There is none of the five points of calvinism that are associated with more confusion than the one commonly called Limited Atonment or particular atonement. The problem comes because we do not tend to understand exactly what Calvinists have historically meant by this point, nor do we understand the alternatives on either side. Logic can be very treacherous when it comes to doctrinal understanding. So, in the following quote from Edwards we will find him steering a middle ground between two sets of rocks which are both in my view errors caused by overuse of what seems like reasonable logic.
The one error is really that of the hypercalvinist, who claims that this doctrine necessarily means that God predestines some men to hell in exactly the same way as he predestines others to heaven. It makes God the author of sin, and it means that the gospel is not a genuine offer of salvation.
The opposite error, is to say that Jesus died in the same sense “for” everyone. This alternative view to Limited Atonement is righly called “Universal Atonement” and of course is intimately linked with Universalism, which argues that all will eventually be saved. This quote from probably the greatest theologican of America, explains it well.
Universal redemption must be denied in the very sense of Calvinists themselves, whether predestination is acknowledged or no, if we acknowledge that Christ knows all things. For if Christ certainly knows all things to come, he certainly knew, when he died, that there were such and such men that would never be the better for his death. And therefore, it was impossible that he should die with an intent to make them (particular persons) happy. For it is a right-down contradiction [to say that] he died with an intent to make them happy, when at the same time he knew they would not be happy-Predestination or no predestination, it is all one for that. This is all that Calvinists mean when they say that Christ did not die for all, that he did not die intending and designing that such and such particular persons should be the better for it; and that is evident to a demonstration. Now Arminians, when [they] say that Christ died for all, cannot mean, with any sense, that he died for all any otherwise than to give all an opportunity to be saved; and that, Calvinists themselves never denied. He did die for all in this sense; ’tis past all contradiction. -Jonathan Edwards , The “Miscellanies”: (Entry Nos. a–z, aa–zz, 1–500) (WJE Online Vol. 13) , Ed. Harry S. Stout, page 1 74