As is his wont, my eight-year-old son had been reading one of his science books in bed last night, and in particular reading about temperatures at the earth’s center. Telling me about it this morning – as, still bleary-eyed, I made my coffee – sparked in him the following chain of thought: If the earth has a center, then that center has to have a center, and that center has to have a center as well, and so on to infinity. But then, he reasoned, the earth would have to be infinitely big, and this would be absurd.My son is very bright and I am used to hearing such thoughts from him, but I was nevertheless mildly startled that he had, however inchoately, more or less stumbled upon the second horn of the dilemma posed by Zeno’s paradox of parts, which (at least on one reading) goes like this: If the world consists of a plurality of things, then the parts that make it up either have no size or they do have size. If they have no size, then nothing has size, since adding together parts with no size can never result in a whole with any size. But if the parts do have size, then they can be divided into parts of smaller size, and those parts into yet smaller parts, and so on to infinity. And in that case the number of parts is infinite. But a thing with an infinite number of parts would be of infinite size. So, if there is a plurality of things in the world, then things either have no size or they have infinite size; and either suggestion is absurd. So the world does not consist of a plurality of things.
This was a teaching moment, so I used it to launch into an impromptu mini-lecture on Zeno’s paradoxes and Aristotle’s response in terms of the distinction between actual and potential infinities. My son loved it. (He also liked that, while moving my coffee cup back and forth through the air to illustrate motion, I managed to spill coffee all over my shirt and pants.)
But now I’m worried. Learning about Zeno and the other Pre-Socratics is what turned me on to philosophy. So, I may have just set my son on the path to becoming a philosopher. Does that count as child abuse?
(Bonus link: Here is a comical comic book treatment of Zeno’s paradoxes. Unfortunately, I can’t show it to my son, for reasons that will be obvious if you read it!)
