R. C. Sproul in The Truth of the Cross (pp. 140-142) on four-point Calvinists:
There are a host of folks who call themselves four-point Calvinist because they can’t swallow the doctrine of limited atonement. Sometimes they say, “I’m not a Calvinist and I’m not an Arminian, I’m a Calminian.” I think that a four-point Calvinist is an Arminian. I say that for this reason: When I have talked to people who call themselves four-point Calvinists and have had the opportunity to discuss it with them, I have discovered that they were no-point Calvinists. They thought they believed in total depravity, in unconditional election, in irresistible grace, and in the perseverance of the saints, but they didn’t understand these points.
Only once have I encountered an exception to this general rule, one self-proclaimed four-point Calvinist who was not a no-point Calvinist. This person happened to be a teacher of theology. I was interested in his position, so I said to him: “I want to hear how you handle this, because I trust you. I know you’re knowledgeable in theology, and I want to hear ho you think this through.” I expected that he would not have an accurate understanding of the T, U, I, and P. But to my astonishment, when he went through them, I found that he had them down as clearly as an strict Calvinist ever articulated them. I was rejoicing, but also amazed. I said, “Now tell me about your understanding of limited atonement.” When he gave me his understanding of limited atonement, I discovered this man was not a four-point Calvinist, he was a five-point Calvinist. He believed in limited atonement and didn’t know it.
My point is that there is confusion about what the doctrine of limited atonement actually teaches. However, I think that if a person really understands the other four points and is thinking at all clearly, he must believe in limited atonement because of what Martin Luther called a resistless logic. Still, there are people who live in a happy inconsistency. I believe it’s possible for a person to believe four points without believing the fifth, although I don’t think it’s possible to do it consistently or logically. However, it is certainly a possibility given our proclivity for inconsistency.