2. Avoid Arguing Over the Meanings of Words
Not having the same definition of a key word in an argument leads to "arguing past each other"---each side is arguing a different topic. Many words have more than one meaning. Be sure you're not arguing past each other by a) defining words at the beginning of the argument, and b) stopping the argument as soon as misunderstanding due to different definitions of key concepts is detected.
Be open to the possibility that you can argue better by accepting an opponent's definition of a word (but if opponent is merely trying to define a concept out of existence, further argument may be futile).
Changing the definition of key terminology in the middle of an argument is an informal fallacy known as "equivocation."
3. Talk about Ideas, Not People
Arguments on the topic of political philosophy may devolve into arguments about politicians. An argument about a politician is a historical analysis. In order to argue about a historical analysis in a convincing way, the arguer will need to know a lot of facts to the point of being a specialist on the topic, as opposed to an argument about political philosophy where you only need to know the rules of logic.
4. Don’t Just Avoid Strawmanning
The straw man—where you erect and destroy an inaccurate caricature of your opponent's position—is one of the most common fallacies in online debates.
You can't win an argument simply by demolishing your opponent's strawman versions of your argument. You have to set forth a persuasive argument, or you can't expect an opponent to be persuaded.
5. Actively Steel-Man Your Opponent
As a corollary of "Follow the argument"(Plato, The Republic, 394d “…wherever the argument, like a wind, tends, there we must go”)---the idea that argumentation is above all a search for truth, you should proactively steel-man your opponent’s position, to help make their argument as strong as possible. Only by arguing against as strong an argument as possible can you be confident that you're getting at the truth.
6. Don’t Argue with Trolls
Not all who pose as arguers have the search for truth as their goal.
A troll seeks, by various techniques, to manipulate an authentic arguer into degrading his logical argument to the level of an angry diatribe. When this happens, the troll has "won" (accomplished his goal for pretending to engage in argumentation).
Don't engage as there is nothing of value to get from that conversation, and it will only be a waste of your time.
7. Keep an Open Mind
As Hans-Hermann Hoppe has said, participation in an argument implies that the arguers can be convinced of the truth of an argument's conclusion by the logical validity and soundness of the argument. This is summed up in the motto "Follow the argument." In other words, when one participates in an argument, there must be the possibility not just of persuading others, but also of being persuaded oneself.
8. Know the Rules of Logic
Since the time of the Ancient Greeks, the methodology of argumentation has been logic.
(This post inspired by a post from Patrick Carroll, writing for FEE 9/23/22)
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