The Catholic / patristic tradition regarding Mother of God or Theotokos ("God-Bearer") take s a little bit of thought, but it's not rocket science. Let's run through a quick version of the rationale:
Luke 1:43 (RSV) And why is this granted me, that the mother of my Lord (kurios) should come to me?
John 20:28 Thomas answered him, “My Lord (kurios) and my God (theos)!”
“Lord (kurios) God (theos)”: Lk 1:6, 32, 68; 4:8, 12; 10:27; 20:37.
Therefore, “Lord (kurios) equals God (theos).
Jesus is called both in John 20:28.
Mary is mother of the Lord (Lk 1:43).
Therefore, she is the mother of God, since Lord=God.
Moreover, we don’t say of mothers that they are the mother of their child’s body, but of the child, and the child has a body and a soul. They didn’t create the soul; God did.
Likewise, with Jesus, Mary was the mother of Jesus, Who is God the Son. Thus, she is the Mother of God. It’s wrong and even illogical to say she was the mother of His body. No; she was the mother of the Divine Person, Jesus, Who had a human nature and also a Divine Nature (that she had nothing to do with). But she is still the mother of the Person, regardless of that, as any mother is the mother of a person who has a soul directly created by God.
Most of the early Protestant leaders understood this and retained the terminology, but John Calvin (the one most influential on later Protestantism) did not. He gives his reasoning in a letter of 27 September 1552 to the French Church in London:
. . . to deal with you with brotherly frankness, I cannot conceal that that title being commonly attributed to the Virgin in sermons is disapproved, and, for my own part I cannot think such language either right, or becoming, or suitable. Neither will any sober-minded people do so, for which reason I cannot persuade myself that there is any such usage in your church, for it is just as if you were to speak of the blood, of the head, and of the death of God. You know that the Scriptures accustom us to a different style; but there is something still worse about this particular instance, for to call the Virgin Mary the mother of God, can only serve to confirm the ignorant in their superstitions. And he that would take a pleasure in that, shews clearly that he knows not what it is to edify the Church.
Just before this, he admitted that some of the objection (among Protestants) wasn't justified, and based in a degree of ignorance:
. . . I doubt not but there may have been somewhat of ignorance in their reproving the way of speaking of the Virgin Mary as the mother of God, and together with ignorance, it is possible that there may have been rashness and too much forwardness, for, as the old proverb says, The most ignorant are ever the boldest.
Ironically, however, it is Calvin himself who shows some degree of ignorance, as to the history of the term (which he knew full well, as a student of the Church fathers and early Church, was used to counter the heresy of Nestorianism). He himself explains it in a way that is perfectly in accord with the Catholic and Orthodox understanding:
She [Elizabeth] calls Mary the mother of her Lord This denotes a unity of person in the two natures of Christ; as if she had said, that he who was begotten a mortal man in the womb of Mary is, at the same time, the eternal God. For we must bear in mind, that she does not speak like an ordinary woman at her own suggestion, but merely utters what was dictated by the Holy Spirit. This name Lord strictly belongs to the Son of God “manifested in the flesh,” (1 Timothy 3:16,) who has received from the Father all power, and has been appointed the highest ruler of heaven and earth, that by his agency God may govern all things. Still, he is in a peculiar manner the Lord of believers, who yield willingly and cheerfully to his authority; for it is only of “his body” that he is “the head,” (Ephesians 1:22, 23.) And so Paul says, “though there be lords many, yet to us,” that is, to the servants of faith, “there is one Lord,” (1 Corinthians 8:5, 6.) By mentioning the sudden movement of the babe which she carried in her womb, (ver. 44,) as heightening that divine favor of which she is speaking, she unquestionably intended to affirm that she felt something supernatural and divine.
(Harmony of the Synoptic Gospels, comment under Luke 1:43; Calvini Opera, ibid., vol. 45, 35)
Simple deductive reasoning . . . Thus, in my opinion, he really has no excuse for his objection. There are only so many grounds to object to Mother of God:
1) If one believes that Jesus isn't God, Mother of God wouldn't apply to His mother. This is not true of Calvin, because, as we plainly see above and in many other of his statements, he holds to the divinity of deity or Godhood of Jesus Christ: God the Son: the second Person of the Holy Trinity.
2) "God" can only refer to the Father and not to Jesus (a variation of #1, thus not applicable to Calvin, either).
3) One can believe that Mary is only the mother of Jesus' human nature, not of a Divine Person with Two natures (divine and human). This is the heresy of Nestorianism. Calvin would seem to deny it also in the above comment, though some sections of other of his writings smack of it: at least in some respects.
4) Lastly, an objection can be made that derives from the fear or concern of it being misunderstood. This is Calvin's rationale. I think it fails, though, because Christianity is the sort of thing that has many elements that people can easily misunderstand or not comprehend correctly in the first place. The Holy Trinity is the most obvious example of that. We don't stop using the term "Trinity" because ignorant people will misunderstand it as three gods or a "three-headed god" (as the Jehovah's Witnesses mock it). Calvin certainly doesn't do so. We don't avoid using the term Hypostatic Union of the Two Natures of Christ, because it is a difficult notion and not all that easy to fully grasp.
Yet when it comes to Mother of God, Calvin changes his mind and advocates the cessation of its use, even though it is perfectly legitimate in and of itself, and he himself understands it to be so.
Furthermore, some of the reasoning he brings to bear for why he thinks so, is immediately suspect. He claims that Mother of God isn't "right, or becoming, or suitable," so that "sober-minded people" should avoid it. And why is that? He provides some reasoning for his assertion: bringing Holy Scripture into it: "for it is just as if you were to speak of the blood, of the head, and of the death of God."
Alright; let's examine this for a moment. Is it completely true? It's correct (as far as I know; I'm pretty sure) that the Bible doesn't refer directly to the "death of God." Yet Jesus is God and Jesus died. It follows the God (the Son) died. It's just one Person of the Trinity, but He did die and He was God. The reasoning is similar to Mother of God.
Scripture also refers to the "head" of God only in non-literal or metaphorical ways: either anthropomorphically or relationally, such as in 1 Corinthians 11:3: "the head of Christ is God." God the Father is a spirit. But that is not, almost certainly, what Calvin was referring to. The place where Calvin stumbles badly in providing biblical disanalogies to Mother of God is in his reference to God's blood: as if that is an unbiblical usage. In fact, it certainly is, as I immediately recalled, from some of my own past apologetics work.
I've found 15 major translations of Acts 20:28 that refer precisely to the "blood" as referring to God the Father. Now, God the Father doesn't have a mother, as Jesus has (nor does the Holy Spirit). Yet, Mother of God was used in Church history, as referring to Jesus alone. Mary bore God, because Jesus was God. It doesn't mean she is greater than God or a second God, because it refers only to the Incarnation. Mary was a creature. Catholics know this, but many Protestants casually think we are too dumb and stupid to comprehend these simple things (which is a large part of the problem). And Calvin thinks many Protestants will be too dumb to grasp it, too, so he thinks it is better to avoid using Mother of God altogether.
Yet, by analogy, if the Bible refers to God's blood (also, in context -- quite remarkably -- , the Holy Spirit's "blood"), when this is not literally true, why can't we use Mother of God, when that is definitely true of one Person of the Godhead? Here is the passage:
NIV Keep watch over yourselves and all the flock of which the Holy Spirit has made you overseers. Be shepherds of the church of God, which he bought with his own blood.
KJV . . . feed the church of God, which he hath purchased with his own blood.
NKJV / NASB . . . the church of God which He purchased with His own blood.
ASV / Moffatt the church of the Lord which he purchased with his own blood.
Phillips . . . at the cost of his own blood.
Jerusalem . . . bought with his own blood.
NEB / REB. . . by his own blood.
Williams / Beck . . . He bought with His own blood.
Amplified . . . with his own blood.
Wuest . . . which He bought for himself through the agency of the blood, the blood which is Hiw own unique blood, possessed by himself alone.
Goodspeed . . . church of God which he got at the cost of his own life.
Goodspeed actually expresses directly the "death of God" or "God died" by referring to the "cost of his own life": referring to God as the subject in the same sentence. The only major exceptions I found were RSV / NRSV ("blood of his own Son") and Barclay ("blood of his own One"). 15 out of 18 translations (or, 83% of them) thus refer to the "blood" of God the Father (even though He literally doesn't have blood. So, what's the problem with Mother of God? There is none: not scripturally speaking. Calvin is all wet. His argument fails; it falls flat.
This also recalls to my mind, Zechariah 12:10, in which God says, "they shall look upon me whom they have pierced" (KJV; cf. NASB, NIV, ASV, etc.). It's God the Son Who was pierced, but here it is referred to the Father as well, which in turn recalls Jesus' language of "he who has seen me has seen the father" (Jn 14:9).
As usual, then, the arguments against Catholic tradition (biblical or otherwise) do not succeed.
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