H. and I were dismayed at some of our seventh- and eighth-graders' writing recently. We thought we had mostly mechanics problems, but some careful probing of their paragraph-composing ability revealed that they needed a refresher course in constructing logical arguments.
So H. spent some time working with them on syllogisms.
You know the sort. All men are mortal. Socrates is a man. Therefore Socrates is mortal. (Although it turns out that there are lots more kinds that I never learned about in school. Fortunately H. is on the case.)
"Might as well do it anyway," I theorized. "It's the sort of thing that lots of people get in school. Can't hurt. Might help."
Today H. gave them a copy of Vizzini's speech from The Princess Bride -- the one with the Battle of Wits over the iocane powder and the two cups of wine -- and challenged the kids to find and articulate as many syllogisms -- explicit and implicit, valid and not valid -- as they could.
It was a very fun lesson to overhear while I was making lunch.
This is the kind of thing they came up with:
- If you are strong, then you trust your strength to save you. You are strong, therefore I can not choose the glass in front of you.
- If you have been to Australia, then you are used to people not trusting you. You have been to Australia. Therefore you are used to not being trusted.
- If I can find out what kind of man you are, then it is simple. This is not simple, therefore I can’t find out what kind of man you are.
- Iocane comes from Australia and Australia is populated by criminals. You obtained the iocane. Therefore you are a criminal.
We were amused to discover that the entire battle of wits includes one incorrect assumption (that one of the goblets is not poisoned) but that Vizzini repeatedly comes to the correct conclusion anyway ("Therefore, I can clearly not choose the wine in front of me" and "Therefore, I can clearly not choose the wine in front of you.")