Limited atonement is the elementary Christian doctrine that states that Jesus Christ came and died for a limited number of people. He did not die for, or redeem, every individual who has or will ever live, but some specific individuals, i.e. His sheep. This does not mean that the power of His death could not have saved all men. The power and efficacy of His death through one drop of His blood could have saved a million worlds. But the Scripture does not dabble in "possibilities." But it most certainly does tell us that the scope of His death is limited. He died for some people, and secured the salvation of those people through his death that took away their sin and imputed His own righteousness to them. This is something Christ accomplished on the cross alone.
Scripture does state that he died for "all men" and that God loves "the whole world." In these cases "all men" does not mean every individual inclusively. Nor does it necessarily follow that Christ died for the whole world because God loves the whole world inclusively. Jesus secured the salvation of those for whom He gave his life, and for those God imputes His righteousness upon them. Jesus does not infallibly secure the salvation of all men, for if this were true, all men would be saved.
As the Maxim goes: God imposed his wrath due unto, and Christ underwent the pains of hell for either:
1) All of the sins of all men - which means all men are saved.
2) Some of the sins of all men - which means men are still in their sins.
3) All of the sin of some men - which is the biblical position.
Arminians must grapple with the fact that Jesus did His saving on the cross. All those for whom he died will be saved in time and justified by God. Arminians probably hate this doctrine more than any other. They say that it limits the value of the atonement or degrades the love of God.
Let there be no misunderstanding at this point. It is the Arminian who actually limits the atonement. The Calvinist limits the extent of it saying that it does not apply to all persons, although he believes that it is efficacious for the salvation of the large proportion of the human race. But the Arminian limits the power of it, for he says that in itself it does not actually save anybody. The Calvinist limits it quantitatively, but not qualitatively; the Arminian limits it qualitatively, but not quantitatively. To use an illustration from Lorraine Boettner, for the Calvinist the atonement is like a narrow bridge that goes all the way across the stream; for the Arminian it is like a great wide bridge that goes only halfway across. So we can see that as a matter of fact, the Arminian places more severe limitations on the work of Christ than does the Calvinist. “The sin of Adam,” says Charles Hodge, “did not make the condemnation of all men merely possible; it was the ground of their actual condemnation. So the righteousness of Christ did not make the salvation of men merely possible, it secured the actual salvation of those for whom He wrought.” 1
1. Hodge, Systematic Theology, Volume 2, Ch. 8