It's been a while since I've read biblical and covenant theology. It's hard for me to synthesize them with philosophical and systematic theology. J. V. Fesko has said that biblical theology is to building as systematic theology is to building inspector. That's the best way I can understand how they relate.
Anyways, a friend and I were discussing covenant theology recently, particularly whether or not the Mosaic covenant was an administration of the covenant of grace to individual Israelites and/or a typological republication of the covenant of works for corporate Israel. My friend thought that Galatians 4:24 was a direct reference to the covenant of works and that the reference to Mt. Sinai was to the eternal moral law of God (which always ought to be obeyed) rather than a synecdoche the Mosaic covenant, but I think I've convinced him that Galatians 3-4:20 sets the context for 4:21-31 to be understood as contrasting the Mosaic covenant with the covenant of grace. This would have interesting implications as to how we understand the purpose for which the Mosaic covenant was given. I was a little rusty while discussing this, so hopefully I can put some of my thoughts in order here.
The covenant of grace, while the same in essence throughout redemptive history, has been administered differently. As the Westminster Larger Catechism puts it:
Question 34: How was the covenant of grace administered under the Old Testament?
Answer: The covenant of grace was administered under the Old Testament, by promises, prophecies, sacrifices, circumcision, the passover, and other types and ordinances, which did all foresignify Christ then to come, and were for that time sufficient to build up the elect in faith in the promised Messiah, by whom they then had full remission of sin, and eternal salvation.
Question 35: How is the covenant of grace administered under the New Testament?
Answer: Under the New Testament, when Christ the substance was exhibited, the same covenant of grace was and still is to be administered in the preaching of the Word, and the administration of the sacraments of Baptism and the Lord's Supper; in which grace and salvation are held forth in more fulness, evidence, and efficacy, to all nations.
When the question is posed as to whether or not the Mosaic covenant falls under the rubric of the covenant of grace as administered in the Old Testament, in comparing the above exposition to Exodus 19:5-6, the answer appears to be negative. The purpose, rather, is to typologically revive the covenant of works.
Now, I have not committed myself to believing that the Mosaic covenant was a covenant merely superimposed onto the administrative history of the covenant of grace, for there are elements in it - especially the ritual laws which were fulfilled by Christ - which seem to indicate otherwise. But perhaps these only served to demonstrate that the covenant of grace was administered under the Mosaic covenant although not by it, since the Mosaic covenant was established upon but did not abrogate the Abrahamic.
If the essence of the Mosaic covenant is Exodus 19:5-6, then it would seem that the Mosaic covenant was with the nation of Israel rather than individual Israelites per se and typified the covenant of works, at least to the extent that such was possible for a collection of sinners. Adam, Israel, and Jesus are all uniquely connected to this covenant. Adam had Eden, Israel had the promised land of Canaan, and Christ has the promised land of new Eden. The former sons of God failed to meet the demands of the covenant of works, though there existence establishes a pattern which helps us to understand Christ's work. In the case of Israel especially, it was impossible for them to actually fulfill the covenant of works:
Even though they were not able to keep this law in the Pauline, spiritual sense, yea, even though they were unable to keep it externally and ritually, the requirement could not be lowered. When apostacy on a general scale took place, they could not remain in the promised land. When they disqualified themselves for typifying the state of holiness, they ipso facto disqualified themselves for typifying that of blessedness, and had to go into captivity. This did not mean that every individual Israelite, in every detail of his life, had to be perfect, and that on this was suspended the continuance of God's favor. Jehovah dealt primarily with the nation and through the nation with the individual, as even now in the covenant of grace He deals with believers and their children in the continuity of generations. - Geerhardus Vos, Biblical Theology pgs. 127-128
The point of "apostasy on a general scale" occurred when the nation as such acted in a sufficiently dissimilar manner to that which was necessary in order for there to be a recognizable connection to the obedience of one who actually rather than merely typologically attempted to fulfill of the covenant of works.
But strictly speaking, every Israelite was a sinner, so each broke this first covenant to which Paul refers in Galatians 4:24. So perhaps the Judaizers in Galatians 4 misunderstand the purpose of the Mosaic covenant by attempting to individualize its promises on the condition of general obedience. Or perhaps insofar as the Mosaic covenant typologically recapitulates the covenant of works, it would be more safe to say they understood its demands applied to themselves (which is true regarding the moral law) but misunderstood their own inability to meet its demands. In this case, they still misunderstood the purpose of the laws of the Mosaic covenant to be a means of salvation rather than a "tutor."
So I suppose all of this means I lean more toward a more Owenian (link) understanding of the Mosaic covenant, although Witsius' position could be arguable as well (cf. pgs. 35-39 here). Fesko's coming out with a new commentary on Galatians this month, so I'm looking forward to reading what more he has to say about this topic.