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Zeno's arrow paradox:

Zeno states that for motion to occur, an object must change the position which it occupies. He gives an example of an arrow in flight. He states that in any one (duration-less) instant of time, the arrow is neither moving to where it is, nor to where it is not. It cannot move to where it is not, because no time elapses for it to move there; it cannot move to where it is, because it is already there. In other words, at every instant of time there is no motion occurring. If everything is motionless at every instant, and time is entirely composed of instants, then motion is impossible.

The paradox says that "in any one (duration-less) instant of time, the arrow is neither moving to where it is, nor to where it is not". But it must be correct if passed time's length is 0 because, for example, if we take a bullet with constant velocity and take an instant time (dt~0) in its movement, obviously we will see that the ratio between the displacement with passed time will be equal to the velocity of the bullet. But if the passed time's length is 0, we no longer say we divide time into small part because it doesn't matter how much times you sum these instant times, you never reach the first time length that you divided.

But if my explanation was correct, it wouldn't be a paradox, so what is the problem with my explanation?

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Let me first state Zeno's Arrow Paradox more clearly:

  1. Time is composed only of instants.
  2. At any single instant, an apparently moving arrow doesn't travel any distance, i.e. the arrow is at rest during every instant.
  3. That means that the arrow is at rest for the entire time period.
  4. Therefore, the arrow cannot be moving at all.

I think your explanation is on the right track.

Possible solutions

One approach to resolving the paradox is this: it's false that the arrow is at rest during every instant of time, since motion is not something that occurs during a single instant of time. If we calculated the speed during an instant it would come out 0/0, and so Zeno is not justified in calling that rest anymore than calling it motion.

Along these lines we could look to calculus to get a precise notion of speed at an instant so that it doesn't come out 0/0. In this case we will find out that the arrow has a certain speed at every instant of time.

There are other possible approaches. We could deny that time is composed only of instants or even claim that instants have a certain finite duration. If true, these also show that the argument is not sound.

Paradoxes in general

One final comment regarding your last sentence. That something is called a paradox does not mean that it has no solutions. A paradox is something that leads to contradiction from apparently true assumptions. Often these assumptions are much debated and reasonably shown to be false. Yet we still call these things paradoxes since the assumptions retain their apparent truth.

Read more here and here.

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