That’s the solution to the Achilles and the Turtle Paradox (also Zeno’s), but the Arrow Paradox (in the comment you replied to) is different.
The Arrow Paradox is simply linguistic confusion, I think. Motion is a relation in space relative to different points of time, Zeno’s statement that the (moving) arrow is at rest at any given instant is simply false (considered in relation to instants epsilon before or after that instant) or nonsensical (considered in enforced isolation with no information about any other instant).
I never found the Arrow Paradox particularly compelling. For the Achilles and the Turtle Paradox I can at least see why someone might have found that confusing.
Remember that these people were writing long before we had calculus. With regard to the Arrow Paradox in particular: if you’re already comfortable with the notion of instantaneous rate of change, there is no paradox here. If you are not, and it seems sufficiently weird, then it may lead you to think there is.
That’s the solution to the Achilles and the Turtle Paradox (also Zeno’s), but the Arrow Paradox (in the comment you replied to) is different.
The Arrow Paradox is simply linguistic confusion, I think. Motion is a relation in space relative to different points of time, Zeno’s statement that the (moving) arrow is at rest at any given instant is simply false (considered in relation to instants epsilon before or after that instant) or nonsensical (considered in enforced isolation with no information about any other instant).
I never found the Arrow Paradox particularly compelling. For the Achilles and the Turtle Paradox I can at least see why someone might have found that confusing.
Remember that these people were writing long before we had calculus. With regard to the Arrow Paradox in particular: if you’re already comfortable with the notion of instantaneous rate of change, there is no paradox here. If you are not, and it seems sufficiently weird, then it may lead you to think there is.
Oops, cached thought—I saw “Zeno’s Paradox” and jumped to the most common one without reading the details.