Argumentum ad cerebrum

We know what ad hominem arguments are, and we don't like them. They hurt, they distract from the real issue and they are far closer to coercion than persuasion. The closest noble purpose of an ad hominem attack is to lower the audience's confidence in the speaker's judgement. But why lower the confidence of the speaker as a person? Why should the audience trust him less? Perhaps in some tirade, the speaker has expressed contradictory interpretations or opinions. Maybe he hasn't thought through all the issues at hand. I would like to think of calling the speaker on mutually contradictory positions an argument ad cerebrum.

This is different from an argument by contradiction, which shows that if several propositions widely held as true are true, the opponent's position must be false. In argumentum ad cerebrum, you show that two or more stances of your opponent are mutually contradicting, forcing him either to abandon the weak link in his chain (perhaps his most recent point) and lose a little credibility with the audience, or hang on to the contradiction at all costs and lose massive amounts of credibility with the audience. More importantly than the speaker's credibility, the entire tuple of ideas contrary to your own is at odds with the audience. They know now at least one must be wrong.

Not only is argumentum ad cerebrum more effective, it is more civil. A successful ad hominem attack leaves your opponent thought of not only as wrong, but as hateful, mean-spirited and unworthy of taking seriously or even human dignity. A successful ad cerebrum attack forces your opponent to yield a talking point, gives the audience another chance to think about the tuple of ideas under question and lets your opponent save face as a human being. Ad cerebrum attacks have nothing to do with the personal faults of your opponent, rather a weakness in the set of positions he holds. Personal faults are the bread and butter of ad hominem attacks.

Argumentum ad cerebrum isn't always available in a debate (though argumentum ad hominem almost certainly is), especially when both sides are well-prepared, mentally clear, intellectually honest and courageous to recognize unpopular consequences of their positions (do we debate issues when one side is bereft of unpopular consequences?). Don't force it if it isn't there, but if you're bristling at your opponent expounding on ideas that are not only different from yours but contradictory, it might be time for a dose of ad cerebrum.

Finally, let me note that I'm not a debater and I don't know Latin. Does this concept exist under another name (granting that it is distinct from argument by contradiction)? A Google search for "agrumentum ad cerebrum" yielded an energy blog, adcerebrum.com, but nothing about styles of argument. Let me know, learning is fun!