In the Matthew and Luke we can read the genealogy of Jesus. While in Matthew 1 it dates back to Abraham, in Luke 3 it goes back to Adam.
What's the significance of this difference?
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Matthew's Gospel is first for the Jews and Luke's Gospel is for the Gentile.
The focus of Matthew is that Jesus is "the King of the Jews", the Messiah promised to Abraham, Isaac, Jacob, who would be a direct-line descendant of King David, etc. The original purpose of Matthew's Gospel was for the Jews, and Papias tells us that Matthew's Gospel was first written in Hebrew for the Jews of Judaea, and only later translated into Greek. Matthew's Gospel seeks to answer the question "Is Jesus of Nazareth the promised Messiah of the Old Testament, the King of the Jews?"
If the royal line of David had continued to rule then, when Joseph, Jesus's adoptive father, died Jesus would have ascended the throne, being the eldest son in the family. (Adoption made no difference, an adopted son in those days having equal rights of inheritance with biological sons.)
So in Matthew's Gospel the focus is on Joseph and not Mary - the genealogy is that of Joseph (Matthew 1:16) and for the same reason in Matthew's Gospel the Lord speaks to Joseph, rather than Mary, about the coming birth; whereas in Luke's Gospel the focus is on Mary with the Angel Gabriel speaking to Mary, and not Joseph.
Notice how Joseph and not Mary is the focus of attention in Matthew's Gospel in Matthew 1:18-25, Matthew 2:13-14 and Matthew 2:19-23.
And notice how the opposite is true in Luke's Gospel: Mary and not Joseph is the focus of attention in Luke's Gospel.
In Luke's Gospel (Luke being a Gentile himself) the focus is that Jesus is the Saviour of the World, the Saviour of all the descendants of Adam and Eve, of both Jews and Gentiles. So Jesus is the fulfilment of the promise God gave to the whole human race when He spoke to Satan in the hearing of Adam and Eve after they sinned:
I will put enmity between you and the woman, and between your seed and her seed; he shall bruise your head, and you shall bruise his heel.
The coming Saviour would be "the seed of the woman", not the seed of a man, hinting that the Saviour when he comes into the world would be born of a virgin. It is fitting that the genealogy which starts with Adam and Eve ends with the virgin mother and the Son.
And so Luke 3:23 ought to read
Jesus, when he began his ministry, was about thirty years of age, (being as was supposed of Joseph,) being of Heli, of Matthat...etc.
or to put it another way, to give the proper sense:
Now Jesus himself, supposedly Joseph's son, was about thirty years old when he began (his ministry) being a son of Heli, son of Matthat .... son of Adam, son of God. ("New Testament Commentary: the Gospel of Luke" by William Hendriksen, Banner of Truth Trust, 1979).
Meaning, Jesus was a descendant of Heli, where Heli was the father of Mary.
Consider these two genealogies:
"Andrew Shanks, being as was supposed (by one or two people) the son of Prince William, being the
son of Prince Charles, being the son of Queen Elizabeth II, being the daughter of Albert, i.e. King George VI, being the son of George V, being the son of Edward VII, being the son of Queen Victoria."
"Andrew Shanks, being as was supposed by one or two people the son of Prince William, being the son of John Shanks, the son of John Shanks, the son of Jesse Shanks."
The first genealogy is a pointless genealogy because only a couple of people believe the premise with which it begins. It is only actually a genealogy of Prince William, not of Andrew Shanks: it fails in its aim to give relevant information about Andrew Shanks.
The second genealogy has Andrew Shanks, not Prince William, as its focus. All of the information relates to Andrew Shanks.
In the same way the genealogy of Luke's Gospel is the genealogy of Jesus Christ, not Joseph. All of the information relates to Jesus Christ.
Jesus, then, was a descendant of David both through his mother and his adoptive father, his mother to fulfil the promise of 2 Samuel 7:12, "I will set up thy seed, which shall proceed out of thy bowels", and his adoptive father to fulfil the promise of, for example, 2 Samuel 7:16 and 7:26. In 2 Samuel 7:12 it is said twice as it were that Jesus would be a biological descendant of David. Luke's Gospel provides the evidence that Jesus of Nazareth fulfils that requirement of the coming Messiah.
For the Holy Spirit to give two genealogies for Joseph, and none for Mary, when Jesus was not even related to Joseph seems to me to be quite an absurd way of demonstrating that Jesus is the promised Messiah, of the seed of David, out of David's bowels (2 Sam 7:12), or showing that He was one of us, a member of the human race. A genealogy through Joseph emphasises and draws attention to the fact he had no human father at all and puts a distance between him and us. A genealogy through Mary, however, rather draws Him in within the circle of the descendants of Adam and draws Him nearer to us and us to Him. Furthermore, to spend so long (Luke 3:23-end of chapter) on a genealogy of someone, namely Joseph, who is not even related to the person of key interest, namely Jesus of Nazareth, seems also an absurd waste of ink.
The gospel of Jesus, written by Luke, has a specific reason for giving the genealogy that he does. Notice where Luke suddenly (almost unexpectedly) places that genealogy. He plonks it right inbetween Jesus' baptism in the Jordan river and the temptations in the wilderness (Luke 3:23-38). Why would a genealogy appear there, in the narrative?
Well, consider that as it ends up with Adam, we are seeing the link (which is an unsmashable chain) from Jesus the Son of God, the second Adam, to the first son of God, the man Adam. The significance here is that we are meant to see that Jesus' temptation and victory needs to be viewed in light of the testing and defeat of the first Adam. To quote from this truly helpful book's chapter on the role of the Holy Spirit in the life of Christ when on earth:
"The conflict in which Jesus engaged is, therefore, to be seen as a re-run of Eden. Like Adam before him, Jesus was incited to 'be as God' and to reject [God's] word. But he chose the way of God-glorifying obedience and suffering instead... Jesus, anointed with the Spirit, was carried obediently and overcomingly through the test of the wilderness... Thus, in the power of the Spirit, in the inhospitable desert which the world had become through the first Adam's sin, the second man, the eschatological Adam (ho eschatos Adam, 1 Cor. 15:45), regained enemy-occupied territory." Sinclair Ferguson, The Holy Spirit, p 49 (ivp 1996)
Luke has a strong emphasis in his account of the role of the Holy Spirit with regard to Jesus. At his baptism, the Holy Spirit descends, fluttering-like as a dove. Luke has a theme of how the Spirit is given regularly in response to prayer and in connection with the advance of the kingdom, hence the Spirit immediately leading Christ into the wilderness and being with him for the duration, for this was the start of Jesus' earthly ministry. After Jesus' triumph over Satan's temptations, Jesus returned to Galilee "in the power of the Spirit" (Luke 4:14). What we see in Jesus was fully realized human holiness and wisdom, over-turning the damage done by the first Adam's lack of holiness and wisdom. As the book further explains:
"The Spirit came upon him while he was praying, following his baptism (Lk. 3:21)... This event marks Jesus' public entrance into and consecration to his messianic ministry... He comes on the scene as the long-awaited prophet of God. In addition, Luke's reference to Jesus being about thirty years of age (Lk. 3:23) probably reflects the age of entry into priestly service. Jesus is thus also viewed as an anointed priest.. Just as the High Priest prepared for his atonement-day ministry by washing and anointing, so Jesus received the washing of this baptism and the anointing of the Spirit with a view to his own priestly ministry. In his water-baptism he consecrates himself by prayer to his coming death-baptism (cf.Jn. 17:19). The heavenly voice he hears echoes the words of enthronement from Psalm 2:7, underlining that Jesus is entering into the ministry of the universal king. The coming of the Spirit therefore is an anointing for the three-fold messianic office prefigured by prophets, priests and kings. ...Jesus is the 'second man' and the 'last Adam' who will become life-giving spirit (1 Cor. 15:45-47)... who will bring rest to a cursed world. ...Thus the Spirit comes on Christ as the head of the new creation." (ibid. pp 45 & 47)
Luke's genealogy is bringing the reader's attention to the critically important bond between the first Adam, who failed at the first temptation, and the second Adam, who triumphed and undid all the damage done by the first man and Satan. That is why that particular genealogy is placed at that particular point in the narrative.
Different genealogy in St. Matthew and St. Luke?
The reason for the differences between these two genealogies are multiple.
It is granted on all sides that the Biblical genealogy of Christ implies a number of exegetical difficulties; but rationalists have no solid reason for refusing to admit any of the attempted solutions, nor can we agree with those recent writers who have given up all hope of harmonizing the genealogies of Christ found in the First and Third Gospels. The true state of the question will become plain by studying the Biblical genealogies of Christ first separately, then in juxtaposition, and finally in their relation to certain exceptions to their harmony.
St. Matthew's genealogy of Christ
The genealogy of Christ according to the First Evangelist descends from Abraham through three series of fourteen members each; the first fourteen belong to the patriarchal order, the second to the royal and the third to that of private citizens. Matthew 1:17, shows that this arrangement was intended; for the writer expressly states: "So all the generations, from Abraham to David, are fourteen generations. And from David to the transmigration of Babylon, are fourteen generations: and from the transmigration of Babylon to Christ are fourteen generations."
The list of the First Evangelist omits certain members in Christ's genealogy:
The writer gives only three names for the time of the Egyptian exile (Esron, Aram, and Aminadab), though the period lasted 215 or 430 years; this agrees with Genesis 15:16, where God promises to lead Israel back in the fourth generation. But according to Genesis 15:13, the stranger shall afflict Israel for four hundred years.
The three names Booz, Obed, and Jesse cover a period of 366 years. Omitting a number of other less probable explanations, the difficulty is solved most easily by the admission of a lacuna between Obed and Jesse.
According to I Paralipomenon 3:11-12, Ochozias, Joas, and Amasias intervene between Joram and Azarias (the Ozias of St. Matthew); these three names cannot have been unknown to the Evangelist, nor can it be supposed that they were omitted by transcribers, for this conjecture would destroy the Evangelist's computation of fourteen kings.
According to I Paralipomenon 3:15, Joakim intervenes between Josias and Jechonias. We may waive the question whether St. Matthew speaks of only one Jechonias or of two persons bearing that name; nor need we state here all the doubts and difficulties connected with either answer.
St. Matthew places only nine links between Zorobabel and St. Joseph for a period covering some 530 years, so that each generation must have lasted more than 50 years. The genealogy as given in St. Luke enumerates eighteen generations for the same period, a number which harmonizes better with the ordinary course of events.
St. Luke's genealogy of Christ
The genealogy in Luke 3:23-28 ascends from Joseph to Adam or rather to God; this is the first striking difference between the genealogies as presented in the First and Third Gospel. Another difference is found in their collocation: St. Matthew places his list at the beginning of his Gospel; St. Luke, at the beginning of the public life of Christ.
The artificial structure of this list may be inferred from the following peculiarities: it contains eleven septenaries of names; three septenaries bring us from Jesus to the Captivity; three, from the captivity to the time of David; two, from David to Abraham; three again from the time of Abraham to the creation of man. St. Luke does not explicitly draw attention to the artificial construction of his list, but this silence does not prove that its recurring number of names was not intended, at least in the Evangelist's source. In St. Luke's genealogy, too, the names Jesse, Obed, Booz, cover a period of 366 years; Aminadab, Aram, Esron fill a gap of 430 (or 215) years, so that here several names must have been omitted. In the fourth series, which gives the names of the antediluvian and postdiluvian patriarchs, Cainan has been inserted according to the Septuagint reading; the Hebrew text does not contain this name.
Harmony between St. Matthew's and St. Luke's genealogy of Christ
The fourth series of St. Luke's list covers the period between Abraham and the creation of man; St. Matthew does not touch upon this time, so that there can be no question of any harmony. The third series of St. Luke agrees name for name with the first of St. Matthew; only the order of names is inverted. In this section the genealogies are rather identical than merely harmonious. In the first and second series, St. Luke gives David's descendants through his son Nathan, while St. Matthew enumerates in his second and third series David's descendants through Solomon. It is true that the First Gospel gives only twenty-eight names for this period, against the forty-two names of the Third Gospel; but it cannot be expected that two different lines of descendants should exhibit the same number of links for the period of a thousand years. Abstracting from the inspired character of the sources, one is disposed to regard the number given by the Third Evangelist as more in harmony with the length of time than the number of the First Gospel; but we have pointed out that St. Matthew consciously omitted a number of names in his genealogical list, in order to reduce them to the required multiple of seven.
Exceptions to the preceding explanation
Three main difficulties are advanced against the foregoing harmony of the genealogies: First, how can they converge in St. Joseph, if they give different lineages from David downward? Secondly, how can we account for their convergence in Salathiel and Zorobabel? Thirdly, what do we know about the genealogy of the Blessed Virgin?
The convergence of the two distinct genealogical lines in the person of St. Joseph, has been explained in two ways:
(a) St. Matthew's genealogy is that of St. Joseph; St. Luke's, that of the Blessed Virgin. This contention implies that St. Luke's genealogy only seemingly includes the name of Joseph. It is based on the received Greek text, on (os enomizeto ouios Ioseph) tou Heli, "being the son (as it was supposed, of Joseph, but really) of Heli". This parenthesis really eliminates the name of Joseph from St. Luke's genealogy, and makes Christ, by means of the Blessed Virgin, directly a son of Heli. This view is supported by a tradition which names the father of the Blessed Virgin "Joachim", a variant form of Eliacim or its abbreviation Eli, a variant of Heli, which latter is the form found in the Third Evangelist's genealogy. But these two consideration, viz. the received text and the traditional name of the father of Mary, which favour the view that St. Luke gives the genealogy of the Blessed Virgin, are offset by two similar considerations, which make St. Luke's list terminate with the name of Joseph. First, the Greek text preferred by the textual critics reads, on ouios, hos enomizeto, Ioseph tou Heli, "being the son, as it was supposed, of Joseph, son of Heli", so that the above parenthesis is rendered less probable. Secondly, according to Patrizi, the view that St. Luke gives the genealogy of Mary began to be advocated only towards the end of the fifteenth century by Annius of Viterbo, and acquired adherents in the sixteenth. St. Hilary mentions the opinion as adopted by many, but he himself rejects it (Mai, "Nov. Bibl, Patr.", t. I, 477). It may be safely said that patristic tradition does not regard St. Luke's list as representing the genealogy of the Blessed Virgin.
(b) Both St. Matthew and St. Luke give the genealogy of St. Joseph, the one through the lineage of Solomon, the other through that of Nathan. But how can the lines converge in St. Joseph? St. Augustine suggested that Joseph, the son of Jacob and the descendant of David through Solomon, might have been adopted by Heli, thus becoming the adoptive descendant of David through Nathan. But Augustine was the first to abandon this theory after learning the explanation offered by Julius Africanus. According to the latter, Estha married Mathan, a descendant of David through Solomon, and became the mother of Jacob; after Mathan's death she took for her second husband Mathat, a descendent of David through Nathan, and by him became the mother of Heli. Jacob and Heli were, therefore, uterine brothers. Heli married, but died without offspring; his widow, therefore, became the levirate wife of Jacob, and gave birth to Joseph, who was the carnal son of Jacob, but the legal son of Heli, thus combining in his person two lineages of David's descendants.
The second difficulty urged against the harmony between the two genealogies is based on the occurrence of the two names Zorobabel and Salathiel in both lists; here again the two distinct lineages of David's descendants appear to converge. And again, two answers are possible:
(a) It is more commonly admitted that the two names in St. Matthew's list are identical with the two in St. Luke's series; for they must have lived about the same time, and the names are so rare, that it would be strange to find them occurring at the same time, in the same order, in two different genealogical series. But two levirate marriages will explain the difficulty. Melchi, David's descendant through Nathan, may have begotten Neri by a widow of the father of Jechonias; this made Neri and Jechonias uterine brothers. Jechonias may then have contracted a levirate marriage with the widow of the childless Neri, and begotten Salathiel, who was therefore the leviratical son of Neri. Salathiel's son Zorobabel begat Abiud; but he also may have been obliged to contract a levirate marriage with the widow of a childless legal relative belonging to David's descendants through Nathan, thus begetting Reza, who legally continued Nathan's lineage.
(b) A more simple solution of the difficulty is obtained, if we do not admit that the Salathiel and Zorobabel occurring in St. Matthew's genealogy are identical with those in St. Luke's. The above proofs for their identity are not cogent. If Salathiel and Zorobabel distinguished themselves at all among the descendants of Solomon, it is not astonishing that about the same time two members of Nathan's descendants should be called after them. The reader will observe that we suggest only possible answers to the difficulty; as long as such possibilities can be pointed out, our opponents have no right to deny that the genealogies which are found in the First and Third Gospel can be harmonized.
How can Jesus Christ be called "son of David", if the Blessed Virgin is not a daughter of David?
(a) If by virtue of Joseph's marriage with Mary, Jesus could be called the son of Joseph, he can for the same reason be called "son of David" (St. Augustine, On the Harmony of the Gospels, II, i, 2).
(b) Tradition tells us that Mary too was a descendant of David. According to Numbers 36:6-12, an only daughter had to marry within her own family so as to secure the right of inheritance. After St. Justin (Adv. Tryph. 100) and St. Ignatius (Letter to the Ephesians 18), the Fathers generally agree in maintaining Mary's Davidic descent, whether they knew this from an oral tradition or inferred it from Scripture, e.g. Romans 1:3; 2 Timothy 2:8. St. John Damascene (De fid. Orth., IV, 14) states that Mary's great-grandfather, Panther, was a brother of Mathat; her grandfather, Barpanther, was Heli's cousin; and her father, Joachim, was a cousin of Joseph, Heli's levirate son. Here Mathat has been substituted for Melchi, since the text used by St. John Damascene, Julius Africanus, St. Irenæus, St. Ambrose, and St. Gregory of Nazianzus omitted the two generations separating Heli from Melchi. At any rate, tradition presents the Blessed Virgin as descending from David through Nathan.