Paul Graham, a programmer, essayist, and venture capitalist, proposed a “disagreement hierarchy” in a 2008 essay entitled, “How to Disagree”, placing different kinds of argument into a seven-point hierarchy and observing that, “If moving up the disagreement hierarchy makes people less mean, that will make most of them happier.”

In his essay, Graham notes that:

The web is turning writing into a conversation. Twenty years ago, writers wrote and readers read. The web lets readers respond, and increasingly they do—in comment threads, on forums, and in their own blog posts.

Many who respond to something disagree with it. That’s to be expected. Agreeing tends to motivate people less than disagreeing. And when you agree there’s less to say. You could expand on something the author said, but he has probably already explored the most interesting implications. When you disagree you’re entering territory he may not have explored.

The result is there’s a lot more disagreeing going on, especially measured by the word. That doesn’t mean people are getting angrier. The structural change in the way we communicate is enough to account for it. But though it’s not anger that’s driving the increase in disagreement, there’s a danger that the increase in disagreement will make people angrier. Particularly online, where it’s easy to say things you’d never say face to face.    (Source:  How To Disagree, 2008,  Paul Graham)

Although originally written as a simple list, Graham’s hierarchy can be represented as a pyramid with the most convincing form of disagreement at the top, and the weakest at the bottom.

Graham's Hierarchy of Disagreement
Source: http://commons.wikimedia.org/wiki/File:Graham’s_Hierarchy_of_Disagreement.jpg

Graham concludes:

The most obvious advantage of classifying the forms of disagreement is that it will help people to evaluate what they read. In particular, it will help them to see through intellectually dishonest arguments. An eloquent speaker or writer can give the impression of vanquishing an opponent merely by using forceful words. By giving names to the different forms of disagreement, we give critical readers a pin for popping such balloons.