Zeno’s Arrow Paradox

The paradox of the Arrow and Aristotle’s solution

As citizens of the modern times, we understand motion as a result of inertia exerted upon that object that gives it the energy to move through space. However, that theory is more or less a book-keeping device to explain why motion take places, but it still cannot specifically clarify how things move. This same phenomenon has puzzled many scholars of ancient times, such as Zeno, who addressed four famous paradoxes concerning motion, with the most basic being the paradox of the Arrow. Aristotle, a famous Greek philosopher, attempted to provide a solution to this paradox but his solution was not completely satisfactory. This is because Aristotle did not directly solve Zeno’s paradox of the Arrow. Instead, he recreated a new set of conditions and assumptions that allows him to explain why the arrow can move over time.

First, Aristotle denounces Zeno’s assumption that the “now” is indivisible. In Book VI of the Physics, he explains that “parts of the now will be the past and part of it will be future” (234a16). To Aristotle, time is a continuum and that by definition means that there can never be an indivisible “now”. For the “now” by definition, means the time between the past and the future. The word “between” confirms the divisibility of the “now”, because “what is between limits in a continuum has the same name as the continuum itself” (234a10). This is contrary to what Zeno assumed. In his paradox of the Arrow, Zeno assumed that “now” is indivisible. So at each “now” during the arrow’s flight from the bow to the target, it is essentially at rest because nothing moves in a “now”. This, then, means that if you add up a series of “now” in which the arrow is at rest, then the arrow is still at rest and cannot be moving. This would contradict with the fact that locomotion exist and makes it difficult to explain how the arrow move from the bow to the target. Aristotle, by redefining the concept of “now”, has modified the most crucial element of this paradox and thus reconstructing the problem into a different one.

Next, Aristotle emphasizes that the arrow’s motion is a change. “Since every change is in time and there is no time in which change cannot occur” (234b20), it does not make sense that Zeno assumed that the arrow is at rest at that moment and no change could take place. Zeno’s logic does not work in this case because there is always the possibility that change can occur at any time. Hence, the argument that the arrow is completely at rest at a moment in time with absolutely no chance of moving and producing a change in space is invalid.