In this paradox, an arrow moving through the air instantaneously occupies a certain volume of space. But space does not move. Therefore an arrow cannot move.
This perhaps is the easiest of Zeno’s paradoxes to dismiss because it is based on an incomplete understanding of motion. The dynamical state of an object in CM requires a specification of position and velocity, but Zeno’s reasoning assumes only position is needed.
The polymath Aristotle was much more than a philosopher, writing influential books on an extraordinary range of subjects. Unfortunately, whilst he was good on many topics, science is not on that list. Because of the authority commanded by his writings, his views of mechanics and therefore of time had a severe and negative influence that lasted the best part of two thousand years. On the subject of motion, Aristotle wrote that
Everything that is in motion must be moved by something. [Aristotle, 1930]
This was refuted by Newton’s first law of motion, also called Galileo’s law of inertia.
On the subject of time, Aristotle wrote that
time is ‘number of movement in respect of the before and after’, and is continuous since it is an attribute of what is continuous. [Aristotle, 1930]
Since Aristotle based this image of time on the assumption that matter is continuous, which we now know to be untrue, we have to reject his argument that time is continuous. This does not prove that time is discrete.