I spoke below (in my post about pi) regarding how appallingly illiterate as a culture we Americans tend to be when it comes to mathematics. This, sadly, is also true of the basic fundamentals of logic. I just now stumbled upon a wonderful page that offers clear and easy to understand examples of the classic logical fallacies. You can find it right here.
Of course, the most frequent fallacy (that I've noticed, at any rate) brought into play during political arguments is that of the "straw man". This is what we call the tactic of misrepresenting one's opponent's position and then knocking it down.
You know what would be fun? Taking each of the fallacies on the page I've linked to here and coming up with a recent example of it being employed on the public stage.
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