Limited Atonement
This is the most contested of the five points. I will try to explain it simply, and I will refer you to the references at the bottom for more information. Limited atonement states that the death of Christ did not pay for (atone) for the sins of the whole world. It paid for the sins of those in Christ. An immediate objection that arises may be John 3:16, “For God so loved the WORLD that he gave his only Son…”
For God 1) loved the world that 2) He gave his only Son. We could say that God loved the world so that he gave his Son to die for the world.
But the second part of the verse is critical in understanding, “… that WHOever believes in him should not perish, but have eternal life.” So, those who believe in Christ will not perish but have eternal life. On the contrary, it is implied that those who do not believe in the Son will perish and not have eternal life. So the giving up of God’s Son does not pay for the sins of the whole world. It blots out the sins of those who identify themselves in Christ. If Christ’s death pays for the sins of the whole world, then it would not just be the believers who would be forgiven. His death would also pay for the sin of unbelief among those who rejected him. But then everyone would be saved, which is obviously not the case. The reference of weeping and gnashing of teeth, and those whose names are not written in the Book of Life are too numerous to reference. Those who do not come to Christ are still in their sins. Only by believing and confessing Christ does one have eternal life (Romans 10:9). Or as God himself said, “Or those eighteen on whom the tower in Siloam fell and killed them: do you think that they were worse offenders than all the others who lived in Jerusalem? No, I tell you; but UNLESS you repent, you will all likewise perish” (Luke 13:5). Unbelief and an unrepentant heart are both two sins which Christ did not die for.
When Paul speaks to the Colossian believers he tells them that, “… he has now reconciled in his body of flesh by his death, in order to present you holy and blameless and above reproach before him” (Colossians 1:21). Before they were drawn to Christ, they were hostile and alien to God. Their sins were not reconciled at that point in time.
References and Additional Readings
Ephesians 1-2, Romans 8:28-30, Romans 9, John 15:16, John 6:65, II Timothy 2:25-26, Hebrews 6:2-3, Acts 13:48 – The most basic breakdown of Calvinism and Arminianism I have seen. Each point summarized in 3 sentences or less. No scripture to explain points though. – A free online resource explaining the five points of Calvinism followed by testimonies of those who have loved and embraced these doctrines.
Chosen by God by R.C. Sproul- A simple book explaining and defining the terms
The Institutes of the Christian Religion by John Calvin- This can be read in its entirety for free at Chapters 21-24 explicitly address election and predestination. You won’t find the TULIP acronym in Calvin’s work, that was added after as a way of summarizing and understanding the points.