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.

The book [Saving Calvinism] argues in each case that the Reformed tradition is broader and deeper than we might think at first glance - not that there are people on the margins of the tradition saying crazy things we should pay attention to, but rather that there are resources within the "mainstream" so to speak, which give us reason to think that the tradition is nowhere near as doctrinally narrow as the so-called "Five Points of Calvinism" might lead one to believe.

The alternative of hypothetical universalism, according to which Christ's work is sufficient for all but efficient only for the elect, was alive and well in early Reformed thought. Moreover - and importantly for our purposes - this view was not regarded as an aberration but as a legitimate position that could be taken within the confessional bounds of Reformed thought. But that means that the Five Points aren't the non-negotiable conceptual core of Calvinism after all.

No confession is inerrant; Reformed Christians are supposed to be those who seek to be constantly reformed according to the Word of God - and that includes our confessions as well.

How many people in the pews know that [ Jonathan Edwards] is both a founder of evangelicalism and, say, an idealist who denied that the material world exists?

In the chapter on the nature of the atonement [in the book saving Calvinism] I argue that it is a mistake to think that penal substitution is the only option on the doctrine of atonement.

I 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.