For many people the most controversial point of the five is the L, which stands for Limited Atonement. By this we mean that Christ's atoning death was for the elect and them alone. The Atonement is limited in its scope. Some people find this 'limitation' unpleasant or uncomfortable and propose a way of getting around the idea of a limited scope of the atonement. Hence, these people are referred to as 4-point Calvinists.
Historically, this position has been called Amyraldism, named after Amyraut, the French theologian who developed the theory. Amyraldians try to do the impossible: keep the atonement efficacious for the elect alone while simultaneously expanding its scope to all men.
When one encounters Amryaldians they will usually always draw attention to the orthodoxy of their doctrine of election to demonstrate that they are true Calvinists. But the real hinge of their system is their doctrine of the atonement which strikes at the heart of genuine Calvinism. In order to propose some form of universal atonement, not unlike Arminianism, Amyraldians affirm a conditional substitution. This is sheer absurdity. If we grant God even the cheapest form of foreknowledge, the condition disappears. Hence, Amyraldism is nothing but an Arminian rejection of a substitutionary atonement. If Christ died in the sinner's place, bearing the penalties for his sin - this sinner must be saved. If all Christ accomplished was to make salvation possible, then even election cannot guarantee its fruition. Amyraldism claims that Christ's death removed the obstacles to salvation. But what obstacles are there, besides sin? If Christ's death removed sin, why then isn't everyone saved? This same flaw haunts Arminianism. If Christ died for everyone, why does anyone at all go to Hell? How is it meaningful to say that Christ died for everyone without exception, yet that this death is only efficacious for the elect? One doesn't need to be a rocket scientist to see how flimsy this logic is.