Based on various sources (the articles Definite Atonement, p. 62 in Essential Truths of the Christian Faith by R.C. Sproul; the video What Is Reformed Theology? by R.C. Sproul; Grace Unknown (chapter 8) by R.C. Sproul).
For whom did Jesus die?
The answer to this question is mostly a logical conclusion based on three other doctrines of Reformed Faith: Total Depravity, Unconditional Election and Irresistible Grace.
From Total depravity we saw that man is radically corrupt; not able to choose God of his own desire. In Unconditional Election we saw that God has chosen those who comprise His church from all eternity according to His good pleasure. Finally, from Irresistible Grace we learned that although we all resist God, for those whom He has chosen, he works regeneration in them to change their desires to be toward Himself.
The phrase Limited Atonement does not mean that Christs atonement is limited in its sufficiency or value. Christs work is sufficient to pay for all of humanitys debt to God. Instead, Limited Atonement (or more precisely, definite atonement) deals with the question of the design of Christs atonement: Why and for whom did God send Jesus to the cross? There are three options:
1. God sent Jesus to redeem everybody (this is universalism which means that everybody will be saved). This view is obviously un-Biblical.
2. God sent Jesus to redeem everyone who would believe (have faith) and take advantage of Christs work. This is the view of Arminians who believe that Christs death was potential atonement, not actual atonement.
3. God sent Jesus to redeem only the elect (the chosen church -- Unconditional Election). This is the reformed view whereby we believe that Christs death was an actual atonement.
There are a few verses that support this point:
"And she will bring forth a Son, and you shall call His name Jesus, for He will save His people from their sins." (NKJ)
Moreover whom He predestined, these He also called; whom He called, these He also justified; and whom He justified, these He also glorified. (NKJ)
"My sheep hear My voice, and I know them, and they follow Me. "And I give them eternal life, and they shall never perish; neither shall anyone snatch them out of My hand. "My Father, who has given them to Me, is greater than all; and no one is able to snatch them out of My Father's hand. "I and My Father are one." (NKJ)
"I pray for them. I do not pray for the world but for those whom You have given Me, for they are Yours. "And all Mine are Yours, and Yours are Mine, and I am glorified in them. "Now I am no longer in the world, but these are in the world, and I come to You. Holy Father, keep through Your name those whom You have given Me, that they may be one as We are. "While I was with them in the world, I kept them in Your name. Those whom You gave Me I have kept; and none of them is lost except the son of perdition, that the Scripture might be fulfilled. (NKJ)
When discussing Limited Atonement, one verse is often mentioned as contradictory: 1 John 2:2:
I John 2:2
And He Himself is the propitiation for our sins, and not for ours only but also for the whole world. (NKJ)
At first glance, this verse appears to contradict the idea of Limited Atonement, but upon closer inspection it does not. The word propitiation means, satisfaction of Gods demands. In view of this definition and if this verse is really talking about the whole world, then we are back to universalism, which is un-Biblical. The phrase whole world in the Bible often means just a larger group of people, not literally the whole world. So, this verse is likely speaking of the two different groups of believers: Jews and non-Jews. John may be saying that Christ is not only a propitiation for our sins (Jewish believers) but for the elect found also throughout the whole world.
1. Definite atonement refers to the scope of Gods design for redemption and the intent of the Cross.
2. All who are not universalists agree that Christs atonement is sufficient for all, but effective only for those who believe.
3. Christs atonement was an actual propitiation for sin, not a potential or conditional propitiation.
4. The atonement in a broad sense is offered to all; in a narrow sense, it is only offered to the elect.
atone - to supply satisfaction for
atonement - the reconciliation of God and man through the sacrificial death of Jesus Christ
redeem - a: to buy back: REPURCHASE b: to get or win back
propitiation - satisfaction of Gods demands; from an old English word, propitiate, which means to appease