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What does the woman mean with "Aristotle's logic" and "fuzz it up"?

Aristotle was a Greek scholar who is often looked upon as the father of logic, or more precisely binary logic. Binary logic is based on the idea that everything is either A or not-A. It is the logic you are forced to use when you take a true or false test. It's also the logic computers are based on. Electricity or not-electricity, 1 or 0. Now for some things binary logic works very well. For example, if you ask a school class, "Who is female?", all the girls will put up their hands and all the boys will keep them down. You get a clear answer, since everyone is either female or non-female.

What if you ask the same kids, "Who likes school?" Some kids may put up their hands all the way (they definitely like school) and others might keep their hand down (they hate school). Most of the kids however will put their hand up and take it down again a few times and then leave it somewhere in the middle. Maybe they like school in general, but there are some bad things about it, or they actually don't like school, but sometimes it's fun.

If we tried to take down these results with binary logic, we would have to reduce each result to the extremes of either loving school or hating school; A or not-A. Here we need a different kind of logic to note the answers accurately; we need a logic where the kids can both like school and not like school at the same time. For that we use fuzzy logic.