AD.] So it is no longer possible for anyone to claim to be a descendant of King David... in fact it is impossible today for anyone to legally prove they are Jewish at all. The Messiah who fulfills the prophecy of 2 Samuel 7:12 must have been born before these records were destroyed, before about 130 AD.
Finally, I can't see the significance of the names of the boys being James, Joses, Simon and Judas, taken from the genealogy of Luke's Gospel. What difference does it really make to any argument about whose genealogy Luke is recording? Besides this, the names of all the boys were extremely common in the New Testament period, and all they really tell us is that the one choosing the names was very conventional in the choice. I take this data from Richard Bauckham's "Jesus and the Eyewitnesses - The Gospels as Eyewitness Testimony", Table 6 on page 85:-
The 99 Most Popular Male Names among Palestinian Jews, 330 BCE to 200 CE.
Many of these names were popular because they were names of the Maccabee/Hasmonean dynasty... the last time the Jews were an independant nation, and were a sign of the Jewish nationalist longing for a return to independance.
So the Hasmonean family names were Hashmon, Mattathias, Simon (called Mathes), Judas (Maccabees), Jonathan (called Apphus), Eleazar (from which derives Lazarus, called Auran), John (Gaddis) and John Hyrcanus. Also in the same family or marrying into the family were the women Salome Alexandra, who married Alexander Janneus, and Mariamme, granddaughter of Hyrcanus II. For the same reason the three most popular female names in the same period were Salome, Mary (Mariam) and Shelamzion (the longer form of Salome) (Bauckham, page 74).