Q&A: Zeno’s Paradox
Zeno’s Paradox
Question
Hello and blessings. I just listened to lesson 7 of the Rabbi’s “Conceptual Analysis,” and there the Rabbi brought up Zeno’s paradox. From what I understood, the Rabbi’s answer to the paradox was that one must redefine the concept of speed not according to its method of calculation (because then indeed one can speak of it only in terms of segments and not points), but according to its essence (something like acceleration / potential speed, in potentia), and also that one must distinguish between “standing still” and “being located,” so that at every point the arrow is not standing still but is located there. Up to here, that is the gist of it as I understood it, briefly.
On Wikipedia the paradox is presented like this:
An arrow is shot at a target. At a certain moment in its flight it is in a certain place, meaning that it is at rest. This description is true of every one of the moments of the arrow’s flight, and therefore the arrow is at rest throughout its entire flight, that is, the arrow’s motion does not exist at all.
I understand that what the Rabbi called “standing still,” they (the Wikipedia writers) called “being at rest,” but it seems from their words that the claim is not that there is no speed (or that our definition of it is mistaken, since it creates a paradox) but that there is no motion. It’s not critical to me what his actual intention was; I just wanted to understand whether the Rabbi’s definition presented in that lesson also solves the problem of defining motion as above. Seemingly it does not, because even if we define speed as the potential ability to change place given the proper conditions (time, open space, etc.), motion apparently cannot be defined that way. I would be glad to hear the Rabbi’s response.
P.S. As I understand it, the paradox as presented on Wikipedia is indeed very strange, since one could seemingly simply say that yes indeed—the definition of motion is the actualization of speed (according to the Rabbi’s definition), and in order for that to be actualized, a certain amount of time is needed. In other words, the concept of motion itself contains within it the displacement of a body from one point in space to another over a certain period of time, and therefore it is indeed impossible for a body to be in motion at a single instant of time.
Answer
I don’t understand the question. Obviously there is motion. The whole problem is that there is no speed at a point in time, and that is what I answered.
Discussion on Answer
That it is not moving.
So, what they wrote on Wikipedia as the conclusion of the paradox—”that is, the arrow’s motion does not exist at all”—means that it has no speed at a point in time?