There is the view I call penal non-substitution, or the penal example view. (It is also called the Governmental View in textbooks of theology.) This is often associated with Arminian theology stemming from the great Dutch jurist Hugo Grotius. However, the view was taken up by [Jonathan] Edwards's disciples in New England, who developed a Calvinistic strand of the doctrine.
Oliver D. CrispI recommend Doug Sweeney's recent book [Jonathan] Edwards the Exegete (Oxford University Press, 2015), which is a terrific treatment of the way in which Edwards was steeped in the Bible, so that it shaped the whole of his thinking.
Oliver D. CrispIt is often reported that the Five Points of Calvinism are the conceptual hard-core of Reformed thought. That is very misleading. The Five Points supposedly originate with the Synod of Dort in the early seventeenth century. Yet we find important Reformed leaders who were signatories to that documentation who don't think that limited atonement is the right way to think about the scope of Christ's saving work. How can this be? The answer that recent historical theology has thrown up is that the canons of the Synod don't require adherence to the doctrine of limited atonement.
Oliver D. Crisp[I'm often called a Deviant Calvinist] but that only goes to underline the point I'm trying to make about the need to broaden our account of the tradition!
Oliver D. CrispThere are constraints on what counts as "Reformed." It's more than a name or a label. It's about belonging to a particular theological stream or tradition, which is shaped in important respects by particular thinkers and their work, particular arguments and ideas, a particular community (especially, particular church communities, denominations, and so on), particular liturgies or ways of worshipping and living out the Christian life, and particular confessions that inform the practices of these communities.
Oliver D. Crisp