Fundamentally, God promised Abraham two things in the Covenant of Circumcision. One promise pertained to his numerous carnal offspring. The other pertained to his single offspring, the Messiah.
The first promise of the the land was to his numerous offspring and was conditioned upon obedience to Mosaic law (Ex.19:5-8; 23:20-22; Deut 4:1; 6:3, 17-18, 24-25; 7:12; 8:1-2; 11:8, 22-24; 29:13; Jer 11:5). The Covenant of Circumcision & the Mosaic Covenant did not operate on different bases.
The 2nd promise of the blessing of the nations was only in his single offspring, Jesus (Gal 3, etc). It is conditioned upon union with Christ, which is summarily referred to as “through faith.” Abraham would be the father of the Messiah who would bless the nations by establishing the New Covenant.
Thus in Gal 3, Paul is not contrasting the Abrahamic Covenant of Circumcision with the Mosaic Covenant. He is contrasting the different Abrahamic promises, which makes much more sense of Gal 3:16. The Judaizers conflated these promises. The 1st promise was to offsprings plural and required one to be circumcised; a Jew. The 2nd promise was to offspring singular (Gen 22:17a vs 17b-18 cf Gal 3:8). Note the ESV’s translation of Gen 22:17b, as well as the commentary in the ESV Study Bible and the Reformation Study Bible (see also T.D. Alexander).
The oath falls into two parts: whereas the first half focuses on Abraham’s many descendants, the second part focuses on a single descendant who will overcome his enemies (Gen. 22:17) and mediate blessing to all the nations of the earth (v. 18). Although the second half of the oath is often taken to refer to all of Abraham’s descendants, Genesis as a whole is interested in tracing a single unique line of offspring that will eventually bring forth a special King who will rule over the Gentiles (see Introduction: History of Salvation Summary), and the reference to “his enemies” points in this direction (see note on 3:15). This is why Paul (Gal. 3:16) can insist on one offspring, who is “Christ” (i.e., the Messiah; cf. Gen. 3:15; 24:60 for “offspring as a particular descendant). And this explains why Isaac is clearly set apart from Ishmael as Abraham’s heir. From the perspective of the whole Bible, this oath to Abraham comes to fulfillment in Jesus Christ (Acts 3:25-26; Gal. 3:16).
–ESV Study Bible
22:17 the gate of his enemies. This is achieved by one of Abraham’s offspring, not all of them. This picks up on the earlier divine promise to Eve that one of her offspring would overcome the serpent. The singular reading is preferable here and fully supported by the Hb. text. As elsewhere in the Abraham narrative, an important distinction is drawn between the patriarch’s many descendants and a future descendant who will come from the unique family line that is traced through Genesis.
–Reformation Study Bible
Paul likewise builds upon this distinction between the seeds in Romans 4, identifying one with circumcision and the law, the other with faith and blessing of the nations.
This understanding of the dichotomous nature of the Covenant of Circumcision is witnessed down through church history across denominational lines.
Augustine
In the preceding book we said, that in the promise of God to Abraham two things were promised from the beginning, the one, namely, that his seed should possess the land of Canaan, which was intimated when it was said, “Go into a land that I will show thee, and I will make of thee a great nation;” (Gen 12:1-2) but the other far more excellent, concerning not the carnal but the spiritual seed, by which he is the father, not of the one nation of Israel, but of all nations who follow the footsteps of his faith, which began to be promised in these words, “And in thee shall all families of the earth be blessed.” (Gen 12:3) And thereafter we showed by yet many other proofs that these two things were promised. Therefore the seed of Abraham, that is, the people of Israel according to the flesh, already was in the land of promise; and there, not only by holding and possessing the cities of the enemies, but also by having kings, had already begun to reign, the promises of God concerning that people being already in great part fulfilled: not only those that were made to those three fathers, Abraham, Isaac, and Jacob, and whatever others were made in their times, but those also that were made through Moses himself, by whom the same people was set free from servitude in Egypt, and by whom all bygone things were revealed in his times, when he led the people through the wilderness. But neither by the illustrious leader Jesus the son of Nun, who led that people into the land of promise, and, after driving out the nations, divided it among the twelve tribes according to God’s command, and died; nor after him, in the whole time of the judges, was the promise of God concerning the land of Canaan fulfilled, that it should extend from some river of Egypt even to the great river Euphrates; nor yet was it still prophesied as to come, but its fulfillment was expected. And it was fulfilled through David, and Solomon his son, whose kingdom was extended over the whole promised space; for they subdued all those nations, and made them tributary. And thus, under those kings, the seed of Abraham was established in the land of promise according to the flesh, that is, in the land of Canaan, so that nothing yet remained to the complete fulfillment of that earthly promise of God, except that, so far as pertains to temporal prosperity, the Hebrew nation should remain in the same land by the succession of posterity in an unshaken state even to the end of this mortal age, if it obeyed the laws of the Lord its God. But since God knew it would not do this, He used His temporal punishments also for training His few faithful ones in it, and for giving needful warning to those who should afterwards be in all nations, in whom the other promise, revealed in the New Testament, was about to be fulfilled through the incarnation of Christ.
City of God Book XVI: The history of the city of God from Noah to the time of the kings of Israel.
Chapter 2.—At What Time the Promise of God Was Fulfilled Concerning the Land of Canaan, Which Even Carnal Israel Got in Possession.
Martin Chemnitz
[T]he covenant which God entered with Abraham contained two parts. The first was the promise of the increase of his posterity, of a definite dwelling place, and a certain realm for the people; likewise it dealt with the protection and preservation and blessing of the realm and the posterity. The second part, which came later and was added to the first part, was the promise of the spiritual blessing in the blessed Seed, Christ.
-Martin Chemnitz, co-author of the Formula of Concord (see more extended quotes here)
John Owen
the Jews of old managed a plea in their own justification against the doctrine of the Lord Christ and his apostles. “We are the children, the seed of Abraham,” was their continual cry; on the account whereof they presumed that all the promises belonged unto them, and upon the matter unto them alone. And this their persuasion hath cast them, as we shall see, upon a woful and fatal mistake. Two privileges did God grant unto Abraham, upon his separation to a special interest in the old promise and covenant: —
First, That according to the flesh he should be the father of the Messiah, the promised seed; who was the very life of the covenant, the fountain and cause of all the blessings contained in it. That this privilege was temporary, having a limited season, time, and end, appointed unto it, the very nature of the thing itself doth demonstrate; for upon this actual exhibition in the flesh, it was to cease. In pursuit hereof were his posterity separated from the rest of the world, and preserved a peculiar people, that through them the promised Seed might be brought forth in the fullness of time, and be of them according unto the flesh, Romans 9:5.
Secondly, Together with this, he had also another privilege granted unto him, namely, that his faith, whereby he was personally interested in the covenant, should be the pattern of the faith of the church in all generations; and that none should ever come to be a member of it, or a sharer in its blessings, but by the same faith that he had fixed on the Seed that was in the promise, to be brought forth from him into the world. On the account of this privilege, he became the father of all them that do believe: for “they which are of faith, the same are the children of Abraham,” Galatians 3:7, Romans 4:11: as also “heir of the world,” Romans 4:13, in that all that should believe throughout the world, being thereby implanted into the covenant made with him, should become his “spiritual children.”
4. Answerably unto this twofold end of the separation of Abraham, there was a double seed allotted unto him; — a seed according to the flesh, separated to the bringing forth of the Messiah according unto the flesh; and a seed according to the promise, that is, such as by faith should have interest in the promise, or all the elect of God…
5... It is true, they were the children of Abraham according to the flesh: but on that account they can have no other privilege than Abraham had in the flesh himself; and this was, as we have showed, that he should he set apart as a special channel, through whose loins God would derive the promised Seed into the world. In like manner were they separated to be a peculiar people, as his posterity, from amongst whom He should be so brought forth.
That this separation and privilege was to cease when the end of it was accomplished and the Messiah exhibited, the very nature of the thing declares; for to what purpose should it be continued when that was fully effected whereunto it was designed? But they would extend this privilege, and mix it with the other, contending that, because they were the children of Abraham according to the flesh, the whole blessing and covenant of Abraham belonged unto them… Seeing, therefore, that their other privilege was come to an end, with all the carnal ordinances that attended it, by the actual coming of the Messiah, whereunto they were subservient, if they did not, by faith in the promised seed, attain an interest in this of the spiritual blessing, it is evident that they could on no account be considered as actual sharers in the covenant of God.
6... It is true, the former carnal privilege of Abraham and his posterity expiring, on the grounds before mentioned, the ordinances of worship which were suited thereunto did necessarily cease also. And this cast the Jews into great perplexities, and proved the last trial that God made of them; for whereas both these, — namely, the carnal and spiritual privileges of Abraham’s covenant, — had been carried on together in a mixed way for many generations, coming now to be separated, and a trial to be made (Malachi 3) who of the Jews had interest in both, who in one only, those who had only the carnal privilege, of being children of Abraham according to the flesh, contended for a share on that single account in the other also, — that is, in all the promises annexed unto the covenant. But the foundation of their plea was taken away, and the church, unto which the promises belong, remained with them that were heirs of Abraham’s faith only.
Exposition of Hebrews, Exercitation 6
John Brown
The word “seed” is a word of ambiguous meaning. It may rather signify descendants generally, or one class of descendants, or a single descendant. The apostle in the concluding part of the verse tells us how it is to be understood in the passage he alludes to. “He saith not, And to seeds, as of many; but as of one, And to thy Seed, which is Christ.’”
These words have very generally been understood as if they embodied an argument, — as if the apostle reasoned from the word “seed” being in the singular, inferring from that circumstance either that the word referred to one class of descendants, and not to descendants of all classes, or to one individual descendant, and not to descendants generally. That this is not the apostle’s reasoning we apprehend is certain; for it is obviously inconclusive reasoning. The use of the plural term might have laid a foundation for the inference that he spake of more than one; but seed being a collective word, its use in the singular lays no foundation for an opposite inference. Even supposing that his Jewish readers might have been imposed on by such a sophism, which is not at all probable, it would not only have been unworthy of his dignity as an apostle, but of his integrity as an honest man, to have used it.
The truth is, there is no ground to suppose that it is the statement of an argument at all. It is just as Riccaltoun observes, “a critical, explicatory remark.” It is just as if he had said, ‘In the passage I refer to, the word seed is used of an individual, just as when it is employed of Seth, Gen. iv. 25, where he is called “another seed,” and said to be given in the room of Abel, whom Cain slew. In looking carefully at the promise recorded, Gen. xxii. 16-18, the phrase “seed” seems used with a different reference in the two parts of the promise — the first part of the 17th verse plainly referring to a class of descendants; the last clause and the 18th verse to an individual, and that individual is Christ.’ There is no doubt that this is the fact — that in the promise, “In thy Seed shall all the families of the earth be blessed,” the reference is not to the descendants of Abraham generally, nor to his descendants by Isaac, nor to his spiritual descendants, but to bis great descendant, the Messiah.
Commentary on Galatians 3:16-17
Turretin
[T]he words epangelias and euangeliou also often occur to designate the covenant of grace. First, it si called epangelia (or “promise”) indeed by way of eminence (kat’ exochen); not only because it is of God and not of men, but also because it is the most excellent of all, as being alone saving. Thus it is distinguished from the promise given to Abraham concerning his fleshly seed in Isaac (Rom. 9:9; Gal 4:23) and concerning the inheritance of the land of Canaan (on that account called “the land of promise,” Heb. 11:9) and from all the other earthly promises given to the Israelite people… It peculiarly denotes the gospel promise concerning the Messiah and the spiritual and eternal benefits to be bestowed by him.
Institutes II.XII.X
Charles Hodge
It is to be remembered that there were two covenants made with Abraham. By the one, his natural descendants through Isaac were constituted a commonwealth, an external, visible community. By the other, his spiritual descendants were constituted a Church. The parties to the former covenant were God and the nation; to the other, God and his true people. The promises of the national covenant were national blessings; the promises of the spiritual covenant, (i.e. of the covenant of grace) were spiritual blessings, reconciliation, holiness, and eternal life. The conditions of the one covenant were circumcision and obedience to the law; the condition of the latter was, is, and ever has been, faith in the Messiah as the seed of the woman, the Son of God, and the Savior of the world. There cannot be a greater mistake than to confound the national covenant with the covenant of grace, and the commonwealth founded on the one with the Church founded on the other.
When Christ came “the commonwealth” was abolished, and there was nothing put in its place. The Church remained. There was no external covenant, nor promises of external blessings, on condition of external rites and subjection. There was a spiritual society with spiritual promises, on the condition of faith in Christ. In no part of the New Testament is any other condition of membership in the Church prescribed than that contained in the answer of Philip to the eunuch who desired baptism: “If thou believest with all thine heart, thou mayest. And he answered and said, I believe that Jesus Christ is the Son of God.” (Acts viii. 37)
Note: I believe Hodge is mistaken in saying there were two Abrahamic Covenants. There was only one: the Covenant of Circumcision. Though he is correct to distinguish between the seeds and the promises.
Note also: R. Scott Clark positively quoted this statement from Hodge to explain his own view in a 2007 series on republication.
T. David Gordon
Paul understood the covenant with Abraham to include essentially three promises: That God would give Abraham numerous descendants (“seed”), that God would give Abraham (and his seed) the land of Canaan, and that God would bless all the nations of the world through Abraham and his seed. Plainly enough, the Israelites became numerous during their four hundred years in Egypt, and equally plainly, through Joshua and the judges, they inherited the land of Canaan. But they did not become the means by which all the nations/Gentiles were blessed until the calling of Paul…
[T]he “Seed” would come through whom the promise would be fulfilled and the nations would be blessed (3:19). Paul identified the “Seed” as Christ (3:16), and argued that the nations are indeed now being blessed by that Seed of Abraham, and that therefore, the temporary covenant made only with Abraham’s descendants must become obsolete and disappear…
[O]ne might argue that Paul perceived the New Covenant realities in Christ as bringing the final third of the Abrahamic promise to fruition.
Abraham and Sinai Contrasted
Conclusion
In light of the above, reformed paedobaptists make two mistakes. First, they collapse the dichotomous Abrahamic Covenant of Circumcision into one by conflating the promises and the seeds, arguing that salvation in Christ was promised to the carnal offspring. Second, they put themselves in Abraham’s place. Rather than recognizing that the promises were made to/concerning Abraham and his offspring, they claim the promises were made to them and their offspring. The Abrahamic promises were not made to “believers and their seed,” but to Abraham and his seeds.
Contrast 