Ever heard of Opposite Day? I'm guessing you have — during every game of tag in elementary school. It turns out, that this idea isn't just a way to make other kids miserable. It's part of a whole category of "exception paradoxes."

If you've spent any time at an elementary school, you've probably heard of "Opposite Day." It's a very special day that means the rules of kickball have just been suspended now that it's your turn, because the other kids hate you. But that's okay, because you hate them right back. Oh, how you hate them.

As a broader concept, it's a day in which the meaning of everything is reversed. I don't know how I first heard of it. Maybe it was a kind of elementary school meme. If your school was like mine, it didn't take kids long to figure out that if you said it was Opposite Day, then clearly it was the opposite of Opposite Day, in which case it was not Opposite Day.

If you think it sounds maddening, you're right, but it's part of a whole group of "exception paradoxes." Philosophy is full of them. Some of them are home truths, like, "There is an exception to every rule," which, if true, means there's an exception to the exception rule — which means it's not a rule. There's even mathematical versions, as the set of numbers not included in sets would cause those numbers to be included in a set.

Kids in my era would solve this by piling on opposites. "It's the opposite of Opposite Day," and so on. This didn't so much reverse the statement "it's Opposite Day" as make it impossible. We could have started thinking of what the opposite of Opposite Day was, and whether it rendered the statement "it is opposite day" true, or whether it just reinforced its falseness. There are some who say that this kind of arguing gets kids thinking about philosophy.

In my school, it was more of a test of endurance and strength. The two kids would add Opposite Days to Opposite Days and the winner was the one who could stick out the argument the longest. Alternately, the winner was the kid who gauged both their own and their opponent's strength and worked up the nerve to slap the bejeezus out of the other kid — who had thus learned the limits of philosophy.

Image: War Museum