Paul Graham provides a valuable public service with an otology of ways to disagree.

• DH0.  Name-calling.
• DH1.  Ad hominem.
• DH2.  Responding to tone.
• DH3.  Contradiction.
• DH4.  Counterargument.
• DH5.  Refutation.
• DH6.  Refutation of the central point.

"Now we have a way of classifying forms of disagreement. What good is it? One thing the disagreement hierarchy doesn't give us is a way of picking a winner. DH levels merely describe the form of a statement, not whether it's correct. A DH6 response could still be completely mistaken.

"But while DH levels don't set a lower bound on the convincingness of a reply, they do set an upper bound. A DH6 response might be unconvincing, but a DH2 or lower response is always unconvincing.

I've felt this instinctively, but it is great to see it cleanly laid out like this.  Especially helpful is the distinction between DH5 and DH6.  Often in debate a counter-argument will attack the weakest side point, without touching the central point.  While such an argument might feel convincing - in fact, it might carry the day - it is logically invalid.  Only DH6 really matters.