"1) OBJECTION: The Saviour was not crucified for the redemption of the entire world.
ANSWER: There is not one among men whose nature was not taken by Christ our Lord, though He was born in the likeness of sinful flesh only, while every other man is born in sinful flesh. Thus, the Son of God, who was God Himself, becoming partaker of our mortal nature without partaking in its sin, granted to sinful and mortal men the grace that those who by regeneration would share in His nativity could be freed from the bonds of sin and death. Accordingly, just as it is not enough that Jesus Christ was born for men to be renewed, but they must be reborn in Him through the same Spirit from whom He was born, so also it is not enough that Christ our Lord was crucified for men to be redeemed, but they must die with Him and be buried with Him in baptism. If that were not so, then after our Saviour was born in the flesh of our own nature and crucified for us all, there would be no need for us to be reborn and to be planted together in the likeness of His death. But because no man attains to eternal life without the sacrament of baptism, one who is not crucified in Christ cannot be saved by the cross of Christ; and he who is not a member of the Body of Christ is not crucified in Christ. And he is not a member of the Body of Christ who does not put on Christ through water and the Holy Spirit. For Christ in the weakness of our flesh underwent the common lot of death, that we by virtue of His death be made partakers of His resurrection. Accordingly, though it is right to say that the Saviour was crucified for the redemption of the entire world, because He truly took our human nature and because all men were lost in the first man, yet it may also be said that He was crucified only for those who were to profit by His death. For St. John the Evangelist says: Jesus should die for the nation and not only for the nation, but to gather together in one the children of God that were dispersed. He came into His own, and His own received Him not. But as many as received Him, He gave the power to be made sons of God, to them who are born not of blood, nor of the will of the flesh, nor of the will of man, but of God. Their condition, therefore, is different from that of men counted among those of whom he said: The world knew Him not. In that sense we may say: the Redeemer of the world shed His blood for the world, and the world refused to be redeemed, because the darkness did not comprehend the light. Yet, there was a darkness which did comprehend the light, that, namely, of which the Apostle says: You were heretofore darkness, but now light in the Lord. The Lord Jesus Himself, who said He came to seek and to save that which was lost, also says: I did not come but to the sheep that are lost of the house of Israel. And St. Paul explains who are those sheep of the house of Israel: For all are not Israelites that are of Israel, neither are all they that are the seed of Abraham children; but in Isaac shall thy seed be called. That is to say, not they that are the children of the flesh are the children of God, but they that are the children of the promise are accounted for the seed. Among them are counted those to whom refers what we quoted above: Jesus should die for the nation, and not only for the nation, but to gather in one the children of God that were dispersed. It is not only from among the Jews but also from the Gentiles that the sons of God, the sons of the promise, are gathered into the one Church by Him who calleth those things that are not, as those that are, and who gathereth together the dispersed of Israel, in order to fulfil the promise of God to Abraham, that in his seed all the tribes of the earth would be blessed."
Prosper of Aquitaine: Defense of St. Augustine, trans., by P. De letter, (New York: Newman Press, 1963), pp 149-151.
"2) QUALIFICATION ARTICLE 9 : Likewise, he who says that the Saviour was not crucified for the redemption of the entire world does not take into account the power of the mystery of the cross, but considers only the portion of mankind who have no faith.
For it is certain that the blood of our Lord Jesus Christ is the price for the redemption of the entire world. But they do not share in the application of this price who either cherishing their captivity refused to be liberated or having been liberated returned to their captivity. The word of the Lord did not fail to be accomplished, nor was the redemption of the world frustrated of its effect. For though the world considered in the vessels of wrath did not know God, yet the same world considered in the vessels of mercy knew God liberated the second, without any previous merit on their part, from the power of darkness and translated them into the kingdom of the Son of His love."
Prosper of Aquitaine: Defense of St. Augustine, trans., by P. De letter, (New York: Newman Press, 1963), pp., 159-160.
"3) OBJECTION Our Lord Jesus Christ did not suffer for the salvation and redemption of all men.
ANSWER: The truly effectual and unique remedy for the wound of original sin, by which the common nature of all men was vitiated in Adam and condemned to death and which is the source of the three forms of concupiscence, is the death of the Son of God, our Lord Jesus Christ, who being free from all necessity to die and the only sinless one, died for sinful men, who are condemned to die. Considering, then, on the one hand the greatness and value of the price paid for us, and on the other the common lot of the whole human race, one must say that the blood of Christ is the redemption of the entire world. But they who pass through this world without coming to the faith and without having been reborn in baptism, remain untouched by the redemption. Accordingly, since our Lord in very truth took upon Himself the one nature and condition which is common to all men, it is right to say that all have been redeemed, and that nevertheless not all are actually liberated from the slavery of sin. It is beyond doubt that the redemption is actually applied only to those from whom the prince of the World has been cast out,' those who are no longer vessels of the devil but members of Christ. His death did not act on the whole human race in such a manner that even those who would never have been reborn in baptism would share in the redemption, but so that the mystery accomplished once for all in the person of Christ should be renewed in each and every man by the sacrament of baptism which he is to receive once also. The beverage of immortality prepared from our weakness and God's power is apt to restore health to all men, but it cannot cure anyone unless he drink it."
Prosper of Aquitaine: Defense of St. Augustine, trans., by P. De letter, (New York: Newman Press, 1963), p., 164.
If one reads through these Prosper quotes carefully, they will be able to see that his point is this: Christ redeemed all men sufficiently, but only the elect efficiently, or Christ suffered for all sufficiently, but only for the elect efficiently, as it is only applied to them. The formula later gets converted into: Christ died for all sufficiently, but only for the elect effectually. Ultimately, the concept of the Lombardian formula (see his Sentences, Book III, Section 20, Paragraph E) goes back to the days of Prosper (who wrote as a defender of Augustine's viewpoint), and even to Ambrose. The early Reformers, such as Musculus, Zwingli, Vermigli, Calvin and Bullinger, knew this well and believed it. It's a shame that this dualistic perspective is being eclipsed by those that read Calvin through the lens of later thinkers (post-Reformational scholastics), rather than through the lens of those who preceeded him (the fathers and the schoolmen), such as Ambrose, Augustine, Prosper, Anselm, Aquinas, Lombard etc. However, the truth is coming out nonetheless :-)