Paul C. answered 06/01/15
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There are a ton of rules of thumb that can help any student think through a challenging counter-argument. Here are some of my favorite.
1) Try to see thing from the other person's perspective. What evidence do they have for their conclusion? How did they go about collecting evidence? What experiences led up to their decision? You can even think about whether emotion or self-interest might be feeding their arguments (though you may want to avoid this last one in some formal debates). Understanding what motivates someone else and the history of how they've got to where they are can be very insightful.
2) Try to list out the different assumptions, premises, or pieces of evidence in their argument. Be as clear and precise as you can. And make sure to write it out. Ask what are their premises? And then how are they connected? Maybe you'll discover they're making hidden assumptions. Now think about each part of their argument in turn. Which are good premises and which aren't? What is their evidence for that premise? Where do they make logical leaps?
3) There are lots of lists of logical fallacies you should look into. Here is a good list: http://utminers.utep.edu/omwilliamson/ENGL1311/fallacies.htm Go through each and see if you can find them making one of those mistakes.
:)