A non sequitur is also a method of comedy. Thinking about this more, it seems that every logical fallacy is a device for comedy. The last example I saw was a straw-man argument. When someone straw-mans you, they're not truly serious. They might think they're serious, but they're really just using comedy to belittle the opposing view. The problem comes when they either don't see it, or even double down.

Framing the Debate

It is perfectly reasonable to discuss the framing of the debate before engaging in the intended debate. Often, an opponent will frame a fallacious structure, to whatever end. To throw mud, to be rude, to suppose a moral or intellectual high ground, whatever. It is important for you to properly understand the opponents position and for your opponent to understand your position. I think establishing this is part of the so called Socratic method. If you can't get past this, there's no point in engaging the challenge.

Socratic irony
Playing dumb.

Argumentum ad lapidem
(Latin: "to the stone") is a logical fallacy that consists in dismissing a statement as absurd without giving proof of its absurdity. An appeal to stone.​ General trash talking. Gaslighting. Ad hominem.

Tu quoque
To discredit the validity of the opponent's logical argument by asserting the opponent's failure to act consistently in accordance with its conclusion. A version of Ad hominem.

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