A term I have found to be in more and more regular use in Reformed circles is "Amyraldianism." I have a suspicion that it is one of those terms, like "supra-" or "infra-lapsarian" or "realized eschatology," that sounds hip to the ears of a certain type of theological geek, even though its exact meaning may not be understood at all. After all, never mind the theological depth, feel the vocabulary…
Now, most people familiar with Reformed theology or Calvinism are aware of the famous five points and their acronym "TULIP": total depravity, unconditional election, limited atonement, irresistible grace, and perseverance of the saints. Many will also know that, of these five points, the "L"’limited atonement’is by far the most controversial. The idea that Christ died only for the elect seems to fly in the face of texts in the Bible that speak of God's universal love, and also makes evangelistic preaching, if not evangelism itself, that much harder. This has led many in the Reformed world to declare themselves as "four-point Calvinists." Many of these four-pointers also like to refer to themselves as Amyraldians, meaning that they believe in an unlimited atonement, at least in terms of its original, narrow intention, whatever the ultimate application of the same might be. It is here that a careful handling of terms is necessary.
At the start of the seventeenth century, there were those in the Reformed world who believed firmly in election but also believed in the universal saving intention of Christ's death. John Davenant, an English delegate to the Synod of Dort, was one such character. This theology was not developed in any highly elaborate way; such theologians were by and large comfortable with asserting a universal will to save in the atonement alongside a more restricted will to save in terms of God's election.
Later that same century, a form of theology was developed at the School of Saumur in France under the leadership of Moses Amyraut and the Scotsman, John Cameron. These men also argued for a universal intention to save in the atonement, but they developed this in the context of sophisticated discussion of God's eternal covenants.
To understand their innovation, it is useful to be reminded of the position of Reformed Orthodox theologians such as John Owen. Owen saw God's decree to elect as logically prior to his decree to appoint Christ as mediator. In other words, the nature of the decree that established Christ as mediator was determined by the logically prior decree to save some and not others (remember: there is no time in God; this ordering is logical, not chronological).
For the Amyraldians, the order was reversed: Christ was first appointed as mediator, and then God decided to elect some and not others. Thus the scope of Christ's mediation was not determined by the particularism of the decree of election. In other words, for Amyraldians it is not simply that they believe in a universal atonement; they build this on a very careful fine tooling of the divine decrees. This is not the type of Calvinism that cries, "But that's just not fair!" The question then arises: Where does the particularism manifest itself in the order of salvation? For Amyraldians, it was in a division in the work of Christ as priest. He died for all; he intercedes only for the elect.
Two things should be noted as a result of this. First, the belief of some who are Calvinistic that Christ died for all is not necessarily Amyraldian. Unless it is tied to a sophisticated reconstruction of the eternal covenants and their implications, it is perhaps better referred to with a more general term such as "hypothetical universalism."
Second, Amyraldianism does not really solve at least one of the problems that some of its modern advocates, such as R. T. Kendall, claim for it. The claim is that Amyraldian views of atonement allow the evangelist or the pastor to say to the people in an unequivocal way that then undergirds both evangelism and assurance, "Christ died for you!" Anyone who understands the Amyraldian scheme, however, is not going to be impressed by such an answer; what they will really want to know is whether Christ is interceding for them. The problem of limitation has simply been shifted from Calvary to the right hand of God the Father.
One last point: although the Reformed Orthodox disagreed with the Amyraldians on this point and even regarded it as a serious error, they still considered them to be brothers and sisters in the faith.