I would like to introduce what I have for a long time called the madman fallacy. Of the informal variety, most people have encountered the madman fallacy before. The name of the fallacy is inspired by the following quote from G. K. Chesterton:
If you argue with a madman, it is extremely probable that you will get the worst of it; for in many ways his mind moves all the quicker for not being delayed by the things that go with good judgment” [Orthodoxy (WaterBrook Press, 2001, p. 17]
One commits the madman fallacy when, in a debate or critical-dialogue context, one’s argument or response to an argument is so outrageously unreasonable, illogical, ill-informed, malformed, or unintelligible that it leaves one’s opponent speechless or befuddled, and so seemingly defeated.
Here’s another way to think about the madman fallacy. Think of arguments as having radar screens, delimiting the logical space of point-counterpoint possibilities. Within the context of an argument, logical responses will register somewhere on the radar screen. But when your opponent’s response just doesn’t mentally register, there’s a good chance you’re the victim of the madman fallacy. (Of course, it’s always possible that the response is logical and you are the dense one. That’s why it’s important to know who you’re dealing with—the madman fallacy is rarely committed by men who are not mad.)