In philosphy, I'm told, there are several characterizations of argument styles.
There are three main ones commonly mentioned: The Straw Man Defense, and the Slippery Slope. And the third one is??? Anyone??? My brain has gone on vacation, and I cannot remember.....
Do you mean fallacies? There are hundreds of fallacies in the literature. You've mentioned two. The third you might be looking for may be called "ad hominem" which is attacking the irrelevant personal characteristics of a person. For example, someone argues that marijuana should be legal, and their opponent responds that they are just a stupid, lawless person who wants to live in anarchy.
There is a non-fallacious form of ad hominem, and it is when a person fails to meet rational standards. If a person uses invalid arguments, bad sources, and personal attacks in their arguments, then saying they are not acting rational is not an illegitimate thing to say. But due to the fact that this is tricky, and most people don't even use logic or fallacies correctly anyway, I tend to not even go that route.
A really good source, if you are interested, is the fallacy files. They have a huge list of the most common.
I don't think I would call the Straw Man Defense and the Slippery Slope argumentative styles, but rather, fallacies. Which hopefully one would do their best to avoid in their arguments! If you were in fact referring to fallacies, I can definitely think of more than three so I'm having a hard time pinpointing the one you are looking for. However, one of the first fallacies that always comes to my mind is the post-hoc fallacy which presents the problem of causality in arguments. Is this what you were looking for? :]
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