Paul's method of interpretation in Galatians 4:21-31 seems a bit unusual as compared to most modern methods. He says these things may be "interpreted allegorically." What is his method of exegesis? How, for example, does he connect Hagar to Mount Sinai in Arabia?
Good question. There are many fascinating aspects of Paul's hermeneutic that come to the fore here, and we need to do some digging to recognize the source of the connections which he makes.
Martin Luther gives a good explanation in his Commentary on Galatians:
Basically the faith in God's promise of a Messiah, that ancient promise to reverse the sin and 'curse' of Adam and Eve was bound up in in symbol, type, metaphor, in Isaac and God's 'blessing' through that seed. The idea Paul uses in 'exegesis' is that patterns and themes of the Old Testament were prophetic, predicting future realities. The reality of his day is that Jews born of Abraham were rejecting the freedom of Jews converted to God by faith in Christ. These Jews no longer had to carry the burden of so many ceremonial rules and the Jews without faith (associated to the slave woman) persecuted the Jewish Christians and tried to bring them down. Hagar was tying to get power over Sarah by making her son the firstborn over Isaac. The firstborn had double rights of inheritance. Sarah argued with her husband because the promise was from her womb so they decided the only way to have peace was cast out the salve family. In the same way Jewish Christians were to cast out those laws and jealous judgments that the legalistic Jews who had no faith in the promised seed, Christ.
So Paul's method is accurate and convincing, helping the new Jewish believers at that time.
I will try to answer your first question, What is his method of exegesis?
If we figure that the Apostle Paul was "educated at the feet of Gamaliel" about Jewish religious law Acts 23:3. He had to use the the Jewish traditions of interpretation· and exegesis that were used at the time, a very common is the Pardes, an acronym formed from the name initials of the following four approaches:
I suggest Paul is using the second level of interpretation: Remez(allegoric)
Why pardes? because it was a basic method of the time of Paul and his school (Hillel, Gamaliel), ignore the traditions of interpretation· and exegesis that were used at the time, is to miss a very important tool for understanding the Word of God. Apostle Paul used a lot of references from Rabbinic traditions
The context is the most important clue to Paul’s line of thinking. He has been telling the Galatians that to turn back to the Law after being set free of it through the grace of Christ is foolish. If the righteous live by faith, those that rely on the law are under condemnation, because man cannot be justified by the law.
With that background, his thinking is more clear. When Paul says, “Now this may be interpreted allegorically: these women are two covenants,” he is setting up Sarah as the new covenant in Christ, and Hagar as the old covenant of the Law. As a result, their sons are compared to the fruits of each covenant.
Ishmael, the literal son of a slave, is a slave to the covenant of the Law. The comparison of Hagar to Sinai firmly roots this metaphor, as Sinai is the location where Moses received the Law.
Isaac (v. 28), however, is a child of promise, of the covenant of Christ and has the promise of grace upon him.
Essentially Paul’s working thesis boils down to this: Ishmael is a slave to the law which cannot justify him, and Isaac is the son of the promise of justification by faith in Christ which will save. Paul hopes to encourage the Galatians to see the law as bondage, and faith as freedom.
Dockery, David S. "The Pauline Letters". Holman Concise Bible Commentary: Simple, Straightforward Commentary on Every Book of the Bible. Ed. David S. Dockery. Nashville, TN: Broadman & Holman Publishers, 1998.
Paul is interpreting the voice of the judge from the four voices (Prophet, Priest, King, Judge) contained in the OT allegory. He is deriving it's meaning from the text rather than imposing his own meaning upon it. However, he is imposing what he knows of Christ and the gospel upon it as he understands that they are shadows 'of the good things coming' (He 10.1) and can now be properly interpreted in light of Christ. This imposition is not 'forced'. It is validated by the text itself. Paul's allegory is not complete, but merely an example of the method used, by which we can see more details of the allegory.
Gal 4.19 ¶ My little children, of whom I travail in birth again until Christ be formed in you,
My little children – Paul sets the stage for the allegory he will present. The Galatians are his children under the promise in the same manner that Ishamel was a child of the law, and Isaac was a child of the promise.
20 I desire to be present with you now, and to change my voice; for I stand in doubt of you.
change my voice – perhaps refering to taking the tone and sense of the judge.
21 ¶ Tell me, ye that desire to be under the law, do ye not hear the law?
hear the law – the law is a reference to the first five books, or to the full collection of scripture from the OT. Since Paul will include references to Isaiah, he is using the latter.
22 For it is written, that Abraham had two sons, the one by a bondmaid, the other by a freewoman.
one by a bondmaid, the other by a freewoman - Although we might dismiss this as a repetition of fact, I cannot find a reference to Sarah as a freewoman, so Paul has already started the interpretation. Her name means 'noblewoman' which is obvious to Jewish children. He is comparing the state of the two women without naming them. Hagar is known to be the handmaid, and by the interpretation of her name and by her actual status, Sarah is the 'noblewoman' or 'freewoman'.
23 But he who was of the bondwoman was born after the flesh; but he of the freewoman was by promise.
but he of the bondwoman - Ishmael composed of ee – he, shama – harken/obey, el – God . By virtual of his name, he represents the law of God which must be obeyed. By this Paul associated Ishamel with the law.
born of the flesh – Paul has extensively used the Christian dualism of flesh and spirit elsewhere. Ishamael was born of the contrivances of Sarai and Abram in contrast to Isaac who was born by the promise (or the spirit) of God.
24 Which things are an allegory: for these are the two covenants; the one from the mount Sinai, which gendereth to bondage, which is Agar.
from Mt Sanai - Ishmael was born under the covenant of Mt Sanai, specifically the Leverite marriage De 25.5-6.
gendereth (begets) to bondage – The Leverite marriage is commanded and disgrace is given to those who don't perform their duty.De 25.9-10
25 For this Agar is mount Sinai in Arabia, and answereth to Jerusalem which now is, and is in bondage with her children.
Agar - the subroot GR meaning sojourn gives her name the meaning she sojourns which is given in dictionaries as flight. A sojourner is one who does not belong here. It is a temporary state. And as in the NT, we a sojourners are in the flesh.
mount Sinai - thorny interpreted by Jesus's parable of the sower validates that cares of the world ensnare the flesh.
Arabia – mixed, desert The meaning of the word confirms the allegory of desolation by the flesh.
I will come back to do the rest when I can. Paul also uses a quote 'out of context' from Isaiah because the Hebrew perspective is that there is only one author and one context.
This can be done from Genesis, but it is a very long story which has a second narrative behind it. From that angle, Paul's hermeneutic is easy to see.
Also see the blessing of Ishmael: Ge 27:40 And by thy sword shalt thou live, and shalt serve thy brother; and it shall come to pass when thou shalt have the dominion, that thou shalt break his yoke from off thy neck.
When Ishamel (law) has dominion, there is no grace. (The yoke of Christ is broken "My yoke is light")