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Today, it is popular to speak of the contradictions in the Bible as if there were obviously many of them. One of the many things pointed to in the Bible as an embarrassing contradiction is the discrepancy between the the genealogical details of the Gospel of Matthew and the Gospel of Luke.
12 And after the deportation to Babylon: Jechoniah was the father of Salathiel, and Salathiel the father of Zerubbabel, 13 and Zerubbabel the father of Abiud, and Abiud the father of Eliakim, and Eliakim the father of Azor, 14 and Azor the father of Zadok, and Zadok the father of Achim, and Achim the father of Eliud, 15 and Eliud the father of Eleazar, and Eleazar the father of Matthan, and Matthan the father of Jacob, 16 and Jacob the father of Joseph the husband of Mary, of whom Jesus was born, who is called the Messiah.
17 So all the generations from Abraham to David are fourteen generations; and from David to the deportation to Babylon, fourteen generations; and from the deportation to Babylon to the Messiah, fourteen generations.
The above passage from the Gospel of Matthew, when compared to a passage from the Gospel of Luke below, looks like they are presenting completely different accounts of Jesus' genealogy.
23 Jesus was about thirty years old when he began his work. He was the son (as was thought) of Joseph son of Heli, 24 son of Matthat, son of Levi, son of Melchi, son of Jannai, son of Joseph, 25 son of Mattathias, son of Amos, son of Nahum, son of Esli, son of Naggai, 26 son of Maath, son of Mattathias, son of Semein, son of Josech, son of Joda, 27 son of Joanan, son of Rhesa, son of Zerubbabel, son of Shealtiel, son of Neri, 28 son of Melchi, son of Addi, son of Cosam, son of Elmadam, son of Er, 29 son of Joshua, son of Eliezer, son of Jorim, son of Matthat, son of Levi, 30 son of Simeon, son of Judah, son of Joseph, son of Jonam, son of Eliakim, 31 son of Melea, son of Menna, son of Mattatha, son of Nathan, son of David...
Though some of the names listed are the same, they are listed in different orders, and some of the names are quite different, as if they were describing two different branches of a family tree. Or, as some have charged, two completely different family trees.
While family trees have multiple branches, and it's quite possible to show someone's ancestry going back to multiple figures by different routes, or even back to the same figures by different routes if a society (like the Jews) practices interarriage regularly, that doesn't explain why Joseph has two fathers.
In the Gospel of Matthew, Joseph's father is listed as Jacob. In the Gospel of Luke, his father is listed as Heli. Aha! A contradiction! Many critics of the Gospels would charge it with the crime of contradiction, at any rate.
This is not a new modern-era criticism of the Gospels, as we see below in a passage from St. Jerome, a priest and monk of Bethlehem who lived from around 340 AD until 420 AD:
This passage is objected to us by the Emperor Julian in his Discrepancy of the Evangelists. Matthew calls Joseph the son of Jacob, Luke makes him the son of Heli. He did not know the Scripture manner, one was his father by nature, the other by law. For we know that God commanded by Moses, that if a brother of near kinsman died without children, another should take his wife, to raise up seed to his brother or kinsman. But of this matter Africanus the chronologist, and Eusebius of Cesarea, have disputed more fully.
Eusebius (born about 260 AD and dead prior to 341 AD) writes in Book I of his famous work Ecclesiastical History that:
For Matthan and Melchi at different periods had each a son by one and the same wife Jesca. Matthan, who traced through Solomon, first had her, and died leaving one son, Jacob by name. As the Law forbade not a widow, either dismissed from her husband, or after the death of her husband, to be married to another, so Melchi, who traced through Matthan, being of the same tribe but of another race, took this widow to his wife, and begat Heli his son. Thus shall we find Jacob and Heli, though of a different race, yet by the same mother, to have been brethren. One of whom, namely Jacob, after Heli his brother was deceased without issue, married his wife, and begat on her the third, Joseph, by nature indeed and reason his own son; whereupon also it is written, And Jacob begat Joseph. But by the Law, he was the son of Heli; for Jacob, being his brother, raised up seed to him. Thus the genealogy, both as recited by Matthew, and by Luke, stands right and true; Matthew saying, And Jacob begot Joseph; Luke saying, Which was the son, as it was supposed, (for he adds this withal,) of Joseph, which was the son of Heli, which was the son of Melchi. Nor could be have more significantly or properly expressed that way of generation according to the Law, which was made by a certain adoption that had respect to the dead, carefully leaving out the word begetting throughout even to the end. ... Neither does this lack good authority; nor has it been suddenly devised by us for this purpose. For the kinsmen of our Saviour according to the flesh, either out of desire to shew forth this their so great nobility of stock, or simply for the truth's sake, have delivered it unto us.
As Eusebius notes, the language Luke uses is different, describing Joseph as son of Heli (or Eli as it is sometimes rendered) rather than as begotten by Heli, because he was begotten by Jacob though still Heli's son according to the Law. And this makes a great deal of sense in a society in which part of the Law's purpose was to ensure family stability and justice in matters of inheritance.
This traditional Judaic distinction between being a man's son by the Law and a man's son by nature is one that any of us should be able to understand. In the West today as in the past, adoption, step-fathers, and absent or dead biological fathers are quite common. Many of us have adoptive fathers, step-fathers, or other male family members raising us who are no less our fathers than our biological fathers, and for whom we are indeed sons.
St. Augustine of Hippo, who lived at around the same time as St. Jerome, makes much the same point in De consensu evangelistarum (On the Harmony of the Evangelists):
He is more properly called his son, by whom he was adopted, than had he been said to have been begotten of him of whose flesh he was not born. Wherefore Matthew, in saying Abraham begot Isaac, and continuing the same phrase down to Jacob begot Joseph, sufficiently declares that he gives the father according to nature, so as that we must hold Joseph to have been begotten, not adopted, by Jacob. Though even if Luke had used the word begotten, we need not have thought it any serious objection; for it is not absurd to say of an adopted son that he is begotten, not after the flesh, but by affection. ... And suitably does Luke, who relates Christ's ancestry not in the opening of his Gospel, but at his baptism, follow the line of adoption, as thus more clearly Him out as the Priest that should make atonement for sin. For by adoption we are made the sons of God, by believing in the Son of God. But by descent according to the flesh which Matthew follows, we rather see that that Son of God was for us made man. Luke sufficiently shews that he called Joseph the son of Heli, because he was adopted by Heli, by his calling Adam the son of God, which he was by grace, as he was set in Paradise, though he lost it afterwards by sinning.
In addition to making the distinction between fatherhood by nature and fatherhood by adoption, Augustine makes the point that sonship is and always has been more than sperm donorship. Fatherhood is first and foremost a spiritual, affective, and formative reality which may include but does not reduce to being the mere biological forebear of the son.
Another great theological mind, St. John Chrysostom, in his homilies, notes another interesting choice of phrasing in the Gospel:
Having gone through all the ancestry, and ended in Joseph, he adds, The husband of Mary, thereby declaring that it was for her sake that he was included in the genealogy.
He observes that though Joseph's lineage is important, it is Mary to whom that lineage leads us, and then to Christ through her motherhood. Joseph was her husband and an adoptive father to Jesus by the Law, and Christ's father who begat Him is our Father in Heaven.
Just as Joseph had two fathers, one by the natural means of begetting a child and another by familial adoption under the Law, Jesus also had two fathers, being the only-begotten Son of God by supernatural means and another by familial adoption under the Law.
Note: The above is a picture of my copy of the Catena Aurea (Volume 1: St. Matthew).