Zeno’s Paradox Illustrated by an Impossible Dance

It may be troublesome to show Zeno’s paradox to a category of incoming freshmen. Due to this fact, I used to be delighted when a pupil of mine pointed me to a scene from the romantic comedy I.Q. from 1994, which completely, and humorously, captures the logic of the paradox also known as “The Stadium.” Zeno argued that, if Being had been infinitely divisible, then movement could be unimaginable.

If house is an infinite sequence of spatial models, then Catherine Boyd (performed by Meg Ryan) would by no means attain Ed Walters (performed by Tim Robbins) on the opposite aspect of the dance flooring.

To get to Ed, Catherine would first should cowl half of the gap between them. Then she must cowl half of the remaining distance, after which half of the gap remaining after that, and so forth advert infinitum. Therefore, she would by no means be united with Ed in a dance as a result of the gap between them would by no means shrink to nothing. The house separating the 2 may at all times be divided into a fair smaller unit.

Having seen the logic of Zeno’s paradox acted out on this video, my college students have a a lot simpler time understanding it. We’re then higher set as much as talk about how this logic makes movement unimaginable. Whereas it’s true that Catherine won’t ever attain Ed, it’s equally true that Catherine can not even start to maneuver towards Ed. Imagining that the dance flooring consists of an infinite sequence of spatial models, Catherine would first should cowl half of the sequence to get to Ed. However earlier than protecting that half, she must cowl half of that half, after which half of that half, and so forth, leading to an infinite variety of steps. Due to this fact, Catherine would by no means even start to maneuver towards Ed, since one can not get to the tip of an infinite sequence.

Having watched this scene with my college students, I discover that I can higher clarify what a reductio advert absurdum is.

Regardless of the impossibility of the couple ever reaching one another, they do, in actual fact, unite in a dance. Reflecting on Catherine’s infallible logic, Ed defiantly asks, “How did that occur then?” “I don’t know,” she responds. In fact Catherine can transfer throughout the dance flooring to get to Ed! And so can all of us as a result of movement is certainly doable. I emphasize to my college students that Zeno is not arguing that movement is unimaginable, however that this absurd conclusion would comply with if one had been to imagine that Being is infinitely divisible. The paradox was constructed as a counterargument to those that denied Zeno’s instructor’s—Parmenides—understanding of Being as one full and indivisible entire. By assuming that such opponents are right, Zeno confirmed that they have to even be dedicated to the absurd place that movement is unimaginable. He decreased his opponents to absurdity to offer assist for his personal view that Being is one and indivisible.

Potential Readings:

Matson, W. I. (1987). A New Historical past of Philosophy: Historic and Medieval. Harcourt Brace Jovanovich.

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