There is, indeed no ambiguity in the words here used by Moses; but I do not agree with others respecting their meaning; for other interpreters take the seed for Christ, without controversy; as if it were said, that some one would arise from the seed of the woman who should wound the serpent’s head. Gladly would I give my suffrage in support of their opinion, but that I regard the word seed as too violently distorted by them; for who will concede that a collective noun is to be understood of one man only? Further, as the perpetuity of the contest is noted, so victory is promised to the human race through a continual succession of ages. I explain, therefore, the seed to mean the posterity of the woman generally. But since experience teaches that not all the sons of Adam by far, arise as conquerors of the devil, we must necessarily come to one head, that we may find to whom the victory belongs. So Paul, from the seed of Abraham, leads us to Christ; because many were degenerate sons, and a considerable part adulterous, through infidelity; whence it follows that the unity of the body flows from the head. Wherefore, the sense will be (in my judgment) that the human race, which Satan was endeavoring to oppress, would at length be victorious. In the meantime, we must keep in mind that method of conquering which the Scripture describes. Satan has, in all ages, led the sons of men “captive at his will”, and, to this day, retains his lamentable triumph over them, and for that reason is called the prince of the world, (John 12:31.) But because one stronger than he has descended from heaven, who will subdue him, hence it comes to pass that, in the same manner, the whole Church of God, under its Head, will gloriously exult over him. To this the declaration of Paul refers,
By which words he signifies that the power of bruising Satan is imparted to faithful men, and thus the blessing is the common property of the whole Church; but he, at the same time, admonishes us, that it only has its commencement in this world; because God crowns none but well-tried wrestlers.
John Calvin, from his commentary on Genesis 3:15