The course of thought is as follows. The main point is that the promises to Abraham continue to hold for Christian believers (Gal 3:17). It might be objected that the law made these promises void. After stating that a human covenant is not invalidated or added to by any one, he would argue from this analogy that a covenant of God is not annulled by the law which came afterwards. But before reaching this point, he must call attention to the fact that the promises were given, not to Abraham only, but to his descendants. Hence it follows that the covenant was not a mere temporary contract, made to last only up to the time of the law. Even a man's covenant remains uncancelled and without additions. Similarly, God's covenant-promises to Abraham remain valid; and this is made certain by the fact that the promises were given not only to Abraham but to his seed; and since the singular, seed, is used, and not seeds, it is evident that Christ is meant.
The promises (αἱ ἐπαγγελίαι)
Comp. Rom 9:4. The promise was given on several occasions.
Were made (ἐρρέθησαν)
Rend. were spoken.
To his seed (τῷ σπέρματι αὐτοῦ)
Emphatic, as making for his conclusion in Gal 3:17. There can be no disannulling by the law of a promise made not only to Abraham, but to his seed.
Not - to seeds (οὐ - τοῖς σπέρμασιν)
He means that there is significance in the singular form of expression, as pointing to the fact that one descendant (seed) is intended - Christ. With regard to this line of argument it is to be said, 1. The original promise referred to the posterity of Abraham generally, and therefore applies to Christ individually only as representing these: as gathering up into one all who should be incorporated with him. 2. The original word for seed in the O.T., wherever it means progeny, is used in the singular, whether the progeny consists of one or many. In the plural it means grains of seed, as 1Sa 8:15. It is evident that Paul's argument at this point betrays traces of his rabbinical education (see Schoettgen, Horae Hebraicae, Vol. I., page 736), and can have no logical force for nineteenth century readers. Even Luther says: “Zum stiche zu schwach.”
Of many (ἐπὶ πολλῶν)
Apparently a unique instance of the use of ἐπὶ with the genitive after a verb of speaking. The sense appears in the familiar phrase “to speak upon a subject,” many being conceived as the basis on which the speaking rests. Similarly ἐφ' ἑνός of one.